ISSN:0069-3022    

DOI:10.1039/GR96764FX001

出版商:RSC    

年代:1967

数据来源: RSC

ISSN:0069-3022    

DOI:10.1039/GR96764BX003

出版商:RSC    

年代:1967

数据来源: RSC

摘要:

3. THEORETICAL CHEMISTRY By J. G. Stamper (The Chemical Laboratory University of Sussex Brighton BN1 9Q4 1967 has not seen any single outstanding achievement in the field of theoretical chemistry. Rather there has been steady progress on a number of fronts some of which are reported here. I have made no attempt to report on progress in scattering theory although this is a very active field of theoretical chemistry, I have commented in some detail on electron correlation Hartree-Fock calcula-tions semiempirical methods and intermolecular forces and there is also a miscellaneous section devoted to several topics which could not be grouped under any single head. At present it is probably fair to say that almost all calculations on the elec-tronic structure of atoms and molecules follow a common basic approach.The problem is thought of as being in two parts the calculation of a molecular-orbital wave-function and a subsequent calculation or estimation of correlation effects. A calculation which leads to a wave-function expressed in terms of molecular orbitals takes account of the electrostatic repulsion between the electrons only by considering that each electron moves in a potential which is the result of averaging the effects of the remaining electrons over their motion. Mathematically this leads to the well-known Hartree-Fock equation. The wave-functions which result from a solution of this equation are suffici-ently accurate for many purposes. They give a very accurate account of the charge distribution in atoms and molecules and a number of other experi-mentally observable qualities (dipole moments diamagnetic susceptibilities etc.).They also give good results for the energy of the system expressed in terms of percentage accuracy. However the total energies of most atoms and molecules are so large compared with chemical energies that the few percent inaccuracy of the Hartree-Fock energy is comparable for example with the bond energy of the molecule. Thus Hartree-Fock calculations of bond energies are usually only accurate to about 50 % and in some cases e.g. F, a known stable molecule is actually predicted to have a negative bond energy. Some other atomic and molecular properties are also badly predicted from the Hartree-Fock wave-functions the nuclear hyperfine coupling constant fQr phosphorous being an example.The remaining energy beyond the Hartree-Fock result is due to the fact that an electron in a molecule actually moves in the instantaneous field of the remaining electrons and the motion of the electrons is thus correlated. Electron Correlation.-A number of methods have been used to introduce electron correlation into atomic and molecular wave-functions. The two most used methods dating back to the very early days of quantum mechanics ar 24 J. G. Stamper the introduction of inter-electronic distances (rij) as explicit variables in the wave-function and the method of configuration interaction (C.I.). In the latter, the wave-function is expressed as a linear combination of determinantal wave-functions in which the leading term is the ordinary molecular orbital wave-function.The application of both methods to simple systems such as the hydro-gen molecule and the helium atom though laborious presents no fundamental difficulties and has been carried out repeatedly with increasing accuracy. When attempts are made to deal with larger systems however both methods quickly become intractable in their basic form. In the case of the rij method the number of rij co-ordinates increases as i N ( N - 1) where N is the number of electrons, while the number of degrees of freedom of the system increases only as 3N so that for quite a small value of N the rij’s cease to be independent and the method fails. In the case of configuration interaction the number of configurations needed for a given accuracy increases rapidly with N so that the complete problem soon becomes unmanageable.One way through this impasse is to deal with the correlation in small sub-groups of electrons independently. The idea originated with theoretical physicists’. working on problems of nuclear structure and its application to chemical systems was probably first suggested by Sinanoglu3 and S Z ~ S Z . ~ Sinanoglu pointed out that pair correlations were likely to be the most impor-tant and that each electron correlated mainly with one other in atomic and molecular systems (the one in the same molecular orbital). He also calcu-lated the correlation energy in the beryllium atom’ using these ideas but esti-mating certain terms. 1967 has seen the first application of this approach to a larger atom by Nesbet.6 In principle the method consists of selecting a group of electrons (say the pair in a 1s orbital) and solving a modified Schrodinger equation (the Bethe-Goldstone equation) for the detailed motion of these electrons in the average potential of the remaining electrons (the so-called Fermi sea or Hartree-Fock sea).Any method may be used to solve the Bethe-Goldstone equation but in practice Nesbet uses a variational method. An important constraint on the solution is that it must be orthogonal to the Hartree-Fock solution. This is very difficult to achieve if a variation function containing r j j is used though this would otherwise be the obvious choice. In consequence Nesbet uses a configura-tion interaction calculation which also allows formulation of the problem in a very simple way.Let Q be the solution of the Hartree-Fock equation and let @$ be a con-figuration (Slater determinant) in which electrons have been excited from spin-orbitals a b . to spin-orbitals i,j . . Then the complete C.I. wave-function can K. Brueckner Phys. Rev. 1954,% 508; 1955,97 1353. H. A. Bethe and J. Goldstone Proc. Roy. SOC. 1957 A 238,551. 0. Sinanaglu J . Chem. Phys. 1962,36,706. L. Szasz Z. Naturforsch. 1960,15a 909; Phys. Rev. 1962,126 169. D. F. Tuan and 0. Sinanogly J. Chem. Phyi. 1964,41,2677. R. K. Nesbet Phys. Rev. 1967,155,51,56 Theoretical Chemistry 25 be written where the summations run over all possible values of abc . . . ijk . . . . The solution of the Bethe-Goldstone equation for the pair of electrons in spin-orbitals a and b is i j where the coefficients C:; are found by the variation principle using the full Hamiltonian operator for the system i.e.by a straightforward matrix diagonali-zation procedure. If the energy obtained as a result of this calculation is Eab, and Eo is the energy obtained from the Hartree-Fock wave-function Nesbet defines the pair correlation energy for the pair ab as The process can then be repeated for all other pairs of electrons and the total pair correlation energy e12 found. e 1 2 = z e a b a b (4) This approach can be extended formally to three electron and larger groups in an obvious way and the total energy of the system then appears as The advantage of this is that although calculation of all the energy increments e requires a solution of the complete C.I.problem for the system it seems certain that each set of increments will be much smaller than the previous set so that a well-ordered set of approximations results. Expectation values of other operators can be treated in the same way as the energy. Nesbet has applied the method to the beryllium and neon atoms with very satisfactory results some of which are given in Tables 1 and 2. Nesbet did not calculate many three-electron terms for neon. The one expected to make the largest contribution gave an approximate e of +O*OOO261 which must be too large since a variational principle is being used and which is fairly small rela-tive to the accuracy of three places of decimals for which he was aiming. These results present a number of interesting features which cannot be commented upon here except to point out that they support the use for calcu-lations of moderate ‘chemical’ accuracy of the idea that each electron correlates principally with one other.Essentially the same approach has been followed by S z a s ~ ~ who has carried out calculations on the beryllium atom using explicit rij functions instead of C.I. He has treated 1s 1s and 2s 23 correlation only and obtains values of eab for these of -0-0423 a.u. and -00445 a.u. which agree satisfactorily with ’ L. Szasz and J. Byme Phys. Rev. 1967,158 34 26 J. G. Stamper TABLE 1 Correlation energies in Be Electron Group eab or eabe (a.u.) 1s 1s 1s 2s 1s 2s 2s 2s Total pairs l s l i 2s ls2s 2s Total triples Total correlation energy Experimental correlation energy -0.041827 -0*000813 - 0.0021 19 0.0453 5 1 + O-ooOo30 + 0.000428 + 0.O009 1 6 - 0.093042 - 0.092 126 - OW3897 TABLE 2 Correlation energies in Ne Total e for all Type of Pair No.of Pairs pairs of type (a.u.) K-shell K-shell 1 - 0.039932 K-shell Lshell 16 - 0.025026 Lshell L-shell 28 - 0.3 17269 - 0.382227 Total pair energy -Experiment a1 correlation energy - - 0.393 the values of Nesbet in Table 1. An interesting finding of Szasz is that the pair energies appear not to be quite additive. The correlation energy obtained by treating the 1s 1s and the 2s 2s pairs simultaneously is less by about 0.003 a.u. than the sum of the energies obtained by treating the two pairs separately. Hartree-Fock Calculations.-The Hartree-Fock wave-function that forms the starting point for the electron-correlation calculations is itself the typical goal of most calculations on small molecules.1967 in common with the past 5 or 6 years has seen a number of such calculations of varying degrees of accuracy. Those reported below illustrate various ways in which this kind of calculation can be of interest. The most striking development in this field has been the attempt to obtai Theoretical Chem is try 27 Hartree-Fock wave-functions for quite large molecules which has been made simultaneously by two sets of workers. Preuss and Diercksen’ have carried out calculations for benzene the cyclopentadienyl anion and cyclopropane together with some smaller systems while Clementi et aL9* have treated tkie NH,-HCI reaction system pyridine pyrrole and pyrazine.One of the biggest problems in trying to calculate Hartree-Fock wave-functions for molecules as large as these is the very large number of multicentre integrals which have to be evaluated. If as is usually the case the molecular orbitals are constructed from Slater-type atomic orbitals (STO’s) Ylmrn exp( - cr) the evaluation of these integrals can be done only by summation over rather slowly-convergent series which requires a prohibitive amount of com-puter time. Both these groups of workers have evaded this difficulty by using Gaussian orbitals (GTO’s) (x’J+”z“ exp( -c?)) as a basis in the calculation for all the integrals needed for this type of calculation can be obtained in closed form when a Gaussian basis is used.The use of a Gaussian basis is not new but it has not been popular in the past because a very much larger number of GTO’s than STO’s is needed to obtain a wave-function of comparable accuracy. For example one STO gives an absolutely accurate result for the hydrogen atom while five or six GTO’s are needed for results of ‘chemical’ accuracy. Thus these calculations must employ very large bases which are made tractable by contraction. This process consists of con-structing certain combinations of GTO’s on each centre which are then treated as a unit in the calculation the coefficients of the GTO’s being kept in constant ratio. The combinations are chosen on the basis of calculations on smaller systems and it has been shown that this process does not significantly decrease the accuracy of what are in any case approximate calculations.A number of interesting results follow from these calculations. One is that in all the aromatic compounds the lowest-lying n-orbital is more strongly bound than the highest o-orbitals. For example the second ionization potential of benzene is predicted to be of a o rather than a n electron. The second is that the nitrogen atom in pyrrole carries a net negative charge which is the result of two opposing effects a transfer of electrons from carbon to nitrogen in theo system and a transfer from nitrogen to carbon in the n-system. This suggests that care is required in the use of Ir-electron only cakulations on such a system. A second kind of application of Hartree-Fock calculations is to smaller molecules in cases where they can throw light on experimental problems.Carlson Claydon and Moser,’ ’ for example have carried out approximate self-consistent field calculations on TiN to assist in the elucidation of its complex electronic spectrum by predicting the kinds of transition to be expected. For many diatomic molecules this kind of prediction can be made using simple H. Preuss and G. Dierksen fnt. J . Quant. Chem. 1967,1,349,357,361,365,369 373. E. Clementi J . Chem. Phys. 1967,46,3851,4731,4737. K . D. Carlson C. R. Claydon and C. Mom J . Chem. Phys. 1967,46,4963. l o E. Clementi H. Clementi and D. R. Davis J . Chem. Phys. 1967,46,4725. * 28 J. G. Stamper qualitative considerations. When transition elements are present however, this is not possible and this kind of calculation can be of great utility.A related use of SCF calculations is that by RichardsI2 on CS. He has carried out an SCF calculation comparable in accuracy to that of Nesbet13 on CO and concludes that thiocarbonyl complexes should be more stable than the corres-ponding carbonyls. The lone pair electrons on carbon are more weakly bound in CS than CO suggesting that CS will form stronger CT bonds to metals while the lowest unoccupied n-orbital in CS lies lower than in CO suggesting that back donation is likely to be more effective. Cade and Huoi4 have made exhaustive Hartree-Fock calculations on the diatomic hydrides of all the first and second row elements. These calculations are for almost all the molecules considered of considerably greater accuracy than any previous calculation the energies being accurate to about 0-02 ev.* The authors present an extended discussion of the results which cannot con-veniently be summarised here but one conclusion which they emphasise is that the difference between their result and the experimental energy is nearly constant over a considerable region near the minimum in the potential energy curve.Thus the correlation energy is almost constant over this region and Hartree-Fock calculations of spectroscopic constants are fairly reliable for these molecules at least. Semi-Empirical Methods.-The authors of the calculations on large mole-cules described in the last section stress that they are only obtaining approxi-mate solutions of the Hartree-Fock equations and it is clear that it will be a long time before exact solutions are available for any considerable number of large molecules.More approximate approaches to calculating the properties of larger molecules are therefore still necessary. The most familiar and successful of such methods is that of Pariser and Parr,15 and Pople16 (the P method) for n-electron systems sometimes referred to as the zero-differential overlap approximation. The principal difficulty in the application of exact non-empirical molecular-orbital calculations to large systems is the very large number of integrals over atomic orbitals which must be calculated stored and handled. In the P method, the number of integrals is drastically reduced by : (i) neglecting all the electron-repulsion integrals in which the same electron appears on two different atoms : (ii) obtaining values for the remaining electron-repulsion integrals by a mixed procedure partly from non-empirical calculation and partly from atomic spectroscopic measurements ; l2 W.G. Richards Trans. Faraday SOC. 1967,63,257. l 3 R. K. Nesbet J . Chem. Phys. 1964,40 3619. l4 P. E. Cade and W. M. Huo J . Chem. Phys. 1967,47,614,649. Is R. Pariser and R. G. Parr J . G e m . Phys. 1953,21,466,767. l6 J. A. Pople Trans. Faraday SOC. 1953,49,1375. * This is the accuracy in the Hartree-Fock energy. There is a much larger difference from experi-mental results due to correlation effects Theoretical Chemistry 29 (iii) treating the nuclei and cr-electrons of the molecule as a fixed core in whose field the a-electrons move.Some of the integrals involving this cort are neg-lected others are obtained from atomic spectral data while one p which corresponds quite closely to the p of Huckel theory is chosen so as to obtain the best fit with experiment. This method has proved very fruitful over the past ten years but it is only comparatively recently that much serious effort has been devoted to extending this kind of approach to other kinds of molecule. One particular exte-sion which appears rather promising is the so called CNDO (complete neglect of differential overlap) method of Pople Santry and Segal.”? 18* l9 In this method all the valence electrons of the molecule are considered ex-plicitly and approximations which are essentially those of the P-method are introduced.There are two features which are new to the theory as compared with the P-method. Firstly p instead of being taken as a constant is set pro-portional to the corresponding overlap integral, p = ptBs where ptB is a constant for a particular pair of atoms chosen to give agreement with more accurate calculations on simple systems.* Secondly in order that the results should be invariant under either a change of axis system or a change from atomic orbitals to hybrid orbitals as a basis (the solution to the full Hartree-Fock equations has this property) it is necessary to ignore differential overlap between different kinds of orbital on the same atom and to set all electron-repulsion integrals involving the same pairs of atoms equal.Although the method was not intially described in the year under review a number of applications and extensions have appeared which suggest that it, or something close to it is likely to be of wide utility in the future. For example it has been applied in its original form to the electronic spectra of small poly-atomic molecules by Kroto and Santry.2’ In their first paper they treat HNO, HCF H2C0 C2H2 and NH, using the virtual orbitals that result from an SCF calculation on the ground state as an approximation to the orbitals occupied in the excited state. As would be expected the excitation energies calculated are rather high (e.g. 6.80 ev for NH3 as against the experimental value of 5-72 ev) but they obtain good agreement in most cases with the observed change in geometry on excitation.The exception is the case of formaldehyde where they predict a planar configuration for both the first singlet and the first triplet excited states. In all cases the geometry depends on a balance between the change in orbital energies on excitation and the change in electron repulsion ” J. A. Pople D. P. Santry and G. A. Segal J . Chem. Phys. 1965,43 S129. J. A. Pople and G. A. Segal J. Chem. Phys. 1965,43 S136. l9 J. A. Pople and G. A. Segal J . Chem. Phys. 1966,44,3289. 2o R. S. Mulliken J. Chim. phys. 1949,46 497. ” H. W. Kroto and D. P. Santry J. Chem. Phys. 1%7,47,792,2736. Such an approximation is not of course a new idea. It goes back at least to 194920 and probably much earlier 30 J. G. Stamper terms and for formaldehyde these two are very similar in magnitude so that the lack of success in prediction is not very surprising.The experimentally estimated barrier to inversion in the singlet state is only 0.081 ev. In their second paper they use a simple procedure to optimise the molecular orbitals for the excited state and obtain somewhat improved values for the excitation energies. They are also able to obtain a non-planar equilibrium con-figuration for the singlet excited state of formaldehyde with an out-of-plane angle of 15" (experimental value 3 1 "). The CNDO approximations have also been used to attack this problem by Dixon22 who using a slightly different set of parameters (CNDO/l instead of CND0/2) and including some one-centre exchange terms obtained comparable results.The one-centre exchange terms are important in accounting for singlet-triplet separation and also in planar n-free radicals in allowing some spin density to appear ino-orbitals thus accounting for isotropic hyperfine coupling. Pople et aL2 have carried out calculations similar to Dixon (but using CND0/2) and have also looked at the question of spin densities in methyl and ethyl radicals. They do not attempt to predict the absolute values of the coupling constants but obtain quite satisfactory results for the ratios of these constants in the two radicals. The original CND0/2 set of approximations have been used in a study of d-orbital participation in bonding in some compounds of elements of the second row of the periodic table.24 The CNDO method does not give any definite method for treating d-orbitals so the authors have made three series of calcu-lations two using different and extreme ways of representing the d-orbitals and the third omitting them altogether.A number of interesting though perhaps rather tentative conclusions are drawn from these results the most striking of which is that the geometries of the molecules they consider which include the celebrated case of the T-shaped ClF, are unchanged by the inclusion of d-orbitals in the basis-set of atomic orbitals. On the other hand charge distributions and dipole-moments are considerably affected by the inclusion of d-orbitals. The most noticeable effect is in compounds where the second row element is in a higher than usual valence state (SO:- SFs PF5 ClF,).When d-orbitals were omitted a large positive charge accumulated on the central atom ; d-orbitals besides strengthening theo bonds allowed a good deal of this charge be back donated through rbonding. The CND0/2 approximations are also able to give a satisfactory account2' of bond lengths in first row diatomics (to 0-05 A) though not of the force constants or dissociation energies in these molecules. A similar set of approximations has been used by Dewar and Klopman26 '* R. N. Dixon Mol. Phys. 1967 12 83. " J. A. Pople D. L. Beveridge and P. A. Dobosh J . Chem. Phys. 1967,47 2026. 24 D. P. Santry and G. A. Segal J . Chem. Phys. 1967,47 158. 25 G. A. Segal J . Chem. Phys. 1967,47,1876. 26 M. J. S. Dewar and G. Klopman J . Amer. Chem. SOC.1967,89,3089 Theoretical Chemistry 31 in a discussion of a large number of hydrocarbons the main difference being the inclusion of certain one-centre and two-centre electron-repulsion integrals neglected in CNDO. Although this procedure destroys the formal invariwce under a change of axis system the authors have found that their results are invariant to the accuracy of their calculations. The results are very encouraging. Not only are the heats of formation of saturated and unsaturated hydro-carbons predicted to an accuracy of “chemical” size (usually better than 4 kcal.) but the correct conformations are predicted for ethane cyclohexane, 2-butene and 1,3-butadiene. On the other hand the calculations predict that n-alkanes should be more stable than branched-chain alkanes which is in contradiction with experimental results.Unfortunately the extended approximations of both Dewar and Klopman,26 and Pople et ~ 2 1 . ~ ~ lack the theoretical justification of the plain CNDO method. The success of the P-method for n-systems has been explained27 by showing that its approximations are equivalent to starting from a symmetrically orthogonalised set of atomic orbitals as basis. Dah12* has shown that the CNDO method can also be rationalised on this basis-but that the various partial extensions cannot. However the proof of the pudding is in the eating and the partial successes of various authors lead one to say with Dewar and Klopman that “this kind of approach has exciting possibilities”. Interatomic Forces.-The interaction between atoms or molecules at moderately large distances is an obvious situation in which a perturbation-theory approach is likely to be fruitful.Indeed such calculations were carried out in the very early days of quantum mechanics by a number of workers, especially London.29 These early workers almost all used a simple product of the wave-functions of the two atoms (or molecules) as the unperturbed wave-function of the system. Such an approach cannot be correct as by the Pauli principle the wave-function for the system must be antisymmetric under any interchange of electrons and electrons cannot therefore be associated with particular atoms. These two different starting points do not lead to significantly different results provided that the overlap between the wave-functions on the two atoms is negligible so that the original method of calculation is satisfactory at large interatomic distances.The interactions of non-bonded atoms and molecuks at intermediate distances have in recent years become of considerable interest since quite accurate potential energy curves for such systems have been derived from atomic beam and other data. Consequently a number of attempts have recently been made to apply perturbation techniques to the situation in which the overlap is not negligible. When this is attempted in a straightforward way a difficulty arises because 27 I. Fisher-Hjalmars J . Chem. Phys. 1965,42,1962. 28 J. P. Dahl Acta Chem. Scad. 1967,21,1244. 29 F. London 2. Physik 1930,63,245 32 J. G. Stamper the unperturbed wave-function is not an eigenfunction of the unperturbed Hamiltonian for the system.This can easily be seen in the case of two hydrogen atoms A and B. Here the simple product function is $ = hA(l)hB(2) while the correct antisymmetrical function is Y = lsA(l)l~B(Z) - 1sA(2)1sB(1). The unperturbed Hamiltonian is the sum of two hydrogen atom Hamiltonians one for each electron HO = HA(1) + HB(2) (6) Here Jr is an eigenfunction of Ho HoY! = 2E,ls~(l)ls~(2) - ~SA(~)HA(~)~SB(~) - ~SB(~)HB(~)~SA(~) (8) If we now carry out a perturbation calculation in the usual way putting H = H o + h V E = E o + h E + Y = Yo + h Y 1 + HoYo + AHOYl + AVY0 = EoY0 + AEIYo + AEOY, (9) (10) HoYo = EoYo (11) we obtain to first order in h In ordinary perturbation theory we have so that all the terms in (10) are of first or higher order in h.In this case where (11) does not hold (10) contains terms of both zero and first order in A. The different orders of perturbation theory are therefore not well defined and what terms should be included in a calculation “correct to second order” is not clear. An additional difficulty arises when an attempt is made in the usual way to calculate the perturbed wave-function in terms of excited-state wave-functions for the unperturbed system. This is because the set of all antisym-metrised products of excited-state functions is overcomplete* and therefore there is no unique way in which the perturbed wave-function can be expressed in terms of them. During the year a number of authors have attempted to solve this problem and several expressions have been obtained for the first and second order energies in such a system.Amos and Musher3’ and Murrell and Shaw3’ 30 A. T. Amos and J. I. Musher Chem. Phys. Letters 1967 1,149. 31 J. N. Murrell and G. Shaw J . Chem. Phys. 1967,46 1768. A complete set is one such that any function can be expressed in terms of it. An overcomplete set is such a set with additional functions in it. It follows that some functions in such a set are in fact linear combinations of other members of the set Theoretical Chemistry 33 avoid the problem of overcompleteness by using an antisymmetrised product only for the unperturbed function and by using simple products of excited-state functions to express the perturbed wave-function.Amos and Musher3' use a dummy coefficient analogous to h in equations (9) to (11) above to define the order of perturbation theory while Murrell and Shaw31 use a projection-operator technique. The two approaches however have been shown to lead to equivalent results.32 An alternative approach which has also received attention during the year is that due initially to Eisenschitz and London.33 This work has been revived and rewritten in a modern form by van der A ~ o i r d ~ ~ who uses the overcomplete set of antisymmetrised products but gives a specific method for choosing the expansion coefficients. Hir~chfelder,~~ in the course of a rather heavily mathe-matical survey of the whole problem has extended the work of van der Avoird to form what he designates as the HAV method and has given a variational principle analogous to the Hylleraas principle36 in conventional perturbation theory for finding the first-order perturbed wave-function and the second-order energy without expanding in terms of any set of excited states.All the approaches agree that the first-order energy (in the case of neutral spherically-symmetric species) corresponds to the Heilter-London (valence-bond) chemical-binding energy which is zero in the absence of overlap while the second-order energy is made up of two types of contribution-the familiar van der Waals dispersion energy due to interaction between an instantaneous dipole in one atom with an induced dipole in the other and additional exchange-type terms. The various approaches differ in detail.The decision as to which of these approaches is the most satisfactory will probably have to await the results of numerical applications which have so far been few. Murrell and S h a ~ ~ ~ have applied their method to the interaction of two helium atoms. The potential energy that they obtain has a minimum energy of -3.3 x ev) at an internuclear distance of 5.5 a.u. (= 2.9 A) and appears to agree with the experimentally derived poten-tial-energy curve to within the limits of experimental error. The general importance of the overlap terms is indicated by a calculation of McQuarrie and Hirschfelder3* on H2+. Using a form of perturbation theory published previo~sly,~' differing considerably in approach and to a smaller extent in results from HAV they obtain the energy accurately up to a distance of 4 a.u.(2 A) while traditional van der Waals forces which consist in this case a.u. (= 8-9 x 32 R. E. Johnson and S. T. Epstein University of Wisconsin Theoretical Chemistry Institute Reports 33 R. Eisenschitz and F. London Z . Physik 1930,60,491. 34 A. van der Avoird Chem. Phys. Letters 1967 1 24. 35 J. 0. Hirschfelder Chem. Phys. Letters 1967 1 325 363. 36 See for example J. 0. Hirschfelder W. Byers-Brown and S. T. Epstein in Adv. Quantum Chem., 1964 I 3' J. N. Murrell and G. Shaw Mol. Phys. 1967,12,475. 39 J. 0. Hirschfelder and R. Silky J . Chem. Phys. 1966,45,2188. NO. WIS-TCI-266 1967. D. A. McQuarrie and J. 0. Hirschfelder J . Chem. Phys. 1967,47,1775 34 J. G. Stamper of a charge-induced dipole interaction can only account for the energy of the system up to 15 a.u.Miscellaneous Topics.-Lower bounds and related topics. Essentially all theoretical chemical calculations involve the use of the variation theorem to find an approximate wave-function for a system. Such calculations therefore, give an upper limit to the energy of the system-and it would often be of interest to have additional information about the accuracy of the result of the calculation such as a lower limit to the energy or limits on the accuracy of the expectation values of other quantities calculated from the wave-function. A number of lower bound formulae exist:' but are all awkward to apply because the expectation value of the square of the Hamiltonian has to be evaluated. This is very much easier to do with Gaussian than with Slater orbitals (cf p.27) and Schwarts4' has investigated the kinds of lower bound which can be expected in Gaussian calculations.Taking a Gaussian calcula-tion of the energy of the hydrogen atom as a simple example a calculation which gives an upper bound-i.e. the ordinary 'calculated' energy-correct to 6 x kcal. mole-' has a lower bound 20 kcal. mole-' too low. In passing this illustrates the way in which quite inaccurate wave-functions can lead to very good expectation values of the energy. Wilson and c o - w ~ r k e r s ~ ~ * ~ ~ have also been looking at the lower boundary question and have used an approximate version of the method of Bazley and to investigate the accuracy of some derived values. Their approximation is only justified when the wave-function is a rather accurate one as it involves neglecting terms of second-order in E(E' = 2 - 2s where S is the overlap of the approximate wave-function with the true one) so they have applied it only to accurate H2 and He wave-functions.For example they calculate the magnetic susceptibility of He from the P e k e r i ~ ~ ~ wave-function as -(la8913 & 3 x cm3 mole-' the limits of accuracy not being large enough to bring it into agreement with the experimental value of (- 1.93 & 0.01) x Group theory of non-rigid molecules. Although group theory is a well-estab-lished and commonly used tool of the theoretical and practical chemist its application to non-rigid molecules and especially those in which there are several possible nuclear configurations with minimum energies (ethane, CH,BH etc.) is less well e ~ t a b l i s h e d .~ ~ ~ 47 In particular Long~et-Higgins~~ maintained that it was not possible to construct the correct symmetry groups for these molecules in terms of the usual symmetry operations of rotation, reflection etc. but instead developed a method in which the symmetry opera-x cm3 mole-'. *' G. L. Caldow and C. A. Coulson Proc. Cambridge Phil. SOC. 1961,57 341. *' C. M. Roenthal and E. B. Wilson,jun. Phys. Rev. Letters 1967,19 143. 43 P. Jennings and E. B. Wilson jun. J . Chem. Phys. 1967,47 2130. '* N. W. Bazley and D. W. Fox Rev. Mod. Phys. 1963,35,712. 45 C. L. Pekeris Phys. Rev. 1959,115 1216. *' H. C. Longuet-Higgins Mol. Phys. 1963,6,445. *' J. T. Hougen Canad. J .Phys. 1964,42 1920. M. E. Schwartz Proc. Phys. SOC. 1967,90,51 Theoretical Chemistry 35 tions were permutations of identical nuclei together with the inversion. The full set of operations so obtained is then broken down into feasible operations (e.g. the operation corresponding to the inversion in ammonia) and unfeasible operations (e.g. the one corresponding to the inversion in methane). In this way a single group is obtained uniquely for all configurations of the molecule. This year Altmann4* has produced a new approach to the problem in which he works in terms of the common idea of symmetry operations as motions of the moleculethough the word motion has to be rather carefully defined. In his method he distinguishes between two kinds of operation-ordinary operations such as rotation and reflection which carry the molecule into a new position but the same configuration and isodynamical operations which transform one nuclear configuration into a &fleerent equivalent configuration.The appropriate symmetry group for the molecule called by Altmann the Schrodinger supergroup contains both kinds of operations and is different in different nuclear configurations. In some cases (e.g. CH,BH2) all the various supergroups are isomorphous with each other and with the Longuet-Higgins group foi the same molecule. In other cases (e.g. (CH,),B) the different supergroups are not isomorphous and only one of them in this case the one for random orientations of the methyl groups is isomorphous with the Longuet-Higgins group. Altmann does not discuss the physical significance of these differences but it appears that one consequence is a change in the degeneracy of some electronic energy levels of the molecule on change of configuration which might well lead to new kinds of vibronic interaction.Natural Geminals. The concept of natural orbitals was introduced about ten years ago by Lowdin4” 5 0 and they have since proved of considerable use in the interpretation of wave-functions for simple systems. They are defined as those orbitals which diagonalise the first-order density matrix. Their interest arises from two properties; (i) a CI wave-function for the system converges to the accurate wave-function most rapidly if a basis of natural orbitals is used, (ii) it is possible to transform any wave-function certainly any CI wave-function into natural orbital form and this form therefore provides a useful way of comparing and analysing various wave-functions.It is possible to extend the idea to functions capable of containing more than one electron and in particular Barnett and Shullsl have calculated natural geminals for a number of four-electron systems. A geminal is a function capable of containing two electrons and natural geminals are obtained analo-gously to natural orbit& by diagonalising the second-order density matrix, and they have analogous proper tie^.^^ It is not yet clear exactly how these natural geminals are to be interpreted particularly the ones with small occupa-48 S. Altmann Proc. Roy. Soc.1967 A 298,184. 49 P. 0. Lowdin Phys. Rev. 1955,97 1474. 50 P. 0. Lowdin and H. Shull Phys. Rev. 1956,101 1730. G. P. Barnett and H. Shull Phys. Rev. 1967,lB. 61. T. Ando Rev. Mod. Phys. 1963,36,690; A. J. Coleman Canad. Math. Bull. 1961,4 209. B 36 J. G. Stamper tion number (i.e. making a small contribution to the wave-function) but one of their properties seems to stand out. If a Hartree-Fock wave-function is converted to natural geminal form, the geminals are not precisely defined. The first two in the case of Be for example. can be taken as either an electron pair in Is Is2 and an electron pair in 2s 2s2 or as any linear combination of these two. When correlation is introduced the linear combinations are defined and are found rather surprisingly to be (Is’ + 2s’) and (ls2 - 2s2) together with correlation terms in each case. It seems therefore that the best geminal expansion for Be and presumably for other systems does not start from a ls2 2s2 base

