ISSN:0308-6003    

DOI:10.1039/PR97370FX001

出版商:RSC    

年代:1973

数据来源: RSC

ISSN:0308-6003    

DOI:10.1039/PR97370BX003

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

2 Theory of Molecular Collisions and Reactive Scattering By J. N. L. CONNOR Department of Chemistry University of Manchester Manchester M13 9PL 1 Introduction This Report is concerned with the theory of low-energy collisions between atoms and molecules. Activity (and progress) has continued unabated in this field during the past few years. A similar growth in experimental methods has oc- curred. The 1973 Faraday Discussion on Molecular Beam Scattering’ provides an excellent overall view of current theory and experiments in molecular collisions. Progress can be judged by comparing the 1973 Discussion with earlier one^.^.^ Molecular scattering was last reviewed in Annual Reports by Fluendy4 in 1970 mainly from an experimental point of view. Since then a large number of reviews and books have been written that deal with molecular collisions.These are considered next. Review of Reviews.-Levine’ has reviewed the molecular collision theory literature for 1965-1971. His review is broad and comprehensive; he discusses many methods for calculating elastic inelastic and reactive collision cross- sections. Levine’s book6 also contains many references to papers on molecular collision theory and develops the underlying theory as well. Nikitin’s book,’ published in 1970 contains an extensive bibliography (ca. 800 references) it provides a useful guide to Russian literature. A very extensive list of references for 1963-1970 is in the Bibliographies’ issued by the Oak Ridge Atomic and Molecular Processes Information Center.‘Molecular Beam Scattering,’ Faraday Discuss. Chem. SOC.,1973 No. 55. ‘Molecular Dynamics of the Chemical Reactions of Gases’ Discuss. Faraday SOC. 1967 No. 44. ‘Inelastic Collisions of Atoms and Simple Molecules’ Discuss. Faraday SOC. 1962 No. 33. M. A. D. Fluendy Ann. Reports (A) 1970,67 151. R. D. Levine MTP International Review of Science Vol. 1 ‘Theoretical Chemistry’ ed. W. Byers Brown Butterworths London 1972 Ch. 7. R. D. Levine ‘Quantum Mechanics of Molecular Rate Processes’ Clarendon Press Oxford 1969. E. E. Nikitin ‘Teoriya Elementarnykh Atomno-Molekulyarnykh Protsessov v Gazakh’ (Theory of Elementary Atomic and Molecular Processes in Gases) Khimiya Moscow 1970. ‘Bibliography of Atomic and Molecular Processes 1963-1 970’ Atomic and Molecular Processes Information Center Oak Ridge ORNL AMPIC 1-14.5 6 J. N. L. Connor Two excellent reviews have recently been written by Secrest’ and by George and Ross.’ Secrest’ reviews the theory of rotational and vibrational energy transfer in molecules :he is careful to point out those theories that have found numerical application and those that have not. Takayanagi’ ’ has also reviewed rotational energy transfer in molecules recently. George and Ross’s review” deals with the quantum dynamics of molecular collisions. Their review is wide-ranging they cover topics such as variational methods Faddeev equations and symmetry effects. Molecular collision theory is based on the quantum theory of scattering; this has been the subject of several recent books.’2-’6 Books have also been written on various aspects of heavy-particle collision theory’ 7-2 ’ that have a bearing on this Report.Levine and Bernstein22 and Child23 have written books on molecular collisions. An admirable book on chemical kinetics emphasizing the Two microscopic approach has been written by Weston and S~hwarz.~~ book~~”~~ on the theory of unimolecular reactions have appeared. Molecular collision theories Dynamical Statistical4ynamical Statistical theories theories theories Figure 1 Molecular collision theories D. Secrest Ann. Rev. Phys. Chem. 1973,24 379. * lo T. F. George and J. Ross Ann. Rev. Phys. Chem. 1973,24 263. 11 K. Takayanagi Comments Atom. Mol. Phys. 1973 4 59. 12 A.G. Sitenko ‘Lectures in Scattering Theory’ (translated from Russian and edited by P. J. Shepherd) Pergamon Oxford 1971. 13 J.-R. Taylor ‘Scattering Theory’ Wiley New York 1972. 14 J. E. G. Farina ‘Quantum Theory of Scattering Processes’ Pergamon Oxford 1973. 15 F. S.Levin and H. Feshbach ‘Reaction Dynamics’ Gordon and Breach New York 1973. 16 D. Rapp ‘Quantum Mechanics’ Holt Rinehart Winston New York 197 1. 17 K. Smith ‘The Calculation of Atomic Collision Processes’ Wiley New York 1971. 18 E. W. Thomas ‘Excitation in Heavy Particle Collisions’ Wiley New York 1972. I9 G. W. McClure and J. M. Peek ‘Dissociation in Heavy Particle Collisions’ Wiley New York 1972; E. W. McDaniel and E. A. Mason ‘The Mobility and Diffusion of Ions in Gases’ Wiley New York 1973.20 R. A. Mapleton ‘Theory of Charge Exchange’ Wiley New York 1972. 21 B. M. Smirnov ‘Asimptoticheskiye Metody v Teorii Atomnykh Stolknoveniy’ (Asymp- totic Methods in the Theory of Atomic Collisions) Atomizdat Moscow 1973. 22 R. D. Levine and R. B. Bernstein ‘Molecular Reaction Dynamics’ Clarendon Press Oxford 1974. 23 M. S.Child ‘Molecular Collision Theory’ Academic Press London 1974. 24 R. E. Weston and H. A. Schwarz ‘Chemical Kinetics’ Prentice Hall Englewood Cliffs 1972. 25 P. J. Robinson and K. A. Holbrook ‘Unimolecular Reactions’ Wiley New York 1972. 26 W. Forst ‘Theory of Unimolecular Reactions’ Wiley New York 1973. Theory of Molecular Collisions and Reactive Scattering 7 Experimental methods and results have been reviewed by a number of These reviews often contain discussions of the relevant theory as well.Several of them deal with molecular-beam method^.^'*^^-^^ Ion-atom and ion-molecule collisions have been the subject of several book^,^^-'^ review articles,3841 and a conference pr~ceeding.~~ The two volumes edited by Frank- lin3* contain a comprehensive set of articles. Bern~tein~~ has written an interesting review of technological applications of molecular dynamics research. Some additional reviews and books will be referred to later in the Report. Finally it is worth mentioning that perusal of the abstracts and lectures of the VIIth and VIIIth International Conferences on the Physics of Electronic and Atomic collision^^^^ reveals some of the current trends in heavy-particle collision theory.Scope of the Report.-The theoretical approaches to molecular collisions are classified in this Report according to a suggestion of Marcus.47 In his scheme l7 J. B. Hasted ‘Physics of Atomic Collisions’ 2nd revised edn. Butterworths London 1972; T. Oka Adv. Atom. Mol. Phys. 1973,9 127. H. S. W. Massey ‘Electronic and Ionic Impact Phenomena’ Vol. 111 ‘Slow Collisions of Heavy Particles’ 2nd edn. Clarendon Press Oxford 1971. 29 MTP International Review of Science Vol. 9 ‘Chemical Kinetics’ ed. J. C. Polanyi Butterworths London 1972. 30 B. P. Levitt ‘Physical Chemistry of Fast Reactions’ Vol. 1 ‘Gas Phase Reactions of Small Moleculq’ Plenum New York 1973. J. Troe and H. G. Wagner Ann. Rev. Phys. Chem.1972,23 3 1 1. 32 M. V. Bazilevski and E. A. Trosman Uspekhi Khim. 1972 41 3 (Russ. Chem. Rev. 1972 41 1); G. M. Nazin Uspekhi Khim. 1972 41 1537 (Russ. Chem. Rev. 1972 41 71 1); J. Dubrin Ann. Rev. Phys. Chem. 1973,24,97;A. A. Westenberg ibid. p. 77. 33 J. E. Jordan E. A. Mason and I. Amdur ‘Physical Methods in Chemistry’ Vol. 1 Part IIID ed. A. Weissberger and B. W. Possiter Wiley New York 1972 Ch. VI. 34 M. A. D. Fluendy and K. P. Lawley ‘Chemical Applications of Molecular Beam Scattering’ Chapman and Hall London 1973. ” J. P. Toennies ‘Physical Chemistry An Advanced Treatise’ Vol. VI ‘Kinetics of Gas Reactions’ ed. H. Eyring W. Jost and D. Henderson Academic Press New York 1974 Ch. 6. 36 M. R. C. McDowell and J. P. Coleman ‘Introduction to the Theory of Ion-Atom Collisions’ North Holland Amsterdam 1970.37 E. W. McDaniel V. cermhk A. Dalgarno E. E. Feiguson and L. Friedman ‘Ion- Molecule Reactions’ Wiley New York 1970. ’* ‘Ion-Molecule Reactions’ ed. J. L. Franklin Plenum New York 1972 (2 vols.). 39 J. E. Parker and R. S. Lehrle Internat. J. Mass Spectrometry Ion Phys. 1971 7 421. 40 L. Friedman and B.G. Reuben Adv. Chem. Phys. 1971 19 33; B. H. Mahan Ado. Chem. Phys. 1973 23 1. 41 B. H. Bransden Rep. Progr. Phys. 1972 35 949. 42 ‘Ion-Molekul Reaktionen’ Ber. Bunsengesellschafi phys. Chem. 1973,77 No. 8. ” R. B. Bernstein Israel J. Chem. 1971 9 615. 44 ‘Electronic and Atomic Collisions’ Abstracts of papers VIIth ICPEAC ed. L. M. Branscomb H. Ehrhardt R.Geballe F. J. de Heer N. V. Fedorenko J.Kistemaker M. Barat E. E. Nikitin and A. C. H. Smith (2 vols.) North Holland Amsterdam 1971. 4s ‘The Physics of Electronic and Atomic Collisions’ VIIth ICPEAC Invited Papers and Progress Reports ed. T. R. Govers and F. J. de Heer North Holland Amsterdam 1972. 46 ‘Electronic and Atomic Collisions’ Abstracts of papers VIIIth ICPEAC ed. B. C. CobiC and M. V. Kurepa (2 vols.) Institute of Physics Beograd 1973. 47 R. A. Marcus Faraday Discuss. Chem. SOC.,1973 No. 55 p. 9. 8 J. N. L. Connor theories are classified as dynamical statistical or statistical-dynamical as in Figure 1. A dynamical theory involves ‘exact’ or approximate solutions of the equations of motion of the colliding partners. Note that the term ‘exact’ includes not only analytical solutions but also numerical ones correct to the number of figures quoted.The equations of motion can be classical or quantum. Statistical theories on the other hand do not require the solution of a dynamical problem. A statisticaldynamical theory (a term invented by Marc~s~~*~~) involves exact or approximate dynamics for some degrees of freedom and a statistical approxima- tion for the remainder. Dynamical theories can be further as in Figure 2. Exact or approxi- mate quantum theories involve a solution of Schrodinger’s equation. Likewise Dynamical collision theories Exact Approximate (quantum classical (quantum classical semi-classical) semi-classical) Static Adiabatic Figure 2 Dynamical collision theories classical theories require solutions of Hamilton’s equations.Classical path theories treat the relative motion classically and the internal states quantum mechanically-these are included in the quantum category. Semi-classical theories involve an asymptotic solution of Schrodinger’s equation :these require real- and complex-valued solutions of Hamilton’s equations. The approximate theories can be further divided into static or adiabatic ones. A static theory has a zeroth-order approximation in which the relative motion is determined by an effective potential averaged over the initial unper- turbed internal states. In an adiabatic theory on the other hand the relative motion in zeroth order is determined by a potential averaged over the locally adjusted internal states.The terms static and adiabatic also include higher-order approximations as well as zeroth Levine,’ Secrest,’ and George and Ross” use different classifications from that above. Clearly all points of view are helpful for understanding the trends and cross currents that pervade the molecular collision theory literature. 48 R. A. Marcus J. Chem. Phys. 1966,452630. O9 R. A. Marcus J. Chem. Phys. 1967,46,959. Theory of Molecular Collisions and Reactive Scattering 9 This Report is mainly concerned with the literature of the past two years (1972 and 1973). No attempt has been made to mention every development that has occurred during that time. Instead some active areas of research have been selected. A large number of references has resulted nonetheless.Potential energy surfaces are considered in Section 2. Sections 3,4 and 5 deal with quantum classical and semi-classical theories respectively. Section 6 is concerned with statistical and statistical-dynamical theories. 2 Potential Energy Surfaces Potential energy curves and surfaces are the starting point for molecular col- lision calculation^.^^-^^ This is evident from the chain Potential energy surfaces -+Cross-sections -+ Rate constants It is therefore appropriate to report briefly some recent developments. Attention will be restricted to potential energy surfaces; the number of calculated diatomic potential energy curves is too numerous to menti~n~~-~~ (let alone discuss). The large number of experimental facts a surface must be capable of explaining in some cases is evident for KICH .56 Recent Calculations.-Progress in reaction dynamics has stimulated the calcula- tion of a large number of ab initio potential energy surfaces.No doubt this trend will continue. Recent ab initio calculations include H,,57 H3+,” H4,59-63 H4+,64 HeH2,65.66 HeH2+,67 HeH3+,68 BeH2+,69 LiH2,70 LiH2+,7 1-73 so ‘Proceedings of the Conference on Potential Energy Surfaces in Chemistry’ ed. W. A. Lester IBM Research Laboratory San Jose California 1971 ; M. Simonetta Topics Current Chem. 1973 42 1. ” 0.Sinanoglu Comments Atom. Mol. Phys. 1972 3 53. ’’ M. A. D. Fluendy and K. P. Lawley Essaysin ’Chem.,1973,5,25; R. Daudel ‘Quantum Theory of Chemical Reactivity’ Reidel New York 1973. s3 H. F.Schaefer tert. ‘The Electronic Structure of Atoms and Molecules A Survey of Rigorous Quantum Mechanical Results’ Addison-Wesley Reading Mass. 1972. ” A. C. Wahl ref. 5 Ch. 2. ’’ J. Goodisman ‘Diatomic Interaction Potential Theory’ Academic Press New York 1973 (2 vols.). s6 R. B. Bernstein and A. M. Rulis Faraday Discuss. Chem. SOC.,1973 No. 55 p. 293. s7 B. Liu J. Chem. Phys. 1973 58 1925. s8 C. W. Bauschlicher S. V. O’Neil R. K. Preston H. F. Schaefer and C. F. Bender J. Chem. Phys. 1973,59 1286. 59 D. M. Silver Chem. Phys. Letters 1972 14 105. 6o D. M. Silver and R. M. Stevens J. Chem. Phys. 1973,59 3378. 61 C. F. Bender and H. F. Schaefer J. Chem. Phys. 1972,57 217. 62 B. Freihaut and L. M. Raff J. Chem. Phys. 1973 58 1202. 63 C. W. Wilson and W.A. Goddard J. Chem. Phys. 1972,56 5913. 64 R. D. Poshusta and D. F. Zetik J. Chem. Phys. 1973,58 118. 65 B. Tsapline and W. Kutzelnigg Chem. Phys. Letters 1973 23 173. 66 H. F. Schaefer D. Wallach and C. F. Bender J. Chem. Phys. 1972,56 1219. 67 P. J. Brown and E. F. Hayes J. Chem. Phys. 1971,55 922. 68 M J. Benson and D. R. Mclaughlin J. Chom. Phys. 1972,56 1322. 69 R. D. Poshusta D. W. Klint and A. Liberles J. Chem. Phys. 1971 55 252. ’O A. C. Wahl A. Wagner and A. Karo ref. 46 p. 44. ” W. A. Lester J. Chem. Phys. 1970 53 151 1. 72 W. A. Lester J. Chem. Phys. 1971,54 3171 ; erratum 1972 57 3028. 73 W. Kutzelnigg V. Staemmler and K. Hoheisel Chem. Phys. 1973 1 27. 10 J. N. L. Connor FH2,53*74.75 C1H2,80 CH3NC,81 and CH2H2.82 Other HF2,76 FLi2,77 LiF2,78*79 surfaces for which calculations have been made include ArH2+,83 NaBrKC1,84 M2X+,85 and (AB)+X-.86 Potential energy surfaces for atom transfer reactions involving hydrogen and the halogens were reviewed in 1971 by Parr and Truh- iar.87 The most accurate potential energy surface to date for collinear H has been computed by L~u.~~ He finds a barrier height of 41.0 kJ mol- with a rigorous upper bound of 43.0 kJ mol-I and an estimated lower bound of 39.7 kJ mol- '.The barrier height lies between those of the Shavitt-Stevens-Minn-Karplus surface" (46.0 kJ mol- ') and the Porter-Karplus surface89 (38.1 kJ mol- '). The reaction path and reaction profile also lie almost entirely between those of the two earlier surfaces.It will be interesting to see how the new surface differs from the older ones in classical and quantum dynamical calculations. There has been considerable interest in the H potential energy ~urface.~~-~~ Experimental evidence gives an activation energy of ca. 170 kJ mol- ' whereas the calculated barrier heights are at least twice this fig~re.~~-~~ A c omprehensive set of calculations has been carried out by Silver and Stevens.60 They calculate the energies of several likely configurations (square rectangle etc.) as well as some that are not so obvious (kite trapezoid etc.). Developments in the theory of non-adiabatic phen~mena~'-~~ have stimu- lated interest in the calculation of excited-state potential energy surfaces as well as those for the ground state.The semi-empirical diatomics-in-molecules method has been effectively used in this ~ontext.~~.~'-~~ Bauschlicher et 74 C. F. Bender P. K. Pearson S. V. O'Neil and H. F. Schaefer Science 1972,176 1412. 75 C. F. Bender P. K. Pearson S.V. O'Neil and H. F. Schaefer J. Chem. Phys. 1972 56 4626; see also H. Schaefer ref. 195 p. 155. 76 S. V. O'Neil P. K. Pearson H. F. Schaefer and C. F. Bender J. Chem. Phys. 1973 58 1126. 77 P. K. Pearson W. J. Hunt C. F. Bender and H. F. Schaefer J. Chem. Phys. 1973,58 5358. " G. G. Balint-Kurti and M. Karplus Chem. Phys. Lerrers 1971 11 203. 79 G. G. Balint-Kurti Mol. Phys. 1973 25 393. S. Rothenberg and H. F. Schaefer Chem. Phys. Lerrers 1971 10 565. " D. H. Liskow C. F. Bender and H. F. Schaefer J.Chem. Phys. 1972,57,4509. J. N. Murrell J. B. Pedley and S. Durmaz J.C.S. Faraday 11 1973 69 1370. 83 P. J. Kuntz and A. C. Roach J.C.S. Faraday 11 1972,68 259. 84 P. Brumer and M. Karplus Faraday Discuss. Chem. SOC.,1973 No. 55 p. 80. 85 S.M. Lin J. G. Wharton and R. Grice Mol. Phys. 1973 26 317. 86 W. S. Struve Mol. Phys. 1973 25 777. ") C. A. Parr and D. G. Truhlar J. Phys. Chem. 1971,75 1844. I. Shavitt R. M. Stevens F. L. Minn and M. Karplus J. Chem. Phys. 1968,48 2700. R. N. Porter and M. Karplus J. Chem. Phys. 1964,40 1105. T. Carrington Faraday Discuss. Chem. SOC.,1972 No. 53 p. 27. 91 J. C. Tully and R. K. Preston J. Chem. Phys. 1971 55 562. 92 R. K. Preston and J. C. Tully J. Chem. Phys. 1971 54 4297. 93 J. C. Tully Ber. Bunsengesellschafr phys.Chem. 1973,77 557. 9* J. C. Tully J. Chem. Phys. 1973 58 1396. 95 J. C. Tully J. Chem. Phys. 1973 59 5122. 96 P. J. Kuntz. Chem. Phys. Letters 1972 16 581. 97 E. Steiner P. R. Certain and P. J. Kuntz J. Chem. Phys. 1973 59 47; F. 0. Ellison and M. J. DelleDonne ibid. p. 6179. Theory of Molecular Collisions and Reactive Scattering 11 find good agreement between the diatomics-in-molecules9 ‘sg2 and ab initio surfacesS8 for the H3+ system. The potential energy points of ub initio calculations must be expressed in a form suitable for dynamical calculations. Classical trajectory calculations for example require the first derivative of the potential. The usual method is a global one the points are fitted to some analytic form. This can be time-con- suming and difficult.An alternative is to fit the surface piece-wise using spline functions.98-’ O0 Th e fitted surface has the desirable property that the first derivative varies in a continuous way. Semi-classical theories of molecular collisions (Section 5) require that the potential energy surface be known for complex values of the internuclear co- ordinates. The usual method is analytic continuation using an analytic form for the surface. Morokuma and George’” have done ab initio calculations for HeH2+ at complex internuclear distances. They have compared the results with various methods of analytic continuation off the real axis. ‘02 Canonical Models.-In many models of molecular collision processes the inter- molecular potentials are chosen to have a simple functional form.The physical dimensions of the problem are often reduced from three to one or two. The advantage of these models is their simplicity essential features of a collision can be isolated from the remaining ones. In addition exact (analytical or numer- ical) solutions may be possible. They can be used to test approximations and gain insight into the collision process. Some of these models have been studied more than others. They have come to be regarded as standard and can be called cunonical models. Table 1 lists a few of them. The table could be made longer by including more collision processes or by choosing more complicated (and realistic) interaction potentials. On the other hand it could be argued that simpler interaction potentials (e.g.square wells) should find a place in the Table. 3 Quantum Molecular Collisions Elastic Scattering.-The elastic scattering of two atoms interacting via a single potential energy curve is well understood. Measurement of differential and total elastic cross-sections provides important information on intermolecular forces.’03-’ O6 H igh-energy scattering has been reviewed by Smith”’ and 98 X. Chapuisat F. Floquet and J. A. Horsley CECAM report on the research workshop ‘Dynamics of Reactive Collisions on Potential Energy Surfaces’ 1973. 99 D. R. McLaughlin and D. L. Thompson J. Chem. Phys. 1973,59,4393. loo J. H. Ahlberg E. N. Nilson and J. L. Walsh ‘The Theory of Splines and their Applications’) Academic Press New York 1967.‘01 K. Morokuma and T. F. George J. Chem. Phys. 1973,59 1959. lo* T. F. George and K. Morokuma Chem. Phys. 1973 2 129. lo3 P. R. Certain and L. W. Bruch ref. 5 Ch. 4. Io4 G. C. Maitland and E. B. Smith Chem. SOC.Rev. 1973 2 181. Io5 I. M. Torrens ‘Interatomic Potentials’ Academic Press New York 1972. ‘06 H. Margenau and N. R. Kestner ‘Theory of Intermolecular Forces’ 2nd edn. Per- gamon Oxford 197 1 lo’ F. T. Smith ref. 45 p. 1. J. N. L. Connor Table 1 Some canonical models for molecular collision processes Collision Typical process Canonical model reference Elastic scattering Vibrational energy transfer Lennard-Jones(12-6) potential Collinear atom-harmonic oscillator collision with exponential repulsion a b c d e,f Rotational energy transfer Atom-rigid rotator collision with Lennard-Jones(12-6) and P,(cos 0) interaction 8 h i Reactive collision Curve crossing Collinear atom-molecule collision with Porter-Karplus potential energy surface Two states linear slopes with constant j,k 1 m,n 0 interaction a K.W. Ford and J. A. Wheeler Ann. Phys. 1959,7,259; * R. B. Bernstein Adu. Chem. Phys. 1966 10 75; J. N. L. Connor Mol. Phys. 1968 15 621 ; 'J. D. Kelley and M. Wolfsberg J. Chem. Phys. 1966,44 324; D. Secrest and B. R. Johnson J. Chem. Phys. 1966 45 4556; f E. Thiele and R. Katz J. Chem. Phys. 1971 55 3195; W. A. Lester Methods Comput. Phys. 1971 10 21 I; A. 0.Cohen and R. A. Marcus J. Chem. Phys. 1970,-52,3140; W. H. Miller J. Chem. Phys. 1971,54,5386;' P. Brumer and M.Karplus J. Chem. Phys. 1971 54 4955; T. F. George and W. H. Miller J. Chem. Phys. 1972 57 2458; J. W. Duff and D. G. Truhlar Chem. Phys. Letters 1973 23 327; E. E. Nikitin 'Chemische Elementarprozesse' ed. H. Hartmann Springer-Verlag Berlin 1968 p. 43; " M. S. Child Mol. Phys. 1969 16 313; O A. M. Woolley Mol. Phys. 1971 22 607. Leonas' O8 and low-energy scattering by T~ennies;'~' the elastic scattering of ions has also been reviewed.' ' A detailed review of singular potentials (such as the Lennard-Jones (12-6) potential) has also been written.' ' ' General discus- sions of atom-atom collisions have been given by Massey' l2 and by Nikitin and Ovchinnikova.' ' Recent experiments have detected the Ramsauer-Townsend effect' l4l1' and orbiting resonances.' ' Child has written' 'a detailed review of orbiting and 18.1 19 resonances within the context of predissociation.Retardation effects have been predicted12' (but not observed'2'); a giant glory effect has also lo' V. B. Leonas Uspekhifiz. Nauk 1972,107 29 (Soviet Phys. Uspekhi 1973 15,266). *09 J. P. Toennies Faraday Discuss. Chem. SOC.,1973 No. 55 p. 129. H. P. Weise Ber Bunsengesellschaft phys. Chem. 1973 77 578. I I I W. M. Frank D. J. Land and R. M. Spector Rev. Mod. Phys. 1971,43 36. Il2 Sir Harrie Massey Contemp. Phys. 1971 12 537; 1972 13 135; 1972 13 375; 1973 14 497. 'I.' E. E. Nikitin and M. Ya. Ovchinnikova Uspekhi fiz. Nuuk 1971 104 379 (Sou. Phys. Uspekhi 1972 14 394). Il4 R. Feltgen H. Pauly F. Torello and H. Vehmeyer Phys. Rev.Letters 1973 30 820. II5 U'.A. Kampe D. E. Oates W. Schrader and H. G. Bennewitz Chem. Phys. Lerrers 1973 18 323. IL6 A. Schutte D. Bassi F. Tommasini and G. Scoles Phys. Rev. Letters 1972 29 979. ' ' M. S. Child 'Diatomic Predissociation Linewidths' in 'Molecular Spectroscopy' ed. R. F. Barrow D. A. Long and D. J. Millen (Specialist Periodical Reports) The Chemical Society London 1974 Vol. 2 Ch. 7. ' Is. R. A. Bain and J. N. Bardsley J. Phys. (B) 1972 5 277. 'I9 D. E. Pritchard and J. Lacy J. Chem. Phys. 1972,56 3180. J. Konrady and J. Sucher Phys. Reo. Letters 1972 28 74. 1. P. Aldridge and J. G. Skofronick Phys. Rev. Letters 1972 28 529. Theory of Molecular Collisions and Reactive Scattering 13 been predicted.' 22 Most methods for extracting information on the potential from the observed scattering are based on semi-classical collision theory ;these are discussed in Section 5.Progress on alternative methods has been report- ed however. '23* '24 Inelastic Scattering.-As Secrestg and Takayanagi' ' have reviewed the theory of inelastic scattering up to 1972 only more recent calculations will be reported. Gordon'25 has drawn up a useful table for inelastic collisions indicating which method (exact or approximate) is most appropriate for a given collision. Experi- mental and other aspects of energy transfer have also been re~iewed.'~,' 26-' 30 Non-reactive inelastic collisions between atoms and molecules can be des- cribed by a set of coupled ordinary differential equations." Exact numerical methods for their solution have been reviewed recently.In particular Gordon' 31 has discussed the use of piecewise analytic solutions Light 132 the exponential method Lester' 33 the solution of the rigid-rotator problem and Secre~t'~~ the amplitude-density method. The numerical methods can be related by the concept of invariant imbedding as emphasized by Levine.' Ne~bet'~'''36 has discussed the relation between numerical methods and the Jost function and Fredholm determinant' of scattering theory. For collisions involving polyatomic molecules the derivation of the close- coupled equations is itself a non-trivial task. This has been considered by Curtiss and co-workers138-'41 in a series of papers. They also consider various approxi- mations.' 38-144 Two exact numerical calculations have recently been carried out for the col- linear collision of an atom with an oscillator.Clark and Di~kinson'~' studied an 12' Yu. N. Demkov and J. Los Phys. Letters (A) 1973,46 13. 123 R. B. Gerber Chem. Phys. Letters 1973,18,436; Phys. Rev. (A) 1972,5,2151;J. Phys. (B) 1972 5 L242. P. C. Sabatier Phys. Rev. (A) 1973,8 589; Internat. J. Quantum Chem. 1973,75,421. 12' R. G. Gordon Faraday Discuss. Chem. SOC. 1973 No. 55 p. 22. E. E. Nikitin Comments Atom. Mol. Phys. 1970 2 59; E. E. Nikitin and S. Ya. Umanski ibid. 1972 3 195; Faraday Discuss. Chem. SOC.,1972 NO. 53 p. 7. 12' H. Pauly Faraday Discuss. Chem. SOC. 1973 No. 55 p. 191. 12* C. B. Moore Adv. Chem. Phys. 1973 23,41. B. F. Gordiets A. I. Osipov E.V. Stupochenko andL. A. Shelepin Uspekhifiz.Nauk 1972 108 655 (Sou. Phys. Uspekhi 1973 15 759). I 30 J. P. Doering Ber. Bunsengesellschafr phys. Chem. 1973 77 593. 131 R. G. Gordon Methods Comput. Phys. 1971 10 81. 13' J. C. Light Methods Comput. Phys. 1971 10 11 1. 13' W. A. Lester Methods Comput. Phys. 1971 10 211. 134 D. Secrest Methods Comput. Phys. 1971 10 243. 135 R. K. Nesbet Comments Atom. Mol. Phys. 1972 3 143. 136 R. K. Nesbet J. Math. Phys. 1973 14 1522. 13' W. P. Reinhardt Phys. Rev. (A) 1973,8 754. 13* L. W. Hunter and C. F. Curtiss J. Chem. Phys. 1973 58 3884. 139 L. W. Hunter and C. F. Curtiss J. Chem. Phys.. 1973,58 3897. I4O D. Russell and C. F. Curtiss J. Chem. Phys. 1973 59 1974. 14' L. W. Hunter and C. F. Curtiss J.Chem. Phys. 1973 59 3889. 14' L. Biolsi J. Chem. Phys. 1973 58 5331. 143 D. Poppe Chem. Phys. Letters 1973 19 63. 144 M. D. Pattengill Chem. Phys. Letters 1973 23 278. 14' A. P. Clark and A. S. Dickinson J. Phys. (B) 1973 6 164. 14 J. N.L. Connor atom-Morse oscillator collision with an exponential repulsion. At low energies the transition probabilities are smaller in general for a Morse oscillator than for a harmonic oscil1ator;at high energies the opposite is true.Eastes and studied an atom-harmonic oscillator collision with a Morse interaction. Reso- nances were found. Their model could serve as a canonical one for resonances in vibrational energy transfer. 147 Resonance effects in collisions have been reviewed recently by Mi~ha.'~~ Other aspects have been reviewed by Levine,' Secrest,' and Child.'l7 Eastes14' has also calculated transition probabilities for the canonical model of an atom-rigid rotator collision (see Table 1) for excited rotational states. These should be useful for comparison with approxi- mate theories. The above calculations are based on amplitude density functions whereas those that follow use Gordon's method. Wagner and McKo~''~ have studied the validity of the breathing-sphere approximation concluding that it can be used to analyse accurately experimental measurements of vibrational energy transfer. Near-resonant vibrational energy transitions for collinear D,-D collisions have been calculated by Alexander.' '' Shafer and GordonlS2 have made a detailed study of the He-H system.They calculate S-matrix elements and from them obtain rotational relaxation times n.m.r. spin relaxation times and Raman lineshapes. They find a potential that fits all the data as well as theoretical calculations at long and short range. The Li' + H system has been studied by Lester and co-workers.'53*'54 They investigate three models these treat H as a rigid rotator an energy- corrected rigid rotator (this includes centrifugal distortion effects) and a vibrating rotator (this uses numerical vibrational wavefunctions). They find that the exact results for the rigid-rotator model are usually within 10%of those for the vibrating rotator but better agreement still is obtained with the energy-corrected rigid- rotator model.At the present time about 100 close-coupled equations can be solved numeric- ally. This limits the close-coupling method since in rotational excitation a very large number of states can participate. Effective potential approximations are being developed that reduce the number of states to be ons side red.'^^-''^ 146 W. Eastes and R. A. Marcus J. Chem. Phys. 1973 59,4757. 14' E. J. Heller Chem. Phys. Letters 1973 23 102. D. A. Micha Accounts Chem. Res. 1973 6 138. 149 W. Eastes J. Chem. Phys. 1973 59 3534. lS0 A. F. Wagner and V. McKoy J. Chem. Phys. 1973,58 2604 5561. lS1 M. H. Alexander J. Chem. Phys. 1973 59 6254. 52 R. Shafer and R. G. Gordon J. Chem. Phys. 1973,58 5422. J. Schaefer and W. A. Leqter Chem. Phys. Letters 1973 20 575; J.Schaefer W. A. Lester D. Kouri and C. A. Wells ibid. 1974 24 185. lS4 W. A. Lester and J. Schaefer J. Chem. Phys. 1973 59 3676. lS5 H. Rabitz J. Chem. Phys. 1972 57 1718. 156 H. Rabitz J. Chem. Phys. 1973 58 3975. lS7 G. Zarur and H. Rabitz J. Chem. Phys. 1973,59 943. lSa P. McGuire Chem. Phys. Letters 1973 23 575. Theory of Molecular Collisions and Reactive Scattering 15 Rabitz uses an effective potential independent of the z component of the rotational quantum number.ls5 -'" Rabitz'" has also developed an exact method based on the shape of the potential matrix that has been applied to elastic scattering. 160 A method using continuous space-filling curves has been described by Rosenthal and Kouri.16' As mentioned in the Introduction approximate theories can be divided into static and adiabatic.Static calculations are more numerous than adiabatic ones because the latter are more complicated to carry out. However if there is con- siderable distortion of the internal motion during the collision the static approxi- mation can be inaccurate (the static approximation neglects this distortion in zeroth order). The adiabatic approximation becomes less accurate at high trans- lational energies :the internal states do not have time to adjust to the fast relative motion. Adiabatic calculations have been carried out recently by Kay and Rice'62 and by Storm and Thiele.'63 Kay and Rice'62 study various basis sets for intra- molecular vibrational energy transfer. Storm and Thiele' 63 introduce a semi- adiabatic approximation which is simpler than the full adiabatic one.'64 They apply it to a collinear atom-oscillator collision.In static calculations the commonest approximations are the distorted-wave and classical-path approximations. The exponential approximation which includes the distorted-wave and other approximations as special cases has been reviewed by Levine.16' A number of applications of the distorted-wave method have been made re~ently.'~~-'~~ In classical-path methods the relative motion is treated classically and the internal motion quantum mechanically. The classical path gives rise to a time- dependent perturbation for the internal states. A general solution for a harmonic oscillator with a time-dependent frequency acted on by a time-dependent force has been given by Chapuisat and Manz.' 75 Classical-path calculations are H.Rabitz J. Chem. Phys. 1971 55 407. I6O R. Conn and H. Rabitz Phys. Rev. (A) 1973,7,658. I6l C. M. Rosenthal and D. J. Kouri. Mot. Phys. 1973 26 549. K. G. Kay and S. A. Rice J. Chem. Phys. 1973,58,4852. 163 D. Storm and E. Thiele J. Chem. Phys. 1973 59 5102. 164 E. Thiele and R. Katz J. Chem. Phys. 1971 55 3195. 16' R. D. Levine Mot. Phys.. 1971,22,497. L. M. Koppel and J. Lin J. Chem. Phys. 1973,58,1869; C. I. Nelson and R. E. Roberts Chem. Phys. 1973 2,445. 16' T. A. Dillon and J. C. Stephenson J. Chem. Phys. 1973 58 2056. J. W.Riehl C. J. Fischer J. D. Baloga and J. L. Kinsey J. Chem. Phys. 1973,58,4571. 169 D. Storm and E. Thiele J.Chem. Phys. 1973 59 3313. 'lo H. K. Shin Chem. Phys. Letters 1973 18 359. D. T. Chang Chem. Phys. Letters 1973 19 86. J. W. Ioup and A. Russek Phys. Rev. (A),1973.8 2898. W. Franssen and J. Reuss Physicu 1973 63,313. D. G.Truhlar J. Chem. Phys. 1973,58 3109. X. Chapuisat and J. Manz Mol. Phys.. 1973 26,1577. 16 J. N.L. Connor numerous. '6-1 * Notable amongst these is the work of Neilsen and Gordon.179 They have made a detailed study of the Ar-HCl system. They make calculations on dipole absorption spectra proton and quadrupole relaxation times Raman scattering rotational relaxation and sound absorption. When energy differences between classical paths are neglected and the frequencies of internal motion set equal to zero the sudden approximation is obtained.A number of calculations recently have applied this to rotational and vibrational rela~ation.'~~-'~~ Reactive Scattering.-The quantum theory of reactive molecular collisions has been reviewed by Light'32,194 and Kouri.19' George and Ross" review the literature up to 1972;therefore only more recent developments will be mentioned. Experimental aspects have also been reviewed.29.' 96-198 A basic difficulty in the theory of reactive collisions is that co-ordinates appro- priate to reactant configurations differ from those for product configurations. For example for the collinear electronically adiabatic bimolecular reaction A+BC-+AB+C the natural co-ordinates for reactants are the distance from A to the centre of mass of BC and the BC distance but for products they are the distance from C to the centre of mass of AB and the AB distance.This difficulty does not arise for inelastic collisions and makes reactive scattering calculations harder to carry out. Reaction co-ordinates go smoothly from reactants to products configurations. The concept of a reaction co-ordinate has been known for a long time yet it was only in 1966 that Child'99 and Marcus2'' independently constructed them in a L76 H. K. Shin J. Phys. Chem. 1973,77 346 1666 2657; J. Chem. Phys. 1973,59 879. 17' L. L. Poulsen P. L. Houston and J. I. Steinfeld J. Chem. Phys. 1973 58 3381. I" T. A. Dillon and J. C. Stephenson J. Chem. Phys. 1973,58. 3849. '79 W. B. Neilsen and R. G. Gordon J. Chem. Phys. 1973,58 4131 4149.'I3' R. A. White A. Altenberger-Siczek and J. C. Light J. Chem. Phys. 1973 59 200. ''' A. P. Clark J. Phys. (B) 1973 6 1153. ''* C. Chang and D. Rapp J. Chem. Phys. 1973,59,972. K. Shobatake S. A. Rice and Y.T. Lee J. Chem. Phys. 1973.59 2483. M. R. Verter and H. Rabitz J. Chem. Phys. 1973 59 3816. '13' S. Saha E. Guha and A. K. Barua J. Phys. (B),1973 6 1824. "'2 J. W. Kuijpers and J. Reuss Chem. Phys. 1973 1 64. Ie7 R. D. Sharma and H. Schlossberg Chem. Phys. Letters 1973 20 5. "I3 J. D. Stettler and N. M. Witriol Chem. Phys. Letters 1973 23 95. L. H. Sentman Chem. Phys. Letters 1973 18 493. I9O P. B. Scott T. R. Mincer and E. P. Muntz Chem. Phys. Letters 1973 22 71; P. B. Scott J. Chem. Phys. 1973. 58 644. 19' T. P. Tsien G. A. Parker and R.T. Pack J. Chem. Phys. 1973,59 5373. '92 A W. Young and H. K. Shin Chem. Phys. Letters 1973 21 267. 193 M. A. Wartell J. Chem. Phys. 1973 58 4700. '94 J. C. Light Ado. Chem. Phys. 1971 19 I. 195 D. J. Kouri 'Energy Structure and Reactivity' ed. D. W. Smith and W. B. McRae Wiley New York 1973 p. 26. Y.T. Lee ref. 45 p. 357. 197 Z. Herman and K. Birkinshaw Ber. Bunsengesellschaft phys. Chem. 1973.77 566. 19' D. R. Herschbach Faraday Discuss. Chem. SOC.,1973 55 p. 233. 199 M. S. Child Proc. Roy. SOC.,1966 A292 272; Discuss. Faraday SOC. 1967. NO.44 p. 68. R. A. Marcus J. Chem. Phys. 1966,45 4493 4500. Theory of Molecular Collisions and Reactive Scattering 17 mathematically meaningful way. The reaction co-ordinate does not have to follow the reaction path (which is the path of minimum energy).Child'99 considered a two-dimensional reaction and Marcus"' a collinear one. Subse-quently reaction co-ordinates have been defined for three-dimensional re-action~,~~ including the possibility of bifurcation202~207*208 '-'09 (AC + B as well as AB + C as reaction products). Marcus calls them 'natural collision co-ordinates' (a good name). The three-dimensional Schriidinger equation is complicated when expressed in natural collision co-ordinates but is somewhat simpler for reactions in a plane. A simple way of extending collinear reactions to three dimensions is to allow the line of atoms to rotate in three-dimensional space.2'O-' ' This model was introduced by Child." Natural collision co-ordinates can be used for exact numerical solutions or for developing approximate theories.They are also used in classical (Section 4) and semi-classical theories (Section 5). Several authors' 949204*2 '6-220 have developed exact numerical methods for reactive collisions based on natural collision co-ordinates. When used in a close-coupled formulation the methods developed for inelastic collisions can be applied. Recent collinear calculations include 0 + HBr,22' H + C12,222 C1 + HI,''' H + H2,216219 and A + BC219 Wu el aI.2'6-219 have studied isotope effects location of barriers and the effect of changing vibration frequency along the reaction path. They have also studied resonances in reactive ~ollisions.~' 6p21 These can arise when the ejfective potential has a well ('Lake Eyring'eit is not necessary for the potential energy surface itself to have one.Resonances have also been studied by analytical It is often useful to understand how the scattering depends on different pieces of the potential surface (location of barriers curvature of reaction path etc). Manz220 has developed a method for this based on the concept of a 'state path sum' (see also ref. 224). 'O' R. A. Marcus Discuss. Faraday SOC.,1967 No. 44 p. 7. '02 R.A. Marcus J. Chem. Phys. 1968,49 2610. '03 E. J. Shipsey J. Chem. Phys. 1969,50 2685. '04 E. J. Shipsey J. Chem. Phys. 1972 56 3843. 'OS R. E. Wyatt J. Chem. Phys. 1972,56 390. *06 M. V. Basilevsky. Mol. Phys. 1972 23 161. '07 S. H. Harms and R. E. Wyatt J.Chem. Phys. 1972 57 2722. R. B. Walker and R. E. Wyatt J. Chem. Phys. 1972,57 2728. '09 J. L. Jackson and R. E. Wyatt Chem. Phys. Letters 1973 18 161. 'lo M. S. Child Mol. Phys. 1967 12 401. 21L J. N. L. Connor Mol. Phys. 1968 15 37. J. N. L. Connor and M. S. Child Mol. Phys. 1970 18 653. J. N. L. Connor Mol. Phys. 1970 19 65. 2L4 W. N. Whitton and J. N. L. Connor Mol. Phys. 1973,26 151 1. R. E. Wyatt J. Chem. Phys. 1969,51 3489. R. D. Levine and S. Wu Chem. Phys. Letters 1971 11 557. 217 S. Wu and R. D. Levine Mol. Phys. 1971 22 881. B. R. Johnson Chem. Phys. Letters 1972,13 172. 'I9 S. Wu B. R. Johnson and R. D. Levine Mol. Phys. 1973.25.609 839. "O J. Manz Mol. Phys. 1974 in the press. 221 E. J. Shipsey J. Chem. Phys. 1973 58 232. "' C.G. Miller J. Chem. Phys. 1973 59 267. 223 R. A. VanSanten J. Chem. Phys. 1972,57 5418. 224 P. B. Middleton and R. E. Wyatt J. Chem. Phys. 1972 56 2702. 18 J. N. L. Connor An exact numerical study of the planar H + H reaction has been made by Saxon and Light,225 using a mixed system of two reaction co-ordinates. A start has also been made on the numerical calculation of bifurcation reaction^.^'^^'^ Natural collision co-ordinates are very convenient for discussing adia- bati~ity'~~,~'' in chemical reactions. For example a vibrationally adiabatic collinear reaction is one that stays in the same vibrational state throughout the collision. From the assumption of vibrational adiabaticity activated-complex theory can be derived.200.20' A number of calculations that make use of vibra-tional adiabatic approximations have been made.199-201~210-215,228 A direct test of vibrational adiabaticity for the collinear H + €4 reaction has been made.229 This was done by projecting the accurate numerical wavefunction on to an adiabatic vibrational basis set at the saddle point.For a range of energies the approximation is good (within 10% of the exact results) but breaks down- as expected-at higher energies when additional vibrational states can be excited and at lower energies when tunnelling is important. The question 'What is tunnelling'?' is discussed in Section 4. Natural collision co-ordinates are also useful for approximate theories of vibrational energy tran~fer~~',~~' in reactions and have also been used to discuss electronic excitation.' 32*23 A different method for overcoming the co-ordinate problem mentioned above makes use of a conformal mapping.234 In this the potential energy surface is mapped on to an infinite strip.The mapping is determined by application of the Schwarz-Christoffel formula.'34 It is instructive to write down the Schrodinger equation for a collinear reaction in (a)conventional co-ordinates (b)natural collision co-ordinates and (c) con-formally transformed co-ordinates. In conventional co-ordinates the Schrodinger equation is where x is the distance from A to the centre of mass of BC and y is the BC distance. In natural collision co-ordinates2" where s is the distance along the reaction co-ordinate r is the perpendicular 225 R.P. Saxon and J. C. Light J. Chem. Phys. 1971 55 455; 1972 56 3874 3885. 226 J. Manz Chem. Phys. Letters 1972 15 136. "' P. B. Middleton and R. E. Wyatt Chem. Phys. Letters 1973 21 57. '" E. f. Shipsey. J. Chem. Phvs. 1973 58 5368 1973 59 5109. 229 J. M. Bowman A. Kuppermann J. T. Adams and D. G. Truhlar Chem. Phys. Letrers 1973 20 229. 230 M. V. Basilevsky Mol. Phys. 1973 26 765. 23 G. L. Hofacker and N. Rosch Ber. Bunsengeseffschuft phys. Chem. 1973 77 661. 2'2 Y. Haas R. D. Levine and G. Stein Chem. Phys. Letters 1972 15 7. 233 H. Nakamura Mol. Phys. 1973 26 673. 234 J. N. L. Connor and R. A. Marcus J. Chem. Phys. 1970,53 3188. Theoryof Molecular Collisions and Reactive Scattering 19 distance to it and q = 1 + ~(s)r, where K(S) is the curvature of the reaction co- ordinate.In conformally transformed ~o-ordinates~~~ where z = x + iy w = u + iu and J(u,v) is the Jacobian J(u,v) = Idz/dw)’. The simplest-looking equation is evidently equation (l) yet the boundary con- ditions it satisfies are more complicated than those of equations (2) and (3). The kinetic energy operator of equation (2) is no longer diagonal; that of equation (3) is. The shape of the potential energy surface is unchanged in equation (2); in equation (3) this is not the case. It is apparent that equations (l)-(3) have a pleasing complementary nature. An exact numerical method not using natural collision co-ordinates has been applied to the collinear H + H reaction by Truhlar Kuppermann and co- ~~rker~.~~~p~~~-~~~ Th ey use a finite-difference boundary-value method.In their informative series of papers they use their exact results to test approximate theories of reactions such as vibrationally adiabatic theory activated-complex theory and statistical phase-space theory (see also Section 6). Other methods for chemical reactions have also been Kouri and co-have continued their development of the channel-operator approach to reactive collisions. They have applied this approach to some simple model problems (square-well potentials infinite central mass). A number of other topics in the theory of reactive collisions such as optical models,249 distorted wave approximations,’ and Faddeev equations have been reviewed by George and Ross. 4 Classical Molecular Collisions The use of classical mechanics to study molecular collisions is well established.Detailed reviews have been written recently by B~nker,’~’ K~ntz,’~’ Ke~k,”~ 235 J. M. Bowman and A. Kuppermann Chem. Phys. Letters 1971 12 1. 236 D. G. Truhlar and A. Kuppermann Chem. Phys. Letters 1971 9 269. 237 D. J. Diestler D. G. Truhlar and A. Kuppermann Chem. Phys. Letters 1972 13 1. 238 D. G. Truhlar and A. Kuppermann J. Chem. Phys. 1972,56 2232. 239 G. C. Schatz J. M. Bowman and A. Kuppermann J. Chem. Phys. 1973,58,4023. 240 D. G. Truhlar A. Kuppermann and J. T. Adams J. Chem. Phys. 1973,59 395. 24’ G. C. Schatz and A. Kuppermann J. Chem. Phys. 1973,59,964. 242 J. W. Duff and D. G. Truhlar Chem. Phys. Letters 1973 23 327. 243 D. J. Diestler J.Chem. Phys. 1971 54 4547; 1972 56 2092. 244 P. McGuire and D. A. Micha MoI. Phys. 1973 25 1335. 245 A. M. Brodsky and V. G. Levich J. Chem. Phys. 1973,58 3065. N. S. Evers and D. J. Kouri J. Chem. Phys. 1973 58 1955. 247 D. J. Kouri J. Chem. Phys. 1973 58 1914. 248 M. Baer MoI. Phys. 1973 26 369. 249 I. Rusinek and R. E. Roberts Chem. Phys. 1973 1 392. 250 R. G. Gilbert and T. F. George Chem. Phys. Letters 1973 20 187. 251 D. L. Bunker Methods Comput. Phys. 1971 10 287. 252 P. J. Kuntz ref. 45 p. 427. 253 J. C. Keck Adu. Atom. MoI. Phys. 1972,8 39. 20 J. N. L. Connor and Polanyi and S~hreiber.,’~ In addition Levine’ and Secrestg discuss classical calculations. Films illustrating different kinds of classical trajectory have been made.255,256 Since it is nearly always possible to calculate exact classical trajectories most calculations fall into this category.However Marcus47 has pointed out one use for approximate classical calculations ;to predict the accuracy of the correspond- ing quantum and semi-classical ones. Classical calculations are the only ones that can be routinely used for three-dimensional reactive collisions. They are most accurate for the calculation of averaged quantities such as average energy transfer. The commonest method uses a random selection of initial parameters from an appropriate distribution (‘Monte Carlo’ method). Non-random methods have also been explored and compared with the Monte Carlo approa~h.~~’~~’~ Elastic and Inelastic Scattering.-The classical deflection function plays an important role in the classical and semi-classical theory of elastic scattering from a central potential.Its properties and methods for its evaluation have continued to attract attenti~n.~’’,~~’ The classical theory of vibrational and rotational energy transfer has been reviewed up to 1972 by Secrest.’ Since that time a number of additional exact calculations have appeared.261-268 N otable amongst them is the work of La Budde and Bern~tein,,~~*,~~ They have made a detailed study of the Li’ + H system (with H a rigid rotator) using the ab initio surface of Le~ter.~”~~ Diffi-culties arise when attempts are made to ‘quantize’ classical trajectory results. La Budde and Bern~tein~~~.~~~ investigate three different methods for this which they compare with the exact quantum results of Lester and Schaefer.‘ 53*154 They conclude that classical calculations may be seriously in error when only a few quantum states are involved.An alternative in this situation is to use semi- classical methods (Section 5). Some approximate calculations on rotational and vibrational energy transfer have also been made re~entIy.~~~.*~~ 254 J. C. Polanyi and J. L. Schreiber ‘The Dynamics of Bimolecular Reactions’ in ‘Physical Chemistry-An Advanced Treatise’ Vol. VI ‘Kinetics of Gas Reactions’ ed. H. Eyring W. Jost and D. Henderson Academic New York 1974. 255 J. C. Polanyi Accounts Chem. Res. 1972 5 161. 56 M. Karplus ‘Collision Dynamics of Chemical Reactions’ 16 mm Colour Sound Film Harper and Row London.237 V. B. Cheng H. H. Suzukawa and M. Wolfsberg J. Chem. Phys. 1973.59 3992. H. H. Suzukawa D. L. Thompson V. B. Cheng and M. Wolfsberg J. Chem. Phys. 1973 59 4000. 259 G. A. L. Delvigne and J. Los Physica 1973 63 339. 260 E. A. Gislason J. Chem. Phys. 1972 56 2493. 261 G. C. Berend and R. L. Thommarson J. Chem. Phys. 1973,58 1256 3203 3454. 262 J. I. Steinfeld Faraday Discuss. Chem. SOC.,1972 No. 53 p. 155. 263 H. Van Dop A. J. H. Boerboom and J. Los Physica 1972,61 616. 264 K. S. Tait C. E. Kolb and H. R. Baum J. Chem. Phys. 1973 59 3128. 265 E. 0.Sire Ber. Bunsengesellschaftphys. Cirem. 1973 77,427. 266 A. G. St. Pierre J. Chem. Phys. 1973 59 5364. 267 R. A. La Budde and R. B. Bernstein J. Chem. Phys.1971,55 5499. 268 R. A. La Budde and R. B. Bernstein J. Chem. Phys. 1973 59 3687. 269 R. A. La Budde J. Chem. Phys. 1972,57 582. 270 R. J. Gordon and A. Kuppermann J. Chem. Phys. 1973,58 5776. Theory of Molecular Collisions and Reactive Scattering 21 Reactive Scattering.-There have been numerous classical trajectory studies of reactive collisions in three dimension^.^ In particular reactions involving hydrogen and halogen atoms have because of their experimental importance been the subject of many calculation^.^^^-^^^ Of these the reactions H + F2 F + H,,H + HF and F + HF have been most st~died.~~’-~~~ Many of these calculations use London-Eyring-Polanyi-Sat0 (LEPS) potential energy sur-faces. Other reactions for which classical calculations have been made recently include HeH’ + H,,286 K + MeI,287 Rb + CH,I,288 and T + CH4.289 Difficulties can arise if long-lived complexes form during the collision many integration steps are then required.Small errors can accumulate and be amplified during the calculation. Special care is needed for this type of trajectory. Calcula- tions involving long-lived complexes have been reported for NaBr + KCl by Brumer and Karplu~~~~ and for K + NaCl by Kwei et Exact classical calculations have been used to study molecular dissoci- A number of ation29 2-294 and the inverse process of recombinati~n.~~~-~~~ calculations using idealized potentials have also been rep~rted.~~~.~~~ 271 C. A. Parr J. C. Polanyi and W. H. Wong J. Chem. Phys. 1973,58 5. 272 R.N. Porter L. B. Sims D. L. Thompson and L. M.Raff J. Chem. Phys. 1973 58 2855. 273 J. B. Anderson and R. T. V. Kung J. Chem. Phys. 1973,58 2477. 274 I. W. M. Smith and P. M. Wood Mol. Phys. 1973,25441. 275 R. L. Wilkins J. Chem. Phys. 1972 57 912; 1973 58 2326 3038; 1973 59 698; J. Phys. Chem. 1973 77,3081. 276 N. C. Blais and D. G. Truhlar J. Chem. Phys. 1973,58 1090. 277 R. L. Jaffe and J. B. Anderson J. Chern. Phys. 1971,54 2224; erratum 1972,56,682. 278 R. L. Jaffe J. M. Henry and J. B. Anderson J. Chem. Phys. 1973,59 1128. 279 J. T. Muckerman J. Chem. Phys. 1972,56,2997; 1972,57 3388. N. Jonathan S.Okuda and D. Timlin Mol. Phys. 1972 24 1143; erratum 1973,25 496. 28 I J. M. Henry J. B. Anderson and R. L. Jaffe Chem. Phys. Letters 1973 20 138.282 L. M. Raff D. L. Thompson L. B. Sims and R. N. Porter J. Chem. Phys. 1972 56 5998. 283 J. M. White J. Chem. Phys. 1973 58 4482. 284 R. L. Johnson K. C. Kim and D. W. Setser J. Phys. Chem. 1973,77,2499. 285 D. S. Perry and J. C. Polanyi Cunud. J. Chem. 1972,50 3916; P. J. Kuntz and A. C. Roach J. Chem. Phys. 1973 59 6299; J. C. Polanyi in ‘Molecules in the Galactic Environment’ ed. M. A. Gordon and L. E. Synder Wiiey New York 1973; K. L. Kompa Topics Current Chem. 1973 37 1. 286 See ref. 99. 287 R. A. La Budde P. J. Kuntz R. B. Bernstein and R. D. Levine Chem. Phys. Letters 1973 19 7; J. Chem. Phys. 1973 59 6286. 288 D. L. Bunker and E. A. Goring Chem. Phys. Letters 1972 15 521 ; D. L. Bunker and E. A. Goring-Simpson Frrraday Discuss.Chem.SOC., 1973 No. 55 p. 93. 289 T. Valencich and D. L. Bunker Chem. Phys. Letters 1973 20 50. 290 See ref. 84. 291 G. H. Kwei B. P. Boffardi and S. F. Sun J. Chem. Phys. 1973,58. 1722. 292 N. J. Brown and R. J. Munn J. Chem. Phys. 1972,56 1983. 293 A. Gelb R. Kapral and G. Burns J. Chem. Phys. 1973 59 2980. 294 V. H. Shui J. Chem. Phys. 1973,58,4868. 295 A. Gelb R. Kapral and G. Burns J. Chem. Phys. 1972 56 4631. 296 A. G. Clarke and G. Burns J. Chem. Phys. 1972,56,4636; 1973 58 1908. 297 W. H. Wong and G. Burns Cunud. J. Chem. 1973,51 111;J. Chem. Phys. 1973,58 4459; 1973 59 2974. 298 P. A. Whitlock J. T. Muckerman and R. E. Roberts Chem. Phys. Letters 1972 16 460. 299 P. J. Kuntz Mol. Phys. 1972 23 1035; Chem. Phys. Letters 1973 19 319; M.T. Marron J. Chem. Phys. 1973,58 153; G. M. Kendall ibid.,1973 58 3523. 300 D. J. Malcalme-Lawes J.C.S. Furuduy 11,1972 68 1613 2051. 22 J. N.L. Connor Natural collision co-ordinates have been used in approximate classical calcu- lations of rotational and vibrational energy transfer in reactive collisi~ns.~~~~~~~ A number of calculations have been made recently comparing classical trajec- tory with exact quantum mechanical res~lts.~~~~~~~*~~~,~~~-~~~ Systems treated 2351242f303.304 include collinear F + H 239 and H + H (on a variety of potential surfaces) and planar H + H2.305 The general conclusions of these comparisons seem to be :(i) classical thresholds are higher than the corresponding quantum mechanical ones (ii) detailed quantum effects are not reproduced classically and (iii) classical results agree with quantum ones on the average.These conclusions can also be understood in the context of semi-classical col- lision theory (Section 5). This is a convenient place to discuss the concept of tunnelling in systems with several degrees of freedom (following the discussion of George and Miller306). It is necessary to have a procedure that defines tunnelling since in an exact quantum mechanical calculation no distinction is made between it and non- tunnelling processes. Two definitions are currently used in the literature. These are based on (a) and (b)dynamics.306 The energetic cri- terion states that a reaction takes place by tunnelling if the collision energy is less than the barrier height.The dynamic criterion recognizes that certain processes may be energetically allowed but dynamically forbidden ;tunnelling is then identified as a dynamically forbidden process. For a system with one degree of freedom these criteria are identical; this is not the case however for several degrees of freedom as dynamics is not determined by energy conservation alone. In the Reporter’s opinion the dynamical criterion is the more meaningful one (in accord with George and Miller306) i.e. tunnelling is a process that does not occur according to classical dynamics. The advantage of (Q) is that it is not necessary to carry out a classical calculation at all. A disadvantage of (b)is that classical trajectories can be ‘quantized’ in more than one way (as mentioned above) which can lead to different classical thresholds (Miller307 gives an example of this).This difficulty can be overcome in the semi-classical theory (Section 5) where quantization is unambiguous and in which tunnelling is associated with complex-valued classical trajectories. Tunnelling in solution has been reviewed recently by Bell.308 He concludes that tunnelling corrections based on a one-dimensional parabolic barrier are sufficient at present in this field. Tully and Preston have developed a method for applying classical trajectories to electronically non-adiabatic c~llisions.~ Their procedure is to’com- 1-g59309 301 S. Wu and R. A. Marcus J. Chem. Phys. 1972,56 3519. 302 N. H. Hijazi and K. J. Laidler J. Chem.Phys. 1973,58 349. 303 D. J. Diestler and M. Karplus J. Chem. Phys. 1971,55 5832. 304 K. P. Fong and D. J. Diestler J. Chem. Phys. 1972 56 3200. 305 R. P. Saxon and J. C. Light J. Chem. Phys. 1972,57 2758. jo6 T. F. George and W. H. Miller J. Chem. Phys. 1972,57 2458. 307 W. H. Miller Faraday Discuss. Chem. SOC.,1973 No. 55 p.71. 308 R. P. Bell ‘The Proton in Chemistry’ 2nd edn. Chapman and Hall London 1973 Ch. 12. 309 R. Diiren J. Phys. (B) 1973,6 1801. Theory of Molecular Collisions and Reactive Scattering 23 pute a trajectory until a region of large non-adiabatic interaction is reached. The trajectory then switches surfaces with probability determined by the Landau- Zener formula and a velocity correction to conserve energy. This procedure which they have called ‘trajectory surface hopping’ has been reviewed by T~lly.~~ The method has given good agreement with experiment.It can also be understood within the semi-classical theory (Section 5). 5 Semi~lassical Molecular Collisioos Semi-classical collision theories involve an asymptotic solution of the Schrodinger equation. They are short-wavelength theories in that they assume that the de Broglie wavelength of nuclear motion is small relative to molecular dimensions. Semi-classical theories give considerable physical insight into collision processes and in numerical applications are often very accurate. The recent literature has however tended to emphasize the numerical aspects rather than the conceptual advantages. The semi-classical theory can handle interference and tunnelling effects that ordinary classical calculations miss.Interference effects in atomic collisions have been reviewed by Massey’ l2 and by Nikitin and Ovchinnikova.’13 Classical cal- culations can be considered as a special case of the semi-classical theory (see below). In practice however it is convenient to deal with them separately. It is appropriate to comment on the confusing nomenclature used in this field. An alternative name to semi-classical that is often applied to problems in one mathematical dimension is ‘WKB’ or ‘WKBJ’. In Russian literature the name ‘quasi-classical’ seems to be used for what is called ‘semi-classical’ here. However ‘quasi-classical’ is also often used to describe classical trajectories that have been ‘quantized’ as discussed in Section 4.In addition ‘semi-classical’ is often applied to theories in which the relative motion is treated classically and the internal motion quantum mechanically-in this Report these are called ‘classical path theories’ (Section 3). Finally it is not uncommon for other meanings to be given to ‘semi-classical’ and ‘quasi-classical’ from those mentioned above or for other words to be used in their place (e.g.‘pseudoclassical’ ‘semi-quantal”). An excellent review of the more mathematical aspects of semi-classical approxi- mations in wave mechanics has been written by Berry and Mount.310 They deal with applications of semi-classical techniques to several branches of physics in addition to molecular collision theory.Their review contains a large bibliography. Norcliffe3’’ has written a timely review on correspondence identities in classical and quantum mechanics with special reference to the Coulomb potential. Elastic Scattering.-The use of semi-classical techniques in elastic scattering is well establi~hed.’~~*~’~ A powerful technique is the use of uniform approxima-tion~,~which have been investigated for small-angle scattering by Mount3’ lo M. V. Berry and K. E. Mount Rep. Progr. Phys. 1972,35 3 15. 311 A. Norcliffe Case Studies Atgm. Phys. 1973 4 No. 1. 312 K. E. Mount J. Phys. (B) 1973,6 1397. 24 J. N. L. Connor and for rainbow scattering by Mullen and Thomas3' Scattering in two dimen- sion~~ ' and from rigid spheres3 ' has also been discussed.There has been considerable interest recently in inversion procedures for obtaining the potential directly from the data in measurements of differential cross-sections. Inversion procedures have been discussed by Remler,3 B~yle,~' Buck,318*3l9 Klingbeil,320 and Prit~hard.~~' An improved method for extracting information from glory undulations has been described by La Budde and Bern~tein.~~~ Greene and Mason323 discuss the physical interpretation of glory undulations. Child1I7 has recently reviewed the theory of orbiting and shape resonances for which moreover experimental detection has been reported.116 They are also important in recombination reactions324 and spectro~copy.~~~-~~~ Child' ' recommends the TuJ= (hou,/2n)In[1 + exp(2neu,)] (4) for calculating the widths of the quasi-bound states.In equation (4),w,,~ is the classical angular vibration frequency for the potential well and mUJis minus the action integral for the barrier.328-331 Equation (4)is derived by the method of comparison equation^,^ 10*3329333in which the Schrodinger equation for the actual barrier is mapped on to the solution for a parabolic barrier. Table 2 com-pares equation (4)with exact results for the broad resonances (ruJ > 10cm-') of H,ground state. InelasticandReactive Scattering.-Significant advances have been made recently in the semi-classical theory of inelastic and reactive molecular collisions. Miller334 and Mar~~s~~~*~~~ have independently developed methods for the calculation of S-matrix elements that use data from classical trajectory calculations.313 J. M. Mullen and B. S.Thomas J. Chem. Phys. 1973,58 5216. 314 M. V. Berry and A. M. Ozorio de Almeida J. Phys. (A) 1973,6 1451. 315 P. E. Siska J. Chem. Phys. 1973 59 3429. 316 E. A. Remler Phys. Rev. (A) 1971,3 1949. 317 J. F. Boyle Mol. Phys. 1971 22 993. 318 U. Buck J. Chem. Phys. 1971,54 1923; U. Buck and H. Pauly ibid. p. 1929. 3'9 U. Buck M. Kick and H. Pauly J. Chem. Phys. 1972,56 3391. 320 R. Klingbeil J. Chem. Phys. 1972,56 132; 1972,57 1066; 1973,59 797. 321 D. E. Pritchard J. Chem. Phys. 1972 56,4206. 322 R. B. Bernstein and R. A. La Budde J. Chem. Phys. 1973,58 1 109. 323 E. F. Greene and E. A. Mason J. Chem. Phys. 1972,57 2065; 1973,59 2651. 324 R.T. Pack R. L. Snow and W. D. Smith J. Chem. Phys. 1972,56,926. 325 G. E. Ewing Angew. Chem. Internat. Edn. 1972 11 486. 326 L. Gottdiener and J. N. Murrell Mol. Phys. 1973 25 1041. 327 W. C. Stwalley ref. 46 p. 40; ref. 145 p.259. 328 J. N. L. Connor Mol. Phys. 1968 15 621. 329 J. N. L. Connor Mol. Phys. 1968 16 525. 330 J. N. L. Connor Mol. Phys. 1972,23 717. 331 J. N. L. Connor Mol. Phys. 1973 25 1469. 332 W. Hecht J. Math. Phys. 1972 13 1291; 1973 14 1519. 333 M. J. Richardson Phys. Rev. (A) 1973,8 781. 334 W. H. Miller J. Chem. Phys. 1970 53 1949. 335 R. A. Marcus Chem. Phys. Letters 1970 7 525. 336 R. A. Marcus J. Chem. Phys. 1971,54 3965. Theory of Molecular Collisions and Reactive Scattering Table 2 Exact and semi-classical (WKB) widths for H ground state“ V J r,J(exact)b/cm- T,,(WKB)’/cm- 11 14 17.9 19.1 8 21 39.4 39.1 7 23 30.4 31.7 6 25 26.5 27.9 5 27 25.1 26.4 4 29 24.7 25.9 3 31 23.6 24.5 2 33 20.4 21.0 1 35 14.1 14.2 0 38 80.0 70.0 Adapted from ref.1 17; Calculated from time delay by R.J. Le Roy and R. B. Bernstein J. Chem. Phys. 1971,54 51 14; Calculated from equation (4). In Marcus’ the WKB (semi-classical) approximation is applied directly to the Schrodinger equation. The phase of the wavefunction satisfies the Hamilton-Jacobi equation of classical mechanics and the amplitude satisfies an equation of continuity of flux. The solution of these two equations involves classical quantities only. Thus the wavefunction is also dependent only on classical quantities.In ordinary classical calculations only real-valued classical trajectories are used. However in the semi-classical theory complex-valued classical trajectories are also required (they are necessary for tunnelling processes). Transitions that require real-valued classical trajectories are called ‘classically allowed’; those that require complex-valued ones are called ‘classically forbidden’. The above procedure is of limited value when conventional co-ordinates are used for the internal states. This is because the wavefunction is singular at turning points (cJ:the one-dimensional WKB wavefunction). A key feature in the development of semi-classical theory therefore was the use of action-angle variables to describe the internal motions.Action-angle variables have the follow- ing desirable properties :335 (a)the use of these variables removes singularities in the unperturbed WKB wavefunction for the internal states; (b) the action variables have a simple (WKB) relation to quantum numbers ;and (c)the initial angle variables occur randomly in the interval [0,1]. It is interesting to note that Bohr called action-angle variables ‘uniformizing variables’.337 It is not necessary to use the action-angle variables throughout the numerical calculation of a trajectory however. It is only necessary to relate them to the other co-ordinates at the beginning and end of the trajectory. Since the wavefunction depends only on classical quantities the theory of canonical transformations can be applied.338,339 This allows different co-337 N.Bohr ‘On the Application of the Quantum Theory to Atomic Structure’ Supple- ment to Proc. Cambridge Phil. SOC.,1924 p. 4. 338 J. H. Van Vleck Proc. Nar. Acad. Sci. U.S.A. 1928 14 178. 339 R.Schiller Phys. Reo. 1962 125 1109. 26 J. N. L. Connor ordinate systems to be investigated and more generally a comprehensive semi-classical theory to be developed.334*340-345 Miller334 used the Feynman propagator as his starting point with results essentially equivalent to those of Mar~us.~~~,~~~ Early researches on the semi- classical theory have been reviewed by Miller,346 and more recently he has written an excellent review that emphasizes transformation aspects of the theory and also discusses recent development^.^^' The first numerical application of the theory was by Miller348,349 to the collinear atom-oscillator problem.Since then this model has been further st~died~~~-~~~ and other calculations have been made for atom-rigid rota-tor,355 collinear H + C1 reaction,356 collinear H + H reaction,306~3s7-359 planar H + H reaction,360 three-dimensional He + and three- HZ,3617362 dimensional H + H reaction.363 In these calculations an S-matrix element is represented by an integral of the form W = g(4 exp [($(a ;$1 dx (5) s in the one-dimensional case. In equation (5) a represents a set of parameters such as energy and final quantum number of the collision appropriate to the transition of interest. When the integral (5)is evaluated by asymptotic techniques the main contribu- tion arises from the saddle points of f(u;x).Each saddle point corresponds to a real- or complex-valued classical trajectory. When the classical trajectories are close together this proximity must be taken into account by the derivation of 340 R. A. Marcus J. Chem. Phys. 1972,56 31 1. 341 R. A. Marcus J. Chem. Phys. 1972,56 3548. 342 R. A. Marcus J. Chem. Phys. 1973 59 5135. 343 B. C. Eu J. Chem. Phys. 1972,57 2531. 344 J. M. Bowman and A. Kuppermann Chem. Phys. 1973 2 158. 345 M. S. Child Mol. Phys. 1974 27 657. 346 W. H. Miller Accounts Chem. Res. 1971 4 161. 347 W. H. Miller Adu. Chem. Phys. 1974 25 63. 348 W. H. Miller J. Chem. Phys. 1970 53 3578. 349 W. H. Miller Chem. Phys. Letters 1970 7 431.350 W. H. Wong and R. A. Marcus J. Chem. Phys. 1971,55 5663. 351 W. H. Miller and T. F. George J. Chem. Phys. 1972 56 5668; ref. 195 p. 76. 352 J. Stine and R. A. Marcus Chem. Phys. Letters 1972 15 536. 353 T. F. George and H. D. Franchino Phys. Rev. (A) 1973 8 180. 354 J. R. Stine and R. A. Marcus J. Chem. Phys. 1973,59 5145. 355 W. H. Miller J. Chem. Phys. 1971 54 5386. 356 C. C. Rankin and W. H. Miller J. Chem. Phys. 1971 55 3150. 357 T. F. George and W. H. Miller J. Chem. Phys. 1972,56 5722. 358 J. M. Bowman and A. Kuppermann Chem. Phys. Letters 1973 19 166; J. Chem. Phys. 1973 59,6524. 359 S. Wu and R. D. Levine Mol. Phys. 1973 25 937. 360 J. J. Tyson R. P. Saxon and J. C. Light J. Chem. Phys. 1973 59 363. 361 J. D. Doll and W. H. Miller J.Chem. Phys. 1972,57 5019. 362 W. H. Miller and A. W. Raczkowski Faraday Discuss. Chem. SOC.,1973 No. 55 p. 45. 363 J. D. Doll T. F. George and W. H. Miller J. Chem. Phys. 1973 58 1343. Theory of Molecular Collisions and Reactive Scattering 27 uniform approximations. Uniform approximations have been derived for two three and many nearly coincident classical trajectorie~.~~~-~~~ They have also been obtained for multidimensional The topological structure of the classical trajectories determines the canonical integral in terms of which the uniform approximation is written. The uniform approximations involve only classical quantities namely classical action integrals and classical transition probabilities. The uniform approximations mentioned above can break down in some cases (i.e.become non-uniform).One such case is when the phase of equation (5) is very slowly ~arying.~~'?~~~ of non-uniform approximations may The use explain (in part) discrepancies that have been reported3 8-360 between semi- classical and exact quantum calculations for the H + H reaction. When many real-valued classical trajectories contribute to the integral (3 interference effects result. Miller355 has shown that these interference effects are quenched if the S-matrix is averaged in various ways-the semi-classical results then reduce to those of the ordinary Monte Carlo method. This quenching is a concrete example of a more general result of Le~ine.~~~ In contrast to interference effects tunnelling is a classically forbidden process that requires complex-valued classical trajectories for its descrip- tion.334*335,374-376 The most powerful method for their calculation is direct numerical integration of Hamilton's equations in complex phase space methods for which have been devel~ped.~~',~~~ Miller has also developed a (called 'partial averaging') whereby some degrees of freedom are treated semi-classically and the remaining ones by the Monte Carlo method.This simplifies the treatment of three-dimensional collisions. Other applications of semi-classical collision theory have been made to bound quasibound and collisional line-broadening in gases.379 The calculations described above use exact classical trajectories but approxi- mations can also be introd~ced.~'~.~~' 364 J.N. L. Connor and R. A. Marcus J. Chem. Phys. 1971,55 5636. 365 J. N. L. Connor Mol. Phys. 1973 26 1217. 366 J. N. L. Connor Mol. Phys. 1974 27 853. 367 J. N. L. Connor Mof.Phys. 1973 25 181. 368 J. N. L. Connor Faraday Discuss. Chem. SOC.,1973 No. 55 p. 51. 369 J. N. L. Connor Mol. Phys. 1973 26 1371. 370 R. A. Marcus J. Chem. Phys. 1972 57,4903. 37' See ref. 354. 372 J. N. L. Connor Chem. Phys. Letters 1974 25 611. 373 R. D. Levine J. Chem. Phys. 1972 56 1633. 374 K. F. Freed J. Chem. Phys. 1972 56 692. 375 P. Pechukas and J. P. Davis J. Chem. Phys. 1972 56 4970. 376 D. W. McLaughlin J. Math. Phys. 1972 13 784 1099. 377 R. A. Marcus Faraday Discuss. Chem. SOC.,1973 No. 55 p.34. 378 I. C. Percival J. Phys. (B) 1973 6 L229.379 D. E. Fitz and R. A. Marcus J. Chem. Phys. 1973 59 4380. 380 R. J. Cross J. Chem. Phys. 1973,58 5178. 381 H. VanDop and A. Tip Physica 1972 61 607. 28 J. N. L. Connor Electronic Transitions.-There has been considerable interest in the semi- classical theory of electronic transitions recently. Non-adiabatic transitions are important in spectroscopy,' as well as in collision processes. 793829383 These calculations introduce semi-classical approximations into coupled sets of differential equations. When only a small number of states are involved the coupled equations can be solved by the same exact numerical methods developed for inelastic ~ollisions.~~"-~~~ For example Mies389 has solved six coupled equations by Gordon's method in the study of fine structure transitions for the collision H+ + F(,P).Particular interest attaches to problems involving two electronic states. The vaiidity of the Landau-ZenerStueckelberg formula has been reviewed by Child390 and Nd~itin.~~' The Stueckelberg method of tracing paths in the complex plane has been the object of critical studies by Crother~~~ and Thorson et Thorson et have also made detailed studies of various approxi- mations used in semi-classical theories of non-adiabatic phenomena. Other recent work is references 395-399. Uniform approximations have been used in the solution of the coupled equations by Eu4Oo A semi-classical theory of electronic transitions for collisions of the type A + BC has been developed by Miller and George.401 Their theory is an exten- sion of the Landau-Zener-Stueckelberg method.They analytically continue the two potential surfaces into the complex plane. Complex-valued classical tra- jectories are then used to calculate S-matrix elements. The method has been applied to the collinear H+ + H reaction.402 Miller and George4" have also 382 H. Gebelein and J. Jortner Theor. Chim. Acta 1972 25 143. 383 Y. B. Aryeh J. Quant. Spectroscopy Radiative Transfer 1973 13 144. 384 R. E. Olson Phys. Rev. (A) 1972,5 2094; T. A. Green ref. 195 p. 281. "' S.A. Evans and N. F. Lane Phys. Rev. (A) 1973,8 1385. 386 R. E. Olson R. Morgenstern D. C. Lorents J. C. Browne and L. Lenamon Phys. Rev. (A) 1973 8 2387. 387 L. Lenamon J. C. Browne and R. E. Olson Phys.Rev. (A) 1973 8 2380. B. R. Johnson and R. D. Levine Chem. Phys. Letters 1972 13 168; B. R. Johnson Chem. Phys. 1973 2 381. F. H. Mies Phys. Rev. (A) 1973 7,942 957. 390 M. S.Child Faraday Discuss. Chem. Soc. 1972 No. 53 p. 18. 391 E. E. Nikitin Comments Atom. Mol. Phys. 1970 1 166; 1970 2 118. 392 D. S. F. Crothers Adu. Phys. 1971 20,405. 393 W. R. Thorson J. B. Delos and S. A. Boorstein Phys. Rev. (A),1971,4 1052; erratum 1972 5 479. 394 J. B. Delos and W. R. Thorson Phys. Rev. Letters 1972 28 647; Phys. Rev. (A) 1972 6 720 728; J. B. Delos W. R. Thorson and S. K. Knudson Phys. Rev. (A) 1972 6 709; erratum Phys. Rev. (A) 1974 9 1026. 395 E. E. Nikitin and A. I. Reznikov Phys. Rev. (A) 1972,6 522. 396 J. E. Bayfield E. E. Nikitin and A.I. Reznikov Chem. Phys. Letters 1973 19 471 ; erratum 1973 21 212. 397 A. M. Woolley and S. E. Nielsen Chem. Phys. Letters 1973 21,491. J98 H. Nakamura Mol. Phys. 1973 25 577. 399 L. P. Kudrin and Yu. V. Mikhailova Zhur. exsp. teor. Fiz. 1972 63 63 (Sou. Phys. JETP 1973 36 33); T. Matsushita and R. Paul J. Chem. Phys. 1973 58 2480. 400 B. C. Eu J. Chem. Phys. 1973 58 472; 1973 59 4705; B. C. Eu and T. P. Tsien Phys. Rev. (A) 1973 7 648. 401 W. H. Miller and T. F. George J. Chem. Phys. 1972,56 5637. 402 Y.W. Lin T. F. George and K. Morokuma Chem. Phys. Letters 1973 22 547. Theory of Molecular Collisions and Reactive Scattering 29 developed an approximate theory that uses only real trajectories. This approxi- mate scheme provides a justification for the 'trajectory surface hopping' method of Tully and 6 Statisticaland Statistical-Dynamical Collision Theories The dynamical calculations reported in Sections 3-5 require exact or approxi- mate solutions of Schrodinger's or Hamilton's equations for the collision.Statistical theories do not require the solution of a dynamical problem. Statistical-dynamical theories treat some degrees of freedom statistically and the remainder dynamically. The best known statjstical theories are activated-complex theory and phase- space theory. George and Ross" have reviewed calculations using phase-space theory. Rebick and Levine have developed a phase-space theory of collision- induced diss~ciation.~'~ Activated-complex theory for bimolecular reactions (collinear and three dimensional) has been tested by Karplus and co-workers using exact classical traje~tories.~'~~~'~ They use the microcanonical form of the There is excellent agreement for the H + H reaction at thermal energies.For reactions having asymmetric potential surfaces the agreement is less good this being due to a non-equilibrium distribution of trajectories and/or a transmission coefficient that is not A difficulty arises in defining the position of the activated complex in reactions with low potential energy barriers. This has been discussed by Wong and Marcus using the concept of minimum state densit y.409,4 ' The quantum form of activated-complex theory has been tested for collinear rea~tions.~~~*~~~,~~~,~~~*~~~~~~ The exact rate constant agrees well with that calculated by activated-complex theory (with a correction for tunnelling) except at low temperature^.^' 1414 A test of vibrational adiabaticity which is a suffi-cient condition for the validity of activated-complex theory has been mentioned in Section 3.229 The experimental characterization of long-lived complexes has stimulated the application of activated-complex theory (in its RRKM form) and other theories 403 C.Rebick and R. D. Levine J. Chem. Phys. 1973,58 3942. 404 K. Morokuma and M. Karplus J. Chem. Phys. 1971 55 63. 40s G. W. Koeppl and M. Karplus J. Chem. Phys. 1971,55,4667. 406 K. H. Lau S. H. Lin and H. Eyring J. Chem. Phys. 1973 58 1261. 407 P. Pechukas and F. J. McLafferty J. Chem. Phys. 1973 58 1622.408 J. B. Anderson J. Chem. Phys. 1973,58,4684. 409 W. H. Wong and R.A. Marcus J. Chem. Phys. 1971,55 5625. 410 W. H. Wong Canad. J. Chem. 1972.50 3386. 411 See ref. 303. 412 S. G. Christov Ber. Bunsengeseilschaftphys. Chem. 1972 76 507; Croat. Chem. Acta 1972,44 67. 413 G. W. Koeppl J. Chem. Phys. 1973,59 3425. 4'4 G. W. Koeppl J. Chem. Phys. 1973,59,2168; E. J. Shipsey J. Chem. Phys. 1973,59 2170. J. N.L. Connor to these In a classical trajectory study of the NaBr + KCl reaction Brumer and KarplusE4 found that the trajectories could be divided into short- and long-lived ones. They compared the latter with RRKM theory with reasonable agreement. Marcus4’ has pointed out that activated-complex theory cannot be used to make predictions on the final state distribution of reaction products (except for the case of a ‘loose’ complex).It can be made to do so if additional dynamical assumptions are added. The resulting theory is then a statistical-dynamical 0ne.416-418 Other statisticaklynamical calculations have been made recently by Hofacker and Levine4I9 and by W~ng.~~’ A new development by Levine Bernstein and co-~orkers~~ is the 1-428 application of information theory to reaction dynamics. They apply it to the following topics (a) the best means of characterizing product energy-state distributions (b)compaction of data and (c) development of measures of the specificity of energy release and the selectivity of energy consumption. The out- come of a dynamical process is compared with its statistical outcome.The ‘surprisal’ of any particular final state is a local measure of the deviation of the observed probability from that expected statistically. An overall measure of this deviation is provided by the ‘entropy deficiency’. Analysis of the surprisal has allowed product distributions to be characterized by translational vibrational and rotational ‘temperature parameters’. This has resulted in a considerable compaction of the data. 4L5 D. L. Bunker and W. L. Hase J. Chem. Phys. 1973,59,4621. 416 J. M. Parson K. Shobatake Y.T. Lee and S. A. Rice Faraday Discuss. Chem. SOC. 1973 No. 55 p. 344. 417 W. B. Miller S. A. Safron and D. R. Herschbach J. Chem. Phys. 1972 56 3581 ; S. J. Riley and D. R. Herschbach J. Chem.Phys. 1973,58 27; D. L. King and D. R. Herschbach Faraday Discuss. Chem. SOC.,1973 No. 55 p.331. 418 S. A. Safron N. D. Weinstein D. R. Herschbach and J. C. Tully Chem. Phys. Letters 1972 12 564; A. B. Lees and G. H. Kwei J. Chem. Phys. 1973,58 1710. 419 G. L. Hofacker and R. D. Levine Chem. Phys. Letters 1972 15 165. “O W. H. Wong Canad.J. Chem. 1972,50,633. 421 R. B. Bernstein and R. D. Levine J. Chem. Phys. 1972 57 434. 422 A. Ben-Shaul R. D. Levine and R. B. Bernstein J. Chem. Phys. 1972,57 5427. 423 A. Ben-Shaul R. D. Levine and R. B. Bernstein Chem. Phys. Letters 1972 15 160. 424 R. D. Levine and R. B. Bernstein Chem. Phys. Letters 1973 22 217. 425 R. D. Levine B. R. Johnson and R. B. Bernstein Chem. Phys. Letters 1973 19 1. 426 R. D. Levine and R.B. Bernstein Faraday Discuss. Chem. SOC.,1973 No. 55 p.100. 427 A. Ben-Shaul Chem. Phys. 1973,1 244. 428 A. Ben-Shaul G. L. Hofacker and K. L. Kompa J. Chem. Phys. 1973 59,4664.

