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.