ISSN:0069-3022    

DOI:10.1039/GR9676400023

出版商:RSC    

年代:1967

数据来源: RSC

摘要:

4. THE KINETICS OF REACTIONS IN SOLUTION By J. E. Crooks (University of Kent at Canterbury) A LARGE proportion of the 4500 papers listed in the ‘Kinetics and Mechanism’ section of Current Chemical Papers for 1967 concern reactions in solution, so that this review must be highly selective. The papers chosen make some point relevant to solution kinetics as a whole as distinct from those in which the concentration-dependence of a reaction rate is used as part of the evidence for a particular reaction mechanism. Papers of such general significance include those concerned with mathematical and theoretical aspects and those concerned with the effect of the solvent on the rate of reaction. Kinetic isotope effects are frequently measured but their significance is still debatable.The study of fast reactions is still sufficiently novel to warrant a more detailed account of methods and results than that for reactions followed by con-ventional techniques. The award of a Nobel prize to Professor Norrish, Professor Porter and Dr. Eigen reflects the rapidly growing interest in this field. Mathematical Aspects.-TTlt~~.orc.tic.ul. There have been several developments in the theory of rates of diffusion-controlled reactions. Bass -and Greenhalg show that the Smoluchowski treatment in which the reaction rate is calcu-lated by assuming that particles of one species are stationary whilst particles of the other species diffuse towards them can lead to a self-contradiction. If the concentrations of the species are not equal the reaction rate depends on which of the species is replaced by stationary sinks.Watts2 gives an alternative treatment for the rate of a diffusion-controlled reaction between ions which predicts slightly faster rates than those calculated from the Debye modification of the Smoluchowski equation. Watts3 extends his treatment to describe slower reactions between ions and to include the contribution due to dissoci-ation of the products of the reaction which gives a lower value of the rate constant. The result agrees with that given by Eigen et ~ 1 . ~ to within the limits of the approximations used. In the derivation of the Smoluchowski equation it is assumed that the concentrations of the diffusing species are zero at a distance from the stationary sinks equal to the sum of the radii of the particles of the two species.Noyes’ takes this concentration as finite and related to the rate at which reaction would occur if diffusion were infinitely fast. Logan6 uses this boundary condition of Noyes to calculate the effect of temperature ’ L. Bass and W. J. Greenhalg Trans. Faraday Soc. 1966,62,715. A. M. Watts Truns. Faraday SOC. 1966,62,2219. ’ A. M. Watts Trans. Faraday SOC. 1966,62,3189. ‘ M. Eigen W. Kruse G. Maass and L. de Maeyer Progr. Reaction Kinetics 1964,2 285. ’ R. M. Noyes Progr. Reaction Kinetics 1961,1 129. S. R. Logan Trans. Faraday SOC. 1967,63,1712 38 J . E. Crooks on the rate of a diffusion-controlled reaction and shows that the observed Arrhenius activation energy is similar to the activation energy of self-diffusion in the solvent i.e.about 3.5 kcal. mole-1 in water. This value has been verified experimentally for ionic reactions by the temperature-jump method and for free-radical reactions by pulse radiolysis. Logan' also calculates the dependence of diffusion-controlled rates on ionic strength using Noyes' boundary con-dition and finds the dependence is less than that predicted by the Brernsted-Bjerrum equation although the discrepancy is small at low ionic strength. The calculated rate is less than that predicted by the simple Debye-Smoluch-owski equation and Logan points out that this makes doubtful the assertion that certain reactions of the hydrated electron are too slow to be diffusion-controlled. Friedman' discusses another weakness in the Smoluchowski equation namely that the molecular nature of the solvent is ignored.There is a hydrodynamic effect due to interactions between solvent and solute molecules similar to that responsible for the electrophoretic effect on the conductance of electrolyte solutions. Smoluchowski himself considered colloidal particles as the solute and so was quite justified in ignoring this effect. The effect is shown to make a reduction of about 15 % in the computed rate constants for ions or neutral species in water which is not really significant in view of the other possible errors. However despite all these criticisms experimentalists still find the Smoluchowski equation adequate as will be shown. Calculation ofrate constants. A method for the elucidation of the kinetics of complex systems is described by Cover.' An 'applied stress' i.e.the volu-metric or electrolytic addition of reagent is imposed on a reacting system at a predetermined rate. If the stress is programmed correctly the behaviour of the system is simplified and rate constants can be calculated. Some prior knowledge of the system is required so that the most useful stress function can be applied. A simple examplelo would be the use of a pH-stat to follow the kinetics of a reaction in which OH- is consumed. The rate at which alkali has to be added to keep the pH constant gives the rate of the reaction. Computers both digital and analogue are being used for the elucidation of complex kinetic schemes. D. F. DeTar and C. E. DeTar" give a general discussion of the design of computer calculations for the kinetics of systems including those with steady-state concentrations of labile species and those involving equilibria.As an example they consider an enzyme reaction the glycolytic pathway in cell metabolism for which Garfinkel and Hess12 pro-duced a model mechanism consisting of 89 equations 24 normal reactants and 13 different enzyme systems containing a total of 41 enzyme intermediates. D. F. DeTar and C. E. DeTar offer to supply a copy of the Fortran I1 pro-gramme and an instruction manual to those interested. However they point ' S. R. Logan Trans. Faraday SOC. 1967,63,3416. * H. L. Friedman J . Phys. Chem. 1966,70,3931. R. E Cover J . Phys. Chem. 1967,71,1990. l o R. P. Bell and B. Coller Trans. Furaday SOC. 1965,61 1445. l 1 D. F. DeTar and C. E. DeTar J .Phys. Chem. 1966,70,3842. '* D. Garfinkel and B. Hess J . Biol. Chem. 1964,239,971 The Kinetics of Reactions in Solution 39 out that no computer programme can be a substitute for chemical knowledge and research judgement. D. F. DeTar13 uses the same programme REMECH, to calculate theoretical yields of various products from the thermal decom-position of benzoyl peroxide for various values of the rate constants in 300 possible elementary reaction steps. Comparison with experimental values shows that only 101 of these steps are significant and the rate constants for these are found. MahoneyI4 investigates the complex kinetics of the oxygen absorption of 9,lO dihydro-anthracene and 2,2’,3,3’-tetraphenylbutane cata-lysed by peroxy- and phenoxy- radicals. The rates of the eleven consecutive and competitive reactions involved are found by fitting the observed rates of oxygen uptake to calculated values using a digital computer.Markisz and Gettlerl5 use a similar method to study the addition of a-hydrogen donor compounds to methyl vinyl ketone a concurrent first- and second-order reaction. Analogue computers can also be used as in Walles and Platt’s16 study of the thermal decomposition of an oxazolidone. Oscillatory reactions. Lindblad and Degn17 use a digital computer to investigate oscillatory reaction systems i.e. those in which a reagent concen-tration increases and decreases in a periodic manner rather than decreasing monotonically. The basic theory was first considered by LotkaI8 for ecological systems to account for periodic variations in the numbers of animals in the wild.A most interesting review of the whole problem is given by Higgins,” whose examples are mainly taken from biochemistry. His article is illustrated with concentration-time plots taken from an analogue computer. There is an intriguing analogy with the oscillations which can be set up in an electronic amplifier in which feedback is excessive autocatalysis being the chemical feedback. Higgins speculates ‘Virtually all the dynamical characteristics associated with modern electronics can be generated through chemical reactions . . . such dynamics may play a role in biological functions including transmission of information and control’. The Role of the &lvent.-Albery2* gives an interesting review of the part played by solvent water in aqueous proton-transfer reactions.The fundamental question is whether the proton is transferred directly from acid to base or by a Grotthus-type mechanism via an H,O bridge i.e. whether the transition-state is like (A) or (B). H \ 0 -___ H ____ S O--H--o--H--S H‘\ / / I D. F. DeTar J . Amer. Chem. SOC. 1967,8!4,4058. l4 L. R. Mahoney J . Amer. Chem. SOC. 1967,89,1895. J. A. Markisz and J. D. Gettler J . Phys. Chem. 1967,71 3053. l6 W. E. Walles and A. E. Platt Ind. Eng. Chem. 1967,59 No. 6,41. P. Lindblad and H. Degn Actu Chern. Scund. 1967,21 791. A. Lotka 2. Phys. Chem. (Leipzig) 1910,72 508. l9 J. Higgins Ind. Eng. Chern. 1967,59 No. 5,19. *’ W. J. Albery Progr. Reaction Kinetics 1%7,4,353 40 J. E. Crooks Albery correlates a large amount of information from relaxation and electrochemical methods n.m.r.Raman line broadening and isotope effects in isotopically-mixed aqueous solutions. His findings are illustrated with detailed potential-energy surfaces showing the difference between stepwise and concerted proton transfer to oxygen and to carbon. The general conclusion is that for diffusion-controlled proton transfers to oxygen and nitrogen the rate-determining step is the formation of a hydrogen-bonded complex between an H,OZ species and the anion followed by fast translations of protons in a Grotthus manner to protonate the anion. However for proton transfer to carbon the reaction occurs via the H30+ species as predicted from con-sideration of the potential-energy surfaces and suggested experimentally by the mixed-solvent isotope effects.Huyser” reviews solvent effects on free-radical reactions explicitly omitting reactions where the solvent is a reactant. Most work has been done on reactions in which the solvent affects the behaviour rather than the formation of a free-radical intermediate. By changing the solvent the reactive intermediate can be made to give different products e.g. the photochemical chlorination of hydrocarbons can be made to occur mainly at tertiary C-H by the use of carbon disulphide as solvent. Variation of rate with solvent properties. It has long been known that the rate of a reaction in solution often depends on the solvent and that large differences may be observed not only between aqueous and non-aqueous solvents but even between different non-aqueous solvents.Predictions of the variation of rate with solvent can be made from thermodynamic data con-cerning the solvent as discussed in a review by EckertZ2 Kondo and Tokuraz3 calculate rates of reaction in mixed solvents from rates in the pure solvents, which are components of the mixtures. Several workers have correlated rates of reaction with some bulk parameter of the solvent such as the dielectric constant or some other measurement of solvent polarity. Del Castillo et ~ 1 . ~ find a linear relationship between the logarithm of the rate of trypsin-catalysed esterolysis and the reciprocal of the dielectric constant of the solvent. Campbell and Hoggz5 use the ET scale of solvent polarityz6 to correlate rates of the reaction of 2,4-dinitrobenzene sulphenyl bromide with cyclohexene in carbon tetrachloride benzene chloroform and acetic acid and find a good straight-line plot of log k against ET over a range of four orders of magnitude in k.Jones and T h ~ r n t o n ~ ~ find the rates of solvolysis of methyl chloromethyl ether in a large number of binary mixed solvents to obey the Winstein equation :28 log k = mY + log k, 21 E. S. Huyser Ado. Free-Radical Chem. 1965,1,77. 22 C. A. Eckert Ind. Eng. Chem. 1967,59 No. 9,20. 23 Y. Kondo and N. Tokura Bull. Chem. SOC. Japan 1967,40,1433. 24 L. M. Del Castillo Y. Bustamente and M. Castaneda-Agullo Biochim. Biophys. Acta. 1966, ” D. S. Campbell and D. R. Hog& J . Chem. Soc. (B) 1967,899. 26 K. Dimroth C. Reichardt T. Siepmann and F.Bohlmann Annalen 1963,661,l. ’’ T. C. Jones and E. R. Thornton J . Amer. Chem. SOC. 1967,89,4863. E. Grunwald and S. Winstein J . Amer. Chem. SOC. 1948,70,846. 128,578 The Kinetics of Reactions in Solution 41 where k is the rate of solvolysis of X in some solvent ko is the rate of solvolysis of X in 80 20 v/v ethanol-water and Y is a measure of the ionising power of the solvent obtained by defining rn as unity for the solvolysis of t-butyl chloride in that solvent. Despite the above it seems likely that good correlations between rates and solvent polarity are rare. There is little or no correlation for the reaction of n-butyl nitrite with a~etamide,~’ the solvolysis of hex-5-enyl p-nitrobenzene-s ~ l p h o n a t e ~ ~ ester and acetal hydrolysis the reaction of isopropylamine with 2-acetylbromo na~hthalene,~ the Curtius reaction of 2-naphthoyl a ~ i d e ~ and the solvolysis of o-halogeno-substituted 2-alkyl t ~ s y l a t e s .~ ~ Cox and McTigue3’ state that it now seems certain that for reactions with no net change in charge the dielectric constant of the solvent has little connection with the rate. It is the solvent-solute interactions often quite specific which are all-important. Soloation. A more fruitful approach to the problem of the variation of reaction rates with solvent is to consider solvation of both reactants and transition states. Parker35 gives a comprehensive review of the kinetic conse-quences of the difference in solvating ability between protic solvents which interact by hydrogen bonding and dipolar aprotic solvents such as dimethyl-sulphoxide.Solvent activity coefficients show that the dipolar aprotic solvation energy for polar molecules can be up to fifty times more than that of protic solvents as long as the solute is not a strong hydrogen-bond donor or acceptor. Protic and dipolar aprotic solvents differ in their ability to solvate anions. Protic solvents have a general hydrogen-bonding interaction with small anions whereas dipolar aprotic solvents which are highly polarisable have a mutual polarisability with large polarisable anions. In terms of what Parker calls ‘the colourful Hard and Soft Acids and Bases principle’ ‘hard’ anions, have strong interactions with protic solvents which are ‘hard’ whereas ‘soft’ anions have strong interactions with dipolar aprotic solvents which are ‘soft’.Parker discusses a large number of S,2 reactions of the type: Y- + R3CX -+ YCR + X -which are much faster in dipolar aprotic solvents than in protic solvents. It is still a matter for debate whether the origin of these large solvent effects lies in differences in the solvation of the reactants or the transition states. Ritchie and Uschold find that proton transfer from 9-methyl f l ~ o r e n e ~ ~ and triphenyl methane37 is much faster in dimethylsulphoxide than in protic 29 Z . Kricsfalussy A. Bruylants and A. Dalcq Bull. SOC. chim. befges 1967,76 168. ’O W. S. Trahanovsky and M. P. Doyle J . Amer. Chem. SOC. 1967,89,4867. ” B. G. Cox and P. T. McTigue Austral. J . Chem. 1967,20 1815. 32 P. J. Taylor J . Chem.SOC. (B) 1967,904. 33 D. C. Berndt J . Org. Chem. 1967,32,482. 34 P. E. Peterson R. J. Bopp D. M. Cheuli E. L. Curran D. E. Dillard and R. J. Kamat J . 35 A. J. Parker Adv. Phys. Org. Chem. 1967,5 173. 36 C. D. Ritchie and R. E. Uschold J . Amer. Chem. SOC. 1967,89 1730. ’’ C. D. Ritchie and R. E. Uschold J. Amer. Chem. SOC ’1967.89,2960. Amer. Chem. SOC. 1967,89 5902 42 J. E. Crooks solvents and consider that proton transfer is slow in protic solvents on account of the need for solvent reorganisation around the transition state. Ritchie et aL3* also attribute to solvation the great acceleration in dimethylsulphoxide solution of the rates of combination of various anions with the stable carbonium ion of 4,4'-bis(dimethylamino)triphenylmethyltetrafluoroborate.On the other hand Cockerill and Sa~nders,~' who find the reaction between 2-phenyl-ethyldimethylsulphonium bromide and OH- to be a thousand times faster in 9.8 M. aqueous dimethylsulphoxide than in water attribute this solely to the greater nucleophilicity of OH - in dimethylsulphoxide. Solvation due to hydrogen-bonding has also received some study. Miotti4' interprets rates of S,2 reactions of benzyl halides in mixed protic solvents in terms of hydrogen-bonding in the transition state. Illuminati et aL4' find that rates of piperidino-dechlorination of meta-substituted chloroquinolines in methanol do not vary much with the nature of the meta-substituent since the substituent affects the strength of hydrogen-bonding in such a way that the change in solvation compensates for the change in reactivity.The course of many organic reactions may be directed by solvation. The stereochemistry of the photo-dimerisation of a~enaphthylene~~ and of cou-marin43 is influenced by the nature of the solvation of the transition state. Wagner44 finds that solvation of the biradical intermediate in the photolysis of ketones favours bond cleavage rather than radiationless decay. Huyser and Kim4' show that solvation of the trichloromethanesulphinyl radical determines whether it adds to cyclohexene or abstracts hydrogen radical solvation favouring addition. Shapiro Duncan and C10pton~~ find that the base-catalysed decomposition of camphor toluene-p-sulphonylhydrazone can give either camphene or tricyclene polar aprotic solvents favouring camphene formation.It is still by no means clear whether reactant or transition-state solvation is more generally important. It might be objected that transition-state solvation is unlikely to be significant since there is not enough time for solvent molecules to orient themselves around a transition state as suggested by Bell.47 Con-clusive evidence on this point is difficult to find but Kresge et ~ 2 1 . ~ ' find that values of ASs for proton transfer to 1,3,5-trimethoxybenzene in aqueous solution suggest that transition-state solvation is possible even for such a rapid process as a proton jump. 3e C. D. Ritchie G. A. Skinner and V. G. Badding J . Amer. Chem. SOC. 1967,89,2063. 39 A. F. Cockerill and W. H. Saunders jun. J . Amer. Chem. SOC. 1967,89,4985. 40 U.Miotti Gazzetta 1967,97,254. 41 G. Genel G. Illuminati and G. Marino J . Amer. Chem. SOC. 1967,89,3516. 42 D. 0. Cowan and R. L. Drisko Tetrahedron Letters 1967,1225. 43 H. Morrison H. Curtis and T. McDowell J . Amer. Chem. SOC. 1966,88,5415. 4* P. J. Wagner Tetrahedron Letters 1967,1753. *' E. S. Huyser and L. Kim J . Org. Chem. 1967,32,618. 46 R. H. Shapiro H. J. Duncan and J. C. Clopton J . Amer. Chem. SOC. 1967,89 1442. *' R. P. Bell Discuss. Faraday SOC. 1965,39,16. 48 A. J. Kresge Y. Chiang and Y. Sato J . Amer. Chem. SOC. 1967,89,4418 The Kinetics of Reactions in Solution 43 Information on solvation from AH* AS* and AC;. Kohnstam4’ reviews the methods of obtaining AC and the interpretations of the values obtained for SN2 solvolyses in mixed organic and aqueous solvents.He gives a thorough account of the difficulties in measuring AC; from the variation of AH* with. temperature as Arrhenius plots generally appear to be linear. Accurate experimental work and careful statistical analysis are needed but it is possible to measure A c t to an accuracy of a few per cent. In conjunction with AS* values information is obtained about the extent of build-up of the reactant solvation shell on formation of the transition state. Solvent transition-state interactions increase the heat capacity of the system so that the increase of solvation consequent on formation of the transition state causes AC to be negative. Robertsonso also gives an account of the precautions necessary to obtain reliable AC values and interprets the results found for SN2 hydrolyses in aqueous solution.He considers that the cause of the variation of AH* with temperature is the temperature-dependence of the free energy of the reactant solvation shell rather than the change in heat capacity of the solvent around the reacting species. This is suggested by the observation that the enthalpy of solution of methane in water changes with temperature at the rate of -52 cal. mole- deg. - ’ at 50° the solvation shell of water around methane becoming less stable with rising temperature. This value is in striking agreement with the typical value of - 50 cal. mole- ’ deg. - found for the AC of SN2 hydrolysis. In conformation of this theory Martin and Robertsons1 find a large variation in AC; for the solvolysis of t-butyl chloride in ethanol-water mixtures in the composition range where there is a rapid change in structural stability with composition.Fagley et a1.” find that AH* and AS* for the solvolysis of fluorobenzyl chlorides in isopropanol-benzene solutions can be entirely accounted for in terms of the thermodynamic properties of the isopropanol component in the mixture. AH* bears no relationship to the heats of solution of the substrates in contrast to the observation of Arnett et aLS3 who find endothermic maxima in the heats of solution of t-butyl chloride in the com-position range where AH’ for solvolysis is at a minimum. Fagley et al. account for the difference in behaviour by saying that solvation of the fluorobenzyl chlorides is not at the reactive centre of the molecule.Parker et al. 5 4 investigate AH’ and AS* for the reversible sN2 decomposition of trimethylsulphonium bromide to methyl bromide and dimethyl sulphide, in dimethylacetamide and in 88 % w/w methanol-water a protic solvent of the same dielectric constant. Both the forward and back reactions are observed, and Parker et al. show that solvent and ionic strength have much more effect 49 G. Kohnstam Ado. Phys. Org. Chem. 1967,5 121. R. E. Robertson Progr. Phys. Org. Chem. 1967,4,213. J. G. Martin and R. E. Robertson J . Amer. Chem. SOC. 1966,88,5353. 52 T. F. Fagley G. A. Von Bodungen J. J. Rathmell and J. D. Hutchinson J . Phys. Chem. 1967, ’’ E . M. Arnett W. G. Bertrude J. J. Burke and P. M. Duggleby J . Amer. Chem. SOC. 1965, 54 Y. C. Mac W. A. Millen A. J. Parker and D.W. Watts J . Chem. SOC. (B) 1967,525. 71 1374. 87,1541 44 J . E. Crooks on the anion-cation reaction than on the reverse dipole-dipole reaction, although both pass through the same transition state. Their conclusion is that it is differences in solvation of the reactants rather than of the transition state, which are important. A similar conclusion is reached by Hiller and Kreuger” who interpret AHS and ASS for the oxidation of formate ion by iodine in aqueous dimethylsulphoxide in terms of weaker solvation of formate by dimethylsulphoxide than by water. Information on solvation and solvent efectsfrorn AVS. Le Nobles6 gives an interesting account of the kinetics of reactions in solution under pressure. He comments that chemists avoid this field because they believe ‘the apparatus is cumbersome expensive and dangerous and the work requires a taste for engineering’.This he says is a misconception the apparatus being as cheap and convenient as a spectrophotometer and. considerably more reliable. The variation of rate with pressure gives the volume of activation AV* which is related to the changing density of the surrounding solvent as the reagents approach the transition state. Pressure is thus a probe uniquely suited to the study of solvation changes during a reaction. Le Noble discusses the experi-mental methods used and tabulates 456 reactions for which A V has been measured. Reactions of different types have different ranges of AVS values; e.g. free-radical formation reactions have AVS ca. + 10 ~m.~/rnole-’ whereas ionisation reactions have AV* ca.- 20 C M . ~ mole-’. It seems that AVS values are not necessarily unambiguous. Golinkin Lee, and HyneS7 find that -AV* for the solvolysis of benzyl chloride in ethanol-water mixtures has a maximum value at a certain solvent composition, paralleling the changes in AHS and AC; already discussed. They show that the changes in AVS are due almost entirely to changes in the partial-molar volume of the benzyl chloride i.e. to changes in the reactant solvation rather than the transition-state solvation. Baliga and Whalle~,’~ in their study of the pressure-dependence of benzyl chloride solvolysis in ethanol-water mixtures find no such maxima or minima in AV* but only a smooth increase in -AT/$ with increasing proportion of ethanol.They also have an explanation for their results stating that maxima and minima in the solvating power of ethanol-water mixtures are to be expected only for measurements at constant pressure, and not for measurements at constant volume. Ewald and Ottley’’ find -AVS for the cyclisation of 4-chlorobutanol to form tetrahydrofuran to be markedly less than - AVS for analogous non-cyclic reactions and attribute this to exclusion of solvent from the centre of the cyclic transition state. Adamson and Stranks6’ find a large -AV* for the thallous-thallic electron-exchange reaction which shows that the transition state must 5 5 F. W. Hiller and J. H. Kreuger Inorg. Chem. 1967,6 528. 56 W. J. Le Noble Frog. Phys. Org. Chem. 1967,5 207. 5 7 H. S. Golinkin I. Lee and J.B. Hyne J . Amer. Chem. SOC. 1967,89 1307. ’* B. T. Baliga and E. Whalley J . Phys. Chem. 1967,71 1166. 59 A. H. Ewald and D. J. Ottley Austral. J . Chem. 1967,20 1335. 6o M. G. Adamson and D. R. Stranks Chern. Comrn. 1967,648 The Kinetics of Reactions in Solution 45 involve a water molecule between the ions. AV* values for transition states involving the expulsion of an aquo-ligand are large and positive. Homolytic scission reactions are characterised by relatively large positive AV* values which are in general presumed to reflect the volume difference between reactant and transition state. However Neuman and B:har6' suggest these large pressure effects are really due to an increase in the rate of the back reaction which occurs before the radicals can escape from the solvent cage.As proof of this hypothesis Neuman and Behar show that AV* is nearly zero for the decomposition of t-butylphenyl peracetate which is not subject to recombination in the cage as the products are stable molecules. Walling and Waits62 also point out that the cage effect determines the efficiency of radical production in homolysis. The rate of decomposition of di-t-butyl peroxide is reduced in solvents of high viscosity which form stronger cages and the reduction in rate at high pressures can be entirely attributed to the increase in solvent viscosity. Lieber Rehm and Wellier63 look for an increase in fluo-rescence with increasing pressure as the increasing viscosity of the solvent slows down the quenching reaction but find the reverse for P-naphthol.They suggest the reason for the observed increase in the rate of diffusion-controlled reactions with increasing pressure is that the faster collision rate means a greater number of collisions between correctly oriented molecules. However the effect of pressure on fluorescence spectra is complex as shown by Braun and F O r ~ t e r ~ ~ who interpret a similar phenomenon for naphthalene in terms of the change in the association equilibrium between the electronically-excited state and the dimeric excimer. Isotope Effects.Cimon and Palm65 review the origins and significance of primary and secondary hydrogen isotope effects in solution with especial reference to enzyme kinetics. Stern and Wolfsberg66 find by detailed calcula-tions that it is legitimate to consider only the parts of the molecule near to the site of isotopic substitution when calculating hydrogen isotope effects.They predict that large changes in parts of the molecule far removed from the position of isotopic substitution will have little effect on the calculated magnitude. This conclusion must be interpreted with care as both theoretical and experi-mental work show that the symmetry of the transition state is of great signifi-cance in determining the magnitude of a primary hydrogen isotope effect. This symmetry may in some circumstances be influenced by substitution in a 'distant' part of the molecule e.g. at the para-position in a benzene ring. More O'Ferrall and Kouba6' carry out model calculations of primary isotope effects for four- and five-centre transition states taking account of bending vibrations and proton tunnelling.Their calculations agree with the usual 61 R. C. Neuman jun. and J. V. Behar J . Amer. Chem. SOC. 1967,89,4549. 62 C. Walling and H. P. Waits J . Phys. Chem. 1967,71 2361. 63 C. 0. Leiber D. Rehm and A. Wellier Ber. Bunsengesellschufr Phys. Chem. 1966,70 1086. 64 H. Braun and Th. F h t e r Ber. Bumengese!lschujt Phys. Chem. 1966,70 1091. 6 5 H. Simon and D. Palm Angew. Chem. Internat. Edn. 1966,5,920. 66 M. J. Stern and M. Wolfsberg J . Chem. Phys. 1966,45,4105. '' R. A. More O'Ferrall and J. Kouba J . Chem. SOC. (B) 1967,985 46 J . E. Crooks simple calculations which take account only of stretching vibrations and confirm that a maximum effect is to be expected from a symmetrical transition state.They also find that the Swain6* relationship relating deuterium and tritium isotope effects i.e. (kH/kD)1.442 = kH/kT is valid. Experimental evidence in favour of this relationship is found by Kresge et aL6’ for the acid-catalysed aromatic hydrogen exchange in 1,3,5trimethoxybenzene. Albery7’ gives a full discussion of the reasons why a more symmetrical transition state should cause a larger isotope effect for proton transfer. The results of his calculations are summarised diagrammatically. An interesting agreement between theoretical and experimental isotope effects is found by Ohno71 for the reaction of the solvated electron with the hydroxonium ion. Arrhenius plots give a difference in activation energy of 1340 cal. mole- for OH and OD bond-fission in the hydroxonium ion which agrees with the theoretical value of 1200 cal.mole-found from i.r. data. Primary hydrogen-isotope efects. Jones et ~ 2 2 . ~ ’ find that kH/kT for proton loss from p - and m- substituted acetophenones varies with the activation energy in a manner consistent with the theory that increasing transition-state symmetry increases the isotope effect. Davis and Kens0n7~ make a similar observation on the hydrolysis of arylboranes; k,/kD for B-H bond breaking increases as the strength of the B-H bond as measured by the stretching frequency decreases. There has been some interest in the use of hydrogen-isotope effects to detect proton tunnelling. Lewis and F ~ n d e r b u r k ~ ~ find values of kH/kD up to 24.2 at 25” for proton transfers from 2-nitropropane to sterically-hindered pyridine bases.They suggest that steric hindrance may favour tunnelling. Jones et also suggest tunnelling to account for anomalous isotope effects in the detritia-tion of o-methyl acetophenone. Bell and O n ~ o o d ~ ~ in a careful study of the kinetics of oxidation of formate and deuterioformate ions by permanganate, find that the isotope effect appears almost entirely in the activation energies, so that the contributions of tunnelling is insignificant. The large variations in isotope effects which can be found in a series of similar reactions due to variations in transition-state symmetry and also possibly to variations in the extent of tunnelling render doubtful any attempt to assign a reaction mechanism on the basis of the magnitude of the isotope effect, but such attempts are not uncommon.Fife77 chooses a mechanism for the hydrolysis of 2-(p-substituted phenyl)-4,4,5,5-tetramethyl-1,3-dioxalans partly on the grounds that the observed isotope effect is 2-4 whereas isotope effects 68 C. G. Swain E. C. Stivers J. F. Reuwer jun. and L. J. Schaad J . Amer. Chem. SOC. 1958, 69 A. J. Kresge and Y. Chiang J . Amer. Chem. SOC. 1967,89,4411. ’O W. J. Albery Trans. Faraday SOC. 1967,63,200. ” S. Ohno Bull. Chem. SOC. Japan 1966,39,2560. 