ISSN:0308-6003    

DOI:10.1039/PR9737000005

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

3 Luminescence Spectroscopy By R. B. CUNDALL and T. F. PALMER Chemistry Department University of Nottingham Nottingham NG7 2RD 1 Introduction Luminescence spectroscopy the study of light emission from excited states of atoms and molecules is not a new technique. The recent rapid increase in its application is due to the availability of reliable instrumentation and to the interest in electronically excited states. The arbitrary selection of references and topics for this Report means that much important work has been omitted; nevertheless it is hoped that the Report will act as a spur to further progress. The extensive analytical applications of fluorescence and phosphorescence are not reviewed here ;a recent book by White and Argauer’ serves as an introduc- tion.All aspects of the subject are discussed in the recent book by Guilbault2 and extensive reviews of techniques and instrumentation have also a~peared.~-~ A revised edition of Berlman’s compilation of fluorescence data for aromatic molecules is an invaluable laboratory manual.’ A monograph details the significant application of luminescence spectroscopy in physical biochemistry.* Luminescence from excited states of atoms and simple molecules has been extensively covered in previous Reports so this one concentrates mainly on the applications to larger molecules. For convenience after a brief discussion of experimental techniques and theory the information is presented by reference to different classes of chemical compound. The main phenomenological distinction between fluorescence and phosphor- escence is the time-scale for the decay of emission after excitation.Fluorescence C. E. White and R. J. Argauer ‘Fluorescence Analysis’ Dekker New York 1970. G. C. Guilbault ‘Practical Fluorescence Theory Methods and Techniques’ Dekker New York 1973. ‘Advances in Analytical Chemistry and Instrumentation Spectrochemical Methods of Analysis’ ed. J. D. Winefordner Wiley New York 1971 Vol. 9. ‘Luminescence Spectrometry in Analytical Chemistry’ ed. J. D. Winefordner S. G. Schulman and T. C. O’Haver Wiley New York 1972. ‘Creation and Detection of the Excited State’ ed. A. A. Lamola Dekker New York 197 1 Vol. 1 Parts A and B. ‘Accuracy in Spectrophotometry and Luminescence Measurements’ National Bureau of Standards Special Publication 378 New York 1973.I. B. Berlman ‘Handbook of Fluorescence Spectra of Aromatic Molecules’ Academic Press New York 2nd edn 197 I. ‘Excited States of Proteins and Nucleic Acids’ ed. R. F. Steiner and I. Weinryb Plenum Press New York 1971. 31 R.B. Cundall and T. F. Palmer lifetimes are ca. 10-* s,a value comparable with vibrational and solvent relaxation and the power of this method for the study of such effects is well demonstrated by the low-pressure high-resolution studies of benzene vapour and by the use of fluorescent probes for the examination of biological cell membranes. The slower decay of excited states by phosphorescence means that the effects of weaker environmental perturbations can be observed.Spectral profiles decay kinetics and polarization properties are all sources of significant information on the structure and properties of the ground and excited states. 2 Theory and Techniques Radiationless processes determine the possibilities for observing luminescence in the statistical and some results applicable to large molecules having a single decomposition mode have been discussed.' General expressions for absorption and resonance fluorescence cross-sections and for emission yields have been derived for large molecules in the statistical limit. Nitzan and J~rtner,'~?'~ exploring the implications of coupling between non-radiative electronic and vibrational relaxation in excited electronic states of large molecules have shown that in the limit of slow vibrational relaxation the general expressions reduce to the time-independent decay of a single vibronic level.Modified expressions are obtained for the fast-relaxation case. The energy dependence of radiati~e'~ and non-radiative" decay from single vibronic states has been discussed by Lin who shows that radiative rate constants depend linearly on the number of quanta excited in a given mode. Of the various experimental techniques used in photochemistry photobiology and photophysics the measurement of fluorescence lifetimes has been the slowest to develop. In the past few years the rapid development of pulsed laser methods and of time-correlated single-photon counting has caused a remarkable change. Fluorescence decay measurements on a nanosecond scale are now made routinely in many laboratories.The fluorescence decay of singlet excited carbon di- sulphide16 in the gas phase and of 9,lO-diazophenanthrene and phenanthrene in solution" have been measured using a N laser. Other such investigations include fluorescence of anthracene solutions,' the effects of pressure on fluores~ence,'~ luminescence including E-type delayed fluorescence of benzophenone,20 and the J. Jortner S. A. Rice and R. M. Hochstrasser Adv. Photochem. 1969 7 149. lo K. F. Freed Topics in Current Chem. 1972 31 105. I' K. G. Kay and S.A. Rice J. Chem. Phys. 1972,57 3041. '2 A. Nitzan and J. Jortner J. Chem. Phys. 1972 57 2870. I' A. Nitzan and J. Jortner J. Chem. Phys. 1973,58 2412. l4 G. R. Fleming 0. L. J. Gizeman and S.H. Lin Chem. Phys. Letters 1973 21 527. S. H. Lin .I.Chem. Phys. 1973 58 5760. L. E. Brus Chem. Phys. Letters 1971 12 116. H. Davey and S. G. Hadley Chem. Phys. Letters 1971 12 57. l8 S. D. Bebenko V. A. Benderskii V. I. Gol'danskii A. G. Lavrushko and V. P. Tyckinski. Chem. Phys. Letters 1971 8 598. l9 P.C. Johnson and H. W. Offen Chem. Phys. Letters 1970,6 505. 2o R. E. Brown L. A. Singer and J. H. Parks Chem. Phys. Letters 1972 14 193. Luminescence Spectroscopy 33 study of charge-transfer complexes.” Pumped dye lasers have been used to study fluorescence decay times in glyoxa122 and iodine mon~chloride~~ and the fluorescence of nitrogen dioxide has been examined in the collision-free region using a dye laser pumped by a flash lamp providing 451.5-460.5 nm light with a bandwidth of 0.08 nm.24 Rhodamine and fluorescein dyes have been shown to provide tunable output in the region 520-650nm with a bandwidth of <0.01nm which would seem to be the first example of a CW tunable laser source.25 Frequency doubling can be used to give a power level of a few mW in the 260-325 nm region A dye laser pumped by a frequency-doubled mode- locked argon ion laser has been described26 and would appear to be especially suited for fluorescence lifetime measurements.The emission of i.r. luminescence from a wide variety of organic compounds following excitation with a carbon dioxide laser would seem to have useful analytical possibilities.’ ’v2’ The development of single-shot techniques to record absorption and emission processes on a picosecond time-scale has been rep~rted.~~-~ An ingenious arrangement using an echelon technique to provide temporal and spectral resolution from a single picosecond pulse has been used for example to obtain the time-resolved emission spectra of rhodamine 6G in ethanol.32 A mode-locked frequency-doubled Nd3+ glass laser giving pulse widths of 3 ps has been used to examine emission from rhodamine 6B in glycerol,33 and the application of picosecond pulse techniques to the study of ultrafast electronic energy transfer processes has been A most interesting development is the measure- ment of two-photon absorption ~pectra,~’ obtained by excitation with a dye laser pumped by a nitrogen laser and monitored by observation of the sample excitation luminescence.The technique can be used for gases liquids dilute solutions and solids. The single-photon time-correlation possesses high sensitivity and reliability and has the added advantage that the instrumentation is com- 21 K. Egawa N. Nakashima T. Mataga and Ch. Yamanaka Chem. Phys. Letters 1971 8 108. 22 J. T. Yardley G. W. Halleman and J. I. Steinfeld Chem. Phys. Letters 1971 10 266. 23 G. W. Halleman and J. I. Steinfeld Chem. Phys. Letters 1971 12 431. 24 P. B. Sacket and J. T. Yardley J. Chem. Phys. 1972 57 152. 25 C. Gabel and M. Hercher IEEE J. Quantum Electronics 1972 QE8 524. 2b R. 2.Bacharach Rev. Sci. Instr. 1972 43 734. ” D. M. Hailey H. M. Barnes C. Woodward and J. W. Robinson Analyt. Chim.Acta 1971,56 161. D. M. Hailey H. M. Barnes and J. W. Robinson Analyr. Chim. Acta 1971 56 175. 29 P. M. Rentzepis Science 1970 169 239. 30 P. M. Rentzepis and C. J. Mitchele Analyt. Chem. 1970 42 A20. ” G. E. Busch R. P. Jones and P. M. Rentzepis Chem. Phys. Letters 1973 18 178. 32 M. R. Topp P. M. Rentzepis and R. P. Jones Chem. Phys. Letters 1971,9 1. 33 K. B. Eisenthal Chem. Phys. Letters 1970 6 155. 34 D. Rehm and K. B. Eisenthal Chem. Phys. Letters 1971 9 387. 3s R. M. Hochstrasser H.-N. Sung and J. E. Wessel J. Amer. Chem. SOC. 1973,95 8179. 36 J. B. Birks and I. H. Munro Progr. Reaction Kinetics 1967 4 239. 37 See W. R. Ware in ref. 5. 38 J. Yguerabide in ‘Methods in Enzymology’ Vol. 26 ‘Enzyme Structure’ ed. C. H. W. Hirs and S. N. Timashelf Academic Press 1972 Part C.39 A. E. W. Knight and B. K. Selinger Austral. J. Chem. 1973 26 I. 34 R. B. Cundall and T.F. Palmer mercially available. The method is of great value in the examination of weak lumine~cence~~'~~ and has been used in the definitive study of fluorescence from single vibronic levels of benzene at very low pressures in the collision-free region.42 This method is also of great importance in biological systems. For example it has been used to study light emission generated from the oxidation of an enzyme intermediate formed between luciferine and Mg2fATP.43 From an analysis of the single-photon decay curves time-resolved spectra were obtained following wavelength normalization. Pulsed light sources suitable for single-photon counting have been discussed by Ware37*44 who suggested that whereas the free running lamp is easier to construct the hydrogen thyratron gated lamp offers greater flexibility.Many w0rkers~~9~' using the single-photon method have experienced rf interference on the measured decay curves produced by the intense electrical discharge of the lamp. It is the experience of one of the authors45 that the rf interference should be removed at source i.e. the lamp housing should be an effective rf shield. Refinements concerned with the photon timing photomultiplier and the signal processing equipment between the photomultiplier and the time to amplitude converter have been proposed,46 and the performance of an RCA C31034 photomultiplier has been described.47 An alternative method4* for deconvoluting fluorescence and phosphorescence curves has been proposed and tested for real and artificially constructed decays and pile-up correction^^^*^' have been made in attempts to increase the efficiency of data collection.A reiterative convolution technique has been used to extract fluorescence lifetimes approaching 0.1 ns from a 2 ns lamp p~lse,~' but since time jitter37 may exceed 50 ps the validity of such procedures is doubtful. Photon counting has been used to measure weak light inten~ity.~' In the digital mode the photomultiplier and associated circuitry provide discrete electron pulses so that the number of pulses counted is directly proportional to the number of pulses incident on the photocathode.The sensitivity of phase- sensitive lock-in amplifiers in luminescence spectroscopy is illustrated by the detection of gas-phase phosphorescence for pyrene and naphthalene5 (a,,ca. which at pressures as low as 4 x Torr shows expected similarities 40 M. Duquesne P. Vigny and N. Gabillat Photochem. and Phorobiot. 1970 11 519. 4' R. R. Alford and N. Ockman J. Opt. SOL..Amer. 1968,58,90. 42 K. G. Spears and S. A. Rice J. Chem. Phys. 1971 55 5561. 43 M. DeLuca L. Brand T. A. Cebula H. H. Selinger and A. F. Makula J. Bid. Chem. 1971,246 6702. 44 W. R. Ware 1969 O.N.R. Technical Report No. 3. 45 T. F. Palmer unpublished results. 46 C. Lewis W. R. Ware L. J. Doemeny andT. L. Nemzek Rev. Sci.Instr. 1973,44 107. 47 R. Reisse R. Creecy and S. K. Poultney Rev.Sci. Instr. 1973 44 1666. 48 W. R. Ware L. J. Doemeny and T. L. Nemzek J. Phys. Chem. 1973,77 2038. 49 P. B. Coates J. Phys. (0, 1972 5 148. C. C. Davis and T. A. King J. Phys. (0, 1972,5 1072. 51 H. E. Zimmerman D. P. Werthemann and K. S. Kamm J. Amer. Chem. Soc. 1973 95 5094. 52 H. V. Malmstadt M. L. Franklin and G. Horlick And-vt. Chem. 1972 44 A63. 53 W. H. van Leeuwen J. Langelaar and J. D. W. van Voort Chem. Phys. Letters 1972 13. 622. Luminescence Spectroscopy 35 to phosphorescence spectra in solid matrices. The range of the detection system was extended by replacing the normal 1600W xenon arc by a pulse quantizer and an argon ion laser frequency-doubled to 257.3 nm. Fluorescence lifetimes of /3-naphthylamine have been measured using a phase- shift method54 in which high-frequency modulation (10-30 MHz) is employed and the phase angle is measured by a phase-sensitive lock-in amplification unit.The phase-shift method has been used to study naphthalene and benzene using an intense light source modulated up to 200 kHz.55*56 Modulation techniques in chemical kinetics including fluorescence spectroscopy have been reviewed by Phillips5’ The use of lock-in amplifiersS8 in fluorescence spectroscopy has been reviewed and their employment in detection of S2 emissions from 1,Zbenz- anthracene and 3,4-benzpyrine has been rep~rted.~’ Arc lamp ripple found in high-pressure mercury and xenon lamps can be dramatically reduced by incor- poration of a lock-in amplifier.60 Errors in luminescence decay curves caused by photomultiplier tube saturation have been discussed6’ and an interesting examination of techniques available for the measurement of photoluminescence lifetimes has appeared.62 Pulse- sampling fluorimetry has been applied to the determination of phosphorescence spectra and lifetimes.63 A number of simple systems for the measurement of fluorescence lifetime^^^-^^ have been reported and a method based on the distortion of an electrical pulse has been di~cussed.~’ Below 4.3 K spin-lattice relaxation becomes slower than phosphorescence from the individual zf (zero field) levels of the lowest triplet states in some aromatic molecules.Methods have been de~eloped~~.~~ which may yield :(i) identification of zf origins of different vibronic levels; (ii) optical detection of zf transitions (iii) relative rates of intersystem crossing processes to different zf levels of the lowest triplet state (iv) conservation of spin direction in triplet-triplet energy transfer.Time-resolved phosphorescence phosphorescence microwave double reson- ance (PMDR) and related techniques have been used at low temperature to 54 E. W. Schlag J. Chem. Phvs. 1969 51 2508. 55 H. E. Hunziker Chem. Ph-vs. Letters 1969 3 504. ” C. S. Burton and H. E. Hunziker J. Chem. Phys. 1970 52 3302. 57 L. F. Phillips Progr. Reaction Kinetics 1973 7 84. T. C. O’Haver J. Chem. Educ. 1972. 49 A131 A211. ’’ C. E. Easterley L. G. Christophorou R. P. Blaunstein and J. G. Carter Chem. Phys. Letters 1970 6 579.6o J. Langelaar G. A. de Vries and D. Bebelaar J. Phvs. (E). 1969 2 149. ‘‘ P. F. Jones and A. R. Calloway Rev. Sci. Instr. 1973 44 1393. 62 J. N. Demas and A. W. Adamson J. Phys. Chem. 1971,75 2463. 63 R. P. Fisher and J. D. Winefordner Analyt. Chem. 1972 44 948. 64 B. Selinger and R. Speed Chem. Instr. 1969 2 91. 65 J. Jessop. R. P. Wayne and T. J. Wayne J. Phys. (E) 1972 5 638. 66 F. E. Lytle Photochem. and Photobiol. 1973 17 75. 6’ K. Osada Rev. Sci. Instr. 1973 44 656. ” M. A. El-Sayed and L. Hall J. Chem. Phys. 1969 50 31 13. 69 M. A. El-Sayed Accounts Chem. Res. 1971 4 23. 36 R.B. Cundall and T.F. Palmer assign the lowest triplet state and to study triplet-state decay processes in benzene,70 anthra~ene,~' substituted naphthalene^,^^ and N-heterocyclic mol- ecules such as the quin~xalines.~~ Pseudo-first-order rate constants for heavy-atom quenching of 57 aromatic compounds induced in bromobenzene solution have been reported74 and were shown to vary from 0.7 x lo7 to 3.0 x lo9s-'.The quenching rate constant has been shown to comprise terms for intermolecular singlet-triplet energy transfer and an induced intramolecular intersystem crossing. The results were consistent with theories dealing with short-range encounters. In connection with inter- system crossing a new method for determining radiative and non-radiative rate constants for Tl -+So transitions has been rep~rted.~' Evidence for intramolecular hydrogen-bonding has been deduced from spectroscopic data on bandwidths for absorption and fluore~cence.~~ Assuming that photostability defined as the reciprocal of the phosphorescence quantum yield is proportional to the rate of internal conversion Otter~tedt~~ has explored the relationship to the energy gap between the first excited singlet and ground states.In hydrogen-bonded systems the photo-excited enol form rearranges to the keto form. SCF LCAO MO calculations suggest that E(S1 -So) is less for the keto form than for the enol. Luminescence results are reported in support of the calculations. The requirement in fluorescence spectroscopy for well-established standards with known fluorescence efficiencies and lifetimes under a variety of conditions is of paramount importance. Melh~ish~~,~~ has examined the methods of reporting fluorescence data and discussed the requirements and use of standards.The lack of suitable standard compounds in the near i.r. and U.V. regions of the spectrum has been pointed out." Demas and Crosby81*82 have critically and comprehensively reviewed methods for determining photoluminescence quantum yields and correcting excitation and emission spectra. A shift in position of the emission spectrum of quinine bisulphate in different solvents83 has been reported. A thorough investigation of the absorption fluorescence and excitation spectra of different commercial samples of quinine bi~ulphate~~ has shown that the spectral fluorescence of the emission remained unchanged and that the fluores- 70 A. A. Gwaiz M. A. El-Sayed and D.S. Tinti Chem. Phys. Letters 1971,9 454. ' R. H. Clarke and C. A. Hutchinson J. Chem. Phys. 197 I 54 2962. 72 S. M. Lyle and E. C. Lim Chem. Phys. Letters 1972 17 367. 73 D. S. Tinti and M. A. El-Sayed J. Chem. Phys. 1971,54 2529. 74 I. B. Berlman J. Phys. Chem. 1973 74 562. 75 R. B. Cundall and L. C. Pereira Chem. Phys. Letters 1972 16 371. 76 I. B. Berlman Chem. Phys. Letters 1969 3 61. " J. A. Otterstedt J. Chem. Phys. 1973 58 5716. 78 W. H. Melhuish see ref. 6. 79 W. H. Melhuish J. Res. Nut. Bur. Stand. (A) 1972 76 547. R. Reisfeld A. Honigbaum and R. A. Velapoldii J. Opt. SOC.Amer. 1971 61 1422. ' J. N. Demas and G. A. Crosby J. Phys. Chem. 1971,75 991. 82 G. A. Crosby J. N. Demas and J. B. Callis see ref. 6. 83 A. N. Fletcher J. Phys.Chem. 1968 72 2742. 84 A. N. Fletcher Photochem. and Photobiol. 1969 9 439. Luminescence Spectroscopy 37 cence quantum yield was constant to within f5 % with excitation from 240 to 400 nm. The quantum yields for fluorescence and phosphorescence of 20 organic compounds and their deuteriated analogues using 9,iO-diphenylanthracene as a standard have been rep~rted.’~ S -P T is found to be the dominant mode for intersystem crossing in benzene but S -P ?;.(j > 1) occurs in the larger aromatics. Deuteriation of polycylics leads to an increase in the radiative lifetimes of the lowest states. Solvent and temperature effects and phosphorescence yields in N-heterocyclics and aromatic carbonyls are discussed in terms of vibronic interactions of m* and nn* states.The need for fluorescence standards at low temperature is pressing. The following values have been reported for fluorescence quantum yields in EPA glass at 77 K :86 9,lO-diphenylanthracene (DPA) Of= 0.95 & 0.05;9,lO-dichloro-anthracene Of= 0.98 f0.05; and phenanthrene (P) Qf = 0.13 & 0.01. DPA and P show no temperature dependence from 300 to 77 K and would appear to be excellent fluorescence standards. It is therefore unfortunate that controversy exists over the absolute fluorescence quantum yield of DPA for which values of Of= lS7and 0.8388 have been proposed. A simple procedure for measuring fluorescence quantum yields as a function of temperature has been reported” and tested for DPA and phenazine. The application of fluorescence spectroscopy to biochemistry for the study of structure and interactions of proteins and nucleic acids has been reviewed.” The use of inorganic ions in glasses and polycrystalline pellets has been discussed in connection with fluorescence standard reference materials.” An interesting technical review92 on the use of light guide systems in the U.V.region of the spectrum is also worthy of mention. Combination of a silica glass core and polymer sheaths leads to fibres capable of transmitting light of wavelengths down to 200 nm. General expressions obtained93 for the time-dependent fluorescence caused by anisotropic rotational diffusion induced by Brownian motion differ from earlier treatments reported by Taog4 and Weber.95i96 Fluorescence polarization measurements on molecules dissolved in liquid crystals have been shown to be useful in gaining information on the absolute orientation of transition moments in molecules.97 The liquid-crystal orientation technique has been used to 85 R.Li and E. C. Lim J. Chem. Phys. 1972,57 605. 86 J. R. Huber M. A. Mahoney and W. M. Mantulin J. Photochem. 1973174 2 67. I. B. Berlman Chem. Phys. Letters 1973 21 344. J. B. Birks Chem. Phys. Letters 1972 17 370. 89 W. M. Mantulin and J. R. Huber Photochem. and Photobiol. 1973 17 139. 90 R. F. Chen see ref. 6. R. Reisfeld see ref. 6. 92 H. Dislich and A. Jacobsen Angew. Chem. Internat. Edn. 1973 12 439. 93 T. J. Chuang and K. B. Eisenthal J. Chem. Phys. 1972,57 5094. 94 T. Tao Biopolymers 1969 8 609.95 R. D. Spencer and G. Weber J. Chem. Phys. 1970,52 1654. 96 G. Weber J. Chem. Phys. 1971 55 2399. 9’ E. Sackmann and D. Rehm Chem. Phys. Letters 1970,4 537. 38 R. B. Cundall and T.F. Palmer determine the polarization of emission from exciplexes formed by the excited states. The heteroeximer formed between pyrene and di~henylamine~~ has been shown to be preferentially orientated with the long axis of pyrene parallel to the electric field. Effects of rotational diffusion have been observed by means of fluorescence polarization measurements on the fluorescence decay of all-trans- 1,6-diphenylhexa-1,3,5-triene(DPH)99in methylcyclohexane paraffin oil and a nematic liquid crystal solution using single-photon counting. Rotation is rapid in methylcyclohexane occurring within 1 ns.In the liquid crystal system no rotation is observed within the time-scale of the experiments (ca. 50ns) and paraffin oil solutions show intermediate behaviour. The DPA molecule in its excited state fits a model in which it is assumed to be a prolate ellipsoid. The results confirm that liquid crystals provide suitable media for studying the spectroscopy of orientated molecules. Fluorescence and phosphorescence polarization of molecules in stretched polymer sheet have been reported"' for DPH which has a large long axis/short axis ratio and for coronene which has a three-fold axis of symmetry. Information on the molecular conformation of the excited states of some luminescent chiral molecules which exhibit some degree of circular polarization of fluorescence and phosphorescence has been obtained.' The polarization dependence of molecular fluorescence excited by simultaneous absorption of two photons has been examined for randomly oriented molecules which do not rotate between absorption and emission.lo2 Aromatic molecules in certain polycrystalline n-paraffin solid solutions yield sharp quasi-linear spectra in which normally broad vibronic peaks are narrowed to only a few cm-'.This is the Shpol'skii effe~t.''~*"~ The degree of fine structure resolution is sensitive to the relative sizes of the solute molecules and the lattice molecules. The linewidths of transitions to upper singlet electronic states of anthracene coronene and 1,12-benzpyrene in Shpol'skii mat rice^''^ have been measured.The data support the contention that in these molecules the upper singlet states are coupled to several intramolecular radiationless decay channels. Magnetic fields have been shown to affect differently the intensities of delayed monomer and excimer fluorescence whereas no effect on the phosphorescence intensity was observed.Io6 This shows that delayed monomer and dimer fluores- cence must arise from two different types of T-T annihilation process. 98 H. Beens H. Mohwald D. Rehm E. Sackmann and A. Weller Chem. Phys. Letters 1971 8 341. 99 E. D. Cehelnik R. B. Cundall J. R. Lockwood and T. F. Palmer J.C.S. Faraday 11 1974 70 244. 100 J. J. Dekkers G. P. Hoornweg G. Maclean and N. H. Volthorst Chem. Phys. Letters 1973 19 5 17.101 I. Z. Steinberg and A. Gafni Rev. Sci. Instr. 1972 43 409. 102 W. M. McClain J. Chem. Phys. 1973 58 324. 103 D. J. Morantz Chem. Phys. Letters 1971 54 1807. I04 B. Linder and S. Abdulnuer J. Chem. Phys. 1971,54 1807. 105 J. L. Richards and S. A. Rice Chem. Phys. Letters 1971 9 444. 106 D. Wyrsch and H. Labhart Chem. Phys. Letters 1971,8 217. Luminescence Spectroscopy 39 Other reports which are of interest are that the assumption that excimer formation is diffusion controlled is invalid in low-viscosity solvents,107 and the description of equipment capable of observing fluorescence in single living cells.' O8 3 Small Molecules Much detailed work continues on the emissions from excited states of small molecules.The structure and reactions of such molecules can be studied in considerable detail. Because of the less complex vibrational motions of such molecules their photophysical behaviour is simpler than that of more complex organic molecules. Transitions between states which require mixing of states are restricted and perturbations such as those occurring during bimolecular collisions are more marked than with more complex polyatomic specie^.'^' Most of the papers in the area deal with nitrogen dioxide and sulphur dioxide an interest certainly associated with the importance of these species in atmospheric pollution. Nitrogen dioxide is readily excited by light from available lasers and conse- quently excitation by highly monochromatic light is possible.' lo The underlying continuum in the fluorescence spectrum decreases in extent as the exciting wave- length increases.The nature of the continuum is uncertain but a radiative lifetime of 5 x lo-' s was estimated. Schwartz and Johnston" used a phase- shift method for measuring the decay of the ,& state in different vibronic levels. Values ranged between 55 and 90p for the radiative lifetimes. Sackett and Yardle~,~ used a tunable dye laser to excite NO fluorescence under collision-free conditions between 451.5 and 460.5 nm. The fluorescence observed in a large cell decayed non-exponentially and zfshowed a marked dependence on structure. It is confirmed that a quasi-continuous absorption underlies the bands in the visible spectrum. The main conclusions are that ,El and 'B states are involved in the fluorescence and that both of these states are perturbed by interaction with vibronic levels of the ground 2A state.Transitions to ,B are stronger than those to the 'El state. The transitions involving the ,B state are responsible for the major structural features. States populated by the quasi-continuum absorption are responsible for the longest-lived fluorescence species. Measurements of Qf for NO2 excited at different wavelengths at various pressures in the presence and absence of foreign gases show that self-quenching obeys Stern-Volmer kinetics whereas quenching by added gases does not. Lifetimes and kinetic analysis demonstrate that the initially formed state is not the emitting state and a mechanism involving two electronic states does not explain the observations.The fluorescence of NO (0.59 Torr) excited by an argon ion laser at 488 nm is lo' R. Speed and B. Selinger Austral. J. Chem. 1969 22 9. lo* E. Kohen C. Kohen B. Thorell and J. M. Salmon Rev. Sci.Znstr. 1973,44 1784. Io9 W. G. Gelbart and K. F. Freed Chem. Phys. Letters 1973 18 470. I lo K. Sakurai and H. P. Broida J. Chem. Phys. 1969,50 2404. 'I1 S. E. Schwartz and H. S. Johnston J. Chem. Phys. 1969 51 1286. IL2 S. Braslarsky and J. Heicklen J. Photochem. 1972113 1 203. 40 R.B. Cundd and T.F. Palme-. quenched by magnetic fields up to 10 kG.' ' Fluorescence from only one state is quenched and the method shows promise for providing information on the nature of different excited states.Dye-laser excitation of NO has allowed a partial rotational analysis of the excited states ,B and 2B and two different fluorescent decay times have been The fluorescence of NO has been investigated at low pressures between 380 and 520nm. The fluorescence efficiency was independent of exciting wavelength between 415 and 520 nm but declined below 415 nm.' l5 Since the dissociation limit for formation of ground states of NO and 0 corresponds to 397.9 nm rotational energy must be used in reaching the dissociation threshold. Numerous papers on SO photochemistry have appeared and early work has been summarized by Phillips.' ' Rao and Calvert '' have re-examined Qf and CD as functions of pressure and wavelength and their results at higher energies are in serious disagreement with those of other workers.At low pressures a significant non-radiative decay of excited states occurs. Hiu and Rice"* have carried out a study of Ofand zffor 10 single vibronic states at 0.1 Torr excited in the range 230-210nm. Below 220.6nm the sharp drop in both Qf and zf indicates dissociation. At zero pressure for wavelengths of excitation greater than 220.6nm Ofis unity although zf varies. A comparison with calculations based on RRKM theory of unimolecular reactions suggests that energy randomiza- tion is incomplete before dissociation owing to very weak coupling between the bending and asymmetric stretching modes. Calvert'l9 considers that non-radiative processes are unimportant in SO singlet-state photochemistry. Brus and McDonald,'" on the basis of experiments in which a dye laser is used to excite SO fluorescence around 26&320 nm suggest that the existence of long fluorescent lifetimes and double exponential decays invalidates previous sugges- tions that unimolecular internal conversion is important in this molecule.Self quenching for SO is efficient and the rate constants are considerably higher than collision rates.12' The emitting 'SO state is not formed initially hence the deviation from Stern-Volmer quenching kinetics.'22 The triplet state of SOz has been studied by the sensitized phosphorescence of biacetyl in the presence of different added gases.'23 The presence of two triplet states other than that which emits appears to be required. Related studies in condensed media can also I l3 R.Solarz S.Butler and D. H. Levy J. Chem. Phys. 1973 58 5172. 'I4 C. G. Stevens M. W. Swagel R. Wallace and R. N. Zare Chem. Phys. Letters 1973 18 465. I I ' E. K. C. Lee and W. M. Uselman Furuduy Discuss. Chem. SOC.,1972 No. 53 125. I I ' D. Phillips in 'Photochemistry' ed. D. Bryce-Smith (Specialist Periodical Reports) The Chemical Society London 1969 Vol. 1 p. 58. I T. N. Rao and J. G. Calvert J. Phys. Chem. 1970,74 681. ILB M.-H. Hui and S. A. Rice Chem. Phys. Letters 1972 17 474. l9 J. G. Calvert Chem. Phys. Letters 1973 20 484. IZo L. E. Brus and J. R. McDonald Chem. Phys. Letters 1973 21 283. Iz1 M.-H. Hui and S. A. Rice Chem. Phys. Letters 1973 20 411. L. Stockburger tert. S. Braslarsky and J. Heiklen J. Photochem.1973/74 2 15. Iz3 A. M. Fatta E. Mathias J. Heicklen L. Stockburger tert. and S. Braslarsky J. Photochem. 1973/74 2 119. Luminescence Spectroscopy 41 be informative e.g. Zeeman effects on the phosphorescence decay of SO in matrices at 4 K.'24 Fluorescence of molecular iodine has been the subject of investigations of energy transfer effects extending over many years. Excitation by the 568.2nm line from a krypton ion laser was used to attempt assignment of the B311~u-X'Cl ~ystem.'~'A theoretical model for the deactivation of vibrationally excited I molecules has recently been proposed.'26 A tunable pulsed dye laser with a bandwidth of 0.34.7 nm and pulses < 10 ns has been used to measure fluores- cence lifetimes and quenching cross-sections for I between 640 and 499.5nm corresponding to u' values of 5-70.'27 z Values are strongly dependent on u' but self quenching is less so.128The effects of applied magnetic fields allow further details of the behaviour of the B311&,states to be determined.'29 Carbon disulphide vapour fluorescence has been measured as a function of exciting wavelength between 290 and 340nm and Aemission between 390 and 540 nm.'6*130 The effect of simple foreign gases makes it necessary to postulate a multistep cascade mechanism for vibrational deactivation.BO ,'31 Hgt,'32 A211 and B2C states of CN,13 C1,SC,'34 A211u vibronic states of N,+,'35and CO; have for example been the subjects of some fairly detailed studies. Fluorescence can be used to study the reactions of atomic species e.g.Lyman a emission from 2P states of atomic hydrogen has been used to show that H('P) reacts with 0,,N, NO N20 CO CO, and SO2 to form hydrides with near unit probability.' 37 Measurements of the efficiency of vibrational energy transfer in CH,F and CH,Cl systems'38 and excitation of N and O2 with neon and sodium ions at energies between 0.3 and 2 MeV139 are examples of other types of system where luminescence provides a convenient parameter for determination of rate data. Chemiluminescence of CO is induced by reactions of the C,O biradical.'40 J. G. Conway B. Mayer J. J. Smith and L. G. Williamson J. Chem. Phys. 1969 51 1671. K. Sakurai and H. P. Broida J. Chem. Phys. 1969,50 557. L. L. Poulsen J. Ross and J. I. Steinfeld J.Chem. Phys. 1972 57 1592. G. A. Capelle and H. P. Broida J. Chem. Phys. 1973,58 4212. G. D. Chapman and P. R.Bunker J. Chem. Phys. 1972,57,2951. G. A. Capelle and H. P. Broida J. Chem. Phys. 1972 57 5027. I3O C. Lambert and G. H. Kimbell Canad. J. Chem. 1973,51 2601. D. K. Russell M. Kroll D. A. Dows and R.A. Beaudet Chem. Phys. Letters 1973 20 153. 13' B. Chakrabati M. Z. Hoffman N. N. Lichtin and D. A. Sacks J. Chem. Phys. 1973 58 405. 133 T. J. Cook and D. A. Levy J. Chem. Phys. 1972,57 5059. 134 J. R. McDonald and L. E. Brus Chem. Phys. Lerters 1972 16 587. '35 D. D. Gray T. D. Roberts and J. L. Morack J. Chem. Phys. 1972 57 4191. 13b J. A. R. Samson and J. L. Gardner J. Chem. Phys. 1973,58,3771;L. C. Lee and D. L. Judge J. Chem.Phys. 1972 57,4443. 13' T. S. Wauchop and L. F. Phillips J. Chem. Phys. 1969 51 1167. 13' E. Weitz and G. Flynn J. Chem. Phys. 1973,58 2679; J. T. Knudtson and G. Flynn J. Chem. Phys. 1973 58 2684. 139 R. A. Langley J. Chem. Phys. 1973 58 3675. I4O W. L. Shackleford F. N. Mastrup and W. C. Kreye J. Chem. Phys. 1972 57 3933. 42 R. B. Cundall and T.F. Palmer The above examples demonstrate how luminescence spectroscopy can be used to investigate molecular dynamics. The availability of new laser sources for excitation makes it certain that activity in this area will increase over the next few years. 4 Aromatic Molecules Benzenoid Compounds.-Most luminescence studies have been made on aromatic molecules because (i) emission yields from m*states are greater than from nn* states and (ii) photochemical effects are in general less marked.A full understand- ing of both the photophysical and photochemical properties of molecules cannot be achieved by emission spectroscopy and triplet yields and chemical product formation must be determined also. A very extensive literature exists on the behaviour of excited states of benzene in all phases. Substituted benzenes have also been studied to extend knowledge of aromatic photophysics. Benzene is an exceptional molecule in that there is considerable spectroscopic information on it and its lower excited states. Attempts to relate photophysical behaviour to this detailed knowledge continue to be made. The unusually discrete nature of the vibronic levels in benzene allows pumping of selected levels with suitably tuned monochromatic light.At low pressures electronic relaxation occurs before collision. The study of single vibronic level fluorescence is one of the most interesting applications of fluorescence spectros- copy and forms the subject of a masterly review by Pa~menter.'~' A more general review of benzene photophysics has been prepared by Cundall and 0gil~ie.l~~ Parmenter and Schuyler 143 have studied the fluorescence spectra originating from individual vibronic levels of benzene excited by light sufficiently mono- chromatic to ensure excitation of single vibronic levels at low pressure. The fluorescence yields drop sharply to zero on excitation of vibronic levels >2500 cm-above the zeroth level of the B, state.The collision cross-section for energy redistribution or relaxation is large and ca. 5 times the gas-kinetic hard-sphere collision cross-section. 144 Evidently redistribution of vibrational energy is more efficient than vibrational transfer. The relationship of fluorescence spectra and efficiencies to lifetimes allows rate constants for specific processes to be assigned and fluorescence decay times at different pressures have been determined for benzene and [2H,]benzene.'45 The definitive work on the decay of well-defined vibronic levels is that of Spears and Rice.42 From their quantum yield and decay time results for assigned vibronic levels it is evident that particular combinations of vibrations critically determine the magnitude of the radiative 14' C.S. Parmenter Ado. Chem. Phys. 1972 22 365. 142 R. B. Cundall and S. McD. Ogilvie 'Organic Molecular Photophysics' ed. J. B. Birks Wiley New York,1974 Vol. 2. I*' C. S. Parmenter and M. W. Schuyler J. Chem. Phys. 1970 52 5366; J. Chim. phys. 1970 67 92; Chern. Phys. Letters 1970 6 339. 144 M. Stockburger and H. J. Kemper Ber. Bunsengesellschafr phys. Chem. 1968 72 1044; H. J. Kemper and M. Stockburger J. Chem. Phys. 1970 53 268; J. Blondeau and M. Stockburger Ber. Bunsengesellschaft phys. Chem. 1971 75 48. 14' M. Luria Israel J. Chem. 1972 10 721. Luminescence Spectroscopy and non-radiative transition probabilities and large variations are possible even for states with the same excess energy. A monotonic dependence of the non- radiative lifetime on the number of quanta in a vibrational progression and the rate of change of lifetime within one progression are quasilinear in the energy range 0--3300cm-'.The sudden increase in non-radiative decay found at 3000 cm- ' is due to a process commonly referred to as Channel 111. This is not intersystem crossing and may involve a chemical rearrangement to an isomer such as benzvalene or fulvene. A similarly comprehensive study has been made with [2H6]benzene and fluorobenzene. C6D6 behaves similarly to benzene146 but the results for C6H,F are complex and this probably represents a limit at the present stage for this type of experiment. Several detailed studies 14' of the quenching of benzene vapour fluorescence taken as a whole show that the lBZustate is quenched by four mechanisms (i) electronic energy transfer as with carbonyl compounds ; (ii) enhancement of Sl-Tl intersystem crossing as occurs in the presence of O2or species containing heavy atoms ;(iii) charge-transfer interaction as with chlorinated molecules and olefins;(iv) chemical interaction as found with olefins.Luminescence has been used to study energy transfer from single vibronic levels of benzene.14* Vibrational energy transfer from the 'BZustate of benzene occurs with increased efficiency as the vibrational energy content increases. Any variation in the efficiency of electronic energy transfer is small. Luminescence methods have been employed to study the role of the 3Blu triplet state in benzene vapour.Ishikawa and Noyes14' used the sensitized phosphorescence from small pressures of added biacetyl. Extensions of this work give in general satisfying agreement with the results of other techniques especially the isomerization of simple olefins like but-2-ene. ' Competitive studies between biacetyl and added gases allow the features of benzene triplet quenching to be determined. ' ' An electron-exchange energy transfer process seems to dominate but the 3Blustate shows an electrophilic character in its interaction with a series of olefins.' 52 No phosphorescence from benzene in the vapour phase has been observed and sensitized luminescence has been used in controversial determinations of the benzene triplet lifetime. Experiments with biacetyl give 26 ps at 20 Torr '53 and 70 ps at 2 Torr.' 54 Determinations by other techniques give equivocal results.It appears that a strong perturbation of the triplet state by ground-state 146 A. S. Abramson K. G. Spears and S. A. Rice J. Chem. Phys. 1972 56 2291. 14' D. Phillips J. Photochem. 1972173 1 97. 14* K. C. Janda J. M. Koert and F. S. Wettack J. Photochem. 1972173 1 345. H. Ishikawa and W. A. Noyes jun. J. Chem. Phys. 1962 37 583. R. B. Cundall F. J. Fletcher and D. G. Milne Trans. Furuduy Soc. 1964 60 1146. G. A. Haninger jun. and E. K. C. Lee J. Phys. Chem. 1969 73 1815. IJ2M. W. Schmidt and E. K. C. Lee J. Amer. Chem. Soc. 1970 92 3579. C. S. Parmenter and B. L. Ring J. Chem. Phys. 1967,46 1998. IS4 E. K. C. Lee H. 0. Denschlag and G. A. Haninger jun.J. Chem. Phys. 1968 48 4541. 44 R. B. Cundall and T. F. Palmer molecules is the process responsible for the short triplet lifetime at the usually encountered pressures.' s5 Early work by Lipsky' 56 showed that in the vapour phase internal conversions of higher electronic levels to S and Tl states were not efficient processes. Gregory Hirayama and Lip~ky'~~ have recently claimed to have observed S -+ So and S2-+ So emissions from p-xylene vapour (4 Torr 25 "C)following excitation at 184.9nm. Emission at A,, 195.0nm is the S +So fluorescence [Or(&) ca. The S2-+ So emission is at 243 nm (Of ca. 1.8 x lo-'). Similar observa- tions have been made with toluene and mesitylene. The S -+ So emission in benzene is obscured by the exciting band but the S -+So transition has Amax at 233 nm.Whether these emissions are due to the transitions assigned by the authors or are emissions from high vibronic levels of S1 remains to be resolved by further work. These observations are striking examples of the increased sensitivity of fluorescence techniques. Environmental effects are more marked in solution than in the gas phase and the possibility of interaction of the excited states with ground-state molecules to form excimers and exciplexes significantly affects photophysical behaviour. Fuchs Heisel and Voltz158 have directed attention to the behaviour of higher vibronic states of benzene in condensed media by using low concentrations of scintillators in benzene solution; at wavelength < 175 nm ionization occurs.Internal conversion of S and S states into S are processes of low efficiency. Another important advance has been achieved by Hirayama Gregory and Lipsky' 59 using techniques permitting measurement of fluorescence yields as low as They detected a fluorescence attributable to a radiative S2-+ So transition and obtained similar results with liquid toluene and p-xylene. Other experimental methods give information on the internal conversion of excited singlet states of benzene. Lumb Braga and Pereira16' found that yields of both fluorescence and phosphorescence decrease at wavelengths <243 nm. Extensive studies of solvent effects have been made for benzene and other compounds'61 in fluid solutions. Eastman16' has shown that the fluorescent state of benzene undergoes a thermal quenching which is not due to impurities.At 77 K the fluorescence yield is 0.2 a value consistent with that in the gas phase. Solvents induce a non-radiative transition from the S state with an efficiency which correlates with the enhancement of the 0-0(Ham) band observed in both fluorescence and absorption. 163 Lifetime measurements show that fluorescence rate constants in dilute solution and vapour phase are identical and phase effects Is5 T. F. Hunter and M. G. Stock Chem. Phys. Letters 1973 22 368. Is6 C. L. Braun S. Kato and S. Lipsky J. Chem. Phys. 1963 39 1645. Is' T. A. Gregory F. Hirayama and S. Lipsky J. Chem. Phys. 1973 58 4697. "* C. Fuchs F. Heisel and R. Voltz J. Phys. Chem. 1972 76 3867; C.Fuchs and R. Voltz Chem. Phys. Letters 1973 18 394. Is9 F. Hirayama T. A. Gregory and S. Lipsky J. Chem. Phys. 1973,58,4686. I6O M. D. Lumb C. L. Braga and L. C. Pereira Trans. Furuduy Soc. 1969 65 1992. 16' J. W. Eastman Spectrochim. Acta 1970 %A 1545. 16z J. W. Eastman J. Chem. Phys. 1968,49 4617. 163 J. W. Eastman and S. J. Rehfeld J. Phys. Chem. 1970,74 1438. Luminescence Spectroscopy 45 almost entirely influence the rate of internal conver~ion.'~~ Cundall and Pereira' 65 measured fluorescence yields and lifetimes under the same conditions for a number of aromatic hydrocarbons including benzene and the effects of temperature and environment were determined. In all aromatic hydrocarbons other than benzene the radiative lifetimes were independent of temperature.Sandros' 66 has determined the triplet yields for several benzenoid hydro- carbons and fluorobenzene in cyclohexane by sensitization of biacetyl phos- phorescence. The triplet yield of 0.25 at room temperature for C6H6 in a 2.0 x moll-'solution showed that under these conditions ca. 70 % of the 'BZustates undergo 'internal conversion or some other as yet unestablished process. The values are in excellent agreement with those determined by olefin isomerization techniques. 167 The triplet-state lifetimes are short owing to a ground-state interaction process similar to those found with other aromatic molecules.168 Values of the triplet and fluorescence yields and fluorescence lifetimes have been measured in a series of solvents by Cundall and Pereira.16' The rate constants for intersystem crossing and fluorescence except in the case of water show little solvent effect.The effects of temperature on fluorescence and intersystem crossing are slight but noticeable whereas the effect of temperature on the non-radiative process other than triplet formation is marked. Similar effects have been observed with C6D6 170 and toluene.171 Elucidation of the so-called Channel I11 in benzene and its derivatives is still awaited.172 The very large increase in rate of the non-radiative processes occurring at energies above 3000cm-' is not general behaviour for the lowest excited singlet states of all benzenoid molecules. For example Rockley and Phillips' 73 found no indication of such a decay channel in p-fluorotoluene even for vibrational energies in excess of 5000 cm-'.Interest in the phosphorescence of benzene at low temperatures is still extremely active. The role of the matrix in the deactivation of aromatic molecules at 77 K and below is not well under~tood.'~~ It is clear that the behaviour is different in single crystals and polycrystalline partially ordered and amorphous glass like the well-known EPA glass. Decay characteristics depend on factors such as rate of freezing. 75 Kilmer and Spangler' 76 find that the phosphorescent 164 T. A. Gregory and W. P. Helman J. Chem. Phys. 1972,56 377. 16' R. B. Cundall and L. C. Pereira J.C.S. Faruduy II 1972 68 1152. K. Sandros Actu Chem. Scund. 1969,23 2815; 1971,25 3651.R. B. Cundall and D. A. Robinson J.C.S. Furuday ZZ 1972,68 1145. 16* J. Langelaar G. Jansen R. P. H. Tettschnick and G. Hoytink Chem. Phys. Letters 1971 12 86. 169 R. B. Cundall and L. C. Pereira Chem. Phys. Letters 1973 18 371. I7O R. B. Cundall S. McD. Ogilvie and R. B. Cundall J. Photochem. 1972/73 1 417. R. B. Cundall L. C. Pereira and D. A. Robinson J.C.S. Furuday IZ 1973 69 701. J. H. Callomon J. E. Parkin and R. Lopez-Delgado Chem. Phys. Letters 1972 13 125. 173 M. G. Rockley and D. Phillips Chem. Phys. Letters 1973 21 181. B. C. Nieman J. Chem. Phys. 1969 50 1660. 175 T. E. Martin and A. H. Kalantar J. Chem. Phys. 1969 50 1486. N. G. Kilmer and J. D. Spangler J. Chem. Phys. 1971 54 604. R. B. Cundall and T.F. Palmer lifetime depends on temperature in the range 6-160 K 7;' = k + k exp(-E/kT) The convenient temperature of 77 K is not sufficiently low for the temperature dependent processes to be fully suppressed.The triplet state of benzene has lower symmetry than that of a regular hexagon in solid matrices.' 77 Phosphores-cence microwave double resonance (PMDR) spectroscopy3 7770*1 78 allows some of the finer details of triplet-state structure population and decay mechanism to be probed. The recent investigation of phosphorescence lifetimes of C6H, and its methyl and deuterio-derivatives suggests a common mechanism for both the effects of solvents and methyl group substitution.' 79 Much work has been done on the photophysics of benzene derivatives in the vapour phase using techniques similar to those mentioned for benzene.This has been comprehensively reviewed by Phi1li~s.l~~ Some more recent work deals with fluorinated benzene derivatives,' 80~1 ' aniline,"* and phenylcyclobutane. '83 Measurements of quantum yields and lifetimes of methyl-substituted benzenes have permitted a theoretical analysis of factors affecting radiative and non-radiative processes.' 84 Correlation of these results with perturbations of molec- ular symmetry caused by substituents which allow intensity borrowing from the allowed 'Elu-'Alg transition has been attem~ted.'~' This treatment neglects the effect of molecular vibrations. In benzenoid derivatives with nitrogen and oxygen substituents more complex luminescence effects are observed.The absorption and luminescence of NN-dimethyl-p-cyanoaniline in different solvents shows several anomalies. Three different fluorescence and two different phosphorescence emissions are found for this molecule. lE6 Other studies have been made on nitroanilines and N-methyl derivatives.' effects in fluorescence quenching have been examined. '88*189 Acid-base catalysis The fluorescence of biphenyl is affected by configurational effects. '90 The broad structureless band at about 250 nm is made up of three transitions a weak transition similar to the 'A-'Lb transition in benzene and two stronger transitions. These have been separated by comparison with rigid analogues such as 9,lO-S. H. Lin Trans. Faraday SOC.,1970 66,1879. J. Schmidt D. A. Antheunis and J.H. van der Waals. Mol. Phys. 1971 22. 1. 17' D. M. Haaland and G. C. Nieman. J. Chem. Phys. 1973,59 1013. K. E. Al-Ani J. Chem. Phys. 1973 59 331 341. M. G. Rockley and D. Phillips Chem. Phys. Letters 1973 20 181. H. von Weyssenhoff and F. Kraus J. Chem. Phys. 1971,54 2387. S. Y.Ho R. A. Gorse and W. A. Noyes jun. J. Phys. Chem. 1973 77 2609. P. M. Froelich and H. A. Morrison J. Phys. Chem. 1972 76 3566. A. Reiser and L. Leyshon J. Chem. Phys. 1972,56 101 1. 0. S. Khalil R. H. Hofeld and S. P. McGlynn Chem. Phys. Letters 1972 17 479. 0. S. Khalil C. J. Seliskar and S. P. McGlynn J. Chem. Phys. 1973 58 1607. I. Avigail G. Feitelson and M. Ottolenghi J. Chem. Phys. 1969 50 2614. G. F. Vesley and B. D. Olafson J. Phys. Chem. 1973,77 1345.Ig0 I. B. Berlman J. Chem. Phys. 1970 52 5616. Luminescence Spectroscopy 47 dihydrophenanthrene and fluorene. The decay times and quantum yields are anomalous owing to crossover to a hidden state.'" The technique of two-photon fluoresoence excitation has wide applicability and potential. Work with a biphenyl crystal at 2 K is the first report of a con- tinuously recorded two-photon absorption spectrum at high resolution. 92 The formation of a triplet excimer of 1,3-diphenylpropane has been observed by its phosphorescence during the softening of a degassed isopentane glass matrix.'93 This is consistent with the earlier suggestions on the role of triplet excimers in shortening the lifetime of aromatic hydrocarbon triplets insolution.' Stilbene and its derivatives provide a vigorous area of photochemical research activity.Normally non-fluorescent cis-stilbene and sterically hindered trans- stilbenes become strongly fluorescent only in very viscous media.'94 The lowest energy gap S,-So is for the perpendicular configuration and a radiationless transition is most probable for this geometry. At high viscosity a potential barrier of varying height affects the rotation required for non-radiative transitions. Similar configurational effects are apparent in the variations of lifetime with exciting wavelength in tetraphenylethylene.' 95 In the case of the aminaphthali- mides single-photon counting has been used to obtain time-resolved fluorescence spectra. 19' Relaxation of solvent explains the time and temperature dependences observed.Polarization studies in ordered liquid crystal media have been made on all-trans- 1,6diphenylhexa- 1,3,5-triene another molecule which exhibits anomalous fluorescence.' 97 Two very interesting examples of fluorescence are (i) a lifetime of 10011s for the triplet-triplet fluorescence of diphenylmethylene' 98 and (ii) a time-resolved fluorescence of some methyl-substituted benzyl triphenylmethyl and diphenyl- methyl radicals trapped in rigid solvents at low temperature ;I9' the fluorescence lifetimes are very long varying from 160 to 530 ns in ethanol. Naphthalenic Compoumls.-The fluorescence and fluorescence decay of naph- thalene vapour have been examined by a number of workers.z00-203 Fluores- cence lifetimes of single vibronic levels204 and the effect of deuteriation on the fluorescence of the excited singlet state2'' have also been reported.Observations of the first excited singlet states of naphthalene and anthracene have been 19' E. C. Lim and Y. H. Li J. Chem. fhys.. 1972 57 5016. I" R. M. Hochstrasser H. N. Sung and J. E. Wessel. J. Chem. fhys. 1973.58 4694. IP3 P.Avouris and M. A. El Bayoumi Chem. fhys. Letters 1973.20. 59. 194 S.Sharafy and K. A. Muszkat J. Amer. Chem. SOC.,1971.93.41 19. 19' H. H.Klingenberg E. Lippert and W. Rapp Chem. fhys. Lerters 1973,18 417. 19' W. R. Ware S. K. Lee G. J. Brant and P. T. Chow J. Chem. Phys. 1971,54 4729. 19' E. D.Cehelnik. R. B. Cundall C. J. Timmons and R. M. Bowley froc. Roy. SOC. 1973 A335 287.19' W. R. Ware and P. J. Sullivan J. Chem. Phys. 1968.49 1145. 199 T. Okamura K. Obi and I. Tanaka Chem. Phys. Letters 1973,20 90. zoo J. 0.Uy and E. C. Lim Chem. Phys. Letters 1970.7 306. J. M. Blondeau and M. Stockburger Chem. fhys. Letters 1971,8 436. 'O2 U. Laor and P. K. Ludwig J. Chem. fhys. 1971.54 1054. '03 P.Wannier P. M. Rentzepis and J. Jortner Chem. Phys. Letters 1971,10 193. '04 E. W. Schlag S. Schneider and D. W. Chandler Chem. fhys. Letters 1971,11 474. 'O' E.C. Lim and J. 0.Uy J. Chem. fhys. 1972,56 3374. R. B. Cundalland T. F. Palmer recorded by a two-quantum absorption process following excitation of the vapour with a giant pulse ruby laser.206 Intersystem crossing rate constants in naphthalene (Tl +So)can be accounted for assuming that Herzberg-Teller vibronic couplings are ~perative.~" Examina- tion of the variations as a function of excitation energy of the radiationless decay rate of naphthalene and naphthylamine and the fluorescence/phosphorescence ratio in quinoxaline have been made.208 It has been suggested that a model for intersystem crossing should be based on compound states in which the initial optically excited vibronic state has isoenergetic vibrational levels of the lowest excited singlet state superimposed.The variations in the radiationless decay rate can be accounted for in terms of mixing between the zeroth-order states. Internal conversion to the ground state is an important process in aromatic molecules also and the variation in the fluorescence quantum yield of naphthalene2'' as a function of excitation energy has been discussed.The S2spectrum of naphthalene210 has been observed using a laser pulse and CW excitation. S3+So fluorescence has been detected in benzene alkyl benzenes naphthalene and pyrene using techniques capable of detecting fluorescence yields as low as 10-6.159 The fluorescence lifetime of naphthalene in various solvents at room temperature has been reported211 and it is apparent that in poly(methy1 methacrylate) the lifetime increases with decreasing tem- perature. The fluorescence and phosphorescence yields and phosphorescence lifetimes of deuteriated naphthalenes in EPA at 77 K have been obtained.212 Examination of the effect of excitation wavelength on the quenching of fluores- cence of aromatic hydrocarbons by carbon tetrachloride213 indicates that the formation of ground-state complexes between the hydrocarbon and carbon tetrachloride is responsible for the variation of quenching efficiency with wave- length.A highly resolved phosphorescence spectrum of naphthalene2I4 in the region 16 880 to 21 224 cm-' has been recorded. The mechanism of non-radiative decay of the triplet states of naphthalene phenanthrene and diphenyl has been studied and the rate constant for intersystem crossing was shown to be of the form2 15.2 16 ~,SC= k& + k;,,exp (-AE/kT) '06 T. S. Jaseja V. Parkash and M. K. Dheer J. Appl. Phys. 1969,40 1882. '07 F. Metz S. Friedrich and G. Hohlneicher Chem. Phys. Letters 1972 16 353.'08 E. C. Lim and C.4. Huang J. Chem. Phys. 1973,58 1247. '09 G. S. Beddard G. R. Fleming 0.L. J. Gizeman and G. Porter Chem. Phys. Letters 1973 18 481. 'lo T. Deinum C. J. Werkhoven J. Langelaar R. P. H. Rettschnick and J. D. W. van Voorst Chem. Phys. Letters 1973 19 29. 'I1 P. F. Jones and A. R. Calloway J. Chim. phys. 1970,67 110. "'G. Heinrich D. Donnert and H. Giesten J. Photochem. 1973174 2 75. 'I3 W. R. Ware and C. Lewis J. Chem. Phys. 1972 57 3546. 'I4 D. M. Hanson J. Chem. Phys. 1969 51 5063. 'I5 P. F. Jones and S. Siegal Chem. Phys. Letters 1968 2 486. 'I6 P. F. Jones and S. Siegal J. Chem. Phys. 1969 50 1 134. Luminescence Spectroscopy The phosphorescence lifetimes of naphthalene and [2H8]naphthalene2 ' are reduced in fluid solution by oxygen quenching and triplet-triplet annihilation.The quenching of deuteriated and undeuteriated naphthalene luminescence by oxygen and nitric oxide has been investigated also in the absence of molecular diffusion.218 Measurement of the phosphorescence yields and lifetimes of phenanthrene pyrene and naphthalene' l9 in fluid solutions has shown that the calculated radiative lifetimes vary little with temperature. Weak phosphores- cenceZZ0 from naphthalene and pyrene has been observed in the gas phase with spectral distributions identical with those observed in the solid phase. Investiga- tion of the effect of deuteriationZZ1 on the phosphorescence lifetime of naphthalene has shown that the presence of protons in the molecule enhances the rate of decay to the ground state.The phosphorescence decay of ['H,]naphthalene was found to be non-exponentialZZ2 in a polystyrene matrix and it has been suggested that conformations of the solute triplet state normally effective in non-radiative decay are constrained in a rigid solvent cage. Temperature effects on the phosphores- cence of naphthalene and other aromatic molecules in poly(methy1 methacrylate) matrixtZ3 suggest that only the non-radiative decay is temperature dependent. The quenching of phosphorescence of polynuclear aromatic hydrocarbons in a loose polystyrene matrix224 has also been reported. The effect of deuteriation on the sensitized phosphorescence of naphthalene phenanthrene and biphenyl in a heavy-atom solvent has been in~estigated.~~' External atom perturbation of the phosphorescence of [2H8]naphthalene by an alkali halide has been explained by complex formation with the halogen.226 The fluorescence of naphthalene-biphenyl mixed crystals227 and pyrene-doped naphthalene crystalsZ2' has been investigated.Several examples of radiation-induced fl~orescence~~~,~~~ of naphthalene and other polycyclic aromatic hydrocarbons have been reported. The fluorescence and phosphorescence yields and fluorescence lifetimes have been measured for a number of alkyl-substituted naphthalene^.^^ ' Since af+ 0,x 1 it was concluded that intersystem crossing is the main non-radiative process. An investigation of the effect of phenyl substitution on the luminescence 217 S. C. Tsai and G.W. Robinson J. Chem. Phys. 1968,49 3184. 218 P. F. Jones and S. Siegal J. Chem. Phys. 1971 54 3360. 219 J. Langelaar R. P. H. Rettschnick and G. J. Hoytink J. Chem. Phys. 1971 54 1. 220 W. H. van Leewen J. Langelaar and J. D. van Voorst Chem. Phys. Letters 1972 13 662. 221 T. D. Gierke R. J. Watts and S. J. Strickler J. Chem. Phys. 1969 50 5425. 222 P. F. Jones and A. R. Calloway J. Chem. Phys. 1969,51 1661. 223 P. F. Jones and S. Siegal J. Chem. Phys. 1969 50 11 34. 2*4 N. E. Geacintov R. Benson and S. B. Pomeranz Chem. Phys. Letters 1972 17 280. 22s S. E. Webber Chem. Phys. Letters 1970 5 466. 226 R. H. Hofeldt R. Sahai and S. H. Lin J. Chem. Phys. 1970,53 4512. 22' T. N. Misra J. Chem. Phys. 1973 58 1235. 228 R. C. Powell J. Chem. Phys.1973 58 920. 229 E. L. Frankevich T. Morrow and G. A. Salmon Proc. Roy. SOC.,1972 A328 445. 230 F. S. Dainton T. Morrow G. A. Salmon and G. F. Thompson Proc. Roy. Suc. 1972 ~328,457,48 1,497 23' A. Reiser and T. R. Wright J. Chem. Phys. 1973,59 3433. 50 R. B. Cuna'ull and T.F. Palmer of naphthalene derivatives232 revealed considerable variations primarily due to interactions between rings. The variations in the fluorescence spectra of 2-phenyl- naphthalene and have been discussed in terms of the photoselection of conformers. Similarly triplet-state configurational changes in rigid glasses are believed to be responsible for the two distinct spectra observed in the phos- phorescence of 1-benzoyl-8-benzylnaphthalene. 34 The fluorescence of P-naphthylamine vapour has been investigated in the low-pressure region (0.5-1.0 Torr) by a phase-shift technique using a modulated light source.235 The results extending over two electronic transitions (250-300 nm) involved direct timing of the relaxation from selected vibronic states and a low-energy state radiative lifdime of 14.7 ns was reported.Mechanisms for the molecular-cationic turnover of P-naphthylamine fluorescence in sulphuric acid-water mixtures and the effect of deuteriation in the turnover region have been discussed.236 The quenching of the fluorescence of a-and B-naphth01~~' by aromatic hydrocarbons in heptane has been discussed in terms of n-H bond formation between the OH group and aromatic molecule. A similar process has been proposed for the fluorescence quenching of aromatic hydrocarbons by alcohols.Measurement of fluorescence decay has been used to investigate the acid dissocia- tion of singlet excited /?-naphthol.238 The fluorescence spectra of substituted naphthalene sulphonates have been shown to be strongly solvent dependent.239 Time-dependent spectral shifts in the fluorescence of 1-anilino-8-naphthalene ~ulphonate~~' have been interpreted in terms of a dipole orientation of the solvent around the electronically excited molecule and it has been suggested that the excited state has higher polarity than the ground state. Fluorescence from ~innoline~~' and phosphorescence from a naphthalene sandwich pair242 have been reported. Anthracene.-The rate constants for oxygen quenching of the triplet states of anthracene and several other polycyclic aromatic hydrocarbons243 have been investigated in detail from triplet-triplet absorption spectra following laser excitation.The decay of triplet-triplet absorption has been used to measure the phosphorescence lifetimes of deuteriated anthracenes in glassy solution at 77 K.244 The temperature dependence of intersystem crossing for anthracene 232 J. B. Gallivan J. Phys. Chem. 1969 73 3070. 233 E. Hughes jun. J. H. Wharton and R. V. Nauman J. Phys. Chem. 1971,75 3097. 234 W. G. Herkstroeter Chem. Phys. Letters 1973 21 256 263. 235 E. W. Schlag and H. V. Weyssenhoff J. Chem. Phys. 1969 51 2508. 236 Th. Forster Chem. Phys. Letters 1972 17 309. 237 B. Ghosh and S. Basu J.Chim.phys. 1968 65 676 1587. 238 M. Ofran and J. Feitelson Chem. Phys. Letters 1973 19 427. 239 E. M. Kosower and K. Tanizawa Chem. Phys. Letters 1972 16,419. 240 S. K. Chakrabarti and W. R. Ware J. Chem. Phys. 1971 55 5494. 241 J. A. Stikeleather Chem. Phys. Letters 1973 21 326. 242 E. A. Chandross and C. G. Dempster J. Amer. Chem. SOC.,1970 92 704. 243 0. L. J. Gizemann F. Kaufman and G. Porter J.C.S. Furuduy II 1973,69 708 721 727. 244 B. R. Henry and J. L. Charlton J. Amer. Chem. SOC.,1973 95 2783. Luminescence Spectroscopy 51 has been investigated in methyltetrahydrof~ran.~~~ It is suggested that above 170 K S1 +T intersystem crossing occurs. The fluorescence quantum yield of anthracene has been shown to be independent of viscosity but dependent on temperature with an intersystem crossing rate constant of the form’46 given earlier for naphthalene phenanthrene and biphenyl.’ s*21 Laser photolysis has been used to detect delayed triplet production arising from electron-transfer fluorescence quenching in anthracene pyrene and other in acetonitrile.A theory has been developed to make model calculations for absorption and emission by a disk of crystalline anthracene in the frequency range of the first electronic band system248 and the fluorescence spectra of anthracene crystals have been recorded.249 Enhancement of fluorescence for ant hracene dibenzanthracene and chrysene has been observed in polymer matrices in the presence of molecular oxygen and a tentative mechanism has been s~ggested.~ Dimethylmercury has been used to enhance spin-orbit coupling in fluid media at room temperature and the effect on the T +So transition has been observed in some substituted anthra~enes.~~ Fluorescence quenching of 1,2-benzanthracene by dimethylmercury has shown that in benzene and toluene the emission spectrum is modified by superposition of a 1,2-benzanthracene-dirnethylmercuryex~iplex.~’~ Measurement of the kinetics and quantum yield of the delayed fluorescence of 1,2-benzanthracene over a large temperature range in ethanol has shown that triplet-triplet annihila- tion is an important process.253 The solvent and pH dependence of the fluorescence of 9-anthroic has been explained on the basis of an acid-base equilibrium and excimer formation is thought not to occur.The absorption and fluorescence spectra of 1- and 2-anthroic acids and anions255 have been investigated. It has been concluded that the fluorescence of 2-anthroic acid originates from the ‘L state in polar solvents and from the ‘Lastate in non-polar solvents. This conclusion is sup- ported by lifetime measurements. The absorption and fluorescence spectra of 1-and 2-anthroic acidszs6 have been measured as a function of pH. It is suggested that a failure to achieve equilibrium is due to the magnitudes of the relevant rate constants. The solvent dependence of 9-methyl anthroate fluore~cence’~~ has been explained in terms of a change in the geometry of the 245 T. F. Hunter and R. F. Wyatt Chem. Phys. Letters 1970 6 221.246 E. R. Pantke and H. Labbart Chem. Phys. Letters 1972 16 255. 247 H. Schomburg H. Staerk and A. Weller Chem. Phys. Letters 1973 21 433. 248 D. P. Craig and L. A. Dissado Proc. Roy. Suc. 1972 A332,419. Z49 E. Glockner and H. C. Wolf Z. Nufurforsch. 1969 Ma 943. 250 P. H. Bolton. R. D. Kerner and A. U. Khan J. Chem. Phys. 1972,57 5604. 25‘ E. V. Donckt M. Matagne and M. Sapir Chern. Phys. Letters 1973 20 81. 252 E. V. Donckt D. Lietar and M. Matagne J.C.S. Furuduy 11 1973 69 322. 253 D. Wyrsch and H. Labhart Chern. Phys. Letters 1971 12 373. 254 T. C. Werner and D. M. Hercules J. Phys. Chem. 1969 73 2005. ’” T. C. Werner and D. M. Hercules J. Phys. Chem. 1970,74 1030. 256 S. G. Schulman A. C. Capomacchia W. L. Paul P. J. Kovi and J.F. Young Z. phys. Chem. 1973,87 308. ”’ T. C. Werner and R. M. Hoffman J. Phys. Chem. 1973 77. 161 1. 52 K.B. Cundall and T.F. Palmer excited state. Fluorescence yields and lifetimes show that quenching by protic solvents is due primarily to an increase in the rate of radiationless decay. The fluorescence decay of phenanthrene vapour2'* has been measured at 0.03 Torr in the collision-free region at varying excitation wavelengths by single- photon counting. The fluorescence lifetimes decreased with increasing excita- tion energy and a deuterium effect was observed. Pyrene.-Fluorescence and triplet quantum yields and fluorescence decay times have been measured for [2H lo]pyrene259 as functions of temperature. Conclu- sions concerning the radiative and radiationless processes are that the radiative rate constant is independent of temperature from -196 to 23°C and that deuteriation has no effect.Intersystem crossing is important at -196"C. At 23 "C both internal conversion and intersystem crossing are significant. The radiative lifetime of the triplet state is between 40 and 55 s. Fluorescence decay from pyrene vapour260 has been shown to have a short-lived component which has been ascribed to emission from a specific vibronic state of S,. Fast intra- molecular vibrational redistribution is thought to produce the manifold of states giving rise to the faster decay. There have been several reports of S -+So fluorescence originating from the second singlet state of pyrene261 and 3,4-ben~pyrene.~~~ Fluorescence emission from both S and S2 states of 3,4-benzpyrene and 1,12-benzperylene has been investigated263 in the temperature range -90 to + 90 "C.The strong temperature dependence of fluorescence from the S state was shown to result from repopula- tion of S suggesting that internal conversion can be reversible in these systems. A theoretical treatment of radiative decay of an excited state of an isolated large molecule has been discussed and investigation of the energy- and time-resolved spectrum of 3,4-benzpyrene vapour in the collision-free region excited by the second harmonic of a ruby laser has revealed the presence of both S -+ So and S -+ So emission.264 The fluorescence lifetime and quantum yield of pyrene and [2H10]pyrene in poly(methy1 methacrylate) have been shown to vary with temperature apd it was concluded that the chemical environment affects the emission properties of pyrene.65 The fluorescence lifetimes of both pyrene monomer and excimer in polymer matrices are affected by pressure.266 The magnitude of the pressure effect does not depend upon concentration deuteriation or presence of oxygen. The pres- lJ8 A. E. W. Knight and B. K. Selinger Austral. J. Chem. 1973 26 499. 259 J. L. Kropp W. R. Dawson and M. W. Windsor J. Phys. Chem. 1969,73 1747. z60 C. J. Werkhoven T. Deinum J. Langelaar R. P. H. Rettschnick and J. D. W. van Voorst Chem. Phys. Letters 1971 11 478; 1973 18 171. 26* H. Baba A. Nakajima M. Aoi and K. Chihara J. Chem. Phys. 1971,55,2433. 262 P.A. Geldof. R. P. H. Rettschnick and G. J. Hoytink Chem. Phys. Lerters 1969 4 59. 263 C. E. Easterly L. G. Christophorou and J. G. Carter J.C.S. Furuduy If 1973,69,471. 264 A. Nitzan J. Jortner and P. M. Renzepis Proc. Roy. SOC., 1972 A321 367. 265 P. F. Jones and S. Siegal Chem. Phys. Letters 1968 2 486. 266 J. J. Kim R. A. Beardslie D. J. Phillips and H. W. Offen J. Chem. Phys. 1969 51 2761. Luminescence Spectroscopy 53 sure dependence of energy transfer from pyrene to perylene has been studied.267 The effects of temperature concentration and pressure on the fluorescence of pyrene in ethanol and cyclohexane have been investigated.268 Compression in ethanol shifts the monomer+xcimer equilibrium towards monomer whereas compression in cyclohexane leads to aggregation and the observation of excimer fluorescence over a large concentration range.The fluorescence and phosphorescence parameters of pyrene 3-chloropyrene and 3-br0mopyrene~~’ have been compared over a range of temperature. The heavy-atom effect is apparent on the parameters which involve a change in multiplicity. Evidence for two intersystem crossing processes in 3-chloropyrene was deduced from the fluorescence lifetime data. The fluorescence decay of pyrene in a liquid crystal system has been investi- gated.270 Other reports of interest are the phosphorescence spectrum of crystal- line ~yrene~~l and the observation of delayed fluorescence from [3Hlo]pyrene doped with fl~orene.~~~ Perylene andRelated Systems.-An orange excimer fluorescence has been observed when pressure is applied to frozen solutions of perylene in cyclo- he~ane.~’~ For the time dependence of the excimer fluorescence decay a radiative lifetime of 80 ns and an activation energy of 670 cm- have been determined.The effect of temperature on the fluorescence and triplet yields and fluorescence life- times of 1,12-benzperylene shows that the fluorescence is Since mf increases and T~ decreases from -196 to 23 “C the radiative rate constant increases with temperature. A temperature-dependent emission from the second excited state of 1,12-benzperylene is believed to be operative. The fluorescence quantum yield is strongly affected by solvent. Fluorescence from ~valene~~~ has been studied as a function of pressure (0-30 kbar) in condensed media at room temperature and 77 K.A red shift was observed in the c1-and p-band in a poly(methy1 methacrylate) matrix and the fluorescence has been shown to be consistent with a two-level emission mechan- ism. Measurements of fluorescence and intersystem crossing for tetracene2 77 in solution have shown that internal conversion from S is an important process. Absorption and emission spectra of deca~yclene~~~ have been reported and it 267 P. C. Johnson and H. W. Offen J. Chem. Phys. 1972,57 1473. 268 P. C. Johnson and H. W. Offen J. Chem. Phys. 1973,59 801. 269 I. Barradas J. A. Ferreira and M. F. Thomaz J.C.S. Faraday ZZ 1973,69 389. 270 Y. Tomkiewicz and A. Weinreb Chem. Phys. Letters 1969 3 229. 271 L.Peter and G. Vaubel Chem. Phys. Letters 1973 21 159. 272 0. Piekcan T. M. Kite A. B. Denison and L. J. No Chern. Phys. Letters 1973 21 161. 273 P. C. Johnson and H. W. Offen Chem. Phys. Letters 1973 18 258. 274 W. R. Dawson and J. L. Kropp J. Phys. Chem. 1969,73 1752. 27s A. Nakajima Chem. Phys. Letters 1973 21 200. 276 P. C. Johnson and H. W. Offen J. Chem. Phys. 1972,57 336. 277 A. Kearvell and F. Wilkinson Chem. Phys. Letters 1971 11 472. 278 C. J. M. Brugman P. J. van Scheerpenzeel R. P. H. Rettschnick and G. J. Hoytink, J. Chem. Phys. 1973,58 3468. 54 R. B. Cundall and T.F. Palmer has been showri that the So-+ S transition is symmetry forbidden. The fluorescence of r~brene’’~ has been investigated and there is some dispute on the effect of temperature on the phosphorescence lifetime of coronene.280 Amlenc.-The laser fluorescence of azulene has been investigated.2819z8z The S2-P S emission spectra of azulene and [2H8]azulene282 have been ob- served by following excitation with the second harmonic of a ruby laser.The fluorescence quantum yield (@sz-,sI)was estimated to be 2 x Excitation at 694.3 nm resulted in an emission in the region 360-450 nm which depended upon the square of the laser intensity and it was concluded that two-photon absorption (So4S 3 S,) occurred. A consistent set of photophysical parameters for azulene has been reported by Birk~.~~~ Quenching of delayed fluorescence in 3,4-benzpyrene and perylene by azulene derivativeszE4 has been used to show that the lowest triplet states of azulene and its derivatives lie only slightly below the lowest excited singlet states.Measurement of the polarized absorption fluorescence and phosphorescence spectra of 1,3-diazoa~ulene~~~ has been reported and discussed. 5 carbonylcompounds Systems containing the carbonyl chromophore continue to attract the attention of many workers. Extensive studies have been carried out on the photochemistry of hexafluoroacetone,’ “-’88 and a revised mechanism for acetone photolysis’ 89 correlates phosphorescence and primary dissociation processes. Rate constants for the quenching of the triplet state of acetone have been reported from absorp- tion and emission studies.290 Quenching of the triplet state of acetone by halogenobenzenes has been investigated using a flash emission te~hnique.’~ It was suggested that quenching occurred by enhanced coupling of the triplet ketone and quencher through a charge-transfer state.Wettack has shown that the fluorescence quantum yield for pentan-2-one decreases with increasing excitation energy in the region 3 13-265.4 nm and is accompanied by an increase in the Norrish Type I1 pro~ess.’~’ Although it was reported that buta-1,3-diene did not quench the fluorescence of pentan-2-one it has since been shown that 279 A. Yildiz P. I. Kissinger and C. N. Reilley J. Chem. Phys. 1968 49 1403. W. R. Dawson and J. L. Kropp J. Phys. Chem. 1969 73 693. ”* D. Huppert J. Jortner and P. M. Rentzepis J. Chem. Phys. 1972 56 4826. ”’ D. Huppert J. Jortner and P. M. Rentzepis Chem.Phys. Letters 1972 13 225. 283 J. B. Birks in ref. 88. 284 P. Kronig 2.phys. Chem. 1973 86 IS. 285 F. P. Burke G. J. Small J. R. Brown andT.-S. Lin Chem. Phys. Letters 1973,19,574. 286 D. A. Whytock and K. 0.Kutschke Proc. Roy. Soc. 1968 Am 503. 287 A. Gandini and K. 0.Kutschke Proc. Roy. SOC.,1968 AM 51 I. z88 A. Gandini D. A. Whytock and K. 0. Kutschke Proc. Roy. SOC.,1968 Am 529 537 541. 289 H. E. O’Neal and C. W. Larson J. Phys. Chem. 1969,73 101 1 ;cf. R. B. Cundall and A. S.Davies. Proc. Roy. SOC.,1966 A290. 563. 290 G. Porter S. K. Dogra R. 0.Loutfy S. E. Sugamari and R. W. Yip J.C.S. Furuduy I 1973,69 1462. 291 R. 0.Loutfy and R. W. Yip Cunud. J. Chem. 1973,51 1881. 292 F. S. Wettack J. Phys. Chem. 1969 73 1 167. Luminescence Spectroscopy 55 penta-l,3diene efficiently quenches the excited singlet states of a number of ketones.293 Dienes must be used cautiously as quenchers of the triplet state.Fluorescence quantum yields and decay times of a number of halogenated ketones in the thermally equilibrated region have been studied in detai1'94*295and it is suggested that state mixing of the n4 transition may be responsible for the variation in the non-radiative rate constants. The fluorescence decay of hexa- fluoroacetone has been examined over a wide pressure range from the thermally equilibrated to the collision-free region.296 Lifetimes were found to be expo-nential in the high- and 1ow.pressure regions but non-exponential in the interrne- diate region. Using fluorescence quantum yields obtained by Kutschke et daa8 the radiative and non-radiative rate constants for singlet excited hexafluoro- acetone have been calculated.Fluorescence excitation emission spectra and quantum yields have been reported for a number of cycl~alkanes.~~~-~~~ For excitation near 3 10 dm Qf is low in all cases (ca. 10-3)303and predissociation is evident in cyclobutanone above 3 kcal mol-' vibrational excitation in the first excited singlet (fin*) state.301 The a C-H stretching mode is believed to be involved in radiationless dea~tivation.~'~ A low-efficiency exciplex mechanism has been suggested for the Stern-Volmer quenching of fluorescence by carbon tetrachloride in a variety of ketones,305 and energy transfer from the triplet states of acetone and biacetyl to deuteriated and undeuteriated olefinic hydrocarbons has been reported.306 Fluorescerfce from the 'A state of formaldehyde has been investigated using the pulsed laser technique over a pressure range of 0.05-10 T~rr.~~~-~~~ Although the fluorescence decay appears to be pressure independent at 337.1 nm for both formaldehyde and [2H]formaldehyde vapo~rs,~~~ other workJo7 has shown that the decay rates increase rapidly with increasing vibrational energy between 308.2 and 353.5nm.The effect of deuteriation is marked and it is suggested that radiationless decay of the excited state occurs via internal conver- sion into high vibrational levels of the ground state.More work on the photo- 293 F. s. Wettack C. D. Renkes M. G.Rockley N. J. Turro and J. C. Dalton J. Amer. Chem. SOC.,1970,92 1743. 294 P. A. Hackett and D. Phillips J.C.S. Faraduy I 1972 68 323 329 335. 295 P. A. Hackett and D. Phillips J. Photochem. 1973/74 2 325. 296 A. M. Halpern and W. R. Ware J. Chem. Phys. 1970,53 1969. 297 A. T. Blades Canad. J. Chem. 1970,48 2269. '" H. M. Frey and I. C. Vinall J. Chem. SOC.(A) 1970 3010. 299 R. G. Shortridge jun. and E. K. C. Lee J. Amer. Chem. Soc. 1970 92 2228. 300 J. C. Hemminger C. F. Rusbult and E. K. C. Lee J. Amer. Chem. SOC.,1971,93 1867. J. C. Hemminger and E. K. C. Lee J. Chem. Phys. 1971 54 1405. 302 T. F. Thomas and H. J. Rodriguez J. Amer. Chem. SOC.,1972,94 5918. 303 R. C. Shortridge jun. C. F. Rusbult and E. K. C. Lee J. Amer. Chem. SOC.,1971,93 1863.304 M. O'Sullivan and A. C. Testa J. Phys. Chem. 1973 77 1830. 305 J. 0. Paulik P. I. Plooard A. C. Somersall and J. E. Guillet Canad. J. Chem. 1973 51 1435. 306 M. W. Schmidt and E. K. C. Lee J. Amer. Chem. Soc. 1970 92 3579 307 E. S. Yeung and C. B. Moore J. Chem. Phys. 1973,58 3988. 308 T. Aoki T. Morekawa and K. Sakurai J. Chem. Phys. 1973 59 1543. 56 R. B. Cundall and T.F. Palmer chemistry of single vibronic levels in formaldehyde would be timely and further information is expected to become available in the near future. The fluorescence and induced phosphorescence of formaldehyde at low temperature have also been in~estigated.~” Detailed studies on the photoluminescence of acetalde- hyde ~apour~’~ have shown that pressure causes an enhancement of fluorescence but the fluorescence quantum yields decrease with increase in the energy of the exciting light.Complementary studies on the triplet-state yield using the olefin isomerization technique3 ’ confirm that at longer excitation wavelengths the major fate of thermally equilibrated singlet excited acetaldehyde molecules is intersystem crossing to the triplet state. Below 313 nm the importance of the initially formed short-lived state increases leading to a decrease in Ofand a corresponding increase in the molecular dissociation process. The lack of a temperature effect on the excited states of acetaldehyde is surprising. It is appa- rent from this and other studies that the often used relationship 7, = q/Of may not be valid for systems in which the fluorescent state is not the state formed in the initial absorption process.A pulsed dye laser has been used to excite propynal vapour at 382.1 nm and the time-resolved luminescence from A” states examined.312 The collision-free lifetime for the ground vibrational level of the ‘A” state was found to be 0.98~~. Quenching cross-sections for 19 different collision partners were measured also. An important study of excited-state relaxation processes in glyoxa13’ has demonstrated the resonant or small-molecule limit of a non-radiative transition. Intersystem crossing from the excited singlet ‘A state to the triplet state (presum- ably 3A,) has been shown to be collisionally induced and glyoxal provides an example of a molecule containing more than three atoms where the resonant effect predicted by theory is clearly displayed.The results also show that inter- system crossing from the triplet to ground states is intramolecular in agreement with theories predicting that the T,-+ So transition is within the statistical limit. A tunable dye laser has been used to excite the 0-0transition of cis-glyoxal near 487.5nm at pressures of 30-150 x 10-3Torr.314 Lifetimes of the resolved fluorescence emission were reported and a zero-pressure lifetime of 0.96 ps was recorded. The triplet (3A,)lifetime of glyoxal has been determined from phos- phorescence decay measurement^.^' A collision-free lifetime of 3.29 ms is reported together with quenching rates and cross-sections for a variety of added gases.The lifetimes of excited states of biacetyl produced by absorption of mono- chromatic light have been rep~rted.~ Intersystem crossing in biacetyl vapour l6 309 J. J. Smith and B. Meyer J. Chem. Phys. 1969,50 456. 310 A. S. Archer R. B. Cundall G. B. Evans and T. F. Palmer Proc. Roy. SOC. 1973 A333 385. 311 A. S. Archer R. B. Cundall and T. F. Palmer Proc. Roy. SOC.,1973 A334 41 1. 312 C. A. Thayer and J. T. Yardley J. Chem. Phys. 1972 57 3992. 313 L. G. Anderson C. S. Parmenter and H. M. Poland Chem. Phys. Letters 1971,8,232. R. A. Beyer and W. C. Lineberger Chem. Phys. Letters 1973 20 600. 315 J. T. Yardley. J. Chem. Phys. 1972,56 6192. l6 H. W. Sidebottom C. C. Badcock J. G. Calvert B. R. Rabe and E. K. Damon J.Amer. Chem. SOC.,1972 94 13 19.Luminescence Spectroscopy 57 has been investigated by examination both of fluorescence from the first excited singlet state and of phosphorescence from the triplet state.31 Low-pressure measurements show that triplet formation occurs in the absence of collisional perturbation. The fluorescence decay of the biacetyl singlet state is insensitive to medium3I8 varying little in going from solution (rf = 12.3 ns 0.05Mbiacetyl in benzene) to vapour (rf = 10.6 ns at 25 Torr and 300 K). Although theory would predict that biacetyl should be classed as a small molecule the evidence clearly indicates that the non-radiative decay is intramolecular and that experimentally biacetyl behaves as a large molecule within the statistical limit. Direct observa- tion of the fluorescence decay of biacetyl vapour using a medium resolution (1-3 nm) tunable dye laser3 l9 has shown that the fluorescence decay is exponen- tial below 2Torr and that the decay time decreases with increasing excitation energy in the region 450-370nm.The quenching efficiencies of biacetyl and argon were measured. From a recent examination of the effect of wavelength and pressure on the fluorescence and phosphorescence of biacetyl vapour Kommandeur et a1.320concluded that on the basis of the structure of the excita- tion spectrum below 22 500 cm-I and the pressure dependence of phos-phorescence biacetyl behaves as a small molecule. Above this energy a sudden transition to large-molecule behaviour is attributed to the presence of a 3B state for which there is theoretical evidence.A deuterium-substitution effect on the phosphorescence lifetime of biacetyl- vapour and crystal has been noted;321 the radiationless rate constants were shown to depend upon the extent of deuteriation and the state of aggregation. Triplet-triplet annihilati01-1~~~ has been observed in flashed solutions of biacetyl camphorquinone and benzoquinone at 25 "C. Relatively few observations have been reported for other diketones. The fluorescence and phosphorescence of penta-2,3-dienone have been examined in the gas phase323 and the triplet states of a number of a-diketones have been studied by examination of the phosphore~cence.~~~ An unusual detected for the cyclic enone bicyclo[3,3,0]oct-l(5)-en-2-onehas been attributed to a large energy difference between the 'nn* and 3nn* states in the aj-unsaturated ketones.There have been a number of investigations on emission from the triplet state of aromatic carbonyl compounds. Phosphorescence from benzophenone and other aromatic ketones in both i~o-octane~~~ and perfluoromethylcyclohexane327 has been examined. In the latter solvent phosphorescence is relatively long-lived 317 C. S. Parmenter and H. M. Poland J. Chem. Phys. 1969 51 1551. '* L. G. Anderson and C. S. Parmepter J. Chem. Phys. 1970 52,466. 319 G. M. McClelland and J. T. Yardley J. Chem. Phys. 1973,58 4368. 320 E. Drent R. P. van der Werf and J. Kommandeur J. &'em. Phys. 1973 59 2061. 321 R. F. Borkman Chem. Phys. Letters 1971 9 77.322 A. Yekta and N. J. Turro Mol. Photochem. 1972 3 307. 323 A. W. Jackson and A. J. Yarwood Canad. J. Chem. 1972,50 1331 1338. 32* P. Gacoin J. Chem. Phys. 1972 57 1418. 325 R. 0.Loutfy and J. M. Morris Chem. Phys. Letters 1973 19 377. 326 W. D. K. Clark A. D. Litt and C. Steel J. Amer. Chem. SOC. 1969,91 5413. 327 C. A. Parker and T. A. Joyce Trans. Faraday SOC. 1969,65 2823. 58 R. B. Cundall and T.F. Palmer and high phosphorescence yields are possible.328 It has been suggested that the short lifetime of the benzophenone triplet in benzene is due to an inter- action between the triplet state and the solvent. In saturated solvents H-atom abstraction has been shown to be important. Phosphorescence has been observed from oxygen-free aqueous solutions of benzophenone and aceto- phen~ne.~~’ Quantum yields of benzophenone-sensitized phosphores~ence~~~ as a function of glass composition have been obtained in the presence of a num-ber of aromatic molecules leading to information on the external heavy-atom spin-orbit coupling effect.A pulsed laser has been used to investigate triplet- triplet transfer from benzophenone to naphthalene by examination of the non-exponential decay of benzophenone phosphorescence. 33 I The biacetyl phosphorescence method has been used to estimate triplet yields and lifetimes for a number of substituted benzophenones and a satisfactory Hammett-type correlation was obtained. 332 pK* values for benzophenone and derivatives have been estimated using the Forster cycle from examination of absorption and phosphorescence emission ~pectra.~ 33 Time-resolved emission from benzophenone has been rep~rted,~ 34 and from a study of the radiative decay of the vapour at low pressure Torr) a rapid crossover to produce non-stationary mixed singlet-triplet levels has been proposed.335 A mechanism has been deduced for the primary photochemical and photo- physical processes of ben~aldehyde~~~ from a detailed examination of the phos- phorescence emission yields lifetimes and product quantum yields.The nn* and nn* triplet energies of p-chloro- and p-met hoxy-benzaldehyde have been obtained from their phosphorescence emission and excitation spectra.j2’ Phosphorescence excitation spectroscopy has provided information338 on the nature of the transitions between the S(nn*) T(m*),and T(nn*) states of acetophenone p- bromoacetophenone and indan- 1-one.Examination of indan- 1-one and related molecules in n-hexane and EPA glass339 has led to the sugges- tion that the dual phosphorescence arises from two nearby states of different orbital type. A tunable dye laser has been used to excite single vibronic levels of the ‘B1 and 3A states of deuteriated and undeuteriated p-benzoq~inone.~~~ It has been concluded from examination of the time-resolved emission at low pressure that the ‘B, state is strongly coupled with vibronic levels of lower excited states. 328 C. A. Parker and T. A. Joyce Chem. Comm. 1968 749. 329 M. B. Ledger and G. Porter J.C.S. Faraday I 1972 68 539.330 S. E. Webber J. Phys. Chem. 1971 75 1921. 331 H. Kobashi T. Morita and N. Mataga Chem. Phys. Letters 1973 20 376. 332 G. Favaro Chem. Phys. Letters 1973 21,401. 333 J. F. Ireland and P. A. H. Wyatt J.C.S. Faraday Z 1973 69 161. 334 G. E. Busch P. M. Rentzepis and J. Jortner Chem. Phys. Lerrers 1971 It 437. 335 R. M. Hochstrasser and J. E. Wessel Chem. Phys. Letters 1973 19 157. 336 M. Berger I. L. Goldblatt and C. Steel J. Amer. Chem. Soc. 1973 95 177. 337 H. Hayashi and S. Nagakura Chem. Phys. Letters 1973 18 63. 338 W. A. Case and D. R. Kearns J. Chem. Phys. 1970.50 2175. 339 M. E. Long and E. C. Lim Chem. Phys. Letters 1973 20 413. 340 L. E. Brus and J. R. McDonald J. Chem. Phys. 1973,58 4223. Luminescence Spectroscopy 59 Vibrational relaxation occurs to the 3A state but the lifetime of this state is controlled by processes other than normal phosphorescence.Other phos- phorescence spectra reported include those of benzophenone crystals341 and of 1-and 2-halogenonaphthalene~~~~ in a variety of matrices. 6 Excimers and Exciplexes The importance of excimers in self-quenching effects and their role in energy migration in aromatic systems is clear although kinetic details are still uncertain. Forster has reviewed the essential principles of the subject. 343 Some indications of the present situation are provided by work with benzene in cy~lohexane~~~ and methylnaphthalene.345 All the schemes used for analysis of excimer formation kinetics are necessarily simplified and it is possible that further progress will be limited by this factor ;for example it is usually assumed that the various processes are independent of solvent composition which is certainly not true in some cases.Intramolecular excimer formation is important in the photophysics of polymers and other molecules. Most published work in this area at the preseni time deals with ex~iplexes~~~ where interaction occurs between an excited state and a ground-state molecule of some other type. The interaction is of a charge-transfer nature as shown by experiments in which a correlation between the electron affinity of the quenching molecule and the rate constant for fluorescence is e~tablished.~~’ The strong dependence of the fluorescence quenching of pyrene by NN-dimethylaniline on the polarity of the solvent is another example of an effect consistent with this Several studies have made use of time-resolved fluorescence spectros- copy to study exciplex formation and decay processes.Systems examined include pyrene-NN-dimet h~laniline,~~~ toluene-l,2,4,5-tetracyanoben~ene,~ naphtha- s’ naphthalene-1 -cyan~naphthalene~~ lene-dieth~laniline,~ ’ and biphenyl-di-et h~laniline.~’ Laser flash excitation techniques3s2 have further elucidated the intersystem crossing of charge-transfer ex~iplexes,~’~ which are often fluorescent and the properties of triplet acceptor charge-transfer states354 are now also under in~estigation.~” 341 J. L. Laporte G. Nouchi and Y. Rousset J. Chem. Phys. 1972 57 1767. 342 L. G.Thompson and S. E. Webber J. Phys. Chem. 1972,76 221. 343 Th. Forster Angew. Chem. 1969 81 364. 344 R. B. Cundall and D. A. Robinson J.C.S. Faraday II 1972 68 113. 345 R. B. Cundall and L. C. Pereira Chem. Phys. Letters 1972 15 383. 346 I. E. Obyknovennaya and A. S. Cherkasov Optics and Spectroscopy 1968 24 22. 34’ A. Nakajima and H. Akamoto BUN. Chem. SOC.Japan 1968 41 1961. 348 W. R. Ware and H. R. Richter J. Chem. Phys. 1968 48 1595. 349 K. Yoshihara T. Kasuko A. Inoue and S. Nagakura Chem. Phys. Letters 1971 9 469. 350 E. Egawa N. Nakashima N. Mataga and C. Yamanaka Buff. Chem. SOC.Japan 1971,44 3287. ”* A. E. W. Knight and B. K. Selinger Chem. Phys. Letters 1971 10 43. 352 M. Ottolenghi Accounfs Chem. Res. 1973 6 153. 353 C. R. Goldschmidt R.Potashnik and M. Ottolenghi J. Phys. Chem. 1971,75 1025. 354 N. Orbach R. Potashnik and M. Ottolenghi J. Phys. Chem. 1972 76 1133. J’s G. Briegleb and H. Schuster Angew Chem. Internat. Edn. 1970 9 369. R. B. Cundall and T. F. Palmer Examples of systems in which exciplex behaviour has been studied by emission spectroscopy are anthracene-~liethylaniline,~’~ aromatic hydrocarbons-amino- alcohols,3s7 anthra~ene-amines,~’~ and dimethoxybenzene chlorides and anhy- dride~.~~~ Intramolecular exciplexes have also been studied in 9,lOdicyano-anthracene4CH2),-naphthalene systems360 in polar and non-polar solvents and compounds of the type361 have been similarly studied by single-photon counting decay techniques. Laser action has been found in an intramolecular exciplex of p-(9’-anthryl)-NN-di- met hylaniline.62 Intermolecular charge-transfer phosphorescence and fluorescence have been observed for biphenyl single crystals containing 1,2,4,5-tetracyanobenzeneas Quenching of aromatic hydrocarbon fluorescence by free radicals such as di-t-butyl nitroxide may involve electron transfer.364 7 Heterocyclic Compormds and Dyes The presence of non-bonding electrons in heterocyclic aromatics makes the luminescence behaviour more complex than that of the analogous hydrocarbons. A careful study ofthe reasons for the failure to detect phosphorescence from pyri- dine has been made.36s From a study of derivatives in which strong long-lived (m*) and short-lived (nn*)emissions are detected it is concluded that the lowest triplet in pyridine is the 3A2 (nn*)state.This state must have a high radiationless transition probability and an exceptionally low radiative efficiency. Recent papers deal with 1,5-naphthylpyridine~,~~~ 2,3- and 2,3,4-amino~yridine,~~’ 4-~tyrylpyridines,~~~ and derivatives.369 A study of the pH and Hammett acidity 3s6 B. K. Selinger and R. J. McDonald Austral. J. Chem. 1972 25 897. 3s7 D. R. G. Brimage and R. S. Davidson J. Photochem. 1972/73 1 79. 358 N. C. Yang and J. Libman J. Amer. Chem. SOC.,1973,95 5783. 359 F. A. Carrol M. T. McCall and G. S. Hammond J. Amer. Chem. SOC. 1973 95 315. 360 M. Itoh T. Mimura H. Usui and T. Okamoto J. Amer. Chem. SOC. 1973,95,4388. ”‘ G. S. Beddard R. S. Davidson and A. Lewis J. Photochem.1972173 1 491. 362 N. Nakashima N. Mataga C. Yamanaka R. Ide and S. Misumi Chem. Phys. Letters 1933 18 386. 363 M. Yagi S. Nagakura and H. Hayashi Chem. Phys. Letters 1973 18 272. 364 J. A. Green. jun. and L. A. Singer J. Chem. Phys. 1973,58 2696. 36s R. G. Hoover and M. Kasha. J. Amer. Chem. SOC. 1969,91,6508. 366 G. Fischer Chem. Phys. Letters 1973 21 305. ”’ S. Hutchandan and A. C. Testa J. Chem. Phys. 1973,59 596. 368 G. Favaro U.Mazzucato and F. Masetti J. Phys. Chem. 1973,77 601. 369 G. Bartocci P.Bartolus and U. Mazzucato J. Phys. Chem. 1973,77 605. Luminescence Spectroscopy 61 dependences of the blue fluorescence of the quinolinium ion and related species shows that the 'L and 'La thermally relaxed states are degenerate and that fluorescence occurs from both.370 Some gas-phase studies on excited states of heterocyclic molecules have been reported.The luminescence of monocyclic diazines shows anomalies which result from the proximity of the two nn* states which arise from the presence of two filled non-bonding orbitals which are close in energy in pyrazine and ~yrimidine.~ Intersystem crossing and fluorescence can occur from the S2 71 level. The S,-S energy gap is 1000-2000cm-' and the slow internal conver- sion must be due to the low density of vibronic states of S near the zero-point level of S . Resonance fluorescence from pyridazine has been studied at low pres~ures.~ 72 Fluorescence yields and lifetimes have been measured for 1-pyrazoline at low pressures for excitation at different wavelengths3 73 The rate constant for fluorescence is practically independent of exciting wavelength but non-radiative rates increase at higher energies.The photophysics of quinoxaline remains the subject of intensive research. Vapour-phase studies show that both structural fluorescence and phosphorescence occur.374 It is unusual for a molecule with a low nn* state to fluoresce with this efficiency. Time-resolved phosphorescence shows emission from two triplets and two spin sub-levels at 1.38 K for quinoxaline in a durene A review of azo-compounds discusses their fluorescence proper tie^.^ 76 The main conclusions are (i) trans-azo-compounds are weakly fluorescent ; (ii) cis-azo-groups in rigid cyclic molecules are strongly fluorescent ; (iii) protonated azo-compounds invariably fluoresce ; and (iv) hydroxy-derivatives fluoresce owing to the formation of tautomeric forms.Energy transfer effects in azo-dyes are of considerable interest and many studies have been made. Forster energy transfer from an excited azo dye monolayer to a luminescent cyanine dye mono- layer has been observed; it was concluded that transfer from vibronic levels occurs at a rate which exceeds thermal relaxation.377 The development of dye lasers has stimulated interest in the photophysics of dyes such as the rhodamine~~~~.~~' 0t her papers pub- and coumarin~.~~~-~~~ 3 70 S. G. Schulman and A. C. Capomacchia. J. Amer. Chem. Sac. 1973.95 2763. 371 Y.H. Li and E. C. Lim Chem. Phys. Letters 1971,9 514.312 A. D. Jordan and C. S. Parmenter Chem. Phys. Letters 1972 16,437. 373 G. L. Loper and F. H. Dorev J. Amer. Chem. Soc. 1973,95,20. 3 74 H. J. Dewey and S. G. Hadley Chem. Phys. Letters 1972 17 574. 375 S. Yamouchi and T. Azumi Chem. Phys. Letters 1973 21 603. 316 H. Rau Angew. Chem. Internat. Edn. 1973 12 224. 317 D. Mobius and G. Dreizler Photochem. and Photobiol. 1973,17,225. 378 D. J. Bradley M. H. R. Hutchinson H. Koetser T. Morrow G. H. C. New and M. S. Petty Proc. Roy. SOC.,1972 A328 97. 319 D. J. Bradley M. H. R. Hutchinson and H. Koetser Proc. Roy. Sac. 1972 A329 105. 380 J. B. Gallivan Mol. Photochem. 1970 2 191. 38 I P. S.Song and W. H. Gordon J. Phys. Chem. 1970,74,4234. 38 2 T.A. Moore W. M. Mantulin and P. S. Song Photochem.and Photobiol. 1973 18 185. 62 R. B. Cundall and T.F. Palmer lished is 1973 deal with phthal~cyanines,~~~ thio-various porphyrin~,~~~,~~~ anth hen one,^^^ cyanine dye^,^^^,^^^ and the effects of anions on the phos- phorescence of cationic dyes.389 8 Polymer and Aggregated Systems Emission spectroscopy is used for the identification of excited states in organic polymers and energy migration and transfer processes within polymer molecules can beassessed. Review articles on this subject have been written by Partridge3” and Fox.391 The formation of excimers is well known in polymers containing aromatic chromophores. A fairly recent study is that of Harrah3” on poly-2- vinylnaphthalene in fluid and glassy solvents at room temperature and 77 K.Excimer emission is observed at all temperatures in glassy solution but this emis- sion is redwed at lower temperatures in fluid media showing that the excimer- forming conformation arises from higher-energy configuration^.^'^ Other systems studied include poly~inylnaphthalene~~~*~~~ and p~lyvinylpyrene.~’~ Luminesoence and emission spectroscopy have been used in the examination of energy transfer effects in polymer^.^^^^^'^ A pulse sampling fluorometer enables time-dependent fluorescence depolariza- tion measurements to be made on polymers containing fluorescent A recent important development has been the use of fluorescence in the study of detergent solutions.399 Pyrene is soluble in micelles of sodium lauryl sulphate and cetyltrimethylammonium bromide.400 The rate of decay of pyrene fluor- escence has been measured by a pulsed ruby laser technique in the presence of quenchers 02,I- and trimethylamine which dissolve in the water layer.The quenching efficiency decreases with time indicating an increase in micellar order. E.s.r. and fluorescence polarization studies extend the laser-derived data and the 383 E. R. Menzel K. E. Rieckhoff and E. M. Voigt J. Chem. Phys. 1973,58 5726. 384 J. B. Callis J. M. Knowles and M. Gouterman J. Phys. Chern. 1973 77 154. 385 M. Gouterman F. P. Schwarz P. D. Smith and D. Dolphin J. Chem. Phys. 1973,59 676. 386 R. 0.Loutfy D. F. Williams and R. W. Yip Canad. J. Chem. 1973,51 2502. 387 D. N. Dempster T. Morrow R. Rankin and G. F. Thompson Chem.Phys. Letters 1973 18 488. 388 C. Vernotte and I. Moya Photochem. and Phorobiol. 1973 17 245. 389 R. A. Berg and A. Ron J. Chem. Phys. 1973,59 3289. 390 R. H. Partridge ‘The Radiation Chemistry of Macromolecules’ ed. M. Dole Academic Press New York 1972 Vol. 1 p. 25. 39‘ R. B. Fox Pure Appl. Chem. 1973 34 235. 392 L. A. Harrah J. Chem. Phys. 1972,56 385. 393 R. B. Fox T. R. Price R. F. Cozzens and J. R. McDonald J. Chem. Phys. 1972,57 2284. 394 R. B. Fox T. R. Price and R. F. Cozzens J. Chem. Phys. 1971 54 79. 395 J. R. McDonald W. E. Echols T. R. Price and R. B. Fox J. Chem. Phys. 1972,57 1746. 396 T. G. Samedova G. P. Karpacheva and B. E. Davydov European Polymer J. 1972 8 599. 397 A. M. North and M. F. Treadaway European Polymer J. 1973,9 609.398 A. M. North and 1. Soutar J.C.S. Faraduy I 1972 68 1101. 399 S. Ikeda and G. D. Fasman J. Polymer Sci. Part A-1 Polymer Chem. 1970 8 991. 400 M. Gratzel and J. K. Thomas J. Amer. Chem. Soc. 1973,95 6885. Luminescence Spectroscopy 63 fluorescence probe technique can be used to determine the absorption of ions on the micelles. Single-photon counting has been employed in similar studies of micelle properties in which naphthalene was used as a probe.401 A method of studying energy transfer in assemblies of this kind has been developed by Shinit~ky.~'* Dye aggregates403 also allow rapid energy transfer because of the exciton coupling which occurs.4o4 Extremely rapid transfer has been established for the quenching of aggregated acridine orange on polyanions by low concentrations of methylene 9 Non-aromatic Hydrocarbons and Derivatives and other Compounds In saturated hydrocarbons where there are no 7t-bonding or non-bonding elec- trons all electronic transitions involve o-bonding electrons.Such transitions occur at higher energies than in unsaturated compounds and photochemical disruption of the molecules is a significant fate of a large proportion of such states. It was a noteworthy discovery in 1969 that saturated hydrocarbons can fluoresce406 although the fluorescence is weak and occurs in a wavelength region outside the range of most fluorimeters (200-230 nm). Fluorescence spectra and quantum yields have been determined for a variety of normal and cyclic alkanes and their alkyl derivative^.^^'^^^^ The quantum yields of n-alkanes increase with chain length although the spectral position is unaffected.Methyl substitution reduces the fluorescence efficiency and the spectrum is red-shifted. For the cycloalkanes only cyclohexane and its alkyl derivatives show any detectable emission. The emitting state appears to be one in which there is a relatively high localization of charge and may be markedly affected by intermolecular interaction in the condensed phase. Since excitation of saturated hydrocarbons occurs in the vacuum u.v. the role of such states in the effect of ionizing radiations is of great interest. Baxendale and Mayer409 have studied the emissions from excited states of liquid n-hexane methylcyclohexane and cyclohexane by pulse radiolysis.The emissions are quenched by benzene and fluorescence from benzene is induced by an efficient energy exchange (k = 2.8 x 10" 1 mol-'s-'). In this case the excited states mainly arise from charge neutralization processes. Helman4I0 has measured fluorescent lifetimes in decalin and dodecane using a pulsed nano- second X-ray excitation technique. 40' R. R. Hautala N. E. Sheve and N. J. Turro J. Amer. Chem. Soc. 1973 95 5508. 402 M. Shinitzky Chem. Phys. Letters 1973 18 247. 403 W. Cooper Chem. Phys. Letters 1970 7 73. 404 M. R. Philpott J. Chem. Phys. 1970 53 968; 1971,54,4223. 40s R. B. Cundall C. Lewis P. J. Llewellyn and G. 0. Phillips J. Phys. Chem. 1970 74 41 72. 406 F. Hirayama and S. Lipsky J. Chem. Phys. 1969 51 3616.407 F. Hirayama W. Rothman and S. Lipsky Chem. Phys. Letters 1970 5 296. 408 W. Rothman F. Hirayama and S. Lipsky J. Chem. Phys. 1973,58 1300. 409 J. H. Baxendale and J. Mayer Chem. Phys. Letters 1972 17,458. 4'0 W. P. Helman Chem. Phys. Letters 1972 17 306. R. B. Cundall and T.F. Palmer Excited states of simple unsaturated hydrocarbons have so far eluded charac- terization by emission methods.411 However the triplet state of acetylene has been postulated412 as the cause of biacetyl phosphorescence in the Hg 63P1 sensitized reaction with acetylene in the presence of biacetyl. A mechanism has been postulated and rate constants have been calculated. Comparison of the absorption and fluorescence spectra of the retinyl polyenes shows that there is a large change in molecular geometry on excitation.413 Changes of polarity and viscosity of the solvent effect large changes in the relationship between absorption and emission which has a low efficiency.An emission from liquid 1,4-dioxan has been detected4I4 and the spectrum yields and lifetimes have been mea~ured.~” No emission was detected in the vapour phase and it is postulated that the liquid-phase fluorescence arises from some form of excited aggregate whose composition varies with dilution. The aggregate concept is in agreement with the large encounter radius for oxygen quenching (1.3nm). The fluorescence is extremely sensitive to the presence of water. An extremely interesting study of the photophysical and photochemical processes in chloro- and bromo-acetylene using a single-photon counting tech- nique has been made.416 Fluorescence yields and lifetimes have been measured for a large number of selected individual vibronic levels.1.r. and U.V. spectra were measured in order to assign the individual transitions. The results were analysed in terms of fluorescence competing with loss of halogen atom and radiative and non-radiative rate constants were calculated. The results suggest that a slow internal conversion S -P So occurs and that vibrational relaxation of the electronic ground state is so slow that randomization of excitation energy does not occur before dissociation. This leads to departure of decomposition rates from the predictions of RRKM theory. There is no particularly simple dependence of the rates of the non-radiative processes on excess vibrational energy of the type found in similar studies with benzenoid corn pound^.^^ This type of experiment is probably one of the most powerful methods currently avail- able for the study of unimolecular reaction rate theory.Fluorescence of tertiary aliphatic amines has been observed in the gas phase.41 The absence of fluorescence from amines with hydrogen or deuterium atoms directly bonded to the nitrogen atom supports the supposition that predissocia- tion involves quantum mechanical tunnelling. 4LLR. M. Gavin jun. S. Risenberg and S. A. Rice J. Chem. Phys. 1973,58 3160. 412 C. S. Burton and H. E. Hunziker J. Chem. Phys. 1972 57 339. ‘I3 A. J. Thompson J. Chem. Phys.1969,51 4106. 4’4 F. Hirayama C. W. Lawson and S. Lipsky J. Phys. Chem. 1970 74 241 1. 4L5 A. M. Halpern and W. R. Ware J. Phys. Chem. 1970,74 2413. ‘I6 K. Evans R. Scheps S. A. Rice and D. Heller J.C.S. Furaduy 11 1973 69 856. ‘I7 C. G. Freeman M. J. McEwan R. F. C. Claridge and L. F. Phillips Chem. Phys. Letters 1971 8 77. LuminescenceSpectroscopy 65 10 Biological Molecules Energy transfer mechanisms are conveniently studied by luminescence tech- niques and structural information has also been obtained. A recent review of the topic has been made by Interest in the mechanism of photosynthesis continues and neon-helium laser excitation has been used for studying the fluorescence of ~hlorophyll.~ l9 Numerous studies of systems which help to understand the details of biological processes have been made.For example Lasser and Feite1son4*' have shown that attempts to measure pK values for excited states of biologically interesting molecules do not give correct results. They have examined the dependence of the fluorescence of riboflavin monophosphate on pH in the presence of bromide ions. It is still necessary for the different moieties in biomolecules to be examined in detail as a preliminary to full understanding of protein and nucleic acid luminescence. Since tryptophan is the most strongly fluorescent amino-acid residue in proteins the properties of excited states of indole continue to be the subject of many investigations. The method of photoselection has been used to determine the polarized fluorescence excitation and emission spectra of indole and some of its derivative^.^^' The results have been compared with theoretical predictions and the first and second excited m*states are assigned 'L,and 'La.The emissions from the 0-0transitions of both states were confirmed for most indoles on the basis of the sharp changes in polarization of the fluorescence bands. It was also shown that the phosphorescence observed in glasses at 77 K originates from 37171* states of the 3L,type. Fluorescence solvent shifts and excited-state pK values have also been reported.422 Horr~cks~~~ has deduced from studies of the quenching of indole fluorescence that hydrogen-bonding is involved and that a proton transfer process could be involved AH* + AH * AH*--AH + A*-+ HAH' A*-+ A +-e-Hydrogen-bonding effects have also been used to explain the quenching of excited indoles by cations like H + and Cu2 +,anions such as NO -and 103-,and sulphur compounds.424 The fluorescence spectra and fluorescence yields of tryptophan and derivatives in water and polar glasses have been measured over a wide temperature range;425 Amaxshifts from 310nm at 80K to 355nm at room temperature.The longest red shift occurs over the range 170-230 K. The fact that there is no iso-emissive wavelength indicates that re-orientation of solvent molecules in the solvent shell of the excited tryptophan molecule is responsible 4'B P. S. Song Photochem. and Photobiol. 1973 18 531. 419 K. Vacek E. Vavrinec and I. Kalousek Photochem.and Photobiol. 1973 17 63. 420 N. Lasser and J. Feitelson J. Phys. Chem. 1973 77 1011. 421 P. S. Song and W. E. Kurtin J. Amer. Chem. SOC. 1969 91 4892. 422 E. Van der Donckt Bull. SOC.chim. belges 1969 78 69. 423 D. L. Horrocks J. Chem. Phys. 1969,50 4151. 424 R. F. Steiner and E. P. Kirby J. Phys. Chem. 1969 73 4130. 425 J. Eisinger and G. Navon J. Chem. Phys. 1969 50 2069. 66 R.B. Cundall and T.F. Palmer for the red shift rather than the formation of a 1 :1 exciplex. In more recent work the fluorescence yields and liftetimes of tyrosine and tryptophan in H,O-D,O and glycerol-water solvents of varying composition have been measured.426 @,/OH < 7D/Z" for both compounds in D20 and H,O and the quenching is attributed in the case of tyrosine to an exciplex involving water.The tryptophan results are explained by an electrostatic interaction of the ammonium group with the carbon atom adjacent to the ring nitrogen. Solvent reorientation effects may also be important. In a study of a large number of proteins where tyrqsine was absent tryptophan fluorescence excited at 295 nm showed no simple relation- ship between amino-acid residue fluorescence and exposure. More recent work on the fluorescence spectra of natural and denatured proteins has enabled a model for the fluorescence properties of tryptophan residues to be substantiated and developed.42' Quenching studies on trypsin by histidine acrylamide and nitrate ion show all residues to be equally susceptible to quenching.428 The pH dependence of tryptophan and tyrosine fluorescence of glucagon have been measured and it has been deduced that base quenching involves a radiationless jinglet excitation energy transfer from tryptophan to tyr~sinate.~,' A delayed fluorescence emission of biphotonic nature originates from tryptophan residues when pepsin and carbonic anhydrase are excited at 77 K in water-ethylene glycol glasses.430 This delayed fluorescence is probably due to ion-electron recombina- tion.Changes of proton structure can be examined by fluorescence techniques. Fluorescence and c.d. spectra of rye phytochrome show no evidence for changes of protein conformation as a consequence of U.V. excitation.431 The interaction of 2-p-toluidinylnaphthalene-6-sulphonate(TNS) a frequently used fluorescent probe with poly-L-lysine has been examined in An especially important paper is that of Brand and G~hlke~~~ which describes the application of the single photon technique for determination of time-resolved spectra to the inter- action of bovine serum albumin with TNS.The change in the form of the fluorescence spectrum with the time elapsed after excitation arises from re- orientation of excited molecules in the solvent cage. Nucleic acids have been the subject of much research also. The bases are only very weakly fluorescent and DNA itself does not fluoresce. Interactions of DNA with various species have been studied e.g. the absorption and prompt fluorescence spectra of 12 cationic absorbates interacting with DNA in the free and bound state.434 The behaviour of proflavine benzoflavine acridine orange and thioflavine T has been studied in detail.Luminescence at 77 K and the 426 R. McGuire and I. Feldman Photochem. and Photobiol. 1973 18 119. 427 E. A. Burstein N. S. Vedenkina and M. N. Ivkova Photochem. and Photobiol. 1973 18 263. 428 D. R. Sellers and C. A. Ghiren Photochem. and Photobiol. 1973 18 393. 429 R. M. Epand Photochem. and Photobiol. 1973 18 245. 430 M. Aubailly M. Bazin and R. Santus Chem. Phys. Letters 1972 13 310. 43' E. M. Tobin and W. R. Briggs Photochem. and Photobiol. 1973 18 487. 432 G. Witz and B. L. Van Duuren J. Phys. Chem. 1973 77 648. 433 L. Brand and J. R. Gohlke J. Biol. Chem. 1971,246 2317. 434 C. A. Parker and T. A. Joyce Photochem.and Photobiol. 1973 18 467. Luminescence Spectroscopy 67 photochemistry at 298 K of a variety of polynucleotides complexed with Ag' have been in~estigated.~~' The latter because of the heavy-atom effect quenches fluorescence and enhances phosphorescence with a reduction of triplet lifetime. Typical examples of recent studies in this area have dealt with the emission proper- ties of 4-thiouridine in aqueous and an examination of excimer fluorescence of the dinucleotide CpC.437 Problems related to vision can be examined by luminescence methods. Polarization of the fluorescence excitation and emission bands of all-trans- retinal in ether at 77 K have been measured.438 The degree of polarization ap- proaches the maximum value of 0.5 showing that a long-axis transition is involved.This is attributed to a 'B -+ 'A transition. The conclusion about the nature of the transition has been contested in view of related experiments. For example studies of the fluorescence of axerophtene anhydro-vitamin A and 2,10-dimethylundecapentaene,as well as retinyl polyenes have been made in glasses at 77 K.439 Radda and Vanderko~i~~' have reviewed in detail the use of fluorescent probes in studying cell membranes. 11 Inorganic Molecules Inorganic ions may fluoresce directly or when combined with an organic ligand to form a highly fluorescent metal chelate. Non-bonding n-electrons lnay be involved in bonding with a metal ion and a strongly fluorescent nn* state results from excitation rather than an nn* state of low fluorescence yield.Over 40 metal ions can be determined by combination with various organic ligands2 Ter- valent rare-earth ions and uranyl compounds are fluorescefit also ; the lumin- escence of the former arises from the presence of the 4f shells in which the electrons are screened by outer-shell electrons. This gives rise to a number of discrete levels which are little affected by the environment. Luminescence may arise from excitation in the 4f levels; 4f+ 5d or change-transfer transitions can occur and there may be transfer of energy from another chromophore to the rare-earth electrons. The possible applications of inorganic ions in laser tech- nology has stimulated studies of inorganic ion luminescence. A shall selection of some references to inorganic systems follows.An important application of rare-earth ions is as sensitive probes for triplet states in inorganic ~hemistry.~~' The transition energies are low so the scope can be very extensive. Lanthanide ions have been used for this purpose. Triplet 433 R. 0. Rabin and L. C. Landry Photochem. and Photobiol. 1973 18 29. 436 N. Shalitin and J. Feitelson J. Chem. Phys. 1973 59 1045. 437 P. R. Callis Chem. Phys. Letters 1973 19 551 438 T. A. Moore and P. S. Song Chem. Phys. Letters 1973 19 128. 439 R. L. Christensen and B. E. Kohler Phorochem. and Photobiol. 1973 18 293. 440 G. K. Radda and J. Vanderkooi Biochim. Biophys. Acta 1972 265 509. 441 N. Filipescu and C. W. Mushrach J. Phys. Chem. 1968,72 3516. R.B. Cundall and T.F. Palmer energy transfer to an organic ligand followed by transfer to the metal ion442*443 is the mechanism involved. It has been established that triplet donors may under- go bimolecular transfer to unchelated rare-earth ions in aqueous solution. Typical of studies with complex ions other than rare-earth ions are those with and r~thenium,~~~.~~~ for which both emksion yields and lifetimes have been measured. Rei~feld~~~ has suggested that rare-earth-doped glasses can be used as relative standards for fluorescence spectroscopy. 442 Y. Matsuda S. Makishima and S. Shionoya Bull. Chem. SOC.Japan 1968,41 1513. 443 M. E. Mooseyan V. A. Gevorkyan and D. Kh. Origorgan Zhur. priklad. Spectroskopii 1968 9 260. 444 R. J. Watts R.W. Harringan and G. A. Crosby Chem. Phys. Letters 1971 8 49. 445 M. K. De Armand and J. E. Hillis J. Chem. Phys. 1971 54 2247. 446 J. N. Demas and G. A. Crosby J. Amer. Chem. SOC.,1970,92 7262. 447 R. Reisfeld. in ref. 6.