72 J. R. Jones R. E. Marks and S. C. Subba Rao Trans. Faraday SOC. 1967,63,111. 73 R. E. Davis and R. E. Kenson J . Amer. Chem. SOC. 1967,89 1384. 74 E. S. Lewis and L. H. Funderburk J . Amer. Chem. SOC. 1967,89,2322. 75 J. R. Jones R. E. Marks and S.C. Subba Rao Trans. Faraday SOC. 1967,63,993. 76 R. P. Bell and D. P. Onwood J. Chem. SOC. (B) 1967,150. ’’ T. H . Fife J. Amer. Chem. SOC. 1967,89,3228. 80,5885 The Kinetics of Reactions in Solution 47 for reactions known to proceed by the alternative mechanism are in the range 1.4 to 1-7. E. M. Eyring et d7' hope to characterise the reacting moieties in enzyme reactions involving proton transfer by comparing isotope effects with those found for simple proton-transfer systems; e.g. k& = 2 suggests an 0-H . . 0 transfer whereas kH/kD = 3 suggests a N-H . . 0 transfer. However Kohn and Gill,79 as a result of their work on the alcoholysis of tri-n-octyl aluminium stress the need for caution in using isotope effects as a mechanistic criterion. The unpredictability of isotope effects is also demonstrated by de la Mare and El Dusouqui" who find a solvent isotope effect of 1.9 on the bromination of phenol in acetic acid despite the prediction of Swain et aLS1 that such an effect would be negligible.The most reliable use of hydrogen iso-tope effects is in deciding which of the two mechanisms is correct when one predicts a large effect and the other none at all. For instance Cerfontain and Telder's' observation of k,/kD = 6.1 for the nitration of anthracene in aceto-nitrile is a clear indication that the breaking of the C-H bond is rate-determining. Similarly the variation of fluorescence intensity with isotopic substitution is used by Stryers3 to diagnose whether excited species are involved in proton-transfer reactions.Solvent isotope efects. The validity of solvent isotope effects appears to be much greater than that of primary isotope effects. Golds4 has shown that the rate of slow proton-transfer reactions should depend 06 the deuterium content of the H,O-D,O mixed solvent in a predictable way partly determined by the Brarnsted exponent a. Gold" tests his theory by evaluating a for the general acid-catalysed hydrolysis of cyanoketone dimethylacetal both from the varia-tion in rate in various H,O-D,O mixed solvents and from the variation in rate with the pKA of the acid catalyst. Excellent agreement is found. A similar agreement is found by Salomaa et aLE6 for the general acid-catalysed hydrolysis of vinyl ethers using the theoretical equations of Salomaa Schlaeyer and LongE7 and of Kresge.88 Kresge and Chiang" also study the hydrolysis of ethyl vinyl ether with similar success.They point out that although the solvent isotope effect in H,O-D,O mixed solvents cannot be regarded as a useful criterion of reaction mechanism it can in favourable cases provide valuable information concerning the nature of the transition state in reactions of known mechanism. In particular it can show the position which the transition state occupies on the reaction co-ordinate for reactions in which proton transfer from the hydro-xonium ion to the substrate occurs in the rate-determining step. 78 M. H. Miles E. M. Eyring W. W. Epstein and M. T. Anderson J . Phys. Chem. 1966,70,3490. 79 E. Kohn and J. M. Gill J . Organometallic Chem. 1967,7 359. P.B. D. de la Mare and 0. M. H. El Dusouqui J . Chem. SOC. (B) 1967,251. C . G. Swain D. A. Kuhn and R. L. Schowen J . Amer. Chem. SOC. 1965,87,1553. H . Cerfontain and A. Telder Rec. Truv. Chim. 1967,86,371. 83 K. Stryer J. Amer. Chem. SOC. 1966,88 5708. 84 V. Gold Trans. Faraday SOC. 1960,56,255. 86 P. Salomaa A. K. Kankaanpera and M. Lajunen Acta Chem. Scand. 1966,20 1790. 8 7 P. Salomaa L. L. Schlaeger and F. A. Long J . Amer. Chem. SOC 1964,86,47. 89 A. J. Kresge and Y. Chiang J. Chem. SOC. (B) 1967,58. V. Gold and D. C. A. Waterman Chem. Comm. 1967,40. A. J. Kresge Pure Appl. Chem. 1964,243 48 J . E. Crooks Secondary hydrogen isotope eflects. Stern and Wolfsberggo show theoretically that there cannot be a secondary hydrogen isotope effect of more than about 1.5% unless there is a force constant change at the isotopically substituted position between reactant and transition state.Kresge and Pretogl agree with this conclusion and point out that the crucial issue in the interpretation of secondary isotope effects is the origin of these changes in force constant. Brown et aLg2 have suggested that the changes are of steric origin the -CD, group being smaller than the -CH group since the amplitude of a C-H vibration is greater than that of a C-D vibration with the same energy. Kresge and Preto test this hypothesis by measuring the equilibrium constant for the ionisation of triphenylcarbinol for varying degrees of ring deuteriation. Ring deuteriation at any point increases triphenyl cation formation but the effect is greatest for deuteriation at the para-position whereas the steric hypothesis would suggest the effect would be greatest for ortho-substitution.Kresge and Preto conclude that the effect is caused by the inductive effect of the C-D group by hyperconjugation as discussed by Halevig3 Heitner and L,effekg4 also test the steric hypothesis by measuring the secondary isotope effect on the racemisation of a highly hindered biphenyl and find no change in the rate when the hindering -CH groups are replaced by -CD3 groups. Koenig and WolP’ measure the secondary isotope effect on the formation of the t-butyl radical by the decomposition of t-butyl perpivalate. They find k Jk, = 1-02 as compared with k JkD = 1.11 for the formation of the t-butyl cation and are able to account for the effect in terms of the hyperconjugative stabilisation of the radical without involving steric effects.Karabatsos et dg6, in a theoretical and experimental study of the solvolysis of 8-methyl naphthyl and naphthoyl chlorides find that less than 10% of the observed secondary isotope effect can be attributed to non-bonded (i.e. steric) interactions most being caused by hyperconjugation. Lee and N0szk6~’ find secondary isotope effects around 1.15 for solvolysis of dimeth~xyphenyl-[~H,]-ethyl p-bromo-benzenesulphonates in accordance with the hypothesis of non-classical carbonium-ion intermediates. Following Streitwieser et aLg8 they attribute secondary isotope effects to the decrease in bending force constant from an initial C-H tetrahedral bending to the lower frequency out-of-plane motion in the transition state.This latter is affected by the proximity of the leaving or entering group. If these are close the out-of-plane bending will have higher M. J. Stem and M. Wolfsberg J . Chem. Phys. 1966,45,2618. 91 A. J. Kresge and R. J. Preto J . Amer. Chem. SOC. 1967,89 5110. 92 H. C. Brown M. E. Azzaro J. G. Koelling and G. J. McDonald J . Amer. Chem. Soc. 1966, ” E. A. Halevi Prog. Phys. Org. Chem. 1963,1 109. 94 C. Heitner and K. T. Leffek Canad. J . Chem. 1966,44,2567. 95 T. Koenig and R. Wolf J . Amer. Chem. SOC. 1967,89,2948. 96 G. J. Karabatsos G. C. Sonnichsen C. G. Papaioannou S. E. Scheppele and R. L. Shone, ’’ C. C. Lee and L. Noszk6 Canad. J . Chem. 1966,44,2491. 88,2520. J . Amer. Chem. SOC. 1967,89,463.A. Streitwieser jun. R. H. Jagow R. C. Fahey and S. Suzuki J . Am-. Chem. SOC. 1958,80, 2326 The Kinetics of Reactions in Solutions 49 energy and so be at a higher frequency. An alternative explanation of a similar phenomenon is given by NikoletiC et dg9 who find secondary isotope effects around 1.1 for the solvolysis of methyl-substituted cyclopropylcarbinyl and cyclobutyl derivatives. They explain this deviation from the theoretical maxi-mum value of 1.4 in terms of hyperconjugative charge delocalisation in the non-classical carbonium ion. Eflectsfor isotopes other than hydrogen. The masses of isotopes of other elements differ proportionally much less than those of hydrogen so that the isotope effects are very small. It is in general not possible to measure the different rates directly and the effects are measured by competitive techniques.The reactants are analysed by mass spectrometer at various intervals after the start of the reaction. Yankwich and Buddenbaum'" discuss sixteen reactions reported in the literature for which the kinetic carbon-isotope effects vary with the inverse-square of the temperature rather than with the reciprocal as theoretically predicted. They attribute this behaviour to the existence of alternative mechanisms for each reaction one of which is favoured in a different temperature range from the other. Smith and Bourns"' use the existence of a nitrogen isotope effect of 1.0091 & 00007 to decide between two possible mechanisms for the carbonyl-elimination reaction of 9-fluorenyl nitrate with acetate ion.Brown and Druryl'' compare experimental and theoretical values for the nitrogen isotope effect in the reduction of nitrate nitrite and hydroxylamine to ammonia to find out whether the cleavage of the N-0 bond is rate-determining. Agarwala Rees and Thodelo3 use a similar tech-nique with sulphur isotope effects to find points of cleavage in the sulphur chains when polythionates are decomposed by acid. Fast Reactions.-Pulse radiolysis. Pulse radiolysis continues to be a popular and fruitful field. In 1967 more work was published concerning this technique for the study of fast reactions than any other. Anbar and Nets"* tabulate rate constants for 660 reactions of the solvated electron 270 reactions of the hydrogen atom in solution and 480 reactions of the hydroxyl radical in solution.Only 19 of the 164 references are to work published more than five years ago, and the more recent results are obtained almost exclusively by pulse radiolysis. Freemanlo' gives a theoretical treatment of the kinetics of the initial reactions after a radiolytic pulse discussing the scavenging of positive ions and solvated electrons in the radiolysis of liquid hydrocarbons. The good agreement with experiment suggests that solvated electrons are formed in non-polar solvents as well as in water. Dainton et aZ.'06 account for differences between rate constants obtained by pulse radiolysis and those obtained by product analysis, 99 M. NikoletiC S. BorEiC and D. E. Sunko Tetrahedron 1967,23,649. loo P. E. Yankwich and W. E. Buddenbaum J .Phys. Chem. 1967,71,1185. lo' P. J. Smith and A. N. Bourns Canad. J . Chem. 1966,44,2553. L. L. Brown and J. S. Drury J . Chem. Phys. 1967,46,2833. Io3 V . Agarwala C. E. Rees and H. G. Thode Canad. J . Chem. 1967,45 181. lo4 M. Anbar and P. Neta Internat. J . Appl. Radiation Isotopes 1967,18,493. G. R. Freeman J . Chem. Phys. 1967,46,2822. G. V . Buxton F. S. Dainton and G. Thielens Chem. Comm. 1967,201 50 J . E. Crooks after continuous radiolysis in terms of the transfer of electrons from one unstable species to another during radiolysis. Anbar et al.107 find that the activation energy of all reactions of the type ea; + X -+ X- is around 3.5 kcal. mole-' the energy of activation of diffusion in water despite the wide range of rate constants. The rate is determined by the probability of finding an electron vacancy on the substrate molecule and low rate constants are caused by a large number of collisions in which the substrate molecule is in an unfavourable electronic configuration.For example for hydroxonium-ion substrate k = 4.0 x 10" 1. mole-' set.-' and ASt = -2.2 cal.deg.-' mole-' whereas for urea substrate k = 2.7 x lo5 1. mole-' set.-' and ASt is -25 cal.deg.-' mole-' This conclusion is borne out by the work of Kevan'08 who finds that the relative rates of reactions of the solvated electron in ice at 7 7 " ~ quantita-tively parallel those in water at 300°K. Gottschall and Hartlog find from the temperature variation of the products from steady-state radiolysis that the activation energy of all reactions of the type eai + X -+ X - is around 3.5 kcal.which they state to be the activation energy of self-diffusion in water taking the value of Wang.'" A clearer picture of the solvated electron is beginning to emerge. Dainton et al.' ' ' show that the kinetic salt effect on the reactions of the solvated electron in methanol is consistent with the solvated electron having a unit negative charge and a diameter of 5 A. Anbar and Neta'12 use the rates of the reaction between the hydrogen atom and the fluoride ion to calculate the redox potential of the solvated electron to be 2.5 volt. This agrees with the value of 2.1 volt found by Baxendale'13 from the rate of reaction between the hydrogen atom and the hydroxide ion. However there are still some mysteries even about the simplest reactions.Barker and Sammon''4 find the rate of combination of hydroxonium and hydroxyl ions produced by pulse radiolysis to be 7.3 x 10" 1. mole-'sec.-' much less than that found by Ertl and Gerischer'" using the temperature-Jump method. The discrepancy is too great to be written off as experimental error. The number of systems studied by pulse radiolysis in 1967 is so great that it is only possible to give a list to indicate the fields of activity. Inorganic species studied include CO,' l6 CNS-,'" and Oi.118 Organic species studied include lo' M. Anbar Z. B. Alfassi and H. Bregmann-Reisler J . Amer. Chem. SOC. 1967,89 1263. lo' L. Kevan J . Amer. Chem. SOC. 1967,89,4238. Io9 W. C. Gottschall and E. J. Hart J . Phys. Chem. 1967,71,2102. J.H. Wang J . Amer. Chem. SOC. 1951,73.510. G. V. Buxton F. S. Dainton and M. Hammerli Trans. Faraday SOC. 1967,63 1191. M. Anbar and P. Neta Trans. Faraday SOC. 1967,63,141. J. H. Baxendale Radiation Res. Suppl. 1964,4 139. G. C. Barker and D. C. Sammon Nature 1967,213,65. 'I5 G. Ertl and H. Genscher. Z . Elektrochem 1961,65,629. 116 Y. Raef and A. J. Swallow J . Phys. Chem. 1966,70,4072. J. H. Baxendale and D. A. Stott Chem. Comm. 1967,699. W. D. Felix B. L. Gall and L. M. Dorfman J . Phys. Chem. 1967,71 384; G. Czapski ibid., p. 1683 The Kinetics of Reactions in Solution 5 1 phenol,' l9 acrylamide,120 pyridine,121 nitrobenzene,'22 nitro~obenzene,'~~ phenylhydr~xylamine,'~~ and the nitroparaffns. l 25 Hagemann and Schwarz'26 study the benzyl radical produced by pulse radiolysis of a-chlorotoluene and ThomasI2' studies the methyl radical in aqueous solution produced by pulse radiolysis of aqueous methyl iodide.N.rn.r. The measurement of the rate of a chemical reaction from the width of the n.m.r. absorption peak of the nucleus whose movement causes the reaction is a popular and successful technique. Several workers have tested its validity by comparing the rates thus obtained with rates for the same reaction found by an independent technique. Griffths and Socrates'28 find good agreement between the rate of hydration of pyruvic acid measured by n.m.r. line-width and the value found by S t r e h l ~ w ' ~ ~ by the pressure-jump method, with conductimetric detection. Luz et al. 30 find that the rate of the acid-catalysed oxygen-exchange on acetaldehyde measured by the width of the "0 peak is the same as the rate of dehydration of acetaldehyde hydrate.' 31 The inversion of the cyclohexane ring is not perhaps a chemical reaction in the strict sense of the term but its rate can be measured.Anet and Bourn'32 measure the rate of chair- to boat-inversion for cyclohexane-C2H by two different methods, line-shape analysis and double resonance. In the less familiar double-resonance technique the equilibrium distribution of spin states for protons on a given site is perturbed by saturation with a strong radio-frequency field. If protons are transferred to another site by a chemical reaction the change in intensity at the second site gives a measure of the rate of the chemical reaction.The range of observable rates is severely limited as the chemical-relaxation time must be of the same order of magnitude as the spin-lattice relaxation time. Anet and Bourn find excellent agreement between values of A H f and ASf found by the two methods although a direct comparison between rates is not possible as the methods are only applicable in different ranges. Rates of internal rotation also hardly count as kinetics but Gutowsky et find good agree-ment between the rates of rotation about the C-N bond in N-methyl-N-benzylformamide calculated from n.m.r. line-width and observed in a mixture 'I9 E. J. Land and M. Ebert Trans. Faraday SOC. 1967,63,1181. K. W. Chambers R. Collinson F. S. Dainton W. A. Seddon and F. Wilkinson Trans. B. Cercek and M. Ebert Trans.Faraday soc. 1967,63 1687. Faraday SOC. 1967,63 1699. "' K.-D. Asmus A. Wigger and A. Henglein Ber. Bunsengesellschaft Phys. Chem. 1966,70,862; K.-D. Asmus B. Cercek M. Ebert A. Henglein and A. Wigger Trans. Faraday SOC. 1967,63,2435. lZ3 K.-D. Asmus G. Beck A. Henglein and A. Wigger Ber. Bunsengesellschaft Phys. Chem., 1966,70 869. I 2 4 A. Wigger A. Henglein and K.-D. Asmus Ber. Bunsengesellschaft Phys. Chem. 1967,71 513. ''' J. Sutton and Tran Dinh Son J . Chim. phys. 1967,64,688. lZ6 R . J. Hageman and H. A. Schwarz J . Phys Chem. 1967,71,2694. ''' J. K. Thomas J . Phys. Chem. 1967,71 1919. 12* V. S . Grifiths and G. Socrates Trans. Faraday SOC. 1967,63,673. lZ9 H. Strehlow 2. Elektrochern. 1962,66,392. 130 P. Greenzaid Z . Luz and D. Samuel J . Amer. Chem.SOC. 1967,89,756. 13' R. P. Bell and P. G. Evans Proc. Roy 'SOC. 1966 A 291,297. 13' F. A. L. Anet and A. J. R. Bourn J . Amer. Chem. SOC. 1967,89,760. 133 H. S. Gutowsky J. Jonas and T. H. Siddall jun. J . Amer. Chem. SOC. 1967,89,4300 52 J . E. Crooks enriched in one rotamer. A similar agreement is found by Mannschreck, Mattheus and R i s ~ m a n ' ~ ~ for the interconversion rate of the rotamers of N-benzyl-N-2,4,6-tetramethyl benzylamide. A considerable amount of work has been done on proton exchange on oxygen nitrogen and carbon. Puar and G r ~ n w a l d ' ~ ~ look for but fail to find, evidence for a Grotthus-type mechanism for proton exchange between salicyclic acid and methanol (c$ Albery2'). Grunwald et al. measure proton exchange rates for phenol in aqueous acid'36 and substituted phenols in methan01.l~' Rabideau and H e ~ h t ' ~ use 1 7 0 n.m.r.line-widths to measure the rates of acid- and base-catalysed proton exchange in water and find rates for the ionic-recombination reaction similar to those found by pulse radiolysis. l4 Ralph and Gr~nwald'~' measure the rate of exchange of triethylammonium ion with H 2 0 by proton line-width and with D20 by observation of the change with time of the height of the HOD proton peak. The symmetrical exchange B + HOH + HB' + BH+ + HOH + B is five times slower than expected from the rate for trimethylammonium and Ralph and Grunwald attribute this to steric hindrance. Grunwald and Ralph'40 measure the rate of breaking the R,N-HOH hydrogen bond and find it to be the rate of diffusion of the water molecule into the bulk solvent.In aqueous sulphuric acid the rate varies inversely with the viscosity over a five-fold range of bulk viscosity as predicted by the Smoluchowski equation. Grunwald and Ralph point out that no dis-continuity is observed in passing from trimethylamine to triethylamine which is evidence against the theory that special ice-like water structures are built up near non-polar organic groups. One of the ethyl groups in triethylamine must be adjacent to the water molecule that is hydrogen-bonded to nitrogen but it does not noticeably affect the kinetics. Day and Reille~'~' find the isotope effect for the diffusion-controlled proton-transfer from trimethylammonium ion to water to be 1.23 as expected for a diffusion-controlled reaction.G r ~ n w a l d ' ~ ~ finds that rates and equilibria for proton exchange of trimethyl-ammonium ion in methanol are similar to those in water. Brauman McMillen, and Kana~awa'~ use the double-resonance technique to measure the rate of proton exchange between fluorenyl lithium and fluorene in dirhethylsulphoxide, as the rate is too slow (k2 = 0.5 1. mole-'sec.-') to observe by the line-width method. The rate of exchange of solvent in the first co-ordination sphere of a metal ion is observed by Wuthrich and C ~ n n i c k ' ~ ~ for vanadyl ion in water, 134 A. Mannschreck A. Mattheus and G. Rissman J . Mol. Spectroscopy 1967,23 15. 13' M. S. Puar and E. Grunwald J . Amer. Chem. SOC. 1967,89,4403. 136 E. Grunwald and M. S. Puar J . Phys. Chem. 1967,71 1842.13' E. Grunwald C. F. Jumper and M. S. Puar J . Phys. Chem. 1967,71,492. 138 S. W. Rabideau and H. G. Hecht J . Chem. Phys. 1967,47,544. 139 E. K. Ralph jun. and E. Grunwald J . Amer. Chem. SOC. 1967,89,2963. f40 E. Grunwald and E. K. Ralph jun. J . Amer. Chem. SOC. 1967,89,4405. 14' R. J. Day and C. N. Reilley J . Phys. Chem. 1967,71 1588. 142 E. Grunwald J . Phys. Chem. 1967,71 1846. 143 J. 1. Brauman D. F. McMillen and Y. Kanazawa J . Amer. Chem. SOC. 1967,89 1728. 14* K. Wuthrich and R. E. Connick Inorg. Chem. 1967,6,583 The Kinetics of Reactions in Solution 53 and by Fratiello Miller and Sch~ster’~’ for AlCl, BeCl, GaCl, SbC15 and TiC1 in NN-dimethylformamide. Line-width measurements can sometimes be interpreted incorrectly. The width of the satellite lines produced by Ig9Hg-H spin-coupling in the ‘Hn.m.r.spectrum of methylmercuric iodide have been taken to give the rate of alkyl but S i m p ~ o n ’ ~ ~ shows the line broadening is caused by relaxation of spin-coupling with the quadrupole halogen nucleus. A similar explanation is also given by Ham Jeffery Mole and Stuart,148 although they still invoke alkyl exchange to explain the collapse of the satellite lines on the addition of AlCl,. Relaxation methods. The temperature-jump method continues to be the most widely used of the relaxation methods. Bewick and Robertson149 test the theory of coupled reactions by measuring the relaxation times for systems in which zinc and copper ions compete for murexide. Good agreement with the generally accepted theory is found in contradiction to earlier work in the same 1ab0ratory.l’~ Rorabacherl” finds that the rate of formation of the monoammine complexes of the divalent first-row transition-metal ions is controlled by the rate of water loss from the M(H,O)i+ .. . . NH complex. There is good agreement with the rate of water exchange in the inner solvation sphere as found by n.m.r. line-width1 ’ This rate-controlling desolvation is common but by no means universal. Kustin et find the rate of formation of the P-aminobutyrate complexes of Mi2+ and Co2+ to be controlled by the rate of chelate-ring closure whereas the a-aminobutyrate complexes form by the usual mechanism. Hurwitz and Kustin’” find the rate of formation of uranyl complexes decreases with de-creasing nucleophilic character of the anionic ligand.The temperature-jump technique has been used by Stuehr’56 for a detailed study of the tautomerism of diacetylacetone which turns out to be a surprisingly complex process. Bio-chemistry seems to offer the most promising field for temperature-jump work. Hammes and S~hirnrnel’~~ apply matrix techniques to the often very difficult problem of calculating rate constants from relaxation times with special reference to enzyme systems. Erman and Hamme~’’~ apply a temperature-and by ultrasonic absorption.’ 14’ A. Fratiello D. P. Miller and R. Schuster Mol. Phys. 1967 12 11 1. 146 E. F. Kiefer and W. L. Waters J . Amer. Chem. Soc. 1965,87,4401. 147 R. B. Simpson J . Chem. Phys. 1967,46,4775. 14’ N. S. Ham E. A. Jeffery T. Mole and S.N. Stuart Chem. Comm. 1967,254. 14’ A. Bewick and P. M. Robertson Trans. Faraday SOC. 1967,63,678. lSo A Bewick M. Fleischmann J. N. Hiddleston and Lord Wynne-Jones Discuss. Faraday SOC., 1965,39 149. D. B. Rorabacher Inorg. Chem. 1966,5 1891. T. J. Swift and R. E. Connick J . Chem. Phys. 1962,37,307. M. Eigen and K. T a m 2. Elektrochem. 1962,66,107. lS4 A. Kowalak K. Kustin R. F. Pasternack and S. Petrucci J . Amer. Chem. SOC. 1967,89,3126. Is’ P. Hurwitz and K. Kustin J . Phys. Chem. 1967,71,324. 15’ G. G. Hammes and P. R. Schimmel J . Phys. Chem. 1967,71,917. J. Stuehr J . Amer. Chem. SOC. 1967,89,2826. J. E. Erman and G. G. Hammes J . Amer. Chem. SOC. 1966,88,5607 54 J . E. Crooks jump to the sample in a stopped-flow apparatus to investigate the reaction of ribonuclease with cytidine 2,3'-cyclic phosphate.There have been some advances in instrumentation for relaxation tech-niques. Caldin and Crooks'59 describe an apparatus in which a temperature-jump is produced by a microwave pulse and use it to measure the rates of the proton-transfer reactions between 2,4-dinitrophenol and the butylamines in chlorobenzene solution. Eyring et al. 16' describe a dissociation field-effect relaxation apparatus used to study the hydrolysis of the uranyl ion. Hoffmann and Pauli'62 describe a pressure-jump apparatus for the study of relaxation processes in the microsecond region. A rectangular pressure-jump of 12 micro-seconds duration and 25 atmospheres amplitude is produced by discharging a capacitor through a flat coil in front of a copper membrane.The formation of the Co2+-malonate complex is studied. In these sophisticated kinetic techniques care must be taken to relate the apparatus design to the system studied. It is a pity that on the evidence of their own published oscilloscope traces many users of the temperature-jump technique seem unaware that a small capacitor of the correct value in the detector circuit would greatly reduce noise and so lead to more accurate results. Flash photolysis. Hayon and M ~ G a r v e y ' ~ ~ produce solvated electrons by flash photolysis in the vacuum u.v. which then react with SO;- COZ- and OH-. Strong and per an^'^^ study the transient iodine atom o-xylene charge-transfer complex produced by flash photolysis. It is more stable than the iodine molecule o-xylene complex as predicted by the Mulliken theory.The variation of the rate of formation with temperature follows the general pattern predicted by the Smoluchowski equation with Stokes-Einstein diffusion coefficients. Wagner'65 shows that the rate of decay of triplet acetone is due to hydrogen-atom abstraction from the solvent in contradiction to the hypothesis of Borkman and Kearns,'66 who state that triplet acetone has only a very short lifetime in solution so that a triplet-energy transfer in pure acetone must be faster than diffusion-controlled. Hammond et ~ 1 . l ~ ~ study steric effects on the rate of energy transfer from triplet fluorenone to various substituted stilbenes. Flash photolysis like temperature-jump is also applicable to systems of biochemical interest e.g.proflavin'68 and the photochromic spiropyrans.'69 Other methods. Gorrell and Dubois' 7 0 use the fluorescence-quenching 159 E. F. Caldin and J. E. Crooks J . Sci. Instr. 1967,44,449. 160 E. F. Caldin and J. E. Crooks J . Chem. SOC. (B) 1967,959. 16' D. L. Cole E. M. Eyring D. T. Rampton A. Silzars and R. P. Jensen J . Phys. Chem. 1967, 71 2771. H. H. Hoffmann and K. Pauli Ber. Bunsengesellschuf. Phys. Chem. 1966,70 1052. 163 E. Hayon and J. J. McGarvey J . Phys. Chem. 1967,71,1472. 164 R. L. Strong and J. Perano J . Amer. Chem. SOC. 1967,89,2535. 166 R. F. Borkman and D. R. Kearns 1. Amer. Chem. SOC. 1966,88,3467. 16' W. G. Herkstroeter L. B. Jones and G. S. Hammond J . Amer. Chem. SOC. 1966,88,4777. K. Kikuchi and M. Koizumi Bull.Chem. SOC. Japan 1967,40,736. 169 M. Mosse and J.-C. Metras J . Chim. phys. 1967,64 691 ; J. Arnauld and M. Mosse Compt. ''O J. H. Gorell jun. and J. T. Dubois Trans. Faraday SOC. 1967,63,347. P. J. Wagner J . Amer. Chem. SOC. 1966,88,5672. rend. 1967,264<= 1145 The Kinetics of Reactions in Solution 55 technique to measure the encounter rate between biacetyl and polycyclic aromatic hydrocarbons. They test the Smoluchowski equation using experi-mental diffusion coefficients rather than those calculated from the Stokes-Einstein equation and find good agreement. The Stokes-Einstein diffusion coefficients are up to three times less than the experimental values as these large, flat molecules can slip sideways through the solvent. Petrucci' 71 measures the rate of association between solvated Mg2 + and SO:- to form Mg2+(H2O),SO;- in water-glycol mixtures from the ultrasonic absorption in the frequency range 50-170 MHz and finds the rate varies with viscosity as predicted by the Smoluchowski equation.Petrucci and Battistini' 72 use the same apparatus to measure the rate of formation of the tetrabutyl-ammonium bromide ion-pair in nitrobenzene-methanol mixtures. Gui'tyai and Mairanovskii' 7 3 use the dropping-mercury electrode to measure the rate of protonation of pyridine 2,6-lutidine and maleate ion in aqueous dioxan. The rates at high dioxan concentration are an order of mag-nitude higher than that predicted by the Debye-Smoluchowski equation, which suggests that the approximations necessary in solving the polarographic equations are invalid under the conditions used.Niirnberg' 74 gives a careful and detailed account of high-level Faradaic rectification a modification of the polarographic technique which enables accurate measurements to be made on the fastest reactions. During the lifetime of each mercury drop a stream of high-voltage microsecond pulses at a repetition frequency of 10 kHz is applied, and the rectified current is plotted against the applied potential. The effective drop-time is thus reduced to one microsecond. Niirnberg gives an extensive review of the theory the apparatus and its applications with 164 references. The ionisation rates for seventeen carboxylic acids are given in good agreement with results from relaxation methods'75 and the rotating-disc electrode.'76 Bimolecular rate constants for fast reactions can also be found by classical methods if the reagents can be used at sufficiently low concentrations.A controlled low concentration of reagent can be maintained by a two-phase liquid system the reagent reacting in say an aqueous layer but being mostly present in the other organic layer. This technique is used by Nanda and S h a ~ m a ' ~ ~ to observe fast alkaline hydrolysis of esters and by Hogeveen et ~ 2 . ' ~ ' to observe the reduction of trimethylcarbonium ions by molecular hydrogen. The concentration of a reagent may also be low as the result of an unfavourable equilibrium constant. Coombes Moodie and Schofield 17' 17' S. Petrucci J . Phys. Chem. 1967,71 1174. 17' S. Petrucci and M. Battistini J . Phys. Chem. 1967,71 1181. V. P. Gui'tyai and S. G Mairanovskii Elektrokhimiya 1966,2 1414. 174 H. W. Niirnberg Fortschr. Chem. Forsch. 1967,8,241. M. Eigen Angew. Chem. Internat. Edn. 1964,3 1. 17' W. Vielstich and D. Jahn 2. Elektrochem. 1960,64,43. 17' A. K. Nanda and M. M. Sharma Chem. Eng. Sci. 1967,22,769. A. F. Bickel C. J. Gaasbeek H. Hogeveen J. M. Oelderik and J. C. Platteeuw Chem. Comm., 1967,634. 179 R. G. Coombes R. B. Moodie and K. Schofield Chem. Comm. 1967,352 56 J . E . Crooks point out that the rate of nitration of alkylated aromatic hydrocarbons is independent of the nature of the alkyl groups and suggest that the rate is controlled by the encounter rate between the hydrocarbon and the nitronium ion. The observed rate is slow because of the low concentration of nitronium ion

ISSN:0069-3022    

DOI:10.1039/GR9676400037

出版商:RSC    

年代:1967

数据来源: RSC

摘要:

5. GASES LIQUIDS AND LIQUID MIXTURES By N. G. Parsonage (Imperial College of Science and Technology London S . W.7) THE most recent occasions on which these topics have been reviewed in the Annual Reports were liquid mixtures by McGlashan' in 1962 simple fluids by Rowlinson' in 1959 and gases liquids and liquid mixtures by Rowlinson in 1955.3 Gases.-Studies of intermolecular forces usually conclude by bemoaning the lack of data of sufficient quality and over sufficient range of temperature, for the second virial coefficient of gases (B) composed of simple molecules. An important recent improvement in this situation was the publication of accurate low-temperature data for argon and krypton by Weir et d4 The Burnett method was used and one noteworthy feature was the manometry.The latter involved a mercury manometer of square cross-section (to facilitate the observation of the meniscus) and led to an accuracy of 2 x atmos. Values of B were given for argon from 8@-190"~ (triple-point = 83.8"~) and for krypton from 110-225"~ (triple-point = 116.0"~) the absolute accuracy ranging from 10 ~ r n . ~ mole-' at the lowest temperature to 1 ~ m . ~ mole- at the highest. Substantial disagreement below 120"~ was found with the only previous set5 of low-temperature virial coefficients for these gases, this being attributed to the greater attention paid to adsorption corrections in the present work. The new data requires a deeper and narrower potential-well than is given by a Lennard-Jones 6-12 potential. Best agreement with experiment was found for a Kihara potential in which all three parameters were treated as adjustable.The potential recommended is with r = R b and y o as the diameter of the hard core such that u = co if R < "p and with the values ~ / k = 163-7 & 0-6",o = 3.15 & O*OOA y = 0.164 (argon) and ~ / k = 213-9 & 1.3" (T = 3.42 0-01 A y = 0.126 (krypton). For comparison the well-depths ~ / k for the Lennard-Jones 6-12 potential as given by Hirschfelder et d6 are 119-8 or 122" for argon and 171 or 158" for krypton. M. L. McGlashan Ann. Reports 162,59 73. J. S. Rowlinson Ann. Reports 1959 56 22. J. S. Rowlinson Ann. Reports 1955 52 56. R. D. Weir I. W. Jones J. S. Rowlinson and G. Saville Trans. Faraday SOC. 1967 63 1320. B. E. Fender and G. D. Halsey J . Chem. Phys.1962,36 1881. J. 0. Hirschfelder C. F. Curtiss and R. B. Byrd The Molecular Theory of Gases and Liquids, Wiley New York 1954 p. 11 10 58 N. G. Parsonage The Burnett method has also been employed by Suh and Storvick' in measurements on methyl chloride at higher temperatures (200-350") and pressures (up to 500 lb. in.-2) although the data above 300" are probably unreliable because of decomposition. A completely different approach is being adopted by Bottomley. In a recent paper with Spurling' he determined dB/dT by a differential method and combined these values with data for B at one temperature to give B for CS,, CH,COCH, CH,Cl and CH30H in the range 50-150". Analysis of B was made in terms of two types of potential for each substance. For CS2, these were the Lennard-Jones 6-12 potential with and without a quadrupole-quadrupole interaction term the latter leading to a quadrupole moment of k9.23 x esu.cm.2 which seems too large. For CH,COCH3 and CH,Cl Stockmayer potentials with and without dipole-induced dipole terms were used the values of the dipole moments and the polarisability being taken from the literature. Each mixture was considered in two ways (a) using the simplest and (b) using the most sophisticated potential for each component. Taking the geometric and arithmetic combining rules for E and 0 respectively, predictions based on (b) were in general in much better agreement with experiment than those using (a). Binary systems involving CF, molecules of which have a large octopole moment are beginning to be studied although the temperatures employed are probably too high for contributions to the virial coefficients from this source to be important.Douslin et al.' have reported a very comprehensive set of PVT measurements by the Burnett method on CF4 + CH4 from 0-350" and with pressures ranging from 1 6 - 4 0 atmos. Values are given for the cross-virial coefficients B,, Cl12 C122 Dll12 Dl12, and Ill,,, which are related to the overall virial coefficients by the equations B = Bllx + 2B,,x1x2 + 4Ol1 12x:x2 + 6Dl122~:~; + 4D1222x1x; + D2222x~. A corresponding-states treatment of the B, values was attempted using for reduction the Boyle temperature (7'') and the Boyle volume (V = TdB/dT,=,,). When the Boyle parameters for the cross interaction were evaluated from those for the pure substances using the usual combining rules TI, = (TIBT2J+ and V = ('" + '$,)' the B12 data failed to fit the corresponding-states plot but better results were obtained when T 1 2 B and '12 were taken directly from the experimental data.The size of the discrepancy was quite striking e.g. TI,, derived from experiment was 467" almost 50" lower than the value obtained from the above combination rule. Kalfoglou and Miller" used the Burnett method for B of CF4 + He at 30" and at 100" intervals from 100-500" with pressures ranging from 3-50 atmos. They were unable to fit their values for B with any simple potential. They also studied He + Ar. Since the data B& c = c11,x + 3c,12x:x + 3c,,,x,x; + c,,,x; D = D,,,,Xf + 8 ' K. W. Suh and T. S. Storvick Amer.Inst. Chem. Engineers J. 1967 13 231. G. A. Bottomley and T. H. Spurling Austral. J . Chem. 1967,20 1789. D. R. Douslin R. H. Harrison and R T. Moore J . Phys. Chem. 1967,71 3477. l o N. K. Kalfoglou and J. G. Miller J . Phys. Chem. 1967 71 1256 Gases Liquids and Liquid Mixtures 59 for pure He and pure Ar were fitted best by 6-exp and Lennard-Jones 6-12 potentials respectively both of these were considered for the fitting of the B12 data but none of the five sets of combination rules tried gave reasonable agreement with experiment. Sass et a2." have also used the Burnett method to obtain data with which to test proposed combining rules. They also found that the rules this time for the Benedict-Webb-Rubin equation were in poor agreement with their PVT data which was for CO + C2H4 at 40 50 75, 100 and 125" and at pressures from 5-500 atmos.Zandbergen and Beenakker' have calculated B values from the volume change on mixing the pure gases. In this way they avoided the considerable dependence on accurate values for the pure components which is a weakness of the usual way of determining B from values of the overall B of the mixture. Systems studied were N + H, Ar + H, and Ar + N and pressures were from 3-100 atmos. The largest volume change measured was 25 ~ m . ~ mole- '. The results suggested that there were important deviations from the arithmetic-mean combining rule for o, and also that &' < ( E E ) ~ for N + H2 and Ar + H,. They have discussed13 these results in terms of the cell-type cor-responding states theories of Prig~gine'~ and Scott15 and have found that the behaviour of the systems lie between those of the 2- and 3-liquid approxima-tions of Scott.Workers in the same laboratory16 have measursd the enthalpy of mixing (AH,) for the same three systems at temperatures from 150-293"~ and at pressures from 30-1 30 atmos. using an isothermal flow-calorimeter. They ~bserved'~ that near the critical temperature of one component it is the H behaviour of that component which mainly determines AH i.e. AH,(x P T) zz x(Ho(xP T ) - Ro(P T)) where the superscript 0 refers to the pure substance and R indicates a molar quantity. They again found that the behaviour lay between those corresponding to the 2- and 3-liquid rhodels. Measurements of the solubilities of benzene naphthalene and anthracene in compressed argon and oxygen have been used by Bradley and King18 to determine B12 for each of the six binary systems at one temperature only.The assumption was made that since the intermolecular-force parameters for Ar and 0 are nearly equal then any difference in the B12 values for Ar and 0 with any organic substance must arise from specific interactions between the 0 and the aromatic molecules. The differences observed were in all cases less than the experimental uncertainty in agreement with the conclusion of Tsubomura and Mulliken' that the charge-transfer absorption of these oxygen systems does not arise from the formation of stable complexes. A. Sass B. F. Dodge and R. F. Bretton J . Chem. and Eng. Data 1967 12 168.l 2 P. Zandbergen and J. J. M. Beenakker Physica 1967,33 343. P. Zandbergen and J. J. M. Beenakker Physica 1967,33,366. I4 I. Prigogine The Molecular Theory of Solutions. North Holland Publishing Co. Amsterdam, Is R. L. Scott J . Chem. Phys. 1956 25 193. l6 M. Knoester K. W. Taconis and J. J. M. Beenakker Physica 1967 33 389. 1957. M. Knoester and J. J. M. Beenakker Physica 1967,33,410. H. Bradley jun. and A. D. King jun. J. Chem. Phys. 1967,47 1189. l9 H Tsubomura and R. S. Mulliken J . Amer. Chem. Soc. 1960,82 5966. 60 N . G. Parsonage Storvick st al. have published several papers in which B is calculated for systems in which the intermolecular potential includes terms for polar inter-actions as well as the usual repulsive and attractive terms. They have handled the configurational partition function by expanding the exponential term before integration in the manner of Pople.20 Thus Suh and Storvick21 have treated the case of non-spherical polar gases by taking the dipole-dipole term as a perturbation on the Kihara core potential with the cores used being selected from a consideration of the geometry of the hydrocarbon homomorph.Examples of the cores used were a triangular prism for CHC1 and a pentagon for CH,COCH,. They found little improvement over the Stockmayer potential for the hydrogen-bonded substances (NH, H,O and CH,OH) but the re-maining compounds (CC12F, CHCl,F CHCl, C2H5Cl CH,Cl CH,COCH,, and CH,F) showed better accord between theory and experiment. De Rocco, Spurling and Storvick22 treated the case of molecules considered as having their centres of force distributed uniformly over a spherical shell and having a central dipole or axially-symmetric quadrupole.There was a considerable im-provement over the Stockmayer potential for CH,CI and reasonable agreement for C6H6 (for which they chose @ = -& 15 x e.s.u. cm.2). Following on from this they2 have calculated C for spherical-shell molecules with an embedded axially-symmetric quadrupole but ignoring non-additivity. The results were generally inadequate to represent the experimental C values. Spurling and Mason24 have questioned the need for the consideration of off-centre dipoles proposed by Dymond and Smith.,’ They point out that the off-centre dipole may be replaced by an infinite number of multipoles centred on the origin and they maintain that values for Band 93 (the dielectric second virial co-efficient) can be calculated to within experimental accuracy by retaining only the dipole and quadrupole terms.However they only give values for CHF,. Since the papers of Stogryn and Hirschfelder,26 on the contribution of dimers to physical properties interest in this topic has continued. Buluggiu and Foglia’ ’ have calculated the concentrations of diatomic ‘molecules’ in Ne Ar Kr and Xe assuming Morse potential interactions and using the Wentzel-Kramers-Brillouin method to determine the vibrational energy levels. Their results covered a range of reduced temperatures (= ~ T E ) from 1-5. Barua and co-workers2* have extended their previous calculation of the contri-bution to B of bound dimers in polar gases to cover metastably-bound dimers.The co-existence of two gas phases (actually with T > T for either pure component) has been found to occur in two types of system mixtures of one polar and one non-polar gas e.g. NH + N, and mixtures of He + a heavy 2o J. A. Pople Proc. Roy. SOC. 1954 A 221,498,508. 21 K. W. Suh and T. S. Storvick J. Phys. Chem. 1967 71 1450. 2 2 A. G. de Rocco T. H. Spurling and T. S. Storvick J . Chem. Phys. 1967,46 599. 23 T. S. Storvick T. H. Spurling and A. G. de Rocco J. Chem. Phys. 1967,46 1498. 24 T. H. Spurling and E. A. Mason J. Chem. Phys. 1967,46,404. 2 5 J. H. Dymond and E. B. Smith Trans. Faruduy SOC. 1964,60 1378. 26 D. E. Stogryn and J. 0. Hirschfelder J. Chem. Phys. 1959,31 1531 1545.27 E. Buluggiu and C. Foglia Chem. Phys. Letters 1967 1 82. 28 A. Saran Y. Singh and A. K. Barua J . Phys. SOC. Japan 1967,22,77 Gases Liquids and Liquid Mixtures 61 compound (polar or non-polar). Jones and Kay2' have investigated this phenomenon in He + n-C4Hlo. A perpetual problem is the reconciliation of the interaction potentials derived from gas data with those from solid-state data. Klein and Munn3' have taken the potentials found by Munn and Smith3' to give the best pre-dictions of B and transport data for Ne Ar Kr and Xe. These potentials were of the form where r = R/o. They calculated the sublimation energy lattice parameter, and bulk modulus for the solids both assuming additivity and allowing for non-additivity by means of the Axilrod-Teller term in the two sets of computa-tions.Inclusion of the latter term considerably improved the agreement with experiment but it was still not good e.g. for Ar the experimental heat of sub-limation is 1846 cal. mole-' as against calculated values of 2112 and 1932 cal. mole- ' respectively. The theory of Monchick and Mason,32 which is based on the assumption that the period of a collision is too short for there to be any appreciable re-orientation during it has been frequently used in the interpretation of the transport data of non-spherical molecules. Thus Pal and B a r ~ a ~ ~ measured the viscosities @l) of H2S SO2 and NH up to 200" by the oscillating-disc method but were unable to fit their data to the above theory. Burch and Raw,34 on the other hand successfully used the theory to fit their data on theq of NH and CH3NH2 to Stockmayer potentials.For mixtures quite good agreement with experiment was obtained with a geometric-mean combination rule for E~~ and the polar coefficient &12 and an arithmetic-mean rule for c12. A very extensive series of determinations of theq of He N, and their mixtures have been reported by Kao and K~bayashi.~' Pressures ranged from 10-500 atmos. and temperatures from -90-50" with at least five different compositions being studied under each set of conditions. At inter-mediate pressures (ca. 120 atmos.) they found both a maximum and a minimum in the graph ofq against mole-fraction. At low pressures only the maximum was found and at high pressures the graph was monotonic. Saxena and M a t h ~ r ~ have pointed out that the potential parameters which fit the high temperature diffusion data of Westenberg et ~ 1 .~ ~ do not reproduce other properties satisfactorily. New self-diffusion (D measurements on argon gas 29 A. E. Jones and W. B. Kay Amer. Inst. Chem. Engineers J . 1967,13,717,720. 30 M. L. Klein and R. J. Munn J . Chem. Phys. 1967,47 1035. 'I R. J. Munn and F. J. Smith J . &em. Phys. 1965,43,3998. 32 L. Monchick and E. A. Mason J . Chem. Phys. 1961,35 1676. 3 3 A. K. Pal and A. K. Barua Trans. Faraday SOC. 1967,63,341. 34 L. G. Burch and C. J. G. Raw J . Chem. Phys. 1967,47,2798. 3 5 J. T. F. Kao and R. Kobayashi J . Chem. Phys. 1967,47,2836. 36 S . C. Saxena and B. P. Mathur Chem. Phys. Letters 1967,1,224. 37 R. E. Walker and A.A. Westenberg J . Chem. Phys. 1958,29,1139,1147; 1959,31,519; 196432, 436; A. A. Westenberg and G. Frazier ibid. 1962 36 3499 62 N . G. Parsonage in the range 77.5-121"~ (also at 294"~) have been presented by de Paz et u Z . ~ * There is good agreement with the results of Winn39 and consistency with both q and B data. Barua et aL4' have reported an improvement in design for the trennschaukel, an apparatus due to Clusius and Huber4' for the measurement of the thermal-diffusion factor (a) by the cascade amplification of the normal separation obtained in a 2-bulb experiment. Until now trennschaukels had always given somewhat low values for a but good agreement was found in this case with 2-bulb results for Ar + N2 and He + Ne. Ghosh Batabyal and Barua4, used the improved apparatus to examine the composition dependence of a for H + He as previous measurements of the thermal conductivity @) had suggested that inelastic collisions involving rotational relaxation were im-portant in this system.Although a graph of 01 versus mole-fraction showed a pronounced minimum the results were in poor agreement with the treatment of Monchick et a1.43 for inelastic processes. A note by H ~ m p h r e y s ~ ~ suggests that 01 in HD + D2 is only slightly composition-dependent in contrast to predictions based on the likelihood of inelastic collisions. Thermal-diffusion factors of mixtures containing small concentrations ( < 5 %) of all possible isotopically-substituted hydrogen molecules in He3 and He4 have been measured by van de Ree et ~ 1 .~ ~ over the range 100-500". Mixtures containing H, D,, and T conformed to the Chapman-Enskog theory with a modified Bucking-ham 6-exp potential and taking the values of the parameters from B andq data. For the HD HT and DT systems it was necessary to include a term in a proportional to the shift of the centre of mass. Systems containing H have also been studied by Mason et aE.46 They have measured the diffusion thermo-effect the inverse of thermal diffusion for H + Ar H + COz and H2 + CH4 at pressures of 1-20 atmos. and room temperature. The results give no -surprises but this appears to be the first measurement of this effect at pressures greater than 1 atmos. An unusual determination of'transport properties nas oeen maae DY Lame-vale et ~ 1 . ~ ~ They have measured the velocity (W) and absorption (a) of ultra-sound in He and Ar up to 1 3 0 0 " ~ and in Ar plasma at 8000"~.They use the expression where f = frequency and y = C,/C,. For a monatomic gas without ionisation 38 M. de Paz B. Turi and M. L. Klein Physica 1967 36 127. 39 -E. B. Winn Phys. Rev. 1950,80 1024. 40 A. K. Batabyal A. K. Ghosh and A. K. Barua J . Chem. Phys. 1967,47,448. 41 K. Clusius and M. Huber Z . Naturforsch. 1955,10a 230. 42 A. K. Ghosh A. K. Batabyal and A. K. Barua J . Chem. Phys. 1967,47,452. 43 L. Monchick R. J. Munn and E. A. Mason J . Chem. Phys. 1966,45 3051. 44 A. E. Humphreys J . Chem. Phys. 1967,47,874. *' J. van de Ree J. Los and A. E. de Vries Physica 1967,34,66. 46 E. A. Mason L. Miller and T. H. Spurling J . Chem.Phys. 1967,47 1669. 47 E. H. Carnevale L. C. Lynnworth and G. S. Larson J . Chem. Phys. 1967,46 3040 Gases Liquids and Liquid Mixtures 63 this may be written asq = const. aW/f2. Theq results agree within a few per cent with independent measurements by normal methods up to 1300"~. At 8000"~, there is reasonable agreement with the calculations of Amdur and Mason.48 Smith et ~ 1 . ~ ~ have extended the previously mentioned treatment of polar gases by Monchick and Mason3' to the case of quadrupolar gases. They found that the quadrupolar contributions to q and DI1 although small must be taken into account if sufficiently accurate parameters for the spherically-symmetric part of the potential are needed for them to be used in conjunction with B values to give the quadrupole moment (0).They also found that the thermal-diffusion factor is the most sensitive to 0 of the transport coefficients. The results of these calculations have been used by Spurling and Mason" to obtain 0 for 9 gases. The values are all reasonable. Loaded spheres that is spherical molecules in which the centre of mass lies at a distance 6 from the centre of the sphere (of diameter cr) have received further attention. Mueller and Curtiss5' have considered collisions between such molecules quantum mechanically and have derived expressions for q 3t and D up to second order in 6/0. Sandler and Dahler52 have shown that a thermal-diffusion factor of the correct order of magnitude can be calculated for the system D + HT by considering it as a system of loaded spheres.Alternative treatments in terms of elastic collisions or rough spheres give values which are too small by factors of ca. 100 and ca. 10 respectively. The Knudsen effusion method for the determination of vapour pressures has been critically examined by Ward et They used a-Pu and gold rendered radioactive by neutron irradiation to give them high detection sensitivity so as to be able to examine the distribution of directions in the escaping molecules. They found that at their pressures ( < 1 x 10- torr) most of the effusing molecules came from the cell wall rather than from a collision in the gas phase and that they could indeed obtain an image of the interior of the cell. Computer with various values for the loss of molecules at the interior surface agree with the experiment and point to the importance of avoiding wall losses.Liquids.-Liquid Ar continues to attract a large amount of attention both experimentally and theoretically. McCain and Ziegler' have reported some new measurements on the vapour-pressure curve from 114.40"~ to the critical temperature which they found to be 150.65 & 0.02"K. There is good agreement with both Clark et ~ 1 . ~ ~ and van Itterbeek et aL5' 48 I. Amdur and E. A. Mason Phys. Fluids 1958,5 370. 49 F. J. Smith R. J. Munn and E. A. Mason J . Chem. Phys. 1967 46. 317 'O T. H. Spurling and E. A. Mason J . Chem. Phys. 1967,46,322. 5 1 J. J. Mueller and C. F. Curtiss J . Chem. Phys. 1967,46 283 1252. " S. I. Sandler and J. S. Dahler J . Chem. Phys. 1967,47 2621. 53 J. W. Ward R.N. R. Mulford and M. Kahn J . Chem. Phys. 1967,47 1710. '4 J. A. Ward R. N. R. Mulford and M. Kahn J . Chem. Phys. 1967,47 1718. " W. D. McCain jun. and W. T. Ziegler J . Chem. and Eng. Data 1967 12 199. A. M. Clark F. Din J. Robb A. Michels,T. Wassenaar and T. Zwietering Physica 1951,17,876. " A. van Itterbeek. J. de Boelpaep 0. Verbeke F. Theewes and K. Staes Physica 1964,30,2119 64 N. G. Parsonage Thomaes et aL5* have continued their measurements ofq of liquefied gases by the capillary-flow method with a paper on CO and N2. Fitting their results to the Theorem of Corresponding States they found good agreement for the reducing parameters with those from critical data for the monatomic gases, CO and N2 but large discrepancies appeared for O2 and CH, e.g. for O2 Elk = 126.41"~ (crit.) 102.27"~ b) and CJ = 3-34 8 (crit.) 2.72 8 (q).De Bock et ~ 1 . ~ ~ have examined the pressure dependence ofq of liquid Ar and O2 up to 150 atmos. by observing the change in electrical resistance of a quartz crystal when at resonance in the fluid due to the viscous damping. Interpretation of the effects of isotopic substitution on the vapour pressures of liquids is usually done in terms of the frequency shifts in going from the liquid to the vapour phase for both the parent and the isotopically-substituted compound.60 Van Hook6' has made such an analysis of his results for four methylacetylenes from 167-255"~. When the acetylenic hydrogen atom was substituted there was an important contribution from the effect on dimerisation. Measurements near the critical point must be carefully designed so as to reduce density differences arising from the gravitational field.This is underlined by the work of Schmidt et aE.62 on C for Xe near its critical point. They found that the singularity occurred 0.32" below the recognised value for T,. V ~ r o n e l ~ ~ had made similar observations for Ar and 02 the discrepancy then being ca. 0.2". The results were discussed with reference to the height of the calori-meter (ca. 10 cm. in Schmidt's work) and the occurrence of peaks in c at different temperatures for material at different heights in the vessel. Determinations of adiabatic compressibility by measuring the velocity of sound and the density have been frequent. Thus Boelh~uwer~~ has examined six n-paraffins from - 20-200" and at pressures up to 1400 atmos.by observ-ing the time for the return of an echo signal to the nearest 0.1 psec. from an oscilloscope trace. Aziz et a1.,65 on the other hand have employed a resonance technique for Ar Kr and Xe up to the neighbourhood of their critical points. The data conformed well to a corresponding-states plot. However a similar study on CF466 showed that this compound obeyed a similar corresponding-states plot to CCl, but markedly different from the simpler molecules. It is suggested that this may be due to a steeper repulsive potential for CF and CCl, which is in accord with the use of an effective 7-28 potential for such compound^.