ISSN:0308-6003    

DOI:10.1039/PR9737000031

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

4 Gas-phase Kinetics and Mechanisms By R. WALSH Department of Chemistry University of Reading Whiteknights. Reading RG6 2AD 1 Introduction The period of this Report is limited to the year 1973 and the content to reactions of large radicals and molecules. 1972 has alas not been covered the enthusiasm of researchers and willingness of publishers having ensured too great a volume of material for inclusion. Even so it has been necessary to restrict coverage of many topics to the briefest mention such is the breadth of field covered by the title. When all this is said and bemoaning the expansion of the literature has become the reviewer’s endemic condition the author still had some anxiety that his coverage of the journals (26 were searched excluding reviews) may have failed to unearth some important contribution.He was comforted by the knowledge that another reviewer in the field’ was happy to limit his report to a ’slightly- more-conscientious-than-usual coverage of major journals’. The cataloguing of kinetic data and their critical evaluation continue and a summary of current efforts appeared this year.2 Amongst new books of interest are those on the subjects of the theory of unimolecular reactions3’ and the kinetics of addition and elimination reaction^.^' A particularly valuable series of essays on free radicals4 has appeared. 2 Theory and Experiment This year has been one of consolidation rather than dramatic development. It has seen the further extension of the molecular beam technique into this area of kinetis5s6 In a series of studies Lee Rice and co-workers5 have examined both the velocity and angular distributions of products from the decomposition A.A. Westenberg Ann. Rev. Phys. Chem. 1973 24 77. L. H. Gevantman and D. Garvin Internat. J. Chem. Kinetics 1973 5 213. (a)W. Forst ‘The Theory of Unimolecular Reactions’ Academic Press London 1973; (6) ‘Addition and Elimination Reactions of Aliphatic Compounds’ ‘Comprehensive Chemical Kinetics’ Vol. 9 ed. C. H. Bamford and C. F. H. Tipper Elsevier London 1973. ‘Free Radicals. I. Dynamics of Elementary Processes’ ed. J. K. Kochi Wiley-Inter- science 1973. J. M. Parson K. Shobatake Y. T. Lee and S. A. Rice J. Chem. Phys. 1973 59 1402 1416 1427 1435. J. T. Cheung J. D. McDonald and D.R. Herschbach J. Amer. Chem. Soc. 1973 95 7889. 69 70 R. Walsh of chemically activated fluoroalkyl radicals (and other F-containing radicals). Statistical theories are inadequate in two ways to explain their results. First for the faster decomposition pathway (methyl elimination) energy randomization is incomplete and second for light-particle (H atom) elimination considerably fewer vibrational modes than the total number available participate in energy redistribution. These results do not necessarily invalidate the RRKM* theory of unimolecular reactions except under extreme conditiqns. However Bunker' has performed trajectory calculations which suggest that RRKM theory over-estimates by more than an order of magnitude the decomposition rate of CH,NC at only 293 kJ mol-' in excess of threshold.At this energy the RRKM rate constant is only ca. 101os-l much slower than the expected rate of internal energy randomization. It is clearly too early to judge the significance of these calculations but a great deal of experimental evidence supports the validity of the RRKM theory (see for example later section on Chemical Activation) to within better than an order of magnitude. Within the framework of the theory useful papers have appeared on methods of calculation of energy level sums and densities for anharmonic oscillators and hindered rotors' as well as a simple collisional model enabling easy derivation of the average energy transferred per collision (E ) in the low-pressure limit of thermal unimolecular reactions.' Some complex trajectories have been calculated for the insertion reaction of 'CH in H, which serves as a useful reminder" that the dynamics of a reaction" usually give a much more complicated picture of reaction mechanism than a simplistic view of a reaction co-ordinate on a potential energy surface.A review has appeared of the VLPP? technique developed by Benson Golden and Spokes,i2 which gives a valuable account of the versatility of the method. A slight disappointment has been its relative inability to distinguish' between loose and tight transition-state models (high and low A factors) for unimolecular decomposithns. A number of reports have appeared of new methods for the direct 14-17 and indirect l8 spectroscopic detection of free radicals in reacting systems.Amongst them the most promising from the point of view of kinetics * RRKM = Rice-Ramsperger-Kassel-Marcus. t Very Low Pressure Pyrolysis. D. L. Bunker and W. L. Hase J. Chem. Phys. 1973 59 4621. * S. E. Stein and B. S. Rabinovitch J. Chem. Phys. 1973 58 2438. J. Troe Ber. Bunsengesellschaft phys. Chem. 1973,77 665. lo I. S. Y. Wang and M. Karplus J. Amer. Chem. SOC. 1973,95 8160. l1 J. C. Polanyi Accounts Chem. Res. 1972 5 161. l2 D. h-f. Golden G. N. Spokes and S. W. Benson Angew. Chem. Internat. Edn. 1973 12 534. I3 See for example M. J. Perona P. C. Beadle and D. M. Golden Inrernat. J. Chem. Kinetics 1973 5 495. l4 D. A. Parkes D. M. Paul C. P. Quinn and R. C. Robson Chem. Phys. Letters 1973 23 425.l5 P. D. Pacey Chem. Phys. Letters 1973 23 394. l6 G. H. Atkinson A. H. Laufer and M. J. Kurylo J. Chem. Phys. 1973,59 350. " T. A. Leggatt and D. A. Kohl J. Chem. Phys. 1973,59,611. l8 (a)E. G. Janzen 1. G. Lopp and T. V. Morgan J. Phys. Chem. 1973,77 139; (b)E. G. Janzen T. Kasai and K. Kuwata Bull. Chem. SOC.Japan 1973,46 2061. Gas-phase Kinetics and Mechanisms 71 would appear to be the modulation technique developed by Parkes and co- worker~.’~ 3 Bond Dissociation Energies The importance of reliable bond dissociation energies for kinetics remains para- mount and so this subject is again included.” It has been recently reviewed by Egger and Cocks.20 Many values for organic C-H bonds are now known and more sophisticated mass spectrometric measurements than hitherto’ are pro- ducing data in better agreement with kinetic methods.22 Three recent values21p23*24 for D(C,H-H) ca.532 kJ mol- have appeared. Amongst n-allylic stabilized radicals substituent effects vary the stabilization energy between 3 1 and 75 kJ mol-’,25-27 although there is some disagreement over chloro-ai1y1.25ay27b E.s.r. data on 2-alkanonyl radicals28 support a small n-allylic inter- action here but the thermal isomerization of acetylcy~lopropane,~~ if it occurs via a biradical mechanism suggests a figure of ca. 30 kJ mol- for this stabiliza- tion energy higher than that observed by iodination kinetic^.^' A cyano-group stabilizes a radical’centre31 by ca. 30 kJ mol-I but there is no stabilization in acryl (vinyl carbonyl) radicals.32 The CF group seems to promote a bond- strengthening effect at BC-X bonds,33 while the C-F bond in perfluorobenzene must be amongst the strongest known.34 An upward revision of the value of as well D(Me,Si-H) has been rep~rted~~.~~as a downward change in D(SiH3-H),37 which makes these Si-H bond strengths much more nearly comparable as suggested by relative abstraction rate studies.3840 Esr.19 D. C. Montague and R. Walsh Ann. Reports (A) 1971 68 175. 20 K. W. Egger and A. T. Cocks Helv. Chim. Acta 1973,56 1517 1537. 21 D. K. Sen Sharma and J. L. Franklin J. Amer. Chem. SOC.,1973.95 6562. 21 D. M. Golden and S. W. Benson Chem. Rev. 1969.69 125. 23 J. R. Wyatt and F. E. Stafford J. Phys. Chem. 1972 76 1913. 24 H.Okabe and V. Dibeler J. Chem. Phys. 1973 59 2430. 25 (a) Z. B. Alfassi D. M. Golden and S. W. Benson Internat. J. Chem. Kinetics 1973 5 155; (6)Z. B. Alfassi and D. M. Golden ibid. p. 295. Zb A. S. Rodgers and M. C. R. Wu J. Amer. Chem. SOC.,1973.95 69 13. 21 (a)A. B. Trenwith J.C.S. Faraday I 1973 1737; (6)A. B. Trenwith. Internaf.J. Chem. Kinetics 1973 5 67. 28 (a) D. M. Camaioni H. F. Walter and D. W. Pratt J. Amer. Chem. Soc. 1973. 95 4058; (6) D. M. Camaioni H. F. Walter J. E. Jordan and D. W. Pratt ibid. p. 7978. 29 A. T. Cocks and K. W. Egger J.C.S. Perkin 11 1973 197. 30 R. K. Solly D. M. Golden and S.W. Benson Internat. J. Chem. Kinetics 1970. 2. 381. 31 D. A. Luckraft and P. J. Robinson Internat. J. Chern. Kinetics 1973 5 137.32 Z. B. Alfassi and D. M. Golden J. Amer. Chem. SOC.,1973 95 319. 33 E.-C. Wu and A. S. Rodgers. Internat. J. Chem. Kinetics 1973 5 1001. 34 M. J. Krech S.J. W. Price and W. F. Yared Canad. J. Chem. 1973 51. 3662. 35 I. M. T. Davidson and A. B. Howard J.C.S. Chem. Comm. 1973 323. 36 R. Walsh and J. M. Wells J.C.S. Chem. Comm. 1973 513. 37 W. H. Deuwer and D. W. Setser J. Chem. Phys. 1973,SS. 2298. 38 E. Whittle ‘Reactions of Free Radicals’ in ‘Chemical Kinetics’ ed. J. C. Polanyi Series 1 Vol. 9 of M.T.P. International Review of Science (Physical Chemistry) Butterworths London 1972 Chap. 3 p. 75. 39 R. E. Berkley I. Safarik H. E. Gunning and 0.P. Strausz J. Phys. Chem. 1973 77 1734. 40 A. Hosaka and F. S. Rowland J. Phys. Chem.. 1973 77 705.72 R. Walsh combined kinetic and equilibrium studies in solution show promise as a tech-nique for determining the strengths of weak 0-H and N-H bonds such as occur in hydr~xylamines.~' Solvent effects largely cancel out and the values obtained should not differ significantly from those applicable to the gas phase. 4 Radical Reactions The kinetics of gas-phase radical reactions in general have been reviewed.42 Radical-Radical Reactions-Methyl radical recombination continues to excite interest and three st~dies'~*~~"*' confirm the previously accepted rate constant of ca. dm3 mol-' s-' but a produced a value greater by more than a factor of two. It is disappointing that discrepancies can still occur in such a well-studied reaction.The pressure-dependent region for the rate constant a more contentious question was shown to at pressures <0.5 Torr. Much more controversial have been recent measurements of recombination rate constants for larger alkyl radicals which are collected together in Table 1. Table 1 Recombination rate constants for alkyl radicals by different techniques log, (k/dm3 mol-s-') at (temp./K) obtained by Radical Radical bufler method VLPP Hydrocarbon pyrolysis (wp Et 10~.~-10~.~ 10'' (80(t900)d (951)' Pr' (415)b 109.7(7ocr80o)d -Bu' 105.4(373)~ 108.8(650)d 10"' (77C855)" (a) R.Hiatt and S. W. Benson J. Amer. Chem. Soc. 1972,94,25 6886. (h) R. Hiatt and S. W. Benson Infernat. J. Chem. Kinetics 1972 4 151. (c) R. Hiatt and S.W. Benson ibid.1973,5 385. (d)Ref. 12. (e) R. M. Marshall and J. H. Purnell J.C.S. Chem. Comm. 1972 764. V) P. D. Pacey and J. H. Purnell Infernat. J. Chem. Kinetics 1972. 4 657. (g) Ref. 54. Three methods have been used to obtain these numbers. The radical buffer technique which depends for its success on the establishment of an equilibrium of the type R' + R'I R'I + R2 in the system probably has a precision of only an order of magnitude since the rate constant depends on estimates of other rate constants and thermochemistry. Similar comments apply to rate constants obtained from hydrocarbon pyrolysis. The VLPP data significantly different from the other two sets are as yet only preliminary. The picture may of course be clouded by activation energy effects although no trends are apparent.It is clear that these radicals do not combine at every collision as was once thought. 41 L. R. Mahoney G. D. Mendenhall and K. U. Ingold J. Amer. Chem. Soc. 1973 95 8610. 42 J. A. Kerr ref. 4 p. 1. 43 (a) F. K. Truby and J. K. Rice Internar. J. Chem. Kinetics 1973 5 721; (b) F. Bayrakceken J. H. Brophy R. D. Fink and J. E. Nicholas J.C.S. Furaduj I 1973 69 228. 44 A. M. Bass and A. H. Laufer Internat. J. Chem. Kinetics 1973 5. 1053. Gas-phase Kinetics and Mechanisms 73 However the particularly low value for t-butyl radical recombination is also hard to swallow in view of the known consistency of radical cross-combination ratios with the geometric mean rule.45 2-Methallyl radicals43 recombine with k = dm3 mol-' s-l a value higher than that for all~l,~~ but there is evidence that for 1-methallyl and more highly substituted ally1 radicals:' recombination rates are less at the more substituted end implying the same trend as for alkyl radicals.Other recombina- tion rate constants recently determined include those for C2H3 ,48u CF :8b NH CONH ,49b CF,CCl ,50 and CH302 .I4 Disproportionation+om-bination ratios have not excited much attention this year. An expected isotope effect was observed for 2CF,H(CF,D)+ CF + CF,H,(CF2D2).51 A useful catalogue of values often individually buried in work of another concern has been p~blished.~' Radical-Molecule Reactions.-Amongst hydrogen-atom abstraction studies the year has been marked by an increasing number of claims of non-Arrhenius behaviour for these processes.The reactions of CH with H2,53 C2H6,53 iso-C4H and ne~-c,H,,~~ fall into this category. Curvature in Arrhenius plots is not usually observable in a single study over a limited temperature range but is apparently necessary to reconcile the results from low-temperature photolytic systems (300-500 K) with intermediate-temperature pyrolyses (600-900 K) and high-temperature (> 1000 K) shock-tube studies. There are a number of theoretical reasons why such curvature might occur and Clark and Dove have performed modified BEBO calculation^^^ which produce rate-constant expres- sions of the form AT" exp (-V/RT)where in practice n 21 M for the models chosen. These values of n are higher than the classical limit of transition-state theory would allow and in the opinion of this reviewer seem to imply something rather unrealistic about the frequency assignment of the transition state.It is also apparent that for some of the reactions investigated the scatter in the experi- mental data obtained within a given temperature range but by different sets of workers is enough still to permit linear Arrhenius plots within experimental error. These problems must clearly be more fully investigated before claims of significant curvature are generally accepted. 45 J. 0.Terry and J. H. Futrell Canad. J. Chem. 1968,46 664. 46 H. E. van den Bergh and A. B. Callear Trans. Faraday Soc. 1970,66,2681. 47 D. C. Montague Internat. J. Chem. Kinetics 1973 5 513. 48 (a) K. 0. MacFadden and C.L. Currie J. Chem. Phys. 1973 58 1213; (b) R. Hiatt and S. W. Benson Internat. J. Chem. Kinetics 1972,4 479. 49 (a)T. Yokota and R. A. Back Internat. J. Chem. Kinetics 1973,5 37; (b) R. A. Back and T. Yokota ibid. p. 1039. 50 R. F. Cullison R. C. Pogue and M. L. White Internat. J. Chem. Kinetics 1973 5 415. st G. 0.Pritchard and D. W. Follmer Internat. J. Chem. Kinetics 1973,5 169. 52 M. J. Gibian and R. C. Corley Chem. Reu. 1973,73 441. 53 T. C. Clark and J. E. Dove Canad. J. Chem. 1973,51. 2147,2155. 54 R. S. Konar R. M. Marshall and J. H. Purnell Internat. J. Chem. Kinetics 1973 5 1007. 55 P. D. Pacey Canad. J. Chem. 1973.51 2416. 74 R. Walsh Other hydrogen-atom abstraction studies have been reported for C,H,56 CF3:7*58 and NH2,49bas well as chlorine-atom transfer by Me3SiS9 and Me3Sn,60 and where Arrhenius parameters have been measured they seem generally reason- able.Because of the advantages of e.s.r. detection of radicals an increasing number of solution studies are appearing in this area. Where non-polar solvents are used Arrhenius parameters are probably transferable to the gas phase. One such study6' reports activation energies for halogen transfer to Bu';Sn and in BuI;Pb radicals. Substituent effects on atom transfers are usually accounted for by a judicious mixture of bond-energy and polar effects. Zavitsas6' has ques- tioned whether the latter are necessary in all cases but the answer would appear to be yes since even with non-polar radicals like Bu' polar effects are evident.63 Some new empirical schemes for predicting activation energies (within 4-8 kJ mol-') have a~peared.~~.~~ Their accuracy is as good as that of the BEBO method.Some relative rates for hot CH366*67 are reported as well as an abstrac- tion by CH at 77 K,68which if it really occurs must be a hot reaction since the activation energy otherwise implied is far too low. The debate over anchimeric assistance by /3 bromine in radical abstractions still rage^,^^.^' but the evidence from the gas phase7' at any rate suggests little effect although the conformation of /I-bromoalkyl radicals7' (and indeed other #I-halogenoalkyl radicals in general7,) is such as to inhibit backside attack in subsequent transfer processes to the radical7' A molecular-beam study of methyl with the halogens has found predominantly backward product scattering implying short-range repulsive interactions.New data on fluoroalkyl radical^'^ and CFBr,76 addition to fluoro-olefins supports earlier conclusions that addition is favoured at the least fluorinated 56 C. F. Cullis D. J. Hucknall and J. V. Shephard Proc. Roy. SOC.,1973 A335 525. 57 M. H. Arican E. Potter and D. A. Whytock J.C.S. Furuduyl 1973 69 1811. 58 N. L. Arthur and B. R. Harman Austral. J. Chem. 1973 26 1269. 59 P. Cadman G. M. Tilsley and A. F. Trotman-Dickenson J.C.S. Furaday I 1973.69 914. 60 D. A. Coates and J. M. Tedder J.C.S. Perkin 11 1973 1570. 61 J. Cooper A. Hudson and R. A. Jackson J.C.S. Perkin 11 1973 1056. 62 A.A. Zavitsas and J. A. Pinto J. Amer. Chem. SOC.,1972 94 7390. 63 W. A. Pryor W. H. Davis and J. P.Stanley J. Amer. Chem. SOC.,1973,95 4754. 64 Z. B. Alfassi and S. W. Benson Internat. J. Chem. Kinetics 1973,5 879. 65 R. R. Baldwin and R. W. Walker J.C.S. Perkin 11 1973 5 361. 66 J. K. Rice and F. K. Truby Chem. Phys. Letters 1973 19 440. 67 C.-T. Tingand R. E. Weston J. Phys. Chem. 1973 77 2257. 68 E. D. Sprague J. Phys. Chem. 1973,77 2066. 69 E. S. Lewis and S. Kozuka J. Amer. Chem. SOC., 1973,95282. 70 (a)K. J. Shea and P. S. Skell J. Amer. Chem. SOC.,1973 95 283; (b)P. S. Skell R. R. Pavlis D. C. Lewis and K. J. Shea ibid. p. 6735; (c)K. J. Shea D. C. Lewis and P.S. Skell ibid. p. 7768. 71 D. S. Ashton J. M. Tedder M. D. Walker and J. C.Walton J.C.S. Perkin II 1973 1346. 72 J. H. Hargis and P. B. Shevlin J.C.S. Chem. Comm. 1973 179. 73 (a)J. Cooper A. Hudson and R. A. Jackson Tetrahedron Letters 1973 831 ; (b)K. S. Chen I. H. Elson and J. K. Kochi J. Amer. Chem. SOC.,1973 95 5341. 74 D. L. McFadden E. A. McCullough F. Kolos and J. Ross J. Chem. Phys. 1973,59 121. 75 D. S. Ashton A. F. MacKay J. M. Tedder D. C. Tipney and J. C. Walton J.C.S. Chem. Comm. 1973,496. 76 J. P. Sloan J. M. Tedder and J. C. Walton J.C.S. Furaday I 1973 69 1143. Gas-phase Kinetics and Mechanisms 75 site and that relative rates are largely although not entirely attributable to varia- tions in activation energy. The addition of acetyl to butadiene is competitive with its thermal fragmentati~n.~~ Some results on atom and radical addition to olefin not in the gas phase but nevertheless of interest to kineticists were reported from the rotating cryo~tat.~~ A number of other addition rate constants are collected in Table 2.Table 2 Radical-addition reactions log1 0 log10 (k/dm3 (A/dm3 Reaction mol-'~-~) mol-'~-~) E/kJmol-' Temp./K Me + SO +MeSO 8.24 298" Et + CO+ EtCO 8.19 20.0 238-37gb Me0 + CO-+ Me + CO 10.2 49.4 396-426' OH + C,H,-+ 9.65 3.8 230-470d CZH + 9.08 8.8 230-470'' ,SO + cis-C,H,+ 11.21 298' ,SO + trans-C,H,+ 11.15 298' CF + CF,NO+ (CF,),NO >7.77 329/ (a)F. C. James J. A. Kerr and J. P. Simons J.C.S. Furuduy I 1973,69,2124. (b)Ref. 89 (c) E. A. Lissi and G. Massif J.C.S. Furaduy I 1973 69 346. (6)I.W. M. Smith and R. Zellner J.C.S. Furuday 11 1973 69 1617. (e) R.A. Cox J. Photochem. 1973 2 1. (f)H.-S. Tan and F. W. Lampe J. Phys. Chem. 1973,77 1335. The first example of a radical displacement (S,2) process at aliphatic un- strained saturated carbon has been observed7' in the gas-phase reaction CF + neo-C,H,,+ CF,CH + But although rate constants have yet to be measured and the process is a minor one in the system. This displacement process and its kinetics at metal and other centres are increasingly under investigation in solution.80 In the ring-opening of cyclopropane by Br stereochemical studies have proved a Walden inversion mechanism at the displacement centre.' ' Unimolecular Radical Reactions.-The intramolecular rarrangements of hydro-carbon radicals in the gas phase have been reviewed.82 Watkins' has obtained for n-hexyl- s-hexyl log (k/s-') = 9.41 -47 kJ mol-'/2.303RT.The 'A' fac-tor although low corresponds to the loss of four internal rotors in the transition state and is therefore reasonable. Not so reasonable however are values in some l7 M. V.Encina and E. A. Lissi J.C.S. Faruduy I 1973,69 1505. '~3 J. E. Bennett and B. Mile J.C.S. Furuduy I 1973 69 1398. 79 R. A. Jackson and M. Townson Tetrahedron Letters 1973 193. A. G. Davies and B. P. Roberts Accounts Chem. Res. 1972 5 381. (a)G. G. Maynes and D. E. Appelquist J. Amer. Chem. SOC.,1973,95 856; (b)K. J. Shea and P. S. Skell ibid. p. 6728. 82 A. D. Stepukhovitch and V. I. Balaban Russ. Chem. Rev. 1972,41,750. 83 K.W. Watkins J. Phys. Chem. 1973 77,2938. 76 R. Walsh cases as low as lo7-lo8 s-’,for such processes supported by Mintz and LeRoyg4 on the basis of calculations on chemically activated radicals. The entropies of the transition states implied by these numbers are significantly lower than those of known cyclic molecules of similar ~tructure,~~ and the proposal of a previously unconsidered configurational entropy adjustment84 does not avoid this dilemma. Much higher ‘A’ factors ca. 10’2.2s-’ are obtained for the similar internal H transfer in photo-excited ketones the Norrish Type I1 process.86 A calc~lation,~ based on Forst’s simplified version of thermal unimolecular reaction theory,88 has been used to show that the pressure dependence of acetyl radical decomposition is more consistent with a high-pressure ‘A’ factor ca.10’2.5s-’,rather than with the previous reported value of s-’. The kinetics of 2-methallyl decomp~sition~~” have been investigated ;those of both propiony18 9b and amid^^^^ radical decompositions have been reinvesti- gated. Methylene and Sily1ene.-The thermochemistry of methylene is still a controver- sial subect. Theoretical calc~lations~~ suggest an energy separation of 46 f.8 kJ mol- ’between triplet (3B1)and singlet (‘A’) methylene. Aclosely similar value is supported by Frey91 on the experimental grounds of approximate relative reactivities of the singlet and triplet. A smaller value of ca. 12 kJ mol-is favoured by Carr9 from the observation that 10% of the products from methylene re- actions in the 355 mm photolysis of CH2C0 come from the singlet form.But ‘CH is known to be much more reactive than 3CH2,93,94 and so this observa- tion must in fact correspond to much less than 10%of the methylene itself being in the singlet form. Indeed if Frey’s argument is correct the reactivity difference is such that at 355 nm only 3CH can be formed and the ‘CH must come entirely from collisionally induced (reverse) intersystem crossing from 3CH,. More recently Carrg5 has argued that the smaller energy difference is supported by chemical activation studies. These latter were interpreted with a stepladder (weak collision) model for deactivation. That such models are required is almost certain in one case where impossible energetics would otherwise result.96 How- ever the insensitivity of experimental parameters (curvature in D/S against pressure-’ plots) to details of the model make these chemical activation 84 K.J. Mintz and D. J. LeRoy Canad. J. Chem. 1973 51 3534. 85 H. M. Frey and R. Walsh Chem. Rev. 1969,69 103. 86 J. Grotewold D. Soria C. M. Previtali and J. C. Scaiano J. Phorochem. 1973,1 471. H. M. Frey and I. C. Vinall Internat. J. Chem. Kinetics 1973 5 523. 88 W. Forst J. Phys. Chem. 1972 76 2507. (a)W. Tsang Internat. J. Chem. Kinetics 1973 5 929; (6)K. W. Watkins and W. W. Thompson ibid. p. 523. C. F. Bender H. F. Shaefer D. R. Franceschetti and L. C. Allen J. Amer. Chem. SOC. 1972,946888. ’’ H. M. Frey T.C.S. Chem. Comm. 1972 1024. 92 R. W.Carr T. W. Eder and M. G. Topor J. Chem. Phys. 1970 53 4716. 93 W. Braun A. M. Bass and M. Pilling J. Chem. Phys. 1970,52 5131. 94 P. S. T. Lee R. L. Russell and F. S. Rowland Chem. Comm. 1971 18. 95 M. G. Topor and R. W. Carr J. Chem. Phys. 1973,58,757. 96 H. M. Frey G. R..Jackson M. Thompson and R. Walsh J.C.S. Faraday I 1973,69 2054. Gas-phase Kinetics and Mechanisms 77 at best poor guides to the thermochemistry of methylene. In one recent study9* the calculated energies quoted were actually incorrect owing to an insufficient vibrational assignment having been made for the activated molecule and its complex. In less controversial areas relative insertion rates by 'CH in alkanes have been ~ummarized.~~ A revised f numberloo for the 3A,-3B1 transition in CH means that earlier quoted absolute rate constants93 need numerical correction.Vacuum-u.v. photolytic sources101p102 produce methylene with a large spread of energy which is carried over into reaction. 1.r. chemiluminescent emission from CO in the reaction of CH with 0 has been interpreted as arising from highly excited formic acid molecule^.'^^ Emission from CH has been seen in flames.lo4 An up-to-date summary of the chemistry of methylene has recently appeared.'O5 From relative rate constant measurements in mixed silane pyrolyses and the reasonable assumption that AH (SiH,) = 242 kJ mol-' Purnell and John'06a have derived absolute rate constants for SiH insertions into H, SiH4 and Si,H,. Relative rates of insertion into a wide variety of substrates are reported.lo6' SiH will add 1,4 to butadiene.'" Si2H4 is probably produced in the pyrolysis of Si3H81°6 and the authors argue that it is more likely to be the species SiH3SiH than SiH,SiH,.Some GeH relative insertion rates have been reported."' Complex Reactions involving Radicals.-These are always difficult to assess but in the absence of a complex knowledge of likely elementary steps together with detailed computer modelling thermochemical criteria lo9 can be used to judge the validity of mechanisms proposed. This has been done in the case of some recent pyrolyses of oxalates' lo and aromatic compounds. '' Amongst paraffin pyrolyses that of iso-C4Hlo shows self-inhibition owing to rapid formation of unreactive 2-methallyl radicals arising from the initially formed product iso- C,H8.Azomethane has been commonly used as a photolytic source of methyl 97 W. L. Hase R. J. Phillips and J. W. Simons Chem. Phys. Letters 1971 12 161. 98 G. B. Kistiakowsky and B. B. Saunders J. Phys. Chem. 1973,77,427. 99 M.L. Halberstadt and 1. Crump J. Phorochem. 1973 1 295. loo J. K. Little and M.J. Pilling J. Photochem. 1973 1 337. lo' P. Ausloos R. E. Rebbert and S. G. Lias J. Photochem. 1973 2 267. lo' K. Dees and R. D. Koob J. Phys. Chem. 1973,77 759. Io3 R. J. Gordon and M. C. Lin Chem. Phys. Letters 1973 22 107. Io4 A. Jones and P. J. Padley Chem. Phys. Letters 1973 20 104. Io5 W. J. Baron M.R. Decamp M. E. Hendrick M. Jones R. H. Levin and M. B. Sohn in 'Carbenes. Vol. I' ed. M.Jones and R. A. Moss Wiley-Interscience 1973 Chap. 1. (a) P. John and J. H. Purnell J.C.S. Furaday I 1973 69 1455; (b) M. D. Sefcik and M. A. Ring J. Amer. Chem. SOC. 1973,95 5168. lo' G. P. Gennano Y.-Y.Su 0. F. Zeck S. H. Daniel and Y.-N. Tang J.C.S. Chem. Comm. 1973 637. log M. D. Sefcik and M.A. Ring J. Organometallic Chem. 1973 59 167. S. W. Benson 'Thermochemical Kinetics' Wiley 1968. 'lo R. Louw M. van den Brink and H. P. W. Vermeeren J.C.S. Perkin 11 1973. 1327. 'IL (a) R. Louw J. W. Rothuizen and R. C. Wegman J.C.S. Perkin If 1973 1635; (b)R. Louw and H. J. Lucas Rec. Trav. chim. 1973,92 55. R. Walsh radicals but its uninhibited pyrolysis has only just been reported' '' in any detail. The system is very complex producing several nitrogen-containing products as well as hydrocarbons and there is evidence for CH and C2H as well as CH as intermediates.High-temperature exchange in the system toluenedeuterium produces ;-order kinetics' ' and a relative positional reactivity for D atoms in addition to toluene of o > rn > p. The mercury-photosensitized decomposition of hydrocarbons has been an important source of alkyl radicals in the past and a unified mechanism for the primary interaction of the excited Hg (of both 63P1 and 63P0)with the alkane has been presented.' l4 In the oxidation of alkenes an oxygen-labelling experiment' l5 has shown that the peroxyl radical I >C(OH)-C-0; breaks down to ketone products without abstracting hydro- I gen intermolecularly to become a hydroperoxide.Methyl isocyanide is argued to be an important molecule in testing thermal explosion theory.'16" The anti- knock phenomenon is discussed in a shock-tube study of the decomposition of tetraethyl-lead. ' With increasing concern over air pollution it is hardly surprising that ozone- olefin reactions are increasingly receiving attention from kineticists. Niki and co-workers have recently measured some gas-phase second-order rate constants for this reaction."' In solution the reaction leads to ozonide formation (the initial molozonide having only recently been detected' l8 at low temperature) but in the gas phase ozonide is not observed and a large variety of other products largely ketones aldehydes and acids is observed.' l9 The mechanism in solu- tion although still controversial,'20 is believed to involve an aldehyde oxide the +-so-called 'Criegee Zwitterion' RCHOO.O'Neal and Blumstein' '' have argued against this mechanism being operative in the gas phase and in favour of bi- radical and monoradical intermediates. Pitts and co-workers' 22 have obtained mass spectrometric evidence for radical intermediates as well as for formation of an a-carbonyl hydroperoxide an important although not very stable product. 5 Molecular Reactions Decomposition to Radicals.-A simple classification of molecules into small and large on the basis of whether thermal fragmentations are at (or near) the low- or 'I2 (a) H. Knoll K. Scherzer and G. Geiseler Z. phys. Chem. (Leipzig) 1972 249. 359; (b) Y.Paquin and W. Forst Internat. J. Chem. Kinetics 1973 5 691. Y. Sato and A. Amano BUN. Chem. SOC. Japan 1973,46,2646. 'I4 (a) H. E. Gunning J. M. Campbell H. S.Sandhu and 0.P.Strausz J. Amer. Chem. SOC.,1973,95 740; (6)J. M. Campbell 0.P.Strausz and H. E. Gunning ibid. p. 746. D. J. M. Ray A. Redfearn and D. J. Waddington J.C.S. Perkin II 1973 540. IL6 (a) H. 0.Pritchard and B. J. Tyler Canad. J. Chem. 1973 51 4001; (b)J. B. Homer and I. R. Hurle Proc. Roy. SOC.,1972 A327,61. '17 D. H. Stedman C. H. Wu,.and H. Niki J. Phys. Chem. 1973 77 251 1. W. G. Alcook and B. Mile J.C.S. Chem. Comm. 1973 575. I l9 Y. K. Wei and R. J. Cvetanovic Canad. J. Chem. 1963 41 913. I2O For leading references see P. S.Bailey T. P. Carter C. M. Fischer and J. A.Thompson Canad. J. Chem. 1973,51 1279. H. E. O'Neal and C. Blumstein Internat. J. Chem. Kinetics 1973 5 397. R. Atkinson B. J. Finlayson and J. N. Pitts J. Amer. Chem. SOC.,1973 95 7592. Gas-phase Kinetics and Mechanisms high-pressure limits for unimolecular behaviour would appear possible. In the former category activation energies are always less than bond dissociation energies and rate measurements usually made with the shock tube have to be related to high-pressure limiting values via unimolecular reaction theory and a knowledge of the collisional characteristics of the system. In this area studies have appeared on decompositions of C02.123NOBr,'24 NOCl,124BrCN,12' NH3,126 NF3,12' CH4,12*SF,,129SF,C1,129 C2H4,13' and N2F4.131 RRKM theory has been applied to some such and methods have been given for estima- ting specific rate constants from spectroscopic data.133 In the large molecule category direct measurements of the rate as a function of temperature will give the high-pressure Arrhenius parameters ;however even here the VLPPtechnique as mentioned requires theory in order to produce them. A selection of data is given in Table 3. Not quoted in the table but of some interest was a study by Table 3 Molecular fragmentation (bond-breaking) reactions Reaction ElkJ mol - Ternp./K C2H6- 2CH3 374' 1200-1400' BusCH2C(Me)=CH C2CI6-+ 2CC13 +Bus + CH,C(Me)=CH 15.6 17.7 276 286 950-1 1 Sod 61 3-473' MeCOCOMe-2MeCO CF,CHO-* CF + CHO Et,CCEt -+ 2Et,C" 16.5 17.0 16.6 283 347 218 648-690' 7 3 3-7 939 542-570h Am'OOAm' +2Am'O 15.8' 1 52' 523433' EtN=NEt -+EtN=N + Et Pr'N=NPr' -+ Pr'N=N + Pr' Bu'N=NBu'-* Bu'N=N + Bu' 16.4' 16.6' 16.4' 208* 200' 179' 670-950' 630-820' 550-710' Me,Tl* Me,TI + Me 15.1 152 452-536k Me,SiSiMe +2Me,Si 17.5 337 7 70-8 72' (a) In solution (probably).(b)Corrected by RRKM theory. (c)A. Burcat G. B. Skinner R. W. Crossby and K. Scheller Internat. J. Chem. Kinetics 1973 5 345. (d) W. Tsang ibid. p. 929. (e)M. L. White and R. R. Kuntz ibid. p. 187. (f)H. Knoll K. Scherzer and G. Geiseler ibid. p. 271. (g)M. T. H. Liu L. F. Loucks and R. C. Michaelson Canad. J. Chem. 1973 51 2292. (h) M.-D. Beckhaus and C. Ruchardt Tetrahedron Letters 1973 197 1. (i) M. J. Perona and D. M. Golden Internat. J. Chem. Kinetics 1973,5,55.Cj Ref. 13. (k)S. J. Price J. P. Richard R. C. Rumfeldt and M.G. Jacko Canad. J. Chern. 1973 51 1397. (0 Ref. 35. lZ3 A. M. Dean J. Chem. Phys. 1973,58 5202. 124 K. K. Maloney and H. B. Palmer Internat. J. Chem. Kinetics 1973 5 1023. Iz5 P. J. Kayes and B. P. Levitt J.C.S. Furuduy I 1973 1413. IZ6 G. A. Vompe Russ.J. Phys. Chem. 1973,47 715. 12' K. 0. MacFadden and E. Tschuikow-Roux J. Phys. Chem. 1973 1475. IZ8 G. A. Vompe Russ.J. Phys. Chern. 1973,47 788. Iz9 A. P. Modica J. Phys. Chem. 1973 77 2713. P. Rost and T. Just Ber. Bunsengesekhaftphys. Chem. 1973,77 11 14. 13' E. Tschuikow-Roux K. 0. MacFadden K. H. Jung and D. A. Armstrong J. Phys. Chem. 1973,77 734. 132 W. Tsang Internat. J. Chern. Kinetics 1973 5 947. 133 M. Quack and J.Troe Ber. Bunsengesellschafr phys. Chem. 1973,77 1020. 80 R. Wulsh Crawford 34 which demonstrated that azoalkane fragmentation is a single-bond- breaking consecutive-step reaction in the gas phase. The situation is more confused in solution'35 where a spectrum of behaviour seems possible. cis-Azoalkanes which may be implicated as intermediates in trans-azoalkane pyroly- 'A' Factors in the range 10"- sis are mysteriously considerably less ~tab1e.I~~ 10" s-have been obtained using Forst theory" applied to chemically activated alcohol R-OH bond-breaking reaction^.'^' However it is not clear whether these estimates have any validity since the theory is applicable only to thermal and not to chemical activation rate constants.88 Molecular Rearrangements and Eliminations.-The pursuit of the mechanisms of these processes is still a major activity amongst organic chemists.The choice has been seen until recently as usually lying between 'concerted' (symmetry- allowed' 38 or ar~matic'~~) pathways or two-step mechanisms involving bi- radicals. Theoretical (MO type) calc~lations'~~ suggest that symmetry-forbidden processes can in some cases compete effectively with biradical pathway^.'^' The concerted symmetry-forbidden transition state is stabilized by interaction of an orbital in a migrating group with a lower occupied (subjacent) MO of the residual molecular framework and may as a result be lower in energy than the biradical. This means that the interpretation of stereochemical labelling experi- ments hitherto regarded as one of the best tests for concertedness is considerably complicated.Stereochemical randomization may result either from intervention of a biradical or from a mixture of concerted allowed and forbidden processes. Some particularly subtle stereochemical experiments have been carried out by the groups of Ber~on'~~~?'~~ Most of these centre around the 1,3- and Ba1d~in.l~~ sigmatropic carbon shift. Ber~on,'~~~ for example has been able to show that in the isomerization of trans-1,2-truns,truns-dipropenylcyclobutane, of four possible stereochemical pathways in the isomerization to 3-methyl-4-trans- propenylcyclohexene effectively only two occur. This is argued as evidence against a biradical since although the two observed processes occurring in approximately equal proportions correspond to one allowed and one forbidden pathway a freely internally rotating biradical would presumably permit all four possibilities.This may well be so but until more is known about the properties 134 R. J. Crawford and K. Takagaki J. Amer. Chem. SOC.,1972 94 7406. 135 (a)N. A. Porter L. J. Marnett C. H. Lochmuller G. L. Closs and M. Shobataki J. Amer. Chem. SOC.,1972 94 3664; (6)J. Hinz A. Oberlinner and C. Riichardt Tetrahedron Letters 1973 1975. 136 N. Porter and M. 0.Funk J.C.S. Chem. Comm. 1973 263. 13' K. J. Mintz and R. J. Cvetanovic Canad. J. Chem. 1973,51 3386. 138 R. B. Woodward and R. Hoffmann 'The Conservation of Orbital Symmetry' Verlag Chemie and Academic Press 1970.139 M. J. S. Dewar Angew. Chem. Internat. Edn. 1971 10 761. I4O (a)J. A. Berson and L. Salem J. Amer. Chem. SOC.,1972,94 8917; (b)W. T. Borden and L. Salem ibid. 1973 95 932. I4I (a)J. E. Baldwin A. H. Andrist and R. K. Pinschmidt Accounts Chem. Res. 1972,5 402; (b)J. A. Berson ibid. p. 407. 142 (a)J. A. Berson and P. B. Dervan J. Amer. Chem. SOC.,1973 95 267 269; (6)J. A. Berson and R. W. Holder ibid. p. 2037. 143 J. E. Baldwin and R. H. Fleming J. Amer. Chem. SOC.,1973 95 5249 5256 5261. Gas-phase Kinetics and Mechanisms 81 of biradicals and particularly their internal rotation rates relative to reclosure,' 44 this issue cannot be regarded as settled. Arrhenius activation energies have been another useful criterion of mechanism in the past.Two problems have recently been highlighted. The first is the dis- crepancy between theory and thermochemical calculation of biradical ener- gie~.'~~.'~~ Theoretical estimates put the energies of both 1,3 and 1,4 biradicals about 25-40 kJ mol- ' above thermochemical estimate^.'^^ The reason for this is not clear. Secondly substituent effects such as the lowering of activation energies by vinyl of 50-60 kJ mol- ',often taken in the past as evidence for a biradical process have to be treated with caution since the discovery that in concerted processes which are slightly polar in nature similar activation energy reductions can be a~hieved.'~' Interestingly phenyl substituent effects have been regarded as diagnostic for both concerted f~rbidden'~'" and biradical processes.'48 Measurements of both Arrhenius parameters for a reaction can obviously still serve as a useful guide to mechani~rn,"~ but interpretations have to be treated with some caution.Only a limited selection of the large number of studies in this area can be included and reference to the original papers should be made for rate data. Rearrangements. A competitive single-pulse shock-tube study' 49 on cyclo-propane shows that up to 1300K,the rate of isomerization to propylene fits lower-temperature data well with a slight but reasonable correction for 'fall-off '. This study casts doubt on the strange effects claimed to occur in other shock-tube studies of this rea~tion."~ Contrary to earlier reports methyl elimination from the biradical intermediate formed from tetramethylcyclopropane is not competi- tive with i~omerization'~'~ up to 1100 K.However methyl elimination does occur from 1,3-biradicals formed in other ways.' lb Substituent effects on cyclo- propane isomerization have been reported for NH ,'52 CN,31 COMe,29 MeO,lS3 and C6HS.lS3 In a series of studies of the epimerization of substituted cyclopropanes in solution Cram and co-workers have shown that both 144 (a)H. E. O'Neal and S. W. Benson J. Phys. Chem. 1968,72 1866; (6)R. G. Bergman and W. L. Carter J. Amer. Chem. SOC. 1969,91 741 1. (a) J. A. Horsley Y. Jean C. Moser L. Salem R. M. Stevens and J. S. Wright J. Amer. Chem. SOC.,1972 94 279; (6) P. J. Hay W. J. Hunt and W. A. Goddard ibid. p. 638.146 L. M. Stephenson T. A. Gibson and J. I. Brauman J. Amer. Chem. SOC. 1973 95 2849. 14' K. W. Egger Internat. J. Chem. Kinetics 1973 5 285. 148 M. J. S. Dewar and L. E. Wade J. Amer. Chem. SOC. 1973.95 290. P. Jeffers D. Lewis and M. Sarr J. Phys. Chem. 1973 77 3027. I5O (a)J. N. Bradley and M. A. Frend Trans. Faraday Suc. 1971,67 72; (6)E. A. Dorko R. W. Crossley U. W. Grimm G. W. Mueller and K. Scheller J. Phys. Chem. 1973 77 143. Is' (a) W. Tsang Internat. J. Chem. Kinetics 1973 5 651; (b) E. B. Klunder and R. W. Carr J. Amer. Chem. SOC. 1973,95 7386. 152 (a) K. A. W. Parry and P. J. Robinson Internat. J. Chem. Kinetics 1973 5 27; (b) D. A. Luckraft and P. J. Robinson ibid. p. 329. J. M. Simpson and H. G. Richey Tetrahedron Letters 1973 2545.82 R. Walsh biradi~al''~and zwitterionic"' intermediates can occur. In the gas phase bi- radicals seem to be the rule and a useful case history of trimethylene summariz- ing both theoretical and experimental work has been published.lS6 In the rearrangement of the substituted cyclopropane exo-tricycl0[3,2,1,0~~~]oct-6-ene,'" a labelling experiment shows the occurrence of an interesting [2 + 2 + 21 process involving two CT components. Vinyl carbenes are implicated in the isomerization of cyclopropenes. 58 Racemization occurs considerably faster than isomerization for an optically active cyclopropene'58b and thus the vinyl carbene seems to show the same propensity to ring-close as trimethylene in spite of the increased strain of the product.Epoxide isomerizations under favourable circumstances occur with C-C bond splitting via a carbonyl ylide,' s9 although usually rearrangement via C-0 bond-breaking predominates.' 6o Further stereochemical evidence16' and iso- tope effects '62 support the intermediacy of a non-planar trimethylenemethane in methylenecyclopropane isomerization. Disagreement over mechanism exists for vinylmethylenecyclopropane rearrangements.'63*'64 Among Cope rearrange-ments that of the long-sought-after cisdivinylcyclopropane was noteworthy. 65 The complicated mechanism situation in the vinylcy~lobutanes'~~ and methyl- enecyclobutanes' 43 has already been mentioned. A 1,3-sigmatropic shift of silicon occurs with inversion. 166 In bicyclic versions of cyclobutane ring-opening reactions alternative pathways are very close in energy.In the bicyclo[2,2,0]- hexanes stereochemical studies '" support a concerted allowed process whereas thermochemistry ' favours an intermediate biradical. The same biradical is implicated in some Cope rearrangement^.'^^ Bicyclo[2,1 llhexane isomerization is non-stereo~pecific.'~~ Hot-molecule effects were observed in rearrangements amongst some C8Hloisomers'70 in the gas phase and one of the likely interme- diates a bis-2,2-biallyl biradical (tetramethylene-ethane) was detected in solution I54 A. B. Chmurney and D. J. Cram J. Amer. Chem. SOC. 1973,95,4237. 155 N. E. Howe E. W. Yankee and D. J. Cram J. Amer. Chem. SOC. 1973 95 4230. 156 R. G. Bergman ref. 14 Chap. 5 p. 191. 157 R.B. Kimnel and R. K. Freeman Tetrahedron Letters 1973 4803. I58 (a)R. D. Streeper and P. D. Gardner Tetrahedron Letters 1973 767; (6) E. J. York W. Dittmar J. R. Stevenson and R. G. Bergman J. Amer. Chem. SOC. 1973,95,5680. 159 R. J. Crawford V. Vukov and H. Tokonaga Canad. J. Chem. 1973,51 3718. 160 M. C. Flowers D. E. Penny and J. C. Pommelet Internat. J. Chem. Kinetics 1973,5 353. 161 W. von E. Doering and L. Birladeanu Tetrahedron 1973 29 499. 162 W. R. Dolbier and J. H. Alonso J. Amer. Chem. SOC. 1973 95 4421. 163 W. E. Billups K. H. Leavell E. S. Lewis and S. Vanderpool J. Amer. Chem. SOC. 1973,95 8096. 164 J. C. Gilbert and D. P. Higley Tetrahedron Letters 1973 2075. 165 J. M. Brown B. T. Golding and J. J. Stofko J.C.S. Chem. Comm. 1973 319.I66 J. Slutky and H. Kwart J. Amer. Chem. SOC. 1973 95 8678. 167 A. Sinnema F. van Rantwijk A. J. de Konig A. M. van Wijk and H. van Bekkum J.C.S. Chem. Comm. 1973 364. 168 E. N. Cain and R. K. Solly J. Amer. Chem. SOC. 1973 95 4791 7884. 169 L. A. Paquette and M. J. Kukla Tetrahedron Letters 1973 1241. 170 (a)W. R. Roth M. Heiber and G. Erker Angew. Chem. Internat. Edn. 1973 12 504; (b)W. R. Roth and G. Erker ibid. p. 505. Gas-phase Kinetics and Mechanisms 83 by CIDNP.17 Hot-molecule effects' 72 persist in bicyclopentene isomerization even in solution.'73 Two studies of trans-cis isomerization of hexa-1,3,5-triene were in reasonable agreement.174i1 75 Some rates were reported for the rarely observed 1,7-sigma- tropic hydrogen shift.' 76 Eliminations.Interest in four-centre eliminations from alkyl halides seems to be declining apart that is from HF eliminations.' 77 Considerable disagreements have existed in the past19 between the groups of Cadman and Tschuikow-Roux. Tsang' 78 has pointed out an inconsistency between the temperatures and times reported by Cadman et al. and recalculated some of their data. However the discrepancies are not entirely removed. clcl or three-centre elimination of HF occurs to about 18% of the total from chemically activated CH3CF2H.179 Other three-centre eliminations are observed from CHF2CF2SiF3 and CHF2CF2SiMe3 to give carbenes.'*' There have been a number of studies of acetates and their derivatives.' '-" All are broadly consistent with the cyclic six-centre polar transition state.A similar though less polar transition complex applies to allyl ether' 86 and allyl amine eliminations.' Molecular H2 elimina- tions are observed from cis-but-2-ene' 88a and ~yclopentene,"~ both undoubtedly via a 1,4 mechanism as was demonstrated in the reverse D,addition to cyclo- pentadiene.' The unimolecular H2 elimination from cyclohexa- 1,3-diene observable at low pressures and high temperatures probably occurs via bicyclo- 88b [3,1,0]hex-2-ene rather than a direct W. R. Roth and G. Erker Angew. Chem. Internat. Edn. 1973 12,503. 172 H. M. Frey and M. C. Flowers J. Amer. Chem. SOC. 1972 94 8636. (a)J. I. Brauman W. E. Farneth and M. B. D'Amore J. Amer. Chem. SOC. 1973,95 5043; (b)G. D. Andrews M. Davalt and J.E. Baldwin ibid. p. 5044. 174 S. W. Orchard and B. A. Thrush J.C.S. Chem. Comm. 1973 14. 175 W. von E. Doering and G. H. Beasley Tetrahedron 1973 29 2231. 176 M. Schabel and G. W. Klumpp Rec. Trav. chim. 1973,92,605. '17 M. V. C. Sekhar G. E. Millward and E. Tschuikow-Roux Internat. J. Chem. Kinetics 1973 5 363. l8 W. Tsang Internat. J. Chem. Kinetics 1973 5 643. 179 K. C. Kim D. W. Setser and B. E. Holmes J. Phys. Chem. 1973,77 725. 180 R. N. Haszeldine P.J. Robinson and W. J. Williams J.C.S. Perkin II 1973 1013 1018. G. Chuchari S. P. de Chang and L. Lombana J.C.S. Perkin II 1973 1961. G. Chuchari I. Martin and A. Maccoll J.C.S. Perkin 11 1973 663. la3 A. Maccoll and S.S.Nagra. J.C.S. Faraduy I 1973,69 1108. Ia4 D. B. Bigley and R. E. Gabbott J.C.S.Perkin II 1973 1293. N. J. Daly G. M. Hewiston and F. Ziolkowski Austral. J. Chem. 1973 26 1259. Ia6 H. Kwart S. F. Sarner and J. Slutsky J. Amer. Chem. SOC. 1973 95 5234. Ia7 K. W. Egger J.C.S. PerkinII 1973 2007. (a)Z. B. Alfassi D. M. Golden and S. W. Benson Internat. J. Chem. Kinetics 1973 5 991 ;(b)Z. B. Alfassi S. W. Benson and D. M. Golden J. Amer. Chem. SOC. 1973 95 4784. D. A. Knecht J. Amer. Chem. SOC. 1973,95 7933. I9O F. A. L. Anet and F. Leyendecker J. Amer. Chem. SOC. 1973,95 156. 84 R. Walsh A number of cyclobutanone decompositions have been reported,'47.' '*' 92 and these are usually consistent with a zwitterionic transition state with the positive centre at C-3 and the negative one at CO although one at least occurs via a biradi~al.'~~' 1,2-Dioxetans decompose with the emission of acetone phosphores~ence,~~~" and the high efficiency of this process argues for a con- certed rather than a biradical pathway.'93b At high Concentrations in solution a second-order quantum chain process can occur.194 A curious consecutive step with concerted biradical decomposition is proposed for 1,2-dioxan (a cyclic peroxide) decomposition for which an unreasonably low 'A' factor of lo''.' s-was ~btained."~ Vinyldiazirine is believed to decompose in two steps.lg6 Molecule-Molecule Reactions.-Bimolecular hydrogen-atom transfers produce radicals which can initiate chains. Rates have been measured for propy1enelg7 and for Me2PH + C2F4.Ig8 High 'A' factors of 10" and 10" dm3 mo1-l s-' were obtained as e~pected."~ For the acid-base reactions of BF with amines very fast rates were obtained,*" whereas for NH + HCl --* NH4Cl apparently less than one collision in lo6 was effective.201 Cycloadditions of halogeno-olefins known to proceed via biradicals can occur with surprising stereo- specificity.202 Just like hydrogen halides,'03 acetic acid204 can catalyse molecu- lar elimination.6 Chemical Activation In addition to possible departures from RRKM theory uncovered in molecular- beam studies,' fluorescent lifetime and quantum yield rneas~rernents~~' reveal a non-random energy distribution in vibronic states which precede dissociation in bromo- and chloro-acetylene. However the RRKM theory seems to apply well to many chemical activation systems on large molecules at not too high excitation energies.206 Remaining uncertainties centre around the efficiency of (a) K.W. Egger J. Amer. Chem. SOC. 1973 95 175; (6) K. W. Egger Internat. J. Chem. Kinetics 1973,5 285; (c)A. T. Cocks and K. W. Egger J.C.S. Perkin II 1973 835. H. M. Frey and H. Hopf J.C.S. Perkin II 1973 2016. (a)N. J. Turro H.-C. Steinmetzer and A. Yekta J. Amer. Chem. SOC. 1973,956468; (b)N. J. Turro and P. Lechtken ibid. p. 265. (a) P. Lechtken A. Yekta and N. J. Turro J. Amer. Chern. SOC. 1973 95 3027; (6)T. Wilson M. E. Landis A. Baumstark and P. D. Bartlett ibid. p. 4765. W. Adam and J. Sanabia Angew. Chem. Internat. Edn. 1973 12 843. M. T. H. Liu and K. Toriyama Canad. J. Chem. 1973,51 2393. M. Simon and M.H. Back Canad. J. Chem. 1973,51,2934. R. Brandon R. N. Haszeldine and P. J. Robinson J.C.S. Perkin II 1973 1295. S. W. Benson Adv. Photochem. 1964 2 1. S. Glicker J. Phys. Chem. 1973,77 1093. '01 R. J. Countess and J. Heicklen J. Phys. Chem. 1973,77,444. '02 R. Wheland and P. D. Bartlett J. Amer. Chem. SOC. 1973 95 4003. '03 S. I. Ahonkhai and E. U. Emovon J.C.S. Faraday I 1973 69 183. '04 D. A. Karaitis V. R. Stimson and J. W. Tilley Austral. J. Chem. 1973 26 761. '05 K. Evans R. Scheps S. A. RiGe and D. Heller J.C.S. Faraday II 1973,69 856. '06 D. W. Setser 'Unimolecular Reactions of Polyatomic Molecules Radicals and Ions' in 'Chemical Kinetics' ed. J. C. Polanyi Series 1 Vol. 9 of M.T.P. International Review of Science (Physical Chemistry) Butterworths London 1972 Chap.1 p. 1. Gas-phase Kinetics and Mechanisms deactivating collisions. In alkyl fluorideszo7 and n-alkyl radicals2'' the strong collision assumption seems to hold whereas in some small-ring hydrocarbons' 5*96 and in photochemical systems209*210 inefficient collisions seem to be the rule. More detailed studies on simple well-defined systems such as those of Troezo9 are called for. This problem and the uncertainty in the energy carried over by methylene make some chemical activation studies on alkanes2' and silanes' rather poor guides to the nature of transition complexes for these molecules. Thus difficulties of reconciliation2" with other data2I3 for C2H,+ 2CH are probably not serious. 20' K. C. Kim and D. W.Setser J. Phys. Chem. 1973,77 2021. 208 E. A. Hardwidge B. S. Rabinovitch and R. C. Ireton J. Chem. Phys. 1973 58 340. '09 S.H. Luu and J. Troe Ber. Bunsengesellschaft phys. Chem. 1973,77 325. 210 S. W. Orchard and B. A. Thrush Proc. Roy. SOC.,1973 A329,233. 211 F. B. Growcock W. L. Hase and J. W. Simons Internat. J. Chem. Kinetics 1973 5,77. '12 W. L. Hase C. J. Mazac and J. W. Simons J. Amer. Chem. SOC. 1973 95,3454. 213 E.V. Waage and B. S. Rabinovitch Internat. J. Chem. Kinetics 1971 3 105.