^' The ultrasonic-absorption coefficient (a) in liquid Ar has been determined 5 8 J. P.Boon J. C. Legros and G. Thomaes Physica 1967,33,547. 59 A. de Bock W. Grevendonk and H. Awouters Physica 1967,34,49. 'O J. Bigeleisen and M. G. Mayer J . Chem. Phys. 1947,15,261; J. Bigeieisen ibid. 1961,34,1485. '' W. A. van Hook J . Chern. Phys. 1967,46 1907. 62 H. H. Schmidt J. Opdycke and C. F. Gay Phys. Reo. Letters 1967,19,887 '' A. V. Voronel' and P. G. Strelkov Pribory i Tekhn. Eksper. 1960 No. 6 111 (translation: 64 J. W. M. Boelhouwer Physica 1967,34,484. " R. A. Aziz D. H. Bowman and C. C. Lim Canad. J . Chem. 1967,45,2079. " R. A. Aziz C. C. Lim and D. H. Bowman Canad. J . Chem. 1967,451037. 67 S. D. Hamann and J. A. Lambert Austral. J . Chem. 1954,7,1; S. D. Hamann ibid. 1960,13,325. Instr. Exptl. Tech. (U.S.S.R.) 1960 No. 6 970) Gases Liquids and Liquid Mixtures 65 by Swyt et ~ 1 .~ ~ from 90-145"~ and at pressures up to 100 atmos. The bulk viscosity h,) is then given by the equation : 01 PW3 (Y - 1)h + f q r l o = - - - - ~ f 2 2 X 2 { c 3 } where f is the frequency h the thermal conductivity andq the shear viscosity. The ratioq,h varies somewhat with density but is in fair agreement with the predictions of the Ri~e-Allnatt~~ and hard sphere7* theories of transport processes. A similar examination of liquid N2 has been made by Singer and Lunsford7 with similar conclusions. Determination of the structure of fluids by direct methods have made considerable progress. The X-ray work of Pings' group will be discussed in the section concerned with the theory of fluids. Br has been studied by X-ray diffraction by Gruebel and Clayton.72 They found that the radial distribution function had two peaks of approximately equal intensity at'4.06 and 5.66 rather than the single peak at 4.6 A which they had expected.They interpreted this as being due to the molecules undergoing hindered rather than free rotation. Weinberg73 has studied the second-harmonic scattering when CCl, is illuminated by laser light. He discussed the polarisation induced in terms of the local field and was thereby able to interpret his results as showing that between 5 and 55" there was a progressive break-up of clusters of orienta-tionally-related molecules. This conclusion is supported by the study of the depolarisation of the laser Raman scattering by Murphy et al.74 They found a significant non-zero depolarisation ratio due to the lower symmetry of the scattering CC14 molecules in the pure liquid and that in mixtures this ratio varies with the nature and concentration of the second constituent (CS2, and its mixtures with C6H6 have been shown by light-scattering and n.m.r.relaxation methods to have considerable order but CC14 + C6H,N02 was di~ordered.~ A completely new technique for studying molecular motion which has particular application to liquids is the scattering of cold neutrons.76 Two types of process elastic and inelastic occur. The former leads to a strong line broadened by the Doppler effect the width of the line giving a measure of the speed of the scattering particles. This information can therefore be related to the self-diffusion coefficient.The inelastic effect arises from the neutron taking up a phonon and can therefore give information on frequency C6H6 P - C ~ H ~ B ~ Z CyClO-C6H12 n-C7H16 CH,CN and CHSOH). C6HsN02 '* D. S. Swyt J. F. Havlice and E. F. Carome. J . Chem. Phys. 1967.47 1199. 69 S. A. Rice and A. R. Allnatt J . Chem. Phys. 1961,34 2144; A. R. Allnatt and S. A. Rice ibid., " H. C. Longuet-Higgins and J. P. Valleau Mol. Phys. 1958 1 284. 71 J. R. Singer and J. H. Lunsford J . Chem. Phys. 1967,47,811. 72 R. W. Gruebel and G. T. Clayton J . Chem. Phys. 1967,47 175. 73 D. L. Weinberg J . Chem. Phys. 1967,47 1307. 74 W. F. Murphy M. V. Evans and P. Bender J . Chem. Phys. 1967,47 1836. '' A. Szoke E. Courtens and A. Ben Reuven Chem. Phys. Letters 1967,1,87. 76 P. EgelstaE Discuss. Faraday SOC.1967 No. 43 149; B. K. Aldred R. C. Eden and J. W. White, 1961,34 2156; P. Gray and S. A. Rice ibid 1964,41 3689. ibid. 1967 No. 43 169 66 N . G. Parsonage distribution within the phase (there are no selection rules to be obeyed). Since isotopic substitution can lead to very large changes of the scattering cross-section it is sometimes possible to assign motion to specific regions of the molecule. The major advances in the theory of fluids have centred on the Percus-Yevick (PY) and the (Convoluted) Hypernetted Chain (HNC) approximation^.'^ They both lead to integral equations from the solution of which the radial distribution function (g(r)) and the total (h(r)) and direct (c(r)) correlation functions may be evaluated. h(r) and c(r) are defined by the equations h(r) = g(r) - 1 and h(r12) = c(r12) + pjc(r13)h(r23)dT3 where p is the number density.The approximation differ in which of the cluster-type integrals to omit from the expressions for h(r) and c(r) but R o ~ l i n s o n ~ ~ ' has shown that the PY approximation can also be deduced from the requirement that c(r) should be short-ranged. Two ways are commonly used for deriving the equation of state from the expressions for h(r) and c(r). These are via the compressibility equation of Zernike and Prins kT(ap/dP) = 1 + pJh(rl,)dz2 and via the virial equation of Clausius. Although both of these equations are exact they lead to different expressions for the equation of state thereby demon-strating an inconsistency which is introduced by the PY and HNC approxima-tions.The approach by way of the compressibility equation is rather more frequently used. Comparisons of these theories have mostly been with molecular dynamics and Monte Carlo experiments for hard spheres at high densities, and with the virial coefficients for hard spheres at low densities. From these the PY approximation seems to be the better. However for molecules inter-acting according to the Lennard-Jones 6-12 or the 6-exp potentials there is evidence that the HNC might be preferable at low temperatures but not at high.77c Mikolaj and Pings7* have discussed the respective merits of the two theories in the light of their data on the X-ray scattering from fluid argon near the critical point. Expressing the assumptions in the forms c(r) = g(r) (1 -exp[u(r)/kT]} for PY and c(r) = h(r) - lng(r) - u(r)/kT for HNC they deduced from their experimentally determined correlation functions the function u(r) which should be independent of T and p.They found that u(r) was insensitive to T but varied considerably with p e.g. the well-depth ~ / k changed from 120-95" over the range p = 0.784.28. It is suggested that these variations with p may be due to many-body interactions. Rushbrooke and Silbert79 and Rowlinson" have shown how the presence of three-body forces may be incorporated into the PY and HNC theories and the former have shown that this modified HNC theory leads to the approximately linear decrease of the well-depth of the effective two-body potential with increase in 77 (') J. S. Rowlinson Reports Progr. Physics 1965 28 169.(*) G. S. Rushbrooke Discuss. Fataday SOC. 1967 No. 43,7; (') J. S. Rowlinson ibid. 1967 No. 43 243. 78 P. G. Mikolaj and C. J. Pings J . Chem. Phys. 1967,46 1401 1412. l9 G. S. Rushbrooke and M. Silbert Mol. Phys. 1967,12 505. J. S. Rowlinson Mol. Phys. 1967 12 513 Gases Liquids and Liquid Mixtures 67 p. Verlet’ has shown that considering only two-body forces the PY and HNC theories may be considered as the first members of two hierarchies of ap-proximations. Machine evaluations for the distribution and correlation functions for the second approximations (PY2 and HNC2) are becoming available and it does appear that they represent considerable improvements.B2 Harris and ClaytonB3 have re-examined the intensity of X-ray scattering from Ar and Xe near their triple points and found much better agreement especially for the outer peaks with the predictions of the HNC theory for a liquid of Lennard-Jones molecules than was obtained from the much earlier measure-ments of Campbell and Hildebrand.B4 One of the surprising things about the Percus-Yevick approximation is that an exact solution of the integral equation is known for hard spheres.77 This analytic solution breaks down at high densities (po3/2$ 3 0-8) and it has been suggested that this point corresponds to a fluid-solid transition.Temperley” has indeed found alternative solutions for these higher densities but HutchinsonB6 has pointed out that these solutions are unphysical in that they would lead to negative values for the intensity of radiation scattered at some angles.Hutchinson then proceeded to show that there can be no acceptable solutions other than the original ones. Considerable interest is being shown in the model of a liquid as a system of random-packed spheres. Thus the ratios of the peak positions in the radial distribution function derived by Scott et from a mechanical model of random-packed spheres have been shown to be in good agreement with the corresponding ratios derived from the X-ray study of Ar and Xe near their triple points.B3 Bernal’s group continue to be very active in this field. TheyB8 have examined the polyhedra which are formed when the planes are drawn bisecting and perpendicular to the lines joining the molecules. They found a high incidence of pentagonal faces and of polyhedra with 13-15 faces results which are in general agreement with their previous work.With the wealth of results for hard-sphere fluids it is not surprising that attempts to use perturbation treatments to extend these to more realistic potentials have been made.B Recently Barker and Hender~on,~’ using this approach have found that for a square-well potential the results are in good agreement with Monte Carlo and molecular-dynamics calculations for this potential. They concluded that failure of the perturbation treatment to con-verge for still more realistic potentials is due to the “softness” of the repulsive potential rather than the presence of the attractive well. L. Verlet Physica 1965 31,959. D. Henderson S. Kim and L. Oden Discuss. Faraday SOC. 1967 No. 43,26.83 R. W. Harris and G. J. Clayton Phys. Rev. 1967,153,229. 84 J . A. Campbell and J. H. Hildebrand J . Chem. Phys. 1943,11,334. 85 H. N. V. Temperley Proc. Phys. SOC. 1964,84,339. 86 P. Hutchinson Mol. Phys. 1967,13,495. G. D. Scott J. D. Bernal J. Mason and K. R. Knight Nature 1962,194,956. J. D. Bernal and J. L. Finney Discuss. Faraday Soc. 1967 No. 43.62 R. W. Zwanzig J . Chem. Phys. 1954,22 1420; J. S. Rowlinson Mol. Phys. 1964,7 349; ibid., J. A. Barker and D. Henderson J . Chem. Phys. 1967,47 2856. 196t48 107. C 68 N . G. Parsonage Phenomena in the neighbourhood of the critical point has been well covered in the report of the conference of that name.9' The report shows clearly and comprehensively the analogies which can be drawn with magnetic phenomena near the Curie point which is a consequence of the similarity between the Grand Partition Function for a lattice-gas and the Constant Field Partition Function for the Ising model.Particular attention was given to the indices with which various thermodynamic quantities approached their critical values e.g. Lt (InlP - P,I/lnIp - p,l} = 6. P=P, P = P, R o ~ l i n s o n ~ ~ " has discussed the experimentally observed values for these indices together with certain restrictions upon the possible values which they can adopt. More recently Green et from observations on Xe COz SF,, and Ar have concluded that 6 is 5 rather than 4.2 a value which was accepted at the conference by Rowlinson but disputed by Fisher.91b Liquid Mixtures.-Tne Average Potential model originally proposed by Prigogine et and S ~ o t t ' ~ has been reviewed at length by Bellemans et In particular they separate the fundamental propositions from certain additional assumptions which were made in the original papers e.g.the use of a Taylor series expansion to represent the properties of the mixture in terms of those of a single reference substance. In effect they94 use a number of reference substances to construct empirical relations between the reduced thermodynamic quantities and the reduced values of T and P. In this way, they were able to overcome the former drawback that in order for example, to predict the excess volume it was necessary to know the temperature deriva-tives of the volume of the reference substance with an accuracy greater than the data could justify.For the reduction parameters for the interaction between dissimilar molecules they found that the use of the usual combination rules (geometric mean for E ~ ~ arithmetic mean for oI2) in general only failed to give the sign of the excess quantity correctly when this quantity was small. Further they found that often quite small changes in s12 and o12 from these values were sufficient to achieve good agreement although the amount of skew of the graph of excess quantity versus mole fraction was often in the wrong direction. Streett and Staveley'' have also discussed the possibility of explaining the excess volumes ((VE) of 8 binary mixtures of liquefied gases by means of the Average Potential model without using the Taylor expansion. They took the data for Ar to define a reduced volume versus reduced tempera-ture curve for P = 0 and considered the average potentials represented by 9 1 Conference on Phenomena in the Neighbourhood of Critical Points.Ed. M. S. Green and J. V. Sengers. National Bureau of Standards Miscellaneous Publication 233 Washington D.C. 1966. (a) J. S. Rowlinson p. 9; (b) M. E. Fisher p. 25. 92 M. S. Green M. Vicentini-Missoni and J. M. H. L. Sengers Phys. Rev. Letters 1967 18 1113. 93 I. Prigogine A. Bellemans and A. Englert-Chwoles J . Chem. Phys. 1956,24 518. 94 A. Bellemans V. Mathot and M. Simon Adv. Chem. Phys. 1967 11 117. 9 5 W. B. Streett and L. A. K. Staveley J . Chem. Phys. 1967,47,2449 Gases Liquids and Liquid Mixtures 69 Scott's 1- 2- and 3-liquid models. They took a range of values for the energy parameter ( E ) for the pure substances and used the usual combination rules, but they were unable to obtain good agreement with experiment.The 2- and 3-liquid models were about equally good but both gave bad agreement for the simplest systems Ar + Kr and Ar + Ar + CH,. Mastinug6 has also used the Average Potential model to discuss his results for V E for solutions of small quantities (0.5-2.0%) of H in N2. The technique adopted was to measure with a differential device the pressure developed when similar volumes of solvent and solution were vaporised into similar volumes. The partial molar volume of Hz was found to be 39.784 ~ m . ~ mole- I whereas a 2-liquid treatment gave the surprising prediction of 166-35 ~ m . ~ mole-'.Of course the wide disparity in the molecular sizes would render this theoretical treatment inappropriate here and Mastinu observed that the same approach applied to mixtures of molecules with similar parameters led to agreement to better than 5 %. Fuks and Bellemansg7 have given some values admittedly of lower accuracy than usual for this field for GE and VE for CH + Kr and N2 + CH,. Findenegg and Kohler9* have also employed the model in their discussion of CUE of binary mixtures of CH,Br.CH,Br and CHzCl.CH2Cl with C6H6. The system is complicated by the change of the ratio of trans- to gauche-forms during the mixing process but allowance for this was made using the dielectric constant data99 for these solutions. C of the CHzCl.CHzCl mixture was slightly positive and was attributed to a simple change in the trans:gauche ratio; for the CH2Br.CH2Br solutions on the other hand it was large and negative and the predicted change in cell size from the model was insufficient to lead to a change of the rotational heat capacity of the required size.Vilcu and Bellemansloo have considered the extension of the model to moderate pressures. They express the reduced volume_ in a power series in the reduced pressure (P) the coefficient of the term in P o being taken from the work of Simon and Mathot' on several substances whilst the coefficients of the terms in f" and P2 were chosen to fit the PV data of liquid Ar up to 300 atmos. Applying these equations to CO + CH and Ar + CH they found that there should be extrema in V E at ca.200 and ca. 100 atmos. respectively although the former result is less certain. Fluid mixtures at high pressure have been examined by Throop and Bear-man''' using the PY equation assuming a Lennard-Jones 6-12 potential. Calculations were given for Ar + Kr Ar + Xe Ne + Kr and Ne + Xe at supercritical temperatures and at densities up to twice the critical density. For constant pressure processes UE V E and GE were all positive at low p, increasing with p to a maximum and then decreasing to small positive or negative values. Constant volume processes gave much smaller excess quan-96 G. Mastinu J . Chem. Phys. 1967,47,338; Rev. Sci. Znstr. 1967,38 1114. '' S. Fuks and A. Bellemans Bull. SOC. chim. belges 1967,76 290. 98 G. H. Findenegg and F. Kohler Trans. Faruduy SOC.1967.63,870. A. Neckel and H. Volk Z . Elektrochem. 1958,62 1104. loo R. Vilcu and A. Bellemans Bull. SOC. chim. belges 1967,76 325. G. J. Throop and R. J. Bearman J . Chem. Phys. 1967,47,3036. 9 70 N. G. Parsonage tities but were more complicated. Snider and Herringtonlo2 have treated a mixture for which the intermolecular potential is represented by a hard-sphere repulsive potential and an otherwise uniform attractive potential. For a pure system of this type Longuet-Higgins and Widornlo3 had found the equation of state : where 5 =7r03p/6 and 0 is the hard-sphere diameter. The first term is that found for hard spheres by the scaled-particle theorylo4 or by the PY theory using the compressibility equation. Lebowitz' O5 had previously extended the scaled-particle model to mixtures.Snider and Herrington found good agree-ment with experiment for the HE SE and VE of Ar + CH, Ar + Kr Ar + N2, O2 + Ar Ar + CO CO + CH4 O2 + N, and N + CO but much poorer agreement for CCl + C(CH,) and CCl + cyclo-C6Hl,. The method also failed for AH of Ne in Ar this being attributed to the less uniform potential experience by the Ne molecules as a consequence of their greater freedom of movement. Scaled-particle theory which as mentioned above gives the same equation of state as the PY approximation (using the compressibility equation) had been applied to non-planar gases in non-polar solvents and in water by Pierotti,lo6 but this work has been criticised as far as water is concerned by Ben-naim and Friedmanlo7 on the ground that it leads to an incorrect tem-perature-dependence for the surface tension.Dymond'" has presented solubility data for 11 gases in (CH,),O at 25" and for 9 gases in cyc1o-C6H,, at various temperatures. All the results refer to P = 1 atmos. Byrns and Mazolog have observed that AE for isotopic mixtures can be closely predicted from the quantum-mechanical version of the theorem of corresponding states if it is assumed that the system is composed uniformly of particles of mass rImT-a where x is the mole-fraction of the particles of mass ma. No complete justification but only a plausible argument is given for this. Harrison and Winnick'" have measured VE at three temperatures for 5 binary mixtures composed from the even n-alkanes Cl0 to (216. VE was always negative and ranged up to -0-14 ~ m .~ mole-'. Deviations from the principle of congruence' l1 averaged only 0-002 ~ m . ~ mole-Since the discovery by Rowlinson et ~ 1 . l ' ~ of the partial miscibility of N. S. Snider and T. Herrington J . Chem. Phys. 1967,47 2248. H. C. Longuet-Higgins and B. Widom Mol. Phys. 1964,8 549. J. L. Lebowitz Phys. Rev. Series A 1964,133,895 ; J. L. Lebowitz E. Helfand and E. Praestgaard, R. A. Pierotti J . Phys. Chem. 1963 67 1840; [bid. 1965,69 281 A. Ben-naim and H. L. Friedman J . Phys. Chem. 1967,71,448. J. H. Dymond J . Phys. Chem. 1967,71 1829. F. L. Byrns and R. M. Mazo J . Chem. Phys. 1967,41 2007. C. Harrison and J. Winnick J . Chem. and Eng. Data 1967 12 176. J. Hijmans and T. Holleman Mol. Phys. 1961,4,91. ''' A. J. Davenport and J.S. Rowlinson Trans. Faraday SOC. 1963,59,78. lo4 H. Reiss H. L. Frisch and J. L. Lebowitz J . Chem. Phys. 1959 31 369. J . Chem. Phys. 1965,43 774 Gases Liquids and Liquid Mixtures 71 systems composed of one short and one long n-parafin the phase diagrams of a number of other such systems have been studied 9ver a'wide range of pressures with similar re~ults."~ Recent systems studied include C3H8 with CH, C02,andN,,114 He + CH,,"' CO withn-C8H,,,n-C ,H,,,n-C,3H,8, H20."* In addition Larkin et ~ 1 . " ~ have examined the phase equilibria of solutions of liquid sulphur in 10 solvents. Analogies between the plait point in a 3-component system at constant temperature and pressure and the situa-tion in a 2-component liquid system at constant temperature (but variable pressure) have been pointed out by Widom.'20 The non-ideality of fluorocarbon-hydrocarbon mixtures which is much larger than would be predicted by solubility-parameter theory has continued to attract attention.Gilmour et have reported on the vapour-pressures of three such alkane-perfluoroalkane mixtures and on the liquid-liquid phase diagrams of these and 8 similar systems. The deviations from solubility para-meter theory in contrast to the composition at the critical solution temperature, were not very sensitive to differences in the molar volumes of the components. This suggested that a formulation of the theory in terms of volume- or surface-fractions was required and subsequent analysis led to a preference for the latter. Fenby and Scott122 have determined HE calorimetrically for 34 of the 78 possible binary systems of the form C6H,F6- + C6H,F6-, and also C6F6.They found a wide variety of types of behaviour. Qualitative interpreta-tion was given in terms of physical (positive) and chemical (negative) contribu-tions but in the absence of auxiliary data on the position of the chemical equilibrium no quantitative discussion was possible. Much of the discussion'23 of transport processes in dense fluids has been concerned with the Ri~e-Allnatt~~ theory. R i c ~ i ' ~ has found that D for H, T, Ne Ar and CH in liquid N is almost independent of mass. Only a theory due to BearmanI2' conforms with this. Measurements of D of N2 and 0 in H20126 show a temperature-dependence which is ca. 10 times and n-C16H34,116 C6H6 -k H20,117 CyClO-C6H, f H20 and n-C,H,,+ -b for C3H7.CsHs C6F6 n-C,H9.C6HS CsF'H and n-C4H9.C6H5 + A.B. Rodrigues and J. P. Kohn J . Chem. and Eng. data 1967,12191 ; J. M. Beaudoin and J. P. Kohn ibid. 1967 12 189. 'I4 J. G. Roof and J. D. Baron J. Chem. and Eng. Data 1967,12,292. C. K. Heck and M. J. Hiza Amer. Inst. Chem. Engineers J. 1967,13 593. G. Schneider Z. Alwani W. Heim E. Horvath and U. Frank Chem.-1ng.-Tech. 1967,39,649. Z. Alwani and G. Schneider Ber. Bunsengesellschaft Phys. Chem. 1967,71,633 C. H. Rebert and K. E. Hayworth Amer. Inst. Chem. Engineers J. 1967,13 118. B. Widom J. Chem. Phys. 1967,46,3324. J. B. Gilmour J. 0. Zwicker J. Katz and R. L. Scott J . Phys. Chem. 1967,71 3259. 'I9 J. A. Larkin J. Katz and R. L. Scott J. Phys. Chem. 1967,71 352.lZ2 D. V. Fenby and R. L. Scott J . Phys. Chem. 1967,71,4103. lZ3 J. A. Palyvos and H. T. Davis J . Phys. Chem. 1967,71,439; A. F. Collings and C. J. Pings ibid., 1967,71 3710; J. Palyvos K. D. Luks I. L. McLaughlin and H. T. Davis J . Chem. Phys. 1967 47, 2082; Ching Cheng Wei and H. T. Davis ibid. 1967 46 3456. F. P. Ricci Phys. Rev. 1967 156 184. 125 R. J. Bearman J . Chem. Phys. 1960 32 1308; F. P. Ricci ibid. 1966 45 3897. R. T. Ferrell and D. M. Himmelblau. J . Chem. find En(!. Durcr. 1967. 12. 1 1 1 72 N. G. Parsonage greater than predicted by Longuet-Higgins and Pople.' 27 A laminar-flow technique has been used by Turner et d.'z8 for the study of the thermal dif-CHCI, CH,COCH + C6H6 and CH3COCH + H 2 0 at 25" have been determined by the spin-echo method.lZ9 A diaphragm cell has been used for the measurement of D12 in CH,OH + CH3.C6H5 at 250.13* fusion Of cc1 + CyClO-C6H1,. D12 for C6H6 + CyClO-C6H12 CH3COCH3 + H. C. Longuet-Higgins and J. A. Pople J. Chern. Phys 1956 25 884. 127 lZ8 J. C. R. Turner B. D. Butler and M. J. Story Trans. Faraday Soc. 1967,63,1906. lt9 D. W. McCall and D. C. Douglas J . Phys. Chern. 1967,71,987. lJo L. W. Shemilt and R. Nagarajan Canad. J. Chern. 1967,45,1143