ISSN:0308-6003    

DOI:10.1039/PR9737000069

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

5 Heterogeneous Catalysis on Metal Oxides By M. S. SCURRELL Department of Chemistry University of Edinburgh West Mains Road Edinburgh EH9 3JJ 1 htroduction Previous reviews of heterogeneous catalysis on solid surfaces in these pages have been devoted to reactions on metals’ and molecular sieve zeolites.* No account of catalysts on metal oxides (excluding in the present context zeolites) has appeared and it is hoped that this review will provide a timely and useful assessment of progress made in recent years. The Report covers work contained in original papers and review articles which have appeared over the period 1971-73. Papers and reviews have where possible been classified according to the type of catalytic process under investigation. Studies devoted exclusively to chemisorption and equilibrium adsorption phenomena have not been included unless they are of direct relevance to or were conducted in close conjunction with investigations of catalytic reactions.A number of books and review articles of a general nature have appeared during the past few years and these will receive brief mention first. Clark3 has presented a clear and rigorous account of theoretical aspects of adsorption and catalysis covering a wide range of catalysts and catalytic reactions. Much of the contribution by Krylov4 concerns discussion of theoretical aspects of the subject in relation to common catalytic processes. Thomas’ has described the selection and applicability of catalysts many of them based on metal oxides for use in the major catalytic processes of industrial importance.Recent reviews dealing with the description and application to heterogeneous catalysis of certain experimental techniques have been given by van Reijen6 (electron paramagnetic resonance) Gravelle’ (heat-flow microcalorimetry) Emmett’ (use of isotope tracers) and Cventanovic and Amenomiyag (temperature ‘ G. C. Bond Ann. Reports 1964,61,99; 1966,63 27. H. F. Leach Ann. Reports (A) 1971,68 195. ’ A. Clark ‘The Theory of Adsorption and Catalysis’ Academic Press New York 1970. 0. V. Krylov ‘Catalysis By Non-Metals (Rules for Catalyst Selection)’ Academic Press New York 1970. ’ C. L. Thomas ‘Catalytic Processes and Proven Catalysts’ Academic Press New York 1970. L. L. van Reijen Ber. gunsengesellschaftphys.Chern. 1971 75 1046. ’ P. C. Gravelle Adu. Catalysis 1972 22 191. P. H. Emmett Catalysis Rev. 1972 7 1. R. J. Cvetanovic and Y. Amenomiya Catalysis Rev. 1972. 6 21. 87 88 M. S. Scurrell programmed desorption). Maatman" has provided a useful guide to the calculation of solid-catalyst site densities in an article devoted to enzyme and solid-catalyst efficiencies. The electronic theory of catalysts continues to provide the basis for much discussion. The application of crystal and ligand field theories to solid catalysts is reviewed by Dowden.' ' The role of electronic effects in determining the nature of reactions on catalysts many of them semiconducting oxides is well covered by several authors. 12-16 Of particular interest is the development of the surface state representation due to Morrison.' A discussion of the mechanism and kinetics of reactions on silica-alumina catalysts has been presented by de Boer and Visseren" and a comprehensive summary of the behaviour of the nitric oxide molecule in heterogeneous catalysis is due to Shelef and Kummer." 2 Hydrogen Exchange Reactions The use of deuterium for investigating the mechanisms of surface reactions involving hydrogen or hydrocarbon molecules continues to attract the attention of many research workers.B~rwell'~ has reviewed the application of the tech- nique and has indicated the most profitable areas for its use. Hydrogen-Deuterium Equilibration.-A detailed investigation2' of the adsorp- tion of hydrogen and the hydrogendeuterium equilibration reaction on alumina has revealed that at least five different states of chemisorbed hydrogen may be detected.The weakest form of adsorbed hydrogen was shown to be the sole species by which hydrogendeuterium exchange took place at low temperatures. This chemisorption obeyed the dissociative Langmuir isotherm at 198 K. A thorough study21 of the activity of magnesium oxide for the exchange reaction at 78K has shown that the only impurity which affects the rate of equilibration consists of protons. By pretreatment of catalysts in O~CUOat temperatures between 500 and 900"Csamples could be prepared with activities differing by more than five orders of magnitude. E.p.r. studies of samples treated in an identical manner to those with which reaction rates were measured revealed the presence of a surface centre the concentration of which was paralleled by the catalytic activity.It was proposed that exchange occurred at this centre which was lo R. W. Maatman Catalysis Rev. 1973 8 1. I D. A. Dowden Catalysis Rev. 1971 5 1. l2 S. R. Morrison J. Catalysis 1971 20 110. l3 V. J. Lee J. Chem. Phys. 1971.55 2905. l4 G. M. Schwab Fortschr. Chem. Forsch. 1972 25 105. A. K. Vijh J. Catalysis 1973,28 329. l6 G. R. Heal Ann. Reports (A) 1971,68 221. l7 J. H. de Boer and W. J. Visseren Catalysis Rev. 1971 5 55. Is M. Shelef and J. T. Kummer Chem. Eng. Progr. Symp. 1971,67 74. l9 R. L. Burwell jun. Catalysis Rev. 1972,7 25. 2o Y. Amenomiya J. Catalysis 1971 22 109. M. Boudart A.Delbouille E. G. Derouane V. Indovina and A. B. Walters J. Amer. Chem. SOC. 1972,94 6622. Heterogeneous Catalysis on Metal Oxides 89 described as an OH- group adjacent to a triangular array of 0-ions situated on a (111) plane of the oxide crystal. Misono and Hall2 used the equilibration exchange in conjunction with a study of the oxidation-reduction properties of copper-substituted hydroxy- apatite Ca,,(PO,),(OH),. They concluded that copper in the cu+ state was much more active than that in the form of Cuo clusters but it was not certain that H,-D exchange was confined to the substrate surface. Two studies of H2-D equilibration catalysed by zinc oxide have been reported. Naito et al.23" examined the behaviour of chemisorbed hydrogen under reaction conditions by volumetric and infrared spectroscopic techniques.Rate constants for HD formation and loss of intensity of the i.r. bands due to ZnH and ZnOH surface species were in good agreement when compared at 273 K. This observation led the authors to conclude that hydrogen chemisorbed as ZnH and ZnOH is the reactive intermediate in the exchange reaction at low temperatures. A first-order dependence of the rate on deuterium (or hydrogen) pressure was found for experiments where hydrogen (or deuterium) was preadsorbed on the catalyst and the Rideal mechanism was invoked to explain the observed kinetics. For hydrogen adsorption the volumetric and spectroscopic results of these authors appear to be in very good agreement with those of Kokes et aL2 The second report is due to Tartarelli et al." and places emphasis on the reaction occurring at higher temperatures (373-433 K) than those used by Naito et al.23 It was found that the rate constant for H,-D exchange above a certain temper- ature was strongly influenced by catalyst particle size.The role of diffusion effects was discussed and a general description of the pore structure proposed. Hydrogen-Deuterium Exchange.-In this section studies of exchange reactions involving hydrocarbon molecules and their interaction with deuterium or deuterium-labelled compounds are discussed. The reaction of propane with deuterium on alumina has been investigated, and evidence obtained for the participation of electron-deficient (Lewis acid) centres on the catalyst.A sharp decrease in activity was noted for alumina samples which contained small quantities of silica and for silica-aluminas containing less than ca. 80 % alumina negligible exchange activity was found. Robertson et examined the exchange of n-butane and isobutane with deuterium on alumina. Both butanes exhibit comparable rates of exchange at 273 K. The exchange of the methine hydrogen of isobutane was very slow even at 425 K. At 316 K the methyl hydrogens of n-butane were exchanged 55 times more rapidly than those 22 M. Misono and W. K. Hall J. Phys. Chem. 1973,77 791. 23 (a)S. Naito H. Shimizu E. Hagiwara T. Onishi and K. Tamaru Trans. Faraday SOC. 1971,67 1519; (6)S. Naito T. Kondo M. Ichikawa and K. Tamaru J. Phys. Chem. 1972,76 2184.24 (a)R. J. Kokes and A. L. Dent Adu. Catalysis 1972.22 I ;(b) R. J. Kokes Proceedings of the 5th International Congress on Catalysis Miami Beach 1972 North Holland Amsterdam 1973 Vol. 1 p. 1; (c) R. J. Kokes Accounts Chem. Res. 1973,6 226. 25 R. Tartarelli M. Giorgini and F. Morelli J. Catalysis 1971 20 141. 26 B. D. Flockhart S. S. Uppal and R. C. Pink Trans. Faraday Suc. 1971,67 513. l7 P. J. Robertson M. S. Scurrell and C. Kemball J.C.S. Chem. Comm. 1973 799. 90 M. S. Scurrell in the methylene groups and the authors conclude that alkyl species possessing carbanionic character are the reactive intermediates in this system. The catalysis of the isomerization and exchange of butenes on alumina has received attention .~~ from two research groups.Sakurai et ~1 examined the isomerization of cis-but-2-ene and but-1-ene in the presence of perdeuteriopropylene. Full isotopic analysis of the propylene was accomplished by measurement of the microwave spectrum. Deuterium on the C- 1 atom in perdeuteriopropylene (i.e. =CD2) showed extensive exchange with the hydrogens in the butenes. It was concluded that the double-bond migration in n-butene on alumina proceeded on protonic sites (formed by adsorption of the olefins) and that deuterium scrambling between the terminal olefins (propylene and but-1-ene) was an independent process. The dual nature of alumina for isomerization and deuterium exchange of but-1-ene has also been demonstrated by Rosynek et a1.29*30 Small quantities of adsorbed carbon dioxide completely poisoned the exchange reaction but at the same time there was no change in the rate or selectivity of the isomeriza- tion process.Carbon dioxide appeared to be an extremely selective poison for the exchange reaction since exposure of alumina catalysts to comparable quanti- ties of sulphur dioxide hydrogen chloride or ammonia produced no significant decrease in activity.*' Two types of centre both of which were active for butene adsorption were identified by temperature-programmed desorption techniques but it was concluded that neither site was primarily responsible for isomerization or exchange reaction^.^' The sites which confer catalytic activity for butene exchange were shown to be those on which the exchange of benzene with deuter- ium occurred.By estimation of the minimum dose of carbon dioxide required for complete elimination of exchange activity3' the concentration of these sites was calculated as 3-8 x 10l2cm-2. Exchange reactions with deuterium and the isomerization of olefins on gallium oxide3' have shown that the oxide converts cis-and trans-isomers of butenes and pentenes without involvement of a double-bond shift. Hydrogens in vinylic and allylic positions were exchanged with high selectivity. Two papers report results for exchange reactions of ketones with deuterium oxide on r~tile~~ and the exchange of 3,3-dimethylbut-l-ene with deuterium oxide or deuterium on oxides including silica-alumina and magnesium oxide. 33 Both reports contain data for isomerization reactions but aspects of the exchange reactions alone are considered here.The exchange of the enolizable hydrogen atoms in ketones with heavy water at 298 K on rutile probably involved the participation of a ~arbanion.~~ The catalyst surface exhibited amphoteric behaviour. In contrast to the situation found when deuterium oxide was used acetone did not exchange with deuterium at 373 K but instead underwent con- densation reactions. This result illustrates that the course of an exchange re- 28 Y. Sakura T. Onishi and K. Tamaru Trans. Faraday SOC.,1971 67 3094 29 M. P. Rosynek W. D. Smith and J. W. Hightower J. Catalysis 1971 23 204. 30 M. P. Rosynek and J. W. Hightower ref. 246 Vol. 2 p. 851. F. B. Carleton H. A. Quinn and J. J. Rooney J.C.S. Chem.Comm. 1973 23 1. 32 I. R. Shannon I. J. S. Lake and C. Kemball Trans. Faraday SOC.,1971,67 2760. Heterogeneous Catalysis on Metal Oxides 91 action may be greatly influenced by the nature of the source of deuterium. Magnesium oxide catalysed the exchange of 3,3-dimethylbut-1 -ene when deuterium was used but replacement was confined to the three vinylic hydro- gen~.~~ In contrast if heavy water was used the overall activity of the reaction was reduced but exchange beyond three hydrogens took place. The latter reaction involves isomerization of the reactant and is considered to proceed uia a car- bonium ion intermediate formed readily if deuterium oxide is present in the system (see also Section 10). Ortho-Para-Hydrogen Conversion.-A study of the low-temperature para-hydrogen enrichment on non-stoicheiometric r~tile~~ has shown that the Ti3 + ions which are the active catalytic centres may be completely covered by adsorbed hydrogen.This has allowed the extent of surface non-stoicheiometry to be directly measured by recording the absolute rate of the enrichment under stan- dard conditions of temperature and pressure. The active Ti3+ ions were not confined to the surface layer alone but were distributed between surface and sub- surface layers. The most active forms of reduced rutile prepared in these studies were estimated to possess not more than ca. 8 x 10’‘ion m-,. An investigation of the conversion of para-hydrogen over chromia at temperatures near the Nee1 point (34 0C)35 has revealed that with a-chromia and microcrystalline chromia- gel the conversion rate fell as the temperature was raised through the transition temperature.With a sample of amorphous chromia-gel no such decrease was observed. It is apparent that the conversion activity increases with crystalline size but is also much enhanced by the independent process of antiferromagnetic ordering. Some publications have appeared dealing with the influence of an external magnetic field on the rate of the para-hydrogen conversion and related reactions. Selwo~d~~ has reported that certain rare-earth oxides become less active when placed in a magnetic field of a few (ca.0-40) oersted. Other oxides of the same series remained unaffected. When the oxides were supported at low surface concentrations on the diamagnetic lanthanum oxide all except gadolinium oxide exhibited the weak-field magnetocatalytic effect.The absence of an effect for this one oxide is considered to be due to the unique electronic configuration of the Gd3+ ion. Rates of reaction were measured at room temperature and it was noted that the position of the ortho-para-H equilibrium was unchanged in the presence of an extrinsic field. In a detailed study3’ of the effect on yttrium and lutetium oxides it was found that a field of 40Oe could reduce the activity of the latter catalyst by 42% and the presence of the Earth’s magnetic field was also detectable. Using higher magnetic fields (up to ca. 2 kOe) than those employed 33 C. Kemball H. F. Leach B. Skundric and K.C. Taylor J. Catalysis 1972,27,416. 34 P. C. Richardson R. Rudham A. D. Tullett and K. P. Wagstaff J.C.S. Faraday I 1972,68 2203. 35 J. A. Arias and P. W. Selwood J. Catalysis 1973 30 255. 3b P. W. Selwood J. Catalysis 1971 22 123. ” K. Baron and P. W. Selwood J. Catalysis 1973 28,422. 92 M. S. Scurrell by Selwood and co-workers Eley et have demonstrated the enhancement of the para-hydrogen conversion activity of neodymium oxide but have found that the rate of ortho-deuterium conversion falls when the extrinsic field is applied. The authors believe that factors other than changes in surface paramagnetism produced by an external magnetic field36*37 are important in explaining the observed results. A tentative explanation for the positive magnetocatalytic effect for para-hydrogen conversion on paramagnetic surfaces is given by Ilisca and Gallais3' who consider the importance of the orientation of surface magneti- za t ion.A theoretical treatment of the magnetic conversion mechanism has been reported by Ilisca and Legrand4' who show that the highest reaction rates are to be expected for those oxides which have the shortest impurity relaxation time. 3 Hydrogenation Reactions The catalytic hydrogenation of olefins over zinc oxide catalysts has formed the basis of several investigations. The elegant work of Kokes and co-~orkers~~ is of particular interest. A combination of spectroscopic and kinetic techniques together with the use of isotopic tracers and adsorption measurements has provided an effective means of studying the nature of surface intermediates.Ethylene was adsorbed on zinc oxide as a surface n-complex. Adsorbed hydrogen atoms produced by heterolytic dissociation of a hydrogen molecule interacted with the adsorbed olefin to produce ethyl groups attached to zinc surface ions as the reaction intermediate with subsequent production of ethane. When deuterium was used instead of hydrogen ['H,]ethane was the exclusive hydro- genation product. A a-ally1 species was produced when propylene was adsorbed on zinc oxide. The isotopic distributions found for products of reaction between propylene and deuterium were consistent with the view that this n-ally1 unit is an important intermediate in the hydrogenation process. Naito et al.23bhave used microwave spectroscopy to analyse deuterium incorporation into reactant and products resulting from the isomerization and hydrogenation of propylene on zinc oxide.They contended that although the 71-ally1 adsorbed species was an intermediate in the isomerization reaction different reactive species took part in the addition process. Baranski and Cvetanovic4' studied the hydrogenation of ethylene on zinc oxide at low temperature (0"C and below). Five forms of chemisorbed hydrogen were identified by temperature-programmed desorption at adsorption temper- atures of -70 to +3OO"C. Only the form which was most easily desorbed reacted readily with ethylene. The overall kinetic representation of the hydro- genation reaction is consistent with that of Kokes and Dent.24" 38 D.D. Eley H. Forrest D. R. Pearce and R. Rudham J.C.S. Chem. Comm. 1972 1176. 39 E. Ilisca and E. Gallais Phys. Reu.(B) 1972 6 2858. 40 E. Ilisca and A. P. Legrand Phys. Reo. (B) 1972,5,4994. 41 A. Baranski and R. J. Cvetanovic J. Phys. Chern. 1971,75 208. Heterogeneous Catalysis on Metal Oxides 93 Naito et aL2 report results for the reactions of deuterium with propylene butene and buta-1 ,Zdiene. Mass and microwave spectroscopic techniques were used to determine the deuterium content and distribution in the reactants and products. The main products of hydrogenation of the above reactants were [’H,]propane [,H,]butane and [,H,]butene respectively. It was proposed that hydrogenation proceeded by interaction between chemisorbed hydrocarbons and deuterium molecules in the gas phase since it was found that the deuterium participated in the addition process in a “molecular form” and that rates of reaction were proportional to the partial pressure of deuterium rather than the amount chemisorbed.Individual and competitive hydrogenations of C2 to C4 olefins have been carried out over cobalt oxide (c0304).42 The reactivity sequence of olefins was C -C > C but it was found that the rate of hydrogenation of propylene was much reduced in the presence of ethylene. The strength of chemisorption of the olefins was calculated to decrease in the series C >> C > C4. It was concluded that the olefins were adsorbed at the active sites for hydrogenation in a z-bonded state similar to that found for silver nitrate-olefin complexes.The behaviour of cobalt oxide and chromia in catalytic olefin hydrogenation and related reactions is discussed by Siege1.43 A comparison of heterogeneous and homogeneous catalysis is made and a theory proposed which attempts to link the degree of co-ordinative unsaturation with elementary reactions of hydrogen and olefins which may occur at surface sites on transition-metal oxides. 4 Oxygen Exchange Reactions Two reviews concerned with ~xygen-transfer~ processes and oxygen-ex~hange~~ on oxides have appeared. In the article by Pa~ravano~~ emphasis is placed on the description and evaluation of models for the transfer reactions and in particu- lar the role played by the bulk electrical properties of the solids and the electrical space charge at the surface.No~akova~~ summarizes a wealth of experimental data for oxygen-exchange processes and considers separately the three reaction types heterophase exchange homophase equilibration and heterophase equilibration. Several papers have been devoted to exchange reactions catalysed by vanadium pentoxide and mixed catalysts containing the oxide. In a re-examination of published data Mann46 concludes that for oxygen adsorption on a variety of vanadium pentoxide and vanadium pentoxide-potassium sulphate preparations the compensation effect operates. Nikisha et aI.47have reported results for the isotopic exchange in molecular oxygen on silica-supported vanadium pentoxide. 42 N.Nihira T. Fukushima K. Tanaka and A. Ozaki J. Catalysis 1971 23 281. 43 S. Siegel J. Catalysis 1973 30,139. 44 G. Parravano Catalysis Rev. 1971,4 53. 45 J. Novikovi Catalysis Rev. 1971 4 77. 46 R. F. Mann Canad. J. Chem. 1971,49 1520. 47 V. V. Nikisha B. N. Shelimov,V. A. Svets,A. P. Griva andV. B. Kazansky J.Catalysis 1973 28 230. 94 M. S. Scurrell Between +20 and -140°Cthe apparent activation energy of the process was very low (0.5-1.0 kcal mol- ’). It was found that fully oxidized preparations were inactive at room temperature and that reduction in hydrogen or in uucuo at 500°C was a necessary activation step. Measurements of e.p.r. spectra of cata- lysts were made and it was concluded that O; and OYadsanion-radicals are active intermediates in the exchange reactions at low temperatures.K akioka et al. have studied the isotopic exchange of “0 in carbon dioxide with lattice oxygen atoms of both pure4’ and molybdenum trioxide doped4’ vanadium pentoxide. With the former catalysts it was shown that the diffusion of oxygen from the surface to the lattice of the oxide was a slower process with a higher energy of activation than the surface exchange step. The order of the exchange reaction with respect to the pressure of carbon dioxide was close to unity. The mechanistic implications of these kinetic data were discussed. Introduction of molybdenum ions into the vanadium pentoxide lattice led to a decrease in the number of surface oxygen ions directly participating in the exchange reaction despite the fact that doping in this way tends to lead to an increase in the mobility of lattice oxygen.Blanchard et al.” have demonstrated that for vanadium pentoxide-molybdenum trioxide mixed oxides containing from 0 to 100% molybdenum trioxide there exists a correlation between the activation energy for isotopic exchange of oxygen and the selectivity of the catalysts for the oxidation of butene and benzene. The maximum activation energy (82 kcal mol- I) and selectivity are obtained for catalysts containing 33 % molybdenum trioxide. The authors conclude that the bond energy of surface oxygen is an important factor in determining the selectivity of a catalyst in oxidation reactions. A related study’ of oxygen exchange and butene oxidation on vanadium pentoxide- titanium dioxide catalysts has shown that the selectivity for oxidation of butene is a maximum for samples containing 20 or 65% titanium dioxide.(Again the authors examined the complete range of molecular composition of the solids.) Selectivities for the oxidation of o-xylene were also determined as a function of titanium dioxide content. There was a good correlation between the selectivities of the oxidation reactions and the activation energy for heteromolecular exchange of oxygen for the entire range of catalyst composition. It has been reporteds2 that the addition of cerium oxide (CeO,) to a vanadium pentoxide catalyst enhances the rate of exchange between lattice oxygen and that in gaseous carbon dioxide but does not change the activity for lattice oxygen-gaseous oxygen exchange.48 H. Kakioka V. Ducarme and S. J. Teichner J. Chim. phys. 1971 68 1715. 49 H. Kakioka V. Ducarme and S. J. Teichner J. Chim. phys. 1971 68 1722. ’’ M. Blanchard G. Longuet G. K. Boreskov V. S. Muzykantov and G. I. Panov Bull. SOC.chim. France 1971 814. * M. Blanchard G. Longuet J. Rivasseau and J. C. Delgrange Bull. SOC.chim. France 1972 307 1. 52 G. V. Antoshin Nguyen Quang Huynh Kh. M. Minachev and D. A. Kondrat’ev Izvest. Akad. Nauk. S.S.S.R., Ser. khim. 1971 2346. Heterogeneous Catalysis on Metal Oxides 95 Popovksii et have studied the homomolecular exchange of oxygen and the oxidation of hydrogen on a series of nickel oxide-magnesium oxide solid solutions of general composition Ni,Mg -,O.The activity per nickel atom present for the hydrogen-oxidation reaction remained constant as x was varied. A (possibly spurious) change in the specific activity for oxygen exchange was noted. Isotopic exchange of oxygen on pure samples of nickel oxide has been investigated by Chaudhri et aLS4Catalysts prepared at different temperatures (350-850 “C) possessed forms of adsorbed oxygen whose activities for the exchange reaction became apparent at different temperatures. Models for the surface states of nickel oxide catalysts were proposed on the basis of the reactivities of adsorbed oxygen species. An attempt to relate the dependence of the activation energy for homomolecular exchange to the strength of the surface-oxygen bond for a series of metal ferrites (MeFe,O,) was made by Muzykantov et a2.” A more novel approach is that applied by Zeif et aLS6 The method of quantum chemical reactivity indices has been used to explain the change in ease of homomolecular exchange observed for the oxides of several first-row transition-series elements.A correlation between the energy of activation for homomolecular exchange and the effective magnetic moment for several of the oxides of rare-earth elements has been obtained by Sazonov et aLS7An increase in magnetic moment was paralleled by an increase in the exchange activation energy. This is attributed to an increase in the strength of the surface-oxygen bond. 5 Oxidation of Organic Molecules The literature dealing with the oxidation of organic materials and especially unsaturated hydrocarbons has increased over the past few years at a tremendous rate.A new series of oxide and mixed-oxide catalysts which are able to promote oxidation pathways in a selective manner has been developed and investigated. Oxidation of Propylene on Binary Mixed Oxides.-Mixtures of bismuth and molybdenum oxides (Bi,O and MOO,) have been widely used for the selective oxidation of propylene. Wragg et a1.,58 using isotopic tracer techniques studied the nature of acrolein produced by the oxidation of propylene using 180-labelled oxygen and catalyst. It was found that the labelling in the acrolein product corresponded in the initial stages of reaction to the labelling of catalyst oxygen and not to the labelling of gaseous oxygen.Thus the authors conclude that the oxidizing species in bismuth-molybdate preparations is the lattice oxide ion. 53 V. V. Popovskii G. K. Boreskov V. S. Muzykantov V. A. Sazonov G. I. Panov v. A. Roshchin L. M. Plyasova and V. V. Malakhov Kinetika i Kataliz 1972 13 727. 54 S. Chaudhri Y. Kera and K. Hirota Bull. Chem. SOC.Japan 1972 45 3301. 55 V. S. Muzykantov V. V. Popovskii G.K. Boreskov G.I. Panov and R. A. Shkrabina Kinetika i Kataliz 1972 13 344. 56 A. P. Zeif B. A. Leizerov Yu. M. Schekochikhin and A. A. Davydov Kinetika i Kataliz 1971 12 928. 57 L. A. Sazonov G. N. Mitrofanova L. V. Preobrazhenskaya and Z. V. Moskvina Kinetika i Kataliz 1972 13 789. 58 R. D. Wragg P. G. Ashmore and J. A. Hockey J. Catalysis 1971 22 49. 96 M.S. Scurrell Novakova and JiruS9 have suggested an alternative explanation for the results of Wragg et aL5* They propose that a rapid exchange takes place between lattice oxygen and H2180 released during the oxidation of propylene by 1802. The point is discussed further elsewhere.60 Dozono et have described experi- ments in which the ammoxidation of propylene was investigated. In an attempt to elucidate the mechanism of the reaction [3-'3C]propylene was used and the 3Cdistribution in the reaction products examined. The results were consistent with the involvement of a symmetrical C unit such as an allylic species. The authors felt however that the ammoxidation of propylene to acrylonitrile does not involve acrolein as a reaction intermediate. Sancier et a1.62have investigated the activity of silica-supported bismuth molybdate catalysts by measurement of the e.s.r.spectra during propylene oxidation. Two resonance signals attributed to Mo5+ surface ions and carbon or hydrocarbon radicals respectively were observed. An inverse relationship between total conversion of propylene and the Mo5+ signal intensity was found but no correlation between the selectivity for acrolein formation and the Mo5 + signal intensity existed. The authors conclude that Mo6 + ions stabilized against slow reduction by a suitable lattice environ- ment take part in the initial stage of the oxidation process. A new mechanism for propylene oxidation has been proposed by Haber and co-w~rkers.~~,~~ The activity and selectivity of the pure oxides bismuth oxide (Bi203) and molybdenum trioxide are considered in relation to the action of the binary mixed catalysts.It is suggested that propylene interacts with a bismuth site to form an allylic species by hydrogen abstraction. Recombination of two such species forming hexa-l$diene which takes place on pure bismuth oxide (Bi203) does not occur on mixed-oxide catalysts because a second hydrogen is abstracted this time by molybdenum centres to produce an ally1 fragment a-bonded to a lattice oxygen. Desorption of this species together with the oxygen results in the formation of acrolein. Margolis et have recently investigated the effects of doping bismuth molybdate catalysts with impurities including alkali-metal ions and transition-metal oxides on the rate and selectivity of propylene oxidation to acrolein.It has been reported that the rate of propylene oxidation on bismuth molybdate is enhanced by the addition of cerium but that the selectivity for acrolein formation is thereby reduced.66 A second series of catalysts active for propylene oxidation comprises binary mixtures of tin and molybdenum oxides. Moro-oka et aL6' demonstrated that tin molybdate catalysts showed a high activity for propylene oxidation to acetone at temperatures far below that at which allylic oxidation took place. Using 59 J. Novakova and P. Jiru J. Catalysis 1972 27 155. 6o R.D. Wragg P. G. Ashmore and J. A. Hockey J. Catalysis 1973,28 337. 61 T. Dozono D. W. Thomas and H. Wise J.C.S. Faraday I 1973 69 620.62 K. M. Sancier T. Dozono and H. Wise J. Catalysis 1971 23,270. 63 J. Haber and B. Grzybowska J. Catalysis 1973 28,489. 64 K. German B. Grzybowska and J. Haber Bull. Acad. polon. Sci. Sir. Sci. chim. 1973,21 319. 65 L. Ya. Margolis 0.V. Krylov and 0.V. Isaev ref. 24b Vol. 2 p. 1025. 66 J. Kustka and J. Tichy Colt. Czech. Chem. Comm. 1972 37,768. 67 Y. Moro-oka Y. Takita and A. Ozaki J. Catalysis 1971 23 183. Heterogeneous Catalysis on Metal Oxides 97 isotope tracing Moro-oka et a1.68investigated the mechanism of the oxidation reaction. When propylene was oxidized by molecular oxygen in the presence of H2180,l8Owas incorporated into the product acetone but not into the acrolein produced simultaneously. The workers conclude that two different active forrfis of oxygen are present on tin molybdate catalysts one of which is derived from water and the other from molecular oxygen.The production of acetone involves that type derived from water but the second type participates in the oxidation of propylene to acrolein. The formation of an isopropyl carbonium ion which subsequently undergoes reaction with the active species of water is considered to be necessary for acetone production. B~iten,~~ investigating kinetic hydrogen isotope effects on reaction rates and product distributions also concludes that acetone and acrolein are produced from propylene by completely separate oxidation routes but provides evidence that the primary oxidation step in both mechanisms consists of hydrogen abstrac- tion from the reactant olefin.Finally some papers have appeared dealing with the properties of uranium- antimony mixed-oxide catalysts and their activity for propylene oxidation. The formation of a phase of composition USb3OIo was paralleled by an increase in catalytic activity for selective acrolein formation and this phase was considered to be the active component of the ~atalyst.~' E.p.r. spectra of catalysts at room temperature71 revealed the presence of species such as Us+, 02-,and 0-. The presence of 0,-or 0-was closely related to catalytic activity for acrolein production. No such correlation was obtained for the Us+species. Elsewhere72 it has been shown that at least two types of lattice oxygen are operative in the oxidation of propylene and that the more mobile but less abundant form is responsible for the formation of acrylonitrile.It is proposed that SbS+ centres stabilized and regenerated by the action of uranium are responsible for the catalytic activity. Oxidation of Propylene on Single Oxides.-Thallium oxide73 and indium oxide74 oxidize propylene with the formation of hexa-1,Sdiene. Further oxida- tion of the diene to carbon dioxide73 or benzene74 has been observed and in the case of indium oxide acrolein is also produced asan initial product. A mechanism has been proposed for reaction on thallium oxide in which the high selectivity for diene production is explained by a two-electron transfer to a surface T13+ion. The rate-determining step for the reaction on indium oxide is thought to involve hydrogen transfer from n-adsorbed propylene to an In3+ ion.The selectivity of cuprous oxide for oxidation of propylene to acrolein is markedly increased when methyl bromide is added at low concentrations to the reactant mixture.75 Y. Moro-oka Y. Takita and A. Ozaki J. Catalysis 1972 27 177. 69 J. Buiten J. Catalysis 1972 27 232. 70 F. Nozaki and H. Okada Nippon Kagaku Kaishi 1972 842. 71 F. Nozaki and K. Sugo Nippon Kagaku Kaishi 1973 690. 72 R. K. Graselli and D. D. Suresh J. Catalysis 1972 25 273. 73 D. L. Trimm and L. A. Doerr J. Catalysis 1971 23 49. 74 D. L. Trimm and L. A. Doerr J. Catalysis 1972 26 1. " L. L. Holbrook and H. Wise J. Catalysis 1971 20 367. 98 M. S. Scurreli Simultaneous measurements of product distributions and electrical conductivity of a crystal of the catalyst indicate that the alkyl halide inhibits the oxidation of Cu' ions.A reaction mechanism involving charge transfer via electronic surface- energy states is proposed. An exploratory study on vanadium pent~xide~~ in which catalytic activity was measured and the structure of the catalyst analysed by X-ray diffraction has revealed that fully oxidized vanadium pentoxide is inactive for oxidation of propylene (and butene). Activity for selective oxidation is associated with the formation of V6OI3by partial reduction whereas further reduction to vanadium dioxide yields a catalyst which promotes complete oxidation to carbon dioxide. Swift et al.77 reported that pure bismuth oxide could be used to oxidize propylene to hexa-1,Sdiene with high selectivity pro- vided that gas-phase oxygen was present.In the absence of oxygen the selectivity for formation of the diene falls during an experiment with a concomitant increase in the yield of the secondary product benzene. Seiyama et al.78have suggested that the behaviour of an oxide in oxidizing propylene reflects the acid-base properties of the catalyst. Thus on acidic oxides the allyl intermediate (cationic) undergoes oxidation to acrolein whereas on less acidic types the intermediate is more radical-like and tends to favour the formation of aromatic material. Oxidation of Butene.-The oxidative dehydrogenation of butene to butadiene is catalysed by the same bismuth molybdates that are employed for propylene oxidation.Schuit and co-workers have made several investigations of the system and have distinguished two catalytically active centres (designated types A and B).79 The conversion of butene into butadiene proceeds by a mechanism which involves the participation of both types of centre. Type A adsorbs and activates molecular oxygen whilst type B allows the chemisorption of the olefin. The effect of the promoters bismuth phosphate ferric oxide and chromic oxide on the rate of the dehydrogenation reaction was investigated using a medium-activity catalyst.*' In a study of the effect of sintering and reduction temperature on catalytic activity it was found that the A-site concentration was independent of the surface area of the catalyst and decreased linearly with the degree of reduc- tion81 The B-sites remained present if a catalyst was reduced below 400 "C but disappeared if reduction was effected above 400 "C.A reaction mechanism for the conversion of butene to butadiene was proposed in which the butene molecule was first adsorbed on a B-site in a o-allyl-bonded state the allyl unit then moving over to an A-site and donating a second hydrogen atom to another B-site. A general study of the preparation characterization and activity of mixtures of bismuth and molybdenum oxides of differing composition has also been made.82 76 M. N. Colpaert Z. phys. Chern. (Frankfurt),1973,84 150. 77 H. E. Swift J. E. Bozik and J. A. Ondrey J. Caralysis 1971 21 212. 7M T. Seiyama N. Yamazoe and M.Egashira ref. 24b Vol. 2 p. 997. 79 I. Matsuura and G. C. A. Schuit J. Catalysis 1971 20 19. P. A. Batist C. G. M. van der Moesdijk I. Matsuura and G. C. A. Schuit J. Catalysis 1971 20 40. I. Matsuura and G. C. A. Schuit J. Catalysis 1972 25 314. P. A. Batist J. F. H. Bouwens and G. C. A. Schuit J. Catalysis 1972 25 1. Heterogeneous Catalysis on Metal Oxides 99 Niwa and MurakamiS3 have investigated the activity of bismuth molybdate catalysts and other binary mixed-oxide systems for the oxidative dehydrogenation reaction. They conclude that the ease of reduction of catalysts falls in a series Bi-W > Sn-P > MOO > Bi-Mo > Sn-Sb > Sb-Mo. The oxidation carried out over uranium trioxide-antimony oxide (Sb203) again yields b~tadiene.~~ In contrast to the behaviour of bismuth molybdate catalysts the double-bond isomerization process is absent in this case.The two catalysts also differ in their ease of reducibility by action of the hydrocarbon in the absence of oxygen. Bismuth-molybdenum mixed oxides can be reduced to a greater extent probably owing to sufficiently rapid diffusion of lattice oxygen. Ferrite catalysts are also effective for the conversion of but-2-ene into butadiene. Rennard and Kehlss have investigated the effect of substituting Cr3+ ions for Fe3+ in octahedral sites in zinc-chromium and magnesium-chromium ferrites. The substitution of Cr3 ions greatly increases the dehydrogenation activity of + the catalysts. The dehydrogenation reaction involves an allylic intermediate and involves the participation of two oxygen species an adsorbed oxygen ion and an 02-lattice oxygen.Cares and HightowerS6 found that both cobalt and copper ferrite spinels were active catalysts for the oxidative dehydrogenation of n-butenes to butadiene. Both catalysts had a tendency to catalyse total oxidation as well and neither was effective for isomerization. Selectivity in the case of the cobalt catalyst was strongly dependent upon the presence of gaseous oxygen. Experiments involving the use of deuterium-labelled molecules indicated that carbon-hydrogen bond cleavage was probably part of the rate-determining step of the reactions on these ferrites. Oxidation of Miscellaneous Organic Molecules.4ermain and Laugier have studied the oxidation of benzene87 and toluene" over 19 metal oxides at tem- peratures of 400-450"C.The activity sequences for the oxidation of the two molecules are substantially the same. The majority of the oxides used effected deep oxidation to carbon monoxide and carbon dioxide. Using the experimental data of Germain and Laugier for benzene oxidation Vijh89 has examined the fundamental factors which determine the catalytic activity of the oxides. A plot of the catalytic activity against the metal oxide bond energy (ie. heats of atomiza- tion per equivalent) yielded a volcano-shaped curve typical of those encountered in the Sabatier-Balandin interpretation of heterogeneous catalysts. Vijh also found that for certain series of semiconductor oxides there exists a reciprocal relationship between the width of the band gap and the activity for oxidation of benzene and several other types of molecule.A similar assessment due to Vijh concerning the data of Germain and Laugier88 for toluene oxidation has been *' M. Niwa and Y. Murakami J. Catalysis 1972 27 26. 84 Th. G. J. Simons P. N. Houtman and G. C. A. Schuit J. Curufysis 1971 23 1 85 R. J. Rennard and W. L. Kehl J. Catalysis 1971 21 282. 86 W. R. Cares and J. W. Hightower J. Catalysis 1971 23 193. J. E. Germain and R. Laugier Bull. SOC.chim. France 1972 2910. J. E. Germain and R. Laugier BuH. SOC. chim. France 1972 541. 89 A. K. Vijh J. Chim. phys. 1973,70 635. 100 M.S. Scurrell presented.” It has been reported’’ that a bismuth uranate catalyst may be used in the oxidative demethylation of toluene.A percentage of the oxygen present in the catalyst causes complete oxidation of the toluene in the initial stages of reaction after which benzene is produced with a high selectivity. It was estimated that 60% of the total oxygen content of the catalyst may be lost during the latter process. The original activity is restored by contact with molecular oxygen. A reaction mechanism involving the participation of a benzoate-like intermediate was proposed. The liquid-phase heterogeneous oxidation of p-xylene with molecular oxygen has been studied using cobalt oxide (CO,O,).~* Only one of the methyl groups present in the molecule was attacked during the reaction and the major products were p-methyl benzyl alcohol p-tolualdehyde and p-toluic acid.It was suggested that the alcohol and aldehyde were produced by parallel routes. Cobalt oxide (Co304)has also been shown to catalyse the liquid-phase oxidation of iso- propylbenzene (~umene).’~ The oxidation process showed characteristics typical of a free-radical reaction. The participation of free radicals during oxidation reactions is also proposed by Gorokh~vatsky,’~ who has suggested that during the liquid-phase oxidation of ethylbenzene or isopropylbenzene for example on metal oxides free radicals are produced on the catalyst surface. These radicals then pass into the liquid phase where reaction products are produced. Therefore it appears that liquid-phase catalytic oxidation reactions are best viewed as heterogeneous-homogeneous processes.Furthermore a similar conclusion is reached by Brown and Trimm9’ for gas-solid oxidation reactions involving benzene that are catalysed by vanadium-molybdenum mixed oxides. It is suggested that a benzene-oxygen adduct is produced on the surface and then desorbs with subsequent reaction to produce maleic anhydride (one major oxidation product) entirely in the gas phase. Substantial amounts of carbon dioxide are produced entirely as the result of surface reactions. Manganese dioxide has been used for the oxidation of cy~lohexane.~~ Again for reaction carried out in the liquid phase it is suggested that free radicals produced on the oxide surface are liberated into the surrounding liquid where chain reactions take place.The selective oxidation of butadiene to maleic anhydride takes place on suitably supported molybdenum oxide.97 E.p.r. measurements together with catalytic studies have revealed that Mo5+ ions formed on silica- and titania-supported catalysts can be easily oxidized and show high selectivity in contrast to those catalyst preparations in which magnesium oxide or alumina act as the support 90 A. K. Vijh J. Chim. phys. 1972,69 1689. 91 J. G. de Jong C. H. E. Guffens and H. S. van der Baan J. Catalysis 1972,26,401. 92 A. G. Caloyannis and W. F. Graydon J. Catalysis 1971 22 287. 9’ G. R. Varma and W. F. Graydon J. Catalysis 1973 28 236. 94 Y. B. Gorokhovatsky ref. 246 Vol. 2 p. 879. 95 D. M. Brown and D. L. Trimm Proc. Roy. SOC.,1972 A326,215.96 H. J. Neuburg J. M. Basset and W. F. Graydon J. Catalysis 1972 25 425. 97 M. Akimoto and E. Echigoya J. Catalysis 1973 29 191. Heterogeneous Catalysis on Metal Oxides 101 material. It was suggested that the high selectivity of certain catalysts was due to the ease of oxidation of Mo5+to a Mo6+=02-unit. Uchijima et a1.98 have investigated the deep oxidation of lower olefins on nickel oxide using a microcatalytic technique. It was suggested that a linear free energy relationship might exist between the rate of reaction and the number and type of allylic hydrogens present. Equations have been derived which predict the rate of oxidation and comparison of the calculated and experimental rate constants indicates that such linear equations are applicable to the reactions studied.6 Oxidation of Inorganic Molecules Oxidation of Hydragem-Popovskii et reported results for the reaction catalysed by oxides of the first-transition-series elements. For the majority of catalysts used rates of reaction were very similar to the rates of catalyst reduction- oxidation at an equilibrium surface state. For vanadium pentoxide and titanium dioxide rates of the catalytic reaction were greater than expected on this basis. Onishi'OO has reported that the rate of oxidation of hydrogen on titanium dioxide (rutile or anatase) was almost the same as that for reduction of the catalyst by hydrogen. Close correlations were obtained between the electrical conductivity of samples the amount of active catalyst oxygen and the reduction rate constant of titanium dioxide by both hydrogen and carbon monoxide.Similar mechanisms for the oxidation of hydrogen and carbon monoxide were considered to operate. Popovskii et ~1.'~' found that the oxidation activity for a series of metal ferrites paralleled their ability to catalyse the homomolecular isotopic oxygen exchange. All ferrites used had similar activities which were considerably lower than those found for cobaltites. An extensive study reported by Boreskov"' revealed that the activity of a transition-metal ion for both the oxidation of hydrogen (and carbon monoxide) and the homomolecular oxygen- exchange reaction could be varied greatly by altering the nature of the solid- state environment. High activities were found for transition-metal ions held in simple oxide lattices and for tervalent ions in spinel compositions.Small con- centrations of these ions in zeolites possessed the lowest activities. It was concluded that the specific catalytic activity of a metal ion was determined by electron transfer between oxygen and the ion. An increase in the covalent character of the metalkoxygen bond led to an increase in catalytic activity. Read and Conradlo3 have investigated the kinetics of hydrogen oxidation on the oxides of neodymium dysprosium and erbium. Similar behaviour was found for all three catalysts; the most likely mechanism was considered to involve a 98 T. Uchijima Y.Ishida N. Uemitsu and Y. Yoneda J. Catalysis 1973 29 60. 99 V. V. Popovskii E.A. Mamedov and G. K. Boreskov Kinetika i Kataliz 1972,13 145. loo Y. Onishi Bull. Chem. SOC.Japan 1971,44 912. '01 V. V. Popovskii G. K. Boreskov Z. Dzeventski V. S. Muzykantov and T. T. Schul-meister Kinetika i Kataliz 1971 12 979. lo* G. K. Boreskov ref. 24b Vol. 2 p. 981. '03 J. F. Read and R. E. Conrad J. Phys. Chem. 1972 76,2199. 102 M. S. Scurrell fraction of the surface covered by molecular hydrogen. For a lanthanum oxide catalyst which had been doped with cerium oxide CeO, (ratio La/Ce = 99) the rate of hydrogen oxidation was found to equal that of hydrogendeuterium equilibration. 'O4 The homomolecular isotopic oxygen exchange did not occur during oxidation and it was suggested that the rate-determining step in the oxida- tion process was the interaction between molecular hydrogen and chemisorbed oxygen.For zinc oxide the observed reaction kinetics have been interpreted in terms of a rate-limiting reaction between hydrogen and oxygen which are both in a chemisorbed state.lo5 Oxidation of Carbon Monoxide.-The oxides of transition-series elements have been widely used to investigate the mechanism of this reaction. On titanium dioxide (anatase or rutile) Onishi lo6 has found that the rutile surface possesses 3-5 times the amount of active oxygen per unit area of surface as anatase. The reaction on both forms of catalyst involved reduction of the oxide by carbon mon- oxide followed by re-oxidation by oxygen. Marshneva et al.lo7 reported that on vanadium pentoxide rates of catalyst oxidation and reduction were similar and were approximately an order of magnitude lower than the observed rate of the catalytic oxidation reaction.Thus it was concluded that lattice oxygen was not primarily involved in the catalysis. Combined catalytic and e.p.r. measurements have revealed that V4+ions may be the active centres for oxidation of carbon monoxide on silica-supported vanadium pentoxide.' 08,' O9 The operation of a chain mechanism involving adsorbed 0,-and 0-ions has been suggested. lo9 Yu Yao"' has presented data for the oxidation of carbon monoxide (and hydrocarbons) over a-chromia. Four samples of catalyst were used and the catalytic activity (and selectivity) was dependent on the morphological structure of the oxide. Carbon monoxide would not react with lattice oxygen at reaction temperatures and adsorption measurements indicated that only a very small fraction of the surface was catalytically active.Manganese dioxide is active for carbon monoxide oxidation and it has been reported' that the catalytic activity is closely related to the presence of oxygen species of high oxidation power. A discontinuous change in catalytic activity was found at a certain partial pressure of carbon monoxide and attributed to a change in crystallographic structure of the oxide surface. Later investigations using a transient response method revealed" that two forms of adssrbed oxygen were responsible for the catalytic activity. One form comprised 0;-or 0-ions and Io4 G. V. Antoshin Kh. M. Minachev and M.E. Lokhuary J. Catalysis 1971 22 1. IoS T. Miura and T. Keii Nippon Kagaku Kaishi 1973 654. Io6 Y. Onishi Buff. Chem. SOC.Japan 1971,44 1460. lo' V. I. Marshneva G. K. Boreskov and V. D. Sokolovskii Kinetika i Kataliz 1972 13 393. lo8 M. Ya. Kon V. A. Svets and V. B. Kazanskii Kinetika i Kataliz 1972 13 735. Io9 V. B. Kazanskii V. A. Svets M. Ya. KOFI V. V. Nikisha and B. M. Shelimov ref. 246 Vol. 2 p. 1423. ILo Y. F. Yu Yao J. Catalysis 1973 2@ 139. 'I1 M. Kobayashi H. Matsumoto and H. Kobayashi J. Catalysis 1971 21 48. 'I2 M. Kobayashi and H. Kobayashi J. Catalysis 1972 27 (a) 100 (b) 108 (c) 114. Heterogeneous Catalysis on Metal Oxides was rapidly regenerated during the oxidation reaction. The other was probably in the form of molecular oxygen which could very slowly transform into the anionic species.The process of oxidation proceeded uiu interaction of carbon monoxide and adsorbed oxygen anions.' 12' The quantity of carbon dioxide held under steady-state conditions exceeded the equilibrium quantity and it was suggested that desorption of carbon dioxide was one of the slower steps in the reaction sequence. Computer-simulated reaction data' lZchave been used to verify the applicability of the transient response method. YuYao113 has also employed the technique for examination of oxidation reactions on nickel oxide microcrystals. The (1 11) face was the major plane exposed. Carbon monoxide or small hydrocarbon molecules were used as reactants and several aspects of the reactions were examined.The kinetic parameters for the (1 11) face were com- pared with those obtained with randomly orientated polycrystalline powders and the geometric effect was found to be small. Deren et al.' l4 reported the effects of doping monocrystalline specimens of nickel oxide with lithium ions. Results for changes in activity of the catalysts for carbon monoxide oxidation were com- pared with those obtained using polycrystalline material and it was concluded that the influence of lithium doping was essentially unchanged on passing from the poly- to mono-crystalline samples. Differences in the specific catalytic activities of the two crystal types were attributed to differences in chemisorptive properties. Using a pulsed microcatalytic method Fesenko et al.' l5 have reported that the oxidation of carbon monoxide over cuprous oxide involves participation of the catalyst oxygen.Oxygen vacancies created by the rate-limiting reduction of the surface by carbon monoxide are rapidly filled by contact with gaseous oxygen. Effects produced during the oxidation of carbon monoxide on zinc oxide have been investigated using e.p.r. spectroscopy by Guelton et al. ' Very similar results to those found during hydrogen oxidation were obtained and a similar mechanism is considered to operate. It is suggested that the reducing species chemisorb by interaction with holes the minority carriers rather than with electrons. Choi and Kim' ''have investigated the reaction kinetics on zinc oxide and conclude that the initial stage involves electron transfer from the catalyst to produce an oxygen anion 0-.Carbon monoxide subsequently reacts with this species and carbon dioxide desorbs from the surface. Morrison and Bonnelle' * studied the oxidation reaction on zinc oxide which had been treated with redox couples deposited on the surface. In these experiments the zinc oxide behaved essentially as the support for the catalytically active sites at which electron transfer took place. Electronic changes at the surface were monitored 'I3 Y. F. Yu Yao and J. T. Kummer J. Catalysis 1973 28 124. 'I4 J. Deren Z. Guzik and J. Sloczynski Bull. Acad. polon. Sci. Ser. Sci. chim. 1972 20 361. 'Is A. V. Fesenko G. P. Korneichuk and V. G. Vysochenko Kinetika i Kataliz 1972 13 237. 'I6 M.Guelton J. P. Bonnelle and J. P. Beaufils J. Chim. phys. 1971 68 1122. ''' J. S. Choi and B. W. Kim Bull. Chem. SOC. Japan 1973,46 21. I") S. R. Morrison and J. P. Bonnelle J. Catalysis 1972 25 416. 104 M. S. Scurrel! by examination of the conductivity of the zinc oxide. The results were explained in terms of the surface-state energy of the additive used. Manganese and chromium additives with a low surface-state energy lead to the formation of an active catalyst. In contrast addition of iron cyanide with a high surface-state energy resulted in the production of an inactive sample. A study of the reaction on zirconium dioxide"g has shown that the catalyst behaves in a very similar manner to titanium dioxide and that a similar mechanism operates (see ref.106) for both oxides. Sazonov et ~1.'~~ have investigated the oxidation reaction over oxides of the lanthanide elements. It was established that the rate of carbon monoxide oxidation increased with increasing mobility of oxygen whereas the rate of carbon dioxide desorption fell as a result of interaction between carbon dioxide and adsorbed oxygen possibly with the formation of a surface carbonate-type complex. A second studyI2' using isotope tracers confirmed that the carbonate- type structure was produced during carbon monoxide oxidation. It was also shown that the catalytic activity for oxidation was a function of the 4p electron configuration of the cation in the oxide lattice. Maximum rates of oxidation were obtained on oxides of elements having the most stable configurations i.e.La3+ Gd3+ and Lu3+. The results were explained in terms of the binding energy of surface oxygen (see also ref. 57) which determines the ease with which carbon dioxide is desorbed from the surface. Simultaneous measurements of the reaction rate and the electrical conductivity of the catalyst have been presented for carbon monoxide oxidation over cerium dioxide by Breysse et ~1.l~~ A mechanism was proposed in which oxidation and reduction of the solid took place. Using a microcalorimetric technique Breysse et ul.' 23 showed that for the catalytic oxidation of carbon monoxide the defect structure of cerium dioxide catalysts is single phased and that the experimental results are consistent with the operation of a reduction-oxidation cycle.Adsorptive and catalytic measurements on thorium dioxide have shown'24 that carbon dioxide may be absorbed in two forms one of which is intermediary in carbon monoxide oxidation whereas the other acts as an inhibitor. Hertl and Farra~to"~ have employed i.r. spectroscopic gravimetric and kinetic techniques to study the oxidation of carbon monoxide and hydro- carbons on a copper chromite catalyst. 1.r. absorption bands assigned to carbon monoxide adsorbed on exposed lattice copper ions were seen when the gas was contacted with the catalyst at room temperature. [Cr-O-CO,]-type units containing unidentate carbonate group were also produced by adsorption on lattice oxide ions. The source of oxygen required was the catalyst and not the gas T.Hamamura Y.Onishi and Y. Iizuka Bull. Chem. SOC.Japan 1972,45 1288. "* L. A. Sazonov E. V. Artamonov and G. N. Mitrofanova Kinetika iKataliz 1971 12 378. I" E. V. Artamonov and L. A. Sazonov Kinetika iKatalir 1971,12,961. lz2 M. Breysse M. Guenin B. Claudel H. Latreille and J. Veron J. Catalysis 1972 27 275. '23 M. Breysse M. Guenin B. Claudel and J. Veron J. Catalysis 1973 28 54. 124 M. Breysse B. Claudel M. Prettre and J. Veron J. Catalysis 1972,24 106. W. Hertl and R. J. Ferrauto J. Catalysis 1973,29 352. 105 Heterogeneous Catalysis on Metal Oxides phase. Below 80 "C oxidation took place via the carbonyl groups whereas above 200 "C the decomposition of the carbonate structure was important. Fuller and Warwick' 26 have examined the reaction over tin (IV) oxide and have found that the kinetic data were consistent with the involvement of a reduction- oxidation sequence.Although re-oxidation at equilibrium was faster than reduction some overall reduction of the catalyst occurred under reaction con- ditions resulting in a partial deactivation. Desorption of carbon dioxide from the surface was rate-determining. The same authors have also rep~rted''~ that coprecipitated tin oxide-copper oxide mixtures (SnO,-CuO) particularly those having a Cu :Sn atomic ratio between 0.5 :1 and 0.6 :1 are very active for low- temperature (<100"C) oxidation of carbon monoxide and are superior to tin(1v) oxide alone. Oxidation of Sulphur Dioxide and Ammonia.-Kato et a1.lz8 have investigated the oxidation of sulphur dioxide on a vanadium pentoxide-potassium sulphate catalyst.Structural and chemical analyses of the catalyst were carried out. It was concluded that the majority of the vanadium was present in the form [v'v0]2+ with smaller amounts in the [VvO,]+ form. The reaction mechanism involved reduction of Vv with sulphur dioxide and oxidation of VIv with oxygen both steps being in equilibrium. Desorption of sulphur trioxide was the rate-determin- ing stage. Further remarks about the validity of reduction-xidation mechanisms for sulphur dioxide oxidation on vanadium oxide catalysts are provided by Mezaki and Kadlec,12' who conclude that the applicability of equations used to describe the reaction models is dependent upon the experimental conditions used.Holbrook and Wise' 30 have examined the selectivity of crystalline cuprous oxide for the oxidation of ammonia with particular emphasis on the electrical properties of the catalyst. It was found that the electronic defect structure of the oxide could be related to catalytic specificity. Oxygen-deficient samples were effective for highly selective conversion into nitrogen. In contrast nitrous oxide was the predominant product on a catalyst containing an oxygen excess. 7 Polymerization Reactions Investigationsof the polymerization of ethylene catalysed by supported chromium oxide (CrO,) have been the subject of several papers. Eley et uZ.'~' reported results obtained using kinetic' la and combined kinetic-i.r. spectroscopic A silica-supported chromium trioxide catalyst was used for these studies.It was found that in order to produce an active catalyst a pre- '" M. J. Fuller and M. E. Warwick J. Catalysis 1973 29 441. M. J. Fuller and M. E. Warwick J.C.S. Chem. Comm. 1973 210. A. Kato K. Tomoda I. Mochida and T. Seiyama Bull. Chem. SOC.Japan 1972 45 690. R. Mezaki and B. Kadlec J. Catalysis 1972 25 454. 130 L. L. Holbrook and H. Wise J. Catalysis 1972,27 322. 13' D. D. Eley C. H. Rochester and M. S. Scurrell (a)Proc. Roy. SOC.,1972 A329 361 ; (b)Proc. Roy. SOC.,1972 A329,375; (c)J. Catalysis 1973,29,20; (d)J.C.S. Faraday I 1973,69 660. 106 M. S. Scurrell treatment procedure involving contact of the oxide with ethylene' or carbon "pd monoxide' at high temperature was necessary.Production of the most active samples was achieved for those conditions which resulted in a partial reduction of the Cr6' ions and it was concluded'310 that Cr5+ or Cr4+ ions could be the active polymerization centres. 1.r. spectroscopic examination of catalysts under reaction conditions revealed the production of surface ethyl species formed by a self-hydrogenation mechanism during the pretreatment contact with ethylene.' lb Catalysts which were active for ethylene polymerization were also able to adsorb carbon monoxide131c and nitric oxide.131d Carbon monoxide adsorption was readily reversible at ca. SO "C ;nitric oxide was largely adsorbed in a more irreversible manner but some desorption could be effected at 50°C. Carbon monoxide and nitric oxide adsorbed on cation centres of active poly- merization catalysts and the nature of the i.r.spectroscopic bands associated with adsorbed nitric oxide was exp1ainedl3ld in terms of the presence of Cr5+ Cr4+ and Cr3 +. The correlation between intensity of the absorption band associated with nitric oxide adsorbed on Cr5+ centres and the catalytic activity was con- sidered to be consistent with these centres being active for the polymerization of ethylene. Vuillaume et ~1.'~~ investigated the nature of the activation process for sup- ported chromium oxide catalysts. The results indicated that during the initial heating and outgassing of impregnated samples an exothermic reaction occurred at ca. 300 "C which resulted in the fixing of the chromium oxide layer by chromo- siloxane bonds.Thus catalyst activity was a function of the rate of heating rather than the total period at which the sample was held at the high temperature. Miesserov' 33 concludes that during initial interaction between ethylene and supported chromium oxide catalysts partial reduction of the Cr6 + ions occurs with production of Cr3+ centres which become alkylated. The active centre is envisaged as a Zenor-double-exchange type containing a Cr6+ ion and a Cr3+ ion the latter being attached to an alkyl unit. Propagation proceeds by olefin insertion at the Cr3 + -C bond. An assertion that high oxidation states of chromium are not responsible for the polymerization activity of these catalysts has been made by Kra~ss.'~~ It is proposed that Cr2+ centres having a high degree of co-ordinative unsatura- tion are present and act as the centres for polymerization.Surface complexes could be made by chemisorption of chlorine nitrogen carbon monoxide and in small quantities ethylene on the active Cr2 + centres. 1.r. spectroscopic results for adsorption of carbon monoxide on active catalysts were in good agreement with those of Eley et a!. Clark and Harris' 35 have investigated the surface reaction between but-1-ene and a silica-alumina catalyst at 30 "C. Calorimetric measurements indicated that 13* G. Vuillaume R. Spitz A. Revillon H. Charcosset P. Turlier and A. Guyot J. Catalysis 197 1 21 159. 133 K. G. Miesserov J. Catalysis 1971 22 340. 134 H. L. Krauss ref.246 Vol. 1 p. 207. 13' A. Clark and J. R. Harris J. Catalysis 1971 21 179. Heterogeneous Catalysis on Metal Oxides 107 dimers were produced at low reactant pressure with an increase in the average degree of polymerization as the pressure was increased. Codimerization of propylene with ethylene over nickel@) oxide-tungsten@) oxide-alumina catalysts has been studied together with an investigation of the isomerization of pentenes.' 36 The ternary mixed-oxide catalyst was more effective for codimerization than one containing nickel oxide and alumina whereas a tungsten oxidealumina sample was inactive. It is suggested that the initial products of the process are mainly n-pentenes which undergo skeletal isomeriza- tion to give isopentenes as secondary products.8 Decomposition Reactions Decomposition of Nitrous Oxide.-The use of the decomposition reaction of nitrous oxide in evaluating the effects of electronic properties of solids on cata- lytic activity is well known. Transition-metal oxides have been widely used for this system and several papers have appeared in the review period which deal with nitrous oxide decomposition over oxides containing transition-metal ions. The emphasis has changed to some extent from the use of pure oxides to studies of catalysis by metal ions in host oxide lattices. Cimino and Schia~ello'~' have studied the catalytic activity of nickel Ni2+ ions in a spinel matrix. Solids having general composition Ni,Mg -xA1204 were used where x was varied from 0 to 1. It was shown that the activity of surface Ni2 ions exposed from octahedral sites + was greater than that of Ni2+ ions exposed from tetrahedral sites.It was also apparent that the distribution of Ni2 + ions between the two environments differed in the surface layers from that found in the bulk. The results were dis- cussed in detail with reference to the stereochemical and electronic environment of the active surface cations. Cimino et uZ.'~* have further demonstrated that the activity of a given transition-metal ion in the nitrous oxide decomposition is dependent on the environment in which it is placed by examination of solid solutions of transition-metal oxides in zinc oxide and magnesium oxide. A given transition-metal ion was more active when dispersed in magnesium oxide than when dispersed in a zinc oxide lattice.Both the co-ordination sym- metry of the ions and the role of the matrix surface in the catalytic reaction step could be important. Nickel ions supported on y-and q-aluminas have also been tested for nitrous oxide decomposition activity.13' It has been shown that high catalytic activity parallels a high ratio of Ni2+ ions in octahedral sites to those in tetrahedral sites. Structural studies of the interaction between nickel oxide and. support aluminas were also of importance in this ~0rk.l~' Solid solutions of cobalt oxide-magnesium oxide (Coo-MgO) have been examined by Cimino and Pepe.141 The Co/Mg atomic ratio was varied between 5 x and 13' A. Kobayashi and E. Echigoya Nippon Kagaku Kaishi 1973 668.13' A. Cimino and M. Schiavello J. Catalysis 1971 20 202. 138 A. Cimino F. Pepe and M. Schiavello ref. 24b Vol. 1 p. 125. 139 M. Schiavello M. Lo Jacono and A. Cimino J. Phys. Chem. 1971 75 1051. I4O M. Lo Jacono M. Schiavello and A. Cimino J. Phys. Chem. 1971 75 1044. 14' A. Cimino and F. Pepe J. Catalysis 1972 25 362. 108 M. S. Scurrell 5 x lo-' and it was found that the specific activity per cobalt ion increased with increasing dilution. Measurements of oxygen adsorption were made during the decomposition reaction and the role of the matrix in the oxygen desorption step was discussed. A comparison of the activities of Co2+ and Ni2 + ions in magnesium oxide was also made and differences found were discussed in terms of the strength of the bond between the transition-metal ion and adsorbed oxygen.Some e.p.r. measurements of the state of copper ions dispersed in magnesium oxide and of their interaction with nitrous oxide have been discussed with reference to the catalytic activity of the samples for the decomposition process. 142 The results have suggested that the activity of cupric oxide-magnesium oxide catalysts may be attributed to the presence of Cu+ ions dispersed in the surface layers of the host oxide lattice. A study of the reaction over nickel oxide supported on silica has been described. The reaction mechanism was elucidated using a dynamic catalytic method and Arrhenius parameters associated with the separate reaction steps have been determined. Read'44 has presented results for nitrous oxide decomposition over neody- mium dysprosium and erbium oxides.The ratedetermining step is considered to be the initial decomposition of the reactant molecule but oxygen desorption is also important in this respect particularly at high oxygen pressures. There was no obvious trend in reactivity over the three oxides. Cracking Catalysis.-Some reports on the catalytic cracking of aromatic molecules have appeared. Hambleton and Hockey'45 investigated the reactivi- ties of samples of silica which had been treated with aluminium trichloride trimethylaluminium or boron trichloride. After hydrolysis Si0,-AlMe samples exhibited cracking activity comparable to that of a commercial silica-alumina cracking catalyst. Lower activity was found for hydrolysed Si0,-AlC13 catalysts and Si0,-BCl samples showed no activity at all above that of the parent silica.1.r. measurements assisted in obtaining a correlation between the cracking activity of the samples and their ability to produce and retain pyridinium ions when exposed to pyridine. Andrku et have examined the mechanism of cracking reactions displaced by butylbenzenes and cumene over silica-alumina. As the alumina content of catalysts increased surface acidity increased and reached a maximum at 25 % alumina content. An activity sequence was found for the ease of cracking of various reactants and it was found that the activity de- creased in the order t-butylbenzene > sec-butylbenzene > cumene. This sequence together with the initial isomeric distribution of product butenes was consistent with the participation of a carbonium ion intermediate.Both Bronsted- and Lewis-type acid centres were involved in the surface reactions. Bourne et 142 D. Cordische F. Pepe and M. Schiavello J. Phys. Chem. 1973 77. 1240. 143 C. C. Yang M. B. Cutlip and C. 0.Bennett ref. 246 Vol. 1 p. 279. 144 J. F. Read J. Catalysis 1973 28 428. '45 F. H. Hambleton and J. A. Hockey J. Catalysis 1971 20 321. P. Andreu G. Martin and H. Noller. J. Catalysis 1971. 21 255. 14' Heterogeneous Catalysis on Metal Oxides 109 al.14’ investigated the cracking reactions of t-butylbenzene on samples of silica containing aluminium atoms in different environments. The acidic properties of the aluminium centres depended upon their location.Catalysts containing aluminium introduced by impregnation techniques were compared with those prepared by cogellation of silica and alumina. The latter samples contained a greater concentration of alumina active for the cracking reaction. In contrast in the impregnated catalysts fewer active aluminium sites were present but these centres had a greater specific activity than those in the coprecipitated material. Ogata et ~21.~~~ have provided an interesting study of the activity of tungsten oxide for the cracking of n-heptane. The nature of the reaction products obtained could be changed by the reduction of tungsten trioxide at progressively higher temperatures. Slightly reduced material catalysed isomerization and central cracking of n-heptane via carbonium ion intermediates.Further reduction gave a catalyst which exhibited activity for demethylation to form methane and normal paraffins by selective scission of the terminal carbon<arbon bond as the pre- dominant process. When the oxide was reduced still further isomerization and central cracking occurred as in the initial case. Tungsten oxide reduced almost to tungsten metal favoured demethylation rather than isomerization and central cracking. Decompositionof Formic Acid.-A study of the factors controlling the selectivity of 3d metal oxides in the catalytic decomposition of formic acid was presented by Criado et al.14’ A comparison of the activation energy of reaction on titanium dioxide vanadium(II1) oxide chromium(II1) oxide manganese(I1) oxide and iron(m) oxide with the ease of decomposition of the corresponding formate supported the view that formate ions participated in the decomposition reactions in both the dehydrogenation and dehydration processes.The rate of the dehydro- genation reaction increased with the increasing ease with which transfer of electrons from the formate unit to the catalyst could take place. It was felt that the dehydration of formic acid proceeded via two mechanisms. One in which the rate-determining step consisted of elimination of water from two surface hydroxy-groups was operative on TiO, V,O, and Cr,O and another in which the rate of reaction was determined by the ease of dissociation of the carbon-oxygen bond of the surface formate took place on Fe,04 and MnO.Formic acid decomposition on metal oxides is the subject of a recent review.”’ Munuera et ~1.~” have investigated the interaction of formic acid with titanium dioxide (anatase) and the mechanism of the catalytic dehydration reaction. Adsorption and temperature-programmed desorption studies were combined with i.r. spectroscopy. It was concluded that the dehydration reaction took place via a surface formate species. The anatase and rutile forms of the oxide show different kinetic behaviour and it is suggested that these reflect the differences in 14’ K. H. Bourne F. R. Cannings and R. C. Pitkethly J. Phys. Chem. 1971,75 220. “* E. Ogata Y. Kamiya and N. Ohta J. Catalysis 1973 29 296. 149 J. M. Criado F.Gonzalez and J. M. Trillo J. Catalysis 1971 23 11. lSo J. M. Trillo G. Munuera and J. M. Criado Catalysis Rev. 1972,7 51. I G. Munuera F. Gonzalez F. Moreno and J. A. Prieto ref. 246. Vol. 2 p. 1159. 110 M. S. Scurrell the atomic structure of the surface. The decomposition reaction has been used to assess the relative importance of electronic and geometric factors in catalysis over sodium tungsten bronzls Na,WO with x lying in the range 0.11-0.85.152 The activities and selectivities of several preparations each having a different value of x were measured. The behaviour of the bronzes in formic acid decomposition was interpreted in terms of geometric rather than electronic factors. A marked change from dehydration to dehydrogenation activity which was seen when x increased beyond 0.7 was related to an ordering of residual sodium vacancies in the catalysts.Dehydration involved adsorption on adjacent sodium and oxygen vacancies whereas dehydrogenation proceeded via adsorption on a sodium cluster site. Miscellaneous Decomposition Reactions.-Solymosi and Gera 53 have examined the decomposition of perchloric acid on zinc oxide. Interaction between the reactant and catalyst at 250°C resulted in the formation of considerable quantities of zinc perchlorate. The catalytic decomposition process took place at temperatures above 310 "C and it was suggested that the participation of surface perchlorate in the reaction was of importance. Magnesium and cadmium oxides were reported to be inactive and it was noted that this is in accord with the greater stabilities of the corresponding perchlorates.Gilbert and Jacobs' 54 also found evidence for participation of perchlorate in the decomposition reaction catalysed by copper chromite alumina ferric oxide-alumina cupric oxide- alumina and manganese@) oxide. The decomposition was thought to proceed via a proton transfer from the reactant to a surface oxide ion followed by decomposi- tion of the perchlorate anion formed in the process. WinterlS5 has reported data for the decomposition of nitric oxide over 40 metal oxides. The reaction mechanism was reported to consist of an initial attack by a nitric oxide molecule at a surface R centre (adjacent anion vacancies each containing a trapped electron) followed by desorption of an 0 molecule.It was found that this oxygendesorption step largely controlled the variation in the catalytic activity over the range of oxides used. The ease of desorption was dependent upon the crystal type of the oxide and a correlation between the activa- tion energy for decomposition and the molecular volume was obtained for several series of catalysts each of which contained oxides of a similar crystal type. It was felt that in this study relationships between semiconduction properties or crystal field effects and catalytic activity were not to be expected. 9 Dehydration and Dehydrogenation Reactions The major part of this section is devoted to consideration of reports of dehydration and dehydrogenation reactions of alcohols over oxides.Also included are a few papers dealing with the oxidative dehydrogenation of alcohols. Reports of some a,' S. S. Mooday and D. Taylor J.C.S. Faraday I 1973,69 289. 153 F. Solymosi and L. Gera J. Phys. Chem. 1971,75 491. lS4 R. Gilbert and P. W. M. Jacobs Canad. J. Chem. 1971 49 2827. 155 E. R. S. Winter J. Catalysis 1971 22 158. Heterogeneous Catalysis on Metal Oxides investigations into the dehydrogenation behaviour of chromia catalysts may be found at the end of the section. General Studies of the Decomposition of Alcohols over Metal Oxides-Alumina has been widely used for the catalytic decomposition of alcohols. Dehydration activity for primary secondary tertiary and alicyclic alcohols has been deter- mined by Knozinger et al.'56 By examination of the product distributions and Arrhenius parameters it has been suggested that the E,-like transition-state struc- ture is influenced by inductive hyperconjugative and steric effects.Elimination of a p-proton from a transposition is potentially subject to a high degree of steric hindrance and cis-preference is therefore often found. An attempt to obtain a linear free energy relationship in the form of a Taft correlation for the dehydration reaction was not successful. Knozinger et al. 57 have further demonstrated that the analysis of mechanistic models for bimolecular ether formation from alcohols over alumina leads to the production of multiparameter kinetic equations. Discrimination between such rival models of which type there appear to be five that adequately describe the kinetics of ether formation from ethanol on q-alumina was not possible.Hertl and Cuenca' 58 have concluded that methanol ethanol propanol and butanol chemisorb on alumina as alkoxy-groups. At high temperatures (>150°C) and in the presence of alcohol vapour or air these groups are converted into carboxy-species. The role played by Lewis-acid surface sites has been stressed. Pines and Brown'59 have reported that ring expansion during the dehydra- tion of cycloalkane-methanols is greater if the alumina has been partially deacti- vated. The presence of sodium ions in the catalysts lowered the amount of double-bond isomerization which took place but did not affect the amount of skeletal rearrangement.Studies of the dehydrogenation and dehydration of alcohols over well charac- terized hydroxyapatite catalysts have revealed' 6o that dehydration rate constants for fifteen reactant alcohols correlate with the Taft a,*constant for a-substitution. Mainly syn-eliminations were observed and appear to take place in the presence of sufficiently acidic surface hydroxy-groups. Results for the dehydrogenation of secondary alcohols suggested that the transition state was negatively charged and it was suggested that an alkoxide ion was the precursor species. Such correla- tions have also been found by Niiyama and Echigoya'61 for alcohol decomposi- tion over alkaline-earth silicates. It was reported that the acid-base properties of both the catalysts and the reactants were co-operative in determining the selectivity of reaction.H. Knozinger H. Buhl and K. Kochloefl J. Catalysis 1972 24 57. H. Knozinger K. Kochloefl and W. Meye J. Catalysis 1973,28,69. W. Hertl and A. M. Cuenca J. Phys. Chem. 1973,77 1120. H. Pines and S. M. Brown J. Catalysis 1971 20 74. Ibo C. L. Kibby and W. K. Hall J. Catalysis 1973,29,#144. Ib1 H. Niiyama and E. Echigoya Bull. Chem. SOC.Japan 1971.44 1739. 112 M. S. Scurrell Reactionsof Methanol.-In part of a general study on the acid strength of sites on silica-alumina catalysts Parera et ul.' 62 have reported that the dehydration of methanol requires the presence of acid sites which are stronger than those necess- ary for the cracking of cumene. Figueras et uI.'~~ have suggested that whereas the dehydration of t-butyl alcohol over silica-alumina occurs on acid sites and pro- ceeds via a carbonium ion intermediate methanol undergoes dehydration uiu interaction at an acid-base pair site.The initial attack is from a basic site to the methyl group of the reactant molecule and alumina is a better catalyst than silica- alumina. 1.r. spectra of adsorbed species recorded during the course of the reaction have enabled Ueno et to investigate the decomposition of methanol on zinc oxide. When [2H,]methanol was used methoxide and formate ions were pro- duced on the surface and deuterium carbon dioxide and carbon monoxide were evolved into the gas phase. It was concluded that the decomposition of the formate ion led to formation of the carbon monoxide.The remaining products were the result of reaction between a methanol molecule and an adsorbed formate ion. Novakova et ~1.'~~ have reported results for the oxidative dehydrogenation of methanol on ferric oxide molybdenum trioxide (MOO,) and a mixed MoV'-Fe"' oxide. Methanol reacts with fresh MOO catalyst in the absence of oxygen to produce formaldehyde and water. Further reaction of methanol leads to reduction of the oxide and to the production of carbon monoxide and carbon dioxide and hydrogen. On Fe,O (again without oxygen) carbon monoxide carbon dioxide and hydrogen are produced initially. Over the mixed oxide only formaldehyde and water are produced. It is concluded that the behaviour of the latter catalyst resembles that of molybdenum trioxide in an unreduced state and it is suggested that the presence of Fe3+ ions hinders the reduction of Mo6+ ions which would otherwise occur with a concomitant decrease in the selectivity for formaldehyde production.The relationship between the structure and composition of iron-molybdenum oxide binary mixtures and their catalytic activity for methanol oxidation has been discussed by Peirs and Leroy.'66 Optimum activity is found by treating a catalyst containing 75 atom % molybdenum at 330 "C. Mann and Dosi' investigated a vanadium pentoxide-molybdenum tri- oxide mixture for the catalytic oxidation by air of methanol. A selectivity for production of formaldehyde of 100%with very high conversion could be achieved. A derived rate expression which assumed a steady state involving a two-stage irreversible oxidation-reduction process was reported to explain the observed reaction kinetics satisfactorily.16' J. M. Parera S. A. Hillar J. C. Vincenzini and N. S. Figoli J. Curulysis 1971,21,70. 163 F. Figueras A. Nohl L. de Mourgues and Y.Trambonze Trans. Faruduy SOC.,1971 67 1155. 164 A. Ueno T. Onishi and K. Tamaru Trans. Furuday Soc. 1971,67 3585. J. Novakova P. Jiru and V. Zavadil J. Catalysis 1971 21 143. Ibb S. Peirs and J. M. Leroy Bull. SOC.chim.France 1972 1241. R. S. Mann and M. K. Dosi J. Catalysis 1973 28 282. Heterogeneous Catalysis on Metal Oxides 113 Reactionsof Ethanol.-The possible importance of electron-transfer mechanisms involved in the dehydrogenation of ethanol on zinc oxide films has been investi- gated by McArthur et It was reported that at low temperatures (< 200 "C) ethanol adsorbs as an electron donor and at higher temperatures (>225 "C) the composite adsorbed layer of reactant and products also behaved as a donor.After examination of the donor or acceptor natures of the individual components present in the reaction it was concluded that the adsorbed layer under reaction conditions comprised ethanol and hydrogen. Field-effect experiments were conducted and showed that the activity and selectivity of the catalyst were unaffected by the application of external d.c. fields up to lo4V cm-It is suggested that the results indicate that the rate-limiting step is not affected by the surface concentration of free electrons and also that the overall reaction rate is not determined by the rates of adsorption-desorption steps.Acetaldehyde was the other dehydrogenation product in this study. Niiyama et ~1.'~'report results for the catalytic decomposition of ethanol over silica-magnesium oxide catalysts. Maximum surface acidity was obtained for an oxide mixture containing 50 mol % magnesium oxide. Basicity increased monotonically with the magnesium oxide content. However the rate of produc- tion of butadiene was a maximum for a mixture containing ca. 85 mol %magnesi-um oxide. Pure magnesium oxide was a very poor catalyst for the production of butadiene and it was concluded that both acidic and basic sites were necessary for this product to be formed.Ethanol decomposes on a boron phosphate catalyst to yield ethylene and diethyl ether as the major products.' 70 The percentage conversion into ethylene increases continuously with increasing temperature whereas that into ether passes through a maximum in the neighbourhood of 300 "C. Legendre and Cornet' 7' reported that ethanol reacts over tantalum oxide (Ta20,) in the presence of oxygen to yield on fresh catalyst ethylene as well as oxidation products. The initial activity of the catalyst was low but continued use resulted in a marked increase in the rate of production of acetaldehyde. It appeared that the fresh catalyst contained acidic sites able to cause dehydration of the reactant and it was suggested that the sites active for oxidation of the ethanol to acetaldehyde might have been produced during the initial stages of reaction.Reactions of Propano1.-McCaffrey et al.'72 have examined the decomposition of propan-2-01 over niobium and molybdenum oxides and over the oxides of the first transition-metal series. Complex behaviour is sometimes observed and secondary products have been detected in dehydrogenation catalysis. Detailed mechanisms for the decomposition reactions were not presented but several correlations were obtained. It was found that those oxides which exhibited 168 D. P. McArthur H. Bliss and J. B. Butt J. Catalysis 1973,28 183. lb9 H. Niiyama S. Morri and E. Echigoya Bull. Chem. SOC.Japan 1972 45 655. "O J. B. Moffat and A. S. Riggs J. Catalysis 1973 28 157. "' M.Legendre and D. Cornet J. Catalysis 1973 25 194. E. F. McCaffrey D. G. Klissurski and R. A. Ross ref. 246 Vol. 1 p. 151. 114 M. S Scurrell oxygen exchange with a high activation energy also displayed a high selectivity for dehydration of propan-2-01. A complementary relationship was obtained which demonstrated that the highest rates of oxygen exchange were seen for oxides which showed a high selectivity for dehydrogenation. For several oxides the high selectivity for propylene formation from propan-2-01 was paralleled by a high selectivity for the production of formaldehyde in the catalytic oxidation of methanol. Finally there existed a relationship between the charge/radius ratio of the metal oxides and the selectivity for propylene formation from propan-2-01.Oxides having high values for this ratio are those over which dehydration is favoured. It is suggested that the key factor in determining the selectivity of a given catalyst is the degree of mobility of surface oxygen species. McCaffrey et ~1.'~~ have also shown that this approach may be extended to a consideration of the activities and selectivities displayed by oxides of the alkaline- earth metals beryllium magnesium calcium strontium and barium. The energy of activation for dehydrogenation varied from 19 kcal mol- 'for beryllium oxide to 45 kcal mol- 'for calcium oxide. The activation energy for dehydration was always higher than that for dehydrogenation for a given oxide in the series. The selectivity for acetone formation from propan-2-01 increased with increasing ionic character of the oxides and was paralleled by an increase in the catalytic activity for oxygen-exchange reactions.It is believed that the degree of ionicity of surface oxygen plays a decisive part in determining the activity of the oxides selectivity being controlled by the mobility of surface oxygen. Kochloefl and Knozinger'74 reported results of a study of kinetic isotope effects in the dehydration of deuteriopropan-2-01s over oxide catalysts. Reactions of propan-2-01 C2H ,]propan-2-01 [CH,CH(OD)CH,] and [*H6]propan-2-ol [CD,CH(OH)CD,] were studied over alumina (partially poisoned with sodium ions) zirconium dioxide titanium dioxide and silica. The mechanism of water elimination changed from predominantly E2-like on alumina to El-like on silica.A linear free energy relationship existed between the observed kinetic isotope effects and parameters of a Taft equation. The dehydration activities of v-,8- and a-aluminas have been discussed by Szabo and Jover.'75 Great similarity in the behaviour of v-and 8-forms was found with the latter slightly more basic and less active for propan-2-01 dehydra- tion The a-alumina appeared to be very inert. The dehydration characteristics of the aluminas have been discussed in terms of their morphology as revealed by electron scanping microscopy. Bremer and Glietsch' 76 report that the specific activities of different transient forms of alumina for propan-2-01 dehydration varied. Measurements of the degree of surface hydration and of the acidities of transient forms of alumina revealed that the catalytic activity for the dehydration reaction was determined E.F. McCaffrey T. A. Micka and R.A. Ross J. Phys. Chem. 1972,76 3372. I74 K. Kochloefl and H. Knozinger ref. 246 Vol. 2 p. 11 71. 17' Z. G. Siabo and B. Jover ref. 246 Vol. I. p. 833. ''~5 H. Bremer and J. Glietsch Z. anorg. Chem. 1972 395 82. Heterogeneous Catalysis on Metal Oxides 115 by the number of surface acid centres.'77 No correlation between activity and the concentration of surface hydroxy-groups was obtained. Kolboe'78 has studied the effects of the morphological character of an oxide catalyst on the kinetics of propan-2-01 dehydrogenation. Two widely differing samples were employed and a knowledge of their individual morphologies was used in predicting the adsorptive and catalytic properties.The results indicate that the influence of specific crystal planes on the overall activity of an oxide catalyst should be taken into account. Uma et ~1.l~~ report that a sample of zinc oxide which showed a defect structure was inactive for the decomposition of propan-2-01 whereas a second sample which showed a normal X-ray pattern exhibited dehydrogenation activity. Samples containing zinc oxide supported on alumina magnesium oxide or titanium dioxide showed much higher dehydro- genation activities than any of the parent oxides. In contrast ferric oxide lost its inherent dehydrogenation activity when supported on alumina but exhibited an enhanced activity for dehydration.It was concluded that magnesium oxide and titanium dioxide supports facilitated the formation ofzinc oxide in a well dispersed and active form. In the ZnO-Al,O sample the catalytic activity occurred at the ZnO-ZnAl,O interface. The pronounced influence of alumina on the catalytic activity of ferric oxide was discussed. Pepe and Stone lB0 have reported detailed results for propan-2-01 decomposi- tion reaction over a-Al,O ,a-CrAl -xO, and a-Cr,O catalysts prepared at high temperature to ensure complete isomorphism. a-Al,O alone is a pre- dominantly dehydrogenating catalyst but becomes dehydrating in nature on the addition of only 0.1 % Cr. Beyond 1% Cr the dehydration activity declines. At x = 0.2 the catalytic reaction is mainly that of dehydrogenation but at x = 2 (a7Cr,0,) dehydration is again favoured.It was concluded that the catalytic properties of transition-metal ions in oxide solid solutions is controlled by the production of active centres by the incidence of electronic coupling between the transition-metal ions and by the electron distribution in the metal-oxygen bond- ing in the solvent oxide. The complex behaviour of magnesium oxide in the catalytic decomposition of propan-2-01 has been described by Klissurski et al.' Dehydrogenation de- hydration and condensation processes take place and reaction products can exert considerable effects on the course of the catalysis. A relationship between the oxygen content of manganese oxides and their dehydrogenation activity has been obtained by McCaffrey et Catalysts having a high O/Mn ratio exhibit a high rate of dehydrogenation of propan-2-01 and also contain oxygen which has a lower binding energy than that present in oxides with low O/Mn ratio.The dehydrogenation activity of manganese ferrites between 306 and 362 "C is I" H. Bremer and J. Glietsch Z. anorg. Chem. 1972 395 91. '" S. Kolboe J. Catalysis 1972,.27 379. R. Uma R.Venkatachalan and J. C. Kuriacose ref. 246 Vol. I p. 245. F. Pepe and F. S. Stone ref. 246 Vol. 1 p. 137. D. G. Klissurski E. F. McCaffrey and R. A. Ross Canad. J. Chem. 1971.49 3778. E. F. McCaffrey D. G. Klissurski and R. A. Ross J. Caralysis 1972 26 380. 116 M. S. Snsrrell reported to be constant.183 It is concluded that either adsorption of propan-2-01 or desorption of propylene is extremely rapid.Reactions of Butanol and Higher Molecular Weight Alcohols.-The catalytic activity of calcium and strontium hydroxyapatites for the dehydration of n- butanol have been compared.' 84 Together with results of spectroscopic studies' 85 the kinetic results suggest that incompletely co-ordinated cations in the lattice form stronger acid sites than the HP042-groups. The active centre is produced by interaction of water molecules with these cations. Miller and WU'~~ have examined the dehydrogenation of isobutyl alcohol over zinc and copper oxides. The effect of oxygen pretreatment on the catalytic activities of these oxides is consistent with a rate-limiting step involving oxygen surface states and hole charge transfer to the adsorbed alcohol.Cupric oxide was much more active than zinc oxide in the temperature range investigated. Chuang and Dalla Lana'87 reported that the selectivity exhibited by y-alumina in the catalytic decomposition of pentan-3-01 is governed by the nature of acidic centres present. Doping of the oxide with sodium hydroxide eliminated Bronsted- acid sites and shifted the selectivity in favour of the dehydrogenation route. It has been suggested' 88 that the selectivity of alumina for decomposition of octan-2-01 is determined by the electronic properties of the solid. The dehydration-dehydrogenation behaviour of thorium oxide has been assessed by reactions involving octan-2-01.' 89 The selectivity was a function of catalyst pretreatment heating in hydrogen and oxygen at 600 "C promoting dehydration and dehydrogenation activity respectively.The selectivity for oct-1-ene formation as compared with oct-2-ene formation was also dependent upon pretreatment. In addition certain thorium oxide preparations were much more selective for oct-1-ene formation than others. It was felt that in the absence of further evidence the changes observed could not definitely be attributed to differences in bulk semiconducting properties of the variously pretreated and prepared catalysts. Dehydrogenatioo Reactions over Chromia Catalysts.-Marcilly and Delmon have studied the dehydrogenation of isobutane to isobutene over a series of chromia-alumina catalysts. Intrinsic activities based on conversion rates per unit area of surface showed a marked minimum for chromic oxide-rich solid solutions.In alumina-rich samples a-phases were almost totally inactive but relatively high activities were exhibited by y-phases. It was suggested that Cr2+ and Cr3 ions were the active dehydrogenation centres and that these were more + likely to be found in the y-phases rather than the strongly covalent a-phases. E. F. McCaffrey and R. A. Ross Canad. J. Chem. 1973,51,2486. Ia4 S. J. Joris and C. H. Amberg J. Phys. Chem. 1971 75 3167. lSs S. J. Joris and C. H. Amberg J. Phys. Chem. 1971,75 3173. la6 K. J. Miller and J.-L. Wu J. Catalysis 1972 27 60. la' T. T. Chuang and I. G. Dalla Lana J.C.S. Faraday f 1972 68 773. B. H. Davis J.Catalysis 1972 26 348. la9 B. H. Davis and W. S. Brey,jun. J. Catalysis 1972 25 81. 190 C. Marcilly and B. Delmon J. Caralysis 1972 24 336. Heterogeneous Catalysis on Metal Oxides 117 Further evidence that dehydrogenation activity is associated with Cr3 + centres is provided by the results of Masson and Delrn~n.”~ Isobutane conversion into butene is promoted ‘on chromia-alumina samples by incorporation of potassium rubidium or caesium oxides. These additives increased the Cr3 + active-site content and inhibited recrystallization to the a-phase. Kazansky et ~1.’’~ have studied the mechanism by which the dehydrocycliza- tion of paraffins takes place on chromia catalysts. It is concluded that n-hexane undergoes conversion into an aromatic molecule via hexene hexadiene and hexatriene intermediates and that since cyclization of the final species can take place in the absence of a catalyst no specific cyclization activity of chromia is needed.Dehydrogenation activity alone is sufficient for the dehydrocyclization process to take place. 10 Isomerhation Reactions Dent and Kokeslg3 suggested that butene isomerization over zinc oxide occurs via the formation of a n-bonded allylic species. But-1-ene was not an intermediate in cis-trans isomerization. Chang Conner and Kokes’ 94 later examined the reactivity of zinc oxide and chromia for butene isomerization. Over chromia the kinetic cis-trans selectivity differed only slightly from the equilibrium ratio except for samples degassed at high temperatures.Over zinc oxide the selectivity was in favour of the formation of cis-butene. A speculative interpretation of the reaction mechanism involving syn- and anti-n-ally1 intermediates was given. Chang and KokesIg5 used kinetic and i.r. spectroscopic techniques to examine the isomeriza- tion of acetylenes over zinc oxide. It was suggested that a propargyl species formed by dissociative adsorption of methylacetylene functions as an intermediate in allene-methylacetylene isomerization. Kokes2&-‘ has summarized the experi- mental data pertaining to isomerization of olefins and acetylenes over zinc oxide. For silica catalysts measurements of kinetic isotope effects have suggested that the abstraction of hydrogen from the catalyst is rate-determining only for the isomerization of allene.No primary isotope effect was found for the reverse isomerization of methyla~etylene.”~ West et uZ.”~ recently suggested that many reactions including those of isomerization reported to be catalysed by silica gel probably occur at impurity sites most likely A13+ ions. It has been reported”* that the activities of several amorphous aluminas (activated at various temperatures) for but-1-ene isomerization correlates with differences in the oxidizing and reducing properties of the catalysts. However the selectivity (cisltrans ratio of but-2-ene produced) remained constant for the whole series of samples. 19’ J. Masson and B. Delmon ref. 246 Vol. 1 p. 183. 19* B. A. Kazansky G. V. Isagulyants M. I. Rozengart Yu.G. Dubinsky and L. I. Kovalenko ref. 246 Vol. 2 p. 1277. 193 A. L. Dent and R. J. Kokes J. Phys. Chem. 1971,75 487. 194 C. C. Chang W. C. Conner and R. J. Kokes J. Phys. Chem. 1973,77 1957. 195 C. C. Chang and R. J. Kokes J. Catalysis 1973 28 92. 196 J. H. Parmentier H. G. Peer and L. Schutte J. Caralysis 1971 22 213. 19’ P. B. West G. L. Haller and R. L. Burwell jun. J. Catalysis 1973 29 486. 19* A. Ghorbel C. Hoang-Van and S. J. Teichner J. Caralysis 1973 30 298. 118 M.S. Scurrell Gati and KnOzingerlg9 reported very valuable results for the isomerization of 14 terminal olefins over alumina catalysts. The double-bond shift reaction was concluded to occur uia an intramolecular proton transfer and the observed cis preference was explained by the relative stabilities of the cis- and truns-conforma- tions of the carbanionic intermediates.A linear free energy relationship between the relative reactivities of the olefins and Taft inductive constants was obtained. Baird and LunsfordZo0 have examined the activity of magnesium oxide for but- 1-ene isomerization. It was concluded that the reaction proceeded via a carban- ionic intermediate on surface sites which were at a maximum concentration following pretreatment at 700°C.It was suggested that 0’-ions located at corners of the cubic oxide lattice were the centres for catalytic activity. Hattori et ~1.’~’ have investigated the activities and selectivities of calcium and magnesium oxide catalysts for the isomerization of but-1-ene. Again maximum activities for both oxides were found as the pretreatment temperature was increased.It was concluded that those sites on which cis-but-2-ene was produced were basic in character whereas these on which the trans-isomer was formed were mainly acidic. Shannon et ul.zozreported that but-1 -ene isomerization takes place over magnesium oxide via allylic carbanion intermediates. The cis-trans isomerization reaction did not occur via but-1-ene as an intermediate and in addition it was concluded that surface hydroxy-groups played no part in the isomerization processes. The pattern of activity for the isomerization of but-1-ene over oxides of the first-transition-series elements showed some similarity to the twin-peak pattern well known for hydrogendeuterium exchange and related reactions.The initial cis-trans product ratios over these oxides were discussed in terms of prob- able reaction intermediates. A detailed examination of the surface and catalytic properties of chromic oxide catalysts has been reported by Cross and Leach.203 But-1-ene isomerized via a carbonium ion intermediate at relatively low pretreat- ment temperatures but catalysts dehydroxylated at high temperatures gave an initial product ratio consistent %ith the involvement of an allylic intermediate. Kemball et aLzo4reported that but-1-ene isomerization over tin oxide (SnO,) at about room temperature was accompanied by the formation of large amounts of butadiene thought to be produced uin a butadiene surface species obtained by the simultaneous removal of two hydrogen atoms from adsorbed but-1 -ene.Isomer- ization of cis-but-2-ene yielded exclusively the trans-isomer and was considered to proceed via an intramolecular mechanism involving a secondary butyl carbonium ion intermediate. The nature of the adsorbed species involved in the isomerization reactions of butenes over rutile has been disc~ssed.~’ In keeping with the amphoteric nature 199 G. Gati and H. Knozinger ref. 246 Vol. 1 p. 819. *O0 M. J. Baird and J. H. Lunsford J. Catalysis 1972 26,440. 201 H. Hattori N. Yoshii and K. Tanabe ref. 246 Vol. 1 p. 233. ’02 I. R. Shannon C. Kemball H. F. Leach in ‘Chemisorption and Catalysis’ Institute of Petroleum London 1971 p. 46. 203 N. E. Cross and H. F. Leach J. Catalysis 1971 21 239.204 C. Kemball H. F. Leach and I. R. Shannon J. Catalysis 1973 29 99. Heterogeneous Catalysis onMetal Oxides 119 of the oxide formation of carbanionic and to a lesser extent carbonium ion intermediates was inferred. An olefin-disproportionation catalyst prepared from hexacarbonylmolyb- denum supported on y-alumina has been shown to effect the isomerization of butenes205 The interconversion of cis-and trans-butenes occurred by a bi-molecular intermediate whereas the double-bond shift reaction was essentially unimolecular. Different types of site were believed to be responsible for the two processes. Batist et have shown that the isomerizati~n of butenes over bismuth molybdate (Bi,03-MOO,) is severely retarded by the oxidation product butadiene.High activation energies were obtained for recirculation experiments whereas for a pulse reactor where diene inhibition was inoperative the activation energy was much lower. It was proposed that isomerization proceeds on those centres which are also active for the oxidation reactions displayed by the catalyst. The exchange and isomerization reactions of 3,3-dimethylbut-1 -ene over silica- alumina and magnesium oxide have been reported by Kemball et a/.33 Slow isomerization took place at high temperatures on magnesium oxide in the presence of deuterium oxide. In contrast interconversion of 2,3-dimethylbut-1- ene and 2,3-dimethylbut-2-ene occurred rapidly at room temperature. It has been reported3 that gallium oxide catalyses the direct interconversion of cis-and trans-isomers of butenes and pentenes at temperatures well below those required for double-bond shift.The formation of vinyl intermediates was con- sidered to be responsible for the observed behaviour. 11 Disproportionation Reactions The disproportionation of propylene on an alumina-supported hexacarbonyl- molybdenum catalyst has been investigated by Davie et aL207 Results of kinetic studies showed that the rate-controlling step was a surface reaction involving two adjacently adsorbed propylene molecules. The reactive surface complex was formulated as Mo(CO),Pr,-. where x was <6 and probably between 3 and 4 (Pr = propylene). By measurement of i.r. absorption spectra of disproportiona- tion catalysts together with their catalytic activities Howe et have shown that supported hexacarbonylmolybdenum undergoes decomposition during the catalyst-activation procedure.It was further shown that for alumina- and magnesium oxide-supported samples the active species was produced as a result of the loss of all six carbonyl ligands and that intermediate sub-carbonyl species were not responsible for the disproportionation behaviour. It was felt that the oxidation state of molybdenum in the active centres was greater than zero. Further spectroscopic investigations have been carried out. Whan Barber and Swift209 have investigated the X-ray photoelectron spectra for alumina-supported 205 E. S. Davie D. A. Whan and C. Kemball ref. 246 Vol. 2 p. 1205. '06 Ph. A. Batist P. C. M. van der Heijden and G.C. A. Schuit J. Catalysis 1971,22,411. *O' E. S. Davie D. A. Whan and C. Kemball J. Catalysis 1972 24 272. '08 R. F. Howe D. E. Davidson and D. A. Whan J.C.S. Furaduy I 1972 68 2266. 209 D. A. Whan M. Barber and P. Swift J.C.S. Chem. Comm. 1972 198. 120 M. S. Scurrell hexacarbonylmolybdenum catalysts and have confirmed that active catalysts are produced by loss of the carbonyl ligands. The loss of activity on exposure of such a catalyst to air is accompanied by oxidation of the molybdenum. E.p.r. spectro- scopy has been used by Howe and Leith2" in an attempt to identify the active molybdenum species. The presence of molybdenum(v) in a square-pyramidal environment was demonstrated but there was no correlation with catalytic activity.It was suggested that the active species was possibly molybdenum(1v). Davie Whan and Kembal121' have reported that the activity of such dispro- portionation catalysts may be greatly increased by pretreatment with a halo- genated olefin. Luckner and co-workers2 12p2 have investigated the disproportionation of propylene over silica-supported tungsten trioxide. Kinetic behaviour was consist- ent with a rate-controlling process involving a dual-site active centre such as a cyclobutane-type intermediate. In addition it was shown213 that during the initial contact of catalyst with propylene significant increases in disproportiona- tion activity may be found. Data were presented which demonstrated that during this activation period catalyst reduction took place together with irreversible adsorption of propylene.Only modest rates of disproportionation were obtained for fully oxidized samples. The effect of the addition of small (ca. 1-3 %) quantities of thallium to molyb- denum oxide-alumina catalysts on disproportionation activity was reported.2 l4 Thallium was equivalent on a molar basis to rubidium in its effectiveness in promoting the selective disproportionation of but-1 -ene at the expense of the double-bond isomerization process. A linear relationship between selectivity and ionic radii of thallium (univalent) and alkali-metal ions (Li' Na' K+ Rb+ and Cs') was obtained suggesting that the polarizability of the impurity cation was an important factor. The dual-site or cyclobutane-intermediate mechanism for disproportionation of propylene was reported to explain the kinetic data obtained by Lewis and Wills215 for cobalt molybdate catalysts.However O'Neill and Rooney2I6 consider that the alternative proposals of Lewandos and in which the carbon-arbon a-bonds of a molecule such as ethylene are ruptured simultane- ously with the n-bonds so that the cyclobutane unit is never formed are supported by their experimental observations. They have reported that the activity of cobalt molybdate catalysts for propylene disproportionation is paralleled by activity for the disproportionation of diazomethane to ethylene and nitrogen. *lo R. F. Howe and I. R. Leith J.C.S. Faruday I 1973,69 1967. 211 E. S. Davie D. A. Whan and C. Kemball Chem. Comm. 1971 1202.'I2 R. C. Luckner G. E. McConchie and G. B. Wills J. Catalysis 1973 28 63. 'I3 R. C. Luckner and G. B. Wills J. Catalysis 1973 28 83. 214 T. P. Kobylinski and H. E. Swift J. Catalysis 1972 26 416. 215 M. J. Lewis and G. B. Wills J. Catalysis 1971 20 182. *I6 P. P. O'Neill and J. J. Ronnery J.C.S. Chem. Comm. 1972 104. '' G. S. Lewandos and R. Petit Tetrahedron Letters I97 1 789. Heterogeneous Catalysis on Metal Oxides 121 12 Photocatalysis Extensive reviews of heterogeneous photocalysis and the electronic theory of photocatalytic reactions on semiconductors have been presented by Steinbach’ * and Wolkenstein’ l9 respectively. The photocatalytic decomposition of nitrous oxide over zinc oxide has been studied by Tanaka and Blyholder.220 Under the conditions used both thermal catalytic and photocatalytic processes occur but each obeys a different rate equation with respect to the partial pressures of nitrous oxide and oxygen.It was concluded that the photocatalytic decomposition occurs viu formation of the N,O -intermediate whereas thermal catalytic reaction probably takes place without electron transfer and involves atomic and molecular species only. Activation energies for photoreactions and dark reactions were 13 and 35kcal mol-respectively. Tanaka and Blyholder2’l have also found differences be- tween the behaviour of zinc oxide for the catalytic oxidation of carbon monoxide in dark and illuminated conditions. For oxidation with nitrous oxide the rate equation is given by rate = kpi,p& (thermal catalysis) and rate = klp~~p~~o (photocatalysis).The former reaction is unlike the latter inhibited by the presence of oxygen. It was suggested that the slow steps of the thermal catalytic reactions of carbon monoxide with oxygen or carbon monoxide with nitrous oxide involve the interaction of weakly adsorbed carbon monoxide and 0-adsorbed on interstitial zinc atoms or ions. Under photocatalytic conditions the slow steps involved reaction between carbon monoxide and 0-or reaction between N,O-and CO+ units respectively on lattice zinc and/or oxide sites with electrons and holes produced by illumination. In contrast to the behaviour shown in these oxidation processes the same workers find that no photoeffects are observed for the hydro- genation of ethylene over zinc oxide.’” It was concluded that the rate of this reaction is not directly controlled by the electronic band structure of the catalyst but that hydrogenation probably proceeds on strained surface sites which are likely to be photoinsensitive.Cunningham et ~l.’’~ have shown that the photocatalytic decomposition of nitrous oxide over pure or doped zinc oxide or over ferric oxide may be related to photocurrents measured in films of the same oxides. Only photons of energy greater than 2 eV produced a photocatalytic effect. The observed results were interpreted in terms of photoinduced changes in the boundary-layer potential from depletive chemisorption of nitrous oxide at the oxide-gas interface. Gaseous iodomethane has been reported to undergo dissociation to give methane in the gas phase on semiconducting zinc oxide at 20 “Cin the absence of ill~mination,’’~ but additional dissociation was observed when a catalyst was 218 F.Steinbach Forrschr. Chem. Forsch. 1972 25 117. 219 Th. Wolkenstein Adv. Catalysis 1973 23 157. ”O K. Tanaka and G. Blyholder J. Phys. Chem. 1971.75 1037. K. Tanaka and G. Blyholder (a)Chem. Comm. 1971 736; (b) J. Phys. Chem. 1972 76 1807. 222 K. Tanaka and G. Blyholder J. Phys. Chem. 1972,76 1394. 223 J. Cunningham J. J. Kelly and A. L. Penny J. Phys. Chem. 1971,75,617. 224 J. Cunningham and A. L. Penny J. Phys. Chem. 1972,76,2353. 122 M. S. Scurrell irradiated with U.V. light of wavelength > 290 nm. Catalysts activated in uucuo at 350 "Cdissociated [2H,]iodomethane to produce methanes containing > 50 % [2H,]methane.In contrast samples Outgassed at 500 "C gave [2H,]methane as the major methane product and also had a higher electrical conductivity. Isotopic distributions of methanes produced on the same samples under dark and illu- minated conditions were similar. The apparent initial quantum efficiency of the process was ca. 3 x 10-but the kinetics were complex and the mechanism not fully understood. Non-porous titanium dioxide (anatase) irradiated in the U.V. range has been reported225 to catalyse the partial oxidation of paraffins and olefins giving ketones with selectivities of up to 75 %. It was shown that hydroperoxide species are not involved as intermediates in the reactions and that surface hydroxyls also play no part.Eley and Zammitt226 have investigated the production of spin centres by y-irradiation of alumina and magnesium oxide catalysts and measured the catalysis of hydrogen reactions on the same samples. Before irradiation y-alumina226" catalysed para-hydrogen and ortho-deuterium conversions and also hydrogen- deuterium equilibration by chemical mechanisms. After irradiation the rate of para-hydrogen conversion was enhanced whereas that for the equilibration reaction remained constant indicating the onset of a paramagnetic mechanism for the former process. In contrast magnesium oxide226b catalyses all three reactions by a chemical mechanism both before and after y-irradiation. One of three surface centres detected using e.s.r.spectroscopy was probably responsible for the catalytic activity. The author expresses his gratitude to Dr. Duncan Taylor for his advice and encouragement during the preparation of this article. 225 M. Formenti F. Juillet P. Meriaudeau and S. J. Teichner ref. 246 Vol. 2 p. I01 1. 226 D. D. Eley and M. A. Zammitt (a)J. Catalysis 1971,21 366; (6)ibid. p. 377.