ISSN:0069-3022    

DOI:10.1039/GR9676400057

出版商:RSC    

年代:1967

数据来源: RSC

摘要:

6. GAS KINETICS By J. A. Kerr (Department of Chemistry The University Birmingham 15) THIS Report is based on publications that appeared between the 1 st November, 1966 and the 15th November 1967. The output of papers on gas kinetics continues unabated ; over 400 were published during this period. Drastic pruning is required to produce a Report of manageable size. Priority has been given to papers concerned with quantitative data on elementary reactions. Processes that are difficult to interpret such as complex pyrolyses and com-bustions are not considered. Unfortunately it has also been necessary to omit ion-molecule and molecular-beam reactions which warrant substantial treatments. The Reporter’s task in gas kinetics has been considerably lightened by the publication of three series of books ; ‘Progress in Reaction Kinetics’ ‘Advances in Photochemistry’ and ‘Progress in Free Radical Chemistry’.So far a total of ten volumes has appeared and their value is orientating the vast literature on kinetics cannot be overestimated. An International Journal of Chemical Kinetics edited by S. W. Benson (Stanford Research Institute) is being started in 1968. After surveying the gas kinetics literature for 1 9 6 6 4 7 this Reporter is convinced of the justification for such a publication. 1. Atomic Reactions.-Over the past few years atomic reactions have constituted one of the most rapidly expanding sections of gas kinetics. The main impetus has been obtained from the discovery of new methods for deter-mining concentrations of atoms. The discharge-flow method has been par-ticularly fruitful in yielding absolute rate constants for combination addition, and transfer reactions of atoms.This topic was reviewed in the 1965 Annual Report by Thrush and Campbell and more recently Thrush’ has written an excellent summary of the method. The production of atoms in discharge-tubes has long been known but their application to quantitative studies of the kinetics of elementary atomic reactions has had to await the development of specific methods for measuring the concentrations of the atoms. In a flow-discharge experiment atoms are produced by pumping metered flows of purified diatomic gases through an electrodeless discharge to give about 1 % dissociation into atoms. In the absence of added reactant gas the atoms decay by recombining either on the surface of the down-stream reaction tube or in the gas-phase.The walls of the reaction vessel can be treated to reduce wall combination. From a knowledge of the flow-rate of the gas and measurement of the decay of atoms down the flow tube the kinetics of the atom decay can ’ B. A. Thrush Science 1967,156,470 74 J . A. Kerr be deduced. The addition of a reactant gas causes an acceleration of the atom decay and the rate constant for the reaction of the atom with the reactant can be obtained from the rate of this acceleration. Several methods for measur-ing the absolute concentrations of reactive species have been devised. Elec-tronic-absorption spectroscopy is particularly suitable for small free radicals such as hydroxy and cyano whereas chemiluminescent recombination reactions have been widely applied for atoms.Mass spectrometry is also suitable provided a molecular-beam inlet system is used to select species that have not undergone wall collisions. More recently e.s.r. techniques have been used successfully to measure absolute concentrations of atoms. Westenberg and Haas have described a method for measuring the rate constants of atom-molecule reactions over the temperature range 300-1000"K by combining a flow-discharge reaction with an e.s.r. spectrometer located at a fixed position outside the reaction zone. Detailed kinetic and dynamic arguments have been put forward in support of the method and the first results (Tables 1 and 2) look most encouraging. Brown and Thrush,6 almost simultaneously with Westenberg and Haas also reported temperature coefficients for atom-molecule reactions involving the determination of atom concentrations by e.s.r.techniques. We can look forward to a wealth of quantitative information on atomic reactions from this important development. Atomic Recombination Reactions.-The experimental results are listed in Table 3. The mechanism of the recombination of nitrogen atoms has been investigated in detail,'"17 and the following reactions established : N + wall =$N, N + N = N2 (3) N + N + M = N2 + M (4) Reaction (3) which was thought to be partly heterogene~us'~ was later shown to be entirely heterogeneous.17 Values of the rate constants (k and k3) have been measured for a variety of surfaces and it has been clearly demonstrated that the homogeneous three-body recombination of nitrogen atoms does not obey a power-law dependence of the type k4 = AT-".A. A. Westenberg and N. De Haas J . Chem. Phys. 1967,46,490; 1967,47 1393. J. V. Michael and H. Niki J . Chem. Phys. 1967,46,4969. J. V . Michael and R. E. Weston J . Chem. Phys. 1966,45 3632. K . Hoyermann H. G. Wager and J. Wolfrum Z . phys. Chem. (Frankfurt) 1967,55,72. J. M. Brown and B. A. Thrush Trans. Faraday SOC. 1967,63,630. A. B. Callear and W. J; R. Tyerman Trans. Faraday SOC. 1966,62,2760. E. L. Wong and A. E. Potter Canad. J . Chem. 1967,45367. l o W. K. Stuckey and J. Heicklen J . Chem. Phys. 1967,46,4843. G. Marsh and J. Heicklen J . Phys. Chem. 1967,71 250. '* R. D. Cadle and J. W. Powers J .Phys. Chem. 1967,71 1702. A. Kato and R. J. CvetanoviC Canad. J . Chem. 1967,45 1845. l4 K. M. Evenson and D. S. Burch J . Chem. Phys. 1966,45,2450. I. M. Campbell and B. A. Thrush Proc. Roy. SOC. 1967 A 296,201. l6 I. M. Campbell and B. A. Thrush Trans. Faraday SOC. 1966,62,3366. M. A. A. Clyne and D. H. Stedman J . Phys. Chem. 1967,71 3071. ' N. Niki and B. Weinstock J . Chem. Phys. 1966,45 3468 Gas Kinetics 75 Campbell and Thrush'6. determined the rates of recombination of oxygen and nitrogen atoms by extending the flow-discharge method to active nitrogen systems in which NO was added resulting in the partial formation of oxygen atoms. The atom concentrations were determined from the intensities of the N2 First Positive and NO p-emissions. The activation energy for the N + 0 + M reaction (E = -270 cal.mole-') is abnormally low for this type of process. Rate constants have been reported for the iodine atom recombination reaction from the rotating-sector photolysis of CF31 in which the parent molecule was the third body.Ig The rate constant was shown to be second-order with a value of 5.1 x 10'' mole-' C.C. set.-' at 3 7 3 " ~ within CF31 concentrations 2-9 x lov6 mole c.c.-l. This result is difficult to reconcile with the many known third-order recombination rate constants for iodine atoms but might be explained if CF31 is a very efficient third body. Table 4 lists the results of shock-tube measurements on the dissociations of diatomic molecules i.e. the reverse of atomic recombination reactions. Benson and De More2' have pointed out the difficulties of deriving rate constants for the recombination process (k,) from measurements of the dis-sociation reaction ( k - 1) via the equilibrium constant K = k,/k - '.In particular, calculation of the activation energy El from shock-tube measurements of E - is likely to lead to large errors since El is a small number and E - a large number with considerable errors. Carabetta and Palmer" were able to follow the kinetics of the dissociation of C12 in a shock-tube by measuring the light emission from the radiative recombination of chlorine atoms : The emission reaction is the reverse of photodissociation and is a two-body process as distinct from normal third-order atomic recombination. Atomic Addition Reactions.-Recent data are summarised in Table 1.The rates of addition of hydrogen atoms to unsaturates have long been sources of contention.22 Examination of Table 1 shows that even for the simplest reactions such as addition to acetylene and ethylene there is still little detailed agreement on the magnitude of the rate constants. The addition of hydrogen atoms to acetylene proceeds through the following mechanism :3 CI + c1 = c1 + hv H + C2H2 = C2H3* C2H3* = C2H2 + H C2H3* + M = C2H3 + M l 8 I. M. Campbell and B. A. Thrush Proc. Roy. SOC. 1967 A 296,222. l9 G. S. Laurence Trans. Faraday Soc. 1967,63 1155. 2o R. A. Carabetta and H. B. Palmer J . Chem. Phys. 1967 46 1325 1333; H. B. Palmer ibid., 1967,47,2116. S. W. Benson and W. B. De More Ann. Rev. Phys. Chem. 1965,16,397. 22 R.J. CvetanoviC Ado. Photochem. 1963,1 11 5 ; B. A. Thrush Progr. Reaction Kinetics 1965, 3,63 TABLE 1 Atomic addition log k (mole-' C.C. set.-') Method (298 K) Atom Substrate H Acetylene Flow discharge, mass spectrometer 9 , 10.34 H Acetylene - d4 Acetylene Acetylene 10.86 D H 10.56 11.56 9 , Flow discharge, [HI by photometry Flow discharge, e.s.r. Flow discharge, [HI by photometry Flow discharge, e.s.r. Flow discharge, e m . Flow discharge, NO2 titration, Thermal probe H H Acetylene 1 0 10 Ethylene 11.29 Ethylene 11.08 H H Methyl-acetylene Isobutene 11.38 Acetylene Ethylene Propyne Isobutene But-1-ene Diacetylene Ethylene Propene But-1-ene cis But-2-ene trans But-2-ene Isobutene Buta-l,3-diene Pent-1-ene Vinyl Chloride Acry lonitrile Flow discharge, e.s.r.99 99 Flash photolysis Flow discharge, mass spectrometer Flash photolysis, CSe, 99 99 99 9 9 9 9 99 ,? 9 9 99 ,, 3, 10.96 11-51 1 1 *60 11.61 a Ref. 3; ref. 4; ref. 5 ; ref. 6; J. M. Brown P. B. Coates and B. A. Thrush Chem. Comm., Comm. 1966,917; A. B. Callear and I. W. M. Smith Nature 1967,213,382; ' ref. 7; ref TABLE 2 Transfer reactions of H N and Reaction Temp. (OK) System H + D2 = HD + D H + N2H4 = NH + NH3 D + H2 = HD + H H + H2S = H + HS H + CH,CHO = CH + CHO D + DNO = D + NO N + 0 = NO + 0 N + CO = NO + CO l80 + 0 = l8OO + 0 l80 + co = l80c + 0 l80 + CO + l8OCO + 0 I 8 0 + N,O = N,I80 + 0 0 + HNO = OH + NO3 l80 + COCl = c'80c1 4- 0 Flow-discharge e.s.r.Flow-discharge e.s.r. Flow-discharge NH, emission Photolysis H,S, in presence CO, Flo w-discharge mass spectrometer mass spectrometer Flow-discharge e.s.r. Flow-discharge indirect, product analysis Photolysis N1802, mass spectrometer Photolysis N1802 mass spectrometer Dz + Hg(3p), 99 7, 99 Photolysis NO, 450-750 450-750 293-349 3 2 3 4 297 298 300-910 291-523 2 9 8 298-391 298-395 298-358 298 29 O + O + O + O + O + O + O + O + O-l-ot ot ot ot ot O + ot O + O + C302 = 3CO H2 = OH + H CH = OH + Me CH = OH + Me CH = OH + Me EtOH = OH + MeCHOH MeOMe = OH + CH20Me Photolysis C302 Flow discharge e.s.r. 9, 9, Static system, mass spectrometer Flow discharge e.s.r.competitive N,O + Hg(3P) competitive N 2 0 + Hg(3P) competitive N*O + Wd3P), 298 300-1000 4 5 0 4 300-1000 375-576 300-1000 298-398 298-398 298-398 7 9, 9 307-398 9 97 Flow-discharge detailed 2 9 9 4 analysis N,O + Hg(3P) 298 detailed analysis Flow-discharge 303 mass spectrometer " Ref. 2; P. K. Ghosh and E. J. Bair J. Chem. Phys. 1966,45,4738; R. L. Wadlinger and B. de R. L. Wadlinger and M. J. Allard ibid. p. 2346; a R. M. Lambert M. I. Christie and W. J. Linnett, J. Chem. Pkys. 1967,46,4075; W. E. Wilson J. Chem. Phys. 1967,46 2017; 'JL. I. Avramenko and 1967,516;' S. Jaffe and F. S. Klein Trans. Faraday SOC. 1966,62,3135; S. Jaf€e and H.W. -ord J. Phys. J.Amer. Chem. Soc. 1967 89 3390; ' ref. 6; ref. 9; ref. 10; ' ref. 11; ref. 12; ref. 13; Y. Takezaki, 1966,44,341 TABLE 3 Atomic recombination reactions A + A + M = A + M dL-A,l/dt = k,CAI2 [MI Reaction Method Temp. (" K) H + H + M = H2 + M Shock tube dissociation HCl, infrared emission Pulsed discharge, afterglow emission Flow and static discharge e.s.r. Flow discharge, NO titration He + He + M = He + M N + N + M = N + M N + N + M = N 2 + M 4000 366 298 29 N + N + M = N + M Flow discharge, NO titration N + N + M = N + M N + 0 + M = N O + M Flow discharge, NO titration Flow discharge, NO titration N + 0 + M = N O + M Flow discharge, NO titration 0 + 0 + M = 0 + M Flow discharge, NO titration 196 298 196 298 298 298 196 298 196 298 298 'T.A. Jacobs R. R. Giedt and N. Cohen J . Chern. Phys. 1967.47 54; K. M. Phys. 1967,46 127; ref. 14; ref. 15; ref. 16; ref. 17; g ref. 18 TABLE 4 Diatomic dissociation reactions A2 + M = A + A+ M (--d[A,lldt = k-l[A,ICMI Reaction Method Temp. (OK) HCI + Ar = H + C1 + Ar Shock tube infrared 3300-5400 emission from HCI HCI + Ar = H + CI + Art Shock tube infrared 2800-4600 emission from HC1 F + Ar = F + F + Ar Shock tube absorption ? spectroscopy Shock tube absorption Kr spectr~scopy Shock tube emission 1735-2582 from radiative recombination C1 ? C1 F + k r = F + F + + Ar = C1 + C1 + (Ar Ar ~~ ~ ~~~~ t Similar results were obtained with DCI. a E. S. Fishburne J . Chem. Phys. 1966,45,4053; Phys. 1967,46,1958.' D. J. Seery and D. Britton J . Phys. Chem. 1966,70,4074; ref. 20 Gas Kinetics 83 The initial addition reaction produces a chemically-activated vinyl radical and hence there is the possibility of collisional stabilisation and pressure-dependent kinetics. This explains some of the discrepancies in the rate constants for the addition reaction since there have been conflicting reports on the pressure-dependence of the reaction. Michael and Niki3 investigated the reaction in a fast discharge-flow system coupled to a time-of-flight mass spectrometer and from the pressure effect on the apparent overall bimolecular rate constant confirmed that the system undergoes a unimolecular reaction that could be treated satisfactorily by the Rice-Ramsperger-Kassel-Marcus theory.Of the isotopic modifications studied by Michael and Niki only the H + C2D2 system reached the unimolecular high-pressure condition within the pressure region 1-2 torr. The previous results of Michael and Weston4 for the H + C2H2 reaction have been rationalised in terms of the pressure-dependent kinetics of the system and the more recent results of Hoyermann, Wager and Wolfrum’ would appear to have been measured in the pressure-sensitive region. The kinetics of the addition of hydrogen atoms to ethylene are also com-plicated by the production of a chemically-activated radical. The additions of hydrogen atoms to acetylene and ethylene produce activated vinyl and ethyl radicals containing approximately the same excess energy but since there are six more degrees of freedom in the ethyl than in the vinyl radical, the pressure-sensitive region will be lower for the hydrogen atom addition to ethylene.Michael and Weston4 deduced a high-pressure limiting value of log k = 11.29 mole- C.C. set.- for the addition of hydrogen atom to ethylene from a discharge-flow system in which the concentration of hydrogen atoms was determined by a photometric method based on the Lyman-cL absorption. On the other hand Brown and Thrush6 obtained log k = 11.08 with e.s.r. detection of the atom concentration. Since both systems were studied below the second-order limit for the addition reaction and the high-pressure values were obtained by rather crude extrapolations the agreement is reasonable. It is clear however, that extended pressure studies are required to obtain reliable rate constants for this type of system.Much information is available on the reactions of carbon atoms mainly with hydrocarbons in condensed phases.23 The first gas-phase reactions of carbon atoms with benzene have now been reported.24 The “C-atoms (t.& 20-5 min.) were produced by nuclear techniques and were thermally equi-librated with added neon. Product analysis revealed that the C6H6-l lC adduct undergoes bimolecular reactions leading to polymer formation rather than fragmentation processes which although energetically possible appeared to require too much internal rearrangement. Active nitrogen systems continue to attract several workers and the reactions of nitrogen atoms have been re~iewed.~’ Arrhenius parameters for the second-23 C .MacKay and R. W. Wolfgang Science. 1965. 148 899 A. P. Wolf. A h . Phvs. Orq. Chm 24 T. Rose C. MacKay and R. W. Wolfgang J . Amer. Chem. SOC. 1967,89 1529. ’’ B. Brocklehurst and K. R. Jennings Progr. Reaction Kinetics 1967,4 1. 1964 2 2 10 84 J . A. Kerr order reaction of nitrogen atoms with ethylene and propene have been de-termined as follows :26 log kCzH4 = 10-2 - (700/2*3 RT) and log kC3H6 = 11.2 - (1,700/2-3RT) mole-1 C.C. set.-'. The mechanism of the reaction of nitrogen atoms with propene has been investigated in detail with I4C-labelled propene and product analysis. 27 Of several mechanisms considered the most likely seems to be the reversible addition of the nitrogen atom to the double bond followed by reversible rearrangement of the excited adduct to an excited azocyclobutyl radical : 4 C H ! /"\ ,CH21* N + MeCH=CH + [MeCH-CH2]* 'N' CH2 The experimental results could be correlated in terms of the decomposition of the two intermediates and the attack of methyl carbene (a decomposition product) or a nitrogen atom on the intermediates.Brown and Thrush6 have studied the additions of oxygen atoms to acetylene, ethylene and propyne in a flow-discharge system with e.s.r. detection of the atom concentrations. The mechanism for the 0 + C2H2 reaction is thought to be 0 + C2H2 = CH + CO 0 + CH2 = CO + 2H CH2 + C2HZ = C3H4 while the initial attack of an oxygen atom on propyne is proposed to be 0 + MeC=CH = MeCH + CO which is a much faster reaction than with acetylene. The initial reaction for the addition of oxygen atom to ethylene has been deduced from the overall stoicheiometry and the hydrogen atom yield to be 0 + C2H4 = Me + HCO and that for diacetylene is proposed to be :7 0 + C4H2 = C3H2 + CO The Arrhenius parameters for a number of reactions of selenium atoms with olefins have been determined by flash photolysis of CSe in the presence of the olefin and the observations of intense-banded systems in the far U.V.which are ascribed to the (olefin-Se)* adduct.* The rates of addition of selenium atoms were measured relative to the rate of addition to ethylene which had previously been determined.28 There is a good correlation between the activation energies for the selenium-atom additions and the ionisation potentials of the olefins.z6 G. Paraskevopoulos and C. A. Winkler J . Phys. Chem. 1967,71 947. '' P. T. Hinde Y. Titani and N. N. Lichtin J . Amer. Chem. SOC. 1967,89 1411 z8 A. B. Callear and W. J. R. Tyerman Trans. Faraday SOC. 1966,62,371 Gus Kinetics 85 Gunning and S t r a u ~ z ~ ~ have comprehensively reviewed the reactions of of sulphur atoms and have continued their investigations3' of these reactions from the photolysis of COS. With light of 2537 A triplet (3P) and singlet ('D) sulphur atoms are produced in the ratio 3 1. The rates of addition of triplet sulphur atoms to a series of olefins have been determined relative to the addition to ethylene at 298"~. It is deduced that triplet sulphur atoms are electrophilic, while a few results on the relative rates of singlet sulphur atoms to olefins indicate that this species is also electrophilic but generally less selective than S( P).Table 5 contains data obtained from fast-flow systems on atom-addition reactions which reveal third-order kinetics. Atomic Transfer Reactions. As seen from Tables 6 and 7 many results have been determined for this type of reaction particularly for reactions of triplet oxygen atoms [O('P)]. The flow-discharge method of studying oxygen atoms involving e.s.r. de-termination of the atom concentrations has already been mentioned. The agreement between the results for the reaction of oxygen atoms with CH4 from the two e.s.r. studies2* is reasonably satisfactory although the results of Westenberg and Haas' are probably to be preferred on the grounds that their temperature range was considerably larger.The rate constants of Wong and Potterg for the 0 + CH4 reaction from a stirred-flow reactor and mass-spectrometric analysis are in excellent agreement with those of Westenberg and Haas although the Arrhenius parameters from a much shorter temperature range are somewhat higher. Heicklen"? '' has devised a neat competitive method for studying the re-actions of O( 3P) atoms produced from the mercury-photosensitised decompo-sition of N 2 0 : Hg* + N 2 0 = Hg + N2 + O(3P) The only oxygen-containing product from the reaction of O(3P) with C2F is CF20 which can be determined by in situ i.r. analysis. Thus when the oxygen atoms are produced in the presence of a mixture of C2F4 and a hydrocarbon the reactions of interest are 0 + CpF4 = CF2O + .0 + RH = products (6) (7) and the ratio of rate constants can be calculated from the expression - RCF,O) [c2H41 RCF2O [RHI kdks = where R is the rate of formation of product X and square brackets denote 29 H. E. Gunning and 0. P. Strausz Adv. Photochem. 1966,4,143. 'O E. M. Lown E. L. Dedio 0. P. Strausz and H. E. Gunning J . Amer. Chem. SOC. 1967,89, 1056; 0. P. Strausz J. Font. E. L. Dedio P. Kebarle and H. E. Gunning ibid. p. 4805 86 J. A. Kerr rc, m N 0" z + z 0 z + Q0" 2 2 + + no" n o II 0 + 0 +so + M = so + M 0 + SO + M = SO + M c1+ co + M = ClCO + M C l + N O + M = C l N O + M 0 + SO2 + M = SO3 + M 0 + SO + M = SO + M Flow discharge 298 air afterglow * Flow discharge 300 SO2 afterglow Flow discharge 300 C1 afterglow Flow discharge 293 C1 afterglow Flow discharge 300 SO2 afterglow Flow discharge 299 e.s.r.D. B. Hartley and B. A. Thrush Proc. Roy. SOC. 1967 A 297 520; F. Kaufman 4541; A. Sharma J. P. Padur and P. Warneck J. Phys. Chem. 1967,71 1602; M. A. A. Proc. Roy. SOC. 1966 A 295 355; C. J. Halstead and B. A. Thrush ibid. pp. 363 380; C. Ward J . Phys. Chem. 1967,71 2124; B. T. Clarke M. A. A. Clyne and D. H. Stedman TABLE 6 Transfer reactions of halogen Reaction System Temp. (OK) C1 + EtCl = HC1 + CH2CH2C1 C1 + MeCHC1 = HCl + CH2CHCl C1 + MeCC1 = HCl + CH,CCl, C1 + EtCl = HCl + MeCHCl C1 + CH2C1CH2C1 = HCl + CHC1CH2C1 C1 + CH2ClCC13 = HCl + CHClCCl, C1 + MeCHC1 = HC1 + MeCCl, C1 + CH2ClCHCl2 = HCl + CHClCHCl, C1 + CHZClCHCl = HCl + CH2ClCC12 C1 + CHC12CHC12 = HCl + CHC12CC1, C1 + C2HC1 = HC1 + C2C1, I + C2H6 = HI + Et I + C3H = HI + Pr" I + C3H8 = HI + Pr' I + isoC,H, = HI + But I + PhI = I + Ph I + CF3H = HI + CF3 I + CF31 = I + CF, Competitive with CHCl or MeCl 77 99 97 99 77 97 77 97 79 Competitive with CHC1 or CH,Cl Thermal iodination 79 99 99 99 79 Thermal reaction with HI Thermal and photochemical iodination 3 2 3 99 79 77 99 77 99 99 99 79 3 2 3 4 97 589-503-77 77 77 648-773 373-Ref.31 ; * C. A. Goy A. Lord and H. 0. Pritchard J . Phys. Chem. 1967,71 1086; ' J. H. Knox 32; ' ref. 19 Gas Kinetics 89 TABLE 7 Cross-combination ratios (@) 'a 'b Me Me Me Me Me Et Et Pr" CF3 cyclo-C,Hej Et Pr" CH,F CHF, CHF, Pr" Pr' Pr' CH2CH=CH2 CYC~O-C~H~~ 2.00 2.02 1.4 2.4 2.4 1.8 2.08 2-04 1.87 2.0 298" 298" 447b 329-585' 564-636* 298" 298" 298" 3 1 3-523f 299-560" ~~ ~ ~ Ref.33; * G. Greig and J. C. J. Thynne Trans. Faraday SOC. 1966,62 3338; G. 0. Pritchard and R. L. Thommarson J. Phys. Chem. 1967,71 1674; R. D. Giles L. M. Quick and E. Whittle, Trans. Faraday SOC. 1967 63 662; ref. 34; G. Greig and J. C. J. Thynne Trans. Faraday SOC., 1967 63 1369. concentration. Hexafluoropropene which is some thirty-times less reactive than C2F4 can also be used in similar competitive experiments since the only important products are CF20 and small amounts of CF,CFO. While such experiments yield rate factors for the reaction of O(jP) with hydrocarbons they do not provide unequivocal evidence as to the mechanism of the reaction.Although it seems reasonable to suppose that the reaction involved is hydrogen abstraction by the oxygen atoms this is not the view held by Avramenko and his co-w~rkers.~ They have studied oxygen atom reactions with hydrocarbons in a flow-discharge system where the rate constants are derived by an indirect method based on product analysis and have consistently proposed that the initial reaction of oxygen atoms with higher alkanes involves C-C rupture. Likewise for the reactions with EtOH and EtCHO they suggest :35 0 + EtOH = MeCHO + H 2 0 = CH,O + H,O + CH, and 0 + EtCHO = Me + CH,O + CHO whereas Kato and C v e t a n ~ v i c ~ ~ and Cadle and Powers" propose the simpler hydrogen abstraction reactions : 3 1 C.Cillien P. Goldfinger G. Huybrechts and G. Martens Trans. Faraday SOC. 1967,63 1631. 32 A. S. Rogers D. M. Golden and S. W. Benson J. Amer. Chem. SOC. 1967,89,4578. 33 J. 0. Terry and J. H. Futrell Canad. J. Chem. 1967 45,2327. 34 J. T. Bryant and G. 0. Pritchard J . Phys. Chem. 1967,71,3439. 3s L. I. Avramenko R. V. Kolesinkova and G. I. Savinova Zzvest. Akad Nauk. S.S.S.R. Ser. Khim. 1967 22 253 90 J. A. Kerr 0 + EtOH = OH + MeCHOH 0 + EtCHO = OH + EtCO A comprehensive study of hydrogen abstractions by chlorine atoms from chloro-ethanes has been rep~rted.~ ' The results (see Table 6) show that chlorine atom attack is faster at the most chlorine-substituted carbon atom.The de-crease in A-factor as the chlorine-substitution is increased is predicted by transition-state theory but the parallel increase in activation energy is not explained by a Polanyi relation since D(C-Cl) = 96 f 2 kcal. mole-' throughout the series of chloro-ethanes. It is apparent that polar effects play an important part in these reactions. The classic example of a 'bimolecular' reaction the H + I reaction, has now been shown to take place entirely by an atomic mechanism. Sullivan36 has photolysed (5780 A) iodine in the presence of hydrogen between 418 and 5 2 0 " ~ and shown that the rate of formation of HI is proportional to the square of the iodine-atom concentrations. The concentrations of iodine atoms were determined photochemically and for the termolecular reaction 21 + H = 2HI a rate constant of log k = 13.88 - (5310/2.3 RT) mole- c.c.set.-' was deduced. Previous thermal data (633-738"~) when treated with the ter-molecular reaction in place of the bimolecular reaction H2 + I = 2HI gave rate constants for reaction (8) corresponding to the same Arrhenius parameters. It was not possible to distinguish between the two kinetically identical mechanisms : H + 21 = 2HI or H 2 + I + M = H 2 1 + M H21 + I = 2HI Several important papers have been published on the kinetics of hot-atom reactions. In particular Wolfgang3' and his group3* have studied the reactions of F* and T* atoms produced by nuclear reactions with various simple molecules such as H, CH4 and CF4 and have successfully analysed their results in terms of the kinetic theory of hot-atomic reactions.2. Radical Reactions.