ISSN:0308-6003    

DOI:10.1039/PR9737000087

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

6 Kinetics of Reactions in Solution By M. H. DAVIES and 6. H. ROBINSON University Chemical Laboratory University of Kent Canterbury Kent England and J. R. KEEFFE California State University San Francisco California 94132 U.S.A. 1 Introduction To attempt in any way to review in a brief Report a field as broad as that implied in the title is clearly an impossibility and the policy adopted by the Reporters has been to concentrate on those areas which have seen considerable advances in knowledge or development and which are of particular interest to them. We are conscious of many omissions but it was decided to adopt an approach which has restricted us to a detailed study of only a few areas rather than a superficial study of many. It is hoped that the range covered has something to offer most kineticists.Our choice of topics reflects our interest in kinetics from a physico-chemical viewpoint and we have been especially interested in work designed to give an insight into the nature of the transition state for a reaction process. Discussion of proton-transfer reactions (by means of inter- and intra-molecular acid-base catalysis and primary secondary and solvent isotope effects) and nucleophilic substitution at saturated carbon reflect this interest. Over the past few years the role of the solvent in solution kinetics has been increasingly stressed and markedly different degrees of solvent participation have been revealed for reactions formally of the same type. Notable progress has been made in theoretical aspects; in particular the study of diffusion-controlled reactions has revealed information about the collision process in solution and the modes of decomposition of the encounter complex.The period since 1970 has seen further refinements of instrumentation for measuring rates of fast reactions in solution. The availability of commercial instruments especially for stopped-flow and temperature-jump measurements has resulted in studies on a wide range of systems in a variety of disciplines. Some idea of the scope offered is given in the last section on applications of fast reaction techniques. The early seventies has seen a revival of interest in colloid science and this has also been reflected in the kinetic arena particularly in the study of micellar 123 M.H. Dauies B. H. Robinson and J. R. Keefe systems. Because of their topical interest the progress made to date is considered in some detail in this Report. We have concentrated our efforts on reviewing developments in the chosen fields over the past three years. References to papers published before 1970 have generally only been included when they are of fundamental importance in the development of the subject. 2 Carbon Acid Reactivity This section deals with proton-transfer processes. Particular emphasis is placed on aspects of kinetics mechanism and transition-state structure and the behaviour of carbon acids will be mainly considered. In the 1971 Report Jones surveyed several aspects of carbon acid chemistry including kinetics and hydrogen isotope effects.' Two other reviews in this area were published by Jones in 1971 and 1972,2 and another concerned directly with kinetics is forth~oming.~ He has also written a monograph on the ~ubject.~ The proceedings of the 1971 Paris conference on transition states have now been p~blished,~ which contain a number of articles on proton-transfer reactions.Most welcome is the second edition of R. P. Bell's classic work.6 Since 1971 progress has been made towards understanding carbon acidity and Bronsted catalysis coefficients. Applications of Marcus theory7 and the use of various kinds of kinetic isotope effect have proved useful. Equilibrium Acidity.-A knowledge of the acidities of carbon acids is important in order to correlate structure with reactivity and this area has continued to receive active investigation.2.8 A major tool for the pK determination of weak acids has involved the use of acidity functions H- which are based on the aqueous standard state but Stewart' and Kreevoy" have called attention to failures in the underlying assumptions.Kreevoy points out that phenols as well as carboxylic acids have pK values which exhibit a sensitivity to substituent effects in water differing from that in partly aqueous media. Values of H-measured with a particular indicator type may correlate linearly with indicator ratios for another sort of acid but unless the slope of H-versus log ([A-]/[AH]) is unity the extrapolation to aqueous solution will give inaccurate dissociation constants.This uncertain procedure may be avoided by the use of other standard ' J. R. Jones Ann. Reporrs(A) 1971 68 101. J. R. Jones Quart. Rev. 1971,25 365; Progr. Phys. Org. Chem. 1972,9 241. J. R. Jones Surveys Progr. Chem. 1973 6. J. R.Jones 'The Ionisation of Carbon Acids' Academic Press London 1973. 'Reaction Transition States' ed. J. E. Dubois Gordon and Breach London 1972. R. P. Bell 'The Proton in Chemistry' 2nd edn. Chapman and Hall London 1973. R.A. Marcus J. Phys. Chem. 1968,72 891. K. Bowden Chem. Rev. 1966,66,119; C. H. Rochester 'Acidity Functions' Academic Press London 1970. A. Albagli A. Buckley A. M. Last and R. Stewart J. Amer. Chem. SOC.,1973 95 471 1. lo M. M. Kreevoy and E. H. Baughman J. Amer. Chem. SOC.,1973,95 8178.Kinetics of Reactions in Solution states and this is exemplified by Ritchie's studies in DMSO.' ' Bordwell et a1.12 are measuring a host of pK values in pure DMSO by means of a variation on Steiner's indicator method.13 The pK for fluorene their reference acid is set at 20.50. Streitwieser's group has accumulated precise data for carbon acids in cyclohexylamine,l4 and in this solvent both intimate and solvent-separated ion-pairs can be important depending on the counterion the anion and some- times the temperature. The pK values in cyclohexylamine are set relative to pK = 18.49 for 9-phenylfluorene. Streitwieser has also established an acidity- function scale for pure methanol containing up to 2.5M-NaOMe using as indicators only hydrocarbon acids having highly delocalized carbanions as conjugate bases.Several generalizations seem possible from the accumulated results. Compared with the gas phase all solvents attenuate acidity differences sometimes causing inversions of the gas-phase order.16 The amount of attenuation depends on the type of acid and the solvent employed. Acids producing highly delocalized anions (e.g. nitroanilines and fluorenes) are often stronger in DMSO than in protic solvents. These acids tend to have relative acidities which are similar in different solvents.' '*14 Acids whose conjugate bases have the negative charge largely localized (e.g. nitroalkanes ketones carboxylic acids phenols water HF and acetylenes) are stronger in protic media and their relative strengths will not in general be quantitatively the same in different solvents."*" However the pK values of bis-sulphonylmethanes and bis-cyanomethanes are probably not greatly different in DMSO and water." Acidities are changed when the conjugate base is ion-paired a condition to which localized anionic bases are especially susceptible.l4 Phenylacetylene for example is stronger in water' ' (probable pK 2 21) than in poorly hydrogen-bonding solvents. However in the latter kind of solvent the acidity is greater when the product is an ion-pair (pK = 23.2 toward lithium cyclohexylamide in cycl~hexylamine~~) than when it is not (pK = 28 in DMS012). The impossibility of setting up a universal acidity scale (even for hydrocarbon acids) in solution is re-empha~ized.'~ A monograph18 on carbon acid acidities containing many useful tables has been published.'I C. D. Ritchie J. Amer. Chem. SOC.,1969 91 6749; C. D. Ritchie and R. E. Uschold ibid. 1968 90 2821. F. G. Bordwell personal communication. l3 E. C. Steiner and J. M. Gilbert J. Amer. Chem. SOC.,1965 87 382. l4 A. Streitwieser and D. M. E. Reuben J. Amer. Chem. SOC.,1971,93 1794; A Streit- wieser C. J. Chang W. B. Hollyhead and J. R. Murdoch ibid. 1972 94 5288; A. Streitwieser C. J. Chang and W. B. Hollyhead ibid. p. 5292; A Streitwieser C. J. Chang and D. M. E. Reuben ibid. p. 5730; A. Streitwieser J. R. Murdoch G. Hafelinger and C. J. Chang ibid. 1973 95 4248. l5 A. Streitwieser C. J. Chang and A. T. Young J. Amer. Chem. SOC. 1972 94 4888. l6 J.1. Brauman and L. K. Blair J. Amer. Chem. SOC.,1968 90 6561; 1970 92 5986; 197 1,93,3911,43 15; R. T. McIver and J. H. Silvers ibid. 1973,95,8462; M. T. Bowers D. H. Aue H. M. Webb and R. T. McIver ibid. 1971 93 4314. ' A. J. Kresge and A. C. Lin J.C.S. Chem. Comm. 1973 761. H. F. Ebel 'Die Aciditat der CH-Sauren' G. Thieme Verlag Stuttgart 1969. 126 M.H. Dauies B. H.Robinson,and J. R.Keefle Mechanism of Proton-transfer Processes.-Some interesting semi-theoretical analyses considering the details of proton-transfer mechanisms have been made. Hine' has re-opened the question2' of whether the proton-exchange reactions of weak oxygen acids in hydroxylic solvents proceed by concerted or stepwise mechanisms. Equilibrium constants for hydrogen-bond formation involving various combinations of reactant and solvent molecules are estimated from their acidities and basicities.These latter values are estimated if necessary by the Bunnett and Olsen method.2 Hine concludes that hydrogen-bonded inter- mediates are often sufficiently stable that the rates of individual steps in a stepwise proton-exchange mechanism need not be impossibly fast to match experiment. Application of the principle of least motion22 then predicts that if a reaction can be stepwise it will be and hence it is concluded that hydrogen exchange between oxygen bases is stepwise and involves hydrogen-bonded intermediates. Crit~hlow~~ has proposed an interesting model for reactions which involve the movement of two or more bonds. He makes the basic assumption that the stepwise processes (the shift of one bond at a time) are non-activated (AGO =AGO for AGO 2 0 and AG =0 for AGO <0).This allows reaction co-ordinates to be defined in terms of energy. In the two-proton-transfer process of Scheme 1 R R I AH + 0 -H + B-5 A-+ H -0' -Hb + B-R R I 'A -'A I AH + 0-+ H,B A-+ Ha -0 + H,B Scheme 1 co-ordinates a and b represent the degrees of formation for the bonds Ha-0 and H,-B respectively (0< a b < 1). If E, is the energy of the system in some configuration (a,b) the expression Eab -ECJb = -defines a,provided that b is invariant. A similar definition applies to b and it follows that the potential-energy surface is E, = aE + bE -abE, where E, E, and E, refer to the stepwise reactions in the proton-transfer scheme.In the present example these quantities are related to the pK values J. Hine. J. Amer. Chem. SOC.,1972,94 5766. 2o W. J. Albery Progr. Reaction Kinetics 1967 4 353. '' J. F. Bunnett and F. P. Olsen Canad. J. Chem. 1966,44 1899. 22 J. Hine J. Org. Chem. 1966 31 1236; J. Amer. Chem. SOC.,1971. 93 3701. 23 J. E. Critchlow J.C.S. Faraday I 1972 68 1774. Kinetics of Reactions in Solution 127 of the species involved. (Nodistinction is made between free and potential energy). The model is applicable to any reaction whose stepwise routes are non-activated and makes predictions in the following areas (1) whether the mechanisms are concerted or stepwise; (2) configurations of the transition state; (3) the effects of substituents.Unless there is an intermediate of lower energy than the reactants or products concerted behaviour is anticipated. Bronsted plots for structural changes in A- and B-are linear and the coefficients ciA and ag respectively give a and b in the transition state aA = a = EJEAB ag = b* = EJEAB Substitution in ROH can lead to non-linear free-energy relationships and Bronsted coefficients greater than unity. Critchlow makes predictions (but only qualitatively) of structure-reactivity relations for carbon acids. His comments are particularly relevant to the results of Bordwell and co-~orkers.’~ He also compares his model with those of Thornton2’ and of Harris and Kurz.26 Kurz and Kurz” have discussed the timing of solvation changes for a proton- transfer reaction.They note that the dielectric relaxation time of water is probably about 100 times longer than the duration of a proton-transfer event. Three mechanistic models are proposed and evaluated by electrostatic calculations on a cylindrical dielectric cavity model in which a point-charged proton moves between two properly oriented bases. In one model the solvent and proton- transfer co-ordinates (r and rp respectively) are ‘coupled’ but in the two others they are ‘uncoupled’. Figure 1 shows the relationships between rs and rp and free-energy profiles for the mechanisms are given in Figures 2A 2B and 2C. The preferred pathway depends on the strength of the solvent-solute interactions. The ‘coupled’ mechanism (A) is predicted to have the unusual feature that the proton is actually in a potential well as it rides from base to base at a rate that is determined by the progressive reorientation of solvent molecules.The transition state has optimal solvation and small bases (e.g. H,O) are expected to react by this route. For large bases however ‘uncoupled’ mechanism (B) is anticipated. This is a three-step process in which the solvent is initially activated into the preferred transition-state configuration. Proton transfer then occurs and the solvent finally relaxes to yield the products. The second ‘uncoupled’ mechanism (C) may be operative for bases of intermediate size but should be very rare. In contrast to (B) proton transfer now passes through a free-energy minimum.Consequently there are two transition states but the acid-base system is no longer optimally solvated in either. The intermediate does however have the preferred solvation. Unusual isotope effects and activation entropies are predicted for this mechanism. Kurz and Kurz compare their approach with 24 F. G. Bordwell W. J. Boyle J. A. Hautala and K. C. Yee J. Amer. Chem. SOC.,1969 91 4002; F. G. Bordwell W. J. Boyle and K. C. Yee ibid. 1970 92 5926; F. G. Bordwell and W. J. Boyle ibid. 1972 94 3907; S. P. Avery and A. R. Butler J.C.S. Perkin ZI 1973 11 10. 25 E. R. Thornton J. Amer. Chem. Soc. 1967 89 2915. 26 J. C. Harris and J. L. Kurz J. Amer. Chem. Soc. 1970,92 349. 27 J. L. Kurz and L. C. Kurz J. Amer. Chem. SOC.,1972 94 4451. M.H. Dauies B. H. Robinson and J. R. Keefle I I 1 /. // I r‘ / / I / rs I1 / / I rs 1 / / 1 ? I11 I / / ! /’ / I /.I 0 C’cp I I I 0 ‘P I Figure 1 Relationships between solvent and proton-transfer co-ordinates (r and rp respect-ively) for ‘coupled’ (--) and ‘uncoupled’ (-.-.-) mechanisms (0 < r, r, < 1) G” Figure 2 Schematic dependence of standard free energy (GO) upon reaction co-ordinates for the models of Kurz and Kurz.27 (A) ‘coupled’ mechanism; (continued on facing page) Kinetics of Reactions in Solution C' 1 1 I I1 111 IV G" rP r* I 1 ! I iI 111 IV Figure 2 (continued) (B)jrst 'uncoupled' mechanism ;(C) second 'uncoupled' mechanism. Values of r and rpare as follows (1) r = rp = 0;(11) r = r,+ rp = 0; (111) r = rs+ rp = 1; (IV) r = rp = 1.[r,* is the value of the solvent co-ordinate in the transition state(s)] 130 M. H. Davies B. H. Robinson and J. R. Keefle experiment on several fronts and suggest a criterion for the first ‘uncoupled’ mechanism (B). They note that proton tunnelling requires that the hydrogen ion move between the two bases with little accompanying heavy-atom (solvent) motion. Recent studies of nitroalkane ionization have shown that large isotope effects and significant tunnelling contributions can be expected for these reac- tion~.~*,~~ Since proton transfer must be rate-controlling the observation of tunnelling indicates the operation of mechanism (B). Kinetics and Briinsted Correlations.-Recent reviews by Mowery and Streitwieser3’ and by Kresge31 are valuable statements of present thinking in this area.Kresge discusses three phenomena which have reawakened interest in the origins of Bronsted correlations. These are (1) curvature; (2) anomalous Bronsted coefficients (those outside the usual range of zero to unity); (3)systematic deviations from Bronsted plots (e.g. the cases of H30+ and OH- in water). Marcus theory’ is used modified and discussed with the general conclusion that even the simplest form of the theory as applied to proton-transfer reactions is qualitatively correct and allows relative values of its parameters to be con- fidently determined. The demonstration of isoinversion in proton-exchange reactions (racemization faster than exchange) is one of the most direct indicators ofa multi-step mechanism for proton transfer from carbon acids.Cram and his colleagues have continued to reveal subtleties in the stereochemistry and mechanisms of exchange for fluorene~,~’ imine~,~ and indene~.~~ Pentamethylguanidine and a cyclic amidine have been used as bases in t-butyl alcohol. They have charge-delocalized conjugate acids which induce isoinversion contributions with substituted fluorenes which had not previously displayed such behaviour presumably because none of the substituents were present which allow the ‘conducted tour’ route3’ for isoinversion. The new pathway is proposed to involve racemization within a non-hydrogen-bonded intimate ion-pair. The indenes allow a variety of reorganization pathways for ion-pairs to be re~ognized.~~ Hine and Dalsin3’ have shown that deuterium exchange (in NaOMe-MeOD) is retarded for the methyl esters XYCHC0,Me when X and Y are alkoxy-groups.Retardation is greatest when X and Y are part of a five-membered ring. They conclude that electron-pair repulsion between the developing carbanionic centre and the oxygen lone pairs is responsible but this interaction can be somewhat reduced by C-0 bond rotation in acyclic cases. 28 E. F. Caldin and S. Mateo. J.C.S. Chem. Comm. 1973 854. 29 J. R. Keeffe and N. H. Munderloh J.C.S. Chem. Comm. 1974 17. 30 P. C. Mowery and A. Streitwieser ‘Ions and Ion Pairs in Organic Chemistry’ ed. M. Szwarc Wiley New York 1974 vol. 2 in the press.3‘ A. J. Kresge Chem. SOC.Rev. 1973 2 475. 32 K. C. Chu and D. J. Cram J. Amer. Chem. SOC.,1972,94 3521. 33 R. D. Guthrie D. A. Jaeger W. Meister and D. J. Cram J. Amer. Chem. Soc. 1971 93 5137. 34 J. Almy D. H. Hoffman K. C. Chu and D. J. Cram J. Amer. Chem. Soc. 1973,95 11 85. ’’ J. Hine and P. D. Dalsin J. Amer. Chem. SOC.,1972 94 6998. Kinetics of Reactions in Solution 131 Pratt and Br~ice~~ have continued the search37 for evidence of the a-effect for the deprotonation of carbon acids. These authors studied the general base- catalysed detritiation of t-butglmalononltrile by several a-effector bases as well as non-a-effectors. The results combined with those obtained by Long’s provide no evidence for increased reactivity with a-effectors.A single Bronsted line covering about 8pK units is observed having a slope (B) equal to 0.8. The lack of an a-effect in proton transfer from carbon acids may be due to the failure of the transferred proton to reduce sufficiently in the transition state the repulsion which exists in the ground state between adjacent electron-pairs on the a-base. Rit~hie~~ has reported rates and equilibrium constants obtained in pure DMSO for the deprotonation of 9-methoxycarbonylfluorene by thiophenoxide acetate and cyanide and of 9-cyanofluorene by azide. With the exception of the cyanide values the data define a reasonable Bronsted plot of unit slope. The data for cyanide taken together with earlier results for five substituted benzoates4’ describe another line with a slope of 0.4.However the rate constant for 9-methoxycarbonylfluorene plus NaOMe in methanol (log K, = 2.6) lies well below either line and this result has led Ritchie to postulate that proton transfer from hydrocarbon acids in hydroxylic solvents is slow owing partly to solvation changes which arise from the necessity to reorganize the hydroxylic solvent from its associated ground state to a suitable orientation for solvation of a carbanionic transition state. Streitwieser and co-workers have continued their extensive work on the kinetics of ionization of hydrocarbon acids in methanol4’ and in cyclohexyl- amine.4244 Ethylene was shown to be slower than benzene at forming the caesium ion-pair in cy~lohexylamine.~~ Owing to the structural similarity expected for the conjugate bases of the two hydrocarbons one can conclude that the ion-pair acidity of ethylene is probably less than that of benzene by at least one pK unit.Similarly Streitwie~er~~ has suggested that toluene has a pK value of 40.9 almost six units greater than that commonly quoted.45 Some a-alkyltoluenes have been studied with lithium cyclohexylamide in cyclohexyl- amine.42 The correlation of rates of tritium exchange with the Q* constants for 36 R. F. Pratt and T. C. Bruice J. Org. Chem. 1972 37 3563. 37 M. J. Gregory and T. C. Bruice J. Amer. Chem. SOC.,1967 89 2327. 38 E. A. Walters and F. A. Long J. Amer. Chem. SOC.,1969,91 3733; F. Hibbert F. A. Long and E. A. Walters ibid. 1971 93 2829; F. Hibbert and F. A.Long ibid. 1971 93 2836. 39 C. D. Ritchie B. McKay and D. J. Wright ref. 5 p. 55. 40 C. D. Ritchie and R. E. Uschold J. Amer. Chem. SOC.,1968 90 3415. 41 A Streitwieser W. B. Hollyhead A. H. Pudjaatmaka P. H. Owens T. L. Kruger P. A. Rubenstein R. A. MacQuarrie M. L. Brokaw W. K. C. Chu and H. M. Niemeyer J. Amer. Chem. SOC.,1971 93 5088; A. Streitwieser W. B. Hollyhead G. Sonnichsen A. H. Pudjaatmaka C. J. Chang and T. L. Kruger ibid. p. 5096. 42 A. Streitwieser P. C. Mowery and W. R. Young Tetrahedron Letters 1972 3931. 43 M. J. Maskornick and A. Streitwieser Tetrahedron Letters 1972 1625. 44 A. Streitwieser M. R. Granger F. Mares and R. A. Wolf J. Amer. Chem. SOC.,1973 95,4257. 45 D. J. Cram ‘Fundamentals of Carbanion Chemistry’ Academic Press New York 1965 p.19. 132 M. H. Davies B. H. Robinson,and J. R. Keefe the alkyl groups supports a general rate-retarding effect of a-alkyl groups for carbon a~id~.~~i~~*~~*~~ On the other hand a-alkyl groups sometimes enhance equilibrium acidities (e.g. nitroalkanest4 and 9-alkylfl~orenes'~). These points are rationalized with the help of the observation that where a-alkyl groups stabilize a conjugate base the central carbon has sp2 hybridization and relatively low negative charge density. This observation allows the postulate that the transition states for proton loss have not undergone extensive rehybridization at the central carbon and may even have more negative charge at that carbon than in the pr~duct.~'*~~*~~ The usual inductive effect of alkyl groups then dominates.Primary isotope effects are large (k,.& 'v 11); hence it is felt that the proton has been about half-transferred in the transition state.41 Similar explanations are possible for the observations of Fukuyama et al.46 and those of Bordwell and B~yle~~ concerning the greater effect of substituents on the rates of ionization than on the equilibrium acidities of nitroalkanes. The anion- destabilizing inductive effect of alkyl groups in solution is to be contrasted with the anion-stabilizing effect of neighbouring alkyl groups in the gas phase.I6 In methanol it is likely that two important types of hydrocarbon acid the indene-fluorene type and the polyarylmethanes are not part of the same Bronsted far nil^.^' Each type provides a linear Bronsted correlation for tritium exchange catalysed by sodium methoxide but the coefficients a are different and the two lines are evidently displaced from one another.Application of the Swain- Schaad relation between deuterium and tritium isotope effects4' allowed estima- tion of the amount of internal return. It was found to be significant for the (weaker) polyarylmethanes but unimportant for the fluorene types. Nonetheless this difference was calculated to have little effect on the Bronsted slopes and probably is insufficient to account for the mutual displacement of the two lines. However one cannot always neglect internal return when interpreting experimental Bronsted slopes. M~rdoch~~ has analysed the three-step Eigen mechanism for proton transfer to determine how well the experimental slope acxp,agrees with a slope a2 calculated for the proton-transfer step alone by means of Marcus theory.' It is the latter step to which the Hammond-Leffler postulate93 should apply and for which a is likely to provide an index of transition- state structure.k k2 k3 AH + B =(AH--B) =(A--HB) A + BH k-I k-2 k-3 reactant product complex complex k, = kik,k3[k-1(k-2 + k3) + k2k,]-' acxp= dlog k,,Jd log K, Provided the velocity constants for complex formation (k, k-, k, and k-,) are invariant to changes in Keq,aexpequals a2 when step (2) is rate-determining 46 M. Fukuyama P. W. K. Flanagan F. T. Williams L. Frainier S. A. Miller and H. Schechter J. Amer. Chem. SOC.,1970 92 4689.47 C. G. Swain E. C. Stivers J. F. Reuwer and L. J. Schaad J. Amer. Chem. Soc. 1958 80 5885. 48 (a)J. R. Murdoch J. Amer. Chem. Soc. 1972 94 4410; (6)personal communication. Kinetics of Reactions in Solution 133 (i.e. k- >> k and k >> kP2). Murdoch’s analysis shows that even when this is the case steps (1) and (3) still exert a thermodynamic influence on a,,,. The conditions k->> k and k >> k- are probably best satisfied by carbon acids of the sort which have delocalized conjugate bases since (a) the C-H group of the acid and the Cd- centre of the conjugate base are poor at hydrogen- b~nding,~.~~ and (b) proton transfer requires extensive charge and solvent re-location. Marcus theory7 continues to be successful in providing a rationale for rate- equilibrium comparisons of proton-transfer reactions.The parameters of the Marcus formalism have now been evaluated for a dozen or so reaction series. 1,50-’3 Values for the energy necessary to form a ‘reactive’ complex W, as well as the intrinsic barrier 1/4,for subsequent transfer of the proton have been tab~lated.~~~’~ Even deviations from the normal Bronsted range 0 < a < 1 have been accommodated but this necessitates the use of further adjustable parameter^.^^,^^*'^*^^ Most discussions of the anomaly indicate its origin to lie in the inconstancy of the intrinsic barrier height for the reaction series. Albery however feels the cause may lie in the (variable) W term.’ Abery” and Kreevoyso have pointed out that values of W calculated for the protonation of diazoalkanes by oxygen acids (and perhaps for other acid- and base-catalysed reactions as well) are too large to be accounted for by the energy necessary to bring the reactants together and to desolvate the catalyst an amount estimated at roughly 5-8 kcal mol- ’.They suggest that the difference represents further solvent reorganization or heavy-atom motion which must be carried out before the proton transfer may occur. The postulate can be equated with the first ‘uncoupled’ mechanism of Kurz and Kurz2’ described earlier in this Report. Albery Campbell-Crawford and Curran’ describe an ‘extended Marcus’ mechanism based on this idea. The extension is that the solvent work terms formerly given as W and W,for the reactant and product sides respectively have each been divided into two parts a first part corresponding to formation of the encounter complex and desolvation of the separated reactants and the second corresponding to further reorganization of the solvent to positions suitable for formation of the proton-transfer transition state.Definitions and a reaction-co-ordinate diagram are shown in Figure 3. It is worth re-stressing that if there is little or no movement of solvent or heavy atom during the proton- transfer step the effective mass along the reaction co-ordinate for that step will be little different from that of the proton itself and tunnelling could be signifi- The numerical accuracy of the calculated Marcus parameters e.g. A/4and W, may be q~estioned.~~’ 49 A.Allerhand and P. von R. Schleyer J. Amer. Chem. SOC.,1963,85 1715. M. M. Kreevoy and D. E. Konasewich Adu. Chem. Phys. 1971 21 243; M. M. Kreevoy and Sea-wha Oh J. Amer. Chem. SOC.,1973.954805. ’ W. J. Albery A. N. Campbell-Crawford and J. S. Curran J.C.S. Perkin ii 1972 2206. 52 R. A. Marcus J. Amer. Chem. SOC.,1969 91 7224. 53 F. Hibbert J.C.S. PerkiniZ 1973 1289. 54 M. C. Rose and J. Stuehr J. Amer. Chem. SOC.,1971 93 4350. M. H. Davies B. H. Robinson,and J. R. Keefe G" 's 'P 1 11 111 IV Figure 3 Extended Marcus mechanism of Albery and co-worker~.~' In general AG; = WRo+ Ws + A(l + AGi/A)2/4 where the following standard free energies are assigned (1) WRo,formation of reactant encounter complex; (2) W, further heavy-atom motion prior to proton-transfer ;(3) W, heavy-atom motion after proton-transfer to form the product encounter complex; (4) Wp dissociation of product encounter complex; (5) 'proton driving force' AG; = AG" -(WRo + Ws + W + W,,); (6) A/4,bprrier for proton transfer at AG; = 0 (the diagram is drawn for this case).Provided the W terms are constant p = (1 + AG;/A)/2. Roman numerals rs,and rp have the same signijcance as in Figures 1 and 2 A simple interpretation of the theory was implied by Marcu~.~ The approach which uses intersecting parabolae as the model is outlined by Newton.55 Kresge and K~eppl~~ have explored the consequences of varying the curvatures of the two parabolae and their distance from each other variations thought to be realistic in representing a Bronsted acid-base series.The general relationship between a and AG"is shown to be slightly sigmoidal rather than linear as predicted by Marcu~.~ It is also suggested that the use of Marcus theory (corresponding to congruent parabolae of a fixed horizontal displacement) to calculate intrinsic barriers may lead to an estimate which is low by perhaps as much as a factor of two. It may be pointed out in this connection that the Marcus equation may be derived by the use of a number of different models.31 It is doubtful whether refinement of these simple models is 55 T. W. Newton J. Chem. Educ. 1968,45 571. 56 G. W. Koeppl and A. J. Kresge J.C.S. Chem. Comm. 1973 371. Kinetics of Reactions in Solution 135 Stuehr and Roses4 point out that successful correlations and the ability to calculate rational values for the Marcus parameters do not constitute a direct test of the theory.It would be valuable for example to demonstrate that the intrinsic barrier for a well-behaved Bronsted reaction series A-H + B *A + HB really is constant as measured by the mean of the barriers for the two identity reactions AH + AS A + HA and BH + Be B + HB. For carbon acids however such a task would present formidable experimental difficulties. The studies of Dogonadze Levich and co-workersS7 on reactions in polar media do not appear to be widely known. This is unfortunate since in the case of proton-transfer processes equations analogous to those of Marcus7 are derived and these may provide a sounder theoretical basis for the analysis of Bronsted coefficients.With regard to carbon acids the question of the existence of distinct Bronsted families arises. Earlier compilations of data do not clarify this matter.2p58 There are now however additional data on the rates of ionization of sulph~nes,’~~~~ phenylacetylene,’ and chloroform,61 all in aqueous solution. The groups of Long,38 Cram,62 and Bergman and Melander63 have provided most of our knowledge concerning the kinetics of cyanocarbon acid ionization. The majority of the kinetic measurements refer to highly endoergic reactions. For these limiting Bronsted slopes small primary kinetic isotope effects and near diffusion-controlled reverse rates indicate almost ‘normal’ acidic behaviour in the Eigen sense.64 However a recent studys9 refers to two nitriles reacting with bases in the ApK region close to zero.Bromomalononitrile (pK = 7.8) seems to be a ‘normal’ acid. On the other hand 4-nitrobenzyl cyanide (pK = 13.4) reacts more slowly than other nitriles. General catalysis by amine bases was easily observed (p = 0.61). The authors conclude that the 4-nitrophenyl group assists proton loss through considerable charge delocalization in the transition state whereas cyano-groups by themselves operate with a much smaller delocalizing effect. Margolin and Long61 have studied the detritiation of chloroform in aqueous buffers and with hydroxide ions in water-DMSO mixtures. General base catalysis was not detectable but the use of an acidity function procedure6’ suggests that /3 = 0.98.However Bell and Cox’‘ warn that varying the basicity of the medium by changing H-may not alter ApK as much as expected. The 5’ E. D. German R. R. Dogonadze A. M. Kuznetsov V. G. Levich and Yu. 1. Kharkats J. Res. Inst. Catalysis. Hokkaido Univ. 1971 19 99 115 and refs. cited therein. 58 (a)R. G. Pearson and R. L. Dillon J. Amer. Chem. Soc. .1953,75 2439; (6) R. P. Bell ‘The Proton in Chemistry’ Cornell University Press Ithaca 1959 pp. 160-165; (c) Ref. 45 pp. 8-13. 59 F. Hibbert and F. A. Long J. Amer. Chem. SOC.,1972,94 2647. 6o R. P. Bell and B. G. Cox J. Chem. SOC.(B) 1971 652. Z.Margolin and F. A. Long J. Amer. Chem. SOC.,1972,94 5108; 1973,95 2757. ’* D. J. Cram B. Rickborn C.A. Kingsbury and P. Haberfield J. Amer. Chem. SOC. 1961 83 3678; D. J. Cram and L. Gosser ibid. 1964 86 5457. 63 N.-A. Bergman Acta Chem. Scand. 1971 25 1517; L. Melander and N.-A. Bergman, ibid. p. 2264. 64 M. Eigen Angew. Chem. Internat. Edn. 1964 3 I. 6J (a) R. P. Bell and B. G. Cox J. Chem. SOC.(B) 1970 194; (6) ibid. 1971 783. ’’ R. P. Bell and B. G. Cox personal communication. 136 M. H. Dauies B. H. Robinson and J. R. Keefe primary kinetic isotope effect for the reaction is k Jk, = 1.42 and together with other results this suggests that the rate-controlling step may be isotopic exchange between the water molecules solvating the trichloromethyl anion. From such an assumption the value pK = 24 for chloroform in water may be calculated.Noting the inability to observe general catalysis with buffer bases in water Margolin and Long6’ argue that the rate constant for the reaction of hydroxide ions with chloroform does not fall low on the Bronsted plot. This contrasts with the behaviour of 1,4-di~yanobut-2-ene.~’ A number of other carbon acids (e.g. carbonyl compounds and nitroalkanes) are similarly ‘slow’ with hydr~xide.~ ‘*67 Retardations in hydronium-catalysed reactions of carbon bases have also been observed. Kresge and LinI7 have re-examined the detritiation of phenylacetylene in water. General catalysis with primary amine bases could be detected (/I= 0.97). In this case the hydroxide rate is 100 times slower than expected. The primary isotope effects are virtually unity and it appears again that hydrogen-ion transfer is not rate-controlling.Kresge and Lin’ ’emphasize that hydroxide ions (and hydronium ions in acid catalysis) might react slowly because they are particularly well hydrogen-bonded with the solvent in aqueous solution. Formation of a hydrogen-bonded complex between a carbon acid and hydroxide is then particularly difficult because of the strong hydroxide ion- solvent interaction. Only acids which are themselves fairly good hydrogen-bond donors (e.g.chloroform) can compete effectively with the water for complexation with hydroxide. Superior hydrogen-bond donors such as N-H and 0-H acids may become part of the hydrogen-bonded network of the solvent along with hydroxide ions in which case hydroxide-ion catalysis could be especially fast occurring uia the Grotthus chain mechanism.’ Hibbert’s studys3 of the water-catalysed detritiation of several bis-sulphonyl- methanes reveals patterns similar to those mentioned above for nitriles and phenylacetylene.Thus a = qsubstratc) = 1.1 f0.1 and recombination of the sulphonyl carbanions with H30+ is virtually diffusion-controlled. A Bronsted coefficient for the reaction of a single sulphone with several bases /IB has also been measured,60 and is approximately unity. The similarity of a and /IB satisfies Albery’s description” of a family of carbon acids having relatively small or constant requirements for solvent reorganization prior to the slow step. Primary isotope effects k JkD are about 2.0 for Hibbert’s reactions.Some of the available rate uersus equilibrium data for carbon acids are collected in Figure 4. Provided that a reasonable attempt is made to keep steric factors constant a rather clear pattern can be seen. Nitroalkanes are slowest carbonyl compounds are intermediate and a third almost ‘normal’ group contains nitriles sulphones acetylenes and chloroform. Certain mixed-functional-group compounds have been studied. For example Barnes and Bell’s work68 on the deprotonation of ethyl nitroacetate (/I = 0.65) shows that this substrate lies with the carbonyl compounds. On the other hand the anomalous 4-nitrobenzyl 67 R. P. Bell ‘Acid-Base Catalysis’ Oxford University Press London 1941 p. 92. 68 D. J. Barnes and R. P. Bell Proc. Roy. SOC.,1970 A318 421. 10 - -8--6- - 0.x 4- x 0 0 - 0 2- * e *t i - O O 0 0- 0 0 - oo O -2 - I# - -4 ----6 -x 0 -8 -A -x s 0 "0 -10-Figure 4 Briinsted plot for carbon acids in water. The open circles are for primary nitro- alkanes and include phenylnitromethane (V.M. Belikov T. B. Korchemnaya and N. G. Faleev Bull. Acad. Sci. U.S.S.R. Div. Chem. Sci. 1969 1383; ref 29) I-nitropropane (V. M. Belikov S. G. Mairanovskii T. B. Korchemnaya and S. S. Noviko! Bull. Acad. Sci. U.S.S.R. Div. Chem. Sci.,1962 605) and nitroethane [ref 65(b)]. The crosses are .foracylic carbonyl compounds and include ethyl pyruvate (R. P. Bell and H. F. F. Ridge-well Proc. Roy. SOC.,1967 A298 178) chloroacetone ethyl acetoacetate ethyl methyl- acetoacetate [ref.58(a)] acetylacetone [refs. %(a) 641 diethyl malonate (R. P. Bell E. Gelles and E. Moller Proc. Roy. SOC.,1949 A198,300) sodium propan-2-one-1-sulphon- ate (ref 68) and dipotassium propan-2-one- 1,3-disulphonate [R.P.Bell G. R. Hillier J. W. Mansfield and D. G. Street J. Chem. SOC.(B) 1967 8271. The closed circles include bismethylsulphonylmethane,bisethylsulphonylmethane bisphenylsulphonylmethane 1,l- bisphenylsulphonylethane (ref 53) 1,l-bisethylsulphonylethane (ref. 53 60),malono-nitrile 1 ,4-dicyano-2-butene t-butylmalononitrile (ref. 36 38) bromomalononitrile (reJ 59) chloroform (ref 61) phenylacetylene (E. A. Halevi and F. A. Long J. Amer. Chem. Soc. 1961,83,2809) and hydrocyanic acid (J. Stuehr E. Yeager T. Sachs and F.Hovorka J. Chem. Phys. 1963 38 587) 138 M. H. Dauies B. H. Robinson and J. R. Keefle cyanides9 does not lie with the other nitriles but again with the carbonyl compounds. Kinetic Hydrogen Isotope Effects-Wolfsberg has reviewed the origin of the isotope-effect phenomenon and its theoretical interpretati~n.~~ He discusses both the determination of harmonic force constants from vibrational spectroscopy and isotope effects on kinetics equilibria and vapour pressures. Secondary Isotope Eflects. Schneider and Stern7' have made a theoretical study of secondary hydrogen isotope effects. They suggest that after applying a small easily evaluated correction factor the logarithm of the rate ratio can be predicted as a sum of isotope effects caused by individual force-constant changes.A similar additivity relationship holds for the associated Arrhenius pre-exponential ratio &/A,,. A method is proposed by which suitable models incorporating the additivity relationships may be constructed for the purpose of making isotope- effect calculations. Such models should allow specific force-constant changes between reactant and transition states to be identified. The use of secondary isotope effects to define isotopic Bronsted coefficients aL has been described by Albery Bridgeland and C~rran.~' Equation (1) is cast in the traditional form of the Bronsted catalysis law but this may be rewritten in terms of fractionation factors [equation (211 as suggested by Gold72(& &,and 4* refer to reactant,product,and transition state,respectively).Using the isotopic pairs HC0,H-DC0,H and CH,CO,H-CD,CO,H to catalyse the decomposition of 3-diazobutan-2-one (an AS,2 process) it was shown71 that both values of aL are the same as the usual coefficient aB,which equals 0.6. Hydronium-ion catalysis gave aL = 0.3 a deviation in the direction expected from Marcus theory7 for a stronger acid. It is pointed out that in determining individual aLvalues for each catalyst one has effectively differentiated the normal Bronsted plot. Wherever applicable this method should be a powerful new tool for the investigation of transition-state structure. The agreement between ctL and aB for the same catalysts is reassuring. There is however a potential difficulty of the same nature as that said to be responsible for Bronsted an~malies.~ A proton-transfer transition state being bimolecular contains both the acid and base moieties.The acid (or base) and its conjugate base (or acid) does not. Isotopes located near the reaction centre could for example experience vibrational compression in the transition state for which there is no counterpart in either the reactant or product. In such a case the effect of isotopic substitution on the b9 M. Wolfsberg Accounts Chem. Res. 1972 5 225. 70 M. E. Schneider and M. J. Stern J. Amer. Chem. SOC. 1973 95 1355. 71 W. J. Albery J. R. Bridgeland and J. S. Curran J.C.S. Perkin ZZ 1972 2203. '* V. Gold Trans. Faraday SOC. 1960,56 255. 73 A. J. Kresge J. Amer. Chem. SOC.,1970 92 3210.Kinetics of Reactions in Solution 139 zero-point energy of the transition state may not be intermediate between the effects on reactant and product states. A number of secondary isotope effects arising from deuteriation of carbon acids have been measured.74 Owing to the extensive structural changes occurring on ionization it is doubtful if unambiguous deductions concerning transition-state structure can at present be made in these cases. Soluent Isotope Efects. Another review of solvent isotope effects has a~peared.~ Schowen’s survey is simple but broad and provides a good entry-route into the literature. An outstanding recent paper in this field is by Gold and Grist.76 They have re-examined the data for the fractionation of deuterium in the aqueous hydroxide ion and propose the following factors (L = H or D) #a 1 1.2-1.5 La-O-(Lb-OLc) +b 2 0.65-4.7 Ipc 2 1.0 The previous model (4 21 0.4-4.5 $b II 0.9-1.0 and 4c21 1.0)is unsatisfactory on several counts not least of which is its inconsistency with the n.m.r.chemical- shift evidence.77 Further since the fractionation factor for L30+ is less than unity a value 4a> 1 is intuitively to be preferred. The analysis of data from studies in H20-D20 mixtures often involves fitting the solvent isotope effects to functions of the type (1 -x + X&)yl -x + x#$’ (3) (There are n and n2 sites with fractionation factors $ and $* respectively and x is the atom fraction of deuterium in the solvent.) A general method has been devised for performing this ~eparation.~~ A ‘reduced’ curvature parameter is evaluated from the experimental data and ‘reduced’ fractionation factors may then be read from a graph.This procedure largely eliminates the tedium of such analyses and ensures in the kinetic case that no transition states are neglected. In general a defined curvature in a plot of solvent isotope effect against solvent composition has two solutions that is two pairs of values for and 42 in function (3). A relevant case in point is the hydroxide ion where the solution now preferred was initially ign~red.~’ Walters and Long” have examined the solvent isotope effect on the detritiation of 1,4-di~yano[l-~H]but-2-ene. Unfortunately they discuss their results in terms of a model for hydroxide with an old value of 6,(0.45) and their conclusions will need revision.There would seem to be no merit in making the arbitrary 74 D. M. Goodall personal communication; A. J. Kresge D. A. Drake and Y. Chiang to be published; M. H. Davies to be published. 75 R. L. Schowen Progr. Phys. Org. Chem. 1971 9 275. 76 V. Gold and S. Grist J.C.S. Perkin II 1972 89. 77 A. J. Kresge J. Chem. Phys. 1963,39 1360; R. Grahn Acta Chem. Scand. 1965 19 153. ” W. J. Albery and M. H. Davies J.C.S. Furaduy I 1972 68 167. 79 V. Gold and B. M. Lowe J. Chem. SOC.(A) 1967 936. ‘O E. A. Walters and F. A. Long J. Phys. Chem. 1972,76 362. 140 M.H. Dauies B. H. Robinson and J. R. Keefe distinction between 'exchange' and 'medium' solvent isotope effects and so the 'medium' formalism should be abandoned since it is merely a phenomenological description and as such is not susceptible to a molecular interpretation.A point cited in its favour is that no specific model for solvation need be assumed.80 The transfer activity coefficients from H,O to L,O are then taken according to the linear free-energy relationship yLzo = ~6,~. However this itself is an assump- tion as it stands but can be justified in terms of 'exchange' effects and corresponds to a model with an infinite number of equivalent solvating A good paper by Dahlberg" fulfils the need for more data on isotopic transfer coefficients for organic solutes. They are mostly near unity. Dahlberg and Long82 have shown that in general the transition-state transfer coefficients do not lie between the reactant and product values.Equilibrium solvent isotope effects have been determined for the ionization of hydrogen fluoride,83 the simplest of the convenient general-acid catalysts for use in aqueous solution. Results are pK = 3.165 f0.007 for HF in H,O and KFO/K:Zo= 2.05 f0.04. For the formation of HF -from HF + F- pK:iO = -0.60 0.01 and K:;O/KY;O = 1.13 f0.03. Accuracy was aided by the direct measurement of fluoride ion activity with a fluoride-ion-selective electrode. Calculations on this system indicate that the major source of the two isotope effects is not zero-point energy differences but a moment of inertia effect. The zero-point energy effects on the ratios KHZ0/KD2Oare actually slightly inverse owing to the absence of bending modes for hydrogen fluoride.Generally weak polyatomic acids have Kf20/Kf;)20N 3 resulting principally from zero-point energy differences. Primary Isotope Eflects. The results of Hibbert (bis-sulphonylmethane~),~~ Margolin and Long (chloroform),6' and of Kresge and Lin (phenyla~etylene)'~ have already been referred to in the Section on Kinetics and Bronsted Correlations (p. 130). Buncel et ~21.~~ have re-investigated the reaction(s) of 2,4,6-trinitrotoluene (TNT) with ethoxide ions in ethanol. At low [TNT] (< moll-') and [EtO-] > 4 x lo-' mol 1-' the results indicated a major reaction occurring 1&20 times slower than a minor but rapidly established equilibrium. The major reaction exhibited a strong kinetic isotope effect kJkD = 7 when [c~-~HJTNT was used and so the authors feel that this reaction represents proton transfer to ethoxide from the methyl group of TNT.The rapidly established equilibrium is probably formation of a sigma complex.85 Melanderg6 has published an interesting note on primary isotope effects in limiting unsymmetrical transition states. He predicts Reactant limit Product limit kdkD= (pRD/pRdf kJkD= OlmIppd'K JKD KJKD D. B. Dahlberg J. Phys. Chem. 1972,76 2045. D. B. Dahlberg and F. A. Long J. Amer. Chem. Soc. 1973,95 3825. 83 A. J. Kresge and Y.Chiang J. Phys. Chem. 1973,77 822. 84 E. Buncel A. R. Norris K. E. Russell and R. Tucker J. Amer. Chem. SOC.,1972,94 1646. C. F. Bernasconi J. Org. Chem. 1971 36,1671. 86 L. Melander Acta Chem.Scand. 1971 25 3821. Kinetics of Reactions in Solution 141 where pRHand pRD are the respective ‘reduced’ masses of the light and heavy reactants and ppHand ppDare the corresponding quantities for the products. It is quite possible for the equilibrium isotope effect KdKD to be inverse. Melander points out that an observed value of kdk as low as unity or even smaller cannot be used to exclude a rate-limiting proton-transfer mechanism. Bergman Saunders and Melander” have performed model calculations on the methoxide- ion-catalysed racemization of 2-methyl-3-phenylpropionitrile.The results com- pared with experimental work confirm that the reaction has a very product-like transition state. The calculations also indicate that experimental isotope effects within 10%of the values for the ‘limiting unsymmetrical’ transition states can be expected only when the proton is less than 1 % or greater than 99%transferred.Harmonys8 has reviewed the quantum-mechanical tunnelling phenomenon in chemistry. By and large the topics discussed are different from those reviewed by Caldin in 1969.89 Schneider and Sterngo have published ‘exact’ calculations of the Arrhenius pre-exponential ratio AJAD. Systematic variation of force- constant changes between ground and transition states resulted in minimum AJAD ratios of not less than 0.7 for the temperature range 2&2000 K. Bell’s suggestion9’ that AJAD ratios less than 0.5 be taken to indicate quantum- mechanical tunnelling is therefore confirmed by these authors at least for reactions having primary kinetic hydrogen isotope effects greater than about 2.7 at 300 K.Caldin and Mateo28 have recently reported a remarkably large primary isotope effect kJkD = 45 f2 at 25”C for the deprotonation of Lt-nitrophenylnitro- methane by tetramethylguanidine (TMG) in toluene. For this reaction AJAD = 0.032 f0.008,well below the value of 0.5 for the onset of tunnelling. The calculated barrier width is 0.08 nm an unusually small value. The use of dichloro-methane as solvent reduced the apparent tunnelling contributions with TMG. Similarly the bases tri-n-butylamine and triethylamine seemed to exhibit more tunnelling in toluene than in the more polar solvent acetonitrile. Since the phenomenon of tunnelling requires that the effective mass along the reaction co-ordinate be very small it is argued that the development of charge in the transition state is accompanied by slight molecular rotation for polar solvents such as dichloromethane and acetonitrile but only electronic polarization in the case of aromatic solvents such as toluene.The isotope effect in mesitylene is reported to be even higher.92 The ionization of phenylnitromethane in water has been studied.29 Rate constants (giving /3 = 0.57) and isotope effects for a variety of bases ranging in strength from water to hydroxide were reported. The now familiar maximum in k& at ApK 2 0 was observed although all the isotope effects are large. The pre-exponential Arrhenius ratio was determined to be AJAD < 0.5 for four N.-A.Bergman W. H. Saunders and L. Melander Acta Chem. Scand. 1972 26 1130. M. D. Harmony Chem. SOC.Rev. 1972 1,211. E. F. Caldin Chem. Rev. 1969 69 135. 90 M. E. Schneider and M. J. Stern J. Amer. Chem. SOC.,1972,94 1517. 91 Ref. 58(b),p. 21 1. 92 E. F. Caldin and S. Mateo personal communication. 142 M. H. Davies B. H. Robinson and J. R. Keefle of the five bases (piperidine seems anomalous). No obvious trend was found in &/A or in E -E; as ApK was varied over about nine units. Tunnelling calculations indicated the difference in isotopic barrier heights to be the same (about 1.0kcalmol-’) for the five bases. These results along with those of other^,^^^^^ indicate that (1) the transfer of the proton and its charge is about half-accomplished in the transition state for a wide reactivity range; (2) the reaction co-ordinate can be well represented by the reorientation of solvent molecules to their transition-state positions followed by a change in the position of the proton with little or no accompanying heavy-atom motion (see Figure 2B); (3) delocalization of the developing negative charge on carbon in the transition state is not extensive.Summmlry-A pattern for carbon acid reactivity is becoming clear. The ‘slower’ carbon acids e.g. nitroalkanes hydrocarbons with aromatic conjugate bases and carbonyl compounds give Bronsted plots which are not sharply curved and reach limiting rates only when AGO is extremely negative. They are slow because of their poor hydrogen-bonding ability and the extensive heavy-atom (solvent) reorganization which must take place.Values of p obtained from a series of bases seem to provide an index of transition-state structure within the context of the Hammond-Leffler postulate.93 Charge delocalization is less advanced than proton transfer. Large primary kinetic isotope effects are observed over a wide ApK range throughout which the transition states remain fairly symmetrical. The temperature dependence of these isotope effects which indicates the importance of proton tunnelling can be a valuable addition to the techniques used to study transition-state structure and can be useful in determin- ing the extent of heavy-atom motion accompanying proton transfer. The ‘faster’ carbon acids (chloroform acetylenes sulphones and most nitriles) are almost ‘normal’ in the Eigen sense.64 That is they provide Bronsted plots with limiting slopes except around ApK N zero.In the exoergic direction the rates are at or close to the diffusion-controlled limit. These substances are relatively ‘fast’ because they have strong hydrogen-bonding ability and because heavy-atom reorganization is not extensive. Primary kinetic isotope effects become small when ApK is about five units removed from zero. This may be either because proton transfer is no longer rate-determining or because the transition states have become very unsymmetrical. In connection with the kinetics of reactions in solution it is of interest that even in the absence of solvent differences in the kinetic behaviour of acids exist.Brauman Lieder and Whiteg4 have observed the following acidity order in the gas phase CH3CH20H > PhCH > CH,OH > CH,=CHCH,. Rate con- stants however do not parallel these acidities as shown in Table 1. The use of carbon acids or resonance-stabilized carbanion bases results in rate retardations far smaller than in solution. 93 J. E. Leffler and E. Grunwald ‘Rates and Equilibria in Organic Reactions’ Wiley New York 1963 p. 158. 94 J. I. Brauman C. A. Lieder and M. J. White J. Amer. Chem. SOC.,1973 95 927. Kinetics of Reactions in Solution 143 Table 1 Rate constants for some gas-phase proton transfers 1 mol-’ s-’ Reaction k/10’’ CH,O-+ CH,CH,OH-+ CH,OH + CH,CH,O-7.2 (k1.8) CH,CHCH,-+ CH,OH-+ CH,CHCH + CH,O-1.5 (k0.2) CH,O-+ PhCH,+ CH,OH + PhCH,-1.2 (kO.1) CH,CHCH,-+ PhCH,-* CH,CHCH + PhCH,-0.45 ( k0.04) It may also be noted that studies on ion-molecule reactions in the gas phase continue to de~elop,~’ and that kinetics and equilibria involving the incrementally solvated hydrogen ions H(OR,),+ and H(NR,),+ (where R = H or CH,) have been mea~ured.’~ In general the bond energies for loss of one solvent molecule from the disolvate are high about 35 kcal mol-’.Successive addition of solvent molecules to the disolvate results in diminishing incremental stabilization AH” for addition ofthe eighth water or methanol molecule being about -10 kcal mol- It is certain that further studies on ion-molecule interactions in the gas phase will be anticipated with great interest by chemists interested in the thermodynamics and kinetics of liquid-phase reaction processes.3 Inter-and Intra-molecular Acid-Base Catalysis Recent cases of acid-base catalysis in reactions involving carbonyl compounds . epoxides and carboxy-derivatives will be considered. In common usage descrip- tions of catalytic nature (e.g.general base catalysis) may either refer to the form of a rate law or indicate a reaction pathway.” The former option is adopted in this Report. Thus a reaction that is subject to general-acid catalysis may involve a general-acid mechanism (i.e.rate-determining protonation of the substrate) or a specific acid-general base mechanism which will be kinetically equivalent (rate-limiting attack by the conjugate base of the acid catalyst following protona- tion of the substrate in a pre-equilibrium).Enolization Reactions.-Hine and co-workers9* have studied the catalysis of hydrogen exchange for [2H6]acetone by means of mass spectroscopy. The rate constant for dedeuteriation by hydroxide differs substantially from those of two previous determination^^^.^^^ but is much closer to the prediction of the Swain- Schaad eq~ation.~’ In methylamine buffers the general-acid-catalysed exchange of the amine (CD,),C NCH contributes to the rate. Further Hine”’ has tested 95 J. L. Beauchamp Ann. Rev. Phys. Chem. 1971 22 552; ‘Ion Molecule Reactions’ ed. J. L. Franklin Plenum Press New York 1972; P. Kebarle ‘Ions and Ion Pairs in Organic Chemistry’ ed. M. Szwarc Wiley New York 1972 vol.1 ;ref. 16. 96 P. J. Dynes G. S. Chapman E. Kebede and F. W. Schneider J. Amer. Chem. SOC. 1972,94 6356. 97 W. P. Jencks ‘Catalysis in Chemistry and Enzymology’ McGraw-Hill New York . 1969 p. 184. 98 J. Hine J. C. Kaufmann and M. S. Cholod J. Amer. Chem. SOC.,1972 94 4590. 99 Y. Pocker Chem. and Ind. 1959 1383. I00 J. R. Jones Trans. Faraday SOC.,1969,65 21 38. J. Hine J. L. Lynn J. H. Jensen and F. C. Schmalstieg J. Amer. Chem. SOC.,1973 95 1577. M. H. Davies B. H. Robinson and J. R. Keefle for bifunctional catalysis in the dedeuteriation of [2-'H]isobutyraldehyde by diamines but finds it in only one case. Iodination studies on the compounds (lH5) have been performed to determine the nature of the catalysis for enoliza- tion.The uncatalysed reactions of (1) and of the corresponding methyl and ethyl esters have closely similar rates solvent isotope effects and activation entropies.' O2 The intramolecular specific acid-general base mechanism thus appears unim- portant. Compounds (3)'03 and the carboxylate anions of (2)'04 and (4)'05 are iodinated at least in part through intramolecular general-base mechanisms. For (9,both the uncatalysed and the general-base-catalysed enolization are anomalously fast.lo6 The same is true of the general-acid catalysis for ketoniza- tion of (6).'07 In both cases concerted intramolecular general acid-base mechanisms would account for the rate enhancement. 0 0 II I1 II CH,C-COH (CH3CH2),N(CH2),CCH, dT3 Vinyl Ether Hydrolysis.-Kresge and Chiang lo* have shown that deviations in the Bronsted plot for the hydrolysis of ethyl vinyl ether correlate with the charge type of the catalysing acid.Using this and related compounds they have also shown that the anion HF,- in contrast to a previous view,log is catalytically inactive.' lo Unlike simple vinyl ethers fl-oxy-a/?-unsaturated ketones exhibit specific acid catalysis and have a solvent isotope effect kHzO/kDzo< 1."' The assigned mechanism is shown in Scheme 2 with the second step rate-limiting. However in the case of p-oxy-+unsaturated esters,' l2 the more usual general- acid pathway reappears presuma5ly to avoid formation of the enol ester. The Io2 J. E. Meany and M. Hegazi J. Phys. Chem. 1972,76 3121. Io3 R.P. Bell and B. A. Timimi J.C.S. Perkin 11 1973 1518. Io4 R. P. Bell B. G. Cox and J. B. Henshall J.C.S. Perkin 11 1972 1232. Io5 H. Wilson and E. S. Lewis J. Amer. Chem. Sac. 1972,94 2283. Io6 R. P. Bell and M. I. Page J.C.S. Perkin 11 1973 1681. lo' A. J. Kirby and G. Meyer J.C.S. Perkin 11 1972 1446. Io8 A. J. Kresge and Y. Chiang J. Amer. Chem. SOC.,1973 95 803. Io9 R. P. Bell and J. C. McCoubrey Proc. Roy. Sac. 1956 A234,192. A. J. Kresge and Y.Chiang J. Amer. Chem. Soc. 1972 94 2814. L. R. Fedor N. C. De and S. K. Gurwara J. Amer. Chem. Sac. 1973,95 2905. IL2 S. D. Brynes and L. R. Fedor J. Amer. Chem. SOC.,1972,94 7016. Kinetics of Reactions in Solution 145 OR' 0 I IICH=CH-cR2 OR' OH' I IIeCH=CH-cR2 OR' OHI I OH + CH-CH=h -+ 0 0 II IICH-CH2-CR2 + R'OH R' R2 = aryl or alkyl residues Scheme 2 Salomaa group113 has carried out an elegant study of the interconversion shown in Scheme 3.Using both carbon-14 and tritium exchange techniques they are able to define the complete free-energy profiles. y2H5 R'R'CH-CH I OC2H5 R' R2 = H ; R' R2 = C1; or R' = H R2 = C1 Scheme 3 Acetals and Keta1s.-Fife has reviewed mechanisms for the hydrolysis of acetals and related compounds.' l4 Both specific- and general-acid pathways are known the latter becoming increasingly favoured as carbonium ion (7) is stabilized and as the pK value of (8)falls. Thus (9)undergoes general-acid-catalysed hydrolysis with the protonation of an oxygen atom concerted with cleavage of the acetal bond as the rate-determining step.' l5 Several intramolecular examples of this A.Kankaanpera P. Salomaa P. Juhala R. Aaltonen and M. Mattsh J. Amer. Chem. SOC.,1973,95 3618. 'I* T. H. Fife Accounts Chem. Res. 1972 5 264. 'I5 B. Capon and M. I. Page J.C.S. Perkin II 1972 522. M. H. Dauies B. H. Robinson,and J. R. Keefe mechanism have been found (ll),"' and (12);"* R = H Ph or 4-N02C,H,]. Anderson and Capon' l9 have tested for intramolecular nucleo- philic assistance in the specific-acid mechanism but find it only for acetals of phthalaldehydic acid and not for aliphatic acetals with potentially participating groups. Some time ago the Bell group'20 proposed an elegant model for hydration reactions of carbonyl compounds based on studies of reaction orders with respect to water in 1,4-dioxan as solvent.Thus the uncatalysed process involves a transition state associated with three water molecules one of which is replaced in the acid-catalysed reaction. Activation entropies have now been determined for the hydration of 1,3-dichloroacetone and are consistent with this mechanism. 12' Extension of this work suggests'22 a similar picture for hemiacetal formation. Thus the addition of methanol to chloral is third-order in the alcohol for the uncatalysed process but exhibits an order of 1-1.6 for general-acid catalysis. Schaleger and co-workers consider'23 that the same type of mechanism is in- volved in the hydrolysis of (13) when catalysed by general acids. H? OH (CH,CH,),k-kH I CH,O Hydrolysis of Epoxides.-In the specific-acid-catalysed ring-cleavage reaction pre-equilibrium protonation may be followed by either unimolecular (A1) or bimolecular (A2) rate-determining steps.Activation entropies (AS",) have been measured124 for (14H16) and on this basis (14) and (15) are assigned A2 mechanisms whereas (16) is classified as A1 despite having a negative volume of activation (Avo,). A second awkward point arises from a reinvestigation12' of E. Anderson and T. H. Fife J. Amer. Chem. Soc. 1973 95 6437. 'I7 B. Capon and M. 1. Page J.C.S. Perkin II 1972 2057. 11* B. Capon M. I. Page and G. H. Sankey J.C.S. Perkin II 1972 529. E. Anderson and B. Capon J.C.S. Perkin II 1972 5 15. lZo R. P. Bell and J. E. Critchlow Proc. Roy. SOC.,1971 A325,35; R.P. Bell J. P. Milling-ton and J. M. Pink ibid. 1968 A303 1. IZ1 R. P. Bell and P. E. Sorensen J.C.S. Perkin II 1972 1740. lz2 R. P. Bell and D. G. Horne J.C.S. Perkin II 1972 1371. lz3 A. L. Mori M. A. Porzio and L. L. Schaleger J. Amer. Chem. SOC.,1972 94 5034. lz4 J. G. Pritchard and I. A. Siddiqui J.C.S. Perkin II 1973 452 and refs. cited therein. M. D. Carr and C. D. Stevenson J.C.S. Perkin II 1973 518. Kinetics of Reactions in Solution 147 RLRZC___CR3R4 \/ 0 AS",cal mol-' deg-' AV",/cm3 mol-I (14) R' R2 R3 = H; R4 = CH,Cl -8.1 -8.5 (15) R',R2,R3 = H; R4 = Me -5.1 -8 (16) R',RZ = H;R3,R4= Me +7.9 -9.2 (17) R' R2 R3 R4 = Me the products from (17) which in contrast to a previous report,'26 are composed of 98 % pinacol and only trace amounts of pinacolone.This demonstrates that the reaction for (17) is A2 and it is hard to understand why (16) should be the exception. Carbinolamine Reactions.-An interesting. development has been the dis-covery l2 '-' 30 of non-linear Bronsted plots for the formation of carbinolamines and acyl-transfer intermediates. These have the same features as observed by Eigen64 for reactions in which proton transfer is the only chemical step. Conse- quently mechanisms involving kinetically significant transport processes for the catalyst have been proposed. Thus in the case of a general-base-catalysed addition of an amine to a carbonyl compound the simplest scheme required to interpret the Bronsted curvature is the stepwise mechanism via (18) with k2[B-] << k-l as shown in Scheme 4.The base catalyst B- and (18) react 0-OH k kJB-1 I R'NH + O=CRLR3=R2-C-R3I R2-C-R3 \-' (fH/INHI I RL-C-R3 I R'NH (19) Scheme 4 according to an Eigen diffusion mechanism,64 and if k << k- carbinolamine formation will not be ultra-fast. A concerted base pathway leading to (19) in a single step would give a linear Bronsted plot. Barnett' 31 has reviewed evidence for what we may call the 'pre-equilibrium-Eigen' mechanism and concludes that it may not be uncommon in carbonyl- and acyl-group reactions. In particular 126 Y. Pocker Chem. and Ind. 1959 332. 12' J. M. Sayer and W. P. Jencks J. Amer. Chem. SOC.,1972 94 3262; ibid. 1973 95 5637. 12' S. M. Silver and J.M. Sayer J. Amer. Chem. SOC.,1973 95 5073. 129 M. F. Aldersley A. J. Kirby and P. W. Lancaster J.C.S. Chem. Comm. 1972 570. IJOM. I. Page and W. P. Jencks J. Amer. Chem. SOC.,1972,94 8828. 13' R. E. Barnett Accounrs Chem. Res. 1973 6 41. M. H. Davies B. H. Robinson and J. R. Keefe it may be easy to confuse a non-linear Bronsted plot with positive deviations for OH-and H20 with linear behaviour. A temperature-jump study of the carbinolamine formation for a secondary amine has been carried Jencks and co-worker~'~~ have examined in detail substituent effects on the dehydration of carbinolamines formed from 4-chlorobenzaldehyde and hydrazines. Both the general-acid and the general- base mechanisms seem to involve cleavage of the carbon-oxygen bond concerted with the proton transfer although in the latter case deprotonation is rather more advanced.An example of an intramolecular general-acid mechanism for carbinolamine dehydration is provided by the Hine who find rate enhancements for the formally uncatalysed reaction of compounds (20).The case for (20; n = 2) is the most convincing. H (20) II = 2-5 Acyl Derivatives.-Pocker and Green report '35 solvent isotope effects for the general-acid- and general-base-catalysed hydrolysis of (21). The values are somewhat similar to those observed for the hydration of acetaldehyde and it is suggested that this arises from a common cyclic mechanism of the type proposed by Bell.'20 The solvent isotope effect for the hydrolysis of the dichloroacetyl- salicylate anion has also been determined' 36 and is linearly dependent upon the atom fraction ofdeuterium in the medium.This is interpreted in terms of transition state (22) with only the fractionation factor 41differing from unity. While this is an appealing model a linear solvent isotope effect does not prove that fraction- ation in only one site is im~0rtant.I~~ In contrast to the acylsalicylates hydrolysis of (23) proceed^'^' in the following way (1) acetyl transfer to give (24); (2) 132 H. Diebler and R. N. F. Thorneley J. Amer. Chem. SOC.,1973 95 896. IJ3 J. M. Sayer M. Peskin and W. P. Jencks J. Amer. Chem. SOC.,1973,95,4277. IJ4 J. Hine M. S. Cholod and W. K. Chess J. Amer. Chem. SOC.,1973 95 4270. IJ5 Y. Pocker and E. Green J. Amer.Chem. SOC.,1973,95 1 13. IJ6 S. S. Minor and R. L. Schowen J. Amer. Chem. SOC.,1973,95 2279. lJ7 A. J. Kresge J. Amer. Chem. SOC.,1973 95 3065. lJ8 A. J. Kirby and G. Meyer J.C.S. Perkin IZ 1972 1446. Kinetics of Reactions in Solution 149 6-expulsion of the acetate ion; (3) hydration of the resulting a-keto-keten to give 2-hydroxycyclohexene-1-carboxylicacid which subsequently ionizes. The specific-base-catalysed hydrolysis of (25) occurs' 39 in part through an intra- molecular general-base-assisted nucleophilic mechanism involving a transition state analogous to (22). Compounds (26t-(29)'40-'42 undergo base-catalysed lactonizdtion with intramolecular nucleophilic attack as the rate-determining step. Of these only (29) is subject to general catalysis and for anionic bases the transition state (30)is pr~posed.'~' It is perhaps surprising that the lactonization (25) (26) (27) n = 1 or 2 .I,,' PCH,OH of (28) is uncatalysed by general bases. The explanation offered'42 is that the ethoxycarbonyl group suffers deactivation by the a-nitrogen atom so that a fully formed alkoxide ion is required before attack can occur. Bowden and Last have demon~trated'~~ that for R' = H Bu' or Ph esters (31) are saponified by carbonyl participation through intermediates (32). However when an a-hydrogen atom is available i.e. R' = R2R3HC carbanion participation is preferred'44 and intermediates (33) are involved (R2 R3 = H ;R2 = H R3= Me; R2 R3 = Me). Neighbouring-group participation in amide hydrolysis is the subject of 139 J.E. C. Hutchins and T. H. Fife J. Amer. Chem. SOC.,1972 94 2837. 140 J. E. C. Hutchins and T. H. Fife J. Amer. Chem. SOC.,1973 95 2282. 14' B. Capon S. T. McDowell and W. V. Raftery J.C.S. Perkin II. 1973 11 18. 14' J. E. C. Hutchins and T. H. Fife J. Amer. Chem. SOC.,1973 95 3786. K. Bowden and A. M. Last J.C.S. Perkin II 1973 345. 144 K. Bowden and A. M. Last J.C.S. Perkin II 1973 351. M. H. Davies B. H. Robinson and J. R. KeejTe an interesting study by Kirby and co-worker~.'~~*'~~ For (34),rate enhancements are critically dependent upon the bulk of R' and R2.Effective molarities of up to 10" moll-' are e~hibited,'~' and ultimately (R',R2= Pr'; R3= Pr") proton transfer involving the tetrahedral intermediates becomes rate-limiting.129 Another instance of rate-determining proton transfer in amide reactions is found in the aminolysis of acetylimidazole by diamine~.'~~ These show rate enhance- ments over the simple aliphatic amines because species such as (35) undergo R R ' Me -0-C-NHlI ,NM% R2 I Im \ CH,-CH (34) (35) intramolecular proton transfer which removes the need of an encounter with an external base catalyst (Im = imidazolium).4 Nucleophilic Substitution Reactions involving Alkyl Halides Mechanism.-Currently two schools of thought eht concerning the mechanism of nucleophilic displacement for alkyl halides. The question at issue is whether the classical SN1and SN2models should be replaced by a 'unified' S,ip mechanism (substitution nucleophilic ion-pair).In 'borderline' cases (order in nucleophile between zero and unity) the rate laws for the contending schemes differ and thus in principle constitute a criterion of mechanism. Considering one nucleo- phile (Nu-) only we have Mechanism Rate law -RNu SNip RX R+X-k2"U-l k,[RX](l + k-,/k,[Nu-])-' k-I k',[RX](l + k;[Nu-]/k;) The S,ip mechanism was originally proposed by Sneen and Larsen14' for the reaction of 2-octyl mesylate with azide in aqueous dioxan. Subsequently 14' A. J. Kirby and P. W. Lancaster J.C.S. Perkin 11 1972 1206. 146 M. I. Page and W. P. Jencks J. Amer. Chem. SOC.,1972,94,8818. 14' R. A. Sneen and J. W. Larsen. J. Amer. Chem. SOC.,1969,91 362. Kinetics of Reactions in Solution 151 however two alternative analyses of their data appeared.Thus the SNl-SN2 scheme can be acc~mmodated'~~ and So can the SN2mechanism with a suitably chosen salt effect.'49 Sneen and Robbins have now countered these interpreta- tion~.'~' They argue that a significant SN1 contribution is ruled out by the observed optical inversion of 2-octyl mesylate and that the salt effect required to fit the data to the SN2 model is without precedent. Sneen has reviewed his studies of the SNip hypothe~is.'~' While he presents a good case for 'borderline' reactions the generality of the scheme must be open to doubt. In an important paper Abraham'52 uses a thermodynamic cycle to calculate the free energy of ion-pair formation (AGYJ for simple alkyl halides in several solvents including water.With primary compounds he finds this to be far greater than the free energy of activation for substitution (AGO,) and hence for these halides he considers that the SNip mechanism must be ruled out. Earlier AGY, for the methyl com- pounds had been estimated by Scott,'53 who employed an extra-thermodynamic method. His values are substantially different from Abraham's and in fact Iower than AG . The comparison is shown in Table 2. Table 2 VufuesofAGY,,/kcal mol- ' in H,O at 25 "C CH,F CH,CI CH,Br CH31 Abraham' 66 61 66 68 Scott ' 53 19 12 10 9 The Sneen gro~p'~~9'~~ have extended their studies to allylic systems. Their stereochemical results indicate that allylically related chlorides react through distinct intimate ion-pairs [e.g.(36) and (37)rather than (38)].C y+flcq,CH3 CH\ / $+/ CH CH\ FC$ /CH3 CH CH CH CH CH + CH c1-c1-c1-(36) (37) (38) The reactions of 1-phenylethyl halides have been examined in three labora- t~ries.'~'*'~~,'~~ For the solvolysis of the optically active chloride in 60% 148 B. J. Gregory G. Kohnstam M. Padden-Row and A. Queen Chem. Comm. 1970 1032. 149 D. J. Raber J. M. Harris R. E. Hall and P. von R. Schleyer J. Amer. Chem. Soc. 1971,93,4821. R. A. Sneen and H. M. Robbins J. Amer. Chem. SOC.,1972 94 7868. R. A. Sneen Accounts Chem. Res. 1973 6 46. 15* M. H. Abraham J.C.S. PerkinZI 1973 1893. 153 J. M. W. Scott Canad. J. Chem. 1970 48 3807. R. A. Sneen and W. A. Bradley J. Amer. Chem. SOC.,1972 94 6975. R. A. Sneen and J. V. Carter J.Amer. Chem. SOC.,1972 94 6990. 156 V. J. Shiner S. R. Hartshorn and P. C. Vogel J. Org. Chem. 1973 38 3604. 15' D. J. McLennan J.C.S. Perkin 11 1972 1577. M. H. Davies B. H. Robinson and J. R. Keefle aqueous ethanol Shiner and co-workers' 56 propose the mechanism RCI =R+CI-R+//C1-products where R+// C1- is a solvent-separated ion-pair and k >> k,. It should be noted that this scheme is kinetically indistinguishable from the Sneen mechanism.' They'56 are able to generate the intimate ion-pair R+C1- from the reaction of styrene and molecular HC1 in dry CF,CH,OH as solvent. It forms both RCl and the solvolysis product. The partition ratio gives k-,/k = 6 and after allowing for solvent effects this becomes k-,/k z 2.5 in 60% aqueous ethanol.Sneen and Robbins'" have also studied 1-phenylethyl chloride but in 100% ethanol. By determining the rate enhancement brought about by added nucleo- philes and carrying out a product analysis they deduce k-,/k = 3.3. The similarity of the two independent estimates of this ratio is very encouraging. Nevertheless it must be pointed out that the applicability of the ion-pair mechan- ism to the 1-phenylethyl halides has been challenged. ' ' Two authors concern themselves with the extent of charge separation in alkyl halide transition states. From a study of solvent effects Abraham' 58 assigns the value 0.7 to t-butyl chloride in polar solvents. This falls to 2:0.5 in non-polar media. As his model for Me,C+ Cl- he takes the ion-pair of tetramethyl- ammonium chloride.In an interesting review Kurzls9 treats the transition states for substitution reactions as Bronsted acid-base systems. By comparing the pK values of the reactant transition state and product for the hydrolysis of methyl chloride he concludes that rupture of the carbonxhlorine bond has scarcely begun in the activated complex. This agrees roughly with earlier solvent- effect studies by Abraham'60 but contrasts sharply with Scott's view'53 that the transition state follows the formation of an ion-pair. The benzyl chlorides constitute another class ofcompound near the mechanistic borderline. The Robertson group'6' have applied their precise conductimetric techniques to the hydrolysis of the 4-chloro- 4-nitro- and 4-methyl derivatives and results are shown in Table 3.In the first two cases the heat capacity of Table 3 Resultsfrom studies of the hydrolysis of substituted benzyl chlorides CH,CI Y AC,",/cal mol- ' deg-' kdk (per atom D) c1 -48 1.030 (65 "C) -NO -49 8 Me Y -79 1.132 (25 "C) activation (AC;,) is near -50 cal mol- deg-' a value which is considered typical for SN2 reactions. On the other hand 4-methylbenzyl chloride has a 15* M. H. Abraham J.C.S. Perkin 11 1972 1343. J. L. Kurz Accounfs Chem. Res. 1972 5 1. M. H. Abraham and G. F. Johnston J. Chem. SOC.(A) 1971 1610. 16' K. M. Koshy R. E. Robertson and W. M. J. Strachan Canad. J. Chem. 1973 51 2958. Kinetics of Reactions in Solution 153 value of Aq which is only a little less negative than that found for t-butyl chloride ( -83162 and -88163 cal mol-' deg- ').Similarly the secondary a-deuterium isotope effect (kJkD)is approaching 1.15 per atom D,which is the figure considered characteristic of the SN1 mechanism when chloride is the leaving Willi and co-~orkers'~~ have determined values of kJkD for the solvolysis of selected benzyl chlorides in 55 % aqueous 2-methoxyethanol. In this solvent they classify 4-methylbenzyl chloride as SN1,3-chlorobenzyl chloride as SN2,and benzyl chloride as intermediate. An interesting method of examining the mechan- istic character of solvolysis reactions has been suggested by Andrews and co-workers.'66 By varying the composition of a mixture of ethanol and 2,2,2-trifluoroethanol they are able to change the nucleophilic and electrophilic nature of the solvent without significantly affecting the dielectric constant.Thus increasing the mole fraction of the fluorinated component increases the solvolysis rate of 4-methylbenzyl chloride but 3-fluorobenzyl chloride solvolyses more slowly. The suggested interpretation is that bond cleavage is the dominant feature of the transition state for the former compound but that in the latter case nucleophilic attack is the more important aspect. The rate for benzyl chloride is relatively insensitive to solvent composition which suggests a finely balanced mechanism. Chlorine isotope effects (k35/k37) offer a potentially valuable tool for probing nucleophilic displacement mechanisms. In recent years mass spectroscopic techniques have been evolved which furnish increasingly reliable data.'67 Taylor and co-workers'68 have determined k3,/k3 for the reactions of t-butyl chloride and n-butyl chloride with thiophenoxide ion in methanol and their results are shown in Table 4. They find the larger isotope effect in the SN1case. Some time Table 4 Chlorine isotope eflects for reactions with thiophenoxide ion in methanol Reactant Mechanism k3Jk3 (at 20 "C) Bu'CI SN1 1.0106 (k0.00015) Bu"C1 SN2 1.OO89 ( k0.00015) ago Hill and Fry'69 reported the same phenomenon for benzyl chloride deriv- atives. However the characteristic values for the SN1 and SN2 mechanisms (1.0078 and 1.0058 respectively) were very different from those of the present 162 S. E. Sugamori and R. E. Robertson J.Amer. Chem. SOC.,1969 91 7254. Ib3 W. J. Albery and B. H. Robinson Trans. Faraday SOC.,1969 65 980. 'b4 V. J. Shiner 'Isotope Effects in Chemical Reactions' ed. C. J. Collins and N. S. Bowman Van Nostrand Reinhold New York,1970 p. 90. lb5 A. V. Willi C. Ho and A. Ghanbarpour J. Org. Chem. 1972,37 1185. I*' D. A. da Roza L. J. Andrews and R. M. Keefer J. Amer. Chem. SOC., 1973,95 7003. 16' J. W. Taylor and E. P. Grimsrud Anafyt. Chem. 1969 41 805. C. R. Turnquist J. W. Taylor E. P. Grimsrud and R. C. Williams J. Amer. Chem. SOC. 1973,95,4133. J. W. Hill and A. Fry J. Amer. Chem. SOC.,1962 84 2763. 154 M. H. Davies B. H. Robinson and J. R. Keeffe example. Recently the Fry group' 70 have performed model calculations which suggest that for SN2reactions k3Jk3 should change monotonically with the extension of the carbonxhlorine bond in the transition state.They also examine the a-carbon isotope effect and predict that it will pass through a maximum about half way along the reaction co-ordinate. The behaviour is reminiscent of primary deuterium isotope effects. Ritchie' 7' has reviewed his fascinating results on the reactivity of nucleophiles towards stable carbonium ions. He correlates his velocity constants k" using the simple equation log k" = log k" + N where k" is the value for water. The nucleophilicity parameter N ,is the same for all carbonium ions there being no analogue of the Swain-Scott 's' value.'72 Moreover rate-equilibrium correlations are not observed either for changing the nucleophile or for a series of cations.This remarkable behaviour may be understood in terms of a mechanism in which the transition state is not far removed from an ion-pair separated by one solvent molecule. Activation Parameters.-Hills and Viana '' claim that the activation parameters for the hydrolysis of benzyl chloride undergo profound changes in the region of 0-10°C. In particular they observe that at unit atmospheric pressure the activation enthalpy becomes negative below 4 "C,the temperature of maximum density for water. This is an intriguing phenomenon but support from other laboratories has not been forthcoming.' 74 Another interesting claim has been that the hydrolysis of t-butyl chloride exhibits a pH-dependent induction period at very low concentrati~ns.'~~ The effect of solvent composition on ACi+ for the same reaction in aqueous-organic mixtures has been examined by Robertson and S~garn0ri.l~~ They find a correlation between this parameter and structural properties of the solvent.This in the case of ethanol t-butyl alcohol and THF AC;+ passes through a minimum occurring at about 5% mole fraction of the organic co-solvent. At this composition the solvent is thought to be highly 'structured'. However even small amounts of acetonitrile 'destructure' the solvent and in this case ACi+ monotonically increases. Wold'78 has taken from the literature temperature-rate-constant data for a large number of reactions in water. He performs a detailed analysis and finds that AC; is not constant but passes through a statistically significant minimum at about 35 "C.This appears to be independent of the substrate and therefore is some facet of the solvent. 170 L. B. Sims A. Fry L. T. Netherton J. C. Wilson K. D. Reppond and S. W. Crook J. Amer. Chem. SOC.,1972 94 1364. C. D. Ritchie Accounrs Chem. Res. 1972 5 348. 172 C. G. Swain and C. B. Scott J. Amer. Chem. SOC.,1953,75 141. 173 G. Hills and C. A. N. Viana Nature 1971 229 194. W. J. Albery and J. S. Curran J.C.S. Chem. Comm. 1972 425. 175 P. A. Adams J. G. Sheppard and E. R. Swart J.C.S. Chem. Comm. 1973 663. 176 R. E. Robertson Progr. Phys. Org. Chem. 1967,4 213. R. E. Robertson and S. E. Sugamori Cunad. J. Chem. 1972,50 1353; J. Amer. Chem. Soc. 1969,91,7254s 17a S. 'Wold J.Phys. Chem. 1972 76 369. Kinetics of Reactions in Solution Any satisfactory theory for the origin of ACi* must account for this behaviour. Davis and H~ne''~ use the concept of water structure to interpret the temperature dependence of the activation volume (dAV/",/dT) for several reactions. Thus this parameter for the hydrolysis of isopropyl bromide and benzyl chloride is negative (Table 5) which is the expected sign for compounds which proceed by Table 5 Values of d AVO,/dT and ACi* for some solvolysis reactions in H20 and D2O (dAVO,/d T)/cm3 mol -I deg-' AC",/cal mol-' deg-' H2O D2O H20 D20 Pr'Br -0.07 -0.12 -59 -66 PhCH2Cl -0.06 -0.20 - - MeOS0,Cl 0.00 0.00 -53 -53 'destructuring' the solvent to reach the transition state.Under these circumstances there is thought to be a positive contribution to AVO arising from changes in the water structure around the substrate which occur on activation. Increasing the temperature progressively breaks up the solvent and AVO therefore falls. In D,O where the hydrogen bonds are stronger than in H20 the change in AVO will be greater. The solvent isotope effect on AC; may be interpreted in similar terms. In the case of methanesulphonyl chloride it appears that activation involves smaller changes in the solvent-solvent interactions. This is ascribed to the greater polarity of the substrate. 5 Developments in Instrumentation for the Study of Fast Reaction Processes No kineticist today would dismiss the rate of a chemical reaction as 'instan- taneous'.A variety of techniques are available for measurements in the sub-second region and this time domain is particularly relevant to the study of biochemical processes. A notable publication appeared in 1969l8Oin which kineticists were instructed in the use of available equipment for studying fast reactions and especially how to exploit a particular technique optimally through personalized design. To this end constructional details are provided from which a kineticist with only basic engineering skills could reasonably expect to equip himself with apparatus for studying systems of interest. The book is especially useful in pointing out the limitations of the various techniques. There are articles on temperature- and pressure-jump instrumentation ultrasonic and electric field methods polarography flow and irradiation techniques (including flash- photolysis laser perturbation and fluorescence methods).In this Report it has been necessary to restrict the discussion to progress made in only a few of the fast-reaction techniques and attention will be concentrated C. S. Davis and J. B. Hyne Cunud.J. Chem. 1973,51 1687. 'Methods in Enzymology Vol. XVI' ed. K. Kustin Academic Press New York and London 1969. M. H. Davies B. H. Robinson and J. R. Keefe on the two most widely used methods stopped-flow and temperature-jump. The time-scales of these techniques are largely complementary and cover the range 10+1-10-3 s for stopped-flow and 10-1-10-6 s for temperature-jump. Stopped-flow Methods.-The fastest relaxation times which can be measured are still of the order of 1 ms.Attempts181 to extend the time range to -100ps by means of high drive-pressures and concentric mixers do not appear to have been widely exploited owing primarily to the problem of cavitation (or bubble forma- tion) on mixing which results in solution turbidity and artefacts superimposed on the relaxation transients. The problem of cavitation (in a Gibson-Milnes stopped- flow device) has been exhaustively investigated by Wong and Schelly,182 who discuss the amplitude and lifetime of the effects in water methanol and benzene. They also investigate the behaviour of different mixer designs and the effect on cavitation of the flow velocity the mixing ratio and the stopping mode.It is clear that artefacts (lasting up to 50ms after stopping) are easily produced at high flow velocities and that cavitation is not easily eliminated. It seems that considerable difficulties are introduced through the common use of an observation chamber having a path length of 2cm. This is seldom required and a cell of 2 mm path length positioned about 5 mm from the mixing chamber is perfectly satisfactory for most applications. The dead time with this arrangement is much less; this obviates the need for high flow velocities and avoids cavitation and shock effects on stopping the flow. Schelly also reports on the use of the stopped-flow device in concentration- and solvent-jump and describes a method of determining chemical relaxation times' 85 from integrated relaxation amplitudes obtained from a concentration jump in a continuous-flow device.A variable-ratio stopped- flow mixing device has been describedls6 featuring a drive system delivering reactant solutions in any of thirteen volume ratios from 1 :100 to 100 :1. Advan- tages are that manipulation of solutions is reduced to a minimum and there is a considerable saving on quantities of reagents and on thermostatting time. The instrument is readily used in a concentration-jump mode. A possible difficulty is that the drive ratios will generally be less precise than for 50 :50 mixing from identical syringes and this could result in less accurate results being obtained unless the instrument is well calibrated beforehand. An all-glass stopped-flow apparatus has been reported.' 87 This instrument is equipped with spectrophotometric detection and precision thermostatting has received special attention.By direct immersion of the coils (containing reactants) and mixing and observation units in the thermostat tank temperature control of the order of kO.01 K is easily obtained. A simple two-jet mixer is used and R. L. Berger and L. C. Stoddart Rev. Sci. Instr. 1965 36 78. M. M. Wong and 2.A. Schelly Rev. Sci. Instr. 1973 44 1226. lS3 Z.A. Schelly R. D. Farina and E. M. Eyring J. Phys. Chem. 1970 74 617. la4 Z. A. Schelly and E. M. Eyring J. Chem. Educ. 1971,48,639. Z. A. Schelly and M. M. Wong Rev. Sci. Instr. to be published. la6 R. A. Harvey and W. 0.Borcherdt Analyt. Chem. 1972,44 1926.lE7 E. F. Caldin A. Queen and J. E. Crooks J. Phys. (E) 1972 6 930. Kinetics of Reactions in Solution the dead time is reported as 4ms. A possible disadvantage for some applications is that large volumes of solution are required. Other stopped-flow devices have been and several reviews at an elementary level have appeared.'" Curiously one of the most dficult time ranges for kinetic investigation is now the 10-to 10s region and this is particularly the case when solids or only sparingly soluble liquids have to be introduced rapidly into solution. A simple device is reported by Stuehr et ul.19' which is suitable for incorporation into a spectrophotometer although other detection methods (e.g.conductance) could presumably be employed. It is claimed that the classical time range can be extended down to t+ -1s in suitable cases.However the major problem in these processes is the rapid formation of a homogenous solution and a better method might be to start off the reaction at a low temperature (i+ -20s) and suddenly accelerate the reaction by mixing and dilution with solvent at the much higher temperature required experimentally. An interesting advance is the use of kinetic data (from stopped flow) as an analytical device and Pausch and Margerurnlg2 have recently demonstrated the approach in an analysis of alkaline-earth ions. A notable development during the past few years has been the combination of the stopped-flow technique with an extended range of detection systems. A stopped-flow instrument with 35Cl n.m.r.detection has been used to investigate the reactions of Hg"(bovine serum albumin) with various ligands,lg3 and a machine equipped with general n.m.r. detection has been described by Syke~.'~~ 1.r. detection has also been employed. 195 Light-scattering detection has been used in an instrument designed by Riesner and B~enemann.'~~ This method has considerable advantages in the study of macromolecular processes since the system is its own indicator of chemical change (no extrinsic or intrinsic indicator probes are required). The authors use a He-Ne laser at 633 nm as the detecting light beam with the advantages of easy alignment coupled with high intensity. It is claimed that a 10%change in mol. wt. at mol. wt. = 25 OOO can be detected at a concentration of 1mg ml-' which is a sensitivity comparable to that of most commercial instruments designed for static light-scattering.It is pointed out that to obtain this degree of accuracy the solutions must be rigorously purified to eliminate dust particles and suitable membranes are suggested. The method is useful for studying such processes as protein-nucleic acid interaction association and dissociation of subunit proteins and the binding of small molecules to '*' E. Y. Alfimova A. N. Sheherban and V. I. Kukushkin Kinetika i Kataliz 1972 13 531 (Kinetics and Catalysis 1972 13 486). P. M. Beckwith and S. R. Crouch Analyt. Chem. 1972,44 221. I9O R. M. Reich Analyt. Chem. 1971 43 85. 19' J. C. Nordlander R. R. Gruetzmacher and J.E. Stuehr Rev. Sci. Instr. 1972 43 1835. 19' J. B. Pausch and D. W. Margerum Analyt. Chem. 1969,41 226 232. 193 J. Sudmeier and J. J. Pesek Inorg. Chem. 1971 10 860. '94 J. Grimaldi J. Baldo C. McMurray and B. D. Sykes J. Amer. Chem. SOC., 1972 94 7641. 19' J. P. Maher personal communication. lg6 D. Riesner and H. Buenemann Proc. Nut. Acad. Sci. U.S.A. 1973 70 890. 158 M. H. Davies B. H. Robinson,and J. R. Keefle nucleic acids with resultant conformational changes. Examples of these processes are experimentally tested and the stopped-flow instrument is employed in an ionic-strength-jump mode to investigate the dissociation of dimers of RNA poly- merase. Because of its versatility and simplicity this technique will no doubt often be used in the next few years.Another example of the application of a stopped-flow light-scattering instrument is by Eyring et al.197*1 98 in their study of the kinetics of membrane solubilization by sodium lauryl sulphate micelles. However in this case the changes in the detection signal are an order of magnitude greater than in the experiments of Riesner et al. A stopped-flow device designed for use with 0.r.d. and fluorescence detection has been de~cribed.'~~ The paper contains an interesting discussion on the measurement of 0.r.d. and the requirement that the light beam must be parallel to the direction of flow. An instrument equipped with polarimetric detection has been designed by Goodall and Cross.'" It is perhaps not generally realized that there are interesting methods available for generating intermediates and following the kinetics associated with their formation and decomposition using a coupled stopped-flow-temperature-jump technique.This method was described some years ago,2o1 but until recently the technique has been rarely exploited. In a study of the formation of Meisenheimer complexes Bernasconi202 has shown that a 1,3-methoxide ion adduct is formed rapidly (in < 1 ms) in the interaction of 2,4,6-trinitroanisole with methoxide ion in methanol. The rearrangement of this adduct to form the thermodynamically more stable l,l-dimethoxy-2,4,6-trinitroanisoleis readily followed by the conventional stopped-flow method. However by applying a temperature jump of 17.5 K to the solution 80 ms after mixing the rate and equilibrium constants for formation of the intermediate are found to be 2 x lo31 mo1-l s-' and -2 1 mol-',respectively.Another interesting example of a stopped-flow study of an intermediate has been published by Gibson203 on the kinetics of oxygen binding to and dissolution from haemoglobin. He describes an experiment in which haemoglobin is exposed only briefly to oxygen in an 'oxygen-pulse' experiment. The technique is to mix a solution of deoxyhaemoglobin containing the reducing competitor dithionite with a solution of oxygen. The oxygen reacts rapidly and competitively with dithionite so that the possibility of oxygen binding to deoxyhaemoglobin is quickly terminated in 1 to 10ms by the disappearance of free oxygen from solution.In this way partially oxygenated haemoglobin is formed from which the oxygen subsequently dissociates with a half-life of -10ms at 2 "C. The intermediate concentrations of partially oxygenated species differ widely from 19' J. J. Auborn E. M. Eyring and G. L. Choules Proc. Nat. Acad. Sci. U.S.A. 1971,68 1996. lg8 G. L. Choules R. G. Sandberg M.Steggall and E. M. Eyring Biochemistry 1973 12 4544. Ig9 K. Hiromi S. Ono S. Itoh and T. Nagamura J. Biochem. 1968 6 64. *O0 D. M. Goodall personal communication. *01 J. E. Ermann and G. G. Hammes Rev. Sci. Instr. 1966 37 746. 202 C. F. Bernasconi J. Amer. Chem. SOC.,1971 93 6975. 203 Q. H. Gibson Proc. Nat. Acad. Sci. U.S.A.,1973 70 1. Kinetics of Reactions in Solution 159 those at equilibrium when because of co-operativity effects only Hb4 and Hb4(02)4 are present.From the kinetic study of oxygen dissociation from the intermediates it is suggested that the Adair Equation and the Monod-Changeux- Wyman model do not adequately represent the kinetics of the oxygen-haemo- globin reaction. A useful instrumental accessory in studies of the above type described by Michaels et a1.,204allows the calculation and recording of the spectra of transient absorbing species in fast kinetic experiments down to the microsecond time-scale using an on-line fully automated system. Another potentially very useful method especially for turbid or optically dense samples is a rapid-readout dual-wave- length spectrophotometric system which has been used by Chance et al.205to study the reaction of oxygen with membrane cytochrome oxidase.A major advance in the stopped-flow method has been the development of digital data-acquisition systems which have several advantages over the analogue methods generally employed in that resolution of transients is considerably improved (an accuracy of <1% is readily achieved) the time and effort required to carry out analysis of rate data are reduced and the analysis of complex transients is simplified. Early systems were described by De Sa and Gibson206 and by Margerum et aL207and the methods have been reviewed by Malmstadt.208 Details of the construction of a fast digital data-capture system [10 bit analogue- to-digital (A to D) converter sampling time 25 ,us] have been published.209 However it should be realised that similar equipment is now readily available commercially and the cost of a suitable system for stopped-flow purposes should be no more than that of a conventional storage oscilloscope and camera.High- speed Ato D converters are discussed by Witt,210 and these would be applicable to the very fast perturbation relaxation methods. However if analogue methods are employed a useful accessory would be a logarithmic amplifier,2’ which converts a first-order oscilloscope record into a linear semi-logarithmic trace. Temperature-jump Methods.-The major technique for step-wise perturbation is the temperature-jump method which has recently been discussed by Caldin2 l2 and reviewed at an elementary level by Schelly and Eyring.’13 A significant advance has been made in the joule-heating temperature-jump method by employing a co-axial cable as ~apacitor.”~ In this way the shape of the discharge pulse can be sharpened and reactions with relaxation times down to ’04 H.B. Michaels T. E. Basser W. B. Taylor and J. W. Hunt Rev. Sci. Insir. 1973 44 1286. 205 B. Chance N. Graham J. Sorge and V. Legallais Rev. Sci. Instr. 1972 43 62. 206 P. J. De Sa and Q. H. Gibson Comput. Biomed. Res. 1969 2 494. 207 B. G. Willis J. A. Bittikofer H. L. Pardue and D. W. Margerum Analyt. Chem. 1970 42 1340. 208 H. V. Malmstadt Analyt. Chem. 1972 44 26. 209 D. S. Gorman and J. S. Connolly Rev. Sci. Znstr. 1972 43 1175. 210 H. Ruppel and H. T. Witt ref. I pp. 316-380. 211 D.McLean and R. L. Tranter J. Phys. (E) 1971,4 455. ’I2 E. F. Caldin Chem. in Britain to be published. ’I3 Z. A. Schelly and E. M. Eyring J. Chem. Educ. 1971 48 695. 214 G. W. Hoffmann Rev. Sci. Znstr. 1971 42 1643. 160 M. H. Davies B. H. Robinson and J. R. Keefe s can be studied. Reactions investigated have been the square-planar- octahedral conformational change in Ni1'(2,3,2-tet)2 and the helix-coil transition in oligonucleotides.2 l6 The laser temperature-jump technique is becoming increasingly powerful as its full potential is slowly being realized. Turner et ~21.~" have described a fast-heating laser temperature-jump instrument employing a neodymium laser in aqueous solution and have neatly overcome the problem of high transmittance of water at 1.06pm by employing the stimulated Raman effect in liquid nitrogen to shift the laser wavelength to 1.41,urn.Because water absorbs very strongly at this wavelength 50% H20-D20mixtures are used so that the possibility of solvent isotope effects may have to be considered. Using a Pockels Cell Q-switch device energies of 2 J in 20 ns are obtained at 1.41pm. This enables relaxation times in the 10-8-10-7 s region to be studied and the iodine-iodide reaction and proflavine dimerization have been successfully investigated. The paper also contains a full discussion of acoustic effects (which can distort the relaxation transients when z > 1 ps) and bandwidth considerations on the optical detection system. An important advantage of the laser temperature-jump technique is that non-conducting as well as conducting solutions may be employed.Caldin Crooks and Robinson218 have described an instrument based on a ruby laser operating in the non-&-switched mode coupled to a dye absorber (vanadyl phthalocyanine) which has been used for studying fast kinetic processes in aprotic solvents. Studies of proton-transfer processes from indicator acids to aromatic amine bases have been carried out219 and the proton-transfer step following fast initial formation of a hydrogen-bonded complex has been found to be slow owing to the need for solvent reorganization. The laser has been coupled to a high-pressure operating up to 3 kbar (coupling of techniques is particularly easy with laser temperature-jump) which enables volumes of activation (AVO+)to be determined both in aqueous and non-aqueous solvents.Spectrophotometric and conductimetric detection is described and results have been reported on ligand-substitution processes involving Ni" and Co"' in water221 and several metal ions in neat In the latter case owing to the viscosity of the solvent all the forward rate-constants are similar (in water they differ by lo4),indicating that the rigid solvent structure dominates the kinetics. A Q-switched laser temperature-jump instrument with conductimetric detection has been described by K~ffer,~~~ continuing the 215 G. W. Hoffmann and D. W. Margerum personal communication. *I6 G. W. Hoffmann and D. Porschke Biopofymers 1973 12 1625. 217 D. H. Turner G. W.Flynn N. Sutin and J. V. Beitz J. Amer. Chem. SOC., 1970 92 4130; 1972,94 1972. 218 E. F. Caldin J. E. Crooks and B. H. Robinson J. Phys. (0, 1971 4 165. 219 J. E. Crooks and B. H. Robinson Trans. Faraday SOC.,1970,66 1436; 1971,67 1707. 220 E. F. Caldin M. W. Grant B. B. Hasinoff and P. A. Tregloan J. Phys. (E) 1973 6 349. 221 E. F. Caldin M. W. Grant and B. B. Hasinoff Chem. Comm. 1971 1351; J.C.S. Faraday I 1972,68 2247. 222 E. F. Caldin and M. W. Grant J.C.S. Faraday I 1973 69 1648. 223 H. Koffer Ber. Bunsengesellschaft phys. Chem. 1971 75 1245. Kinetics of Reactions in Solution 161 approach initiated by Hoffmann et al.224 Pressure-shock effects were avoided by special cell construction and temperature jumps of 0.4K were obtained.A Q-switched laser temperature-jump apparatus for relaxation studies in micro- samples has been constructed by Rigler Jost and DeMae~er~~~ which is parti-cularly suited to biological studies when only small samples (-5p1) may be available for study. A fibre-optic light guide is used to connect the laser to the microcell which has the advantages of equalizing the energy in the laser beam and easy alignment and operation. The possibility of using the focused laser for direct excitation of intact single cells is discussed. Chance and Erecinska226 have combined stopped flow and flash photolysis using a liquid dye-laser in their study of the cytochrome-oxygen reaction in mitochondria. The use of liquid dye-1ase1-s~~’ as heating sources is appealing as there is a greater choice of wavelengths compared with solid-state lasers and sub-microsecond pulses are available.One possibility might be based on the type of dye-laser described by Bunkenberg,228 which produces a 200mJ pulse in <1p. The wavelength range is tunable from 420 to 630nm. Lasers are also used in photochemical kinetics and the field is reviewed in a very lucid article by Porter and Patter~on.’~’ Fluctuation Methods.-An important review article on the chemical and biological applications of laser light scattering has been published.230 The theoretical analysis required to explain the spectrum of scattered light by the effect of a chemical reaction has been steadily developed23 1-236 and experiments have also been carried A similar process that of the fluctuations in fluorescence emission from chemically reactive systems has been studied.23 * This has led to the development of a most interesting new technique of potentially wide application.’ 39 In the method known as fluctuation spectroscopy the kinetic parameters characterizing a chemical reaction are obtained from the noise or fluctuations emitted from the detector monitoring a system at equi- librium.Conductivity (in the case described) and optical monitoring (absorption and fluorescence) are obviously suitable candidates. The fluctuations arise from the fact that although a system is at macroscopic equilibrium there will 224 H. Hoffmann E. Yeager and J. E. Stuehr Rev. Sci. Instr. 1968 39 649. 225 R. Rigler A. Jost and L. De Maeyer Exp.Cell Research 1970,62 197. 226 B. Chance and M. Erecinska; Arch. Biochem. Biophys. 1971 143 675. 227 T. W. Hansch ‘Topics in Applied Physics’ Vol. 1 ed. F. P. Schafer Springer Verlag 1973. 228 J. Bunkenberg Rev. Sci. Instr. 1972 43 497. 229 G.Porter and L. Patterson Chem. in Britain 1970 6 246. 230 J. R. Shapley and J. A. Osborn Accounts Chem. Res. 1973,6 305. 231 B. J. Berne and R. Pecora J. Chem. Phys. 1969 50 783. 232 L. Blum J. Chem. Phys. 1969,51 5024. 233 J. M. Schurr J. Phys. Chem. 1969.73 2820. 234 D. L. Knirk and Z. W. Salsburg J. Chem. Phys. 1971,54 1251. 235 V. A. Bloomfield and J. A. Benbesat Macromolecules 1971 4 609. 236 S. B. Dubin ‘Methods in Enzymology’ ed. Colowitch and Kaplan Vol. XXVI C Academic Press New York and London 1972 p.119. 237 Y. Yeh and R. N. Keeler J. Chem. Phys. 1969,51 1120. 238 D. Magde E. Elson and W. W. Webb Phys. Rev. Letters 1972 29 705. 239 G. Fehrer and M. Weissman Proc. Nut. Acad. Sci. U.S.A. 1973,70 870. 162 M. H. Davies,B. H. Robinson and J. R. Keefle be small microscopic changes in concentration of the species around the equil- ibrium values. It should be noted that the method is completely different from techniques such as ultrasonic absorption or dielectric relaxation in that no external perturbation is applied. It is important to eliminate artefact noise sources (i.e.those not due to chemical reaction) in the experiment and these may be recognized since the chemical noise amplitude can be calculated. This should become easier as the technique develops and the frequency dependencies of various types of noise are recognized.In the paper a full account of theory and experiment is given and kinetic results are reported for the ion-association of beryllium sulphate. Results agree well with those obtained by relaxation methods. A similar technique has been used by Vasilescu et in their study of the change in binding of sodium counter-ions to DNA during a helix-coil transition (effected by a temperature change). The technique provides information about the helix-coil transition itself the free ion-atmosphere the average number of free ions in solution and hence the number of sodium ions ejected from the DNA during the thermal rearrangement. Pressure-jump Method.-The pressure-jump method has continued to be extensively utilized although at first sight it might seem inferior to the temperature- jump technique owing to the longer perturbation time.However systems with small values of AHo can be studied there is no necessity to use conducting media and there is no slow effect such as that due to cooling in the temperature-jump method. A piessure-jump instrument utilizing thermometric detection has been In this detection mode the change in temperature as the reaction proceeds to the new equilibrium position on pressure release is monitored by means of a thermistor of low heat capacity. This method should be capable of wide application. The authors claim that they can detect a temperature change of K and relaxations in the 100ms-100s region can be studied.The response of the instrument is limited by that of the thermistor detector which is of the order of 30 ms. It is of course necessary to correct for the temperature jump due to the adiabatic expansion (AKd) on pressure release and this is largely compensated by a differential arrangement in which ACdcancels in two parallel cells. The theory is based on that for the thermal-maximum method of Bell and Cl~nie.’~~ The rate of hydration of propionaldehyde in water was studied which is rather too rapid for conventional methods to be used. Other workers have continued to study such systems as the dynamics of metal-ligand substitution reactions’ 44-’ 46 and aggregation processes’ ’,’48 240 D. Vasilescu M. Tebene H. Kranck and B.Camus Biopolymers 1971 12 223. 241 J. Helisch and W. Knoche Ber. Bunsengesellschufrphys. Chem. 1971 75 951. 242 W. Knoche and G. Weise Chem. Instr. 1973 5 91. 243 R. P. Bell and J. C. Clunie Proc. Roy. SOC.,1952 A16 212. 244 G. Macri and S. Petrucci Inorg. Chem. 1970 9 1009. 24s D. Saar G. Macri and S. Petrucci J. Inorg. Nuclear Chem. 1971 33 4227. 246 G. Platz and H. Hoffmann Ber. Bunsengesellschaft phys. Chem. 1972 76 491. 24’ K. Takeda and T. Yasunaga J. Colloid Interface Sci. 1972 40,127. 248 S. Harada H. Tanabe and T. Yasunaga Bull. Chem. SOC.Japan 1973,46 3125. Kinetics of Reactions in Solution 163 using the pressure-jump technique with conductimetric detection. Atemperature-jump apparatus for operation at high pressures has also been described.249 An instrument with optical detection has been reported,250 and utilized in the study of the isomerization of bovine serum albumin at neutral pH using phenol red as indicator.’’’ Two relaxation times are observed and after detailed analysis the fast one was interpreted in terms of the binding of dye to the protein and the slower one was thought to be due to a protein conformation change.Eyring et ~1.~’~ studied the interaction of methyl orange with /?-lacto- globulin between pH 2 and 3.7 (by temperature jump) and also observed two relaxation times both of which were interpreted as due to intramolecular indicator-protein interactions. The monomer-dimer equilibrium in the protein could not be detected. Electric-field-jump Methods.-Another interesting large-perturbation relaxation method which could find more extensive application is the dissociation-field effect (electric field jump) with spectrophotometric detection.An apparatus has been designed by Eyring et al. 253 which has several novel features and closely resembles that of the fast-heating temperature-jump apparatus described previously214 in that relaxation times down to 30ns can be measured. The machine is used to follow the ionization of acetic acid coupled with bromocresol green as indi~ator.~’~ The full kinetic analysis for this system (where both reactions relax over the same time range) is given which should have useful applications. Photochemical Perturbation Methods.-Recently it has been found that lasers can often be used to perturb the equilibrium of a system containing a photo- sensitive component.An early example of this method was reported by Goodall and Greenhow,” ’who used a Q-switched neodymium laser with conductivity detection to excite water vibrationally and to perturb the equilibrium H20 *H+ + OH-. Results for the reverse combination of ions agree with those obtained by microwave temperature-jump methods. Another example256 concerns the conformational change (square-planar to octahedral) exhibited by the reaction of Ni1’(2,3,2-tet) with water. Using a Q-switched neodymium laser (2 J 30 ns) photochemical excitation resulted in a 5 % change in the concentration of the square-planar species. This is followed by return to equilibrium with a relaxation time of approximately 300ns and because of the large concentration change this could be easily monitored 249 A.D. Yu M. D. Weissbluth and R. A. Grieger Rev. Sci.Instr. 1973 44 1390. 250 D. E. Goldsack and P. M. Waern Analyt. Biochem. 1969 28 273. 25’ D. E. Goldsack and P. M. Waern Canad. J. Biochem. 1971,49 1267. 252 J. Lang J. J. Auborn and E. M. Eyring J. Biol. Chem. 1971 246 5380. 253 S. L. Olsen R. L. Silver L. P. Holmes J. J. Auborn P. Warrick and E. M. Eyring Rev. Sci. Instr. 1971 42 1247. 254 J. J. Auborn P. Warrick and E. M. Eyring J. Phys. Chem. 1971 75 2488. 255 D. M. Goodall and R. C. Greenhow Chem. Phys. Letters 1971,9 583. 256 K. J. Ivin R. Jamison and J. J. McGarvey J. Amer. Chem. SOC. 1972 94 1763. 164 M. H. Davies B.H. Robinson and J. R. Keefle spectrophotometrically with no bandwidth problems. Recently Sutin and Creutz2” have compared the photochemical and temperature-jump methods. Another interesting study by Hasinoff 258 utilizes a ruby laser for excitation. The fast recombination process of carbon monoxide and myoglobin is investigated as a function of pressure. The photochemical perturbation method looks to be most promising but must be used with caution until the factors responsible for the laser perturbation are clearly understood. Amplitude Method.-It is perhaps not generally realized that there is extra information on thermodynamic parameters to be obtained from relaxation experiments through an analysis of the relaxation amplitude as a function of c~ncentration.~’~ Recent applications confirm the value of the approach” 1*260 and in favourable cases the equilibrium constant K AHo (from temperature jump) and AVO (from pressure jump) can be obtained.Fluorescence Detection Methods.-Among optical detection methods in fast- reaction studies fluorescence detection is particularly attractive because of the high sensitivity which is attainable. With absorbance detection reagent concen- trations below mol I-’ can seldom be monitored whereas with fluorescence detection concentrations of lop8moll-’ can easily be detected. In fact the sensitivity is only surpassed by radioactive labels. This high sensitivity can be important for relaxation experiments since it permits the study of the kinetics of chemical systems with high equilibrium constants (K E lo8 1 mol-’).Also diffusion-controlled reactions can in certain cases be studied in the stopped-flow time range since very low concentrations may be employed. Fluorescence is more specific than absorption and fluorescence emission is often sensitive to small changes in environment of the fluorescent probe so that additional processes may be investigated. Another important advantage is that in contrast to the electronic absorption spectrum the molecular basis for changes in quantum yield can often be elucidated. Fluorescence polarization can also be employed which allows the investigation of freedom of motion of the probe or of the structure to which it is attached. A temperature-jump apparatus has been designed by Rigler Rabl and Jovin261 which is equipped to measure changes in absorption fluorescence and fluorescence polarization.A 200 W Xe-Hg lamp is employed since the fluorescence emission depends directly on light intensity. Reflectance measurements can also be made when optically dense solutions are employed. The instrument is used to measure the interaction of the acridine dye proflavine with calf-thymus DNA. At a dye concentration of 2 x lob6mol I-the signal- to-noise ratio in the fluorescence mode is superior to that in the absorption mode by a factor of almost ten. Many systems are available which are amenable to a fluorescence study. Fluorescent probes are often found naturally as intrinsic 257 N. Sutin and C. Creutz J. Amer. Chem. Soc. 1973 95. 7177.258 B. B. Hasinoff to be published. 259 R. Winkler and M. Eigen unpublished results. 260 C. Kuehn and W. Knoche Trans. Faraday SOC.,1971 67 2107. 26‘ R. Rigler C.-R. Rabl and T. Jovin Rev. Sci. Instr. 1974 45. 580. Kinetics of Reactions in Solution 165 probes in biomaterials262 such as aromatic amino-acids in protein molecules,263 in the cofactor NADH and as flavines in various flavine enzymes. In addition it is possible in many cases to label structures with fluorescent probes for example t-RNA may be labelled in the anticodon loop with acridine dyes or ethidium bromide.264 A vast number of extrinsic fluorescent are also available (eg. acridine dyes,266 naphthalene~ulphonates~~~) for the study of small molecule-macromolecule interactions and the possibilities are discussed in an excellent review on fluorescence relaxation spectroscopy by Rigler and Ehren- berg.268a Also important is the article by Yguerabide268b on nanosecond fluoroescence spectroscopy of macromolecules.The use and advantages of the fluorescence technique for following the dynamics of interconversion of inter- mediates in enzyme reactions have been discussed by G~tfreund.~~~ The study of the kinetics of the binding of small fluorescent molecules to poly- peptides DNA,270 and membranes should greatly benefit from relaxation measurements with fluorescence detection since the fluorescence emission is dependent on probe environment and for DNA there are at least two binding sites one of which is thought to represent the intercalation of the probe into the double-helical structure.There have been recent developments in the theory of these binding processes which are directly applicable to relaxation experiments. Binding is co-operative and a based on a linear king lattice of equivalent binding sites with co-operative nearest-neighbour interactions has been successfully tested exper- imentally in the study of the kinetics of binding of acridine dyes to polypeptides (e.g. poly-a-L-glutamic acid)2 72 and polymers (poly-acrylic This work stresses the importance of establishing a sound theoretical basis for the inter- pretation of relaxation kinetic data. 262 L. Stryer Science 1968 162 526. 263 J. J. Holbrook Biochem. J. 1972 128 921. 264 W. Wintermeyer and H. G.Zachau F.E.B.S. Letters 1971 18 214. 26s P. G. Popov K. I. Vaptzurova G. P. Kossekova and T. K. Nikolav Biochem. Pharmacol. 1972 21 2363; R. A. Kenner and A. A. Abodevin Biochemistry 1971 10 4433; J. R. Brocklehurst and G. K. Radda 'Probes of Structure and Function of Macromolecules and Membranes' Vol. 11 Academic Press New York 1971 p. 59; D. C. Ward and E. Reich J. Biol. Chem. 1969 244,1228. 266 G. Lober and G. Achtert Biopolymers 1969 8 595; U. Pachmann and R. Rigler Exp. Cell Research 1972,12 602. "' L. Stryer J. Mol. Biol. 1965 13 482; E. Daniel and G. Weber Biochemistry 1966,5 1893; W. 0. McClure and G. M. Edelman ibid. 1967,6 559. 268 (a)R. Rigler and M. Ehrenberg Quart. Reo. Biophys. 1973 6 139; (b)J. Yguerabide 'Methods in Enzymology Vol.XXVI Part C' ed. C. H. W. Hirs and S. N. Timasheff Academic Press New York 1972 p. 498. 269 J. J. Holbrook and H. Gutfreund F.E.B.S. Letters 1973 31 157. "O G. G. Hammes and C. D. Hubbard J. Phys. Chem. 1966 70 2889; H. J. Li and D. M. Crothers J. Mol. Biol. 1969 39 461 ; D. E. V. Schmechel and D. M. Crothers Biopolymers 1971 10 465; C. Steenbergen jun. and S. C. Mohr ibid. 1973 12 711; W. Muller D. M. Crothers and M. J. Waring European J. Biochem. 1973 39 223. 271 G. Schwarz European J. Biochem. 1970 12,442; Ber. Bunsengesellschaft phys. Chem. 1972 16 373. 272 G. Schwarz S. Klose and W. Balthasar European J. Biochem. 1970 12 454; G. Schwarz and W. Balthasar ibid. 1970 12 461. 273 G. Schwarz and S. Klose European J. Biochem. 1972 29 249. 166 M.H. Dauies B. H. Robinson and J. R. Keefle 6 Applications of Fast -reaction Techniques SoluteSolvent Interactions.-Solvent -structure perturbations accompanying reactions in solution have been much studied in the past few years. Medium- range forces are involved so that the region outside the first solvation shell should often be considered. In addition the relative influence of steric hydro- phobic coulombic dispersive and solvent-stiffness factors on solvation (i.e. solvent-solute and solvent-solvent interactions in a microscopic environment) is now recognized to be of considerable significance. A useful review by Grunwald and Ralph274 attempts to resolve the factors responsible for the solvation of amines in water and other hydroxylic solvents.The major reaction process of interest is that of rupture of the R,N...HOH hydrogen bond between the amino-nitrogen atom and the adjacent water molecule. Rate constants are strongly dependent on the R groups and the authors make a case for interpretation of the rate change based primarily on dispersion (or van der Waals) forces between the base and attached water rather than on enhanced solvent-solvent interaction (iceberg effect) in the presence of hydro- carbon groups. The recent ultrasonic measurements on the deprotonation of amines by OH-are also pertinent to the discussion.275 Bennetto and Caldir~~~~ have carried out a detailed study on the effects of solvent on the rates of ligand substitution (and solvent exchange) on metal ions and have concluded that solvent-structure effects predominantly determine the kinetics.They suggest that the Eigen-Wilkins f~rmulation,~~’ which has been a useful generalization for the kinetics of ligand substitution on metal ions in aqueous media may have to be modified for interpretation of data in solvents other than water. Other papers relevant to this discussion are those of hem me^,^^^ on the factors influencing outer-sphere complex formation in solution and Wendt,279 on the kinetics of ion dimerization. There have been many studies of ligand-substitution processes involving labile metal ions since the advent of methods for studying fast reactions and there is a copious literature on the subject. Electron-transfer reactions were extensively reviewed in the 1969 Report,280 a most lucid description of the subject was presented by Diebler28’ in 1970 and there have been two recent Specialist Periodical Reports on the subject.282 The problem of distinguishing between hydrophobic and dispersive interactions (collectively known as stacking interactions) has been highlighted re~ently~~~.”~ 274 E.Grunwald and E. K. Ralph Accounts Chem. Res. 1971 4 107. M. Eigen G. Maass and G. Schwarz 2.phys. Chem. (Frankfurt) 197 1 74 3 19. 276 H. P. Bennetto and E. F. Caldin J. Chem. SOC.(A),1971,2191,2198; J. Solution Chem. 1973 2 217. 27’ R. G. Wilkins Accounts Chem. Res. 1970 3 408. P. Hemmes J. Amer. Chem. SOC. 1972 94 74. 279 H. Wendt Ber. Bunsengesellschaft phys. Chem. 1970 74. 593. 280 S. B. Brown and P.Jones Ann. Reporrs (A) 1969 66 107. ”‘ H. Diebler Ber. Bunsengesellschafr phys. Chem. 1970 74 268. D. N. Hague in ‘Inorganic Reaction Mechanisms’ ed. J. Burgess (Specialist Periodical Reports) The Chemical Society London 1971 vol. 1 p. 210; 1972 vol. 2 p. 196. 283 B. H. Robinson A. Loffler and G. Schwarz J.C.S. Furaday I 1973 69 56. 284 D. Porschke and F. Eggers European J. Biochem. 1972 26 490. Kinetics of Reactions in Solution 167 in studies of the process of molecular association in aqueous solution. Porschke and Egger~~*~ have measured the kinetics of self-association of N6Ng-dimethyl- adenine by sound absorption in the 10-100MHz region. The formation of stacks is found to be close to a diffusion-controlled process but with a rather high activation energy of +6 kcal mol-’.The authors suggest that there may be a characteristic difference (manifested in the thermodynamic terms AHo and AVO) between stacking forces involving non-polarizable species (e.g. hydrocarbon chains which aggregate to form micelles) and compounds with high polarizability and prominent dipoles (e.g.nucleotides nucleosides and acridine dyes). Dynamics of Micellar Processes.-Micellization and Solubilization. To demon-strate the application of fast-reaction methods in hitherto unexplored research areas an excellent example is the study of the special process of molecular aggregation known as micellization (micelle formation and breakdown). This is a process of fundamental importance both industrially and biomedically.Although the equilibrium thermodynamic properties of micelles have been well studied kinetic studies could not be carried out until the relevant fast-reaction techniques had been devised. However it was clear that a micelle possessed a dynamic structure and that there was a rapid exchange of surfactant units in the micelle with free unassociated surfactant in solution. Early temperature-jump experi- ments were performed by Kresheck et al,,285and the stepwise-aggregation model developed in their paper is that most generally employed today. They ascribe the rate-limiting step in the dissolution of a micelle to the release of the first molecule of monomer from the micelle. This assumption then leads to a predic- tion of a linear dependence of the reciprocal relaxation time (z-’) on micellar concentration from which the rate constant characterizing dissolution can be found.Eyring et a1.286 have used the temperature-jump method with absorbance and light-scattering detection to study the rate of dissolution of the negatively charged micelle formed by sodium dodecyl (lauryl) sulphate (SDS) and the pressure-jump method with conductimetric detection287 has also been used for the same system. In general these results provide evidence in support of the Kresheck model and linear plots are found for z-uersus micelle concentration. Analysis of the results indicates micelle lifetimes in the 10-3-10-1 s region the values depending on the chain length of the surfactant and the nature of the ionized head-group.However Hermann and Kahlweit288 were unable to confirm the linear dependence of 7-l on micelle concentration above the critical micelle concentration (CMC) ;in addition relaxation effects could be observed well below the CMC. It was shown that the addition of ‘structure breakers’ (e.g.urea) increased the rate constant for breakdown as expected and addition of octan-1-01 (up to 2 x moll-’) changed the rate constant for dissolution presumably owing to the formation of mixed micelles. 285 G. C. Kresheck E. Hamori G. Davenport and H. A. Scheraga J. Amer. Chem. SOC. 1966,88 246. 286 B. C. Bennion L. K. J. Tong L. P.Holmes and E. M. Eyring J. Phys. Chem. 1969 73 3288; B. C. Bennion and E. M. Eyring J. Colloid Interface Sci. 1970,32 286. 28’ K. Takada and T.Yasunaga J. Colloid Interface Sci. 1973,45 406. 288 U. Hermann and M. Kahlweit Ber. Bunsengesellschafi phys. Chem. 1973,77 I1 19. 168 M. H. Dauies B. H. Robinson and J. R. Keefe An interesting discussion point is that analyses of n.m.r.289 and ultrasonic suggest very much shorter micellar lifetimes compared to results obtained by stopped-flow temperature-jump and pressure-jump methods a time factor of lo3-lo4 being involved. Unfortunately it is generally not possible to investigate the same surfactant systems using the different methods but for SDS relaxation times of s are found by ultrasonics and -10-2sby pressure jump and temperature jump. There has been controversy recently as to which dynamic process isactually being observed by the ultrasonic technique since the method is not specific to a particular reaction.The perturbation of equilibria involving either micelles and monomers or micelles and counter-ions might be observed. If the latter were the case this would certainly explain the discrepancy but this does not appear likely following recent experimental An acceptable explanation which is at present being canvas~ed,~~~*~~~ is that the ultrasonic and other small-perturbation techniques essentially measure the dynamic exchange of monomers with the micelle aggregate whereas the large-perturbation techniques (including stopped-flow concentration-jump) involve dissolution and complete fragmentation of micelles which is a much slower process. A serious handicap to kinetic studies is that there is still no really satisfactory model for aggregation to form micelles although several have been proposed.293 Clearly confusion exists as to which aggregated species may actually be regarded as micelles as opposed to oligomers (molecular aggregates containing 2-10 units but without the characteristic micellar property of solubilization).Some model systems for aggregation fail to predict the abrupt change in observable parameters which is identified with the CMC. The presence of significant concentrations of pre-micelle aggregates should certainly be considered since their existence would radically alter the present approach to the kinetic analysis if positive evidence could be found. Experiments on non-ionic surfactants have also been carried by means of both the stopped-flow and temperature-jump techniques monitoring the intrinsic U.V.chromophore in the surfactant. It is interesting that these large- perturbation techniques also produce results differing by an order of magnitude the stopped-flow technique giving the faster rate. This would seem to indicate that the micellization process is more complex than has been assumed to date and it would appear that the concentration- and temperature-jump techniques are monitoring different aspects of the overall mechanism. Hence the various 289 N. Muller J. Phys. Chem. 1972 76 3079. 190 T. Yasunaga S. Fujii and M. Miura J. Colloid Interface Sci. 1969 30,399; R. Zana and J. Lang Compt. rend. 1968 266 C 1377; E. Graber and R. Zana Kolloid-Z. 1970 238 439; P.J. Sams E. Wyn-Jones and J. Rassing J.C.S. Furaday 11 1973 69 180. 291 J. Rassing P. J. Sams and E. Wyn-Jones to be published. 292 N. Muller ‘Reaction Kinetics in Micelles’ ed. E. Cordes Plenum Press New York 1973. 293 P. J. Sams E. Wyn-Jones and J. Rassing Chem. Phys. Letters 1972 13 233. 294 J. Lang J. J. Auborn and E. M. Eyring J. Colloid Interface Sci.,1972,41 484; J. Lang and E. M. Eyring J. Polymer Sci.,Part A-2 Polymer Phys. 1972 10 89. Kinetics of Reactions in Solution 169 techniques should be seen as complementary and we can hope that a combined approach using a variety of fast-reaction techniques will help to reveal detailed aspects of these important processes occurring in the sub-second time-range. An interesting series of experiments could presumably be carried out using the new technique of fluctuation spectroscopy using both absorbance detection (to detect solu bilization equilibria) and conductance detection (to detect monomer- micelle exchange).Eyring et uI.~~’*98 have performed stopped-flow light-scattering experiments in a study of the solubilization of plasma membranes by SDS. Rate constants in the millisecond region are found. Before leaving the subject of micellization and solubilization by micelles the interesting e.s.r. and n.m.r. work of Oake~~~’ on the solubilization of spin-probes and the interaction of paramagnetic manganese ions with micelles should be mentioned.296 The latter experiments enable the outer surface of the micelle to be investigated.There is an interesting review by Nagakawa and Jiz~moto~~’ on the e.s.r. spectra of solubilized radicals in micelles. Micelle-catafysed Reactions. The whole field of micelle-catalysed reactions in solution is developing very rapidly at the present time but the area is not reviewed in this Report as there are several excellent upto-date commentaries available.298 Interest in reversed or inverted micelles e.g. alkylammonium carboxylates and phospholipids formed in aprotic solvents is growing because these micelles are useful industrial additives and can be used as model systems for enzymes and membranes. They also offer attractive possibilities for organic synthesis. A remarkable catalysis rate has been observed by Fendler and Fendler,299 who measured a dramatic rate acceleration (>lo3)for the mutarotation of glucose in the presence of reversed micelles in aprotic solvents.DWusioocontrolled Reactim Processes.-Progress has been made through ex’periment in understanding the process of diffusion together of reactants to form an intermediate complex with the right configuration for further reaction. In aprotic solvents the medium cannot co-operate directly in a proton-transfer process by means of a Grotthus chain-type mechanism as has been observed in water as solvent but for certain very fast reactions (e.g.proton transfer between phenolic acids and aliphatic amines in aprotic solvents) the diffusion step or reorientation within the encounter complex is still rate-limiting. By means of a microwave temperature-jump apparatus which is suitable for use with dipolar 295 J.Oakes J.C.S. Faraday II 1973 69 1324. 296 J. Oakes J.C.S. Faraday II 1972,68 1464. 297 T. Nagakawa and H. Jizomoto Kolloid-Z. 1972 250 594. 298 E. H. Cordes and R. B. Dunlap Accounts Chem. Res. 1969 2 329; E. J. Fendler and J. H. Fendler Adu. Phys. Org. Chem. 1970 8 271 ;‘Reaction Kinetics in Micelles’ ed. E. H. Cordes Plenum Press New York 1973; E. H. Cordes and C. Gitler ‘Progress in Bioorganic Chemistry Vol. 2’ ed. E. I. Kaiser and F. J. Kozdy Wiley New York 1973. 299 E. J. Fendler J. H. Fendler R. T. Meday and V. A. Woods Chem. Comm. 1971 1497; J. H. Fendler J.C.S. Chem. Comm. 1972 292. 170 M. H. Davies B. H. Robinson and J. R. Keefe aprotic solvents Caldin.et dJoO have measured the rates of formation of contact ion-pairs on reaction of 2,4-dinitrophenol with a series of aliphatic amine bases.Rate constants for ion-pair formation do not correlate with the equilibrium constants for the reaction indicating that the proton-transfer step is not rate- limiting. It is concluded that the aliphatic groups on the amines restrict the approach of the OH group of the nitrophenol to the lone pair on the nitrogen. The nature of this steric effect is discussed in detail. Very similar systems have been studied by Ivin et a1.,301and they also find that rate constants for ion-pair formation are a factor of 5-35 below the limit set by the simple Smoluchowski equation (210” 1 mol-’ s-’). In their later paper the possibility of relatively slow rotation of reactants within the encounter complex is considered and it is shown that incorporation of this extra step in the mechanismprovides a reasonably satisfactory explanation for the rate-constant dependence on temperature and solvent viscosity.The microwave temperature-jump instrument used has been de~cribed.~” Temperature jumps of 0.5 K are obtained in dipolar aprotic solvents in 1 ps and both conductimetric and spectrophotometric detection are employed. The sample cell is thermostatted by means of an efficient gas-flow system. The kinetics of the reaction between tri-n-butylamine and the substituted phenol tetrabromophenolphthalein ethyl ester (Magenta E) have been inves- tigatedJo3 in a series of aprotic solvents.Again the rate constants are a factor of 15-30 less than the calculated values for a strictly diffusion-controlled process. The rate data. for a wide range of acid-base reactions are considered and a hypothesis is proposed which envisages initial formation of the ‘encounter’ complex followed by rotation of this species (within the lifetime of the encounter complex) to a configuration where reaction to form a hydrogen-bonded complex or ion-pair can proceed. A feature of the mechanism is that the lifetime of the ‘encounter’ complex is longer than 10-9s and this is thought to be due to dispersive and dipole-dipole interactions. Alternative schemes are considered but are found to be unsatisfactory. However not all proton transfers between oxygen and nitrogen centres are rapid.The rate constant for proton transfer from the indicator phenolic acid bromophenol blue to the weak base pyridine in a variety of aprotic solvents (E = 2-9) can be measuredJo4 in the stopped-flow time-range and a good correlation is obtained between the forward rate constants [k = (7-650) x lo31 mol-s-‘3 and the solvent polarity parameter E, indicating that solvent reorganization is required in the rate-limiting step which in this case must be proton transfer from an intermediate hydrogen-bonded complex to the ion-pair. 300 E. F. Caldin J. E. Crooks and D. O’Donnell J.C.S. Furuduy I 1973 69 993. 30’ K. J. Ivin J. J. McGarvey E. L. Simmons and R. Small Trans. Furuduy Soc. 1971 67 104; J.C.S. Furuduy I 1973,69 1016. 302 K. J. Ivin J.J. McGarvey and E. L. Simmons Trans. Furuduy Soc. 1971 67 97. 303 G. D. Burfoot E. F. Caldin and H. Goodman J.C.S. Furuduy I 1974,70 105. 30* G. Gammons B. H. Robinson and M. J. Stern J.C.S. Chem. Comm. 1972 1157. Kinetics of Reactions in Solution The kinetics of formation of the donor-acceptor complex between tetracyano- ethylene and hexamethylbenzene have been studiedJo5 in 1-chlorobutane as solvent at 190 K and in chlorobenzene-n-heptane (4060%v/v) at 213 K. Experimental rate constants of 1.45 x lo8 1 mol-' s-' and 8 x lo8 1 mol-'s-' respectively were found which may be compared with the calculated diffusion- controlled values of 1.7 x lo91mol-' s-' and 2 x lo91 mol-'s-'. The low value in 1-chlorobutane was attributed to the need for some desolvation on forming the transition state in this solvent.Desolvation is also suggested in an explanation of the low rate constant (at 298 K) of 6.2 x lo9 1 mol-'s-' (Smolu-chowski value 1.5 x 10'O1mol-'s-') for the formation of tri-iodide from iodide and iodine in water217 and for the stacking of the planar dye acridine orange in aqueous solution.306 The recombination rate-constant for the reaction of the anion of bromocresol green with hydrogen ion has been investigated by the electric-field-jump method in glycerol-water mixtures in order to study primarily the effect of viscosity on ion-recombination kinetics.307 To fit the data over all solvent compositions the authors introduced an 'ion-pair' intermediate and they suggest that in water the 'proton-transfer' within the 'ion-pair' is rate-limiting whereas in 70 % glycerol the overall reaction rate is diffusion-controlled.The recombination of the methyl orange and methyl red anions with hydrogen ions in water has also been in~estigated.~'~ Methyl red reacts at the diffusion-controlled limiting value but the reaction of methyl orange is a factor of ten slower. It is concluded that the rate of protonation of these azo-species is strongly influenced by ortho-substituents in the adjoining phenyl group. 305 E. F. Caldin J. E. Crooks D. O'Donnell D. Smith and S. Toner J.C.S. Furaday I 1972 68 849. 306 B. H. Robinson A. Seelig and G. Schwarz to be published. 307 P. Warrick jun. J. J. Auborn and E. M. Eyring J. Phys. Chem. 1972 76 1184. 308 R.G. Sandberg G. H. Henderson R. D. White and E. M. Eyring J. Phys. Chem. 1972,76,4623.

ISSN:0308-6003    

DOI:10.1039/PR9737000123

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

7 Physical Properties of Polymers and their Solutions By J. M. G. COWIE Department of Chemistry University of Stirling Stirling FK9 4LA 1 Physical Chemistry of Polymer Systems Introduction.-It is now four years since the last Annual Report on the physical properties of polymer systems appeared. As that concentrated predominantly on work appearing up to and including 1969 this Report will highlight the main trends since then covering the period 1970-73. No attempt is made to include every reference on the topics covered which will be concerned only with synthetic organic polymers. Polymer Solutions -’Iheory.-‘It is well known that statistical mechanics provides a tool for the description of the relationship between the macroscopic behaviour of substances and/or molecular properties.Clearly the same principles apply to polymer science as to the study of small molecules.’ These words open Hiromi Yamakawa’s book’ on modern polymer solution theory which is undoubtedly the most important treatise on polymer science to appear during the period covered by this Report. Much of its strength lies in the fact that the author is a leading authority in this field and has contributed extensively to the development of the subject. The treatment of polymers in solution is based on two major concepts (i) the recbgnition that a polymer chain can be approximated by a random-flight model and (ii) that in very dilute solutions the polymer molecules are sufficiently well separated to allow the analogy of a ‘gas’ of polymers in a liquid continuum to be drawn.The main theme in the book is a description of a number of theories based on these premises which are now generally classified under the heading ‘the two-parameter theory’. This states that the various properties of dilute polymer solutions may be described in terms of only two fundamental quantities (r2)o the unperturbed mean-square end-to-end distance of the polymer chain and 2 the excluded-volume parameter. In order to demonstrate how these may be formulated Yamakawa begins by dealing with the various distributions and averages used to describe a single flexible linear polymer chain as a function of the number of chain segments n and the mean bond length 1. In the simplest case H. Yamakawa ‘Modern Theory of Polymer Solutions’ Harper and Row New York 1971.173 J. M. G. Cowie the statistical properties of the random-flight chain can be analysed by the Markoff method to yield (r2)r = n12 where (r2)f is the mean-square end-to-end distance of a chain with unrestricted rotation about main-chain bonds. This is an unrealistic description and the restrictions imposed by short-range effects are then .outlined leading to the replacement of 1 by ‘u’,defined as the unperturbed effective bond length and (r2), = nu2 now refers to an unperturbed flexible chain with only short-range interactions operative. In addition this section encompasses the problems of ring branched star and stiff-chain conformations. Since publication further work has appeared on the shape of random-flight chains2v3 and the radius of gyration of ring polymer^.^ The unperturbed chain only exists when the polymer solution is pseudo-ideal -at the theta temperature for the system-and it is much more likely that the polymer will be dissolved in a good solvent which expands the coil.This means that the problem of long-range interactions must be met and this is introduced in the next chapter with a consideration of these long-range effects as embodied in the parameter p. Here p describes an effective volume from which all chain segments are excluded except one. The excluded-volume effect causes chain expansion and hence deviation from the simple Markoff model. To allow for this the dimensions of the expanded chain (r2) can be expressed in the form (r2> = (r’>,a The parameter aR is the linear expansion factor which Flory demonstrated to be a function of n but the exact relation depends on the theoretical approximations.The excluded-volume problem can be dealt with on two levels. The first re- cognizes that perturbation theory can be used directly to derive an expression for the coil dimensions in terms of a power expansion in p which can be applied to polymers dissolved in poor solvents where p is vanishingly small. For polymers dissolved in good solvents the situation is more complex as the excluded-volume effects are large and this requires the introduction of approximations. Much of this part of the book is devoted to the various treatments while concentrating predominantly on the two-parameter concept.Both approaches use the same relation for the excluded-volume parameter Z Z = (+na2)fflnL As fin2 can be deduced from thermodynamic measurements the following chapter is concerned with the thermodynamic behaviour of dilute solutions. This is followed by two extensive chapters on light scattering and the frictional behaviour of polymers before returning to an analysis of experimental data using the two-parameter approach. The latter is ultimately a test of whether or * K. SolE and W. H. Stockmayer J. Chem. Phys. 1971,54 2756. K. Sole J. Chem. Phys. 1971 55 335. K. SolE Macromolecules 1972 5. 705. Physical Properties of Polymers and their Solutions not the various solution properties such as the intrinsic viscosity [q] the second virial coefficient A, and the expansion factor can be reduced to a common dependence on 2 for data derived in different solvents and at different tempera- tures.Here disagreements begin to appear which will be mentioned later but in general the two-parameter theory appears well founded. The use of extrapola-tion methddp to .obtain unperturbed dimensions from data obtained in good solvents is now widely used but the precise form of the relation such as the widely employed Stockmayer-Fixman equation (SF) [q]/M* = KO + C@oBM* depends on the coefficients in the perturbation series a; = 1 + CIZ -... at small 2,where a, is the expansion coefficient derived from [q] measurements. Experimental results show that the original SF equation derived for a series with C = 1.55 led to curved plots at high values of 2.Empirical modifications gave two equations [q]/M*= KO +0.346QOBM* for 0 < a < 1.6 and [q]/M* = 1.05KO+ 0.287@0BM* for 0 < a; < 2.5 which suggests that C should lie in the range 1.05 < C < 1.55.Theoretical justification for these relations has been presented by Yamakawa and Tanaka,' who have obtained a value of C = 1.06 from a rigorous evaluation of the Zimm- Hearst theory. Yamakawa's book contains a wealth of detailed information but for those who wish a more distilled version of the salient features some of the original papers or short reviews may be of use ;in particular those on the excluded-volume effect6 and viral coefficients' are helpful.Subsequent contributions to a theoretical understanding of dilute-solution behaviour have been made by Bloomfield and McKenzie,' who estimated the excluded-volume effect while treatments ofstiff chains without excluded volumeg and the frictional coefficients of coils'o have been published. Improved distribution functions characterizing one- two- and threedimen- sional radii of gyration (S2)* have been presented by Forsman et UI.,"~'~ who formulated the problem of the dependence of (S2) on n in terms of a series of H. Yamakawa and G. Tanaka J. Chem. Phys. 1971,55 3188. 'H. Yamakawa Pure Appl. Chem. 1972,31 179. ' E. Casassa Pure Appl. Chem. 1972 31 151. V. A. Bloomfield and D. S. McKenzie J. Chem. Phys. 1970,52,628. H. Yamakawa and M. Fujii Macromolecules 1973 6 407.lo A. Horta Makromol. Chem. 1972 154 63. " R. Hoffman and W. C. Forsman J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 607. S. K. Gupta and W. C. Forsman Macromolecules 1972 5 779. 176 J. M. G.Cowie convolution integrals. Solution of these leads to results in good agreement with the asymptotic values obtained by Fixman and the final expression indicates a fifth-power dependence. A similar fifth-power dependence of a on n was obtained by Fujita and Norisuye' and by Alexandro~icz~~*' using Monte Carlo techniques. Light-scattering theory has also received some attention. Horta16 has used the boson formulation of Fixman to examine the effect of the excluded volume on the particle-scattering factor P(0) of linear chains; however a lack of ap- propriately good experimental data did not allow an adequate test of the result to be carried out.A companion paper" examined the magnitude of the error involved when a Gaussian approximation is used to calculate P(0)and shows that this could become significant if measurements are made using incident light with short wavelengths or if large coils are being studied. The mean-squared optical anisotropy (7') of a polymer has also come under consideration; Patterson and Flory" have derived a method of calculating (y') from measurements of the depolarized Rayleigh scattering from dilute solutions. The method has been tested for n-alkanes" and oligomers of poly(ethy1ene oxide)' dissolved in optically isotropic liquids. Assignment of appropriate values for the bond optical anisotropies in conjunction with rotational isomeric state theory gave (y2) in good agreement with the experimental results.An extensive series of papers by Huggins outlines a new approach to the interpretation of the thermodynamics of polymer The model adopted is one in which the liquid is composed of chemically uniform segments with average contact surfaces and energies. These remain constant at any given temperature but the relative number of contact areas for each contact type can vary to minimize the Gibbs free energy of the system. Ditonic systems (containing only two types of segment 1 and 2) have been treated and the thermodynamic quantities are derived as a function of these parameters. Thus the enthalpic contribution to the interaction parameter arises from the equilibrium between the various types of contact between the segment surfaces ;the relevant parameters l3 H.Fujita and T. Norisuye J. Chem. Phys. 1970,52 11 15. l4 Z. Alexandrowicz and Y. Accad Macromolecules 1973 6 251. Z. Alexandrowicz Macromolecules 1973 6 255. l6 A. Horta European Polymer J. 1970 6 1253. A. Horta Macromolecules 1970 3 371. G. D. Patterson and P. J. Flory J.C.S. Faraday 11 1972,68 1098. G. D. Patterson and P. J. Flory J.C.S. Faraday ZZ 1972 68 11 11. 2o M. L. Huggins J. Phys. Chem. 1970 74 371. 21 M. L. Huggins Polymer 1971 12 389. 22 M. L. Huggins J. Polymer Sci. Par! C,Polymer Symposia 1971,33 55. 23 M. L. Huggins J. Phys. Chem. 1971,75 1255. 24 M.L. Huggins Macromolecules 1971 4 274. 25 M. L. Huggins J. Paint Technol. 1972 44 55. 26 M. L. Huggins Pure Appl. Chem. 1972 31 245. 27 M. L. Huggins Polymer J. 1973,4 502. M. L. Huggins. Polymer J. 1973 4 511. Physical Properties of Polymers and their Solutions 177 are E~, the energy difference between (1-1) or (2-2) contacts and (1-2) contacts and r,, the ratio of the segment 2 contacting surfaces to that of segment 1. Both must be derived from experimental heats of mixing. The entropic contribution comes from the segment orientational randomness and the non-random distri- bution of intersegment contacts and involves a parameter k,! which must be determined empirically at present. The theory has been applied with some success to selected non-polar systems but it remains to be adequately tested only when more data are available which may enable more precise interpretations of the several new parameters to be made.Polymer Solutious -Experimental.-A number of studies on the hydrodynamic behaviour of homopolymers in dilute solution have been published. These fall into two main categories those concerned with the verification and elaboration of dilute-solution theory and those reporting measurements of solution para- meters such as Mark-Houwink equations unperturbed dimensions characteristic ratios and steric factors (a). The latter group are more numerou~~~-~~ and 29 G. Moraglio G. Gianotti F. Zoppi and U. Bonicelli European Polymer J. 1971 7 303. 30 C. Booth and R. Orme Polymer 1970 11 626.31 R. Jerome and V. Desreux European Polymer J. 1970 6 171. 32 K. S. V. Srinivasan and M. Santappa Polymer 1973 14 5. 33 H. L. Wagner and C. A. J. Hoeve J. Polymer Sci. Polymer Phys. Edn. 1973 11 1 189. 34 A. Cervenka Makromol. Chem. 1973 170 239. 35 V. N. Tsvetkov 1. N. Shtennikova E. I. Rjumtsev and Yu. P. Getmanchuk EurzqGan Polymer J. 197I 7 767. 36 A. H. Fawcett and K. J. Ivin Polymer 1972 13 439. 37 N. Hadjichristidis M. Devaleriola and V. Desreux European Polymer J. 1972 8 1193. 38 M. Tricot and V. Desreux Makromol. Chem. 1971 149 185. 39 J. Stejskal M. J. Benes P. Kratochvil and J. Peska J. Polymer Sci. Polymer Phys. Edn. 1973 11 1803. 40 R. H. Marchessault K. Okamura and C. J. Su Macromolecules 1970 3 735.41 J. Cornibert R. H. Marchessault H. Benoit and G. Weill Macromolecules 1970 3 741. 42 (a) T. Matsumoto N. Nishioka and H. Fujita J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 23; (b)A. Kotera T. Saito Y.Shimoda and N. Onda Reports Progr. Polymer Phys. Japan 1971 14 35. 43 G. Gianotti U. Bonicelli and D. Borghi Mukromol. Chem. 1973 166 235. 44 A. R. Shultz A. L. Bridgman E. M. Hadsell and C. R. McCullough J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 273. 45 G. Moraglio G. Gianotti and U. Bonicelli European Polymer J. 1973 9 623. 46 A. Stokes European Polymer J. 1972 6 719. 47 G. Allen and J. McAinsh European Polymer J. 1970 6 1635. 48 K. Matsumura Polymer J. 1970 1 322. 49 Y. Izumi K. Shinbo N. Kato A. Chiba and Y.Miyake Polymer J. 1973 4 183. 50 Y. Izumi and Y. Miyake Polymer J. 1973 4 205. 51 K. Matsuo and W. H. Stockmayer J. Polymer Sci.,Polymer Phys. Edn. 1973 11 43. 52 M. Pizzoli G. Stea G. Ceccorulli and G. B. Gechele European Polymer J. 1970 6 1219. 53 G. Ceccorulli M. Pizzoli and G. Stea Makromol. Chem. 1971 142 153. 54 G. Ceccorulli and M. Pizzoli Chimica e Industria 1972 54 420. 55 K. Sakato and M. Kurata Polymer J. 1970 1 260. 56 G. Sitaramaiah and D. Jacobs Polymer 1970 11 165. 57 L. A. Utracki Polymer J. 1972 3 551. 58 G. Sitaramaiah and D. Jacobs Makromol. Chem. 1973 164 237. Table 1 Mark-Houwink relations for homopolymers in dilute solution [q] = KM' with concentration units g cm-I 4 00 w* cm g Polymer Solvent Temp./K mol-* V 0 Ref.Polybutene Phenetole 8 = 337.5 11.3 (isotactic) Anisole 6 = 362 11.1 -29 Diphenyl ether 8 = 421 10.3 0.50 Polybutene Phenetole 8 = 334 10.5 (atactic) Anisole 8 = 356 10.8 -29 Diphenyl ether 8 = 414 10.4 0.50 Poly(but-1-ene oxide) Benzene 298 1.59 Hexane 298 1.43 n-Butanol 298 1.96 730 1.71 30 Isopropyl alcohol 8 = 303 11.10 0.50 Poly(t-butyl acrylate) Butanone 298 0.32 Acetone 298 0.47 Methanol 298 1.60 640 2.30 31 Pentane 298 2.20 0.57 Hexane 8 = 297.2 4.90 0.50 Poly(ethy1 acrylate) Acetone 308 4.15 Butanone 308 2.03 673 2.15 32 n-pro pano 8 = 312 7.89 Polyethylene 1-Chloronaphthalene 403 5.55 1,2,4-TrichIorobenzene 403 3.92 106.3 -33 Chlorobenzene 408 4.48 0.7 1 -34 Poly(buty1 isocyanate) Carbon tetrachloride 298 3.16 1.20 -35 % Poly(cyc1ohexene sulphone) Dioxan 298 0.57 -1.24 36 a Benzene 298 1.33 is Poly(cyc1opentene sulphone) Dioxan 298 0.53 0.76 -1.17 36 9 Poly(cyclohexy1 methacrylate) Benzene 298 0.35 0.77 Cyclohexane 298 0.89 9 Dioxan 298 1.20 590 2.50 37 2.Butanone 298 1.23 0.65 n-Butanol 8 = 296 4.46 0.50 Poly(pheny1 methacrylate) Benzene 298 0.57 "a 9- Dioxan 298 0.54 Butanone 298 0.95 670 2.80 Acetone 298 1.49 "a Poly(deca hydro-8-naphthyl -600 2.90 37 4 met hacry late) Poly(B-naphthyl met hacryla te) -3. 660 3.10 37 Poly(4-chlorophenyl metha- Dioxan 298 0.61 h crylate) Benzene 298 0.92 605 2.61-38 % Carbon tetrachloride 298 2.00 0.58 2.75 2 Poly-[ 1-(2-hydroxyethyl)-O.5M-KCI 298 0.40 0.70 -3.10 39 L" trimethylammonium benzene- 3 sulphonate methacrylate] 5 Poly-[ 142-hydroxyethy1)-O.5M-KCl 298 0.26 0.7 1 2.74 39 8 pyridinium sulphonate methacry late] h f Poly(8-h ydroxybutyrate) Chloroform 303 0.77 40 2,2,2-Trifluoroethanol 303 2.5 1 41 3 Polyisobutene Heptane 298 1.63 i? Cyclohexane 298 1.19 -42a L.l Isoamyl isovalerate 8 = 295.1 11.40 0.50 Di-isobutyl ketone 8 = 335.1 -717 1.74 42b trans-Pol yperitanamer Toluene 303 5.2 1 0.69 C yclohexane 303 5.69 99 1 1.26 43 Isoamyl acetate e= 311 23.40 Poly-(2,6-diphenyl-I ,4-Chloroform 298 3.21 phenylene oxide) Benzene 323 1.97 0.64 44 Polypropene Isoamyl acetate e = 307 16.85 (at ac t ic) Isobutyl acetate 0 = 331 15.85 Biphenyl 8 = 402 12.80 0.50 45 Diphenyl ether e = 419 12.56 Pol ypropene Biphenyl 8 = 398 14.1 5 (isotactic) Diphenyl ether e = 416 13.0 0.50 45 L 00 0 Table1 (Contimred) 102K/ 10" cm3 g-9 (r;lM)f Polymer Solvent Temp./K mol-+ V /cm 0 Ref Poly(propene sulphide) Benzene 304 0.50 0.78 -46 Polysulphone A Dimethylformamide 298 0.33 0.64 753 '1 47 Poly(o-chlorostyrene) Butanone e = 298 4.60 0.50 -2.15 48 Pol y(p-chlorostyrene) ---2.29 49.50 Poly(p-fluorast yrene) Carbon tetrachloride e = 298 8.28 Benzene 298 4.05 -51 Chloroform 298 1.61 Butanone 298 1.11 0.73 Pol y(m-fluorostyrene) Carbon tetrachloride 298 6.56 Benzene 298 1.53 -51 Chloroform 298 1.28 0.70 Butanone 298 1.38 Pol y@-methoxyst yrene) Toluene 298 1.05 Toluene 296.4 0.92 Chlorocyclohexane 296.4 1.77 n-Amy1 acetate 296.4 5.50 0.52 636 2.40 52-Methyl isobutyl ketone 8 = 296.4 6.40 0.50 54 t-But ylbenzene e = 325.2 7.40 0.50 Isoamyl acetate 8 = 348.0 6.90 0.50 -Dichlorodecane 8 = 365.6 Poly(a-met hy lstyrene) Benzene 303 1.03 0.72 650 Poly(N-vin ylcarbazole) Benzene 298 3.05 0.58 Cyclohexanone 298 2.00 i:::] Tetrahydrofuran 298 1.44 0.67 619 Chloroform 298 1.36 Tetrachloroethylene 298 1.29 0.68 Poly(viny1 chloride) Mesityl oxide 298 Di-2-ethylhexyl 298 phthalate Diethyl phthalate 1' 577 2.84 58 298 22.0 0.46 0"::; 0.50 Poly-( 3-vinylpyridine) o-Dichlorobenzene 298 0.012 Tetrahydro fur an 298 0.032 Chloroform e = 298 0.051 Bisphenol A polycarbonate -920 1.35 88 182 J.M. G. Cowie pertinent data are summarized in Table 1. These contain a number of 0-solvents for the various polymers which have enabled direct measurement of the un- perturbed dimensions to be made but these have also been estimated in a large number of cases by extrapolation procedures such as the Stockmayer-Fixman method mentioned earlier. Of particular interest are the large values for o obtained for the methacrylate series37 with very bulky ester side-groups poly(N- ~inylcarbazole),~~ and poly-( 3-~inylpyridine).~~ At the other extreme low values of o have been reported for substituted polys~lphones~~ and polysulphone A,47 the latter being approximately unity. The values suggest that these are very flexible polymers ;Allen47 interprets the result as indicating the rigidity of the backbone segment containing the phenylene groups with free rotation about the ether oxygen whereas I~in~~ points out that the low values of o could indicate very similar energy levels for the trans and &gauche rotations about C-S bonds.Steric parameters have also been reported for poly(p-brom~styrene)~~ and polyacrylonitrile.60 Also reported are dilute- solution studies on poly(dimethylsiloxane),6' poly(methylphenylsiloxane),62 poly(fluoroalkoxy-phosphazenes),63and poly(trimethylsiloxanetitanoxanes),64 whose properties can be rationalized if the repeat unit is assumed to contain a cube-shaped Ti,,O, structure. A helix-coil transition was detected in poly@- hydroxybutyrate) in mixed solvent media:' and a relatively rigid rod-like conformation with a fold helical structure has been proposed4' for the polymer in 2,2,2-trifluoroethanol.The conformation of oligomeric poly(propene glycols) has been examined in both polar and non-polar solvents. In water65 and other high-dielectric media66 a tightly coiled conformation is in evidence whose structure is thought to be like an impermeable disc composed of three tightly folded rods. This is believed to be the best model for chains with M -= 1000. Meyerhoff et ~ studied molecular 1.~~9~~ weights up to 4OOO in acetone and benzene and found that gaussian coil behaviour was attained above M = 2000 in these solvents. In acetone A2was negative at low M then rose to a maximum at M = 400 followed by a decrease; this be-haviour has been observed in other polymers.Small-angle X-ray scattering was used to measure coil sizes but these did not agree with the classical theories. Modification of the expression for the frictional coefficient to [f]= 16.4(SZ)f 59 P. Karayannidis and A. Dondos Makromol. Chem. 1971 147 135. 6o K. Kamide and T. Terakawa Makromol. Chem. 1972 155 25. * J. Brezezinski Z. Czlonkowska-Kohutnicka B. Czarnecka and A. Kornas-Calka European Polymer J. 1973 9 733. 62 K. A. Andrianov S. A. Pavlova I. I. Tverdokhlekova N. V. Pertsova and A. Temni-kovskii Vysokomol. Soedinenii (A) 1972 14 18 16. b' G. L. Hagnauer and N. S. Schneider J. Polymer Sci. Parr A-2 Polymer Phys. 1972 10 699. 64 D. E. G. Jones and J. W. Lorimer Polymer 1972 13 265. 65 L.Sandell and D. A. I. Goring Macromolecules 1970 3 50. 66 L. Sandell and D. A. I. Goring Macromolecules 1970 3 54. 67 G. Meyerhoff Makromol. Chem. 1971 145 189. 68 G. Meyerhoff U. Moritz R. G. Kirste and W. Heitz European Polymer J. 1971 7 933. Physical Properties of Polymers and their Solutions 183 gave a better description of the experimental data where the proportionality constant is now larger than that theoretically predicted. One particularly important quantity which can provide significant information to aid elucidation of chain conformation is the temperature coefficient of the mean-square unperturbed dimension expressed as (d In (r2)o/dT). Although important this coefficient is also difficult to measure accurately and agreement between workers is often poor.It can be determined in a number of ways by measuring (r2), in different O-solvents by measuring [q] as a function of temperature and using an extrapolation technique or from thermoelastic measurements. A number of authors have reported such measure-mentS,29,45,50.69-71 which are listed in Table 2. Table 2 Temperature coeficients of unperturbed chain dimensions Method and Temp. lo3dln(r2),/dT Polymer range/K /K-Ref Pol ybutene Several &solvents -0.80 29 (isotactic) 333423 Pol ybutene 293413 -0.40 29 (atactic) Poly(ethy1ene Thermoelastic -0.14 to -0.28 71 oxide) d[ql/d T -0.85 to -1.13 Polypropene Two 8-solven’s -3.0 45 (isotactic) 398-416 Pol y propene Four O-solvents -1.8 45 (atactic) 3074 1 9 Poly(dimethy1-S-F plots from [q] in +0.8 69 siloxane) bromobenzene 353-393 Poly(met hylphenyl- [q]in isopropylcyclohexane -3.0 69 siloxane) 298-348 Poly(b-chloro-Eleven 8-solvents +0.48 50 styrene) 258.3-348.7 Poly(p-met hoxy- Four O-solvents 0 52 styrene) 296.4-365.6 Poly(tetrahydr0-Five &mixtures of -2.0 70 furan) chlorobenzene-octane KO 283-353 Light-scattering measurement + 11.0 70 of (S)& Natural rubber Thermoelastic +0.38 to +0.54 403,404 (cross-linked) The discrepancies obtained when different measuring techniques are used are highlighted in a comparison between the negative values reported for poly- b~tene~~ in a selection of &solvents and the positive values reported by Mark and Flory ”from stress-temperature measurements using amorphous networks.69 G. G. Kartasheva E. G. Erenburg and I. Ya. Poddubnyi Vysokomol. Soedinenii (B) 1972 14 665. lo J. M. Evans and M. B. Hugh European Polymer J. 1970 6 1161. ’’ F. de Candia V. Vittoria U. Bianchi and E. Patrone Macromolecules 1972 5 493. ’* J. E. Mark and P. J. Flory J. Amer. Chem. SOC.,1965. 87 1423. 184 J. M. G.Cowie Even data from the same laboratory may vary as with poly(ethy1ene oxide),’l where thermoelastic and viscosity measurements led to negative coefficients which differed both from each other and quite markedly from the +0.23 x K-I reported by Mark and Fl~ry,~~ again from thermoelastic effects. Considerable criticism has been levelled at the use of the thermoelastic method for measurement of (d In (r2)o/dT) but many workers support the technique and de Candia’s71 results and criticisms have been refuted.74 The situation is still rather confused; good agreement between thermoelasti~~~ and d[q]/dT measurements6’ for poly(dimethylsi1oxane) have been obtained although the values are higher than in earlier work by Ciferri76 and Bianchi et Of course one should not ignore the possibilities of specific solvent effects.de Candia’s7’ results were solvent-dependent but it was suggested that the reasons for the discrepancy between the methods could be due to intermolecular contributions tof (the energy term in the force-temperature measurement) which should have a strictly intramolecular character. Similar intermolecular contributions could come from the creation of supermolecular structures in the swollen network.Alternatively specific solvent effects could appear in measurements of [q]e when a variety of 8-solvents are used. This effect has been carefully examined by Kotera et al.,78 who measured [q]e for polystyrene in a range of 8-solvents which were classified into four homologous groups cycloparaffins esters alcohols and chloroparafhs. The resulting scatter was considerable and gave a range of (dln (r2)o/dT) values between (-0.3 and -2.0) x K-’ . Care in the selection of solvents is also emphasized by Evans and who used mixed solvents to obtain consolute liquids. Their value for the temperature coefficient as obtained from viscosity measurements was in good agreement with the theoretically expected value but direct measurement of the unperturbed dimensions by light scattering gave a vastly different value.In theory the latter method is most direct and should lead to an accurate evaluation of (d In (r2)o/dT) but in this system there was a significant preferential adsorption effect which apparently led to considerable coil expansion over that of the unperturbed state. These authors79 have also presented a method of analysing the variations in In [q] which allows evaluation of both 8 temperature and (d In (r2)o/dT). The dependence of (r2)if on solvent has been discussed by Dondos and Benoit,” who have found that polar solvents in particular can alter dimensions. This has been reported also for poly(viny1 chloride).81 For ternary systems they have obtained a distinct relationship between KO and the excess free energy of mixing AGE for the binary liquid mixture.In general KO (and hence the coil 73 J. E. Mark and P. J. Flory J. Amer. Chem. Soc. 1965 87 1415. 74 J. E. Mark and P. J. Flory Macromolecules 1973 6 300. 75 J. E. Mark and P. J. Flory J. Amer. Chem. Soc. 1964 86 138. 76 A. Ciferri Trans. Faraday SOC. 1961 57 853. 77 U. Bianchi E. Patrone and M. Dalpiaz Makromol. Chem. 1965,84 230. ’I3 A. Kotera. T. Saito N. Yamaguchi K. Yoshizaki Y. Yanagisawa and H. Tsuchiya Reports Progr. Polymer Phys. Japan 1971 14 31. 79 J. M. Evans M. B. Hugh and R. F. T. Stepto Mukromol. Chem. 1971 146 91. A. Dondos and H. Benoit Macromolecules 1971 4 279. L. A. Utracki Polymer J. 1972 3 551.. Physical Properties of Polymers and their Solutions 185 dimensions) is larger than expected when AGE is positive and smaller when AGE is negative. Again reports tend to vary ;mixed 8-solvents of increasing polarity toluene-octane (1 1.4) CC1,-MeOH (5.3 I) benzene-MeOH (4.7 l) CHC1,-Pr‘OH (1.39 l) and dichloroethylene-acetone (1.4 1) had no reported effect on the unperturbed dimensions of polychloroprene.82 The effect of thermo- dynamic interactions on the coil size of poly(p-ch10rostyrene)~~ showed little variation when the polymer was dissolved in either an exothermic or endothermic solvent. A further complication can arise in certain instances when the solvent may aid a conformational change in the polymer as the temperature is increased.Thus conformational changes have been observed to occur in poly(p-bromosty- and poly(methy1 metha~rylate)~~’ rene),830,bpoly-(2-~inylpyridine),~~’ when dissolved in benzene dioxan acetone or THF. The conformational transition could be suppressed by addition of a solvating polar solvent which apparently maintained the chain rigidity as the temperature was raised. This suggests that the changes involved only short-range interactions perhaps indicating the presence of some helical sequences which would be stabilized by solvents such as chloroform or DMF. A related study on the behaviour of poly(methy1 metha- ~rylate)~~ in mixed solvent media showed that a conformational change could be induced by altering the solvent composition. Unperturbed dimensions have also been reported for p~lyacrylates,~’ and poly(isobuty1 methacrylate),86 which was found to be less extended than the related n-butyl ester.The temperature dependence of the unperturbed dimen- sions of a series of polyesters poly(tetramethy1ene adipate) poly(octamethy1ene sebacate) and poly(&-caprolactone) showed that an increase in the methylene content of the chain actually led to an increase in the characteristic parameter.87 A second group of papers concerned primarily with testing dilute-solution theory have examined the hydrodynamic behaviour of narrow-distribution polymer samples in great detail. One of the open questions to be answered is what is the asymptotic behaviour of the expansion factor a? Here there is some disagreement.The various research groups interested in these problems find that their data agree at low a but diverge at large a when measurements are made in good solvents. Two groups of opinion exist and the major points of difference are (i) the value of the interpenetration function Y = A2M2/4n*N,(S2)*; (ii) whether or not a is uniquely dependent on 2. Group I believe that Y reaches an asymptotic value between 0.25 and 0.3 and that a depends only on 2,whereas group I1 82 A. V. Gevorkian and L. Kh. Simonyan Uch. Zap. Erevan. Univ. Estestu Nauk. 1971 No. 2 47. 83 (a)P. Karayannidis and A. Dondos Makromol. Chem. 1971 147 135; (6) A. Dondos P. Rempp and H. Benoit ibid. 1973 171 135. 84 A. Dondos Makromol Chem. 1972 162 113. ” S. A. Pavlova G.I. Timofeeva and V. M. Men’shov J. Polymer Sci.,Part C Polymer Symposia 1972 39 I 13. sf M. M. Zafar R. Mahmood and S. Wadooi Makromol. Chem. 1972 160 313. ” M. R. Knecht and H. G. Elias Makromol. Chem. 1972 157 1. W. R. Moore and M. A. Uddin European Polymer J. 1970 6 121. 186 J. M. G.Cowie suggest that the value is lower Y < 0.2 and that data cannot be reduced to a common dependence of a on 2. A number of papers support the group I view with studies using poly(p-bromostyrene),8g~go p~ly(p-methylstyrene),~'poly-~tyrene,~~,~~ and polyisobutene,42 where Y was always greater than 0.25 for large a. Lower values of Y were obtained by Kato et a1.94395using monodisperse poly(a-methylstyrene) but these results are regarded by Yamakawa as peculiar to Kato's samples.This criticism is hardly justified and more constructive reasons can be given centred on the different methods of data analysis which can be employed. The method of calculating coil sizes differs; for example group I uses square-root plots from the light-scattering measurements whereas group I1 select (S2) to gain best agreement between the experimental and theoretical particle scattering functions. The calculation of 2is also open to variation. The original work by Berryg6 on polystyrene only gave partial support to the two- parameter theory but recalculation of his data improved the agreement sig- nificantly. The recalculation involved the method in which Z was derived. This parameter depends on the binary cluster integral P and this cannot be estimated directly from experiment.Berry assumed a linear relation of the form B = BOU -6/77 where Po is a temperature-independent constant. Calculation of Po from data at or near the 6 temperature allows fi and hence 2 to be obtained over a limited temperature range. This linear relationship can hardly be valid over a wide range however if one accepts the existence of a lower critical solution temperature (LCST) in the system which would necessitate a parabolic form for the P-T relation. This was considered by Ei~hinger,'~ who obtained a first-order correction from the value of the LCST and corrected the over-estimated values of 2 reported by Berry. This brought the data more into line with the Yamakawa group. A recent paper by Nakatag8 outlines an alterna- tive method for calculating P (expressed in the form B = P/m2,where m is the molecular weight of a segment) which is founded on a semi-empirical equation of Stockmayer.Here Bo is obtained from the intercept of a plot of (1 -6/T)/A against M2(1 -6/T)/(S2)*,but again a linear form of the B-T relation is assumed. One additional point of interest is that Nakata has derived an ap- proximate closed form for the Yamakawa-Tanaka' perturbation expansion which is a5 -= 1.9142 89 Y.Noguchi A. Aoki G. Tanaka and H. Yamakawa J. Chem. Phys. 1970,52 2651. 90 K. Takashima G. Tanaka and H. Yamakawa Polymer J. 1971 2,245. 91 G. Tanaka S. Imai and H. Yamakawa J. Chem. Phys. 1970,52,2639. 92 A. Yamamoto M. Fujii G. Tanaka and H. Yamakawa Polymer J.1971,2,799. 93 M. Nakata Makromol. Chem. 1971 149 99. 94 T. Kato K. Miyaso I. Noda T. Fujimoto and M. Nagasawa Macromolecules 1970 3 777. 95 1. Noda K. Mizutani T. Kato T. Fujimoto and M. Nagasawa Macromolecules 1970 3 787. 9h G. C. Berry J. Chem. Phys. 1966,44,4550; 1967,46 1338. 97 B. E. Eichinger J. Chem. Phys. 1970 53 561. M. Nakata Makromol. Chem. 1973 167 273. Physical Properties of Polymers and their Solutions This is again a fifth-power dependence of 01 on 2,and at present the consensus of opinion favours this form. Additional experimental support for the Yamakawa- Tanaka relations comes from Bohdanecky and Petrus," who examined the excluded-volume effect in [q] from measurements near the &temperature for a number of systems.The equation derived to estimate C1was (d In [t,~]/dT),-(d In K$dT) = C,(4nbN,)-'((S2)o/M)-' x (dA,/dT),Mf A value of C z 1.06 was obtained in good agreement with Yamakawa and Tanaka. Although the evidence tends to support the validity of the two-parameter approach and the Yamakawa school of thought experimental limitations may keep this an open question for some time. The values quoted by Kato et al.94 for coil sizes do differ slightly from those reported earlier,"' and improved mea- surement of (S') could help in data analysis. This could be achieved by carrying out light-scattering measurements at much lower angles and a specially designed instrument for this purpose has been described."' Methods have also been proposed for more accurate treatment of light-scattering data102"~b and for measuring coil sizes down to about 10 .,.Io3 The application of heterogeneity corrections,' 04*'O5 as applied to extrapolation techniques used to calculate the unperturbed dimensions has been described based on a Zimm-Schulz distribu- tion function.Such improvements may still not be enough as an extensive study of butyl rubber in seven failed to produce conclusive evidence concerning the asymptotic behaviour of Y in spite of a wealth of good data. Indeed one cannot help wondering whether solvent effects play a bigger part than anticipated in such studies and to what extent the reported conformation change in p~ly(p-bromostyrene)*~" affects the study reported by Takashima et aLgO Star-and Combbranched Polymers.-The success of the two-parameter theory in providing a framework within which a unified treatment of dilute-solution para- meters is possible might tend to lead to a complacent attitude.One might well consider that the existing points of difference are relatively minor but this is rapidly dispelled when branched-chain structures are considered. It soon becomes obvious that the existing theory is limited to linear polymers and cannot account for the dilute-solution behaviour of non-linear structures. 9q M. Bohdanecky and V. Petrus European Polymer J. 1972,8 893. loo J. M. G. Cowie S. Bywater and D. J. Worsfold Polymer 1967 8 105. I0' H. Utiyama and Y. Tsunashima Appl. Optics 1970 9 1330. Io2 (a) H. Fujita Polymer J.1970 1 537; (b) W. Miller and R. F. T. Stepto European Polymer J. 1971 7 65. Io3 I. N. Serdyuk and S. K. Grenader J. Polymer Sci. Part B Polymer Letters 1972 10 241. Io4 W. Sutter and A. Kuppel Makromol. Chem. 1971 149 271. lo' R. E. Bareiss Makromol. Chem. 1973 170 251. '06 J.-G. Zilliox Makromol. Chem. 1972 156 121. J. M. G.Cowie For branched and star-shaped polymers differences immediately emerge (i) the &temperature is lower than for the linear polymer (ii) coil expansion is decreased by branching and (iii) the radius of gyration of branched and star structures is considerably larger than calculated from random-flight statistics. Systematic studies are complicated by the increased number of variables; in addition to differences in backbone chain length both the length and frequency of the branches can be altered and will affect the solution behaviour.Several excellent papers have been published by the Strasbourg grouplo6-' lo in which star-and comb-branched polystyrenes were examined by light scattering viscosity and diffusion in good and poor solvents. Zilliox'06 observed a decrease in &temperature which was a function of the branch length. Candau and Rempp'" found that the geometric dimensions of the polymer increased with the frequency and length of the branches and that the coil expansion depended on the number but not the length of the branches. The lowering of the 8-temperature' ' was studied for branched polystyrene and branched polyisoprene where it was found that the &temperatures measured by two techniques namely A and precipitation were always lower than for the linear homologues and decreased with increase in branching frequency.As the segment density is always much higher in the branched polymers the idea of multiple contacts has been used to modify the classical dilute-solution theory. A general equation for the calculation of the unperturbed dimensions of comb polymers has been developed by Tung' ' ' and the Flory-Orofino theory has been extendedlog to include three terms in the series expansion of the segment interaction coefficients which results in a further term in the expansion describing the thermodynamic functions. This new term depends on the third power of the segment concentration and is finite when A = 0.Consequently 8-conditions defined in terms of A = 0 have no physical meaning in these systems and in addition Candau et suggest that branched molecules are also non-gaussian under the conventional &condition defined by a linear expansion factor of unity. Similar conclusions have been reached by other workers.' 12-' l4 Both melt and solution viscosities of star and branched polystyrenes have been examined.' ''-' Four- and six-branched star polystyrenes had lower limiting lo' F. Candau P. Rempp and H. Benoit Compt. rend. 1971 273 C 1733. lo' F. Candau and P. Rempp European Polymer J. 1972 8 757. Io9 F. Candau P. Rempp and H. Benoit Macromolecules 1972 5 627. ll0 F. Candau C. S. Strazielle and H. Benoit Mukromol. Chem. 1973 170 165.L. H. Tung J. Polymer Sci. Polymer Phys. Edn. 1973 11 1247. IL2 G. C. Berry J. Polymer Sci.,Part A-2 Polymer Phys. 1971 9 687. IL3 J.-C. Meunier and R. G. van Leemput Mukromol. Chem. 1971 147 191. lL4 J. Pannell Polymer 1971 12 558. J. E. L. Roovers and S. Bywater Macromolecules 1972 5 384. IL6 M. Kurata M. Abe M. Iwana and M. Matsushima Polymer J. 1972 3 729. IL7 L. A. Utracki and J. E. L. Roovers Macromolecules 1973 6 366. 11' I. Noda T. Horikawa T. Kato T. Fujimoto and M. Nagasawa Macromolecules 1970 3 795. l9 K. Kamada and H. Sato Polymer J. 1971 2,489. lZo K. Kamada and H. Sato Polymer J. 1971 2 593. IZ1 J. Pannell Polymer 1972 13 2. Iz2 T. W. Bates European Polymer J. 1972 8 19. Iz3 T. Fujimoto H. Narukawa and M. Nagasawa Macromolecules 1970 3 37.Physical Properties of Polymers and their Solutions 189 viscosity numbers [& than the corresponding linear polymers [?,?I1 and the ratio [&/[v]l was larger in poor solvents than in good.115 The corresponding ratio for the sedimentation constants was higher than expected for star polymers' l5 but close to the theoretical prediction for randomly branched structures. l6 Similar results were obtained for randomly branched poly(methy1 metha- crylate),' 19,1 2o where the Zimm-Kilb theory' 24 for the viscosity of branched polymers could be applied near the &temperature although results were less conclusive in good solvents. This can be contrasted with data for comb- branched polystyrene which were in better agreement with the Thurmond-Zimm theory.'25 Melt viscosities were also found to be dependent on branch frequency and structure.'21-'25 These studies on branched-chain structures suggest that solution theory may require a complete rethinking to broaden the coverage and encompass both linear and branched chains.Quasielastic Laser-light Scattering.-The frictional properties of polymers in solution have received somewhat less attention. The concentration dependence of the sedimentation constant in the region of the &temperature is found to be in accord with the Pyun-Fixman theory for p~lystyrene'~~.'~' and poly(a- methylstyrene).'28 Sedimentation measurements have also been used to detect long-chain branching in poly(viny1 chloride).' 29 Conventional diffusion measure- ments have been rep~rted'~~-'~~ which were concerned mainly with the con- centration dependence but renewed interest in diffusion measurements is being stimulated by the development of a relatively new technique quasi-elastic laser- light scattering.The principles of light scattering are well established. When a polymer solution is irradiated by light from a monochromatic source the concentration and density fluctuations in the system arising from Brownian motion cause light to be scattered. As the scattering is from polymers which are undergoing continual random motion a Doppler shift will be observed. Consequently the light scattered will have a frequency distribution differing from that of the incident beam. This spectrum of frequencies consists of a Rayleigh line centrally located about the incident frequency and two symmetrical Brillouin wings one on either side.Iz4 B. H. Zimm and R. W. Kilb J. Polymer Sci.,1959 37 19. IZs C. D. Thurmond and B. H. Zimm J. Polymer Sci. 1952 8,477. 12' T. Tsuja and H. Fujita Polymer J. 1973 4 409. V. Petrus I. Danihel and M. Bohdanecky European Polymer J. 1971 7 143. A. Kotera T. Saito and T. Hamada Polymer J. 1972 3 421. W. I. Bengough and G. F. Grant European Polymer J. 1971 7 203. C. J. Vadovic and C. P. Colver J. Polymer Sci. Polymer Phys. Edn. 1973 11 389. A. Kotera T. Saito H. Matsuda and K. Takemura Reports Progr. Polymer Phys. Japan 1971 14 39. 13' A. Kotera N. Yamaguchi K. Takemura and N. Takahashi Reports Progr. Polymer Phys. Japan 1972 15,63.133 A. Kotera and H. Matsuda Reports Progr. Polymer Phys. Japan 1972 15 67. 134 B. Porsch and M. Kubin European Polymer J. 1973 9 1013. 190 J. M. G.Cowie The width of the frequency distribution of the Rayleigh peak can be related to the causal effects of polymer chain motion. According to theory135 the shape of the Rayleigh line should have a continuous Lorentzian distribution emanating from the translational diffusion of the molecules. The frequency distribution can be expressed as 0 const.(p//lr) Z(0) = (0-Oo)2 + p' where 16n2fi2DTsin2 (8/2) B= 1 and liis the solvent refractive index DTthe translational diffusion constant 8 the scattering angle and lothe wavelength of the incident beam of incident angular frequency coo.Thus if the broadening of the Rayleigh line can be measured information on the diffusion constant and possibly intramolecular chain motions can be obtained. This is technically rather difficult as the Doppler shift is usually very small for polymer solutions but by using a laser light source with narrow band widths and improved techniques in optical heterodyne and homodyne (self beat) spectroscopy meaningful results can be obtained. The methods have been extensively reviewed by C~U,'~~ Peticolas,' 37 and recently by Jamieson and Maret,'38 among others. A considerable amount of work has been published on biological macromolecules but synthetics have also been studied. Reed and Frederi~k'~'analysed the spectra for low- and high-molecular-weight polystyrene in cyclohexane and found increasing deviations from a Lorentzian distribution with increasing chain length.It was suggested that these deviations were due to the presence of contributions from other relaxation processes such as rotary diffusion and intramolecular motion but while the actual interpretation was inconclusive it did show that the calculation of DTmay be complicated by secondary effects. A further study of the problem using polystyrene in butan-2- showed that highly accurate measurements are necessary to detect the extent of the deviations even at high molecular weight. Latex spheresI4' or dilute ludox solutions'42 have been used for calibration purposes and theoretical expressions for the spectrum expected for polydisperse latex spheres have been derived.143a9b The molecular weight and concentration 13' R. Pecora J. Chem. Phys. 1968,49 1032. 136 B. Chu Ann. Rev. Phys. Chem. 1970 145. 13' W. L. Peticolas Adv. Polymer Sci. 1972 9 285. 138 A. M. Jamieson and A. R. Maret Chem. SOC. Rev. 1973,2 325. 139 T. F. Reed and J. E. Frederick Macromolecules 1971 4 72. 140 0. Kramer and J. E. Frederick Macromolecules 1972 5 69. S. P. Lee W. T. Scharnuter and B. Chu J. Polymer Sci.,Part A-2 Polymer Phys. 1972 10 2453. 14' D. B. Sellen Polymer 1970 11 374. 143 (a) D. S. Thompson J. Chem. Phys. 1971 54 1411; (b) D. S. Thompson J. Phys. Chem. 1971,75 789. Physical Properties of Polymers and their Solutions 191 dependence of DT have been reported for polystyrene'u with an accuracy of f3 % while the importance of removing dust from solutions'45 has also been emphasized.King and his c~-workers'~~-~~~ ha ve examined the concentration dependence of DT for polystyrene in good and poor solvents expressed in the form DT(c)= Di(1 + k,~+ k;c2 + .. .) and compared their results with the theories of Pyun-Fixman Yamakawa and Imai. In &solvents none of the theories describe ki which was always negative for cyclohexane solutions but there was a trend towards the Pyun-Fixman theory at low molecular weights. In butan-2-one k was negative at low M tending towards zero at about M = 3 x lo' and again agreement between theory and experiment was disappointing. Different diffusional modes,' 'O which are dependent on the ionic strength have been detected in solutions of partially hydrolysed polyacrylamide.Polydispersity effects have also been calculated for coils' 51*1'2 and rods,'53 together with the distribution functions for both homodyning and heterodyning techniques. It has been shown'" that D' values calculated from heterodyning spectra are close to 2-average values but that the spectral shape is relatively insensitive to the sample molecular-weight distribution. Form factors have been derived for both flexible and stiff linear chains.lS4 The Rayleigh spectra can be used to calculate M,,but the value was found to depend on the distribution function chosen for the calculation.' 55 Alternatively one can measure the Brillouin scattering and compare the ratio J of the intensity of the Rayleigh peak with the sum of the intensities of the side peaks.This is described by Carpenter et ~1.l'~ and the form of the equation is BKc (-1 ~ = + 2A2c + 3A,c2 + . (J -J,) M where Jo is the value of J for pure solvent c is the polymer concentration and the constants are B and K. Results were in good agreement with other methods. In general the technique of laser-light scattering has many advantages. Direct measurement of D' at a given concentration does not involve extensive extrapola- tion and only requires small amounts of material. Measurements are rapid and 144 N. C. Ford F. E. Karasz and J. E. M. Owen Discuss. Faraday SOC.,1970 No. 49 p. 228. 145 0. Kramer and J. E. Frederick Macromolecules 1971,4 613. 14' T.A. King and W. I. Lee J. Phys. (E) 1972 5 1091. 14' T. A. King A. Knox W. 1. Lee and J. D. G. McAdam Polymer 1973 14 151. 148 T. A. King A. Knox and J. D. G. McAdam Polymer 1973 14,293. 14' T. A. King A. Knox and J. D. G. McAdam Chem. Phys. Letters 1973,19 351. A. Jamieson and C. T. Presley Macromolecules 1973. 6 358. "' J. E. Frederick T. F. Reed and 0.Kramer Macromolecules 1971 4 242. W.-N. Huang E. Vrancken and J. E. Frederick Macromolecules 1973 6 58. H. Maeda and N. Saito Polymer J. 1973,4 309. S. Fujime and M. Maruyama Macromolecules 1973 6 237. 155 T. F. Reed Macromolecules 1972 5 771. G. A. Miller F. I. San Filippo and D. K. Carpenter Macromolecules 1970 3 125. 192 J. M. G. Cowie independent of the magnitude of DT,thereby enabling slowly diffusing species to be studied with reasonable accuracy.Although there are still problems as- sociated with data analysis the method has other applications yet to be explored and areas of study such as aggregation effect^,'^^-'^^ the kinetics of rapid equilibria and macromolecular reactions and various other relaxation pheno- mena merit immediate investigation. Polymer Solutions -Thermodynamics.-The majority of workers exploring the field of polymer solution thermodynamics are concerned with measurements made in dilute solution. A large number have been published by Maron and his co-workers'60 in which the systematic analysis of a variety of systems using the Maron theory,16' has been carried out. These are predominantly heat of dilution measurements but other measurements mainly for polystyrene' 62 or ethylene have been reported.The interdependence of the enthalpic and entropic contributions to the second virial coefficient was examined by Lechner and S~hulz,'~~ who showed that the data should be converted to reduced quantities if a realistic comparison was to be made between polymers with widely differing chain flexibility and geometries. It was found that the reduced values of A2 and A2,swere predominantly functions of the enthalpy contribution. Wolf' compared the temperature and pressure dependence of these quantities with the predictions of the Prigogine correspond- ing states theory,' 66 but only qualitative agreement was obtained. At the other end of the concentration scale gas-liquid chromatography (g.1.c.) has been applied to the measurement of thermodynamic data at very high polymer concentration^.'^^-'^^ The polymer under study was used as the V.A. Bloomfield and J. A. Benbasat Macromolecules 1971 4 609. I 58 J. A. Benbasat and V. A. Bloomfield Macromolecules 1973 6 593. I 59 S. Fujime Macromolecules 1973 6 36 1 160 (a) C. A. Daniels S. H. Maron and P. J. Livesey J. Macromof. Sci. 1970 B4,47; (b)S. H. Maron and F. E. Filisko ibid. 1972 B6,79; (c)S. H. Maron and F. E. Filisko ibid. p. 41 3 ;(6)S. H. Maron and F. E. Filisko ibid. p. 57; (e)S. H. Maron and M.4. Lee ibid. 1973 B7 29; U,S. H. Maron and M.4. Lee ibid. p. 47; (g) S. H. Maron and M.-S. Lee ibid. p. 61 ;(h)C. A. Daniels and S. H. Maron ibid. 1972 B6,1. 16' S.H. Maron J. Polymer Sci. 1959 38 329. 162 (a)G. Lewis and A. F. Johnson Polymer 1970,11 336; (b)S. Morimoto Bull. Chem. SOC.Japan 1971 44 879; (c) K. Tamura S. Murakami and R. Fujishiro Polymer 1973 14 237. Ib3 A. Kagemoto Y. Itoi Y. Baba and R. Fujishiro Makromof. Chem. 1971 150 255. 164 (a) M. D. Lechner and G. V. Schulz European Pofymer J. 1973 9 723; (6) M. D. Lechner and G. V. Schulz Makromol. Chem. 1973 172 161. 16' B. A. Wolf J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 847. Ib6 I. Prigogine (with the collaboration of A. Bellemans and V. Mathot) 'The Molecular Theory of Solutions' North Holland Amsterdam and Interscience New York 1957. 16' (a) D. Patterson Y. B. Tewari H. P. Schreiber and J. E. Guillet Macromolecules 1971,4 356; (b)W.R. Summers Y. B. Tewari and H. P. Schreiber ibid. 1972 5 12; (c) Y. B. Tewari and H. P. Schreiber ibid. p. 329; (6)H. P. Schreiber Y. B. Tewari and D. Patterson J. Polymer Sci. Polymer Phys. Edn. 1973 11 15. 16* W. E. Hammers and C. L. de Ligny Rec. Trav. chim. 1971,90 912. (a)N. F. Brockmeier R. W. McCoy and J. A. Meyer Macromolecules 1972 5 130; (b)N. F. Brockmeier R.W. McCoy and J. A. Meyer ibid. p. 464. Physical Properties of Polymers and their Solutions stationary phase and the solvents were introduced into the carrier gas. Retention times can then be related to the interaction parameter xfor very concentrated solutions. The method described by Schreiber et ~1.'~~ yields activity coefficients and vapour-polymer equilibrium ratios at infinite dilution both rapidly and accurately.A variation'69 of the method allows xto be estimated as a function of solution composition in the range 0-10 % solvent in polymer. This is achieved by using higher concentrations of solvent (up to 60molX) in the carrier gas. The method has been used successfully to estimate xfor-systems composed of hydrocarbon solvents and rubber '67c p~lyethylene,'~~~*'~~~ polyisobutene,'68 polystyrene,' 69aand poly(dimethylsiloxane).'67b This technique is a useful addition to thermodynamic studies but perhaps the most significant contribution in the past ten years to the interpretation of the thermodynamics of polymer solutions is the development of the Flory-Prigogine corresponding states theory where the Flory theory'70 is a particular case of the more general Prigogine approach.'66 One particularly attractive feature of the theory is that it is a three-parameter treatment in which the particular importance of the free volumes of the components of the solution is emphasized. The new factor which accounts for the disparity in size between a polymer chain and a solvent molecule i.e. 'the free volume dissimilarity' has a significant influence on the thermodynamic properties of the solution. Also introduced by Flory is the concept of segment surface areas or sites which is similar to the ideas of Huggins mentioned earlier. The various terms in the theory can be estimated from a knowledge of structural factors and the equation of state parameters but for the exchange interaction parameter X,,a value must be assigned arbi- trarily.The theory has been tested17' using experimental data derived from calori- metry osmotic pressure and vapour sorption measurements. Enthalpies of mixing have been determined for polyisobutene in hydrocarbon solvents,' 72 polylactones,' 73 poly(ethy1ene oxide) and poly(propene oxide),' 74 and polybut- 1-ene.'75 In all cases the theory failed to predict the enthalpy change in a quanti- tative manner. Adjustment of X12could improve this but the value was often unrealistic.' 72 Large negative values of X12were obtained for both poly(ethy1ene oxide) and poly(propene oxide) which were attributed to specific interactions between polymer and solvent possibly of a charge-transfer nature. The observa- tion that X,,passed through a minimum with increasing solvent (n-alkane)17' chain length was attributed to loss of order in the higher alkanes.Poor agreement 170 (a)P. J. Flory. J. Amer. Chem. SOC.,1965 87 1833; (b)P. J. Flory J. L. Ellenson and B. E. Eichinger. Macromolecules 1968 1 279; (c) P.J. Flory Discuss. Furuduy SOC. 1970 No.49 p. 7. 17' (a)P. J. Flory and H. Hocker Trans. Furaday Soc. 1971 67 2251 ;(b)P. J. Flory and H. Hocker ibid. p. 2258; (c)H. Hocker H. Shih and P. J. Flory ibid. p. 2270. 17* A. H. Liddell and F. L. Swinton Discuss. Faraduy Suc.. 1970 No.49 p. 115. 17' G. Manzini and V. Crescenzi Polymer 1973 14 343. '74 (a)C. Booth and C. J. Devoy Polymer 1971 12 309; (6)C. Booth and C. J. Devoy ibid. p. 320. 17' G. Delmas and P. Tancrede European Polymer J.1973 9 199. J. M. G. Cowie was also found for entropy of dilution and the excess-volume parameter'76 in poly(dimethylsi1oxane) solutions. As the equation of state parameters assume an important role in these calculations these have received attention.' 77 Interest has also beer) focused on the concentration dependence of the interaction para- meter x1.17' Okazawa and Kanek~'~'' observed that the temperature depen- dence was in agreement with the predictions of the Flory-Prigogine theory and used the data to predict LCST for polyisobutene-n-alkane solutions but the quantitative agreement was rather poor. In general the agreement between theory and experiment is bad for polymer solutions; in fact it is poor even for smaller molecules'79*'80 and aspects of the failure of the corresponding states theory have been discussed.Table 3 LCST for quasi-binary solutions at M = co LCS T/K Polymer Solvent (M = 00) $1 Ref Polyethylene n-Pentane -353 n-Hexane 406.3 181a n-Heptane 446.9 -1.2 2;i n-Octane 483.0 -1.1 Pol ypropene Diethyl ether 383 -0.24 (at ac t ic) n-Pentane 397 -0.30 181b n-Hexane 441 -0.33 1 n-Heptane 48 3 -0.43 Polystyrene Cyclohexane 486 -1.19 Methylcyclohexane 484 -0.94 1 Toluene 550 -1.92 Benzene 523 -1.79 Butan-2-one 422 -0.5921 Cyclopentane 427 -0.858 Butan-2-one 417.9 Benzene" 514 Et h y1benzene" 568 Poly(p-chlorostyrene) Isopropyl acetate 348.7 -0.360 t-Butyl acetate 338.4 -0.323 n-Pentyl alcohol 323.1 -0.489 1 n-Propyl alcohol 300.8 -0.696 Poly(a-methylstyrene) Cyclohexane 456 Methylcyclohexane 434 181h Butyl chloride 412 Measured at finite molecular weight.' P. J. Flory and H. Shih Macromolecules 1972 5 761. "' (a) H. Shih and P. J. Flory Macromolecules 1972 5 758; (b)H. Hocker G. J. Blake and P. J. Flory Trans. Faraday SOC.,1971 67,2251 ; (c) Y. Tsujita T. Nose and T. Hata Polymer J. 1972 3 581 ;(d)D. A. Isacescu I. V. Ionescu M. Leca C. Roncca D. Mihaita and E. Rizescu European Polymer J. 1971 7,913. (a) H. Vink European Polymer J. 1971 7,141 1; (6)A. Muramoto Polymer J. 1970 1 450; (c) T. Okazawa and M. Kaneko ibid. 1971 2 747; (6)J. Pouchly and D. Patterson Macromolecules 1973 6,465. D.W.Dreifus and D. Patterson. Trans. Faraday Soc..1971 67 631. IB0W. E. Hammers C. L. de Ligny and L. H. Vaas J. Polymer Sci. Polymer Phys. Edn. 1973 11 499. Physical Properties of Polymers and their Solutions A major drawback is the observation that the characteristic parameters derived for the components vary with temperature instead of remaining constant. This can be overcome to some extent by a judicious choice of an appropriate reference temperature. It should be stressed however that the tnost encouraging feature is that qualitative agreement is obtained and many of the inadequacies of the classical theory such as the occurrence of volume changes on mixing and the existence of an LCST are accounted for if somewhat crudely. Although still in a rudimentary state the qualitative agreement achieved by the theory should encourage refinements to the proposed model which may lead to improvement.In this respect the investigation of lower critical solution phenomena could prove helpful. Phase Equilibria and the LCST.-The existence of ad LCST is now accepted as being a general phenomenon of polymer solutions and can be explained in a satisfactory qualitative manner by the three-parameter Flory-Prigogine theory. Some attempts have been made to obtain a quantitative prediction of the LCST. Flory extrapolated equation-of-state data for polystyrene to temperatures in the vicinity of the LCST and calculated OLCST = 474 K for cyclohexane solutions.171c This is in reasonable agreement with that quoted in Table 3 where the results from a number of sources are summarized.Good agreement was also obtained for polyethylene solutionslgl" when the Flory equation was used but this was not so impressive when the Patterson-Prigogine equation was employed mainly owing to the neglect of the interactior) parameter. The molecular weight dependence of LCST has been expressed as by Patterson and Delmas,lg2 where r is the ratio of the molar volumes of polymer and solvent c1 is determined by the number of external degrees of freedom of the solvent molecule 7 is a parameter reflecting the free-volume change vz is a term characterizing molecular differences between solvent and polymer seg-ments and vl is the reduced volume of the solvent. The spread between the upper and lower critical solution temperatures and their variation with molecular weight have been successfully described for a number of systems qualitati~ely.'~''~~ To obtain absolute agreement it is usually necessary to employ a temperature-shift factor but recent work suggests '*I (a)F.Hamada K. Fujisawa and A. Nakajima. Pol-vmer J. 1973 4 316; (b)J. M. G. Cowie and I. J. McEwen J. Polymer Sci. Polymer Phys. Edn. 1974 It 441 ;(c)S.Saeki N. Kuwahara S. Konno and M. Kaneko Macromolecules 1973 6,246; (d)S. Sacki N. Kuwahara S. Konno and M. Kaneko ibid. p. 589; (e) Y. Baba Y. Fujita and A. Kagemoto Makromol. Chem. 1973,164,349; (f)V. M. Andreeva A. A. Anikeeva S. A. Vshivkov and A. A. Tager Vysokomol. Soedinenii (B) 1970,12,789; (g)Y. Izumi and Y. Miyake Polymer J. 1972 3 647; (h) J. M. G. Cowic and I.J. McEwen un- published results; (i) A. V. Gevorkyan L. Kh. Simonyan A. A. Gevorkyan and G. A. Chukhadzhyan Vysokomol. Soedinenii (E) 1972 14 745. I* ' D. Patterson and G. Delmas J. Polymer Sci. Part C Polymer Symposia 1970 30 1. J. M. G. Cowie that selection of equation-of-state data at the appropriate temperature will reduce the discrepancy.' 83 Interesting phase diagrams have been measured for polymers dissolved in poor solvents.' 84 The high molecular weight fractions were insoluble but those of lower molecular weight were found to be soluble and 'hour glass'-shaped cloud-point curves were obtained for polystyrene in acetone and to a lesser extent in diethyl ether. The main factor contributing to this behaviour is the free volume difference reflected in the very high expansion coefficients of the solvents.This affects the value of the interaction parameter x to the extent that increasing the chain length of the polymer forces x above the critical value at finite M and the two critical solution temperatures coalesce. These systems have no unique theta temperature. Similar behaviour was observed in ternary systems by Wolf et UL''~ for a solvent-non solvent-polymer system and by Cowie and McEwen'86 for a co-solvent system. At least two types of LCST can be distinguished. Some systems exhibit phase separation at temperatures below the boiling point of the solvent. Examples of these are given in Table 3 for poly(p-chlorostyrene) and are normally attributed to specific solvent-polymer interactions.The more commonly observed LCST occur above the solvent boiling point and must be studied in closed systems where the pressure now exceeds atmospheric. Consequently the influence of pressure on polymer solutions is of importance in this context. Pressure can have a signifi- cant effect on the cloud-point curves as demonstrated for polystyrene-acetone ;''' application of 20 bar opened up the hour-glass phase diagram to produce separate UCST and LCST. However as the pressures generated during an LCST measure- ment are normally much lower the LCST is usually only a degree or two higher than the equivalent value at atmospheric pressure; for example (dT/dP) = 0.44 K bar-' for polyisobutene-2-methylbutanesolutions.'87u Some important work has appeared on the pressure dependence of chain dimensions and the second virial coefficient measured by light scattering.' 88 In general A2 increased with applied pressure but the influence on the chain dimensions is less regular ; t'he effects are related to the variation produced in x or Z by the pressure.Phase equilibria in the upper critical region continue to be subjected to careful examination. A number of attempts have been made to modify the Flory- Huggins equations by incorporating the concentration dependence of the interaction parameter x. While some authors use a truncated power series Koningsveld and Kleintjens' have derived a closed expression which proved Ia3 J. M. G. Cowie and I. J. McEwen Macromolecules in the press. (a)K. S. Siow G. Delmas and D.Patterson Macromolecules 1972,5,29; (b)J. M. G. Cowie A. Maconnachie and R. J. Ranson Macromolecules 1971 4 57. Ia5 B. A. Wolf J. W. Breitenbach and H. Senftl J. Polymer Sci. Part C Polymer Sympo- sia 1970 345. ls6 J. M. G. Cowie and I. J. McEwen J. C. S. Faraday I 1974,70 171. (a) L. Zeman J. Biros G. Delmas and D. Patterson J. Phys. Chem. 1972,76 p. 1206; (b)L. Zeman and D. Patterson ibid. p. 1214. lSa (a) G. V. Schulz and M. Lechner J. Polymer Sci. Part A-2 Polymer Phys. 1970 8 1885; (b) G. V. Schulz and M. Lechner European Polymer J. 1970 6 945; (c) D. Gaeckle and D. Patterson Macromolecules 1972 5 136; (d)C. J. McDonald and S. Claesson Chem. Scripta 1973 4 155. ls9 R. Koningsveld and L. A. Kleintjens Macromolecules 1971 4 637. Physical Properties of Polymers and their Solutions 197 successful for linear polymers.A more general form covering copolymers and branched chains was subsequently developed by Kennedy et ~l.,'~~ who pre- sented closed-form expressions for the chemical potential spinodal and con- solute states. Afurther extension of the treatment to include the possible tempera- ture dependence of x was made by Emmerik and smolder^,'^' who have also carried out a comprehensive examination of the phase equilibria in binary and ternary solutions containing poly-(2,6-dimethyl-l,4-phenyleneoxide). Calcula- tions by SO~C,'~~ using a modified Flory-Huggins approach illustrate the vast differences in shape that the cloud-point curve can adopt for different molecular weight distributions.Bimodal cloud-point curves for narrow-distribution polymers in two-polymer-ne-solvent systems have also been found. 193 The thermodynamic constraints on the O-temperature have been discussed by Kennedy'94 and a more rigorous definition 'the O-temperature is that tempera- ture at which the kcond virial coefficient is zero in a specified limit M - a,for any polymer-solvent system at a given pressure' is proposed. It is suggested that on this basis the conventional extrapolation procedures used to estimate T = 8 using phase separation data are in error. This is illustrated for poly- styrene-cyclohexane for which a O-temperature about 3 K lower than the pres- ently accepted value is estimated. A lower &temperature for the same system was also reported by Kuwahara et ~1.,'~'but this was attributed to the use of ultra-dry solvent.Spinodal and consolute state relations have also been treated for quasi- ternary systems on the basis of the lattice the~ry.'~~",'~~ While the theoretical treatments lead to expressions for both the cloud-point curves and spinodal conditions it is normally the cloud-point curves which are measured experimentally. The suggestion that the spinodal decomposition in a polymer solution was impossible to measure'97 has been refuted by recent work. Light-scattering theory shows that the scattering intensity will increase to very high values in the vicinity of the spinodal. The procedure developed by Scholte' 98 to measure spinodal curves depends on plotting the scattering intensity at I9O J.W. Kennedy M. Gordon and R. Koningsveld J. Polymer Sci. Part C Polymer Symposia 1972 39 43. 19' (a)P.T. van Emmerik and C. A. Smolders J. Polymer Sci. Part C Polymer Symposia 1972 39 73; (b) P. T. van Emmerik and C. A. Smolders ibid. p. 31 1; (c) P. T. van Emmerik and C. A. Smolders European Polymer J. 1973,9 157; (4P. T. van Emmerik and C. A. Smolders ibid. p. 293; (e) P. T. van Emmerik C. A. Smolders and W. Geymayer ibid. p. 309. 19' K. Sole Macromolecules 1971 3 665. 193 (a)R. Koningsveld H. A. G. Chermin and M. Gordon Proc. Roy. Soc. 1970 A139 331; (6) D. G. Welygan and C. M. Burns J. Polymer Sci. Polymer Letters Edn. 1973 11 339. 194 (a)J. W. Kennedy J. Polymer Sci. Part C,Polymer Symposia 1972,39,71; (b)H.A. G. Chermin and J. W. Kennedy Macromolecules 1972 5 655. 195 N. Kuwahara M. Nakata and M. Kaneko Polymer 1973 14,415. 196 (a) R. Koningsveld Chem. Zvesri 1972 26 263; (6) H. A. G. Chermin Ph.D. thesis University of Essex 197 1. 19' R. Koningsveld Adv. Colloid Interface Sci. 1968 2 151. 19' (a)Th. G. Scholte J. Polymer Sci. Part A-2 Polymer Phys. 1971,9 1553; (b) Th. G. Scholte J. Polymer Sci. Part C Polymer Symposia 1972 39 28 1. 198 J. M. G. Cowie zero angle for a given concentration as a function of reciprocal temperature. This is repeated for a number of concentrations to build up the curve. Laser homodyne spectroscopy has been used in a similar fashion but the authors express some doubt as to the accuracy of their extrapolation method.'99 Both procedures rely on measurements made above the cloud-point curve and so extrapolations to spinodals are often of necessity rather long.A much more promising technique has been developed by Gordon et dZoO The principle of the method called pulse induced critical scattering (PICS) is to effect very rapid critical scattering measurements in both the stable and metastable regions. Use of a laser beam and small samples are features of the experimental design and an important aspect of the method is that measurements of scattering intensities which need only be relative are complete before actual phase separation can occur in the metastable region (less than 5 s). Penetration into the metastable region between the cloud-point curve and the spinodal is achieved using rapid thermal pulses from a base temperature located above the cloud-point curve.In between pulses the solution is returned to the base temperature. Although an extrapolation procedure is still required (recipro- cal scattering intensity against temperature) the penetration into the metastable region is sufficiently deep to make this very short and quite accurate. As the shape of the spinodal is strongly dependent on the weight and Z-average mole- cular weights the development of the PICS technique could provide a useful tool for polymer characterization. Few publications on the method exist at present but a recent one2' gives a comprehensive description of the application of PICS to the study of thermo- dynamic and kinetic effects in polymer solutions.Also confirmed was the dependence of the spinodal loci on M and to some extent on M,. The application of light scattering to the measurement of thermodynamic functions,202 critical opalescence,203 and an estimation of particle size in and the mechanism of spinodal decomposition204 have been reported. An interesting method of measuring the Flory parameter X,,was reported by Booth and Pickles,20s who examined the phase separation in mixtures of low molecular weight poly(ethy1ene oxide) and poly(propene oxide) liquids. Large values of X,,were found once again. Differential thermal analysis (d.t.a.) has also been used to study phase equilibria LCST,Z06 and the solution process of polyolefin crystals.207 19' N. Kuwahara D. V.Fenby M. Tamsky and B. Chu J. Chem. Phys. 1971,55 1140. M. Gordon J. M. G. Cowie B. Ready and J. Goldsbrough U.K.P.61071/1970; 275311971;275411971 ;275511971. 201 K. W. Derham J. Goldsbrough and M. Gordon paper presented at 12th IUPAC Microsymposium Prague August 1973. 'O' Th. G. Scholte European Polymer J. 1970 6 1063. '03 (a)W. Borchard Ber. Bunsengesellschaftphys. Chem. 1972,76 224; (6)B. Chu ibid. p. 202; (c)A. Vrij and M. W. J. van den Esker J.C.S. Faraday II 1972 68 513. *04 (a)J. J. van Aartsen European Polymer J. 1970 6 919; (b) J. J.van Aartsen ibid. p. 1105. 'OS C. Booth and C. J. Pickles J. Polymer Sci.,Polymer Phys. Edn. 1973 11 595. '06 (a)A. Kagemoto Y.Baba and R. Fujishiro Makromol. Chem. 1972,154 105; (6)K. Tamura Y. Baba K. Nakatsukasa and R.Fujishiro Polymer J. 1972 3 28. lo' H. P. Schreiber J. Appl. Polymer Sci. 1972 16 539. Physical Properties of Polymers and their Solutions Refractive Index and Cohesive Energy Density.-Light-scattering studies require accurate measurement of the refractive index increment (dfi/dc) but standard instrumentation is often limited by the range of refractive indices which can be covered. This problem has been recognized by Kratochvil and Babka,208 who have modified the cell in the Brice-Phoenix instrument to allow highly refractive liquids to be handled. The basic cell design remains unaltered but by replacing the inclined plane face with glass having fi = 1.62 total reflection is avoided up to a value of fi = 1.72 for the measured liquid.Cell modification is also described for a Jena interfer~meter.~" Lorimer2" has developed a relation based on the theory of Onsager and Bottchen for the refractive index which is apparently more accurate than the Lorenz-Lorentz equation. The influence of molecular weight on (dfi/dc) has also been examined2' ' and results indicate that (dfi/dc) will depart from its asymptotic limit in the range M = 5 x lo4 to lo5 for polystyrene. A somewhat lower limit of M = lo4 for polystyrene in benzene was obtained by Hert and Strazielle2' lC and these authors also examined (dfi/dc) in mixed solvent systems taking into consideration the additional variables of temperature and mixture composition. The possibility that (dfi/dc) can vary with chain length is often overlooked and must be considered in light-scattering measurements involving short chains.A relation between (dfi/dc) and the density increment has been used to calculate the partial specific volume of a polymer in solution,212 and a method of calculating the refractive index of a polymer solution from a knowledge of the density and the specific refraction of the components has been outlined.213 Cohesive energy density (CED) measurements have also been reported and the novel use of gas chromatography for this purpose has been described. The CED of p~lyethylene~'~ was estimated by determining the retention time of solvents passing over a polyethylene-coated column and correlating this with the activity coefficient at infinite dilution. The assignment of a CED value to random copoly- mers has been discussed by Schneier.21 An attempt to extend the Hildebrand concept of solubility parameter [= (CED)*] to the prediction of polymer-solvent miscibility by Chen2' involves a two-dimensional approach.In a purely qualitative sense the method appears to be as effective as the more complex three-dimensional approach of Hansen. A more rigorous approach to solubility-parameter theory2" illustrates the apparent compatibility of this concept with the newer Flory theory of the liquid state. It has been shown that correspondence with the predictions of the Flory '08 P. Kratochvil and J. Babka J. Appf. Polymer Sci. 1972 16 1053. '09 I. Baltog C. Ghita and L. Ghita European Polymer J. 1970 6 1299. 'lo (a)J. W. Lorimer Polymer 1972 13.46; (b)J.W. Lorimer ibid. p. 274. 'I1 (a)J. W. Lorimer and D. E. G. Jones Polymer 1972 13 52; (b)D. Margerison D. R. Bain and B. Kiely ibid. 1973,14 133; (c) M. Hert and C. Strazielle European Polymer J. 1973 9 543. "'Th. G. Scholte J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 519. 'I3 H.Looyenga J. Polymer Sci. Polymer Phys. Edn. 1973 11 1331. 'I4 S. K. Ghosh Makromol. Chem. 1971 143 181. '15 B. Schneier J. Appl. Polymer Sci. 1972 16 1515. 'I6 (a) &-A. Chen J. Appl. Polymer Sci. 1971 15 1247; (b) S.-A. Chen ibid. 1972 16 1603. 'I ' J. Biros L. Zeman and D. Patterson Macromolecules 197 1 4 30. J. M.G. Cowie theory can be obtained by treating free-volume effects in the solubility-parameter approach. This method of approaching the problem of polymer solution thermo- dynamics has also been used by Dayank2l8 Utracki219 has attempted to correlate the solubility parameter of the solvent with the binary cluster integral or at least the non-polar contribution to this parameter.89 Evidence for such a relationship was found and fell into two distinct groupings one for linear and another for non-linear solvent molecules.This highlights the need for a symmetry factor in the solubility-parameter theory which may have an important bearing on the thermodynamics of polymer solubility. Mixed Solvents .-When specific conditions are required for polymer solution study (e.g.pseudo-ideal solutions) they are often obtained most easily by means of mixed solvents. Mixtures can be used successfully if the attendant problems are recognized.These include selective adsorption of one component of the solution by the polymer and the effect this has on the polymer dimensions and other dilute-solution parameters. The problem of the dependence of (r2)if on the thermodynamic properties of the solvent mixture has been studied most notably by Dondos and Benoit.220 They have concluded that (r2)$ depends both on the solvent-solvent interactions and on the polarity of the polymer. In all cases KO which is derived from Stock- mayer-Fixman plots is taken as a measure of (r2)i and the excess free energy AGE of the mixture is regarded as the thermodynamic function of interest. One can also express AGE as the interaction parameter x12. Comparison of KO obtained for a single theta solvent with KY measured in a mixture shows that when AGEis positive then KY is larger than expected and smaller when AGEis negative.This is expressed in a linear relationship between {KY/[&KB(l) + 42K&2)]} and AGE where 4 is the volume fraction KY,KB(l),and KB(2)are the values obtained in the mixture and in liquid components (1) and (2) respectively. This linear relation holds good for a mixture of two good solvents but when solvent-precipitant mixtures were studied deviations were observed. The linear relation was reaffirmed when corrections were made for preferential adsorption effects in the solutions. Benoit and Dondos22’ have shown that if preferential adsorption is evident in a consolute mixture for which A2 = 0 then the slope of the Stockmayer-Fixman plot is not zero as expected but is proportional to the preferential adsorption parameter A*.This was not con- firmed for poly(p-methoxystyrene) in a number of where the slope was always found to be zero even when A* # 0. It has been suggested220b that medium-range effects are responsible for the variation of (r2)8 with x12 J. Dayantis J. Polymer Sci. Part C Polymer Symposia 1972 39 35. (a)L. A. Utracki J. Appl. Polymer Sci. 1972 16 1167; (6) L. A. Utracki Polymer J. 1972 3 551. (a)A. Dondos and H. Benoit European Polymer J. 1968,4,561; (b)A. Dondos and H. Benoit ibid. 1970 6 1439; (c) A. Dondos and H. Benoit Macromolecules 1971 4 279; (4A. Dondos Compt. rend. 1971 272 C 1419; (e) A. Dondos and H. Benoit Macromolecules 1973 6 242.’” A. Dondos and H. Benoit J. Polymer Sci. 1969,7 335. ’’’ A. Mattiussi E. Conti and G. B. Gechele European Polymer J. 1972.8. 429. Physical Properties of Polymers and their Solutions 201 but Pouchly and Patterson22 have proposed an alternative explanation. They have considered the concentration dependence of x represented as x = xo + ~‘4~ and have introduced this into the expression for the effective interaction parameter x of a mixture x = u1(x?3 +-d343) -I-u2(x:3 4-x:343) -u~u2[x12-2xT(1 -&)I where ui = 4i/(4i+ +j) and xT is a ternary interaction parameter included to compensate for deviations from the value of AGM calculated using the Flory- Huggins theory. In this context xT should always have the same sign as xI2 and be numerically smaller than (x12/2).The expression for x can be used to modify the Stockmayer-Fixman equation and to introduce a factor which predicts the variation of K with x12 as observed experimentally. Light scattering is the most commonly used means of studying preferential adsorption in mixed solvent but n.m.r. relaxation methods2’ and the ultracentrifuge226 have also been used to some effect. Fujishige and Elias2” reported that the atactic form of poly(methy1 methacry- late) preferentially adsorbed acetone to a much greater extent than the isotactic form in acetone-CHC13 mixtures but that little difference in A* could be detected when benzene replaced CHCl . In contrast no difference in A* could be found for the different stereo-regular forms by Kratochvil et ~1.,~’*who suggested that aggregation effects may have interfered with Fujishige’s measurements.Small differences in A* between the stereo-regular forms of poly(methy1 methacrylate) in other mixtures have been reported,225d but it appears that stereostructure is not a major influence on the magnitude of A*. Perhaps more important is the effect of chain length ; it was shown that A* increased with decreasing molecular weight.229 This is a result of the probability of intramolecular segment contacts upsetting the number of binding sites available for solvent on a polymer chain and examination of polydispersity substantiates this view. This has important consequences in the study of comb- and star-branched pol~rners,’~’ where the dependence of A* on molecular weight is more complicated than for 223 J.Pouchly and D. Patterson Macromolecules 1973. 6 465. 224 (a) B. Chaufer B. Sebille and C. Quiveron Compr. rend. 1972 274 C 764; (b) L. Moldovan and C. Strazielle Makromol. Chem. 1970 140 201 ; (c) B. Sedlatek P. Kratochvil and D. Strakova Coll. Czech. Chem. Comm. 1972 37 970; (6)Z. Bardet H. Maillols and J. Maillols J. Chim. phys. 1973 70 615. 225 (a)S. Brownstein S. Bywater and J. M. G. Cowie Trans. Faraday SOC.,1969,65,2480; (b) H. Lutje. Makromol. Chem. 1971 142 81 ; (c) H. Lutje J. Polymer Sci. Part C Polymer Symposia; 1972 39 325; (d)K. Sat0 and A. Nishioka Polymer J. 1972 3 245. z26 (a)J. M. G. Cowie R. Dey and J. T. McCrindle Polymer J. 1971.2 88; (b)A. Rosen-thal Macromolecules 1972 5 310.227 (a) S. Fujishige and H.-G. Elias Makromol. Chem. 1972 155 127; (6)S. Fujishige and H.-G. Elias ibid.,p. 137. 228 P. Kratochvil D. Strakova and D. K. Carpenter Makromol. Chem. 1972 162 275. 229 A. Dondos and H. Benoit Makromol. Chem. 1970 133 119. 230 (a) M. Hert C. Strazielle and H. Benoit Makromol. Chem. 1973 172 169; (6)E. F. Casassa Polymer J. 1972 3 517. 23’ M. Hert C. Strazielle and H. Benoit Makromol. Chem. 1973 172 185. 202 J. M. G. Cowie linear polymers. The increase in preferential adsorption at shorter chain lengths in linear polymers was manifest in higher coil expansion near the O-p~int.~~~ Some insight into the mechanism of co-solvency is obtained from preferential adsorption It is found that at the co-solvent composition which is most compatible with the polymer A* is very close to zero.As the composition is changed there is preferential adsorption of the liquid in the mixture which has been depleted by this change. In effect the preferential adsorption can be seen as a mechanism which attempts to regain the composition of the best mixture by attracting the deficient solvent component to the vicinity of the polymer coil when the polymer is dissolved in a mixture whose composition is not the optimum. The synergistic effects of co-solvents have been reported for polyethylene,234 poly(methy1 metha~rylate),~~~ and poly-(2-hydroxymethacry-Some progress in formulating a satisfactory theoretical description of selective adsorption has been made.237 Excluded-volume effects in mixed solvents have received further attention.The advantages of mixed solvent systems in the study of copolymer solutions were examined by Kratoch~il.~~~ Segment heterogeneity can cause problems in copolymer solutions and optical masking of one component can allow the study of the other by light scattering. This can be achieved most easily by using solvent mixtures to obtain the correct refractive index General selection rules are proposed to ease the problem of solvent selection. Selective adsorption in copolymer solutions can have a marked effect on refractive index increment values and A* is found to be largest for alternating copolymers where the number of heterogeneous contacts is a maximum. Deviations due to selective adsorption effects decreased through random to block copolymers where the required corrections were small.Acoustic and Electro-optical Studies.-The application of acoustical methods to the study of polymer solutions has recently been reviewed by Pethri~k~~~" and covers most of the relevant work to date. The acoustic technique is potentially useful for studying molecular motions and relaxation processes for both polar and non-polar polymers whereas the more widely employed dielectric measurements 232 A. Dondos K. Viras and F. Aroni European Polymer J. 1973,9 1051. 233 (a)J. M. G.Cowieand J. T. McCrindle European Polymer J. 1972,8 1185; (b)J. M. G. Cowie and J. T. McCrindle ibid. p. 1325. 234 N. Das and S. R. Palit J. Polymer Sci.Polymer Phys. Edn. 1973 11 1025. 235 P. C. Deb and S. R. Palit Makromof. Chem. 1973 166,227. 236 K. Ddek and B. Sedlafek European Pol.vmer J. 1971,7 1275. 237 (a)M. Yamamoto J. L. White and D. McLean Pol,vmer 1971,12 290; (6)J. Pouchly A. Zivny and K. Sole Coll. Czech. Chem. Comm. 1972 37 988; (c) A. Zivny and J. Pouchly J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 1467 1481. 238 M. Yamamoto and J. L. White Macromolecules 1973 5 58. 239 (a) Z. Tuzar P. Kratochvil and D. Strakova European Polymer J. 1970 6 11 13; (b) P. Kratochvil and Z. Tuzar Chem. Ztyesti. 1971 25 190; (c) J. PodeSva and P. Kratochvil European Polymer J. 1972 8 1179; (6)P. Kratochvil B. SedlaEek D. Strakova and Z. Tuzar Makromol. Chem. 1973 166 265. 240 (a)R. A. Pethrick J. Macromol.Sci. 1973 C9,91; (6) A. M. North Chem. SOC. Rev. 1972 1 49. Physical Properties of Polymers and their Solutions 203 are restricted to polar materials. Recent advances in this field have been reviewed by North.240b Some interesting work on rigid siloxane polymers,241 including ladder struc- tures and stiff-chain polyis~cyanates~~~ has appeared. The poly( butyl isocyanate) chain has been studied most often and exhibits a high degree of order in solution. The chain conformation was observed to change from a rigid rod-like shape at low molecular weight to a flexible coil at high molecular weight.242e Tsvetkov concluded that the molecule has a planar cis conformation. Other confirmed the transition from rod to coil and agree that the onset of flexibility occurs above M = 5 x lo4.There is also a tendency to favour the idea of a helical form at low M,242cSbut the data are inconclusive. Other poly(alky1 isocyanates) exhibit similar propertie~,~~~~*~J but in contrast the aromatic derivatives were found to behave like statistical coils with flexibilities comparable with other synthetic polymers. 242e Mobile liquid-crystalline structures were detected in solutions of poly(pheny1- methacrylic esters) of cetyl- and nonyl-oxybenzoic acids which emanate from the extremely long ester ~ide-chains.~~~ Polymer Compatibility.-Mixtures or blends of two or more polymers are rarely compatible and will tend to form heterogeneous solids. The extent of the incom- patibility affects the properties of the blend and can be assessed in several ways.A critical discussion of the methods based on the viscosities of solutions244 comprising liquid (l),polymer (2) polymer (3) has been presented by Vasile and S~hneider.~~’ These authors have suggested that two types of compatibility can be distinguished (i) a true compatibility and (ii) a pseudocompatibility arising from specific interactions between functional groups. Systems in the second category are believed to have a very slow rate of phase separation and con- sequently appear to be compatible.246 Light scattering is also a useful tool to study these ternary systems.247 Cantow and his co-workers have used a technique whereby polymer (2) is dissolved in an isorefractive mixture of solvent (1) and polymer (3).This optical masking of the 241 (a) V. N. Tsvetkov K. A. Andrianov G. I. Okhrimenko and M. G. Vitovskaya European Polymer J. 1971,7 1215; (6)V. N. Tsvetkov Makromol. Chem. 1972 160 1; (c) V. N. Tsvetkov K. A. Andrianov N. N. Makarova M. G. Vitovskaya E. 1. Rjumtsev and I. N. Shtennikova European Polymer J. 1973 9 27. 242 (a)H. Plummer and B. R. Jennings European Polymer J. 1970,6 171 ;(b)L. J. Fetters and H. Yu Macromolecules 1971,4,385; (c)B. R. Jennings and B. L. Brown European Polymer J. 197 1,7 805 ;(6)T. C. Troxell and H. A. Scheraga Macromolecules 197 1 4 528; (e)V. N. Tsvetkov I. N. Shtennikova E. I. Rjumtsev and Yu. P. Getmanchuk European Polymer J. 1971 7 767; u> L. J. Fetters J. Polymer Sci. Part B Polymer Letters 1972 10 577. 243 V.N. Tsvetkov E. I. Rjumtsev I. N. Shtennikova E. V. Korneeva B. A. Krentsel and Yu. B. Amerik European Polymer J. 1973 9 481. 244 (a) D. Feldman and M. Rusu European Polymer J. 1971 7 215; (b)B. Bohner D. Berek and S. Florian ibid. 1970 6 471 ;(c) D. Feldman and M. Rusu ibid. p. 627. C. Vasile and I. A. Schneider Makromol. Chem. 1971,141 127. 246 C. Vasile and I. A. Schneider European Polymer J. 1973 9 1063. 247 (a) R. Kuhn H.-J. Cantow and S. B. Liang Angew. Makromol. Chem. 1971 18 93; (b)R. Kuhn S. B. Liang and H.-J. Cantow ibid. p. 101 ;(c) R. Kuhn V. Bugdahl and H.-J. Cantow ibid. p. 109; (4R. Kuhn V. Bugdahl and H.-J. Cantow ibid. p. 109. 204 J. M.G. Cowie second polymer component means that the behaviour of the first polymer can be studied separately and the interactions compared in the presence and absence of polymer (3).This then provides a measure of the compatibility of the two polymers in that solvent. Solution calorimetry248 and differential scanning calorimetry249 have been applied ;the latter will show whether or not two glass transitions are present in the mixture and this together with mechanical measurements provides an indication of the heterogeneity in a mixture. To some extent the compatibility of polymers cast in a film can be controlled by the solvent used to prepare the mixture,250 and this is also true for copolymers. The problem has been approached on the basis of the interaction parameters x and while it is generally accepted that two polymers in solution are incompatible when xZ3is unfavourable Zeman and Patterson251 have shown that this is only true at high polymer concentration or when x12and x1 are of equal magnitude.In dilute solution then the controlling factor is the difference between x12 and XI 3. Random Copolymer Solutions.-Incompabitility effects are not confined to blends or mixtures of polymers ;copolymers will also exhibit properties arising from adverse interactions between comonomers. In random copolymers this is manifest in deviations from property additivity rules based on the composition which are caused by the presence of heterogeneous contacts between the two or more types of monomer unit in the system. Even when the comonomers are relatively compatible as in poly(styrene-co-p-rnetho~ystyrene),~~~ the Mark- Houwink exponents for the copolymers are lower and the unperturbed dimen- sions are always larger than those of the parent homopolymers.Some enhancement of solubility was obtained in methylcyclohexane solutions of p~ly(styrene-co-a-methylstyrene).~ 53 The &temperatures plotted as a func- tion of copolymer composition were always below the line joining the &values for the homopolymers. This is in agreement with the solution behaviour of statistical and alternating copolymers of styrene and methyl metha~rylate.'~~ In cyclohexanol which is a &solvent for both homopolymers there is a distinct lowering of the O-temperature with the alternating copolymer being a more effective depressant than the random structure.This trend was borne out by the fact that the block copolymers had much the same O-temperature as the homopolymers although this could have been a fortuitous elimination of inter- and intra-molecular interactions. Calculation of the characteristic parameter C showed that for block copolymers C could be approximated 248 P. Novakov Ch. Konstantinov and P. Mitanov J. Appl. Polymer Sci.,1972 16 1827. 249 G. A. Zakrzewski Polymer 1973 14 347. 250 M. Bank J. Leffingwell and C. Thies Macromolecules 1971 4 43. 251 I. Zeman and D. Patterson Macromolecules 1973 5 513. 252 (a) M. Pizzoli and G. Ceccorulli European Polymer J. 1972 8 769; (b) M. Piuoli G. Ceccorulli and G. Stea Makromol. Chem. 1973 164 273. 253 D. J. Goldwasser and D. J. Williams Macromolecules 1973 6 353.2s* T. Kotaka T. Tanaka H. Ohnuma Y. Murakami and H. Inagaki Polymer J. 1970 1 245. Physical Properties of Polymers and their Solutions 205 from the compositional average of the homopolymers but for random and alternating copolymers C was larger than predicted by the compositional rule. This discrepancy was greatest for the alternating structures and so the extent of the deviations could be related to the proportion of heterogeneous diads present in the chain. Long-range effects embodied in x,were more difficult to establish. No effect of sequence length on the sedimentation behaviour of block and random copolymers of butadiene and a-methylstyrene could be detected,’ 55 but this is probably not the most sensitive diagnostic technique.Other workers256 have examined the internal plasticizing effect of copolymerization as reflected in the glass transition temperature and mechanical response. Dilute-s~lution~~~ properties and solubility parameters’ * have been reported. BIock Copolymer Solutiolrs.-Recent improvements in synthetic techniques have led to the preparation of well-characterized block copolymers. This in turn has stimulated interest in their dilute-solution behaviour and morphology. Several workers have attempted to reduce the difficulties and rather tedious effort involved when trying to establish the true M of a copolymer by light scattering. Normally M has to be determined from measurements in at least three solvents which have as widely differing refractive indices as possible.259 Kratochvil et a1.260have outlined the conditions which should achieve the greatest accuracy in light scattering for a copolymer with comonomers A and B ; the three solvents should meet the requirements (i) first solvent :vA and vg both high and of the same sign ; (ii) second solvent lvAI large vg = 0; (iii) third solvent vA = 0 lv9l large; where v = (dfi/dc).The task of solvent selection can be made easier if mixed solvents are used and v is measured after equilibrium dialysis to eliminate possible errors arising from preferential adsorption effects. When this is done the classical relationship for copolymers derived by Bushuk and Benoit261 can be used. Urwin and Girolamo262 have established a computer program to handle the combinations of data required for the calculation of M,,but they found that high-precision experimental work was required for accurate analysis.Light-scattering data 25’ K. F. Elgert and E. Seiler Makromol. Chem. 1972 151,83. 256 (a)E. F. Jordan G. R. Riser B. Artymyshyn S. Smith and A. N. Wrigley J. Polymer Sci. Polymer Phys. Edn. 1973,11 1475; (b)E. F. Jordan B. Artymyshyn G. R. Riser J. Nidock and A. N. Wrigley J. Appl. Polymer Sci. 1973 17 1545; (c) E. F. Jordan G. R. Riser B. Artymyshyn and A. N. Wrigley ibid. p. 1569. 257 (a)A. Dondos European Polymer J. 1971,7,405; (b) M. Morimoto and Y. Okamoto J. Appl. Polymer Sci. 1972 16 2795; (c) K. S. V. Srinivasan and M. Santappa J. Polymer Sci. Polymer Phys. Edn. 1973 11 331. 258 B. Schneier J.Polymer Sci. Part B Polymer Letters 1972 10 245. 259 T. Kotaka T. Tanaka and H. Inagaki Polymer J. 1972,3 327. 260 P. Kratochvil B. Sedlaeek D. Strakova and Z. Tuzar Makromol. Chem. 1971 148 271. 261 W. Bushuk and H. Benoit Canad. J. Chem. 1958,36 1616. 262 J. R. Urwin and M. Girolamo Makromol. Chem. 1971 142 161. 206 J. M. G. Cowie can be used to estimate the chemical heterogeneity of copolymers,263 although the sensitivity of the method may well be over-rated. A nomogram for this purpose has been constructed264 and tested for model systems,265 but in practice it works most effectively for high molecular weight samples with low hetero- genei ty. Many authors use osmotic pressure266 or sedimentation equilibrium methods259 to determine the molecular weight.AB and ABA poly(styrene-b- isoprene) copolymers have been used frequently in solution studies because of the availability of good samples. Girolamo and Urwin266 established O-condi- tions for AB poly(styrene-b-isoprene) using cloud-point and A2 = 0 criteria. In contrast to random and block poly(styrene-co-methyl metha~rylate),~~~ the &temperature in several solvents passed through a maximum as the copolymer composition was varied except in cyclohexane solutions where 8 increased monotonically. In this solvent there was evidence of intramolecular phase separation a common feature of many copolymer solutions. The maximum &temperature is believed to occur when the structure is as random as possible with the maximum number of hetero-contacts in the solution.When the un- perturbed dimensions were measured267 they were found to be a linear function of copolymer composition and the characteristic ratio could be calculated from where x is the mole fraction. The general principle that the properties of these copolymers are close to the weighted averages of the homopolymers was con- firmed by Prud’homme et u1.268uExceptions to this rule are found for copolymers dissolved in selective solvents in which intramolecular phase separation occurs but even in such cases it may depend on the temperature of measurement. When [q] was measured as a function of temperature for cyclohexane solutions of AB poly(styrene-b-isoprene) a discontinuity was detected at a temperature called the transition temperature (q) A significant lowering of by Urwin.268b*c the unperturbed dimension was found on decreasing the temperature from above to below Tpand this was large enough to be interpreted as a conformational transition.Below Tp,the polystyrene block collapsed in the poor solvent cyclo- hexane but the isoprene block was selectively expanded. Above Tp the poly- styrene block expanded and created a somewhat poorer environment for the polyisoprene block ;this tended to produce a much more even distribution of segments in solution with an interpenetration of the blocks. Consequently the number of hetero-contacts increased above Tp and this random distribution means that C^,”can again be calculated from the composition rule given above. 263 J.Lamprecht C. Strazielle J. Dayantis and H. Benoit Makromol. Chem. 1971 148 285. 264 J. VorliCek and P. Kratochvil J. Polymer Sci. Polymer Phys. Edn. 1973 11 855. 265 J. VorliCek and P. Kratochvil J. Polymer Sci. Polymer Phys. Edn. 1973 11 1251. 266 M. Girolamo and J. R. Urwin European Polymer J. 1972,8 299. 267 J. R. Urwin and M. Girolamo Makromol. Chem. 1972 160 183. 268 (a) J. Prud’homme J. E. L. Roovers and S. Bywater European Polymer J. 1972 8 901; (6) M. Girolamo and J. R. Urwin ibid. 1971 7 693; (c) J. R. Urwin and M. Girolamo ibid. p. 785. Physical Properties of Polymers and their Solutions 207 This behaviour has been observed for the same block copolymers in other selective solvents i.e. poor for one block but good for the other such as decalin and methylcy~lohexane.~~~ Agreement is not unanimous as Plante et ~21.~~’ found no conformation transition between 283 and 333 K for AB or ABA blocks in toluene dioxan isobutyl methyl ketone or cyclohexane.Sharp breaks in [ql-temperature curves were detected by D~ndos~~l in solutions of ABA poly- (methyl methacrylate-b-styrene). Again at low temperatures there was a segregated conformation with few heterocontacts but as the temperature rose the conformation became increasingly gaussian as the number of hetero-contacts increased. This conformational change was substantiated by light scatter- ing.271,272 are of the opinion that the two-parameter Girolamo and Ur~in~~~ theory is valid for copolymers in good solvents where substantial interpenetration of the blocks is evident.In selective solvents this is probably true above Tp but below this temperature the segregation of blocks makes this a doubtful assumption and such concepts as a &state become open to question. In selective solvents block segregation can lead to micelle foimation. This effect has been studied by light scattering274 in solutions of ABA poly(styrene-b- butadiene). Addition of ethanol to a dioxan solution of this block copolymer selectively precipitated the butadiene block but the solvated polystyrene blocks were able to hold the copolymer in solution. In doing so micelles were formed of average size 52 nm. The general condition for micellization is then use of a solvent which is good for one block but a precipitant for the other and this can be achieved most easily through the use of mixed solvents.The solubilization of homopolymer in a micelle and the difficulties this can present when attempting to separate homopolymer from copolymer in a mixture have been recognized.275 Micellar formation has been detected in AB poly(styrene-b-dimethylsiloxane) solutions,276 but in ABA the preferred conformation was one of randomly interpenetrating coils in toluene butan-2-one or cyclohexane. The solution properties of graft copolymers are also strongly dependent on the solvent and Price and have shown that micelles form in poly(styrene-g- isoprene) with the graft chains holding the main chain in solution. The incompatibility of the component blocks in a copolymer can depend on a number of variables such as the molecular weight the nature of the solvent 269 (a)J.R. Urwin and M. Girolamo Makromol. Chem. 1971 150 179; (b)J. R. Urwin and M. Girolamo Austral. J. Chem. 1971 24 729. 270 J. P. Plante N. Ho-Duc and J. Prud’homme European Polymer J. 1973 9 77. 27’ (a)A. Dondos Makromol. Chem. 1971 147 123; (b) A. Dondos P. Rempp and H. Benoit Polymer 1972 13 97. 272 T. Tanaka T. Kotaka and H. Inagaki Polymer J. 1972 3 338. 273 M. Girolamo and J. R. Urwin European Polymer J. 1972 8 I1 59. 2’4 Z. Tuzar and P. Kratochvil Makromol. Chem. 1972 160 301. 275 (a)Z. Tuzar and P. Kratochvil Makromol. Chem. 1973 170 177; (6) A. Skoulious P. Helffer Y. Gallot and J. Selb ibid. 1971 148 305. 276 (a)J. C. Saam D. J. Gordon and S.Lindsey Macromolecules 1970 3 1; (b) M. J. Owen and T. C. Kendrick ibid. p. 455. ’17 W. G. Davies and D. P. Jones Ind.and Eng. Chem. (Product. Res. and Development) 1971 10 168. 278 C. Price and D. Woods Polymer 1973 14 82. 208 J. M. G. Cowie or the chain architecture.279 Differences are obvious between the behaviour of di- and tri-block polymers;259 generally speaking AB blocks will dissolve in selective solvents for either block but in ABA blocks the solubility is governed by the A subchains rather than the central block. Optical anomalies in light-scattering measurements were highlighted by Prud’homme and Bywater.280 Normal Zimm plots were obtained when the refractive index of the solvent used was significantly different from either block but distorted plots arising from intermolecular interferences appeared when the solvent refractive index approached that of either block.When conditions for microphase separation in block copolymers are calculated as a function of the interaction parameter xfor a copolymer of fixed composition and molecular weight they predict that phase separation becomes increasingly unlikely as the number of blocks in the chain increases.28’ This isin agreement with the experimental observations. Block Copolymer Morphology.-The microphase separation and solvent effects observed in solutions of block copolymers bear some relation to the ultimate morphology of the block copolymer in the bulk state. It is generally accepted that a ‘domain’ structure is formed with each type of block either aggregating into limited regions (domains) or forming a matrix in which domains of the other block are embedded.The fine structure has been studied using X-ray (including small angle) scattering phase-contrast microscopy and electron microscopy. In the latter method staining with OsO has proved useful for copolymers containing dienes282-284 and poly(ethy1ene-g-vinyl acetate).285 Several etching techniques have been proposed for multiphase blends,286 ABS and high-impact polystyrene,287 a freeze-etching method for latex particles,288 and a freeze- etching-replication process for samples of both block and graft copolymers in preparation for electron micro~copy.~ 89 Several structural forms have been identified and described variously as (i) hexagonal (ii) reverse hexagonal (iii) linear or lamellar and (iv) irreg~lar.~~’.~~’ The type of structure obtained during film casting290” is found to be dependent 279 H.Ohnuma T. Kotaka and H. Inagaki Polymer J. 1970 1 716. 280 J. Prud’homme and S. Bywater Macromolecules 1971,4 543. 281 S. Krause Macromolecules 1970 3 84. *” P. R. Lewis and C. Price Polymer 1972 13 20. 283 C. Price A. G. Watson and M. T. Chow Polymer 1972 13 333. 284 T. Uchida. T. Soen T. Inoue and H. Kawai J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 101. ”’ Y. Jyo C. Nozaki and M. Mutsuo Macromolecules 1971,4 517. 286 G. C. Eastmond and E. G. Smith Polymer 1973 14 509. 287 C. B. Bucknall I. C. Drinkwater and W. E. Keast Polymer 1972 13 115.288 R. Reed and J. R. Barlow Polymer 1972 13 226. 289 C. Price and D. Woods European Polymer J. 1973 9,827. 290 (a) A. Douy and B. Gallot Makromol. Chem. 1973 165 297; (6) M. Gervais A. Douy and B. Gallot Mol. Crystals Liquid Crystals 1971 13 289; (c) A. Douy and B. Gallot Makromol. Chem. 1972 156 81. 291 H. Kawai T. Soen T. Inoue T. Ono,and T. Uchida Mem. Fac. Eng. Kyoto Uniu. 1971 33. 383. Physical Properties of Polymers and their Solutions 209 on the solvent the temperature copolymer composition and the rate of sample preparation. Lewis and Price282-292 found that for films of ABA poly(styrene-b-diene) the slower rate of casting resulted in greater domain ordering. Uchida et al.284 obtained five types of domain structure by changing the fractional composition of two components in a solvent mixture but this aspect of selective solvent control has not been studied very fully.The effect of chain structure on morphology was examined by Price et al.283 using AB poly(styrene-b-isoprene) but although an ordered arrangement of quite regular domains was found for single chains and both three- and four- branched star conformations the detailed morphology was apparently unaffected by the chain geometry. As the rate of evaporation can play a significant part in altering the final morphology of a sample Gallot and Sadr~n~~~ have attempted to ‘freeze’ the structure present in a solution by photopolymerizing methyl methacrylate added to the solution to form a restraining network. In this way they were able to observe a gradual change from spherical to cylindrical to lamellar structures as a function of increasing copolymer concentration in the initial solution.Much of the work on the effect of external factors on the domain structure of copolymer samples has been comprehensively covered by Kawai et who provide a good synopsis of work in this area up to 1971. More recently a review paper by Sadron and Gal10t~~~ has appeared which focuses attention on the relation between the concentration of copolymers in selective solvents and the mesomor- phic structures formed. A study of solvent localization in these mesomorphic phases has also been made.295 A quite specific and very regular three-dimensional orthorhombic lattice structure composed of spherical polystyrene aggregates in a polybutadiene matrix has been proposed296 for samples of ABA poly(styrene-b-butadiene) and low-angle X-ray scattering data have been interpreted as fitting this face- centred cubic structure.The model has been criticized297 mainly on the grounds that the difficulties encountered in analysing the results cast serious doubt on this postulate :indeed the reported X-ray data may not even match the suggested A similar view has been expressed by Kim,299 who concedes that although a superlattice-like structure may exist to some degree,300 the existence of a highly ordered structure remains unproven. 292 P. R. Lewis and C. Price Polymer 1971 12 258. 293 B. Gallot and C. Sadron Macromolecules 1971,4 514. 294 C.Sadron and B. Gallot Makromol. Chem. 1973 164 301. 295 A. Douy and B. Gallot Compr. rend. 1973,276 C 391. 296 (a) D. McIntyre and E. Campos-Lopez Macromolecules 1970,3 322; (6)E. Campos-Lopez D. McIntyre and L. J. Fetters ibid. 1973,6 415. 297 A. Skoulious Macromolecules 1971 4 268. 298 W. R. Krigbaum S. Yazgan and W. R. Tolbert J. Polymer Sci. Polymer Phys. Edn. 1973 11 51 I. 299 H. Kim Macromolecules 1972 5 594. 300 G. Kampf H. Kromer and M. Hoffmann J. Macromol. Sci. 1972 B6,167. 210 J. M.G.Cowie A statistical thermodynamic treatment of phase separation301 showed that polystyrene domain formation was favoured by surface-energy terms in ABA poly(styrene-b-butadiene). The domain sizes were found to be inversely pro- portional to temperature and thermal treatment could lead to a reorganization of the internal structure increasing its regularity.302 The thermodynamic factors controlling stable domain formation showed that results could be sensitive to differences in the cohesive energy den~ity.~'~.~'~ A treatment of phase separa- tion in a two-block polymer as a mutual excluded-volume effect suggested that only partial separation would occur unless the solvent was poor enough to act as a selective precipitant for one The influence of the Benard effect on the anisotropy of films cast from solution has been highlighted by Krigbaum et The Benard effect describes thecellular ordering of convection currents during solvent evaporation which leads to macroscopic hexagonal cell structures in the film and ordering in the polymer phase.Quite marked changes in morphology can be obtained if impurities such as homo polymer^^^^ or di-blocks in tri-block preparations3" are present. Small quantities of impurities can be tolerated and often create a more regular distribu- tion of domains but solubilization of larger quantities enlarges the domains so much that the phase boundaries become diffuse. This can have a distinct influence on the mechanical properties.308 1onomers.-The ionomers constitute an interesting group of ionic copolymers. They are now generally defined as random copolymers prepared from vinyl and acid monomers which are capable of forming intermolecular ionic bonds. The morphology is again believed to be a domain structure with ionic groups clustering together to form polar domains in a matrix of amorphous polymer.There are differences of opinion as to the size of the ionic aggregate and two models have been used to account for the properties (i) a homogeneous model and (ii) a cluster In the homogeneous model the ionic groups are believed to be distributed as dimers throughout an amorphous phase with no aggregation larger than 2nm. Evidence to support this picture has been 30* U. Bianchi E. Pedemonte and A. Tuturro Polymer 1970 11,268. 302 E. Pedemonte A. Tuturro U. Bianchi and P. Devetta Polymer 1973 14 145. 303 D. F. Leary and M. C. Williams J. Polymer Sci. Polymer Phys. Edn. 1973 11 345. 304 M. Gervais G. Jouan and B. Gallot Compt. rend. 1972 275 C 1243. 305 J.Pouchly A. Zivny and A. Sikora J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 151. 306 T. Inoue T. Soen T. Hashimoto and H. Kawai Macromolecules 1970,3 87. 307 L. J. Fetters B. H. Meyer and D. McIntyre J. Appl. Polymer Sci. 1972 16 2079. (a) K. E. Cunningham M. Auerbach and W. J. Floyd J. Appl. Polymer Sci. 1972 16. 163; (b) R. E. Cunningham and M. L. Wise ibid. p. 107. 309 E. P. Otacka J. Macromol. Sci.,1971 C5,275. Physical Properties of Polymers and their Solutions 211 obtained by Otacka and Kwei3" and by Roe.311 The results of Marx et and others314 lend credence to the cluster model. Eisenberg and Navrati13' have tended to adopt an intermediate description. They found that a breakdown in linear viscoelastic theory occurred when the mole % of salt in styrene-methacrylic acid copolymers exceeded 6%.This was interpreted and substantiated on theoretical as indicating the presence of dimers at low ionic concentrations which increased in size to give trimers tetramers and so on as the amount of acid monomer in the ionomer increased. Eventually microphase separation and clusters could occur at high ionic concentrations. A new model proposed by Marx et ~1.,~fits these observations. The acid aggregates are pictured as being homogeneously dispersed throughout the amorphous phase and each aggregate contains two or more acid groups depend- ing on the copolymer composition and the amount of water present. The aggre- gates are never as large as suggested in the cluster model and so this is much closer to the homogeneous model in concept.The revitalized 'fringe-micelle' structure has also been suggested as a suitable model structure.318 Viscoelastic Properties of Solutiom.-The viscosity of a dilute polymer solution is commonly used to estimate the molecular weight of a polymer. Such solutions are also viscoelastic. This is not quite so obvious but arises because the flow of solvent restricts the number of possible conformations a chain can adopt thereby reducing the entropy and raising the free energy which is elastic energy. To explain the phenomenon a 'bead and spring' model was adopted first by Rouse then by Zimm and later by Tschoegl and used to relate the molecular parameters such as solvent viscosity and relaxation time to the frequency dependence of the storage modulus (G') and the loss modulus (G").The theories contain just one adjustable hydrodynamic interaction parameter h* but are valid only at infinite dilution. This presents experimental difficulties as the elasticity of the polymer chain tends to be swamped by the solvent viscosity and very sensitive measure- ments are required to detect this contribution. Progress towards this end has been made gradually over a number of years and with the development of the 310 E. P. Otacka and T. K. Kwei Macromolecules 1968 1,401. 311 R. J. Roe Amer. Chem. Soc. Div. Polymer Chem. Polymer Preprints 1971 12 730. 312 (a) P. J. Phillips J. Polymer Sci. Part B Polymer Letters 1972 10 443; (b) P. J. Phillips F. A. Emerson and W. J. McKnight Macromolecules 1970 3 767.313 C. L. Marx J. A. Koutsky and S. L. Cooper J. Polymer Sci. Part B Polymer Letters 1971,9 167. 314 (a)F. L. Binsbergen and G. F. Kroon Macromolecules 1973,6 145; (6)T. Kajiyama T. Oda R. S. Stein and W. J. McKnight ibid. 1971 4 198; (c) T. Kajiyama R. S. Stein and W. J. McKnight J. Appl. Phys. 1970 41 4361. (a) A. Eisenberg and M. Navratil J. Polymer Sci. Part B Polymer Letters 1972 10 537; (b)A. Eisenberg and M. Navratil Macromolecules 1973 6 604. 'I6 A. Eisenberg Macromolecules 1970 3 147. 317 C. L. Marx D. F. Caulfield and S. L. Cooper Macromolecules 1973,6 344. 318 R. G. L. Johnson B. W. Delf and W. J. McKnight J. Polymer Sci. Polymer Phys. Edn. 1973 11 571. 212 J. M. G. Cowie Schrag-Birnboim multiple lumped res~nator,~'~*~~' measurements over a wide range of frequency and viscosity are now possible which can be extrapolated to infinite dilution with accuracy.Experimental data in 0-solvents for p~lystyrene,~~' poly(a-p~lybutadiene,~~~ methyl~tyrene),~~~ are all in excellent agreement and poly(dimethyl~iloxane)~~~ with the Zimm theory if a value of h* = 0.25 is used and the frequency of measure- ment is not too high. In good solvents the agreement is poorer and h* must be altered to a lower value.323 In some cases the Tschoegl theory is best if a non- gaussian factor is introduced. The results suggest that at least in the low- frequency range the viscoelastic behaviour is relatively insensitive to chemical structure. This alters markedly with the introduction of branching which affects the longer relaxation times.Osaki and S~hrag~~' have evaluated the Zimm-Kilb theory for star polymers using exact eigenvalues for star-branched chains of equal-length branches. The shapes of the theoretical curves are now a function of the number of branches but agreement with experiment though good requires use of a wider range of h* values possibly because of the non-gaussian character of branched structures. For star-shaped polystyrene with nine arms the agreement was good if h* = 0.4 was used for &solvents and 0.25 for a-chloronaphthalene solutions.326 Similarly polybutadiene stars were close to the Zimm-Kilb predictions for h* = 0.1.322In comb-branched p~lystyrene~~' solutions both the low-frequency [G'] and reduced steady-state compliance J:R were found to be relatively insensitive to branching.Work on these branched structures makes it quite clear that both the hydrodynamic interaction and the segment concentration are important factors controlling the viscoelastic behaviour of polymer solutions. The Zimm theory is invalid for high frequencies but as high-viscosity solvents create similar conditions deviations in viscous liquids have been examined for poly~tyrene.~~~.~~~ The behaviour is close to the predictions of the Peterlin theory which is a bead and spring model modified by the introduction of an 'internal viscosity' factor.330 This measures the opposition of the polymer to the rate of change of its shape in solution but more data are required before the physical significance of the parameter is properly understood.Two approaches to the study of viscoelasticity in polymer solutions are possible;one can either develop better experimental methods for infinite dilution ' J. L. Schrag and R. M. Johnson Rec. Sci. Instr. 1971 42 224. 320 J. L. Schrag and J. D. Ferry Faraday Symposia 1972 No. 6 p. 182. 32 R. M. Johnson J. L. Schrag and J. D. Ferry Polymer J. 1970 1 742. 322 K. Osaki Y. Mitsuda R. M. Johnson J. L. Schrag and J. D. Ferry Macromolecules 1972 5 17. 323 K. Osaki J. L. Schrag and J. D. Ferry Macromolecules 1973 5 144. 324 T. C. Warren J. L. Schrag and J. D. Ferry Macromolecules 1973 6,467. 325 (a)K. Osaki and J. L. Schrag J. Polymer Sci. Polymer Phys. Edn. 1973 11 549; (6) K.Osaki Macromolecules 1973 5 141. 326 Y. Mitsuda K. Osaki J. L. Schrag and J. D. Ferry Polymer J. 1973 4 24. 327 Y. Mitsuda J. L. Schrag and J. D. Ferry Polymer J. 1973 4 668. 328 D. J. Massa J. L. Schrag and J. D. Ferry Macromolecules 1971 4 210. 329 K. Osaki and J. L. Schrag Polymer J. 1971 2 541. 330 A Peterlin J. Polymer Sci. Part B Polymer Letters 1972 10 101. Physical Properties of Polymers and their Solutions 213 measurements or formulate a better theory to incorporate concentrated solutions. The latter approach has been attempted by Everage and Gordon331 using continuum mechanics to relate the mechanical behaviour to molecular weight molecular weight distributions and the solution interaction parameter. The theory has produced a constitutive equation which remains to be tested.On moving from dilute to concentrated solutions and ultimately to the bulk polymer the importance of entanglements and molecular weight distribution increases. Results in concentrated solutions that aggregates form whose behaviour is closer to the Rouse theory and only when these break down to discrete molecules in dilute solution is there agreement with the Zimm theory. Melt viscosities qo of narrow-distribution polystyrene showed only a gradual change in slope when plotted as a function of chain length which was inter- preted on the basis of only partial entanglement.332 Earlier work on melt viscosities exhibited a sharp change in slope and the value of the critical entangle- ment molecular weight M was estimated from the break point.A re-examination of these data suggests that a continuous function of the form qo = KIMw+ K2Mw34 is a much better repre~entation.~~~ The steady-state compliance J is also a useful quantity which can be used to gain some insight to the molecular mechanism operatihg during the slow de- formation of the polymer. The dependence of J on A4 has been examined above and below M,. Above M, J was independent of M,334while below J was proportional to M in agreement with the Rouse theory. For four- and six-branched polystyrene the effective entanglement molecular weight Me above which J," became independent of M was given by Me = M,/$2 where $ is the volume fraction of the polymer.335 The concentration dependence of J has been found to be fairly complex.336 The importance and influence of branching in viscoelastic measurements has been stressed337 and J," has been found to be much higher for comb338 and four-branch polystyrene339 than for the linear chains.331 (a) R. J. Gordon and A. E. Everage J. Appl. Polymer Sci. 1971 15 1903; (b) A. E. Everage and R. J. Gordon ibid. 1972 16 1967. 332 R. I. Wolkowicz and W. C. Forsman Macromolecules 1971 4 184. 333 M. M. Cross Polymer 1970 11 238. 334 (a) N. Nemoto M. Moriwaki H. Odani and M. Kurata Macromolecules 1971 4 21 5; (6)W. C. Uy and W. W. Graessley ibid. p. 458; (c)S. Onogi T. Masuda and K. Kitagawa ibid. 1970 3 109; (d)M.Fujiyama and H. Awaya J. Appl. Polymer Sci. 1972 16 275; (e) H. Odani N. Nemoto S. Kitamura M. Kurata and M.Tamura Polymer J. 1970 1 356; cr)T. Masuda K. Kitagawa and S. Onogi ibid. p. 418; (g) N. Nemoto H. Odani and M. Kurata Macromolecules 1972 5 531. 335 L. A. Utracki and J. E. L. Roovers Macromolecules 1973 6 373. 336 (a) N. Nernoto T. Ogawa H. Odani and M. Kurala Macromolecules 1972 5 641 ; (6)Y. Einaga K. Osaki M. Kurata and M. Tarnura ibid. p. 635; (c) Y. Einaga K. Osaki M. Kurata T. Sugie and M. Tamura ibid. 1973 6 598; (d)M. Sakai T. Fujimoto and M. Nagasawa. ibid. 1972 5 786. 33' T. Masuda Y. Nakagawa Y. Ohta and S. Onogi Polymer J. 1972 3 92. 338 (a)T. Fujimoto H. Kajiura M. Hirose and M. Nagasawa Polymer J. 1972 3 181; (b)T. Fujirnoto H. Narukawa and M. Nagasawa Macromolecules 1970 3 57. 339 T. Masuda T. Ohta. and S. Onogi Macromolecules 1971 4 763.214 J. M. G.Cowie A new and potentially fruitful area of viscoelastic study has been opened with the availability of sharp-distribution polymer samples.340 Improved correlation between mechanical behaviour and molecular-weight distribution is now possible and by creating blends of these fractions the sensitive relations between composi- tion and properties can be demonstrated.341 The effect of chain-length dis- tribution has been most noticeable in the rubbery region342 and binary poly- styrene blends show a two-step rubbery plateau suggesting that two types of entanglement coupling may The effects of entanglement on relaxation times have been considered in a modified Rouse theory for polydisperse polymers.344 Order in Amorphors Polymers.-A growing body of evidence exists which supports the idea that limited order exists in the glassy and rubbery phases of amorphous polymers and that the random-coil conformation is not uniformly .~~~ adopted throughout the sample.Geiszler et ~1 detected a transition at ap- proximately 15-20 K above the glass-transition temperature 3,in butadiene- acrylonitrile copolymers which suggests that some degree of order was present in the rubbery region. As more energy was required to destroy these regions completely than was necessary to overcome the glass transition the existence of a mesomorphic phase above 5was postulated. This could be a result of ordering and association among nitrile groups in the polymer. The phenomenon has been confirmed in other polymers polyisobutene films were found to contain small amounts of highly ordered and a modular morphology has been detected in amorphous p~lystyrene,~~~~~~' poly(ethy1ene tere~hthalate),~~~ poly~arbonate,~~~~~~' polyethylene and Heueu rubber.352 Additional evidence of ordering in polyisobutene was obtained in a study of the glass transition using positron annihilation as a probe.353 Measurement of the distribution of positron lifetimes indicated that about 40-50 % of the sample was in an ordered state even up to 80-90 K above <.340 D. J. Plazek and V. M. O'Rourke J. Polymer Sci. Part A-2 Polymer Phys. 1971 9 209. 341 (a) See papers in 'Proceedings of 5th International Congress on Rheology,' ed. S. Onogi 1970 Vol. 3; (b) K.Murakami K. Ono K. Shiina T. Ueno and M. Matsuo Polymer J. 1971 2 698. 342 W. F. Knoff I. L. Hopkins and A. V. Tobolsky Macromolecules 1971 4 750. 343 T. Masuda K. Kitagawa T. Inoue and S. Onogi,Macromolecules 1970 3 116. 344 E. Menefee J. Appl. Polymer Sci. 1972 16 2215. 345 W. A. Geiszler J. A. Koutsky and A. T. Dibenedetto J. Appl. Polymer Sci. 1970 14 89. 346 S. Krishnamurthy and D. Mclntyre J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 647. 347 A. Siegmann and P. H. Geil J. Macromol. Sci. 1970 E4,239. 348 G. S. Y. Yeh J. Macromol. Sci. 1972 B6,451. 349 P. J. Harget and A. Siegmann J. Appl. Phys. 1972,43,4357. 3s0 W. Lin and E. J. Kramer J. Appl. Phys. 1973,44 4288. 351 A. Siegmann and P. H. Geil J. Macromol. Sci. 1970 B4,557. 352 G. S.Markova Y. K. Ovchinnikov and E.B. Bokhyan Reprint 111-42 IUPAC Helsinki 1972. 353 J. R. Stevens and R. M. Rowe J. Appl. Phys. 1973,44,4328. Physical Properties of Polymers and their Solutions 215 To account for these observations a two-phase structural model has been proposed for the amorphous state.354 The model comprises ordered domains of 24nm diameter with distinct boundaries embedded in a truly random intergrain region. The excess free volume is believed to be located in the inter- domain region. A similar type of domain model for linear amorphous polymers introduces the concept of permanent and transitory interactions between loops and strands at the surfaces of quite large domains.355 Both types of interactions influence the mechanical properties but only the transitory interactions affect the flow be- haviour.Data supporting the concept of lateral ordering in amorphous polymers have been reviewed by Yeh356 and this together with the more recent work casts serious doubt on the idea of a structureless amorphous state. Ordered structures may arise from (i) lateral ordering (ii) helical sequences or (iii) departure from random-coil statistics in the melt and indeed Boyer is of the opinion3” that an irregularly folded chain is a more likely conformation in the amorphous state than a random coil. 2 Molecular Motions Glass Transitions.-A theory of the glassy state based on a hole concept for simple liquids has been offered by Nose.358 The glass is represented as a quasi- equilibrium state with holes frozen into it and these distinguish it from the liquid or crystalline state.Calculation of the pressure dependence of shows that (dT$dP) < A/l/Aa,where Aa and A/l are the thermal expansion and compressi- bility changes on moving from a glass to a rubber. The isofree volume theory predicts an equality for this relation and the inequality suggests that either the entropy or the enthalpy are the controlling factors and so the approach to an understanding of 3 should be isoenergetic. Support for the isoenergetic theory comes from Ichihara et af.,359who have studied the compression of glassy polymers. These authors conclude that if pressure is applied to all polymer glasses they will eventually reach a state of compaction in which all possess the same enthalpy.They have confirmed the predictions for (d T‘dP). Consequently they favour the isoenergetic description of 3,for this reason and also because no compaction of a glass should occur at if the fractional free volume is constant. This would be contrary to experimental 354 G. S. Y. Yeh J. Macromol. Sci. 1972 B6,465. 355 (a) S. M. Aharoni J. Appl. Polymer Sci. 1972 16 3275; (6) S. M. Aharoni ibid. 1973 17 1507. 356 G. Yeh Crit. Rev. Macromol. Sci. 1972 1 173. 357 R. F. Boyer presented at the Seventh Swinburne Award Address London 1972. 358 (a)T. Nose Polymer J. 1971 2 124; (b)T. Nose ibid. p. 427; (c)T. Nose ibid. p. 437; (6)T. Nose ibid. p. 445; (e)T. Nose ibid. 1972 3 1 ; v) T. Nose ibid. p. 196. 359 (a) S. Ichihara A.Komatsu Y. Tsujita T. Nose and T. Hata Polymer J. 1971 2 530; (b)S. Ichihara A. Komatsu and T. Hata ibid.,p. 644; (c)S. Ichihara A. Komatsu and T. Hata ibid. p. 650. 216 J. M. G. Cowie observation. The theory bears some similarity to the Miller360 criterion for T which is expressed in terms of the conformational entropy. Quach and Si~nha~~' have adopted the view that although experiment confirms the inequality (dT$dP) < (Ap/Aa),the experimental definitions of the various quantities may be in error. New definitions were presented within the framework of a modified cell theory for liquids and polymers,362 which revert once more to agreement with the free-volume theory. Re-examination of these definitions has led G~ldstein~~~ to the opinion that the original ones are appropriate and the evidence in support of an isoenergetic theory is correct.The debate continues. and The chain-length dependence of .T for p~lypropene~~~poly(viny1 was found to bear some relation to the predictions of the Gibbs- Dimarzio theory but this was not true for poly(dirnethylsilo~ane),~~~ for which was only slightly dependent on M and even then only for quite short chains. When ionic polymers were examined the relationship was more ~omple~~~~,~~~ and of the general form 7 = 4q/4fB where A and B are constants characteristic of the polymer qis the cation charge and a is the internuclear distance between cation and anion at closest approach. A review paper by Ei~enberg~~~ contains a more detailed description of these systems.The effect of tacticity on T has been examined for p~lypropene,~~~ poly(t-butylethylene oxide),370 poly(methy1 metha~rylate),~~ and poly(ethy1 a-chloro- a~rylate).~~~ The expected difference in was found for the two a-substituted polymers with the syndiotactic form having the higher <. The reverse was true for poly(t-butylethylene oxide) where <for the isotactic form was largest. A large part of the research effort in this area has been centred on the effect of crystallinity on q. Jordan et ~1.~'~ have examined the influence of side-chain crystallinity on the T of selected copolymers of alkyl acrylates incorporating either n-octadecyl acrylate or vinyl stearate as comonomer. The expected increase in was observed when the concentration of the comonomer was 360 A.A. Miller Macromolecules 1970 3 674. 361 (a)A. Quach and R. Simha J. Appl. Phys. 1971,42,4592; (b)A. Quach and R. Simha J. Phys. Chem. 1972,76,416. 362 T. Somcynsky and R. Simha J. Appl. Phys. 1971,42,4545. 363 M. Goldstein J. Phys. Chem. 1973 77 667. 364 J. M. G. Cowie European Polymer J. 1973,9 1041. 365 G. Pezzin F. Zilio-Grandi and P. Sanmartin European Polymer J. 1970 6 1053. 366 J. M. G. Cowie and I. J. McEwen Polymer 1973 14 423. 367 A. Eisenberg H. Matsuura and T. Yokoyama Polymer J. 1971 2 117. 368 A. Eisenberg and K. Takahashi J. Non-Cryst. Solids,1970 3 279. 369 A. Eisenberg Macromolecules 1971,4 125. 370 N. Doddi W. C. Forsman and C. C. Price Macromolecules 1971,4 648. 37' S. Bywater and P.M. Toporowski Polymer 1972 13 94. 372 B. Wesslen R. W. Lenz W. J. McKnight and F. E. Karasz Macromolecules 1971,4 24. 373 (a)E. F. Jordan D. F. Feldeisen and A. N. Wrigley J. Polymer Sci. Part A-I Polymer Chem. 1971 9 1835; (6) E. F. Jordan B. Artymyshyn and A. N. Wrigley ibid. p. 3349; (c)E. F. Jordan ibid. p. 3357. Physical Properties of Polymers and their Solutions 217 sufficient to allow significant crystallization of its side chain to occur. Multiple transitions are commonly observed in polymer samples but when there is ap- preciable crystallinity the interpretation of the nature of each transition can become confused. Nowhere is this more true than in the data reported for polyethylene; approximately 50 papers have appeared since 1953 and as yet there is no unanimous acceptance of one value for T.The most frequently reported centre on 250 195 and 150 K and the lowest one is usually termed the y-relaxation. especially the earlier reports favour the higher value as T for semi-crystalline polyethylene and the middle value for amorphous samples. Recently Stehling and Mandelke~n~~~ and Beatty and Kara~z,~~~ in particular have come to the conclusion that the y-transition is the q for amorphous material. This is based on observed heat-capacity and expansion- coefficient changes in this temperature region of sufficiently high magnitude to represent a glass transition. The reader is recommended to recent reviews by B~yer,~~~ who has gathered and attempted to weigh the extensive data.It is soon obvious that an unambi- guous interpretation of multiple transitions is extremely difficult and Boyer has applied certain criteria which are believed to characterize the glass transition. These are (i) AaT = 0.113 (ii)a < = 0.164 and (iii) AC,T = 105J g- '. Sharma et aL3" have gathered relevant data for a wide range of polymers and have shown that criterion (i) is invalid as the factor is not constant but varies with q. The criticism is partially offset38' by using integrals in the expression to allow for the temperature dependence and free volume. B~yer~~~~ has concentrated mainly on C data to make the point that he favours T = 195 & 10 K for amorphous polyethylene. The implication of this proposal is that a sub-glass molecular motion must then be associated with a heat-capacity change and theoretically it could be detected using differential scanning calorimetry.No one has reported this as yet probably because sufficiently sensitive instrumentation has only recently become available. Methods of predicting q for polymers and copolymers have been proposed. We~land~~' has presented a method based on group increments which are assigned and totalled for a given chain. JohnstonjE3 has developed an additive 374 K. H. Illers Kolloid-Z. 1972 250 426. 375 G. T. Davis and R. K. Eby J. Appl. Phys. 1973,44,4274. 3'6 S. H. S. Chang Amer. Chem. SOC. Div. Polymer Chem. Polymer Reprints 1972 13 322. 377 F. C. Stehling and L. Mandelkern Macromolecules 1970 3 242. 378 C.L. Beatty and F. E. Karasz Bull. Amer. Phys. Soc. 1971 16 1391. 379 (a)R. F. Boyer Thermal Analysis 1971,3 3; (6) R. F. Boyer presented at the Seventh Swinburne Award Address London 1972; (c) R. F. Boyer J. Macromol. Sci. 1973 B7 487; (d)R. F. Boyer Macromolecules 1973 6 288. 380 S. C. Sharma L. Mandelkern and F. C. Stehling J. Polymer Sci. Part B Polymer Letters 1972 10 345. 38' (a) R. Simha and C. E. Weil J. Macromol. Sci. 1970 B4,215; (6) R. Simha ibid. 1971 5 331. 382 H. G. Weyland P. J. Hoftyzer and D. W. Van Krevelen Polymer 1970 11 79. 383 (a) N. W. Johnston J. Macromol. Sci. 1973 A7 531; (b) N. W. Johnston Macro-molecules 1973 6 453. 218 J. M. G. Cowie relationship for copolymers using the values for the homopolymers and the sequence distribution of the comonomers in the chain.Neutron Scattering.-Access to cold neutron sources (i% 0.5 nm) has provided an exciting new probe for the study of motion and chain dimensions in polymer systems. Low-angle scattering from deuteriated poly(methy1 methacrylate) glasses384 and polystyrene in deuteriated polystyrene matrix,385 in solution,386 and in the have yielded measurements of the radius of gyration in good agreement with those estimated by conventional procedures. Low-frequency motions in polymers have been investigated using quasi-elastic neutron scattering and an excellent review by Allen and Higgin~~~~ covers much of the work including polymer systems up to 1973. It can be expected that this technique will contribute valuable information to the study of long-range conformational motion and side-group movement in polymeric chains.Dynamic Mechanical Measurements.-Thermomechanical spectra yield infor- mation on molecular motions in a polymer sample throughout the whole range of mechanical states. Dynamic methods such as the torsional pendulum generate these spectra but may require substantial specimen sizes. A semi-micro method developed by Gillham called torsional braid analysis (TBA) overcomes this by using a composite specimen comprising an inert-glass braid impregnated with polymer. Additional advantages are that non-self-supporting polymers are easily handled and in situ reactions can be studied during a measure- ment. The method however only gives relative values of the mechanical prop- erties.Gillham389 has reviewed the technique and its applications up to 1972. Since then some interesting work has been reported on an unusual family of poly(carbaborane4oxane) high-temperature elastomers.390 Two different types of carbaborane cages were incorporated in the chain and compositional changes could be used to alter the melting and glass-transition temperatures. TBA is readily suited to the measurement of the thermomechanical response of high-temperature and relatively intractable polymers such as polynorborna-2,5- diene,391poly(phenylq~inoxaline),~~~ and has been used to and polyimide~,~~~ 384 R. G. Kirste W. A. Kruse and J. Schelten Makromol. Chem. 1972 162 299. ’13’ D. G. H. Ballard G. D. Wignall and J. Schelten European Polymer J.1973 9,965. 386 (a)H. Benoit D. Decker J. S. Higgins C. Picot J. P. Cotton B. Farnoux G. Jannink and R. Ober Nature Phys. Sci. 1973,245 13; (6)J. P.Cotton B. Farnoux G. Jannink and C. Strazielle J. Polymer Sci. Polymer Symposia 1973 42 981. ”’ (a)J. P. Cotton B. Farnoux G. Jennink J. Mons and C. Picot Compf. rend. 1972 275 C 175; (6)J. P. Cotton B. Farnoux G. Jennink C. Picot and G. C. Summerfield J. Polymer Sci. Polymer Symposia 1973 42 807. 388 G. Allen and J. S. Higgins Reports Progr. Phys. 1973 36 1073. 389 J. K. Gillham Crif. Rev. Macromol. Sci.,1972 1 83. 390 (a) M. B. Roller and J. K. Gillham J. Appl. Polymer Sci. 1972 16 3095; (6) M. B. Roller and J. K. Gillham ibid. p. 3105; (c) M. B. Roller and J. K. Gillham ibid. 1973 17 2141.391 M. B. Roller J. K. Gillham and J. P. Kennedy J. Appl. Polymer Sci. 1973 17 2223. 392 (a) J. M. Augl and H. J. Booth J. Polymer Sci.,Polymer Chem. Edn. 1973 11 2179; (b)J. M. Augl and H. J. Booth ibid. p. 2195. 393 J. K. Gillham J. Appl. Polymer Sci. 1972 16 2595. Physical Properties of Polymers and their Solutions 219 monitor thermal cross-linking and chain-cyclization reactions394 of polymers on the braid. Two damping peaks detected during the curing of thermosetting resins have been identified as representing the gel point and the glass transition in the system ;395 thus TBA is capable of following the property changes in a cross- linking resin and shows that this depends on the curing temperature. For temperatures above only gelation is observed ; for temperatures below only vitrification occurs ;and at intermediate temperatures both are detected.TBA has proved useful for the thermomechanical study of poly(dimethy1-siloxane) liquids366 and for investigating the damping at the melting transition of poly(ethy1ene oxide).396 A large number of papers have been devoted to the systematic and detailed investigation of the mechanical response of various polymer systems but as they are of specific interest rather than general they will not be catalogued here. Of these a few of special interest describe the polarization of polymer films to form electrets.397 A strong d.c. electric field is applied at high temperature and then the sample is cogled under an applied electric field. The depolarization current is then measured as a function of temperature and sudden changes occur which can be correlated with molecular motion in the glass or crystalline phase.The method could prove more sensitive to low-frequency motions than the established viscoelastic techniques. Elastomers.4ne point of contention remaining unresolved in the molecular theory of rubber elasticity centres on the form of the expression for the free energy of network deformation. The incorporation of a logarithmic form and the value of B in the equation AG,,JRT = (u/2)(lf + i;+ A -3) -Bu In Axl.,,lz are open to argument. As it is difficult to prepare networks with a precisely known structure to allow calculation of u the number of elastically effective cross-links one must use methods which eliminate u from the calculations.This can be achieved by comparing networks swollen in different solvents and cross- linked in the swollen state and in this way Froelich et have confirmed the need for the logarithmic term. They also estimate B = 2/f wheref is the function- ality of the cross-link. A general conclusion arrived at by a number of workers is that networks prepared in solution have different topologies from those cross- linked in the bulk state and that the former behave ideally obeying gaussian theory.399 This could be due to a lower proportion of physical entanglements 394 J. K. Gillham and K. C. Glazier J. Appl. Polymer Sci. 1972 16 2153. 39s P. G. Babayevsky and J. K. Gillham J. Appl. Polymer Sci. 1973 17 2067. 396 B.Hartmann Polymer 1972 13,460. 397 (a)T. Takamatsu and E. Fukada Polymer J. 1970 1 101 ;(6) J. van Turnhout ibid. 1971 2 173; (c) E. Fukada and T. Sakurai ibid. p. 656; (d)E. Sacher J. Macromol. Sci.,1972 B6,365; (e)E. Sacher ibid. p. 377; U,H. Sasabe and S. Saito Polymer J. 1972 3 624. 398 D. Froelich D. Crawford T. Rozek and W. Prins Macromolecules 1972 5 100. 399 (a)R. M. Johnson and J. E. Mark Macromolecules 1972,541 ;(b)C. Price G. Allen F. de Candia M. C. Kirkham and A. Subramanian Polymer 1970 11 486; (c) W. Brostow Macromolecules 1971,4 742; (4F. de Candia ibid. 1972,5 103 220 J. M. G. Cowie which contribute to the non-ideality of the network being formed in the solution cross-linking process. Alternatively the non-ideal behaviour may originate from ordering in the amorphous state which is reduced when cross-linking of the swollen polymer takes place.Some evidence of the presence of mesomorphic phases in cross-linked polymers has been obtained by Prin~.~" The Flory-Huggins theoretical approach to network swelling has been developed by Treloar for cylinders subjected to torsion and axial e~tension.~" The method has been successfully applied to the common p~lydienes.~~~ Thermo-elastic measurements of rubber in torsion403 gave a value of d In (r2)o/dT of +0.43 x K-' in good agreement with later results by Price et uL404 Contributions to theory have come from Goebel and T~bolsky,~'~ who have formulated a new equation for the volume dilation of a rubber during extension and Ei~hinger,~'~ who used graph theory to calculate distribution functions for perfect phantom networks.Some work on the properties of interpenetrating networks (IPN) has been published. Sperling et uL407 prepared IPN from the incompatible pair poly(ethy1 acrylate) and poly(methy1 methacrylate) but could only detect one broad glass transition rather than two. Bamford et aL408found two values when poly(viny1 trichloroacetate) was cross-linked with polystyrene or poly(methy1 methacrylate) and a system similar to an AB block copolymer with a domain structure was formed. A more careful definition of the types of IPN by S~erling,~" points out that a 'joined' structure is composed almost entirely of intramolecular cross- links and is easier to prepare. A 'sequential' IPN is one in which both polymers are in the network form and ideally all cross-links are intermolecular.Sequential IPN of poly(dimethylsi1oxane) and poly(methy1 methacrylate) were quite opaque had two values and behaved somewhat like a thermoplastic elastomer. Electron micrographs support the interpenetrating and reveal a cellular morphology of about 100nm and phase domains of lOnm in some IPN.41 Limited control over the morphology could be effected by altering the composition of the network components. 400 (a) E. Pines and W. Prins J. Polymer Sci. Part A-2 Polymer Phys. 1972 10 719; (6) M. Ilavsky and W. Prins Macromolecules 1970 3 425. 40 ' (a)L. G. R. Treloar Polymer 1972,13,195; (6)K. M. Loke M. Dickinson and L. G. R. Treloar ibid.p. 203. 402 A. N. Gent and T. H. Kuan J. Polymer Sci. Polymer Phys. Edn. 1973 11 1723. 403 P. H. Boyce and L. G. R. Treloar Polymer 1970 11 21. 404 C. Price K. A. Evans and F. de Candia Polymer 1973 14 338. 405 (a)A. V. Tobolsky and J. C. Goebel Macromolecules 1970 3 556; (6) J. C. Goebel and A. V. Tobolsky ibid. 1971 4 208. 406 (a)B. E. Eichinger Macromolecules 1972,5 496; (6) B. E. Eichinger ibid. p. 647. 407 L. H. Sperling D. W. Taylor M. L. Kirkpatrick H. F. George and D. R. Bardman J. Appl. Polymer Sci. 1970 14 73. 408 C. H. Bamford G. C. Eastmond and D. Whittle Polymer 1971 12 247. 409 L. H. Sperling and H. D. Sarge J. Appf. Polymer Sci. 1972 16 3041. 'I0 A. J. Curtis M. J. Covitch D. A. Thomas and L. H. Sperling Polymer Eng. Sci. 1972 12 101.(a) V. Huelck D. A. Thomas and L. H. Sperling Macromolecules 1972 5 340; (6) V. Huelck D. A. Thomas and L. H. Sperling ibid. p. 348. Physical Properties of Polymers and their Solutions 221 Crystallization.-The Avrami equation is still widely used in the analysis of crystallization kinetics but it has many limitations. The exponent n is not always an integer as predi~ted,~' 2414 although it has been used successfully for poly- (propene oxide)?" nylon 6,416nylon 8,417and nylon 12,418if one allows for the effects of secondary crystallization. The temperature of crystallization also altered n;414,416 for polyethylene Mandelkern4' found that the Avrami equation was adhered to at high temperature while at lower temperatures the onset of deviations from the theory was a function of both A4 and the crystallizing temperature.Price and Th~rnton~~' found that n was only slightly affected if the crystal-growth pattern was assumed to be rod-like rather than spherical. A more radical approach was made by Danusso et uI.,~~'who proposed a new two-range nucleation model. They argued that the Avrami theory leads to a two-parameter equation with an ambiguous character for n which is related to both growth and nucleation. A three-parameter equation was developed to overcome this defect but it appears to have excited little interest from workers in the field. More recently Gandica and Magi11422 developed a universal rela- tionship for polymer crystallization which leads to a corresponding states equation and can be used to provide a master curve for polymers at various temperatures crystal modes and tacticities.Booth and Hay4' 'believe that fractionation during isothermal crystallization may complicate the kinetic analysis but the contrary view is expressed by Kamide and Yamag~chi.~'~ Fractionation is sometimes claimed to be respon-sible for lamellar but again this is disputed by those who prefer to think this is due to annealing of the An attempt to resolve the problem of fractionation effects426 was unsuccessful because the data could not be inter-preted in a satisfactory way. La~ritzen~'~ has developed a kinetic theory of lamellar growth rate based on the assumption that isothermal crystallization proceeds through .the growth of lamellae which then provide a substrate for 'I2 C.Borri S. Briickner V. Crescenzi G. Della Fortuna A. Mariano and P. Scarazzato European Polymer J. 197 1 7 15 15. 'I3 A. Booth and J. N. Hay Polymer 1971 12 365. 'I4 S. Gogolewski and E. Turska J. Appl. Polymer Sci. 1972 16 1959. 'I5 (a)C. Booth D. V. Dodgson and I. H. Hillier Polymer 1970 11 11 ;(6)D. R. Beech and C. Booth ibid. 1972 13 355. 416 (a)E. Turska and S. Gogolewski Polymer 1971,12,616; (6)E. Turska and S. Gogolew-ski ihid. p. 629. 'I7 G. Ceccorulli and F. Manescalchi Makromol. Chem. 1973 168 303. F. Manescalchi R. Rossi and A. Mattiussi European Polymer J. 1973 9 601. 'I9 E. Ergoz J. G. Fatou and L. Mandelkern Macromolecules 1972 5 147. 420 F. P. Price and J. M. Thornton J. Appl.Phys. 1973,44 4312. ''I F. Danusso G. Tieghi and V. Felderev European Polymer J. 1970 6 1521. 422 A. Gandica and J. H. Magill Polymer 1972 13 595. 423 K. Kamide and K. Yamaguchi Makromol. Chem. 1972 16 219. '"T. Kawai M. Hosoi and K. Kamide Makromol. Chem. 1971 146 55. 425 A. Mehta and B. Wunderlich Makromol. Chem. 1972 153 327. 426 F. C. Stehling E. Ergoz and L. Mandelkern Macromolecules 1971 4 672. 427 (a)J. I. Lauritzen J. Appl. Phys. 1973,44,4353; (6)J. I. Lauritzen and J. D. Hoffman ibid. p. 4340. J. M. G. Cowie further growth; this remains to be tested. Some progress in the theoretical description of copolymers has been made.428 The experimentally determined melting temperature of a polymer T is normally lower than the thermodynamic melting point T; of the perfect crystal.The major limiting factor to the attainment of T is the thickness of lamellar crystals and the difference between T and Ti can be expressed in terms of the lamellar thickness [ and end interfacial energy ere. In the Flory-Vrij theory partially crystallized chains are taken into account and the equation is T = T:[1 -(2ae/AhC)]/[l -(RT In I/AhtC)] where Ah is the enthalpy of fusion t the number of times a chain folds into a crystal and I is a parameter to allow for different degrees of order in the crystal. Thus a low T can be associated with a high 0 and a low [. The main emphasis has been on the determination of oeand its behaviour with chain length. Booth and his co-~orkers~~’ have concentrated predominantly on poly(ethy1ene oxide).With short chains available the possibility arises of obtaining crystallites with different chain-folding morphologies. They found that low molecular weight polymer formed lamellar crystals with thicknesses which corresponded to extended chains once folded twice folded and higher. The crystal type was also a function of M the molecular weight distribution and the crystallizing temperature. An increase in oewith M was observed but credecreased when the extent of folding increased for any given chain length. fa to^^^' agrees essentially with this general trend. The effect of different end groups was also Substitution of the OH terminal group by C1 phenoxy- or acetoxy-groups raised T because of an increase in cre.This led to the conclusion that hydrogen- bonding in the hydroxy-terminated polymer stabilizes the interfacial layers.For BAB poly(ethy1ene oxide-b-propylene oxide) cre was found to increase markedly432 as the length of the propylene oxide block increased and T was depressed accordingly. The depression of the corresponding ABA blocks was not nearly so great. 428 E. Helfand and J. I. Lauritzen Macromolecules 1973 6 63 1. 429 (a)D. R. Beech C. Booth D. V. Dodgson R. R. Sharpe and J. R. S. Waring Polymer 1972,13,73;(b)D. R. Beech C. Booth I. H. Hillier and C. J. Pickles European Polymer J. 1972 8 799; (c) D. R. Beech C. Booth C. J. Pickles R. R. Sharpe and J. R. S. Waring Polymer 1972 13 246; (d)P. C. Ashman and C. Booth ibid. p. 459. 430 J. M. Barrales-Rienda and J.G. Fatou Polymer 1972 13 407. 431 (a)C. Booth J. M. Bruce and M. Buggy Polymer 1972,13,475;(b)P. C. Ashman and C. Booth ibid. 1973 14 300. 432 (a) C. Booth and C. J. Pickles J. Polymer Sci.,Polymer Phys. Edn. 1973 11 249; (b) C. Booth and D. V. Dodgson ibid. p. 265.