-Several reviews of free-radical reactions have been published. Friswell and G o w e n l ~ c k ~ ~ have critically compiled kinetic and thermochemical data and information on inorganic hydrogen- and alkyl-36 J. H. Sullivan J . Chem. Phys. 1967,46 73. 3' R. Wolfgang Progr. Reaction Kinetics 1965 3,97. 38. J. F. J. Todd N. Colebourne and R. Wolfgang J . Phys. Chem. 1967,71,2875; D. Seewald and 3y N. J. Friswell and B. G. Gowenlock. A h . Frc~c~-Reiclic~ciI Chc~r 1965. 1 39 1967. 2. 1 R. Wolfgang J . Chem. Phys. 1967.46 1207 Gas Kinetics 91 containing radicals of the elements of groups 11-VI. Although the amount of quantitative kinetic information on these radicals is small there is now a sub-stantial body of related thermodynamic data including heats of formation of the radicals and compounds and bond-dissociation energie~.~' The reactions of halog~nomethyl~' and a l k o ~ y ~ ~ radicals have also been rcviewed.There has been much discussion concerning the addition of iodine atoms to olefins giving rise to planar or tetrahedral radicals. The present position has been summarised in a joint paper,43 in which it is agreed that either the planar radical configurations are more stable than the tetrahedral or the barrier to in-version of tetrahedral carbon atoms is much less than that for tetrahedral nitrogen compounds. Crosley and B e r ~ o h n ~ ~ claim to have made the first actual detection of radicals or hydrogen atoms during a steady-state gas-phase photolysis.Their system consisted of applying the principles of optical pumping to the vacuum U.V. (1048 and 1067 A) photolysis of ethane in the presence of rubidium. The pumped gas atoms spin-orientated rubidium were produced in a magnetic field via the selective absorption of polarised light. In the presence of unpaired electrons the spin polarisation is lost and hence the atoms or radicals can be detected. Combination and Disproportionation Reactions. Since the general features and patterns of reactivity of radical-radical reactions are now reasonably well established interest in these systems seems to have waned. Most of the available information4' on combination reactions R + R = R, (9) has been derived from rotating-sector experiments although other methods are also available.The results show that the A-factors (A,) correspond approxi-mately to the collision numbers and the activation energies (E,) are close to zero. A much simpler experimental problem is to measure the cross-combina-tion ratio of rate constants (4) for a pair of radicals: R + R = R, (9) This ratio is defined as +(Ra,Rb) = kll/(k9kl,,)k and for a large number of radical pairs + has been observed2'F4' to be close to two indicating that the combinations are occurring on every collision with zero activation energies. 40 J. A. Kerr Chem. Rev. 1966,66,475. 41 J. M. Tedder and J. C. Walton Progr. Reaction Kinetics 1967,4 37. 42 P. Gray R. Shaw and J. C. J. Thynne Progr. Reaction Kinetics 1967,4 63. 43 R. M. Noyes D.E. Applequist S. W. Benson D. M. Golden and P. S. Skell J . Chem. Phys., D. R. Crosley and R. Bershon J . Chem. Phys. 1966 45 4353; D. R. Crosley ibid. 1967,47 1967,46 1221. 1361. 44 4s J. A. Kerf and A. F. Trotman-Dickenson Progr. Reaction Kinetics 1961 1,107. 92 J . A. Kerr Disproportionation reactions are usually considered with combination reactions since unlike other metathetical reactions their rates are comparable with combination reactions. For like radicals the reaction is R + R = R,H + olefin R + R = R,H + olefin (12) and the autodisproportionation-combination ratio of rate constants is given by A(R,,R,) = ki,/kg while for unlike radicals we have (13) and the cross-disproportionation-combination ratio is defined as A(Ra,R,,) = k13/k11.Many A values for alkyl and other radicals have been de-termined21.45,46 and as a general rule A shows little or no variation with temperature. For alkyl radicals A values can be reasonably well predicted from their relation with the entropy differences of the products of dispropor-tionation and the product of ~ombination.~~ There has been much speculation on the structures of the transition states in disproportionation and combination reactions and particularly whether they are identical or different. The issue is not yet clear although the weight of opinion seems to favour different com-plexes.21 Controversy has arisen regarding the rate constant for the reaction : 2cc13 = C2C1 (14) A preliminary p ~ b l i c a t i o n ~ ~ on the photochlorination of CHCl by the rotating-sector method reports log k = 8-55 mole-' C.C.set.-' at 345°K for the reaction CCI + C1 = CCI + C1 and hence from the previously determined ratio log(k1,/k14+) = 2.24 it follows that log k14 = 12-62 mole-' C.C. see.-'. This result is considerably lower than the value log k14 = 13.9 mole- C.C. set.-' determined by Tedder and W a l t ~ n ~ ~ from rotating-sector experiments on the addition of CC1,Br to C2H4 at 350-446 OK. The self-consistency of the latter experiments is remarkably good consider-ing the experimental difficulties of the technique while it is difficult to assess the results on the photochlorination of CHC13 since full experimental details are still to be published. It has been pointed that the higher value of log A14 leads to more reasonable A-factors for the addition and transfer reactions of CCl radicals and that the c$ values for CCl radicals do not indicate an ab-normally-low rate constant for reaction (14).On these grounds the higher value of kI4 is to be preferred. An interesting application of the toluene-carrier method for studying pyrolytic reactions has been made to determine the rate of the combination reaction4' (16) Me + PhCH = PhEt A F. Trotnian-Dickcnson Proc. Clicrii Soc 1964 249. 4 7 G. R. De Mart and G. H. Huybrechts Chrm. Phys. Letters 1967,1,64. 48 J. M. Tedder and J. C. Walton Trans. Faraday Soc. 1967 63 2464; J. M. Tedder and J. C. 49 Walton Chem. Comm. 1966 140. R . J. Kominar. M. G. Jacko. and S. J. Price. Ccrncrd. J . Ch~rii 1967. 45. 575 Gas Kinetics 93 By analysing for the methane ethane and ethylbenzene in the products of the pyrolyses of gallium and thallium trimethyls and mercury dimethyl it has been shown that log k = 11.20 - 200/2.3 RT mole-' c.c set.-' at 529-799"~.The concentration of benzyl radicals was monitered by the rate of formation of methane and the known rate constant for methyl attack on toluene. The value of A16 is in excellent agreement with that calculated from the relation log ( A / A - 16) = AS/2.3 R and the experimental A-factor for the pyrolysis of ethyl benzene. O Cross-combination ratios 4 are listed in Table 7. The value @(Me,cyclo-propyl) = 1.4 is somewhat lower than the expected result of about two but the difference is probably due to the difficulty of obtaining quantitative data on cyclo-alkyl radicals.The latest results for fluorinated alkyl radicals are quite normal whereas the early results on 4 values were anomalous since allowance was not made for the fact that the activated fluoro-alkanes formed in the combination reaction can undergo an elimination reaction under certain conditions to give HF and an olefin51 (see section on activated molecules). Table 8 summarises the data on disproportionation-combination reactions. A(Bu",Bu") has been shown to be 0.14 independent of temperature from a careful study of the photolysis of a~o-n-butane.~~ This result is in keeping with TABLE 8 Disproportionation-combination reactions R + R' = RH + Olefin (d) R + R' = RR' (4 k,/k = A(R,R') R R' A(R,R') Temp. ( O K ) R R' A(R,R') Temp. (OK) Me Me Me Et Et Et Pr' Pr' Pr' Pr' Et Pr' Pr" Et Pr' Pr" Et Pr' Pr' Pr" 0.036 0.163 0-058 0.135 0.180 0.066 0- 124 0.687 0.58 0-409 298" 298" 298" 298" 298" 298" 298" 298" 295-339' 298" Pr" Pr" Bun Me Me Me0 NO NO H S Me Et Pr" Bun HCO Me0 Me0 Pr' Pr' HS Me 0.057 0-1 54 0.14 5.8 1.9 0.17 0.22 0.04 67 0 * 1 5 4 3 0 298" 298" 300-400' 303-376d 3 14-365" 314" 4 2 3 - ~ l 5 3 ~ 378-422g 3 h 298' Ref.33; S. E. Braslavsky J. Grotewold and E. A. Lissi J . Chem. SOC. (B) 1967 414; ' ref. 52; ref. 53; M. J. Yee Quee and J. C. J. Thynne Trans. Faraday SOC. 1966,62,3154. f B. E. Ludwig and G. R. McMillan J . Phys. Chem. 1967,71,762.gG. A. Hughes and L. Phillips J . Chem. SOC. (A) 1967,894; P. Fowles M. De Sorgo A. J. Yarwood 0. P. Strausz and H. E. Gunning J . Amer. Chem. SOC. 1967,89 1352; A. Good and J. C. J. Thynne, Trans. Faraday SOC. 1967,63,2708. G. L. Esteban J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. 1963 3873. " R. D. Giles and E. Whittle Trans. Faraday SOC. 1965,61 1425. 5 2 W. E. Morganroth and J. G. Calvert J . Amer. Chern. SOC. 1966,88 5387. 53 M. J. Yee Quee and J. C. J. Thynne Trans. Faraday SOC. 1967,63 1656 94 J. A. Kerr other n-alkyl radicals and obeys the A relation with the entropy differences of the products. The previously reported higher values for A(Bu" and the temperature coeficient for this ratio would now appear to be in error owing to complications with the sources of the radicals.The radical-radical reactions of methyl ethyl n- and iso-propyl radicals have been studied from the high-intensity photolyses of the corresponding azo-compounds at room temperat~re.~~ Under these conditions the concen-trations of the radicals are very high and the radical-radical reactions pre-dominate. The results summarised in Table 8 in the main confirm the previous 'best available' values of these ratios.46 The A values reported for oxygenated radicals are considerably higher than for the analogous alkyl radicals and furthermore the results do not fit the A relation with the differences in entropies of the products.42 The autodispropor-tionation of formyl radicals has been suggested to go via the reaction 2HC0 = H2 + 2CO and although no quantitative results were available it was clear from the product analyses that A(HC0 HCO) is very high.53 Radical Transfer Reactions.As usual most of the free-radical transfer reactions reported are concerned with the abstraction of a hydrogen atom. These reactions have been reviewed," and the general features are well established. The activation energies which seldom exceed 15 kcal. mole- are governed by the enthalpy change of the reaction and by polar effects. Un-fortunately there are no quantitative methods for dealing satisfactorily with these effects. The A-factors however can be calculated reasonably well from the transition-state theory and for hydrogen atom abstraction by Me the expec-ted range is log A = 11.5 rf 0.5 mole-' C.C. set.-'.The results for hydrogen atom abstraction reactions are summarised in Table 9. The reaction of methyl radicals with benzene is of interest, The most recent results were obtained at high temperatures in a flow sy~tem.~' Under these conditions the rate of combination of methyl radicals was in the pressure-dependent region but when this was taken into account the results for reaction (17) were in good agreement with previous determinations. EI7 has been taken62 in conjunction with the activation energy for the reverse 54 J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. 1960 1602; J. C. J. Thynne Trans. 5 5 A. F. Trotman-Dickenson Adv. Free-Radical Chem. 1965 1. 1. 56 R. J. CvetanoviC and R. S. Irwin J . Chem. Phys. 1967,46 1694. 57 M. Krech and S. J. W.Price Canad. J . Chem. 1967,45 157. 58 J. A. Kerr D. H. Slater and J. C. Young J . Chem SOC. (A) 1967 134. 5 9 T. N. Bell and B. B. Johnson Austral. J . Chem. 1967 20 1545. 6o D. G. Home and R. G. W. Norrish Nature 1967,215 1373. 61 A. J. Dijkstra J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1967 105,864. Faraday SOC. 1962,58 1533. F. J. Duncan and A. F. Trotman-Dickenson J . Chem. SOC 1962,4672; W. Fielding and H. 0. Pritchard J . Phys. Chem. 1962 66 821 Gas Kinetics 95 TABLE 9 Abstraction of H atoms by radicals R + HS = RH + S (a) 2R = R (b) ( E - 9%) log A,? Temp. (OK) R HS* kcal (mole-' C.C. mole - sec. - ' Me Propene But-1-ene cis-But-2-ene trans-But-2-ene Isobutene Benzene Acetone CH,FCOMe MeOCOOMe PhOCH, CF,CHO C,F,CHO C,F,CHO CFzHCOCFzH CYC~O-C 3H 5 C H 0 NH,CH,CH,NH, NH2CH2CH2NH, ND,CH,CH,ND, Me,SiH SiHF, SiHCl, MeSiHCl, Me3SiC1 Me,SiCl, MeSiC1, CF MeF CH2F2 CF,Me CF,HCF,H SiHC1, C A H CH,F CH,FCOMe CF,H MeCOMe CCl CH,CH==CH, CH3CF=CH2 Me0 MeOCOOMe 7.2 7.3 7.6 8-2 7.9 9.3 9.4 4.6 4.3 7.4 10.5 8.7 9-8 10.3 8.7 7.3 6.8 7.9 7.0 8.7 8.5 7.2 11.5 11.6 11.5 11-2 11.2 13.5 12.4 11.5 6.9 6.7 9-0 - 6.3 - 6.6 5.9 10.3 11.0 11.1 11.4 11.0 10.8 11.4 10.1 10.3 10.2 11.7 12-1 12.9 13.2 12.3 10.9 10.3 10.3 11.1 12.4 13.4 11.8 13.4 13.2 12.9 12.2 11.9 12.2 12.0 11-3 12.1 10.0 10.9 - 12.0 - 12.0 10.8 353453" a a a a 99 97 9 ) 9 ) 744--8Wb 329-Wd 299-560' 3 14--366f 453-5399 40 1-444h 398-43gh 373-473' 360-450' j i 403-503' 99 99 330-445k 34347ok 303-393k 3 1 5-395k 337-47 1 361455k 3 7 8 4 7 g k 469-632' 448436' 566478' 5 10-683' 507-724' 329-585d 395483" 3 6 2 4 5 4 3 14--366f 83-563" 299-560 J .A. Kerr TABLE 9-continued Temp. ( E - +&J log 43 ( O K ) R HS* kcal (mole- ' C.C. mole - ' sec. -Pr" MeCOMe 8.4 10.7 403-503' Bun (Bu"N) 7.1 11.2 377-520' OH CH4 5.0 13.7 ? P C2H6 3.6 14.1 2 9 8 4 2 3 P NF cyclo-C,H1 13.4 9.1 334-3914 * Atom in italics is abstracted; t based on log k = 13.34 (mole-' C.C. set.-'); ref. 56; ref. 57; ' L. Endrenyi and D. J. Le Roy J . Phys. Chem. 1967 71 1334; * G.0. Pritchard and R. L. Thom-marson J . Phys. Chem. 1967,71,1674; ref. 34; M. J. Yee Quee and J. C. J. Thynne Trans. Faraday SOC. 1966,62,3154; M. F. R. Mulcahy B. G. Tucker D. J. Williams and J. R. Wilmshurst Austral. J . Chem. 1967 20. 1155; E. R. Morris and J. C. J. Thynne Trans. Faraday SOC. 1967 63 2470; G. Greig and J. C. J. Thynne Trans. Faraday Soc. 1966,62,3338; P. Gray and A. A. Herod Trans. Faraday SOC. 1967,63,2489; Ir ref. 58; ' R. D. Giles L. M. Quick and E. Whittle Trans. Faraday SOC., 1967,63 662; ref. 59; J. M. Tedder and J. C. Walton Trans. Faraday SOC. 1967,63 2678; ' ref. 52; P ref. 60; ref. 61. reaction E - 7 to obtain values of the bond strength D(Ph-H) = 102 and 105 kcal. mole- '. Rogers Golden and B e n ~ o n ~ ~ have subsequently determined D(Ph-H) = 112 PhI + HI + C,H + I2 and since this is now a well-established method for yielding reliable bond-dissociation energies it is clear that the previous determinations based on the hydrogen atom abstraction reactions are seriously in error.It has been suggested that the reaction of a methyl radical with benzene in the gas-phase does not involve hydrogen atom abstraction as shown by reaction (17) but that the radicals add to the benzene ring to give a resonance-stabilised cyclohexadienyl radical that subsequently reacts with another methyl radical to form methane :32 1 kcal. mole-' from an equilibrium study of the system 0 + Me = CH4 + Me Me If this mechanism is correct the products of the reaction of methyl radicals with benzene should contain toluene.The reactions of methyl and CF radicals with organosilicon com~oundsS8- 5 9 are among the first quantitative kinetic results for this class of substrates. The A'-factors for some of the methyl reactions are abnormally high and they 9 Gas Kinetics 97 have been explained by invoking ionic participation in the transition state, ofthe type previously suggested to be involved in disproportionation reactions.,' It is also very difficult to reconcile the reported Arrhenius parameters for methyl and CF radical attack on SiHC1,. More work is obviously needed on these systems. The rates of reaction of hydroxy radicals with methane and ethane have been studied by flash photolysing the hydrocarbons in mixtures with water and argon.60. 6 3 The rate of disappearance of the radicals was followed spectro-scopically ; so-called kinetic spectroscopy.The Arrhenius parameters listed in Table 9 for methane and ethane are not in very good agreement with rate constants reported by Greiner63using the same method or with other published data on these reactions.64 Comparatively few results have been reported on radical reactions involving the transfer of atoms other than hydrogen. King and S ~ i n b o u r n e ~ ~ have pointed out the difficulties of obtaining quantitative data on the halogen abstractions Me + RX = MeX + R where X = C1 or Br arising from complications involving the generation of radicals by hydrogen atom abstraction. A competitive study of the reactions CF3 + I2 = (3'31 + I CF + HI = CF3H + I (18) (19) has been carried out by Amphlett and Whittle.66 From the previously de-termined rate constant for reaction (18) they deduce log k = 11.73 - (500/ 2.3RT) mole-' C.C.set.-'. Whittle and c o - ~ o r k e r s ~ ~ have now completed studies of the reactions CF3 + X2 = CF,X + X CF3 + HX = CF3H + X where X = C1 Br and I and have discussed the results in terms of thermo-dynamic data available on these systems. A rate constant of log kZ0 = 12-17 - (23,500/2.3 RT) mole- C.C. set.-' has been obtained for the reaction (20) by generating the NF radicals from the equilibrium dissociation of N2F4 and observing the pressure change in the presence of C1F,.67 NF + ClF = NF + ClF, 6 3 N. R. Greiner J . Chem. Phys. 1967 46 2795 3389. 64 L. I. Avramenko and R. V. Kolesnikova Adv.Photochem. 1964 2,25; P. Gray and A. Jones, Canad. J . Chem. 1967,45 333. K. D. King and E. S. Swinbourne J . Phys. Chem. 1967,71,2371. 66 J. C. Amphlett and E. Whittle Trans. Faraday SOC. 1967 63 2695. '' G. von Ellenmeder E. Castellano and H. I. Schumacher Z . phys. Chem. (Frankfurt) 1967, 56 20 98 J . A. Kerr Radical Addition Reactions. As for transfer reactions the general features of free-radical addition reactions to multiple bonds seem to be well established. The activation energies usually fall within the range 5-15 kcal. mole' and the A-factors within the range predicted by transition-state theory, mole- ' C.C. set.- Unfortunately compared with hydrogen atom abstraction reactions there is much less quantitative data available on addition reactions.The experimental difficulties are much greater with addition reactions since the initial product is a free radical which may undergo a variety of further re-actions. Even for simple systems such as Me + C2H = Pr" the accuracy of the rate constants is not very good as shown by the data in Table 10 which includes two recent determinations. Since there are no obvious TABLE 10 Arrhenius parametersfor the reaction Me + C2H = Pr" Source of Me Temp. E log A and system (OK) (kcal. mole-') (mole-' C.C. set.-') (Me,CO)2 397-43 1 8-7 product analysis (Me,C0)2 395-432 7.8 product analysis Me2C0 403-503 6.8 product analysis (MeCO), 353-453 7-9 mass balance 12.1" 1 Mb 11.1' ll.9* ~~ ~~ ~ R. K. Brinton J. Chem. Phys. 1958,29 781; A. M. Hogg and P.Kebarle J . Arner. Chem. Soc., 1964,86,4558; L. Endrenyi and D. J. Le Roy J. Phys. Chem. 1967,71,1334; ref. 56. reasons for selecting one result in preference to the others it would seem best to take the average Arrhenius parameters and obviously significant errors should be attached to such values. This lack of accuracy in determining rate constants for free-radical addition reactions means that caution should be exercised in making deductions on the detailed mechanisms of these reactions based on small differences in Arrhenius parameters. CvetanoviC and Irwins6 have developed a useful variant of the mass-balance method for studying the addition reactions of methyl radicals to olefins. Small amounts of biacetyl were photolysed in the presence of the olefin and a reference hydrocarbon isobutane.Under the experimental conditions the important reactions are MeCOCOMe + hv = 2MeCO (A Gas Kinetics 99 MeCO = Me + CO (B) Me + Me3CH = CH + Me,C (21) Me + 0 1 = R' (22) Me + 0 1 = CH + R" (23) Radical-radical reactions can be neglected provided the concentrations of olefin (01) and isobutane are far in excess of the methyl concentration. A steady-state treatment yields so that plots offversus [RH]/[Ol] yield values of k,,/k, and k 2 1 / k 2 2 . In the limiting case with [Ol] = 0 the expression becomes (&O/&H4) - 1 = 0 and this was confirmed experimentally although minor corrections were necessary for addition methyl reactions at low temperatures and low RH concentrations. The advantage in using biacetyl as a methyl source in preference to acetone is that the ratio CO/CH is unity with biacetyl even although all the MeCO radicals do not decompose by reaction (B).Accordingly it is possible to work at lower temperatures with biacetyl than with acetone. Temperature coefficients of the ratios k 2 ~ / k Z 2 and k z l / k Z 2 were obtained and the Arrhenius parameters for reactions (22) and (23) listed in Tables 11 and 9 were deduced TABLE 11 Radical additions to unsaturates R + S = R S Radical Substrate Temp. E log A mole - ') sec - l ) (OK) (kcal. (mole-' C.C. Me Propene But- 1 -ene cis-But-2-ene trans-But-2-ene Is0 butene 2-Methyl but-2-ene 2,3-Dimethylbut-2-ene Buta-1,3-diene Allene Propyne Sulphur Dioxide Et Allene 353-453 3 5 3 4 5 3 3 5 3 4 5 3 353-453 3 5 3 4 5 3 3 5 3 4 5 3 3 5 3 4 5 3 353-453 3 7 3 4 8 3 3 7 9 4 6 5 298-437 374-471 7.4 7.2 7.5 8.1 6.9 -6 -7 4.1 8-1 8.8 1.5 9.2 11-5" 11-3" 11.0" 11.5" 11.5" - 10.5" - 10.3" 11.2" 11.3' 11-7' 1 0*8d 1 1.5' D 100 J .A. Kerr TABLE 1 1-continued Radical Substrate Temp. E log A mole- I ) sec. - l ) (" K) (kcal. (mole- C.C. Pr' Pr' Pr" But CH,COMe CCl, Allene Prop yne Ethylene Prop yne Ethylene Propene 2-Fluoropropene Hexafluoropropene Ethylene Propene But-1-ene cis-But-2-ene trans-But -2-ene Isobutene 2-Me t hyl bu t -2-ene 2,3-Dimethylbut-2-ene Cyclopentene Vinyl chloride Vinyl bromide Ethylene Isobutene 36-73 36-39 385-439 403-503 395-483 362-454 415-485 3 5 1 4 2 8 334-391 334-391 334-39 1 314-373 314-373 314-373 334-39 1 351-405 351-405 403-503 334-391 245-333 245-333 7.2 5.7 5.1 6.6 3.4 3.2 6.2 15.5 13.7 13.6 11.9 11.9 11-8 10.1 8.3 11.0 12.9 13.2 1-1 1.7 -6 10.7' 9.7' 10.1' - 9.3' 11.1' 10.2f 9*8f 9.5f 1 0*6g 10.28 10.18 9-58 9.58 9.8g 9.08 8*3g 8.98 9.49 9.6g 1 1.Oh 12.5' ~ ~~~ Ref.56; * ref. 68 ; ' R. R. Getty J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1967, 1360; * A. Good and J. C. J. Thynne Trans. Faraday SOC. 1967,63 2708; L. Endrenyi and D. J. Le Roy J . Phys. Chem. 1967,71 1334; J. M. Tedder and J. C. Walton Trans. Faraday SOC. 1967, 63 2678 ; 8 ref. 61 ; L.I. Avramenko L. M. Evlashkina and R. V. Kolesnikova Izvest. Akad. Nauk. S.S.S.R. Ser. Khim. 1967 259. from the known rate constant for reaction (21). The outstanding advantage of the method is that it yields reliable relative rates of addition of methyl even in cases such as 2 methyl and 2,3-dimethylbut-2-ene where the abstrac-tion of hydrogen atoms predominates over the addition reaction. There is reasonable agreement between the k 2 2 / k 2 values and the corresponding ratios obtained in iso-octane solution,69 on the assumption that the A-factors for the various olefins are approximately the same. CvetanoviC and Irwin have also drawn up a useful summary of relative rate constants for additions of atoms radicals and biradicals to unsaturate^.^^ It is interesting to note that the additions of alkyl radicals to allene occurred exclusively at the terminal carbon atoms.68 Meunier and Abel17* have shown R.R. Getty J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1967 979; 6 9 M. Feld and M. Szwarc J . Am. Chem. SOC. 1960,82 3791 and references cited therein. 70 H. G. Meunier and P. I. Abell J . Phys. Chem. 1967,71 1430 Gas Kinetics 101 that in the additions of CF,I and Me1 to allene the CF and methyl radicals also add exclusively to the terminal atoms. There has been considerable dis-cussion over the years regarding the orientations of free radical and atomic additions to allene." The results on the methyl and CF additions have been interpreted as indicating that polar effects are not important. While the electro-philic CF radical would be expected to add to the point of highest electron density i.e.the terminal carbon atom the 'slightly nucleophilic' methyl radical should add to the central carbon atom if polar effects were the only consideration. NF radicals have been added to olefins by generating the radicals from the equilibrium dissociation of tetrafluorohydrazine :61 NZF4 + 2NF, Since D(NF,-NF,) is only 20 kcal. mole-' the concentration of NF is appreciable at low pressures and temperatures above 3 7 3 " ~ . For the series of NF additions listed in Table 11 a general mechanism has been established : NF + 01 = NF,OI* NF,Ol* + Mol = NF,O1 + Mol NF + NF,Ol = 01(NF2), (24) ( 2 5 ) (26) (27) (28) NF,OI* = NF + 01 NF,Ol = NF + 0 1 The concentration of NF2 radicals is known from the total pressure of N,F4 and NF radicals and the dissociation constant of N,F4.0 1 is the olefin of known initial concentration NF,Ol* is a vibrationally-excited radical and Mol is any molecule in the system capable of removing the excess energy. A steady-state treatment yields : where kobs is defined by d[Ol(NF,),]/dt = kob,[O1][NF,] and OI(NF,) is the bis-difluoro-amine product that is analysed. Less than 5 % of hydrazine and olefin were consumed and hence their concentrations were taken to be constant during the run. Two series of experiments were carried out for each compound at each temperature. In one series [Moll was kept constant and [NF,] varied; l/kobs was plotted against l/[NF,] and the intercept on the l/k,,bs axis gave (l/kz4)(l + k,,/k,,[Mol]) while the slope gave (1/kz4){l + k,5/k,,[Mol])(k27/k,8).Thus k,,/k,* was obtained by dividing the slope by the intercept. Similarly k,5/k,6 was determined from plots of 1 kobs against l/[Mol] with [NF,] constant and k24 could then be derived from either set of observations by substituting the appropriate value of kZ5/k2 or k27/k28. H. G. Kuivila W. Rahman and R. Fish J An~rr. Chew. Soc. 1965 87 2835 TABLE 12 Radical elimination reactions Reaction Temp. (OK) C2H6 = 2Me CH2:CH(CH2),CH:CH2 = 2CH2:CHCH2 MeCMe,CH,CH CH = But + CH,CH CH, EtOOEt = 2Et0 Me,CHOOCH(Me) = 2Me,CHO Me,CHOOCH(Me) = 2Me2CH0 N-F,* = CF + N, MeN:NMe = 2Me + N, Me,NN:NNMe = N + 2Me,N Me,Hg = 2CH + Hg Me,SiSiMe = 2SiMe, Me,SiSiMe = 2SiMe, Et = H + C2H4 Pr" = Me + C2H, CH,:CH(CH,),CH:CH = 2CHz:CHCHz ~ ~ ~~~~ 9 13-999 850-950 1000-1 130 407-458 4 0 7 4 5 8 3 7 8 4 2 2 3 9 6 4 4 3 5 5 3 4 2 3 4 0 0 4 8 585-4574 977-1070 628-796 93 5- 1044 9 13-999 53 3-5 7 Bu" = Et + C2H4 BUS = Me + C3H6 EtCO = Et + CO PhOCH = PhCHO + H MeSO = Me + SO2 CF,CO = CF3 + CO NFZC2H4 = NF2 + C2H4 NF2C3H6 = NF2 + C3H6 NF2C4H8 = NF2 + MeCH:CHMe 432-520 533-4513 300-523 303-353 45 3-5 39 298-43 7 3 7 3 4 2 8 334-39 1 334-39 1 Second-Order Reactions (A - mole-' C.C.C,H + M = 2Me + M 9 13-999 Et + M =C2H4 + H + A4 9 13-999 EtCO + M = Et + CO + M 303-3 5 3 Ref. 72; * R. J. Akers and J. 3. Throssell Trtrus. Ftrrtrtltrv Sot,. 