ISSN:0308-6003    

DOI:10.1039/PR9737000173

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

8 Electrolyte Solutions By H. P. BENNETT0 Department of Chemistry Queen Elizabeth College Campden Hill Road. London W8 7AH 1 Introduction At the present time increasing numbers of books and journals make it a daunting task to broaden one’s chemical knowledge even marginally beyond specialized personal interests and this introduction is therefore clouded by a recent protest’ against the proliferation of journals which gains the sympathy of the writer but is unlikely to influence publishers. There are encouraging signs however that the output of material (which like fuel consumption cannot increase indefinitely) is accompanied by some fortunate rationalization between closely related topics in different corners of Physical Chemistry. This chapter attempts to draw atten- tion to these desirable cross-links and hopefully maintains the critical approach adopted by the authors of previous report^.^.^ No attempt is made to provide a complete coverage of the literature a task which has been very adequately performed in the recent Specialist Periodical but books of special interest which have since appeared are briefly mentioned.The second volume of the timely series6-* on ‘Water’ deals at length with water in crystalline hydrates and maintains the high standards of Volume 1. A short chapter by Franks on solutions of simple non-electrolytes illustrates the limita- tions in our understanding of even these the simplest of aqueous solutions. Volume 3 is of special interest since it covers the properties of electrolyte solutions.A variety of interesting papers presented at a Symposium held in honour of Frank appears in a double issue of the Journal ojSolution Chemistry,together with reveal- ing discussion^.^ The well-known series ‘Modern Aspects of Electrochemistry’ Chem. in Britain. 1974 10 32. A. D. Pethybridge and J. E. Prue Ann. Reports (A) 1968 65 129. D. R. Rosseinsky Ann. Reports (A) 1971 68 81. A. K. Covington and T. H. Lilley in ‘Electrochemistry’ ed. G. J. Hills (Specialist Periodical Reports) The Chemical Society London 1972 Vol. 2. T. H. Lilley in ‘Electrochemistry’ ed. G. J. Hills (Specialist Periodical Reports) The Chemical Society London 1973 Vol. 3. ‘Water A Comprehensive Treatise’ ed. F. Franks Plenum Press New York Vol. 1 ‘The Physics and Physical Chemistry of Water’ 1972.Ref. 6 Vol. 2 ‘Water in Crystalline Hydrates; Aqueous Solutions of Simple Nonelec- trolytes’ 1973. ’ Ref. 6 Vol. 3 ‘Aqueous Solutions of Simple Electrolytes’ 1974. J. Solution Chem. 1973 2 95-356. 223 224 H. P.Bennett0 continues to emphasize the properties of the electrolyte-electrode interface as the focal point of electrochemistry. The latest issue” gives space to an interest- ing survey by Mandel on a new interdisciplinary subject bioelectrochemistry. The scope this offers and a measure of its progress may be judged from the collected papers of the first International Symposium.’ la Proceedings of a second meeting held in October 1973 are expected to be available in 1974.lIb The literature reflects the growth of interest in non-aqueous and mixed solvent systems; this is most noticeable from the increased number of references cited in the ‘Electrolyte Solutions Bulletin’,’2 which continues to provide a valuable survey.Non-aqueous systems are discussed in the accompanying report l3 by Cox and will not be dealt with specifically though some overlap is inevitable. However a recent specialist text ‘The Physical Chemistry of Organic Solvent Systems’,I4 deserves our interest because of its coverage of many theoretical aspects of electrolyte solutions. Well-written extended accounts are presented of thermodynamic measurements acid-base properties conductance and spectro- scopy. Shorter discussions on solvent effects in reaction kinetics and organo- electrode processes are likely to be soon outdated in view of the pace of recent developments.The first volume of a monumental reference series on ‘Non-aqueous Electrolytes’ by Janz and Tomkins’ lists conductance data and contains a valuable section on purification methods. Volume 2 in preparation will contain the summarized results of e.m.f. studies. Those who are more practically orientated will also be interested in the Proceedings of a Symposium on the subject of ‘Ion Selective Electrodes’ which have appeared in an inexpensive book form.16 The contributions mainly from Eastern Europe are in English with editing by Pungor. A revised edition of Bates’ standard work’ ’on pH expands those chapters dealing with the establish- ment of pH scales in non-aqueous and mixed solvents and with acid-base phenomena in these media.The famous Weissberger series has added two volumes on ‘Electrochemical Methods’;’’ in part IIAreadable up-to-date chap- ters are devoted to potentiometric methods (redox and pH methods and ion- selective electrodes) conductance transport numbers polarography and related lo ‘Modern Aspects of Electrochemistry’ No. 8 ed. J. O’M. Bockris and B. E. Conway Butterworths London 1973; cf. D. M. Draiic. in ‘MTP International Review of Science Physical Chemistry,’ Butterworths London 1973 Series One Volume 6. I ’ (a) ‘Biological Aspects of Electrochemistry’ (Proc. of 1st C.I.T.C.E. International Symposium Rome 1971) ed. G. Milazzo P. E. Jones and L. Rampazzo Birkhauser Verlag Basle 197 1 ; (b)Bioelectrochemistry and Bioenergetics 1974 1.I * ‘Electrolyte Solutions Bulletin’ ed. A. K. Covington University of Newcastle Library. l3 B. G. Cox Ann. Reports (A) 1974 p. 249. ‘Physical Chemistry of Organic Solvent Systems’ ed. A. K. Covington and T. Dickin- son Plenum Press London 1973. Is ‘Nonaqueous Electrolytes Handbook’ G. J. Janz and R. P. T. Tomkins Academic Press New York 1972. l6 ‘Ion Selective Electrodes’ ed. E. Pungor Akademiai Kiado Budapest 1973. I ’ R. G. Bates ‘Determination of pH ; Theory and Practice’ Wiley-Interscience New York 1973 2nd edn. ‘Techniques of Chemistry’ Vol. 1 ‘Physical Methods of Chemistry’ Part IIA ‘Electro- chemical Methods’ ed. A. Weissberger and B. W. Rossiter Wiley-Interscience New York 1971. Electrolyte Solutions 225 electroanalytical techniques.In a similar vein the first volume of a series’’ entitled ‘Techniques of Electrochemistry’ describes the measurement of reversible electrode potentials overpotentials double-layer and adsorption phenomena surface area and porosity and electrode processes. These volumes do much to remedy the lack of authoritative summaries on the techniques of electrochemistry. Finally since the electrochemistry of future generations depends to some extent on the education given in this one some notes on a few of the many recent texts may be of interest. Whereas the importance of mathematics as an integral part of chemistry has been recognized,” the gap between the mathematical grasp of the average student and that which writers would like them to have is much in evidence.Such is the case in the finely produced but difficult new edition of Moore’s ‘Physical Chemistry’,’ where the treatment of electrochemistry is commendable but the omission of the concise summary of ‘ionic equilibria’ from the previous edition is regretted. Bockris continues to add to his now formidable output. With Fredlein he has compiled a stimulating monograph ‘A Workbook of Electrochemistry’,’’ which leans towards the more recent develop- ments of the subject. It will provide insight and amusement to research workers and a challenge to the more sophisticated undergraduate. A more conventional work ‘Electrochemical Science’,’ reproduces much of the material of ‘Modern Electr~chernistry’’~ in a shorter but still readable form.It has the authors’ characteristic emphasis on the chemistry of electrode processes and contains more than a suggestion of propaganda. A short tidy text25 in the Oxford Series contains a good summary of the chemistry of molten salts but surprisingly gives only passing mention to the solvation of ions. 2 Structural Aspects The structural properties of water6 and simple sol~tions~*’~ continue to receive attention. While new attempts to describe the pure liquid favour the cell” and lattice’* models and the importance of quantum effects in hydrogen bonds is ~tressed,~’ a good description of the heat capacity is still lacking. Walrafen continues his experimental approach to the problem with a study of the weak l9 ‘Techniques of Electrochemistry’ ed.E. Yeager and A. J. Salkind Wiley New York 1972 Vol. 1. ’O C. A. Coulson Chem. in Britain 1974 10 16. 2’ W. J. Moore ‘Physical Chemistry’ Longmans London 1973 5th edn. (U.K.). 22 J. O’M. Bockris and R. A. Fredlein ‘A Workbook of Electrochemistry’ Plenum Press New York 1973. 23 J. O’M. Bockris and D. M. DrBziC ‘Electrochemical Science’ Taylor and Francis London 1972. 24 J. O’M. Bockris and A. K. N. Reddy ‘Modern Electrochemistry’ Plenum Press New York 1970 Vols. 1 and 2. 25 J. Robbins ‘Ions in Solution (2); An Introduction to Electrochemistry’ Oxford University Press Oxford 1972. * ‘Water and Aqueous Solutions Structure Thermodynamics and Transport Proper- ties’ ed. R. A. Horne Wiley-Interscience New York 1972.l7 0.Weres and S. A. Rice J. Amer. Chem. SOC.,1972 94 8983. D. A. Lavis J. Phys. Chem. 1973 6 1530; D. E. O’Reilly Phys. Rev. (A) 1973 2; 1659. 226 H. P. Bennett0 Raman bands in water.29 The controversial non-electrolyte urea has been termed a ‘structure breaker’ on the evidence3’ of its effect on the activation parameters for aqueous fluidity but a study by Lucas31 of hydrophobic hydra- tion suggests that the variations of solute partial molar properties arise from the properties of the pure liquid rather than from solute structural effects. Clearly some separation into specific hydrogen-bonding effects and hydrophobic effects would be desirable. Separation of different hydrophobic effects is evident from a of the heat capacities of bolaform electrolytes in H20 and D,O; the AC; values are related to the number of carbon atoms between nitrogen centres.The formation of weak hydrogen bonds between neon and water33 may be of more than novel interest in view of the experimental scope of molecular beam electric resonance spectro~copy.~~ Earlier reports35 of structure-induced effects of dissolved gases on the pH of water have now been attributed to the presence of CO in the solutions,36 and the apparent failure of Henry’s law in solutions of mixed gases,37 has been q~estioned.~~ Praises to the scientific method were sung at the funeral of ‘anomalous water’ (p~lywater)~~ which has been removed to the area of silicate chemistry by its dis~overer,~’ but the spectre of thermal anomalies lives on ;a reputable experimental school has detected a sizeable ‘kink’ in the temperature dependence of the energy-volume coefficient for aqueous solutions.41 An interesting stage of development has been reached when fine probes (e.g.spectro~copy,’~*~~.~~ neutron ~cattering~~) ellip~ometry,~~ are revealing details of the molecular structure and dynamics in solutions yet it remains a problem to fit the information into a coherent theory compatible with thermodynamic res~lts~~,~’ and consistent with statistical mechanical appro ache^.^^.^^ Attempts 29 G. Walrafen and L. A. Blatz J. Chem. Phys. 1973 59 2646; also ref. 9. 30 J. L. Macdonald J. Serphillips and J. J. Guerrera J. Phys. Chem. 1973 77 370. 3’ M. Lucas J. Phys. Chem. 1973,77 2479.32 J. A. Burns and R. E. Verrall J. Solution Chem. 1973 2 489; see also F. Franks D. S. Reid and A. Suggett in ref. 9. 33 M. Losonczy J. W. Moskowitz and F. H. Stillinger J. Chem. Phys. 1973 59 3264. 34 T. R. Dyke B. S. Howard and W. Klemperer J. Chem. Phys. 1972 56 2442. 35 E. M. Holleran J. T. Hennessy and F. R. LaPietra J. Phys. Chem. 1967 71 3081. 36 G. H. Fricke R. L. Carpenter and R. Battino J. Phys. Chem. 1973,77,826. 37 D. M. Maharajh and J. Walkeley J.C.S. Faraday Z,1973 69 842. 38 A. L. Myers and J. A. Quinn Nature 1972 239 32. 39 L. Allen New Scientist 1973 59 376; cf. J. Finney ibid. p. 382. 40 B. V. Djerjaguin and N. V. Churaev Nature 1973 244 430; cf. ibid. 1973 245 343. 41 I. Lee and J. B. Hyne Cunad. J. Chem. 1973,51 1885. 42 Ref.14 Chap. 4. 43 M. J. Blandamer ‘Introduction to Chemical Ultrasonics’ Academic Press London 1973. 44 W. K. Paik in ‘MTP International Review of Science Physical Chemistry’ Butter- worths London 1973 Series One Volume 6. 45 P. S. Leung and G. J. Safford J. Solution Chem. 1973 2 525. 46 H. S. Harned and B. B. Owen ‘Physical Chemistry of Electrolytic Solutions’ Reinhold New York 1958. 47 R. A. Robinson and R. H. Stokes ‘Electrolyte Solutions’ Butterworths London 2nd edn. 1959. 48 H. L. Friedman in ‘Modern Aspects of Electrochemistry’ no. 6 ed. J. O’M. Bockris and B. E. Conway Butterworths London 1971 ; H. L. Friedman Chem. in Britain 1973 9 300. 49 ‘Ionic Interactions’ ed. S. Petrucci Academic Press New York 1971 Vol. 1. Electrolyte Solutions 227 to accommodate both the solvational and interionic aspects of such a theory inevitably lead to the question ‘how structured are electrolyte solutions?’ which not only invites the dangers of looking at one sort of structural index in isolation but involves difficulties of definition.Perhaps the best descriptions are those thermodynamic parameters (the more the better) which render unnecessary the terms ‘structured’ ‘degrees of structure’ and ‘structuredness’. Even ‘struc- ture’ can lead to ambiguity. An explicit meaning,” ‘the mutual relation of the constituent parts of a whole as determining its peculiar nature or character’ might be used together with a hypothetical scale for simple substances fixed by the perfectly ordered crystal at one extreme and the completely random gas at the other.Unfortunately these states do not ordinarily exist; the complex electronic structures of solvent molecules give rise to the intermolecular forces which in turn determine the familiar bulk physical properties of a medium.” Meaningful correlation of solvent structural effects may therefore require reference to some system of corresponding states and moves in this direction are already to be found in the field of reaction kinetic^,'^-'^ where AH* -AS* relations are linked with solvent properties. The influence of solvent structure often appears to be minimized at high temperatures where fluid properties tend to converge.54 Reports of AH -AS correlations in the thermodynamic properties of electrolytes are also ~ommon,~*~~-~’ and may be further clarified now that investigations other than those in water at 298 K and 1 atm are on the increase.Some of the recent work at high temperatures and pressures has been inter- preted with a surprising simplicity. For example Norths8 has presented a treatment for equilibrium constants in aqueous solution in which the hydrated solutes are considered to be incompressible and the pressure dependence of AVO is presumed to be proportional to the change in number of solvated mole- cules released in the reaction. A simple relation accounts for the ionization constants up to 12000atm and improves on earlier equations which show deviations above 2Watm. The derivation of solvation numbers from com- pressibilities and ionic vibration potentials however has led to a controversys9 which shows that these coefficients continue to be usefully picturesque6’ but difficult to define unambiguously.Shorter Oxford English Dictionary. ” G. C. Maitland and E. B. Smith Chem. SOC.Rev. 1973 2 181. ” C. E. Waring and P. Becher J. Chem. Phys. 1947 15 488. 53 H. L. Frisch T. A. Bak and E. R. Webster J. Phys. Chem. 1962 66 2101. ’4 H. P. Bennett0 and E. F. Caldin in ref. 9; see also C. M. Criss ref. 14 chap. 2 ’’ E. M. Arnett J. Phys. Chem. 1972,76 2474. s6 J. H. Norman P. Winchell and R. J. Thorn Inorg. Chem. 1971 10 2365. 57 R. Lumry and S. Rajender Biopolymers 1970 9 1125; D. J. G. Ives and P. Marsden J. Chem. SOC.,1965 649. 58 N. A. North J. Phys. Chem. 1973 79 931; CJ L.B. Yeatts and W. L. Marshall J. Phys. Chem. 1972 76 and refs. therein. 59 J. E. Desnoyers J. Phys. Chem. 1973,77 567. 6o J. O’M. Bockris and P. P. S.Saluja J. Phys. Chem. 1972 76 2140. 228 H. P.Bennett0 3 Electrolyte Solution Theory The theory of Debye and Hucke16’ has reached and passed its fiftieth year with little comment. As a vehicle for the extrapolation and correlation of data it has quietly become the cornerstone of our understanding of electrolyte solutions but the present position is here examined in view of the active challenge of modern alternatives. Debye-Huckel Theory.-We can profitably look back on the developments over the past half-century noting’some aspects which may be unfamiliar to many who are usually concerned only with the ‘route to infinite dilution’.Like jazz and short skirts many ideas of the early twenties are in good trim but it appears that some problems remain unresolved. The concept of non-ideality resulting from long-range forces between ions in solution had been considered by many people before 1923 but did not readily gain acceptance in the face of heavy opposition led by Arrhenius. Milner’s (1912) account62 of the electrostatic virial though later found to be fundamentally correct,61 was not popular on account of the complex numerical methods used. A period of confusion and controversy then followed the appearance in 1918 of Ghosh’s ill-fated lattice theory which described the concentration dependence of the osmotic coefficients and conductance behaviour in terms of a simple cube-root law.63 The theory was inadequately formulated and contained errors of fact and logic ;by 1923 it had been discounted and only its postulate of explain- ing electrolyte non-ideality in terms of coulombic effects is retained in Debye’s theory.In the years 1918 -1923 which S~atchard~~ described as a ‘swear word’ period an effective execution of the lattice theory was performed principally by Partington Kraus Kendall and (inevitably) Arrhenius6’ Bjerrum at first made use of the cube-root law,66 but little mention of it was made in the literature until Frank re-examined the empirical basis of the cube-root law and put forward his novel views on the ‘quasi-lattice loud'.^^*^* The way had been cleared for Debye’s theory by the keen interest in some important but empirical work during the years preceding.Lewis and Randall69 had established ionic strength as an ionic concentration scale and Bronsted’s principle of specific interactions7’ underlined the importance of the effects on a given species owing to ions of the opposite sign. (The limitations of the principle “ P. Debye and E. Huckel Phys. Z. 1923,24 185; ‘Collected Papers of P. J. W. Debye’ ed. R. M. Fuoss Interscience New York 1954. ’’ R. S. Milner Phil. Mag. 1912 23 551 ; Trans. Faraday SOC. 1919 15 148. 63 J. C. Ghosh J. Chem. SOC.,1918 113 449 707. 64 G. Scatchard Chem. Rev. 1933 13 1. 65 H. M. Dawson Ann. Reports 1922 19 15. 66 N. Bjerrum Z. Elektrochem 1918 24 321 ;Z. anorg. Chem. 1920 109 275.’’ H. S. Frank and P. T. Thompson J. Chem. Phys. 1959,31 1086; see also R. A. Robin-son and R. H. Stokes in ref. 47. 68 ‘Structure of Electrolytic Solutions’ ed. W. J. Hamer Wiley New York 1959. 69 G. N. Lewis and M. Randall ‘Thermodynamics and the Free Energy of Chemical Substances’ McGraw-Hill. New York. 1923. ’’ J. N. Bronsted and V. K. La Mer J. Amer. Chem. SOC.,1924,46 1098 and refs. therein. Electrolyte Solutions have more recently been re~ealed.~’) Debye’s more rigorous approach achieved its full impact following the appearance of Noyes’ critical English language treatment,72 and in the next ten or so years the theory was applied to many dif- ferent properties of solutions. These developments may be traced in the Annual Reports for this period.65,73-75 The testing of a limiting law requires accurate data extending to very low concentrations but the challenge to experimenters was accepted and amongst the most searching of critical investigations were those of La Mer and ~o-workers,~~,~~ whose solubility determinations were extended to moll-solutions.The results confirmed that in general the limiting law was satisfactorily approached for 1 1 electrolytes in aqueous and non-aqueous solvents and at elevated temperatures but many more stringent tests did not stop the seal of approval being given at a meeting to mark the ‘coming of age’ of the theory.77 At this time the mathematical inconsistency of the Poisson-Boltzmann equation used by Debye was clearly demonstrated by On~ager,~~ and deserves some amplifi~ation.~~,~~*~~~~’-~~ The Poisson equation (1)* is derived from Coulomb’s law and requires that electrostatic fields should be superimposable to give a charge density p(r).4 is (1) * Confusion over units and concentration scales has sometimes led to inconsistencies in Debye-Huckel calculations (e.g. for limiting slopes). SI units are preferred and the following type of formulation is recommended. A is the distance of separation of two point charges which gives a coulombic interaction energy IEl = 2kT joules (i.e. the Bjerrum distance) and A and B are the familiar non-SI constants of the theory where E~ is the permittivity of a vacuum and E the relative permittivity .(or dielectric constant) of the solvent. 71 R. H. Wood and R.W. Smith J. Phys. Chem. 1965,69,2974. 12 A. A. Noyes J. Amer. Chem. SOC. 1924,46 1080 1098. 13 J. E. Coates Ann. Reports 1925,22 27; J. E. Coates and J. A. V.Butler Ann. Reports 1926 23 21 ;H. Hunter Ann. Reports 1927 24 22. 74 J. H. Wolfenden Ann. Reports 1932 29 21. 7s R. P. Bell Ann. Reports 1933 30 21. 76 V. K. La Mer C. V. King and C. F. Mason J. Amer. Chem. SOC. 1927 49 410; J. W. Williams Chem. Rev. 1931 8 303. 71 Chem. Rev. 1933 13 1. 78 L. Onsager Chem. Rev. 1933 13 73; CJ R. H. Fowler Proc. Cumb. Phil. SOC.,1925 22 861. 79 F. Vaslow ref. 26 Chapter 12. 80 B. E. Conway in ‘Physical Chemistry An Advanced Treatise’ ed. H. Eyring Academic Press New York 1970 Vol. 9B. 81 G. Braunstein in ref. 49. 230 H.P. Bennett0 the average potential at any point. Strictly speaking this equation is only valid for a system of charges at rest. The charge density (p = &eni) is found from the Boltzmann equation in the form n = n exp [ -W(r)/kT] (2) where W(r)is the potential of mean force and no is the average number of ions at any point in the bulk of solution. Equations (1) and (2) are combined to form the Poisson-Boltzmann (PB) equation The relation between charge and potential in equation (2)is non-linear and W(r) cannot be identified with the average electrostatic potential 4 of equation (1); fluctuations in W(r)give exponential movements of ions rather than linear ones as required by equation (l).79The combination of equations (1) and (2) also leads to the nonsensical result that the electrostatic effects of two ions k and 1 do not have the symmetrical reciprocal relationship required for thermodynamic consistency (4) (2) = (2) Most authorities agree that for a sufficiently dilute solution the PB equation may be linearized thus allowing 4 to be used in the calculation of average charge distribution.Even in dilute solutions however there is a finite probability that ions will approach one another to within a distance where Ze4 > kT and it is therefore only at zero concentration that the equality of Zec$ with W is valid and the inconsistency disappears [equation (5)]. The linearization should be regarded as a necessary requirement of the primitive Debye-Hiickel model. W lim [exp( -W/kT)]= 1 N 1 -(5) m-0 kT The inclusion of the ion-size parameter ‘a’ and higher terms of the expansion lead in the simplest case of a 1 1 electrolyte to equation (6),for the activity coefficient in which X and Y terms are functions of IC and a and the cubic and lny = -A,Born*(l + aBOrnf)-’+ -2 -2Y3) + -2 (2 )’(? (2 )5 higher terms are customarily neglected unless E is small.** Experimental results are better fitted by judicious adjustment of a a catch-all correction for close- range and ‘hard core’ effects by including the higher terms and by use of an additional linear parameter in m.79 These methods are to be preferred to the use 82 T.H. Gronwall V. K. La Mer and K. Sandved Phys. Z. 1929,29 358. Electrolyte Sohtions 231 of polynomial fits which obscure the theoretical basis of the extrapolation and sometimes conceal experimental inaccuracies but not too much significance can be attached tothe value of a.The certainty of values of a derived from experi- mental ‘best fits’ depends greatly on the accuracy of the res~lts.~~~*~ None of these practically expedient procedures solves the fundamental problem however nor does the assumption of Bjerrum ion-pairing which avoids the inconsistency by arbitrarily defining the onset of association in terms of A (even when r > A, Ze+/k T need not be small). The inconsistency of association constants obtained from different theories and from experiment has led recent investigators85986 to refine the ion-pairing concept in relation to the Debye-Huckel equation.One treatment shows that a degree of dissociation at infinite dilution can be expressed as where b is the Bjerrum parameter defined by The only arbitrary parameter is a so that for purely electrostatic attraction no other assumptions are required by the model. Nevertheless all extensions to the Debye-Huckel equations must be regarded as semi-empirical and since Onsager and many others have failed to find a satisfactory solution there would seem to be little hope for the primitive model although it continues to attract attention.87i88 It would be surprising if experiment did not reveal evidence of the theoretical limitations mentioned above but the only serious early misgivings were those arising from Lange’s determinations of heats of solution (AHsol)and dilu- ti~n.~**’~*~’ The limiting law is approached but not convincingly and large deviations from the limiting slope plus the specificity of effects for different ions could not be adequately accounted for.The effect was attributed to a net decrease in long-range ion-solvent interaction possibly the first time that the two types of interaction had been linked. A thorough examination of tests of the theory reveals that many critics have been generous especially though not exclusively for cases involving non-symmetrical and higher valency electrolytes and solvents of low er for which the consequences of the inconsistency of the PB equation are more serious.80 To state that the theory is obeyed ‘less well’ for these cases is an understatement only the sign of the effects can be predicted with any 83 T.Mussini Chimica e Zndustria 1973,55 637. 84 H. P. Bennett0 and J. J. Spitzer J.C.S. Furaday Z 1973 69 1491. H. Falkenhagen and W. Ebeling in ref. 49. 86 H. Yokoyama and H. Yamatera Chem. Letters 1973 337. C. W. Owthwaite Mol. Phys. 1972 21 and refs. therein. A. S. Blokhin and G. A. Martynov Electrochimiya 1973 4 494. E. Lange and A. L. Robinson Chem. Rev. 1931,9 89. 232 H. P. Bennett0 ~onfidence.~~ Even when conditions are favourable the slope of an extrapolation may not always approach the theoretical limiting value the line may be linear but the slope in error or the discrepancy can be greater for larger ions when the approximation should be most appropriate.That the ion-size or other parameters may provide a better extrapolation does not affect the argument that the law is less satisfactory than one might expect for dilute solutions where KU << 1 even allowing for experimental error. It has recently been ~tressed~*~*~~ that the excess functions for electrolytes are subject to the 'compensation law'57990 through which enthalpic and entropic contributions to a free energy function tend to cancel. If this is also true of the coulombic contributions AH and AS functions should provide a better test of interionic theories. Thus the temperature coefficients of activity (partial molal heat contents) are more sensitive than the y values themselves. Clear evidence of odd behaviour is described by Harned and and we may look for examples in recent calorimetric work in water and in mixed and non-aqueous solvents.Many instances of satisfactory agreement with theory may be fo~nd,~'-'~ have measured but there are notable exceptions. Chang and Cri~s~~ AH,, for NaClO in NN'-dimethylformamide in the range 10-75 "C. At lower temperatures the extrapolations are satisfactory but in the higher range the observed limiting slope reaches nearly four times the theoretical value. Similar discrepancies are noted for solution of bivalent salts in solvents of high dielectric constant,95 reminiscent of earlier results in liquid ammonia.96 (In this solvent it is difficult to rationalize y+ results from e.m.f. studies97 with ion-pairing invoked in the interpretation of conductance beha~iour.~~ The slope of the AH,, us.rn) plot rapidly increases in dilute solutions and it must change direc- tion dramatically in order to approach limiting law behaviour ;99 further accurate examination perhaps employing flow microcalorimetry,' O0 would be desirable.) Campbell and Bhatnagar"' have measured AH,, for NaClO and dioxan- H,O mixtures and find that the experimental concentration dependence crosses the positive theoretical slope as the dioxan concentration is increased. Near the 50% composition it changes sign and in 70% dioxan it is markedly negative. 90 D. J. G. Ives and P. Marsden J. Chem. SOC.,1965 649. 91 W. L. Marshall and R. Slusher J. Chem. Thermodynamics 1973 5 189. 92 D. D. Ensor and H. L. Anderson J. Chem. and Eng.Data 1973 18 205. 93 C. F. Boudreau and C. A. Wulff J. Chem. Thermodynamics 1970 2 125. 94 S. Chang and C. M. Criss J. Solution Chem. 1973 2 457; see also A. S. Levine and S. Lindenbaum J. Solution Chem. 1973 2 445; C. de Visser and G. Somsen J.C.S. Faraday I 1973 69 1440. 95 A. Finch P. J. Gardner and C. J. Steadman J. Phys. Chem. 1971,75 2325. 96 S. R. Gunn and L. C. Green J. Phys. Chem. 1960 64 1066. 97 J. Sedlet and T. De Vries J. Amer. Chem. SOC.,1951 73 5808; and ref. 41. 98 V. F. Hnizda and C. A. Kraus J. Amer. Chem. SOC.,1949.71 1565. 99 Such a change seems unlikely in view of a comparable picture for the solubilities of salts at very low ionic strengths; see V. J. Anhorn and H. Hunt J. Phys. Chem. 1941 45 35 1. loo J.-L. Fortier P.-A.Leduc P. Picker and J. E. Desnoyers J. Solution Chem. 1973 2 467. Io1 A. N. Campbell and 0.N. Bhatnagar Canad. J. Chem. 1971.49 217. Electrolyte Solutions 23 3 The AH,, us. mf plot shows a minimum at mf = 0.6 and the proposition is made that dioxanation of ions decreases in favour of hydration as the concentration is increased. This unusual effect calls for investigation at lower concentrations and suggests that the interdependence of interionic effects and structure in a mixed solvent is greater than has been previously supposed. It also shows that much care must be exercised in using extrapolation procedures. The alkylammonium halides' O2 are a class of electrolytes which appear to exhibit 'non-electrical attractive forces' in ~olution.~'~' Recent AH,, results illustrate the variety of O3 concentration dependences in H20'049'05 and in N-methylacetamide (NMA),'" while the extrapolation of apparent molal values (4")is found to be similar in H20,106.107 NMA and f~rmamide.''~ The evidence does not bear out earlier well-supported interpretations invoking water-structure,"' but again might appear to connect the coulombic and structural contributions and point to an interpretation in terms of a 'statistical lattice' model.'09 Wood and Belkin' lo find low values for excess enthalpies and entropies of tetraethanolammonium bromide in water in the range 0.5-3m by comparison with tetrapropylammonium bromide.The substitution of hydroxy-groups for terminal methyl groups results in a drastic change of properties and is attributed to the destruction of hydrophobic hydration ;the solvation interactions thus appear to be predominant in these concentrated solutions.It is clear from past and recent evidence that deviations from the Debye- Hiickel law cannot unambiguously be attributed to solvation or ion-association effects. Debye6' always emphasized the limiting character of his law but he believed' ' the shortcomings of his simple coulombic description were due to non-coulombic effects. But though these effects may well be important there seems to be enough theoretical and experimental evidence to suggest that the coulombic picture provided for moderately dilute solutions is an incomplete one and it may be argued that in consequence many assignments of ion-pairing and structural effects of ions are questionable.A pessimistic view is that the descrip- tion of the effect of ions in the solution on a particular ion is only correct when there are no ions present or that the theory starts correctly in the limit of infinite dilution and gets steadily worse. Frank's assessment that the linearized PB equation cannot realistically describe the distribution of 1 1 electrolytes in solutions more concentrated than 0.001m,applies the 'limiting axiom' to the 'real' solution and poses the question 'can the model describe any real solution?' Io2 T. S. Sarma and J. C. Ahluwalia Chem. SOC.Rev. 1973 2 203; W.-Y. Wen ref. 26 chap. 15. '03 G. Kelbg Z. phys. Chem. (Leipzig) 1960 214 8 26 141 153. J. Falconi Ph.D.thesis University of Delaware 1972; see W. Y. Wen J. Solution Chem. 1973 2 253. Io5A. S. Levine and R. H. Wood J. Phys. Chem. 1973,77 2390. lo6 F. Franks and H. T. Smith Trans. Faraday SOC.,1967 63 2586. lo' R. W. Kreis and R. H. Wood J. Phys. Chem. 1971 75 2319. Ref. 7 p. 40. log Ref. 46 p. 367. 'lo R. H. Wood and F. Belkin J. Chem. and Eng. Data 1973 18 184. ' P. Debye in 'Electrolyte Solutions' ed. B. Pesci Pergamon Oxford 1972. 234 H. P. Bennett0 This opinion is made more palatable by the existence of alternative approaches (see ref. 112 and sections below) and does not imply that the primitive model has nothing further to offer. Several lines of investigation show that a consistent merging of equations (1) and (2) must produce an ill-defined oscillating solu- for 4 at some high concentration when KU -1-2 which might ti~n'~*"~~''~ describe the onset of quasi-lattice behavio~r~~,~' or discontinuities in solution proper tie^.^^ Another possibility is that in a real solution the atmosphere- potential near an ion is dominated by the nearest ions may be of positive or negative sign and has non-spherical symmetry.This would require a general- ized Poisson law of the form (9),which could provide more meaningful solutions v2@ = fK2$ (9) than the PB equation. In replacing equation (9)by equation (3),two tacit assump- tions are made which are glossed over in most discussions. The assumption of spherical symmetry allows the field around an ion to be the same in all directions so that it is a function of the distance and not the direction;'15 this rules out discreteness of charge6' in the ionic atmosphere.The assumption of one partic- ular sign denies the possibility of lattice formation. Neither assumption seems to be obvious or logical and in making the simplification it appears that a work- able solution has been trapped in the PB equation which in its linearized form imposes an idealized model on the three-dimensional structure. To conclude the problem which remains is not the one which Debye and Huckel tackled magnificently to produce an attractively simple limiting law and an eminently applicable picture of the ionic atmosphere ;rather it is to find an alternative for the concentration range of practical importance.'' Statistical Mechanical Calculations.-By comparing the calculated thermodyna- mic properties of model solutions with the thermodynamic excess functions of real aqueous solutions it is possible to reach detailed conclusions about the contributions of solvation to interionic effects and to other solute-solute forces.',' '791 '* No attempt is made here to discuss the many recent results in this field but a particularly interesting summary by Rasaiah' l9 is recommended. In simple terms the method sets out to calculate the potential of average force W(r),represented by the sum of pair potentials for all configurations.'20 For ions k I these pair potentials are represented by an equation of the type (lo) I" D. G. Hall J.C.S. Faraday 11 1973 69 975. F.H. Stillinger and R. Lovett J. Chem. Phys. 1968 48 3858. J. C. Rasaiah D. N. Card and J. P. Valleau J. Chem. Phys. 1972 56 248; J. C. Rasaiah ibid. p. 3071. I ' Ref. 46 p. 47. l6 W. D. Bancroft J. Amer. Chem. SOC.,1926 48 94. I H. L. Friedman 'Ionic Solution Theory' Wiley-Interscience New York 1962; H. L. Friedman C. V. Krishnan and C. Jolicoeur Ann. New York Acad. Sci. 1973 204,79. I l8 R. 0. Watts in 'Statistical Mechanics' ed. K. Singer (Specialist Periodical Reports) The Chemical Society London 1973 Vol. 1 p. 56. 11' J. C. Rasaiah in ref. 9. J. E. Mayer J. Chem. Phys. 1950 18 1426. Electrolyte Solutions 235 in which the terms on the right are the respective contributions from long-range (coulombic) and short-range interactions.In the derived binary distribution function the first term is expressed as an expansion in (ekel/4mO~,r) which in its first approximation yields the Debye-Huckel limiting law directly. Without provision for the short-range repulsive forces however the higher approximation of the expansion is divergent so that the method faces a situation paralleled by the use of a in the Debye-Huckel theory and can never be entirely rigorous.’ 2’ 9122 The sensible solution of the equations requires evaluation of the second ‘hard- core’ term of equation (lo) which caters for the effects of solvation solvent 4kdr) = okl(r) + (10) structure ionic polarizability quantum-mechanical repulsions etc. and it is in the calculation of these contributions from reasonable physical models that many recent advances have been made.The concepts of structural effects of ions on the medium are incorporated by considering the properties of the solvent co-spheres’ 23*124 which surround each ion. When overlap of co-spheres occurs the sum of the co-sphere volumes is reduced; the return of a portion of solvent to its ‘normal state’ is considered to give a free energy change so that the change in the chemical state of the solvent contributes to the potential of force between the solute species. This contribution called the Gurney potential,’ l7 is correspondingly assigned to the term u;.(r). An interesting comparison is made with the model for hydrophobic interactions used by Yaacobi and Ben-Naim12’ in discussing the excess functions of methane and ethane in water-ethanol mixtures.In co-sphere treatments the operation of the ‘compensation la^'''^'^ for changes in solvent structure within the co- spheres leads to some uncertainties and the definition of co-sphere volume seems to be rather arbitrary. A further refinement of the model takes into account the ‘granularity’ of the solvent,’ l9 which superimposes a small oscillation upon the potential function and may have a considerable effect on the short-range forces. Models of solutions have been studied’17 up to a concentration of 1 mol 1-’ for alkali halides alkaline earth halides tetra-alkylammonium halides non- electrolytes and various mixtures. When the solvation parameters are adjusted to fit the experimental data good agreement is claimed for osmotic and activity coefficients heats of dilution and apparent molal volumes.The picture which emerges is to some degree exigent of the intuitive model used for the calculations and in view of the corrections for the various interactions it is difficult to judge whether the description of the solution is realistic or merely functional. For the purposes of application the theory would seem to offer a significant improvement The necessity to assign finite radii to the ions in all statistical approaches was first realised by H. Kramers. See R. P. Bell ref. 75. 12’ R. H. Stokes J. Chem. Phys. 1972 56 3382. H. S. Frank Z. phys. Chem. (Leiprig) 1965 228 364. 124 R. W. Gurney ‘Ionic Processes in Solution’ Dover New York 1953 p. 251. 12’ M.Yaacobi and A. Ben-Naim J. Solution Chem. 1973,2,425; see also H. L. Friedman and C. V. Krishnan in ref. 9. H. P. Bennett0 on the extended Debye-Huckel theory if simple methods for representing the various parameters can be devised. Care will be needed in using the theory since most experimental work is done at constant pressure whereas the theoretical equations apply to a state of osmotic equilibrium; i.e. V is the independent variable.8' Friedman has discussed the conversion of conventional thermo- dynamic relations from the Lewis-Randall convention to the forms required for use in the McMillan-Mayer system.'26 The study leads to the conclusion that for nearly ideal mixtures liquid structure effects associated with the packing of molecules contribute a negative term to the potential of force between solute particles in the solvent.Further results of statistical calculations will be awaited with interest especially when they are complemented by the results of computer simulation 'experi- merits' 118,119.12 7 As in the Debye-Huckel theory the statistical picture for electrolytes having ions of unequal radii presents some difficulties and it would be useful (but expensive) to have comparisons from the Monte Carlo method for ions which do not have the rather conventional value of 4.25 Both types of study have yet to attempt the description of solutions in solvents other than water surely a major requirement for any solution theory and until they are tested in this way the results and some of the underlying concepts should perhaps be viewed with reservation.Even for the interactions in a system of noble gas molecules the pairwise additivity assumption is an approximation,' 28 and total confidence in this postulate for solutions cannot be upheld in view of the admitted possibility of simultaneous overlap of more than two co-spheres.' 17i129 An other source of errors may exist in the energetic co-operativity of hydrogen-bonding in water,6 which imposes its own orientational restrictions. Unfortunately the effects of orientation-dependent forces have not been evaluated although it is known that the number and kind of terms which appear in the series for the interaction energy of the pair correlation function are related to the symmetry of the molecules.' 30 (An interesting new application of n.m.r.spectroscopy may throw light on such problems; it has been shown that interionic forces can be studied through the enhancement of spin relaxation times for 'Li' produced by excess of Mn2+ or Ni2+ in the A separate question relates to the radial symmetry assumed for the coulombic potential ;as in the treatment of the Poisson equation (9) it has always been expedient to rule out any dependence of the potential on the direction of the radius vector. Whether this is justified or not may have to be decided by more rigorous tests of the statistical methods against experimental data. A complex approach to the thermodynamics of aqueous electrolytes has recently been formulated by Pit~er.'~~ A system of equations is developed on the basis of an analysis of the Debye-Huckel model together with the results of lZ6 H.L. Friedman J. Solution Chem. 1972 1 387 413 419. 12' D. N. Card and J. P. Valleau J. Chem. Phys. 1970 52 6232. lz8 J. S. Rowlinson Discuss. Faraday SOC.,1965 No. 40 p. 19. lz9 F. Vaslow J. Phys. Chem. 1967 71,4385. I3O W. A. Steele J. Chem. Phys. 1963 39 3197. 13* L. P. Hwang C. V. Krishnan and H. L. Friedman Chem. Phys. Lerrers 1973,20,391. K. S. Pitzer J. Phys. Chem. 1973 77 268; K. S. Pitzer and G. Mayorga ibid. p. 2300. Electrolyte Solutions 237 calculations for 'hard core' effects and an ionic strength dependence is proposed for the effect of short-range forces in binary interactions. The equations yield values of activity and osmotic coefficients for single and mixed electrolytes which are in fair agreement with experiment up to concentrations of several molal a distinct improvement on the earlier formulations of S~atchard~~ and of Guggen- heim.'33 A similar objective is achieved by Robinson and Bates,'34 who use a simpler hydration convention which permits calculation of single ion activities for unassociated electrolytes.Specific differences in values of yi are accounted for in terms of solvent activity and a fixed hydration number characteristic of each ionic species which is assumed to be zero for C1-. Both of these treatments provide a valuable means of estimating ionic activities at high concentrations. Solutions as Lattices-The idea that ions in a solution will naturally tend to assume a lattice-like arrangement springs from intuitive feeling.This concept has been adamantly resisted since the time of Gh~sh~~ by most electrochemists but is acceptable to students of fused salts and concentrated solutions.49 While it is easy to appreciate that quasi-crystalline behaviour can exist in a concentrated solution,' 35 most authorities doubt the integrity of such structures in more dilute solutions on the grounds that any simple 'lattice expansion' would be eradicated by thermal motions. It is often suggested however that a change of structure occurs at some critical concentration where the oscillating nature of electrical potentials which is characteristic of the lattice vanishes and the solution there- after takes on the cloak of the Debye-Huckel lattice Both the experimental evidence79 for such discontinuities and the theoretical predictions of where they occur are uncertain but the concentration is considered to be beyond the range (ca.0.0014.5 moll-') in which many properties of solutions exhibit a dependence on the cube-root of concentration. The cube-root relation is an accurate natural law which has been well described by Frank68*69 and other~,'~*'~~*' 37 and is often rediscovered by experimentalists after a period of torture at the hands of the ion-size parameter of the Debye-Huckel the~ry.~~,'~~ Thus the activity coefficients are well represented by an equation of the form logy = -Ac' + BC (11) where A is now a Madelung-like constant for the crystal and B is a constant of unknown significance.In a recent report Bahe' 39 correlates the partial molal heat contents of nine electrolytes in water against a cube-root function (Figures 1 and 2). This picture may be compared with the one presented by Harned and and else~here.~~,~~.~~ Some theoretical justification for the constant B of equation (11) is given'39 in terms of repulsive energy (ccl/r3) generated from E. A. Guggenheim and J. C. Turgeon Trans. Furuduy SOC.,1955 51 747. '34 R. A. Robinson and R. G. Bates Analyr. Chem. 1973.45 1666. See also ref. 9. 135 H. Bertagnolli J.-V. Weidner and H. W. Zimmermann Ber. Bunsengesellschafr phys. Chem.. 1974,78 1. 136 E. Glueckauf in ref. 68. 13' J. E. Desnoyers and B. E. Conway J.Phys. Chem. 1964,68,2305. 13' A. Vesala Suomen Keni.. 1973. 46,43. '" L. W. Bahe J. Phys. Chem. 1972 76 1062 1608. H. P. Bennett0 Figure 1 The variation of apparent relative partial molar heat contents (negative heats of dilution) of NaCl with the cube root of the molar concentration at 25 "C at low con- centrations. Experimental slope 217.0; predicted slope 21 7.5 (Reproduced by permission from J. Phys. Chem. 1972,76 1609) the interaction of the dielectric gradient near ions with the classical coulombic field first predicted by Friedman.' ' Though B still remains an adjustable parameter the existence of quasi-lattice behaviour in solutions of moderate concentration seems to be the most acceptable interpretation of the results and receives support from a consideration of the working range of the law.Its extension into the more dilute range is generally more pronounced for electrolytes of higher valency which usually have higher lattice energies. Where the limiting law is closely approached the cube-root law is less in evidence and vice versa. This is well illustrated by the precise activity coefficients of HCl. In H,O the limiting law is fair but the cube-root relationship is e~act;"~.'~~ in methanol the cube-root law similarly extends to below 0.002rn.84In general there is an overlap of the concentration ranges in which the two laws apply and though this makes the analysis of results difficult it may give a clue to the manner of formation of the Ghosh lattice. When ions are progressively added to a Debye-Huckel cloud each is presumed to be fully used in the formation of ionic atmospheres.For large values of KU the electrical free energy is given by Gclcc= ( -z~e2/4n&,&,a) (12) comparable with the coulombic stabilization for a cubic crystal having a as the smallest anionation distance; only the 'Madelung constant' is missing. 140 I4O R. A. Robinson and R. H. Stokes ref. 47 1st edn. 1955 p. 238. Electrolyte Solutions KCL NaCl KB r t t-\"\ t t \O I I I 1 0.2 04 0.6 0.8 1.0 1.2 1.4 1.6 t/mol 1-1 Figure 2 Correlation of I,(= R -Fl;) with concentration for 1 1 electrolytes at 25 "C. Each division on the ordinate represents 100 cal mol-'. Data for each salt are displaced 100cal mol-' from euch neighbour and the right angle adjacent to each salt represents the origin (0,O) for that salt (Reproduced by permission .from J.Phys. Chew. 1972 76 1609) However the electrical stabilization predicted by the limiting law is too great. The real behaviour is closer to that expected for build-up of a lattice in which successive additions of ions contribute less and less to the energy of the dis- tr1buti0n.l~~The two representations can be both compatible and comple- mentary since a lattice-cloud presumably degenerates on dilution and takes on spherical character at infinite dilution where it is indistinguishable from the Debye ionic atmosphere. The assumption of a radially symmetric distribution of ions is probably correct in this limit but there is no guarantee that it remains so in solutions of practical interest where the symmetry might become or be of a type dictated by the solvent or be typical of the solid crystal.At what point such a change might be expected to begin is debatable and it could be 14' J. Sherman Chern. Reo. 1932 11 93. 14' L. Onsager J. Phys. Chem. 1939,43,189. The minimum energy for a set of point dipoles is attained in a hexagonal close-packed crystal. 240 H. P.Bennett0 argued that for a 1 1 electrolyte it occurs when more than two ions are present in the solution. The solvent is imagined to play a role in the formation of a lattice-like dis- tribution. It is easy to envisage a difference between the solvent lying between ions of like sign and that lying between ions of unlike sign and the popular co- spherelZ4 concept might therefore appear in a coulombic guise.Dielectric gradient effects near the ions are also clearly im~0rtant.l~~ It should be noted that recent Monte Carlo calculations for a primitive model 1 1 electrolyte (r = r = 4.25A)fail to predict any distinct oscillatory character in the dis- tribution function for a solution at high concentration.’ 27 [Unsymmetrical and high-valence electrolytes do appear to give oscillations in g(r),but probably not in ‘dilute solutions’.] The computer simulation does not however take into account the molecular structure of the solvent though this factor can be built into statistical models. The main weakness of the quasi-lattice concept is the lack of a firm theoretical basis.Further tests of Bahe’s theory’ 39 are awaited with interest but the major problem is the integration of the two observed laws. Unlike the Debye-Huckel theory which is firmly anchored by the limiting-law the lattice theory seems to provide no common point of reference for all electrolytes. The choice of the reference state is however rather one of convenience and some other state such as that of ‘persisting structure’ may eventually prove to be more acceptable than infinite dilution.’39 It appears that a basic postulate of structure is necessary in setting out to describe any distribution function ; in Debye’s formulation it is implicit in the statement that ‘in a volume of solution near a central ion there are more ions of unlike sign than of like sign’,6’ and an alternative postulate may be hidden in some other empirical relationship such as the cube-root law.The scope for testing the idea is at present surprisingly limited because so much work has been concentrated on dilute solutions in order to derive precise standard state solvation coefficients. Sensitive tests in many solvents will be necessary to distinguish between a Debye lattice and any other since the free energy difference is expected to be ~ma11.l~~ However the enthalpies of the two types of distribution will differ and a fuller account of these parameters should clarify the nature of structure in solutions of intermediate concentrations. 4 Thermodynamics of Ionic Solvation The elucidation of primary interactions between ions and solvate molecules in the gas phase continues.Leaders in this field are Kebarle and co-workers who have extended their mass spectrometric studies of hydrated protons,’44 and have placed the strength of the interactions of some solvent molecules with C1- in the order H,O > MeOH > MeCN just that expected from the study of ‘solvent activity coefficient^'.'^ Solvation of 0,-by these ligands is also 143 R. W. Gurney ‘Ions in Solution’ Dover New York 1962. 144 R. Yamdagni J. Payzant and P. Kebarle J. Amer. Chem. SOC.,1972,94,7627;Cunud. J. Chem. 1973 51 2507. Electrolyte Solutions 241 observed and a later study throws light on the interactions of protons in mixed hydrate-ammoniate complexes. 14’ Su and Bowers’46 have investigated the effect of molecular size in ion-polar-molecule collision reactions of C,H,+ with NH, MeNH, Et,NH and Me3N and correlate the rate constants for proton- transfer with the polarizability of the substrate.An interesting theoretical of cation hydration compares the results of semi-empirical and ab initio calculations with experimental results from mass spectrometry and there is hope therefore that the results of gas-phase and theoretical studies will eventually be usefully compared with estimates of primary solvation parameters obtained from solution work. An assessment of the relative influence of the primary interactions and that of solvent structure would provide insight into many present problems particularly in mixed aqueous systems.These continue to be popular for obvious practical reasons but are prone to uncertainties in the interpretation of results. One important aspect concerns the bonding effects in mixed solvate complexes and is of concern to those interested in ligand-sub- stitution proces~es.’~~ Another is that perennial headache specific solvation which is yielding to examination by n.m.r. methods. 149 Much information in mixed solvents has been accumulated from e.m.f. studies,’” in the form of the free energies of transfer of electrolytes from water (AGP). For many years Feakins and co-workers have been resolutely active in this field,”’ and have latterly received much support notably from De Ligny,’” Kundu,’ 53 Roy,’ and their co-workers. The methanol-water system is partic- ularly well chartedlS4 with reliable (and some not so reliable) data and has been a centre of attention for those attempting to evaluate single-ion solvation coeffi- cients in different solvent^.'^^'^^ A recent report discusses cross-checks on the differences AGP(C1- -Br-) AGP(C1- -I-) by independent studies both of the more conventional HX cell and of double cells which incorporate amalgam electrodes.The agreements found are gratifying and important in an area where the certainty in interpretation of subtle solvent effects may hinge on the relia- bility of data. Inflections in the plots of AGp oersus solvent composition have been tenuously attributed to the ‘non-electrolyte effects’ which may be elaborated as follows. In order to become solvated a solute must find or create some room in the solvent structure and for the simplest case the cavity-forming process may be 14’ J.D. Payzant A. J. Cunningham and P. Kebarle Canad. J. Chem. 1973,51 3242. 146 T. Su and M. T. Bowers J. Amer. Chem. SOC.,1973,95 7609 761 I. 14’ P. A. Kollman and I. D. Kuntz J. Amer. Chem. SOC.,1972 94 9236. I 48 D. N. Hague in ‘Inorganic Reaction Mechanisms’ ed. J. Burgess (Specialist Periodical Report) The Chemical Society London 1973 Vol. 2. 149 A. K. Covington K. E. Newman and T. H. Lilley J.C.S. Faraday I 1973 69 973; A. Clausen A. A. El-Harakany and H. S. Schneider Ber. Bunsengesellschaft phys. Chem. 1973,77,994. 150 M. Salomon in ref. 14. ” D. Feakins and P. J. Voice J.C.S. Faraday I 1972 68 1390.I 52 D. Bax C. L. De Ligny and M. Alfenaar Rec. Trav. chim. 1972,81,452. 5’ K. K. Kundu and K. Mazumdar J.C.S. Faraday I 1973,69,730,806 and refs. therein. ’” C. F. Wells J.C.S. Faraday I 1973,69 984. Is’ 0.Popovych Crit. Rev. Analyt. Chem. 1970 1,73. H. P. Bennett0 quantified in terms of the shape and size of the molecules and the intermolecular forces; this concept is used in the scaled-particle theory description of simple solutions.’ 56 For a dissolved ion an analogous effect is presumed to contribute to the free energy in addition to electrolytic effects which are of both short and long range. [A contribution from cavity-formation is included in the term &(r) of the statistical mechanical description mentioned above.] All attempts to unravel the two types of contribution would appear to have an arbitrary basis since the structural influences of an ion and a non-electrolyte are intrinsically differentlS1 but in principle it is possible to effect a separation on empirical grounds e.g.a value of 4G:(ion) may be corrected for the ‘non-electrolyte effect’ by subtraction of the Aq for a noble gas molecule of the same size as the ion.’52 It turns out however that a more suitable subtraction is one which uses the noble gas molecule ofthe same electronic structure as the ion rather than one of the same size.’ ’ This is reasonable if one considers firstly that the effective radius will be slightly larger than the crystallographic one (a hydrated radius of the Stokes type is not appropriate in view of the great lability of the primary solvation shells) and secondly that an important contribution to the close- range interaction will come from dispersion interactions.The new procedure gives an improved linearity to the plots of AGP(MC1) versus reciprocal cation radius and it appears that the contributions to the solvation of alkali-metal cations are simply (i) primary interactions of the ‘acid-base’ type (ar; ‘),Is7 (ii) secondary Born-type interactions and (iii) dispersion interactions normally included in (i). According to this model the inflections in the plots of AG,’ versus solvent composition for both cations and noble gases arise mainly from the changes in the dispersion interactions (i.e.‘polarizability’) afforded by the solvent which also largely determine the structpral peculiqrities of the medium itself.These ideas are also pertinent for Group I1 cations,”* where the AG values are similarly interpreted with the aid of Pearson’s ‘hard’ and ‘soft’ concept. As a result of the aforementioned correction the single ion values obtained from the univalent cation plots are certainly more reliable than those from any anion plot since in this case the halide-solvent interactions are probably more complex and the extrapolation to r;’ = 0 is a much longer one anyway. However the separation of AGP into single-ion values by any procedure is still hazardous and will remain so until some aspects of ionic solvation are better clarified; but while single-ion quantities are not essential to this better understanding they are undoubtedly of great practical value e.g.in setting up pH scales for mixed solvents.17 Some progress towards understanding the ‘non-electrolyte effect’ in other mixed solvents has been made in a recent study of the thermodynamics of transfer af some non-electrolytes from water to DMSO-water methanol-water and dioxan-water mixtures.’ 59 The transfer of ions to non-aqueous solvents is dealt ”’ E. Wilhelm and R. Battino Chem. Rev. 1973 73 1. D. Feakins and P. Watson J. Chem. SOC.,1963 4734. Is’ D. Feakins A. S. Willmott and A. R. Willmott J.C.S. Furuduy I 1973 69 122. Is9 B.G. Cox,J.C.S.PerkinIZ 1973 607. Electrolyte Solutions with elsewhere,13 but we Mention an experimental approach made to the problem of liquid-junction potentials between different solvents ;'6o some empirical rules may enable the single-ion transfer coefficients to be simply estimated with sufficient accuracy for useful application in physical organic chemistry.Elsewhere Frank16' has returned to the same problem and discusses the computer slmula- tion of the behaviour for 8concentration cell with transference. There would seem to exist a possibility for determining single-ion activities from the rapid time-rise of the cell potential. The marked differences in solvation of cations and anions are generally considered to reside in the primary interactions.' 51 Secondary solvatidn is a complicating factor however and the relative importance of the two types of interaction is not unequivocally established.The problem may be partly resolved through investigations of 'iso-dielectric' sy~terns.~~,'~~ The chemical nature of solvation is revealed in Aq values for solvent mixtufes having a uniform permittivity since the Born-type interactions are invariant and there is thus considerable scope for the application of this method in a variety of mixtures over a wide range of E,. For instance in methanol-propene glycol mixtures methanol is the more 'basic' molecule with respect to ion solvation,'62 and changes of anionic solvation apparently dominate AG in protic-hydroxylic mi~tures.'~ Further work promises to clarify the ways in which the 'acid-base' interactions are modified by co-operative 15' solvent-~tructural,~~~~ 63 and specific solva- tion14' effects.An attempt to link such effects with kinetic parameters in a general way has been recently described. 164 The methods of separation of thermodynamic solvation parameters into single- ion quantities have been widely re~iewed,'~.'~~.'~~~'~~ but some uncertainty still exists concerning 'real' free energie~."~*'~~*'~~ The method based on the direct measurement of Volta-potential differences,' le9 clearly described by Case,'67 avoids the uncertainties of extrapolations of data against some function of the crystal radii,'" or of a similar extra-thermodynamic assumption,' 71 but it requires the estimation of surface potentials. Ibo B. G. Cox A. J. Parker and W. E. Waghorne J. Amer. Chem. SOC.,1973 95 1010. 16' R. N. Goldberg and H.S. Frank J. Phys. Chem. 1972,76 1758. 162 K. K. Kundu A. L. De and M. N. Das J.C.S. Dalton 1972 386 and preceding papers. K. G. Breitschwerdt and H. Wolz Ber. BunsengeseNschaftphys. Chem. 1973,77 1OOO. H. Strehlow W. Knoche and H. Schneider Ber. Bunsengesellschaft phys. Chem. 1973 77 760. Ib5 C. M. Criss in ref. 14. J. I. Padova in 'Modern Aspects of Electrochemistry' no. 7 ed. J. O'M.Bockris and B. E. Conway Butterworths London 1972. 16' B. Case in 'Reactions of Molecules at Electrodes' ed. N. S. Hush Wiley-Interscience London 197 1. '68 J. E. B. Randles Trans. Faraday SOC.,1956. 52 1573. Ib9 B. Case and R. Parsons Trans. Faraday Soc. 1967 63 1221; V. A. Rabinovitch T. E. Alekseeva and L. A. Voronina Elektrokhimiya 1973 9 1434. P.L. Mateo G. G. Hurtado and J. B. Vidalaba Anafes de Quim. 1973 69 717. I" R. Alexander A. J. Parker J. H. Sharp and W. E. Waghorne J. Amer. Chem. SOC. 1972 95 1148. H. P.Bennett0 The surface potential167 is an important property which has relevance to many problems e.g. electrode kinetics,17* but it is only indirectly related to the ther- modynamics of ion solvation. The passage of ions through interfaces in the transfer of complete electrolytes from one solvent to another is a process re- quiring zero work,lS5 and the standard free energy of transfer AG thus adequately describes the differences in solvation energies ; no qualifying term 'hypothetical' is needed That the measured quantities are independent of surface properties is clear from the agreements between transfer data obtained with electrodes having different surface characteristics; e.g.one may use either a calomel or a silver-silver chloride electrode in conjunction with a hydrogen electrode to obtain the same value of AG. The single-ion values obtained by extrapolation are no less real than any others since the implication is made that only the differences in solvation for an ion in two bulk solvents is being considered for which surface processes are of no importance. Though it is sometimes said to be necessary to know 'real' free energies of transfer in order to understand ionic solvation the literature shows otherwise. It might be a logical step (and one that would cause least confusion to outsiders) to omit the term 'real' and to tabulate only free energies of transfer.'Real' values would then require correction by a surface-potential term but the fact that the uncertainties in estimating this term are about as great as those of the extra-thermodynamic assumptions argues for this compromise. Fortunately the results from two types of experiment are in sufficient agreement that the same conclusions about ion solvation are reached. '50*167*169 The direct method of measurement may be refined e.g. by further examination of the concentration dependences of the compensation potentials and surface potentials; the extra- polations on the other hand can be improved along the lines indicated earlier. When the quantitative results from both sources agree it may be claimed that the correct absolute single-ion transfer values have been obtained.An approach which might be followed in the future is the determination of the entropies of transfer from temperature coefficients of the Volta potentials ;an advantage would be that higher temperatures would minimize the surface structural effects and hence the solvent surface potentials. Two important papers on entropies of solution have a~peared.'~~.'~~ One deals with ions in water and gives support to the well-known structural concept of Frank and Wen;'73 the other discusses entropies of transfer from water to non-aqueous solvents. '74 5 Transport and Related Properties The long debate over the relative merits of different forms of the Fuoss-Onsager conductance equation and its modern equivalents appears to be largely resolved ; M.Salomon J. Electrochem. SOC. 1971 118 1609. B. G. Cox and A. J. Parker J. Amer. Chem. SOC. 1973.95 6879. M. H. Abrahams J.C.S. Faraday t 1973,69 1375. Electrolyte Solutions 245 an excellent summary is given by Fernandez-Prini.' 75 The conductivities of 1 1electrolytes can be fairly well correlated but the less popular unsymmetrical and multivalent electrolytes do not so conform and even a sophisticated treat- ment' 76 requires an additional parameter in concentration to fit experimental results. The reasons may perhaps be sought in the same fundamental weaknesses as are present in the Debye-Huckel theory for other than very dilute solu- tion~,~~,~~ and the credibility of the equations proposed also greatly depends on one's faith in the various correction terms which seem to be a function of time and fashion.The impressive agreement of different equations for dilute solutions may convince the investigator that ion-association has some real significance but small values of the' derived constants should be treated circumspectly. In more concentrated solutions where the equations do not agree,' 75 spectro-scopic measurements may provide some useful comparisons and recent n.m.r. work,' 77 anda Raman study,' 78 giveindependent evidenceofcontact and solvent- separated ion-pairs agreeing in one case' 78 with ultrasonic relaxation measure- ments. Any doubts about conductance theory could be partially ascribed to mere prejudice if it were not for the additional evidence from transference number measurements.' 79 The Fuoss-Onsager equation for the concentration depen- dence takes the form for a 1 1 electrolyte where /3 is the electrophoretic parameter.Even in water the results are less than adequately described by this relation,'80 but in other solvents it fails almost ~ompletely.'~~.'~~ Wildly unrealistic values of a are required and there are sharp minima in the plots of t+(c) against c for the limiting transport number (calculated from results at a concentration c using different values of a in the several equations). In Spiro's words,'79 'one is indeed forced to wonder whether the conductance sum cancels out some aspect of theory that is revealed only by testing the conductance ratio'.The little work that has been done on electrolytes of other valence types in water often shows a similar failure of the limiting Onsager 1aw,46*181 and is all too readily dismissed as experimental error. It seems not unreasonable to suppose that the start of divergence of the various conductance equations marks the onset of behaviour which might be R. Fernandez-Prini ref. 14 chap. 5; see also G. J. Hills in 'Electrochemistry' ed. G. J. Hills (Specialist Periodical Reports) The Chemical Society London 1970 Vol. I p. 73 and M. Wootten in ref. 5 p. 20. 176 T. J. Murphy and E. G. D. Cohen J. Chem. Phys. 1970,53,2173. 17' M. S. Greenberg R. L. Bodner and A. 1. Popov J. Phys. Chem. 1973,77,2449. ' 78 A. R. Davis and B. G. Oliver J. Phys. Chem.1973 77 13 15. 179 M. Spiro ref. 14 chap. 5. D. P. Sidebottom and M. Spiro J.C.S.Furuday I 1973.69. 1287. For other recent work see G. A. Vidulich C. P. Cunningham and R. L. Kay J. Solution Chem. 1973 2 23 (methanol); A. R. Tourky S. Z. Mikhail and A. A. Abdel-Hamid Z. phys. Chem. (Leipzig) 1973 252 289 (t-butyl alcohol-H,O). E.g. see J. L. Dye M. P. Faber and D. J. Karl J. Amer. Chem. Soc. 1960 82 314. H. P. Bennett0 better described by another theory (which need not rule out ion-pairing but would put it into a different context). Some efforts in the direction of a lattice theory'82 are certainly more successful than the usual approach for moderately dilute solutions ;in HCN the conductance of KCl obeys a cube-root law while in N-methylacetamide several salts obey a square-root law far beyond the Debye-Hiickel-Onsager range but the slope is wrong.82 While further accurate data are necessary it is tentatively suggested that the minima in the plots of t+(c) 0s. c found by Sidebottom and Spiro coincide with the takeover of quasi-lattice properties. Recently reported cases of ion-aggregation5 might be interpreted in a similar way. Interest has grown in the transport by ions of non-electrolytes in mixed solvents which has important implications to-specific s~lvation,'~~ kinetic^,'^' and transport processes in biological systems.' ' solvent-exchange The Washburn number'" of water W, in a binary aqueous mixture is the number of moles of water transported per faraday towards the cathode in an electrolysis relative to the co-solvent.It should not be confused with 'solvation number'; the relation of W to the transport numbers t+ ,t-,and the number of moles of water n and h-transported (relative to methanol) by the cation and anion respectively is given by W = n+t+-n-t-(14) A precise e.m.f. method' 83 employing cells with and without a liquid junction gives W at infinite dilution of electrolyte as an average for an interval in the solvent composition range. In methanol-water mixtures,'84 little specificity in W is found among different cations for alkali-metal chlorides but solvent structure has a profound effect on the relative solvation of halide ions by the two solvent components (i.e.n-) and two regions of structural peculiarity are identi- fied.Parallels may be drawn between the solvent effects on Washburn numbers and the self-diffusion of water in methanol-water mixtures.' 85 The solvent-sorting effect of ions which is also present in glycol-water mixtures,'86 does not appear to stem from variations in transport number with solvent composition and is confirmed by the results from a vapour pressure meth~d.'~' In saturated KCl however the lower W and W,values show that the differences in composi- tion between the primary solvation shells of the ions and the bulk solvent are much smaller than at low salt concentrations presumably because the structural influence of the solvent medium has been eliminated. Further developments in the theory and interpretation of transport properties appear to lie in the direction of transition-state theory.17' The application to la2 G.Kortiim and H. Quabek Ber. Bunsengesellschaft phys. Chem. 1968 72 53; cf. J. F. Casteel and E. S. Amis J. Phys. Chem. 1973 77 688. IE3 D. Feakins and J. P. Lorimer Chem. Comm. 1971,646. D. Feakins K. H. Khoo J. P.Lorimer and P. J. Voice J.C.S. Chem. Comm. 1972 1336. T. Erdey-Gruz G. Inzelt and C. P. Fodorne Magyar Kkm. Fu/y&rar 1973 79 20; 173. IE6K. H. Kho0,J.C.S. Faraday I 1973 69 1311. C. L. De Ligny and A. G. Remijnse J. Electroanalyt. Chem. 1973,45 488. Electrolyte Solutions 247 conductivity pioneered by Hillsla8 promises to integrate solvation with solvent effects and is supported by a recent study of five electrolytes near the phase transition in N-methylacetamide.' 89 The values of E for conductance are very close to E for viscous flow in the pure liquid indicating that cavity formation is a process common to both transition states.The transition-state treatment for the viscous effects of electrolytes (Jones-Dole B coefficient^'^') established by Nightingale,'" has been given a somewhat different form by Feakins and co-worker~.'~' For small ionic solutes a simple relationship results from the consideration of the solution in the limit of infinite dilution. In equation (15) B = (Vq -V;)/lO00 + V;[(Ap;* -A/A; *)/lOMlRT] (15) Vy and Vi are the partial molar volumes of the solvent and solute respectively; ApY* is the activation free energy for viscous flow of the solvent and Apl* the 'ionic activation free energy' at infinite dilution.The structural effects of ions are thus meaningfully separated into quantities formally relating to the sizes of the ions the fluid properties of the solvent and the ion-solvent interactions and the possibilities for combining the results of thermodynamic and transport properties are obvious. However the precise measurement of B coefficients is no easy matter and the comparability of results is still affected by the lack of con- formity in the assignment of a value to the Debye-Hiickel parameter A of the Jones-Dole equation (16) qr= 1 +A&+BC (16) in which q is the viscosity relative to that of the pure solvent; probably the experimentally determined value of A should be used. A case may be made for thinking that if the theoretical limitations inherent in the A coefficient are not recognized in the separation of A and B some lattice-coulombic effects6' may be partly reflected in the derived B values.The consequences of this may not be too serious however if both the B coefficients and the lattice phenomenon have a common origin in solvation and its attendant modifications of solvent organiza- tion around the ions.'39 Unfortunately it is not yet possible to be sure of the dielectric properties in this region though some recent studies may be noted.' 92-' 95 The future for a structural theory of solutions appears to lie in the coalition of ideas from transport kinetic and thermodynamic studies and will need to place emphasis on parameters such as those appearing in equation (15) in the hope that the mystery will be taken away from B coefficients the electrophoretic effect etc.Some established correlations suggest further possibilities e.g. that "* S. B. Brurnmer and G. J. Hills Trans. Furaday SOC.,1961 57 1816 1823. P. P. Rastogi Z. phys. Chem. (Frankfurt) 1973 85 1. E. R. Nightingale and R. F. Benck J. Phys. Chem. 1959 63 1777. 19' D. Feakins D. J. Freemantle. and K. G. Lawrence J.C.S. Furuduy I 1974 70,795. 19' G. Schwarzenbach L. Fabbrizzi P. Paelotti and M. C. Zobrist Helo. Chim. Acru 1973 56 670. 193 J. T. Edward J. Chem. Phys. 1972 57 5251. 194 R. Fernandez-Prini J. Phys. Chem. 1973,77 1314. 19' S. K. Jalotta and R. Patterson J.C.S. Furaduy I 1973 69 1510. H. P.Bennett0 the B coefficients relate to AV" for ionic cond~ctance.'~~ What then is the behaviour of B when the pressure is varied in view of the single value of AV* found'96 when the solution is compressed to the specific volume of the solvent? The solubilities of gases in a pure solvent approach a common value at the solvent boiling (as does the solvent vi~cosity);~~ this suggests that 'non-electrolyte effects' will also converge and inspection of the limited data on B coefficients shows a similar trend. Since the Onsager treatment of transport numbers,' 79 diffusion etc. is unreliable for describing concentra- tion dependences in solutions of moderate concentration a lattice theory might be more compatible with the results together with descriptions of the solvent- exchange proces~,~~*'~~ namics.'99 non-Brownian motions,'98 and solution micrody-196 S.B. Brummer and A. B. Gancy ref. 26 chap. 19. 19' 0.Ya. Samoilov ref. 26 chap. 14. 198 H. L. Friedman ref. 26 chap. 18. 199 I. R. Lantzke D. E. Irish and T. E. Gough ref. 14 chap. 4; H. G. Hertz ref. 8 chap. 7.

ISSN:0308-6003    

DOI:10.1039/PR9737000223

出版商:RSC    

年代:1973

数据来源: RSC

摘要:

9 Electrolyte Solutions in Dipolar Aprotic . Solvents By B. G. COX Department of Chemistry The University of Stirling Scotland 1 Introduction Large and often spectacular changes in the reactivities of ions when transferred from water to various non-aqueous solvents have resulted in much interest in the properties of electrolyte solutions in non-aqueous solvents. Much of this interest was generated by the observation of very large rate increases in many organic reactions involving anions when the solvent was changed from a protic solvent (i.e. a solvent containing relatively acidic protons) such as water or methanol to a dipolar aprotic solvent such as dimethylformamide.1~2 In this Report the thermodynamics of transferring ions from aqueous to various non-aqueous solvents together with the effect of solvent on acid-base behaviour and conductance of electrolytes are considered.A discussion of recent studies of ion solvation in non-aqueous solvents using various spectro- scopic techniques is also included. The solvents considered have generally been limited to those having dielectric constants greater than CQ. 30 because in solvents of lower dielectric constant ion aggregation is so extensive that it becomes very difficult to observe the behaviour of solvent-separated ions. Table 1 lists the more common solvents studied together with some of their relevant physical properties. 2 Thermodynamics of Ion Solvation The observed changes in standard free energy when an electrolyte MX is trans- ferred from a reference solvent 0 to another solvent S are commonly reported as free energies of transfer (AG,,)3-5 or as solvent activity coefficients (0ys),2*6-'o ' A.J. Parker Quart. Rev. 1962 16 163. A. J. Parker Chem. Rev. 1969,69 1. D. Feakins A. S. Willmott and A. R. Willmott J.C.S. Faruday I 1973 69 122. M. H. Abraham J.C.S. Furuduy I 1973 69 1375. B. G. Cox and A. J. Parker J. Amer. Chem. SOC.,1973.95.402. ' R. G. Bates in 'The Chemistry of Non-Aqueous Solvents' ed. J. J. Lagowski Aca- demic Press New York. 1966 vol. 1 p. 97. ' 0. Popovych Crit. Rev. Analyt. Chem. 1970 1 73. I. M. Kolthoff J. J. Lingane and W. D. Larson J. Amer. Chem. SOC.,1938,60 2512. E. Grunwald and B. J. Berkowitz J. Amer. Chem. SOC.,1951 73 4939. lo H. Strehlow in ref.6 p. 129. 249 Table 1 Physical Properties of Solvents Dielectric Dipole Mol. Density d2' const. moment Rrjructice Viscosiry/ Solvent" Wf. I3.p.pc /gm cm-j E (at 25 "C) PD index nD CP(at 25 "C) H20b 18 100 0.9982 78.5 1.84 1.333 0.89 MCOH~ 32 65.0 0.7914 32.6 1.70 f.3288 0.547 EtOH 46 78.3' 0.7895' 24.3' 1.69 1.361 1' 1.ac TFE 100 74' 1.3826(2,T,' 26.7' 2.03' t .291' 1.78W HCONH,' 45 193 1.134 109.5 3.25 1.M53 3.31 NMF 59 183' 1.011' 186.9' 3.82' 1.431Y 1.65k DMFb 73.1 1525 0.9445 36.7 3.82 1.4269 0,7% DMAC? 87.1 165.5 0.9366 37.8 3.79 1.435 1 0.919 DMSob 78 189 1.1014 48.9 4.3 .4783 2.000 MeCNb 41 80.1 0.7856 37.5 3.84 .3441 0:345 TMS 20 285' 1.2618(j0",-)i 43.3(, .c)i 4.69' .474200 10.1.3(, ",-)i Me,CO 58 562 0.792' 20.7' 2.88' .3588' 0.316' MeNO,' 61 100.8 1.1354 38.6 3.44 .3935 0.62 HMPA~ 79 235 1.0253 29.6 5.37 .45a2 3.34 NMepyb 99.202 1.0327 31.5 4.09 .4706 1.83 PC __ 102 24 1.7' 1.0257' 64.9 4.94' 1.4212' 2.5 1' a Abbreviations are TFE trifluoroethanol; NMF N-methylformamide; DMF dimethylformarnide; DMAC dimethylacetamide DMSO dimethyl sulphoxide; TMS tetramethylene sulphone (sulfolane); HMPA hexamethylphosphoramide {[(CH,),N],PO 1; NMepy N-methyl-2-pyrrolidone; PC propylene carbonate; ref. 2; 'Handbook of Chemistry and Physics' 50th edn. Chemical Rubber Co. Cleveland. Ohio 1969-1970 ref. 93; J. Murto. and E.-L. Heino Suomen Kem. 1966 39 B 263; 'P. Rohdewald and M.Moldner J. Phys. Chem. 1973 77 373; R. M. Meighan and R.H. Cole J. Phys. Chem. 1964.68 503; * C. M.French and K.H. Glover Trans. Furuduy SOC.,1955,51 1418; ' ref. 94;j ref. 45; ' ref. 121; I ref. 91. Electrolyte Solutions in Dipol~r Aprotic Solvents 25 1 the latter also being called medium effect^,^'^ distribution coefficients,8 or degenerate activity coefficient^.^,' The two quantities are simply related by equation (l) where pS(MX)and po(MX) are the standard chemical potentials of AG,,(MX) = $/MX) -po(MX) = RTlnoyi+oyi-MX referred to infinite dilution in solvents S and 0,respectively. In this Report results are quoted as free energies of transfer the molar concentration scale being used. The free energies of transfer may be readily converted to the molal or mole fraction concentration scales. For dilute solutions these are related by equations (2) and (3) where (c) (m),and (q) refer to values on the molar molal AGtr(m) -4Gtr(c) = I! T In (dolds) (2) and mole-fraction Concentration scales respectively and M and d are the mole- cular weight and density respectively of the solvents.For electrolytes and other electrically neutral combinations of ions as well as for neutral molecules free energies enthalpjts and entropies of transfer from one solvent to another are well-defined thermodynamic quantities which may be unambiguously determined from thermodynamic measurements such as solu- bilities or e.m.f. values of suitable cells. However the interpretation and predic- tion of the chemistry of ions in different solvents and in general theories of ion-solvent interactions are conveniently expressed in terms of the behaviour of individual ions in different solvents.Since the separation of thermodynamic properties of electrolytes into those of the individual ions cannot be done within the framework of classical thermodynamics to do this requires the use of an extrathermodynamic assumption. Most of the assumptions currently in use are based on the concept that for a sufficiently large ion particularly one whose charge is 'buried' at the centre of inert ligands the changes in free energy or enthalpy on transfer between solvents closely resemble those of another solute of similar size and structure but having a different charge (e.g.a neutral molecule or an ion of opposite charge). Some of the solute pairs that have been considered are Ph,As+ and Ph,B-; Ph,As+ and Ph,C; Ph4B- and Ph4C; and (C5HJ2-Fe+ (ferricinium) and (C,H,),Fe (ferrocene).The results of studies carried out prior to 1970 have been comprehensively reviewed by Pop~vych,~ and studies since then' '-''have generally involved comparison of results given by different apumptions' '-' or extensions of methods previously Parker and co-wprkers have compared the I1 R. Alexander A. J. Parker J. H. Sharp and W. E. Waghqrne J. Amer. Chem. SOC. 1972,95 1148. lZ 0.Popovych A. Gibofsky and D. H. Berne Analyr. Chem. 1972,44 81 1 ; H. Berne and 0.Popovych ibid. p. 817. l3 B. G. Cox and A. J. Parker J. Amer. Chem. SOC. 1973.95.402. I' C. L. De Ligny H. J. M. Denessen and M. Alfenaar Rec. Trav. chim. 1971,90 1265. D. Bax C. L. De Ligny and M.Alfenaar Rec. Trav. chim. 1972,91 452 1225. l6 D. Bax C. L. De Ligny and A. G. Remijnse Rec. Trav. chim. 1973 92 374. " C. V. Krishnan and H. L. Friedman J. Phys. Chem. 1971,75 3606. 252 B. G. Cox results of a number of different assumptions for the free energies' ' of transfer of Ag+ between a variety of solvents. Provided that one of the solvents involved was not water or to a lesser extent methanol agreement between the results given by various assumptions was generally within 1kcal mol-' over a total range of 20 kcal mol-'. Results for transfer from water were rather more scat- tered and comparison was hampered by lack of reliable values of the solubilities of sparingly soluble BPh4- salts (AgBPh4 Ph,AsBPh,) in water. Kolthoff and Chantooni,' by measuring the equilibrium constant for the reaction BPh,-+ AgI(s) GAgBPh,(s) + I-were able to determine accurately the solubility of silver tetraphenylborate in water and methanol and the solubility of tetraphenylarsonium tetraphenylborate in water has since been obtained by a similar method.lg The results of these and other similar studies,20 together with the measured enthalpies of transfer of Ag' and Br- between a variety of solvent^,'^ led to the conclusion that of the various assumptions proposed the assumption that the free energies of transfer of the tetraphenylarsonium and tetraphenylborate ions between solvents are equal (and similarly for the enthalpies of transfer) is experimentally the most convenient one and gives results that are both consistent with those of other assumptions and chemically sensible.An alternative assumption,' ' that liquid junction potentials between Ag/AgClO (0.01moll-') half cells in different solvents when linked by a salt bridge of tetraethylammonium picrate (0.1moll-') in one of the solvents are negligible gives very similar results to the Ph4As+ Ph4B- assumption for free energies of transfer of Ag'. It is experimentally the simplest of the assumptions to determine single-ion free energies of transfer but less convenient for the measurement of enthalpies of transfer.13 This as- sumption is dependent on the transfer of large ions of comparable mobility across a liquid junction." It has been pointed out22 that if the solvents concerned in such cells interact strongly then there may be a significant contribution to the liquid junction potential from the transport of solvent molecules across the interfaces.Evidence for this particularly for cells with interfaces between water and solvents such as DMF DMSO,or N-methylpyrrolidone has been reported,21 but the effect may be diminished by the use of a suitably inert solvent in the salt bridge. Alfenaar de Ligny and co-workers'&' have published further results based on a method proposed earlier23 in which they assume that free energies of transfer of an ion can be split up into an electrostatic term which approaches zero as the ionic radius increases and a neutral term which approaches the free energy of transfer of a neutral molecule of the same radius (r).Thus for example AG,,(K+) is obtained by extrapolating plots of AG,,(K+) + AGJX-) -AGtr-I. M. Kolthoff and M. K. Chantooni jun. Analyt. Chem. 1972,44 194. l9 B. G. Cox and A. J. Parker J. Amer. Chem. SOC. 1972,94,3674. 2o I. M. Kolthoff and M. K. Chantooni jun. J. Phys. Chem. 1972,76,2024. 21 B. G. Cox A. J. Parker and W. E. Waghorne J. Amer. Chem. SOC. 1973 95 1010. 21 M. Alfenaar C. L. De Ligny and A. G. Remijnse Rec. Trav. chim. 1967,86,986. 23 M. Alfenaar and C. L. De Ligny Rec. Trav. chim. 1967,86 929. Electrolyte Solutions in Dipolar Aprotic Solvents 253 (neutral molecule) us. l/r to r = co for a series of anions X-of increasing size. Such plots require long and frequently non-linear extrapolations but by allowing for ion-dipole and ion-quadrupole interactions' 'J'they have estimated AGtr values for single ions.Where comparison with independent methods is pos- sible,' '9'' agreement is reasonable. AGJH') from water to 50% (w/w) aqueous dioxan agrees well with that based on the Ph,As+ Ph,C assumption given by Grunwald Baughman and Kohn~tam,~~ and values for transfer of a variety of ions from water to methanol agree within 1 kcal mol-' with those quoted by Kolthoff and Chantooni,20 based on the Ph,As+ BPh4-assumption. For transfer of ions to acetone agreement with values based on the Ph,As+ BPh,- assumption' 'l2O is less good values differing by some 2 kcal mol-'. It does however seem difficult to justify the use of such a complicated procedure requiring large numbers of experimental measurements together with para- meters such as the quadrupole moments of the solvent molecules particularly as the theoretical basis of the method is no more sound than that of the much simpler methods mentioned above.Recently several a~thors"~~'~~~ have commented on the possibility of ions such as Ph,As+ Ph4P+ and BPh4- having specific interactions with water and a number of other solvents. Coetzee and Shar~e,~' from an n.m.r. study of the effects of various solutes on solvent proton chemical shifts find that if the chemical shifts induced by ClO,- (in solvents other than water) or Et,N+ (in water) are assumed to be zero then solvent chemical shifts induced by Ph4As+ and Ph4P+ are different from those induced by BPh,-. The relevance of these results to the question of the suitability of the use of Ph,As+ and BPh,- to obtain thermodynamic properties of individual ions of course depends upon the validity of the assumptions used by Coetzee and Sharpe to obtain individual ion-induced chemical shifts and the difficult problem of how to relate chemical- shift differences to the magnitude of interaction energies involved.Jolicoeur et a1.26 note very small differences in the partial molal volumes of Ph,As+ and BPh,-in both water and methanol the individual values being based on assumed partial molar volumes for H+ in water and Br- in methanol. Krishnan and Friedman '' find from measurements of the enthalpy of transfer of tetra-alkylam- monium perchlorates from propylene carbonate to dimethylformamide that there is a linear relationship between AHtr(C,,H2,,+ 1)4N+ C104- and n the number of carbon atoms in the alkyl chain.Extrapolation of such a plot to n = 0 gives a value that is somewhat arbitrarily assumed to equal AHtr(C104-). A similar plot for AHtr(C,,H2,,+ l)4N+Br- against n for transfer from methanol to propylene carbonate is linear over the region n = 34. Extrapolation of this linear portion to n = 0 gives a value some 2.5 kcal more negative than the value of AHtr (Br-) based on the assumption that AH,,(Ph,As+) = AH,,(BPh4-). Krishnan and Friedman conclude that the solvation enthalpy of BPh,-in 24 E. Grunwald G. Baughman and G. Kohnstam J. Amer. Chem. SOC.,1960,82 5801. " J. F. Coetzeeand W. R. Sharpe J. Phys. Chem. 1971 75 3141.'' C. Jolicoeur P. R. Philip G. Perron P. A. Leduc and J. E. Desnoyers Cunad. J. Chem. 1972,50 3167. 254 B. G. Cox methanol and by implication in water must be considerably more negative than that of Ph,As+ but this conclusion hardly seems justified. The present situation can probably best be summarized by noting that a number of assumption^,^^' ',13 the most convenient and generally accepted of which is the Ph4As+ BPh,- assumption give a set of consistent (within 1-2 kcal mol- I) and reasonable values for single-ion free energies and enthalpies of transfer between solvents. Caution should be exercised in attempting to interpret energy changes of less than 1-2 kcal mol- ',particularly when one of the solvents is water but this is probably not a limitation to theory in its present state of development.Differences between ions of equal charge and total changes for whole electrolytes are of course independent of any assumption and limited only by experimental accuracy. Free Energies of Transfer of Ions-The free energies of solution (AG,) of a variety of electrolytes in several solvents have been collected together in Table 2. Solubility products (KJ can be readily obtained from AG by use of equation (4). AG = -RTln K, (4) Such free energies of solution normally come directly from solubility measure- ments11*20,27 or from free energies of solution in water combiqed with free ener- gies of transfer to the solvent in question obtained from e.m.f. measurements on reversible cells.3,28-30 The use of amalgam electrodes in electrochemical cells has recently been reviewed by Bennetto and Willm~tt.~' The results in Table 2 show that most simple electrolytes are more soluble in water than in any of the non-aqueous solvents.Formamide and from more limited results N-rnethylf~rmamide'~~~~ are also good solvents for most simple electrolytes. Ph,As+ and BPh -salts are however generally considerably more soluble in the various non-aqueous solvents. Most electrolytes are significantly less soluble in acetonitrile and propylene carbonate than in the other solvents in Table 2. Similarly low solubility has also been observed in tetramethylene sulphone (sulfolane)' 1,33 and acetone.' ',15 To facilitate comparison between ions of like charge and to enable discussion of these solubility changes in terms of the effect of the solvents on the free energies of the anions and cations involved free energies of transfer of individual ions from water to various non-aqueous solvents are presented in Table 3.With the exception of those for N-rnethylf~rmamide'~'~~ these results are based on the assumption that AG,,(Ph,As+) = AG,,(BPh,-). Thus for example AG,,(Ag+) = AG,,(AgBPh4) -$AG,,(Ph,AsBPh,) and so AGJCl-) = AG,,(AgCl) -AG,,-(Ag') etc. the required free energies of transfer of whole electrolytes coming from the results in Table 2. 27 M. H. Abraham J.C.S. Perkin 11 1972 1343. 28 M. Salomon J. Electroanalyt. Chem. Interfacial Electrochem. 1970 26 3 19. 29 D. P. Boden and L. M. Mukherjee Electrochim.Acta 1973 18 781. 30 D. Feakins and P. J. Voice J.C.S. Faraday I 1973,69 1711. 31 H. P. Bennetto and A. R. Willmott Quart. Rev. 1971,25 501. 32 E. M. Luksha and C. M. Criss J. Phys. Chem. 1966,70 1496. 33 J. A. Starkovich and M. Janghorbani J. Inorg. Nuclear Chem. 1972 34 789. Electrolyte Solutions in Dipolar Aprotic Solvents Table 2 Standard free energies of solution (AC,) of 1 1 electrolytes in solventsa at 25 "C (molar scale in kcal mol-l)b Salt H,O' MeOH HCONH DMF DMSO PC MeCN LiCl -9.9 -5.9d -8.9' -4.2' -5.0' 5.1g 7.39 -LiBr -13.6 -9.gd -11.8' -11.1f -0.6' -LiI -18.6 -16.4d --19.2' -8.1' NaCl -2.1 2.9' -0.7" 6.4' 6.8' 10.6' 11.3' NaBr -4.1 0.6d -0.6' -6.9h KCl -1.2 4.4' 1.O' 7.5' -9.5' 10.8' KBr -1.4 3.4' -0.7" 3.9' 1.8' -7.8' KI -2.8 2.2d -2.1' -2.gh 2.7h --5.7' KCIO 2.7 6.4' KBPh 10.2' 7.1' 4.1' --4.4' RbCl -2.0 4.2h 0.0' -6.39 9.9h RbBr -1.6 3.7' -4.3' 2.4' 4.79 7.6' RbI -2.0 --1.99 3.3h RbBPh 11.6' 8.2' --3.9' CSCl -2.2 3.5' -0.2' 6.9' -3.99 9.4' CsBr -0.4 3.8' -4.9' -3.P 7.9' CSI -0.1 3.9h -0.7' 2.3' -1 .6g 4.2h CSClO 3.3 6.8' --5.5' AgCl 13.3 18.2' 12.9' 20.1' 14.7' 27.2' 17.8' AgBr 16.8 21.1' 15.8' 20.8' 15.0' 28.0' 18.9' AgI 21.8 25.3' 19.9k 2 1 .9' 17.0' 29.2' 19.7' Am 11.7 16.0' 10.9k 16.0' 9.4' 22.4' 13.5' AgOAc 3.6 9.1' -14.3' 6.7' -11.8' AgBPh 23.4' 19.6' 1 4.0' 10.2' 6.5' 17.4' 10.2' TIC1 5.0 8.8' -13.2' 9.2' 16.99 18.0' TlBr 7.3 11.2' -6.7" 17.1g 17.7' -TII 9.5 --6.4" 1 6.2g NEtJ 1.2" 3.On -3.7" 3.2" -3.6" Ph,AsI 6.9' 3.1' 2.7' 2.6' -2.3' 3.7' Ph,AsC10 1 1.4k 7.1' --4.8' Ph,AsBPh 23.5" 1 2.2' 1 2.Ok 5.3' 5.8' 6.3' 7.8' Abbreviations as in Table 1; 1 cal = 4.184 J; 'Values from standard compilations i.e.W. M. Latimer 'Oxidation Potentials'; 2nd edn. Prentice Hall New Jersey; F. D. Rossini et al. 'Selected Values of Chemical Thermodynamic Properties' U.S.National Bureau of Standards Circular 500 and supplementary notes 27&l to 270-3; N. A. Izmailov Run. J. Phys. Chem. 1960 34 1142; 'ref. 36; M. Salomon J. Elecrrochem. SOC.,1970 117 325; gref. 37; 'J. Pavlopoulos and H. Strehlow Z. phys. Chem. 1954 202 474; ref. 20; j ref. 44; Ir ref. 1 1 ; ' M. Breant and G. Demarge-Geunn Bull. SOC.chim. France 1969 2935; "ref. 81; "ref. 27; "ref. 19. 256 B.G. Cox Table 3 Free energies of transfer of ions" (AGtr) from water to non-aqueous solventsb at 25 "C (molar scale in kcal mol-I)' Ion MeOH HCONH NMeFd DMF DMSO Me,CO' PC MeCN H+ 2.6' --3.4' -4.5' -0.7 -11.1 + Li 1.0 -2.3 -3.5 -5.3 -3.5 -5.3 7.1 Na 2.0 -1.9 -1.9 -2.5 -3.3' -2.6 3.3 + K+ 2.4 -1.5 -2.0 -2.3 -2.9 0.7 0.8 1.9 Rb+ 2.4 -1.3 -1.8 -2.4 -2.6 0.5 -1.3 1.6 cs 2.3 -1.8 -1.7 -2.2 -3.0 0.4 -3.5 1.2 + Ag++ 1.8 -3.7 -4.1 -8.0 1.5 3.3 -5.2 T1 1.0 --2.8 -6.0 -2.0 2.2 NEt,' 0.2 --2.0 -1.2 --2.1 Ph,As+ -5.6 -5.7 -9.1 -8.8 -7.1 -8.5 -7.8 c1-3.0 3.3 4.9 11.0 9.2 14.0 10.1 10.1 Br-2.7 2.7 3.6 7.2 6.1 10.5 7.8 7.6 I-1.6 1.8 -4.5 3.2 6.7 4.6 4.5 N -2.5 2.9 -8.2 5.7 10.9 7.1 7.O ClO,-1.4 -0.4 -3.6 -1.1 OAc-3.7 -14.8 11.1 -13.4 BPh,-5.6 -5.7 -9.1 -8.8 -7.1 -8.5 -7.8 Based on the assumption AG,,(Ph,As+) = AG,,(BPh,-) applied to results in Table 2; Abbreviations as in Table 1; 1 cal = 4.184 J; ref.14; 'refs. 11 and 15; ref. 20. The striking increase in the free energy of the small anions with high charge density (Cl- Br- N3-,and to a lesser extent I-) on transfer to all of the dipolar aprotic solvents is consistent with the large rate increases observed in reactions undergone by these anion^.^.^^ Limited results for fluoride salts in DMF35*36 and propylene carbonate3' suggest free-energy increases for F-some 3-4 kcal mol-' larger than for C1-. Das and Kundu3' report a rapid decrease in the ionization product of water with increasing DMSO content of mixtures of DMSO and water the result suggesting a large increase in the free energy of OH-in the mixtures.These results are all consistent with the suggestion1Y2 that the loss of hydrogen-bonded stabilization of small anions when transferred to aprotic solvents from water and to a lesser extent from methanol formamide and N-methylformamide is a major factor in determining their increased reac- tivity. The very large increase in the free energy of acetate and similarly large values for benzoate ions20s39 compared with C1- again presumably reflect a considerable stabilization of these anions by hydrogen-bonding in water. Kolthoff and Chantooni,4° from solubility measurements and measurements with an Ag/AgIO electrode find surprisingly large values for AGtr(I03-) for transfer 34 B.G. Cox and A. J. Parker J. Amer. Chem. SOC.,1973,95,408. 35 C. M. Criss and E. Luksha J. Phys. Chem. 1968,72 2966. 36 E. Luksha Ph.D. Thesis University of Vermont 1965. 37 M. Salomon J. Phys. Chem. 1970 74 2519. 38 A. K. Das and K. K. Kundu J.C.S. Faraday I 1973,69 730 1983. 39 M. K. Chantooni jun. and I. M. Kolthoff J. Phys. Chem.. 1973,77 1. 40 I. M. Kolthoff and M. K. Chantooni jun. J. Phys. Chem. 1973 77 523. Electrolyte Solutions in Dipolar Aprotic Solvents 257 from water to MeOH MeCN and Me2S0 values being much larger than those for NO,- C104- and C1- and very similar to those for acetate. The only exception to the generally observed increase in anion free energies on transfer from water (for small anions) seems to be for transfer to trifluoroethanol,' which appears to solvate ions such as C1- more strongly than does water.Such a result is not surprising in view of the relatively acidic OH proton of trifluoro-ethanol. The larger and more polarizable anions show as expected considerably smaller increases in free energy on transfer from water. An extreme example of the difference between small anions and large polarizable anions is seen in the free energies of transfer of C1- and BPh4- from water to DMF which differ by 20 kcal mol- '. Similar conclusions may be reached from the results of studies of the free energies of transfer of trihalide ions compared with the simple halide ions41v42 and anions of the type AgX compared with X-.39 The results for the free energies of transfer of cations in Table 3 do not present such a clear picture as those of the anions.They suggest that solvents such as the various amides and DMSO which contain relatively basic oxygen atoms solvate cations better than water. Limited results obtained in N-methyl-2- pyrrolidone' 1*43 and HMPA' ' suggest similar behaviour for these solvents. The positive free energies of transfer of most cations to propylene carbonate which correlate well with measurements of association constants for water with Li' Na+ and K+in propylene arb on ate,^^ imply only a weakly basic oxygen atom in the molecule. The large decrease in the free energy of transfer of Ag+ to acetonitrile contrasts sharply with the behaviour of the other cations studied. This result together with an even larger decrease for Cu' has been discussed45 in terms of Pearson's hard and soft both Ag+ and Cu+ being described as soft.Even more remarkable differences were observed45 for transfer into two 'thio' solvents dimethylthioformamide (DMTF) and hexamethylphosphorothioic amide. The free energies of transfer of Ag' and Cu' from water to DMTF were some 35 kcal mol- ' more negative than that of Na+ and salts such as AgI were found to be soluble in DMTF to the extent of at least 1 moll-'. Independent support for the view that the single-ion values in Table 3 are at least qualitatively correct comes from studies of complex formation between Ag + and DMF:' DMSO;* HMPA,49 and acetonitrileso in a variety of solvents. 41 C. Sinicki Bull. SOC.chim. France 1970 1643. 42 F. G. K. Baucke R. Bertram and K. Cruse J. Electroanalyt. Chem. Interfacial Electro- chem. 1971,32 247. 43 M. Breant C. Buisson M. Porteix J. L. Sue and J. P. Terrat J. Electroanalyt. Chem. Interfacial Electrochem. 1970 24 409. 44 D. R. Cogley J. N. Butler and E. Grunwald J. Phys. Chem. 1971 75 1477. " W. E. Waghorne Ph.D. Thesis Australian National University 1972. 46 R. G. Pearson Survey Progr. Chem. 1969,5 1. 47 D. C. Luehrs J. Inorg. Nuclear Chem. 1971 33 1971. 4R D. C. Luehrs R. W. Nicholas and D. A. Hamm J. Electroanalyt. Chem. Interfacial Electrochem. 197 1 29 41 7. 49 D. C. Luehrs J. Inorg. Nuclear. Chem. 1972 34 791. 50 S. E. Manahan and R. T. Iwamoto J. Electroanalyt. Chem. Interfacial Electrochem. 1967 14 213.258 B. G. Cox DMSO forms stronger complexes than both acetonitrile and DMF which were ofsimilar strength as expected from Table 3 and the variation in the strength of complex formation with a solvent correlates well with the free energies of transfer of Ag' given in Table 3 and elsewhere for other solvents.' ' Enqalpies and Entropies of Tramfer of Ions-While from a practical point of view free energies of solution or transfer of electrolytes are of major importance it is often possible to obtain much more detailed information about solvation phenomena from a consideration of enthalpies and entropies of solution of electrolytes. In particular such studies4,' 'may lead to increased understanding of the rather complicated changes occurring when electrolytes are dissolved in water.Enthalpies and entropies of solution of a variety of electrolytes in water and of transfer from water to several solvents are listed in Tables 4 and 5. Entropies of solution (AS,) and transfer (AStr)have been obtained by the application of equa- tion (5) to the data in Tables 2 4 and are quoted as values of 298AS (correspond-AG = AH -TAS (5) ing to T = 25 "C) to facilitate comprison of the relative effects of AHtrand ASlr in determining the total free-energy changes. Enthalpies of solution have most commonly been obtained directly from calorimetric measurements of heats of 9 3955 soh tion ' 2-s4 or precipitation' of electrolytes or less conveniently from the temperature dependence of the e.m.f. of electrochemical ce11s.28*56~s7 Kr ishnan and Friedman' have pointed out a number of inconsistencies in published data on heats of solution of electrolytes particularly in methanol and DMF in some cases arising from a considerable concentration dependence of the heats of solu- tion at very low concentration^.^^ Their work together with recent works9 which has attributed some of these effects to solvent impurities has removed many of the previous anomalies and has been used in preference to earlier work where any differences arise.The most striking feature of the enthalpies reported in Table 4 is that despite the fact that most simple electrolytes are less soluble in the non-aqueous solvents than in water the enthalpies of transfer from water are almost all negative.The only exceptions to such behaviour are certain salts in propylene carbonate and also most of the tetra-alkylammonium salts. Accompanying these decreases in enthalpy are very large decreases in entropy (Table 5),particularly for the dipolar aprotic solvents where values of 298ASIrvary between -7 and -15kcal mol- '. It is noticeable that for salts containing 'organic' ions (NEt,' Ph,As+ BPh,-) B. G. Cox G. R. Hedwig A. J. Parker and D. W. Watts Austral. J. Chem. 1974. 27 477. 52 C. De Visser and G. Somsen J. Chem. Thermodynamics 1973 5 147. 53 R. Fuchs and C. P. Hagen J. Phvs. Chem. 1973 77 1797. 54 D. S. Gill J. P. Singla R. C. Paul and S. P. Narula J.C.S.Dalton 1972 522. 55 Y.C. Wu and H. L. Friedman J. Phys. Chem. 1966,70 501. 56 M.Saloman J. Electrochem. SOC.,1970 117 325. 57 J. N. Butler and J. C. Synnott J. Amer. Chem. SOC.,1970 92 2602. '* R. P. Held and C. M. Criss J. Phys. Chem. 1967 71 2487. 59 Y. A. Tsai and C. M. Criss J. Chem. and Eng. Data 1973 18 51. Electrolyte Solutions in Dipolar Aprotic Solvents Table 4 (continued) AH,,/kcal moI -' Salt H,O (AHJ MeOH HCONH N MeF DMF DMSO PC MeCN NEt,CI -3.0" 4.0' -4.7d 5.4" 6.3' 4.3' -NEt,Br 1.4" 3.Sd 1.4' 3.7" 0.8' 1.9" 3.5' NEt,I 6.8" 1Sd --3.3d -1.9" -0.7' -2.1' NBu,CI -7.39 --8.7' 9.9k 10.7" --NBu,Br -2.28 6.4d 6.4" 7.6' 6Sk 7.9" NBu,I 3.V 4.8' -1.od 3.4h 4.1" 2.7" -Ph,AsC1 -2.6' 1.6d -0.4d 1.7" 2.9" Ph,AsBr 1.8' -0.5" --1.8" 0.0" -0.5" Ph,AsI 8.3" 0.4" -1.9" -7.6" -4.9" -2.6" -4.1" Abbreviations as in Table 1 ; 'I cal = 4.184 J; Enthalpies of solution of electrolytes in water.Values from V. B. Parker 'Thermal Properties of Aqueous Uni-Univalent Electrolytes' U.S. National Bureau of Standards NSRDS-NBS2 Washington D.C. 1965; ref. 17; ref. 54; 1 ref. 59; ref. 62; ref. 37; G. Somsen and L. Weeda Rec. Trav. chim. 1971,90 81 ; ref. 55; 'ref. 53; ' ref. 4; ref. 51 ;" C. V. Krishnan and H. L. Friedman J. Phys. J Chem. 1969,73 3934; E. M. Arnett and D. R. McKelvey J. Amer. Chem. SOC.,1966,88 2598; R. W. C. Broadbank S. Dahl an Ondona K. W. Morcom and B. L. Muju Trans. Faraday Soc. 1968 64 331 I ; ref. 13; 'C. De Visser and G. Somsen Rec. Trav. chim. 1971 90,1129; C. De Visser and G. Somsen J. Chem. Thermodynamics 1972,4 31 3; ' Y.-C. Wu and H.L. Friedman J. Phys. Chem. 1966,70 2020; ref. 61. Electrolyte Solutions in Dipolar Aprotic Solvents 26 1 Table 5 Entropies of transfer (AS,,)n of 1 1 electrolytes from water to non- aqueous solventsb at 25 "C 298AS,,/kcaI mol -' (molur scdr) Salt H20 (298ASJd MeOH HCONH DMF DMSO PC MeCN -LiCl 1.0 -7.7 -1.5 -8.2 -6.9 -7.8 -LiBr 1.8 -2.0' -8.5 -7.8 -8.1 -LiI 3.5 -2.6' -10.2" -8.5 -10.6 -NaCl 3.0 -7.0 -4.4 --7.5 -NaBr 4.0 -8.7 -5.1' -11.8 -8.9' -7.6" NaI 5.3 -8.9' -5.5' -13.4' -9.6' -10.4' -12.9' NaClO 7.1 -9.3' ---12.1" -K C1 5.3 -8.1 -5.5 --9.2 -KBr 6.6 -8.7 -5.7 -14.2 -11.1 -9.2' KI 7.7 -7.3 -6.6 -15.1' -11.7' -11.5 -12.7 KBPh -0.8 --2.7' 0.6' -1.0 -2.1 -RbCl 6.1 -8.1 -5.4 --7.6 RbI 8.0 -6.4' -14.7' -10.7 -13.2 -RBPh -0.1 -0.6 -2.2' 0.6" 0.5' -CSCl 6.5 -7.1 -5.4 --5.8 -csI 8.2 -5.3 -14.8 -11.1" -8.7 -CsBPh 0.4 0.3' -2.w 1.1" 2.0' -AgCl 2.4 -8.4 -4.2 -10.0 -10.2 AgBr 3.4 -7.3 -12.4 -9.3 -10.2 -13.0 AgI 5.1 -9.2 --9.6 -10.2 -12.2 AgN 5.2 -9.2 -13.2 -11.4 -9.8 -12.3 NEt,I 5.6 -0.2 -5.9 -3.9 -4.5 Ph,AsBr -2.1 -2.5' -0.9" 0.7' -0.3' Ph,AsI 1.4 4.2 2.3 -1.0 -1.1 2.0' 0.9 Values obtained by application of equation (5) to data in Tables 2 and 4; 'Abbrevia-tions as in Table 1 ; 1 cal = 4.184 J; Entropies of solution of electrolytes in water (molar scale).Values from ref. 65; 'AG, values from Table 3. entropy decreases are considerably smaller and attention has been drawn to similar results for Pr,N+ and Bu,N+ by Abrahams.60 Other important features of the results in Tables 4and 5 are perhaps best seen from a consideration of single-ion enthalpies and entropies of transfer.Such values based on application of the Ph,As+ Ph,B- assumption to the results in Tables 4and 5 are listed in Table 6. With the exception of Li+ simple ions such as those of the alkali metals halide ions Ag' and N3-show an approximately constant loss of entropy on tranfer from water to the dipolar aprotic solvents. Observed entropy losses correspond to 298AS, of ca. 5-7 kcal mol-I (AS, ca. 17 23 cal K-' mol-') and are relatively independent of the ion or solvent. Similar conclusions may be reached from the entropies of transfer of electrolytes from water to sulfolane' 1333,61 and N-methylpyrrolidone.' 1,43362 Thus the 6o M.H. Abrahams J.C.S. Chem. Comm. 1972 888. 61 G. Choux and R. L. Benoit J. Amer. Chem. SOC.,1969,91 6221. 62 R. Fuchs J. L. Bear and R. F. Rodewald J. Amer. Chem. SOC.,1969,91 5797. 262 B. G. Cox Table 6 Enthalpies and entropies of transfer of ion? from water to non-aqueous solventsb at 25 "C (a) AH,,/kcal mol -ion H2O MeOH HCONH DMF DMSO PC MeCN + Li 0 -5.2 -1.3 -7.7 -6.3 0.4 -+ Na 0 -4.9 -3.9 -7.9 -6.6 -2.1 -3.1 K+ 0 -4.4 -4.0 -9.4 -8.3 -5.0 -5.4 Rb' 0 -3.6 -4.1 -9.0 -8.0 -5.6 -6.2 + cs 0 -3.2 -4.1 -8.8 -7.7 -6.2 -Ag + 0 -5.0 -5.4 -9.2 -13.1 -3.0 -12.6 NMe,' 0 0.4 0.2 -3.9 -3.9 -4.6 -3.7 EtN,' 0 2.2 1.8 -0.2 1.o -0.2 -0.4 BUN,' 0 5.2 6.8 4.3 6.1 3.8 4.4 Ph,As+ 0 -0.4 -0.1 -4.7 -2.8 -3.6 -2.5 c1-0 2.0 0.8 5.1 4.5 6.7 4.7 Br-0 0.9 -0.4 0.8 0.8 4.2 2.0 I-0 -0.5 -1.8 -3.3 -3.2 -0.2 -1.7 N -0 0.1 -0.3 -0.6 3.9 2.1 C104-0 -0.6 -4.8 -6.0 -4.6 -3.7 -BPh,-0 -0.4 -0.1 -4.7 -2.8 -3.6 -2.5 (b) 298ASJkcal mol-ion H2O (298ASJ" MeOH HCONH DMF DMSO PC MeCN + Li -1.4 -6.7 1.0 -2.4 -2.8 -4.9 -Na + 1.o -6.9 -1.6 -5.4 -3.1 -4.7 -6.2 K+ 3.2 -6.8 -2.5 -6.9 -5.4 -5.8 -7.3 Rb' 4.1 -6.0 -2.8 -6.6 -5.4 -4.3 -7.8 + cs 4.3 -5.5 -2.3 -6.6 -4.7 -2.7 -Ag + 0.5 -6.8 -1.7 -5.1 -5.1 -6.3 -7.4 NEt4+ 1.3 2.0 -1.8 2.2 -1.7 Ph,As+ -4.0 5.2 5.6 4.4 6.O 4.9 5.3 c1-2.0 -1.0 -2.5 -5.9 -4.7 -3.4 -5.4 Br-3.0 -1.8 -3.1 -6.4 -5.3 -3.6 -4.6 I-4.3 -2.1 -3.6 -7.8 -6.4 -4.8 -6.2 N -4.5 -2.3 -7.9 -6.3 -3.2 -4.9 BPh,-4.0 5.2 5.6 4.4 6.0 4.9 5.3 a Values obtained by application of assumptions AH,,(Ph,As +) = AH,,(BPh,-) and AS,,(Ph4As') = AS,,(BPh,-) to data in Tables 4 and 5; *Abbreviations as in Table I; 1 cal = 4.184 J; * Entropy of solution of ions in water from the crystal state.Values from ref. 65. differencesin the free energies of transfer of say CI-and I-to the various dipolar aprotic solvents largely result from differences in the enthalpies of transfer. Similarly the results in Table 6 suggest that differences in free energies of transfer of anions and cations (Table 3) are largely determined by differences in the enthalpies of transfer. For transfer between dipolar aprotic solvents entropy Electrolyte Solutions in Dipolar Aprotic Solvents 263 changes are very small and essentially independent of the free energies of transfer.Thus for example for transfer between DMF and acetonitrile AG,,(Ag -+ Na+) = 6.9 kcal mol-' with AH,,(Ag+ -Na+) = 8.2 kcal mol-' and 298AS,,-(Ag' -Na') = 1.3 kcal mol-'. It seems then that provided the interactions between the ion and surrounding solvent molecules are sufficient to freeze out the translational entropy of the solvent molecules the entropy losses are relatively independent of the magnitude of the interaction energy. Such entropy losses might be expected to be related to the entropies of freezing of the solvents which are fairly constant for the dipolar aprotic solvents reported here.' ' Transfer of 'organic' ions R4N+,60 Ph,As+ and BPh4-between the dipolar aprotic solvents also results in only small entropy changes.This again contrasts sharply with the transfer of such ions from water to these solvents which leads to a significant increase in entropy the value increasing as the length of the alkyl chains of R4N + increases.' *60 The large negative entropies of transfer of simple inorganic ions from water to dipolar aprotic solvents and the contrasting positive entropies of transfer of the 'organic' ions almost certainly reflect the large entropy and enthalpy changes occurring when the ions are dissolved in water. Following the work of Frank and Evans,63on the effect of ions on the structure of water a considerable amount of evidence supporting their general conclusions has been Thus solution of ions in water produces a decrease in entropy in the immediate vicinity of the ion and an increase in entropy in a region further from the ion.The latter is due to disruption of the water structure by the solvated ions whose bound water molecules are incorrectly oriented to fit into the hydrogen-bonded structure of water. In Table 6 the entropies of solution of ions in water from the crystal state,6' based on the assumption that the entropy of an ion in a crystal is independent of the crystal lattice holding it,66 are listed. After allowing for a normal increase on transfer from the solid to the liquid state (298A$, ca. 3 kcal ion- ' for a molar solution)6' the results suggest a net loss of entropy for solution of Li+ varying to a slight gain for solution of Cs' with similar variation for anions F- to I-.The variation from Li+ to Cs' and F-to I- presumably reflects the variation in the number of water molecules held in the immediate vicinity of the ion. However in the dipolar aprotic solvents which unlike water show no anomalous entropy behaviour when for example non-polar solutes are dissolved in them while entropy losses resulting from 'freezing' of solvent molecules in the vicinity of the ion may be similar to those in water there should be no compensating gain in entropy comparable to that resulting from the structure-breaking effect of the solvated ions in water. Such an effect will also cause an increase in the enthalpy of solution of these ions in water relative to the dipolar aprotic solvents because of the unfavourable enthalpy of breaking hydrogen bonds.The relatively " H. S. Frank and M. W. Evans J. Chem. Phys. 1945 13 507. 64 H. G. Hertz Angew. Chem. Internat. Edn. 1970 9 124. " B. G. Cox and A. J. Parker J. Amer. Chem. SOC.,1973,95,6879. " W. M. Latimer 'The Oxidation States of the Elements and Their Potentials in Aqueous Solution' 2nd edn.. Englewood Cliffs N.J.,1952. 264 B. G. Cox smaller decrease in entropy on transfer of Li’ and also F-from water may be a result of larger numbers of water molecules being ‘frozen’ around the ions relative to dipolar aprotic solvent molecules because of the ability of water molecules to transfer charge through hydrogen bonds. Such an effect should be even more pronounced for multiply charged ions. The observed increase in entropy on transfer of the larger ‘organic’ ions from water is typical of the behaviour of non-electrolytes which has been interpreted as being due to an increase in the structure of water in the presence of the non- electrolyte^.^^^^^ These results suggest that the charge on these large ‘organic’ ions is relatively unimportant in determining their solvation behaviour.The behaviour of the electrolytes in the other protic solvents methanol formamide and N-methylformamides ’ is difficult to interpret in detail but in general is intermediate between the behaviour in water and in the dipolar aprotic solvents. This suggests that the effects due to the hydrogen-bonded structure of these solvents are similar to but smaller than those in water. 3 Acid-Base Equilibria Large changes in the positions of acid-base equilibria are frequently found on transfer from water to dipolar aprotic solvents.These are often of considerable practical importance both in the quantitative analytical determination of weak base~~~~~and in the promotion of many base-catalysed elimination reactions’ and reactions involving the ionization of carbon acids.70 Recently much interest has been centred on the use of acet~nitrile~~,’’ and ~ulfolane~~~~ as media for acid-base studies. Both have very low proton basicities and are much weaker acids than water. Consequently very high acidities and basicities can be reached enabling very weak acids and bases to be studied. Perchloric acid solutions in ~ulfolane~~ have been used to titrate a considerable range of weak bases including acetone methanol and acetic acid and even protonation of acetonitrile and nitrobenzene has been observed conductimetrically.Quantitative determination of pK,’s in sulfolane however has been hampered by difficulties with the use of glass and hydrogen elec- trode~.~’*~* Perchloric acid solutions (>1moll-’) in sulfolane have been known to explode spontaneously6* and the use of HSbC1 has been recommended for analytical purposes. pK determinations in acetonitrile present less of a problem as the glass electrode responds reversibly to hydrogen activity over a very wide range,73 and the indicator method with p-nitrobenzyltriphenylphosphonium perchlorate as the reference acid has also been successfully used.71 67 J.F. Coetzee and R. J. Bertozzi Analyt. Chem. 1973,45 1064. R. L. Benoit and P. Pichet Electroanalyt. Chem. 1973 43 59. 69 J. F. Coetzee and R. J. Bertozzi An&. Chem. 1971 43 961. 70 J. R. Jones ‘The Ionisation of Carbon Acids’ Academic Press London 1973 Ch. 6. 71 0.Vikane and J. Songstad Acta Chem. Scand. 1973,27,421. 72 I. M. Kolthoff and M. K. Chantooni J. Amer. Chem. SOC. 1973 95,4768. 73 J. F. Coetzee and G. R. Padmanabhan J. Amer. Chem. SOC. 1965,87 5005. Electrolyte Solutions in Dipolar Aprotic Solvents 265 Extensive studies of acid-base equilibria in DMSO and DMF have also been carried out. Experimental methods used include conductance mea~urements,~~*~~ potentiometric measurements with glass74,76-78 and hydrogen electrode^,^' and spectrophotometric measurements.7497 7,80 Dissociation constants of a variety of acids in acetonitrile DMF and DMSO are listed in Table 7. Also given for comparison are the corresponding values in Table 7 Dissociation constants of acids in solvents" at 25 "C pK values Acid H20b MeOH HCONH2 DMF DMSO MeCN Hydrochloric -7' 1 .2d -3.4' 2.0' 8.9' H ydrobromic -9' -1.8' 1.8' 5.5' Picric 0.7 3.8' 1.21 1.2' -0.3' 8.9' -Dichloroacetic 1.29 6.4d 2.91 7.2' 5.9B Chloroacetic 2.86 7.7d 4.6.' 9.e Acetic 4.76 9.6' 6.9h 13.6' 12.6' 22.4' Benzoic 4.20 9. 1' 6.21 12.3' 1 1.0' 20.7' rn-Bromobenzoic 3.81 -11.3' 9.7k 19.5' rn-Nitrobenzoic 3.49 -5.4/ 10.8' 9.2' 19.3k p-Nitrobenzoic 3.43 -5.9' 10.6' 9.0' 18.7' 3,s-Dinitrobenzoic 2.82 -8.9k 7.4' 16.9' Phenol 9.98 14.2' ->lSd 16.4' 27.2' Anilinium ion 4.60 -4.1f -10.6"' -rn-Nitroanilinium ion 2.46 --1.3" a Abbreviations as in Table 1 ; A.Albert and E. P. Serjeant 'Ionization Constants of Acids and Bases' Methuen London 1962; 'R. P. Bell 'The Proton in Chemistry' 2nd edn. Chapman and Hall London 1973 p. 86; B. W. Clare D. Cook E. F. C. KO Y.C. Mac and A. J. Parker J. Amer. Chem. Soc. 1966 88 1911; 'ref. 75;'F. H. Verhoek J. Amer. Chem. SOC.,1936,58,2577;EN. M. Ballash E. B. Robertson and M.D. Sokolow- ski Trans. Faraday SOC.,1970 66 2622; B. Nayak and U. N. Dash Austral. J. Chem. 1973 26 111; 'ref. 83; 'I. M. Kolthoff M. K. Chantooni and S. Bhowmik J. Amer. Chem. SOC.,1968 90 23; 'ref. 77; ' U. N. Dash and B. Nayak Austral. J. Chem.1.972 25,941; ref. 87; 'ref. 80. water methanol and formamide. In Table 7 dissociation constants (K,)for the equilibria HA %H++ A-in solvent S are defined by equation (6)and refer to infinite dilution in solvent S. Dissociation constants for cationic acids (HA') are similarly defined. The difference between the pK of acid HA in solvent S and a reference solvent 0is simply related to the free energies of transfer of the species 74 I. M. Kolthoff M. K. Chantooni and H. Smagowski Analyt. Chem. 1970 42 1622. 75 R. L. Benoit and C. Buisson Electrochim. Acta 1973 18 105. 76 J. Juilliard J. Chim. phys. 1970 691. 77 I. M. Kolthoff and M. K. Chantooni J. Amer. Chem. Soc. 1971,93 3843. 78 C. D. Ritchie and R. E. Uschold J. Amer. Chem. Soc. 1967,90 2821.79 J. Courtot-Coupez and M. Le Demezet Bull. SOC. chim. France 1969 1033. R.G. Bates L. Johnson and R. A. Robinson Chem. anulit. 1972,17 479. 266 B. G. Cox involved HA A- and H' by equation (7) and similarly for acid HA+. For (PKA -(PKJO = [AGtr(H+) + AGtr(A-) -AGtr(HA)I/RT (7) neutral acids HA AGJHA) from water to the dipolar aprotic solvents is normally negative and so leads to an increase in pK,(HA). The magnitude of this effect however is not large. For the transfer between water and DMSO of acetic acid AGJHOAc) = -1.2 kcal mol- (corresponding to 0.9 pK units),8' and transfer of a variety of esters from water to DMSO and acetonitrile results in free-energy decreases of less than 3 kcal mol- 1.82 Chantooni and Kolthoff E3 have measured the solubilities of a variety of substituted benzoic acids and their corresponding methyl esters in acetonitrile DMF and DMSO.The free energies of transfer of the esters from acetonitrile to the other two solvents are very small (<0.5 kcal mol-') but those of the acids are ca. -1.5 kcal mol- ',which they attribute to the effect of hydrogen-bond formation between the acids and the basic oxygens of DMSO and DMF. From the known solubilities of some of the acids in waterE4 together with Chantooni and Kolthoffs results,83 it is possible to calculate free energies of transfer of the acids from water to these solvents. For transfer from water to DMF AGlr values for benzoic and rn-and p-nitrobenzoic acids are -3.3 -2.6 and -2.5 kcal mol- ' respectively.Corresponding values for transfer to acetonitrile are -2.0 -2.2 and -1.5 kcal mol- '. In general then the free-energy decrease on transfer from water to the dipolar aprotic solvents of the neutral acids in Table 7 should be less than ca. 3 kcal mol- '(corresponding to an increase of <2.2 pK units). The observed increases in pK of neutral acids on transfer from water shown in Table 7 are entirely consistent with the behaviour expected from the results of the studies on the free energies of transfer of ions reported in Section 2. Thus pK,'s are highest in acetonitrile which poorly solvates both anions and cations and the results in DMSO and DMF are consistent with a large decrease in anion solva- tion outweighing the favourable proton solvation arising from interaction with the basic oxygen atoms.Where sufficient data are available it is possible to test quantitatively the consistency of the directly measured pK,'s with the results of the ion-solvation studies by means of equation (7). For benzoic acid substitution in equation (7) of the pK in water (4.2) together with the free energies of transfer to acetonitrile of H+ and OBz- obtained from electrochemical and solubility measurements ( +1 1 .O and +9.7 kcal mol -respectively2') and the above value of the free energy of benzoic acid (-2.0 kcal mol- ') leads to a predicted value of pK = 20.9 in excellent agreement with the directly measured value of 20.7." A similar treatment for transfer of benzoic acid to DMF leads to a calculated value of pK = 11.9 compared with the measured value of pK = 12.3.It is noticeable that within a given series of related acids (e.g. substituted benzoic acids halogen-substituted acetic acids and phenol and picric acid) J. Courtot-Coupez M. Le Demezet A. Lavenan and C. Madec J. Electroanalyt. Chem. Interfacial Electrochem. 197 I 29 2 1. 82 B. G. Cox J.C.S. Perkin 11 1973 607. 83 M. K. Chantooni and I. M. Kolthoff J. Phys. Chem. 1973,77 527. 84 The Merck Index ed. P. G. Stecher Merck (USA) 8th edn. 1968. Electrolyte Solutions in Dipolar Aprotic Soluents 267 the pK,’s in the dipolar aprotic solvents are considerably more sensitive to the effect of substituents than they are in water. This is presumably because increases in acidity caused by substituents result at least partially from increased delocaliza- tion of the negative charge on the anion an effect which also tends to decrease the solvation of such ions by water relative to the dipolar aprotic solvents.Recent measurements on halogen-substituted acetic acids in the gas phase,85 which suggest a difference in pK between acetic acid and dichloroacetic acid of 15 units compared with 6.4 in DMF and 3.5 in water are consistent with this explanation. One other phenomenon frequently observed in dipolar aprotic solvents is that of homoc~njugation~ 1*77,83 in which the anion A-associates with the neutral molecule (HA) by means of hydrogen-bonding i.e.A-+ HA %(AHA)-. This again presumably results mainly from the very high activity of the ions A-in the dipolar aprotic solvents relative to water.The behaviour of the cationic acids (HA’ % H + A) of which the anilinium + and m-nitroanilinium ions are typical examples depends primarily on the dif- ference of the solvent effects on the activity of the proton and the cation HA+. In DMSO the pK of the rn-nitroanilinium ion is slightly lower than in water,80 and values for a variety of substituted anilinium ions in mixtures of DMSO and waters6 suggest that this behaviour is quite general. This is not unexpected as the solvation of the proton and the anilinium ions by DMSO relative to water may be rather similar and the neutral anilines should be more stable in DMSO. The increases in pK on transfer to acetonitrile for the anilinium ion and substituted anilinium ions87 of some 6 pK units are as expected considerably less than those observed for the neutral acids.The results in Section 2 suggest that the major reason for this increase is the large increase in the free energy of the proton when transferred from water to acetonitrile. Formamide is known to be a good solvent for ions (Section 2) and this is borne out by the pK,’s shown in Table 7. These are in general only slightly higher than the corresponding values in water. Similar results have been found when N-methylpropionamide is used as the solvent.88 4 Conductance A substantial body of data on the conductivities of ions in non-aqueous and in particular dipolar aprotic solvents now exists. Conductivities of electrolytes in HMPA,89-9 propylene carbonate,’ and trifl~orethanol’~ have recently 792 been reported.In addition comprehensive studies in ~ulfolane,~~ DMSO,” ’’ K. Hiraska R. Yamdagni and P. Kebarle J. Amer. Chem. SOC.,1973,95,6833. E6 K. Yates and G. Welch Canad. J. Chem. 1972,50 474. J. F. Coetzee Progr. Phys. Org. Chem. 1967 4 45. E. S. Etz R. A. Robinson and R. G. Bates J. Solution Chem. 1972 1 507. E9 P. Bruno M. Della Monica and E. Righetti J. Phys. Chem. 1973 77 1258. 90 S. Bhandani Indian J. Chem. 1972 10 88. 9’ U. Mayer V. Gutmann and A. Lodzinska Monatsh. 1973 104 1045. 92 L. M. Mukherjee D. P. Boden and R. Lindauer J. Phys. Chem. 1970,74 1942. ’’ D. F. Evans J. A. Nadas and M. A. Matesich J. Phys. Chem. 1971 75 1708. 94 A. P. Zipp J. Phys. Chem. 1973 77 718. ’’ N. P.Yao and D. N. Bennion J. Electrochem. Soc. 1971 118 1097. 268 B. G. Cox DMF,96-97 and acetoneg8 have supplemented data previously obtained in these solvents. The determination of single-ion conductivities in non-aqueous solvents has been hampered by experimental difficulties encountered in the application of standard methods of obtaining transport numbers.99 This has led to the use of various empirical methods to determine single-ion conductivities. These are usually based on the assumption that the constituent ions of certain reference electrolytes such as tetraisoamylammonium tetraisoamylboride have equal mobilities. Recent measurements of transport numbers in DMSO,' O0 propylene carbonate,g2 DMF,96 and acetonitrile'O' have largely removed this problem although transport numbers in HMPA and trifluoroethanol have not yet been reported.In the solvents where transport numbers have been reported agree- ment between single-ion conductivities obtained from transport-number mea- surements and those based on the reference electrolyte assumption is generally excellent. Thus Mukherjee Boden and Lindauerg2 found a value of Ao(I-) in propylene carbonate equal to 18.78cm2 Int R-'equiv.-' from transport-number measurements and 18.76Cm2 Int. R-'equiv.-' when it was assumed that A0(Ami4N') = A0(Ami4B-). Similarly measured and estimated values ofA' for ions in acetonitrile'" agreed within 0.35 conductivity units and within 0.5 conductivity units in DMS0.'00*'02 In all cases agreement between estimated and measured single-ion values appears to be at least as good as agreement between conductivities determined in a given solvent by different investigators.Information on ion-solvent interactions from conductivity studies comes principally from two sources. From measurements of the variation of equivalent conductances with concentration it is possible to estimate ion-pair association constants (where ion-pair formation occurs). Such a procedure is not entirely straightforward as the resulting association constants are somewhat dependent upon the equations used to allow for the effect of interactions between the electric charges of the free ions on the observed condu~tance.~~ The relative values of the association constants for different electrolytes in a given solvent however seem to be less dependent upon the equations used.The variation of the association constants with solvent can generally be interpreted in a relatively straightforward manner in terms of the solvation effects discussed in Sections 2 and 3. Thus Mayer Gutmann and Lodzinskagl find that although LiCl and LiBr are associated in propylene carbonate they are completely dissociated in HMPA in agreement with expectations from ion-solvation studies in the two solvents." Similarly ion-association constants in trifluoroethanol compared with those 96 R. C. Paul J. P. Singla D. S. Gill and S. P. Narula fndian J. Chem. 1971 9,981. 97 V. M. Ryabikova B. S. Krumgal'z and K. P. Mischchenko Russ. J. Phys. Chem. 1971,45 1451. 98 H. C. Brookes M.C. B. Hotz and A. P. Spong J. Chem. SOC. (A) 1971 2410 2415. 99 R. A. Robinson and R. H. Stokes 'Electrolyte Solutions' 2nd edn. Butterworths London 1965. loo A. G. Nelson and D. N. Bennion J. Electrochem. SOC. 1973,120 71. lol C. H. Springer J. F. Coetzee and R. L. Kay J. Phys. Chem. 1969,73,471. lo2 M. Della Monica D. Masciopinto and G. Tessari Trans. Faraday SOC. 1970 66 2872. 269 Electrolyte Solutions in Dipolar Aprotic Solvents in ethanol are consistent with enhanced anion solvation in triflu~roethanol.~~ Copper(I) and silver([) perchlorates in acetonitrile behave as strong electrolytes,' O3 contrasting sharply with the alkali-metal perchlorates which have association constants in the range 10-20 in this Electrolytes are normally com- pletely dissociated in formamide,' O5 as expected and only very weakly associated in N-methylformamide.'06 In most of the above references the absolute magni- tudes of the ion-pair constants and their variation with ion size in a given solvent are also considered in terms of the theories of Bjer~um'~' and FUOSS,"~ but discussion of this is beyond the scope of this Report.The second source of information on ion-solvent interactions is the limiting ionic conductances and their variation with solvent. The limiting ionic conduc- tances of ions in a number of dipolar aprotic solvents are given in Table 8. The Walden products (qn') where q is the viscosity of the solvent have also been included in Table 8. The simplest starting point for a discussion of ionic conductances is probably Stokes' Law in which the limiting conductance of a singly charged ion (A') of radius r, moving through a continuous medium of viscosity q,is given by equa- tion (8).Thus the Walden product (A'q) should be inversely related to the size i.' = 0.82/qrs (8) of the moving ion (including solvation sphere) which in turn should be related to the strengths of the ion-solvent interactions. A comparison of Walden products for cations and anions suggests that such an interpretation may be at least qualitatively reasonable. In water K+ and C1- have almost equal Walden products whereas in all of the dipolar aprotic solvents qAo(K+)<< @'(Cl-). This suggests a large decrease in the size of solvated C1- relative to K+ on transfer from water.A number of authors89~97~98~'05*'06 have treated the problem more quantitatively following a suggestion by Robinson and Stokesg9 that equation (8) be modified by arbitrarily adjusting the constant so that the calculated values of rs agree with the crystallographic radii of the tetra-alkylammonium ions which are assumed to be unsolvated. Hydration numbers of the various ions are then obtained from equation (9) where rcoris the solvated radius of the ion obtained from the modified Stokes equation rc is the crystallographic radius and V is the volume of a solvent molecule. Hydration numbers obtained in this manner seem generally reasonable but it is difficult to assess their physical significance. Comparison of Walden products in the various dipolar aprotic solvents however does not lead to any obvious correlation between the free energies of lo' H.L. Yeager and B. Kratochvil J. Phys. Chem. 1969,73 1963. Io4 R. L. Kay B. J. Hales and G. P. Cunningham J. Phys. Chem. 1967,71 3925. R. C. Paul J. P. Singla D. S. Gill and S. P. Narula Indian J. Chem. 1971 9 981. Io6 R. C. Paul D. S. Gill J. P. Singla and S. J. Narula Indian J. Chem. 1971 9 63. lo' N. Bjerrum Kgl. Dan. Vidensk. Selsk. 1926 7 9. Io8 R. M. Fuoss J. Amer. Chem. SOC.,1958.80 5059. Table 8 Limiting ionic conductances (A') and Walden products (qA') in solvents" at 25 "C Vulues of Lo/cm2 Into-' equiv.-';qL0/p cm2 Into-' equiv.-HMPA' H 20b DM F' ~~so~.~ PCP TMS~ Me2COi MeCNJ Ion 1' '710 Lo qL' 1' '11' 1' '11' A' '120 1O q1' A' '11' Lo '11' H+ 349.8 3.1 32.7k 0.26 15.4 0.31 ---100 0.32 Li 38.6 0.34 23.6 0.19 11.2 0.22 6.8 0.23 7.3 0.18 4.3' 0.44 84.1 0.27 69.3 0.24 + Na 50.1 0.46 30.0 0.24 14.5 0.29 5.9 0.20 -3.6 0.37 87.1 0.28 76.9 0.27 + K+ 73.5 0.65 31.7 0.25 15.1 0.30 6.1 0.20 12.0 0.30 4.1 .0.42 75.6 0.24 83.6 0.29 Rb+ 77.8 0.69 32.4 0.26 ---4.2 0.43 -85.6 0.30 cs 77.2 0.69 34.6 0.28 ---4.3 0.44 -87.3 0.30 + Ag+ 61.9 0.55 35.2 0.28 16.6 0.33 -~ ---86.0'" 0.30 __-Me,N+ 44.9 0.40 38.8 0.31 18.7 0.37 -4.3 0.44 93 0.29 94.5 0.33 Et,N+ 32.6 0.29 36.0 0.29 17.2 0.34 9.4 0.31 13.3 0.33 4.0 0.41 86 0.27 84.8 0.29 Pr,Nf 23.4 0.21 29.8 0.24 13.6 0.27 7.1 0.24 -3.2 0.33 70 0.22 70.3 0.24 Bu,N 19.5 0.17 26.4 0.21 11.8 0.24 6.1 0.20 9.4 0.24 2.8 0.29 62 0.20 61.4 0.21 + c1-76.4 0.68 56.5 0.45 22.9 0.46 21.9" 0.73 20.2 0.51 9.3 0.96 110 0.35 89" 0.31 Br-78.1 0.70 53.1 0.42 23.5 0.47 18.0 0.60 19.3 0.48 8.9 0.92 122 0.39 101 0.35 I-76.8 0.68 51.2 0.41 23.1 0.46 -18.8 0.47 7.3 0.75 121 0.38 102 0.35 ClO,-67.4 0.60 59.3 0.47 24.2 0.48 15.2 0.51 18.8 0.47 6.7 0.69 114 0.36 104 0.36 OAc-40.9 0.36 -~ ------107P 0.37 Pic -30.4 0.27 57.4 0.46 16.8 0.34 11.3 0.38 -3.8 0.39 90 0.28 78 0.27 SCN --59.3 0.47 -20.1 0.67 22.9 0.57 126 0.40 BPh,-19.79 0.18 -11.1 0.22 6.0' 0.20 -2.5 0.25 -58.3 0.20 Abbreviations as in Table 1 ; ref.99; ref. 96; ref. 95; ref. 100; f ref. 89; 8 ref. 92; ref. 94; ref. 98; j ref. 101 ; Ir ref. 97; ' R. Fernandez-Prini and J. E. Prue Trans. Furuduy SOC.,1966,62 1257; ref.103; "ref. 91 ; "ref. 87; P ref. 39; 9 J. F. Skinner and R. M. Fuoss J. Phys. Chem. 1964 68 1882; 'ref. 90. Electrolyte Solutions in Dipolar Aprotic Solvents 27 1 transfer of the ions and the variation in Walden products. Thus solvated cations in DMSO and DMF appear to have smaller solvated radii than in acetone and similar to those in acetonitrile. Also the solvated radius of Na' on transfer from DMF to acetonitrile increases relative to that of Ag' despite the much more favourable free energy of solvation of Ag' (Section 2). The conductance of Cu' in acetonitrile is however considerably smaller than that of other cations of similar crystallographic radii. O9 Both anions and cations have considerably higher Walden products in sulfolane than in the other dipolar aprotic solvents but this may not have any physical significance.The viscosity of sulfolane is at least three times higher than that of any of the other solvents so that any limita- tions of the simple relationship between conductance and viscosity indicated by Law would be much more apparent in this solvent. It was shown in Section 2 of this Report that the entropies of transfer of elec- trolytes from water to the dipolar aprotic solvents were essentially constant and independent of the corresponding free energies of transfer. It is reasonable that the entropy loss on solution of an ion and the solvated radius of the ion may be related as both presumably depend on the extent of restriction of the motion of surrounding solvent molecules relative to the ion.Beyond a certain level further increase in specific ion-solute interactions should not result in further significant losses in entropy or increase of solvated radius (once the first solvation sphere is complete). It may be significant in this context that apart from some anions in sulfolane the Walden products of simple ions are generally much higher in water than in any of the dipolar aprotic solvents whereas they are lower for the larger tetra-alkylammonium ions and the tetraphenylboride ion. A modification of the Stokes continuum theory to allow for retardation due to relaxation of the solvent dipoles around a moving ion has been proposed by Zwanzig.'" Zwanzig's equation has been tested in a number of solvents and the results of Yao and Benion" in DMSO which suggest that the predicted Walden products show the correct general variation with the crystallographic radii of the ions but differ considerably in magnitude from the experimental values appear to be typical.5 Spectroscopic Studies Spectroscopic studies of ion solvation may complement the techniques mentioned above as they enable a more direct study to be made of the effects of ions on the properties of the solvent. The effects of added electrolytes on the n.m.r. chemical shifts of solvent protons and the i.r. spectra of solvents provide examples of this. In addition certain ions such as 23Na and 35Cl may be studied directly using the n.m.r. technique. A disadvantage common to all of the spectroscopic techniques is the necessity of using concentrated electrolyte solutions (frequently > 1 moll-l) which often results in extensive ion-pair formation thus complicating the inter- pretation of the results.'09 H. L. Yeager and B. Kratochvil J. Phys. Chem. 1970,74 963. 'lo R. Zwanzig J. Chem. Phys. 1963 38 1603. 272 B. G.Cox In certain favourable cases where exchange of co-ordinated solvent molecules with the bulk solvent molecules is slow it is possible to observe separate n.m.r. signals for protons on free and co-ordinated solvent molecules. Crea and Lincon"' found that when A13+ Ga3+ or In3+ (perchlorates) were dissolved in trimethyl phosphate (TMP) two separate TMP 'H n.m.r. signals were ob- served these being assigned to free and co-ordinated TMP.Integration of the peak areas showed a co-ordination number of 6 for each ion. Addition of acetone had no effect on the co-ordination of TMP but addition of water resulted in successive replacement of TMP by water in the co-ordination sphere. A similar study of GaCl solutions ( >3 moll-') in acetonitrile' '*using 'H n.m.r. and 71Ga n.m.r. spectroscopy showed much lower co-ordination numbers indicating the formation of complex GaCl species. Lanthanide salt solutions in water-acetone mixtures at temperatures below -60 "C'l3 were found to be entirely co-ordinated to water molecules but addition of DMSO resulted in replacement of some of the co-ordinated water molecules by DMSO. Extensive complex formation was observed with nitrate ions but not with perchlorate ions.For most ions particularly at temperatures around 25 "C solvent exchange is very rapid on the n.m.r. time-scale and the observed chemical shifts represent a weighted average of those resulting from solvent molecules in the vicinity of the ions and in the bulk solvent. For salts not containing paramagnetic ions ob- served shifts are small and in all cases assumptions are required to separate effects due to anions and cations. Coetzee and Sharpe' l4 have measured the effects of a variety of salts on the 'H n.m.r. shifts of acetonitrile DMSO and sulfolane. For each solvent shifts due to Li+ were greater than those due to Na+ and K+ and those due to C1- greater than those of Br-or I- but the differences were very small. Infrared measurements in acetonitrile showed similar trends although it was observed that variation in anions resulted only in variations in the C-H stretching frequency whereas variation in cations affected both the C-C stretch and in particular the C EN stretching frequencies.N.m.r. studies of this type are probably more useful in mixed solvents where by comparing ion-induced solvent shifts in mixtures with those in the puresolvent it is possible to obtain information about the relative abilities of two solvents to solvate an ion. Stengle Pan and Langford"' have measured 35Cl- 79Br- and 1271- chemical shifts in mixtures of water and acetonitrile. The results suggest preferential solvation of these anions by water with the effect decreasing in the order C1- > Br-> I-.The authors point out that preferential solvation by water will be accentuated by the high water activities in the mixtures. 23Na chemical shifts in several binary solvent mixtures' l6 indicate strong preferential solvation by DMSO in mixtures with acetonitrile nitromethane and even pyri- dine. J. Crea and S. F. Lincon Znorg. Chem. 1972 11 1 13 I. S. F. Lincon Austral. J. Chem. 1972 25 2705. l3 A. Fratiello V. Kubo and G. A. Vidulich Znorg. Chem. 1973 12 2066. 'I4 J. F. Coetzee and W. R. Sharpe J. Solution Chem. 1972 1 77. 'Is J. R. Stengle Y.-C. E. Pan and C. H. Langford J. Amer. Chem. Soc. 1972,94,9037. R. H. Erlich M. S. Greenberg and A. I. Popov Specrrochim. Acta 1973 29A,543. Electrolyte Solutions in Dipolar Aprotic Solvents Popov and co-workers' ''-' ha ve measured the chemical shifts of 23Na' in a variety of solvents relative to that in water.They found an excellent cor- relation between the 23Na chemical shifts and Gutmann's donor numbers.'20 These latter are simply the heat of complex formation between a solvent S and antimony pentachloride in 1,2-dichloroethane and represent an attempt to define quantitatively the electron-donating ability of solvent S. Several spectroscopic studies of ionic solvation in propylene carbonate have been reported. Cogley Butler and Gr~nwald~~ have determined equilibrium constants for association of water with Li+ Na' K' and C1- from measure- ments of chemical shift of water at low concentrations in propylene carbonate. The affinity of water at low concentrations in propylene carbonate for alkali- metal cations correlates well with the free energies of transfer of these ions from propylene carbonate to bulk water reported in Section 2.The results for C1- suggest that the stabilization of C1- in water by co-operative interactions is at least as important as direct co-ordination of the ion by water molecules. New bands in the i.r.I2' and far-i.r.'22 region have been observed when alkali-metal and silver salts are dissolved in propylene carbonate. These have been attributed to solvated propylene carbonate and in particular the bands in the region 112 cm-' (Cs') to 397 cm-' (Li') have been attributed to cation-solvent vibration bands.12* New bands in the far-i.r. have also been observed in solutions of sodium and potassium salts in sulfolane.'23 The bands which were independent of the anion present (I- ClO,- and BPh4-) were both weaker and at lower frequency than corresponding bands observed in DMS0.lZ4This is consistent with the results of free-energy studies which suggest that sulfolane is a much poorer solvent for cations than DMSO.The observed independence of the bands on the anion probably indicates that any ion pairs formed are solvent-separated ion pairs rather than contact ion pairs. Solubility and e.m.f. measurements in nitromethane' ' show that nitromethane is a very poor solvent for ions. This has been confirmed qualitatively by the results of several spectroscopic studies. Both i.r. 125 and n.m.r. studies"6 suggest preferential solvation of cations by acetonitrile in mixtures of acetonitrile and nitromethane.Similar studiesI2 ' also suggest that acetone and propylene carbonate also solvate cations more strongly than does nitromethane. Infrared measurements in acetone and acetone-nitromethane mixtures126 showed new peaks attributable to metal ion-acetone vibrations but showed no evidence of ' M. Herlem and A. I. Popov J. Amer. Chem. SOC.,1972,94 141 3. 'I8 R. H. Erlich and A. I. Popov J. Amer. Chem. SOC.,1971 93 5620. 'I9 R. H. Erlich E. Roach and A. I. Popov J. Amer. Chem. SOC.,1970,92,4989. ' 2o V. Gutmann 'Coordination Chemistry in Non-aqueous Solutions' Springer-Verlag Vienna 1968. H. L. Yeager J. D. Fedyk and R. J. Parker J. Phys. Chem. 1973,77 2407. "' M.S. Greenberg D. M. Wied and A. I. Popov Spectrochim. Acta 1973 29A 1927. T. L. Buxton and J. A. Caruso J. Phys. Chem. 1973,77 1882. B. W. Maxey and A. I. Popov J. Amer. Chem. SOC.,1969,91 20. A. Regis and J. Corset Canad. J. Chem. 1973 51 3577. M. K. Wong W. J. McKinney and A. I. Popov J. Phys. Chem. 1971,75 56. 274 B. G.Cox metal ion interaction with nitromethane. The involvement of both the metal ion and acetone in the vibrations was confirmed by measurements involving 6Li+ and [2H6]acetone. It appears that the major advantage of the spectroscopic techniques lies in the possibility of a more detailed look at ion-solvent interactions at a molecular level. Information of a quantitative nature has to date been rather limited because of the difficulty of relating observed spectral shifts to the magnitudes of interaction energies.The studies have however provided independent qualitative con- firmation of the interpretation of thermodynamic studies of ion solvation.

ISSN:0308-6003    

DOI:10.1039/PR9737000249

出版商:RSC    

年代:1973

数据来源: RSC