1967 63. 124 J. Chem. 1966,44,2211; ref. 73 ; C.Leggett and J. C. J. Thynne Truns. Faraday SOC., L. Phillips J. Chem. SOC. (A) 1967 894; E. W. Neuvar and R. A. Mitsch J . Phys. and K. J. Laidler Canad. J. Chem. 1966,44 2927; A. Good and J. C. J. Thynne, Waring and R. Pellin J. Phys. Chem. 1967,71 2044; ref. 74; [ref. 75; ref. 52; J. Chem. 1967,45,1315; J. C. Amphlett and E. Whittle Trans. Faraday SOC. 1967,63,80; Trans. Faraday SOC. 1967.63 2480; M. F. R. Mulcahy B. G. Tucker. D. J. Williams, Chem. 1967 20 1155; A. Good and J. C. J. Thynnc Trtrtis. Furtrcltrj Soc. 1967 63, fall-off region. 'I2 M. C. Lin and M. H. Back Canad. J. Chem. 1966,44,2357; 1967,45,2115. 'I3 W. Tsang J. Chem. Phys. 1967,46,2817. l4 S. J. Band I. M. T. Davidson C. A. Lambert and I. L. Stephenson Chem. ' I 5 J. A. Connor R. N. Haszeldine G.J. Leigh and R. D. Sedgwick J. Chem 104 J . A. Kerr Temperature coefficients yielded the Arrhenius parameters for the addition reactions (24) listed in Table 11. The results for the decompositions of the ther-mally equilibrated radicals [reaction (27)] which are given in Table 12 have been deduced on the assumption of zero activation energy and an arbitrary A-factor for reaction (28). show a regular trend with the structure of the olefin : The activation energies for the addition reactions, E24 = 15.5 - 1.8 (number of alkyl substituents on double bond) By comparison with other radical additions the results indicate that the NF, radical is an electrophilic species. Thus if the addition of the radicals was at a specific carbon atom attack would occur on the most substituted carbon atom to form a o-complex.It would also be expected on this basis that Eethylene > Epropene * Ebut-Zene > Ejsobutene. Since these predictions were not confirmed it was concluded that the initial radical attack was on the double bond forming a n-complex rather than at a specific carbon atom. Support for this conclusion was taken from the fact that the pattern of reactivity of NF additions to olefins closely resembles that for oxygen atoms where a n-complex appears to be involved. The issue regarding o- or n-complexes between NF2 and olefins is not,’however so clear cut. Additional important evidence concerns the addi-tions of NF to cis- and trans-but-2-ene. The cis-isomer is found in the products of the addition of NF to trans-but-2-ene and conversely the trans-isomer is produced from NF addition to cis-but-2-ene.This is in accord with the pro-posed mechanism involving the reversible formation of the adduct radical and is good evidence in support of the mechanism. At the same time it would seem to indicate the formation of a o-complex from addition to the butenes since the isomerization would be less likely from a n-complex. The idea of relating the activation energy for a free-radical addition reaction to the localisation energy or the difference in n-energy between the adduct radical and the parent olefin has been extended76 to include addition re-actions to unsymmetrical olefins. R + CH,=CHR’ = RCH,CHR’ R + CHR’-LH = RCHR’CH, (29) (30) For such a pair of reactions the A-factors have been assumed to be equal and the activation-energy difference (E29-E,,) which is then a measure of the relative rates of addition have been compared with the differences in localisa-tion energies [E,(29) - E,(30)] calculated by a Huckel LCA0‘-MO technique.The experimental activation energies for CCl additions to fluoroethylenes,” correlate well with the calculated localisation energies and the general con-clusion has been reached that the direction of addition in these reactions is determined mainly by the relative stabilities of the adduct radicals. 3. Unimolecular Reactions.-A notable feature of unimolecular reactions 7 6 J. B. Flannery J . Phys. Chem. 1966,70 3707. 77 J. M. Tedder and J. C . Walton Trans. Faraday SOC. 1966,62 1859 TABLE 13 Unimoiecular isomerisation Reaction cis-FN NF = trans-FN NF n-c.,H = s-c,Hl CH,CCl,CH = CH,ClCCl CH, r---l I Me,CCH CHCH = Me,C CHCH CH2 Me,CCH:CMeCH = Me,C:CHCMe:CH, CH,CMe:CMeCH = CH,:CMeCMe:CH, kF,C(CF3) C(CF3)CF2 = CF C(CF3)C(CF,) CF, cis-CH CHCH CHCH,Me = cis,trans-MeCH CHCH CHMe CH CHCH CHCHMeCH CH = CH,CH CHCMe CHCH CH CH,:C:CHCH,CH,CH:CH = CH,:CHC(CH,)CH,CH:CH, I I I * In dimethyl phthalate solution; * J.Binenboym A. Burcat A. Lifshitz and J. Shamir, ref. 84; ref. 85; J. P. Chesick J. Amer. Chem. SOC. 1966,88,4800; H. M. Frey and B. D. H. Lister J. Chem. SOC. (A) 1967 26; K. W. Egger J . Amer. Chem. SOC. 1967,89,3688 106 J . A. Kerr is the increasing application of the Rice-Ramsperger-Kassel-Marcus (RRKM) theory as exemplified in the treatment of Wieder and Marcus.78 The theory is not readily explained in a short space but several summaries have been made.’l* 79 Continuing success is still being met however with the classical Rice-Ramsperger-Kassel (RRK) theory” of unimolecular reactions in cases where the information for RRKM calculations is not readily available.Isomerisation Reactions. These reactions were considered by Frey in the 1960 Annual Report and cis-trans isomerisations were reviewed in 1 964.81 Brief summaries have also appeared in the Annual Reviews of Physical Chemistry. Over the past five or six years however such a volume of work on unimolecular structural and geometric isomerisations has appeared that a separate review and assessment seems highly desirable. Unfortunately limitations of space preclude mention here of all but the most recent data which are summarised in Table 13.The first Arrhenius parameters for the thermal isomerisation of a simple alkyl radical have been determined by Endrenyi and Le Roy.8’ The activation energy 10.8 kcal. mole-’ for the isomerisation of n- to sec-pentyl is reasonable but the A-factor lo7 set.-' is abnormally low. Much of the interest in studying isomerisations of small ring compounds lies in elucidating the transition states in these reactions. While it is now generally accepted that cyclopropane and cyclobutane compounds undergo structural and geometric isomerisations via biradical intermediates,’ ‘3 86 the evidence is not conclusive in all cases. Interesting results have been reportedS3 on the isomerisation of 1,l-dichlorocyclopropane which yields 2,3-dichloro-propene.The reaction is proposed to occur via chlorine atom migration, *.q “t€g involving the intermediate H,C-CCl on the basis that the most stable biradical CCl,CH,CH, would not give the observed product. The results are quite different however for the isomerisations of fluorocyclopropanes,87 where it has been established that fluorine atom migration does not occur. Thus with 1,l-difluorocyclopropane the products were CF,=CHMe and CH,=CHCF,H.88 Biradical formation seems probable with fluorocyclo-7 8 G. M. Wieder and R. A. Marcus J . Chem. Phys. 1962,37 1835. ’’ B. S. Rabinovitch and D. W. Setser Adu. Photochem 1964 3 1. S. W. Benson ‘The Foundations of Chemical Kinetics’ Mc-Graw-Hill New York 1960.A. S. Cundal1,Progr. Reaction Kinetics 1964 3 165. L. Endrenyi and D. J. Le Roy J. Phys. Chem. 1966,70,4081. K. A. W. Parry and P. J. Robinson Chem. Comm. 1967 1083; R. Fields R. N. Haszeldine, and D. Peter ibid. p. 1081. 84 H. M. Frey B. M. Pope and R. F. Skinner Trans Faraday SOC. 1967,63 1166. 85 H. M. Frey D. C. Montague and I. D. R. Stevens Trans. Faraday SOC. 1967,,63 372. 86 D. W. Setser and B. S. Rabinovitch J . Amer. Chem. SOC. 1964 86 564; R. J. Ellis and H. M. Frey J . Chem. Soc. 1964 5578. B. Grzybowska J. H. Knox and A. F. Trotman-Dickenson J . Chem. SOC. 1963,746. F. Casas J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. 1965 1141. 8 Gus Kinetics 107 propanes. Since chlorine atom migration occurs at some stage in the isomerisa-tion and fluorine atom migration does not it may be that quite different mechanisms operate for fluoro- and chloro-compounds.The temperature- and pressure-dependence of the ’ 3C isotope-effect on the isomerisation of cyclopropane have been in~estigated.~’ At a pressure of 1 atmos. the effect can be expressed by the relation log (k12c,Jk12c,13cH 1 = -0003 + (19.1/2.3 RT). 13C isotope labelling had the same effect up02 the isomerisation as deuterium labelling and it was concluded that the isomerisa-tion involves considerable ring relaxation or in other words supports a biradical intermediate. Isotopic labelling has also been appliedg0 in the case of the isomerisation of vinyl cyclopropane to cyclopentene. With vinylcyclopropane labelled with D in the C2 ring position loss of stereospecificity was about five-times faster than isomerisation to cyclopentene.This was interpreted in terms of a biradical mechanism although the evidence was not conclusive. Frey and co-worker~~~* 85 have studied the isomerisations of cyclobutene and a variety of methylcyclobutenes to 1,3-dienes. These reactions are thought to proceed via a ‘conrotary’ mechanism in which there is rotation of the C3 and C4 atoms on the ring coupled with appreciable stretching of the C3-C4 bond. Benson and De More2’ have suggested an alternative transition state involving partial ion-pair formation. A distinct pattern of reactivity in the isomerisations of methyl-substituted cyclobutenes can now be discerned.84 The activation energy can be increased or decreased depending upon the posi-tion of methyl substitution but owing to the significant spread of A-factors the effect of methyl substitution on E is not additive.On the other hand a good correlation is achieved by comparing the effect of methyl substitution for each carbon atom in the ring on the free energy of activation (AGS) calculated from the rate constant at a fixed temperature. This is simply an alternative way of expressing the effect of substitution on the rate constant. Thus the average changes in AGS for substituting a methyl group in the 1,2 and 3 positions are 1.17,0.83 and - 1.76 kcal. mole- ’. The correlation is such that it is now possible to predict AGS and hence rate constants for the isomerisations of methyl-substituted cyclobutenes that have not yet been studied.Molecular Elimination Reactions. Recent data are summarised in Table 14. Some years ago Maccoll and Thomasg3 suggested that the mechanisms of dehydrohalogenations of alkyl chlorides and bromides in the gas-phase could involve heterolytic character. It was subsequently suggested that these gas phase reactions were somewhat analogous to SN1 or E l reactions in solution. 89 L. B. Sims and P. E. Yankwich J . Phys. Chem. 1967,71 3459. 90 M. R. Willcott and V. H. Cargle J . Amer. Chem. SOC. 1967,89 723. 91 K. A. Holbrook and A. R. W. Marsh Trans. Faraday SOC. 1967,63,643. 92 N. Capon A. Maccoll and R. A. Ross Trans. Faraday SOC. 1967,63 1152. ’’ A. Maccoll and P. J. Thomas Nature 1955 176 392 TABLE 14 Molecular elimination reactions Reaction Temp.(OK) Cyclohexa-1,3-diene = benzene + H 6 3 5 Cyclohexa- 1,Cdiene = benzene + H 603-663 1 Methylcyclohexa-l,4-diene = toluene + H 587435 3 Methylcyclohexa-1,4-diene = toluene + H 56-14 Me3CC02Et = Me3CC02H + C2H4 62-94 Me,SiCH,CH,Cl = Me,SiCl + C2H4 573-6 Et3SiCH,CH2Cl = Et,SiCl + C2H4 573-659 Me2CCH20cH2 = Me,C:CH + CH,O 673-723 Bu”OCH:CH = MeCH,CH:CH + MeCHO 590-4550 ClCOOH = HCl + CO 288-343 EtCl = CH2:CH2 + HCl 675-794 Me(CH,),CHClMe = Me(CH2)4CH CHMe + HCl 598-658 MeCH(0Et)Cl = CH,:CHOEt + HCl 4 3 7 MeCH,CHBrCH,Me = MeCH CHCH,Me + HBr 558-621 a S. W. Benson and R. Shaw J. Amer. Chem. SOC. 1967,89 5351 ; S. W. Benson and H. M. Frey and D. H. Lister J. Chem. SOC. (A) 1967 509; H. M. Frey and D. H. Cross and V. R. Stimson Austrul.J . Chem. 1967,20 177; I. M. T. Davidson M. R. g G. F. Cohoe and W. D. Waters J. Phys. Chem. 1967,78 2326; * T. 0. Barnkole and R. J. Jensen and G. C. Pirnentel J. Phys. Chem. 1967,71 1803; j ref. 91 ; li C. J. Harding, 1967 289; ’ R. L. Failes and V. R. Stirnson Austrul. J. Chem. 1967,20 1553; ref. 92 Gas Kinetics 1 09 The transition state was formulated as R R I I H X with the P-H atom playing a part analogous to that of the solvent in SN1 or El reactions in solution. This idea of a ‘quasi-heterolytic’ transition state has been extended to include other types of molecular elimination reactions and the situation has been reviewed.94 One of the most striking applications of the ‘quasi-heterolytic’ hypothesis is that the activation energy for the elimination of HX from an alkyl halide RX can be estimated from the equation E(HX) = 0*29D(R+X-) where D(R ‘X-) is the heterolytic bond-dissociation energy corresponding to the process RX = R+ + X-.Benson and B o ~ e ~ ~ have also considered the energetics of the transition state in gas-phase HX eliminations and the reverse additions of HX to olefins and have successfully calculated activation energies in terms of a ‘semi-ion pair’ model in which the double bond is partially polarised with formal charges of +* at each carbon atom and there is cor-responding parallel polarisation at H and X. The question of whether the decomposition of neopentyl chloride involves a molecularg6 or free-radicalg7 mechanism appears to have been largely resolved. By studying the reaction in a vessel from which bromides had been excluded the products of the reaction were showng8 to include (i) 2 methylbut-1-ene and (ii) 1,l-dimethylcyclopropane and 2-methylbut-2-ene.Product (i) was unaffected by the presence of added olefin whereas products (ii) were greatly reduced by the olefin. It was thus inferred that the dimethyl cyclo-propane and 2-methylbut-2-ene are formed from a free-radical split while the 2 methylbut-1-ene arises from a molecular process. Capon Maccoll and Rossg2 have made a careful study of the pyrolysis of 3-bromopentane in the presence of cyclohexene. The dehydrobromination reaction was shown to be homogeneous first-order and consistent with a molecular elimination. The free-radical chain mechanism for the pyrolysis of bromides proposed by Wojciechowski and Laidler,99 is not valid under the fully inhibited conditions.Holbrook and Marsh” have made a detailed investigation of the effect of pressure upon the elimination of HCl from EtCl. The limiting high-pressure 94 A. Maccoll and P. J. Thomas Progr. Reaction Kinetics 1967 4 119; A. Maccoll ‘Studies in 95 S. W. Benson and A. N. Bose J . Chem. Phys. 1963,39,3463. 96 A. Maccoll and E. S. Swinbourne Proc. Chem. SOC. 1960,409. 97 K. H. Anderson and S. W. Benson J . Chem. Phys. 1963,39 1673. 98 J. S. Shapiro and E. S. Swinbourne Chem. Comm. 1967,465. 99 B. W. Wojciechowski and K. J. Laidler Trans. Faraday SOC. 1963,59 369. Structure and Reactivity’ Ed. J. Ridd Methuen London 1966 110 J . A. Kerr rate constant (see Table 14) is in reasonable agreement with previous results.The pressure fall-off curves fitted those calculated from RRK theory with the number of effective oscillators taken as S = 12. Fall-off curves calculated from RRKM theory were displaced towards higher values of k/k than the experimental curves. In the later case all vibrational modes were taken to be active and the calculations were relatively insensitive to the structure of the activated complex. Other RRKM calculations on the rates of decomposi-tion of ethyl and t-butyl chlorides have suggested that not all vibrational modes are effective in intramolecular energy transfer. O0 Radical Elimination Reactions. Over the years much attention has been focussed on this type of unimolecular reaction because of its application to the determination of bond-dissociation energie~.~' It is usually assumed that E for the reverse radical-combination reaction is zero and hence E for the radical-elimination reaction can be equated with the dissociation energy of the bond broken.At one time it was thought that the A-factors for radical elimination reactions should be close to 1013 set.-' i.e. of the order of a vibrational frequency and there is sometimes a tendency for this notion to persist. In accord with transition-state theory it is now well established that the A-factors for these reactions can be several powers of ten in excess of lo1 3 particularly if two large radical fragments result from the decomposition.21 One of the most interesting developments for many years in the field of pyrolysis has been described by Benson and Spokes.'" The reactions were carried out at very low pressures (- lob6 torr.) by passing the gas through a cylindrical reaction vessel with a small exit aperture at carefully-controlled temperature and analysing the products and unreacted parent molecules in a quadrupole mass spectrometer.At the very low pressures energy transfer occurred mainly through collisions between the gas and the walls of the reaction vessel. The average number of gas-wall collisions (Z,) was determined from the ratio of internal surface-area of the reaction vessel to the area of the exit aperture. A number of reaction vessels were used with values of 2, from 90-9000. Of several reactions the decomposition Pr'I = C,H + HI has been most extensively studied.The extent of decomposition was obtained from the mass-spectral analyses of the products and reactants and kinetic equations have been derived pertaining to the low-pressure pyrolysis condi-tions from which the rate constants were obtained. It was noted from a com-parison of the observed rate constants with the known high-pressure limiting rate constants (k,) that the rate of decomposition was limited by the rate of energy transfer even in the 9000-collision reaction vessel. Good agreement was obtained between the observed rate constants and the values derived from k , by an RRK treatment involving 15 or 18 effective oscillators. The low-pressure pyrolysis method lends itself to extensive temperature variation and thus gives loo H. Heydtmann Chem. Phys. Letters 1967 1 105.S. W. Benson and G. N. Spokes J . Amer. Chem. SOC. 1967,89,2525 Gas Kinetics 111 a large range of rate constants extending well into the pressure fall-off region for many molecules. It should also prove useful in obtaining information on energy transfer with walls and added gases. In addition the products of pyrolytic reactions can be directly determined. Quantitative results on radical elimination reactions are given in Table 12. There seems at last to be some measure of agreement between the A-factors, or rate constants for the pyrolysis of ethane and those calculated from the reverse radical-recombination reaction via the equilibrium constant. For the reaction 2Me = C2H (31) the corrected pyrolysis data72 lead to log k 3 1 = 12.58 mole-' C.C.set.-' at 5 0 0 " ~ which is about a factor of six lower than the value directly determined at lower temperatures. Tsang7 has developed a competitive shock-tube method of studying pyroly-tic reactions and has reported Arrhenius parameters for a number of elementary hydrocarbon radical- elimination and other reactions. As a general rule the activation energies determined by Tsang for C-C fission in hydrocarbons have been in reasonable agreement with the bond-dissociation energies, whereas the A-factors have been 1-3 powers of ten lower than the values calculated from the entropy change for the reaction and the known or assumed rate constants for the reverse radical recombination reactions. The latest results on the shock-tube pyrolysis of 4,4'-dimethylpent-l-ene are given in Table 12.The activation energy (E = 65.5 kcal. mole-') leads to a value of ca. 9 kcal. mole-' for the allylic resonance energy based on the accepted value4' of ABF (But). There are good reasons for believing that the allylic resonance energy is nearer to 13 kcal. mole-' which implies that E for the pyrolysis of 4,4'-dimethylpent-l-ene has been overestimated. If this is the case the reported A-factor is also high and hence the divergence between the A-factor of the decomposition reaction and that estimated from the reverse re-combination reaction is even greater than suggested. There seems no prospect of reconciling the A-factors for the shock-tube pyrolyses of hydrocarbons with the A-factors for radical recombination reactions. Two determinations of the rate constant for the pyrolysis of hexamethyl-disilane have been reported.74* Haszel'dine and ~ o - w o r k e r s ~ ~ have studied the reaction in a flow system at pressures less than torr by measuring the rate of disappearance of the disilane mass-spectrometrically.The mechanism d the reaction was by no means established however and a range of Arrhenius parameters was determined as given in Table 12. A-factors as low as 10" sec. - for this type of process are quite incompatible with transition-state theory and furthermore at the low pressures of the experiments it is possible that the reaction was in the pressure fall-off region. For these reasons the value of D[(Me),Si-Si(Me),] reported by Haszeldine and co-workers would seem to be a gross underestimate and the results of Davidson et al.74 are much to be preferred 11 2 J .A. Kerr Activated Molecule Reactions. For the present purposes activated molecules are considered to be in their electronic ground-states but contain excess vibrational energy over and above that due to their ambient temperature. Such molecules are most conveniently produced by exothermic chemical reactions, or by dissociation of a molecule following the absorption of a quantum of light. The general features of chemically-activated molecules have been described by Rabinovitch and Flowers,lo2 and Rabinovitch and S e t ~ e r ~ ~ have sum-marised recent data on the unimolecular decompositions of activated alkanes and alkyl radicals. Activated molecules formed by the reaction of CH with olefins have also been discussed.' O3 Emphasis has subsequently switched to studying molecular elimination reactions from chemically-activated alkyl chlorides and fluorides.So far three methods of forming chemically-activated alkyl halides have been studied. The combination of alkyl radicals gives rise to activated molecules containing excess energy equivalent to the C-C bond dissociation energy i.e. in the range 85-90 kcal. mole-' : Me + CH,CF,H =EtCF,H* Me + CH,Cl =EtCI* The fluoroalkyl radicals can be produced from the photolysis of the correspond-ing or from the reaction of CH radicals from ketene or diazo-methane with a f l u ~ r o a l k a n e ' ~ ~ CH + MeCF,H = Me + CH2CF2H Chloroalkyl radicals are produced from the CH reaction with chloroalkanes,'06 CH + MeCl = Me + CH,C1 Alkyl fluorides of much higher energy-content can be generated by the insertion of singlet CH (photolysis of ketene in the presence of 0,) into C-H bonds of fluor~alkanes,'~~* ' 0 5 CH + MeF = EtF* Here the excess energy in the EtF* is estimated to be 115 kcal.mole-'. Activated ethyl fluoride has also been formed by the reaction Et + F2 = EtF* +F which occurs when fluorine is reacted with ethane. '04 The enthalpy change of reaction (32) is 69 kcal. mole-' and it has been argued that this mostly resides in the ethyl fluoride. B. S. Rabinovitch and M. C. Flowers Quart. Rev. 1964 18 122. H. M. Frey Progr. Reaction Kinetics 1964 2 131 ; H. M. Frey in 'Carbene Chemistry' by J. A. Kerr A. W. Kirk B. V. O'Grady and A. F. Trotman-Dickenson Chem.Comm. 1967,365. J. C. Hassler D. W. Setser and R. L. Johnson J . Chem. Phys. 1966,45 3231; J. C. Hassler and D. W. Setser ibid. pp. 3237 3246; D. W. Setser and J. C. Hassler J . Phys. Chem. 1967 71, W. Kirmse Academic Press London 1964 p. 2 17. lo' J. A. Kerr B. V. O'Grady and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1966 1621. 1364 Gas Kinetics 113 TABLE 15 Elimination of hydrogen halides @om activated alkyl halides at room temperature Alkyl Halide System kelk (cm.) EtF MeCHF, CH,FCH,F MeCF, CF,HCF2H EtCF,H EtCF,H MeCF,Me MeCF,Me EtCl CH,C1CH2C1 MeCHCl, CHCl ,CH ,C1 Fluorides CH + MeF Me + CH,F Me + CH,F Et + F2 CH + CHZF, Me + CHF, 2CH,F 2CH,F Me + CF3 2CF,H Me + CH2CF2H* CH + MeCF,H Me + CF,Me* CH + MeCF,H Chlorides Me + CH2C1* Me + CH2C1* Me + CH2Cl* 2CH2C1* 2CH2C1* Me + CHC12* CHCl + CH2C1* CHCl + CH2C1* 351a 14" 7tb 0.07" N 10C.d 5.t' 2f.s 5 b - 1.4h v.low' < 0.47' 1.24' <4*1" 19' 2 9 27Tj 28ti 1.8' 1.6t' 2.2' 3.51' 116i * Radicals produced from abstraction by CH,; t results obtained under different conditions of M from other results for same molecule; Ref. 104; * G. 0. Pritchard and R. L. Thommarson J . Phys. Chem 1967,71 1674; ref. 105; ref. 107; ref. 34; re6 108; ref. 109; W. G. Alcock and E. Whittle Trans. Faraday SOC. 1965 61, 244; R. D. Giles and E. Whittle $id. p. 1425; G. 0. Pritchard and J. T. Bryant, J . Phys. Chem. 1965,69 1085; j ref. 106. Since theenergy contents ofthealkyl halides produced by these three methods, are considerably in excess of the activation energies for the dehydrohalo-genation reaction the molecules react in this way unless collisionally deacti-vated : EtX* -+ CH2=CH + HX (e) lo' G.0. Pritchard J. T. Bryant and R. L. Thommarson J. Phys. Chem. 1965,69,2804. lo' G. 0. Pritchard M. Venugopalan and T. F. Graham J. Phys. Chem. 1964,68,1786. lo9 S . W. Benson and G. Haugen J. Phys. Chem. 1965,69 3898 114 J . A. Kerr EtX*+ M - Etx + M A steady state treatment yields the expression REt X I R C Z H 4 = (ks/ke)CMl and thus k$k can be determined by plotting the ratio of alkyl halide to olefin, i.e. stabilisation to elimination products against the concentration or pressure. Some allowance ,is usually made for the variations in collisional efficiencies of different moecules in the system.Since k,/k is given by (alkyl halide/olefin) (l/[M]) it is convenient to express the ratio in pressure units and a summary of results for eliminations from various activated alkyl halides is given in Table 15. It follows from this convention that the k,/k values denote the pressure at which k = k,. Benson and Haugenlo9 have interpreted the results'08 on the reactions of activated alkyl fluorides from the combination of radicals in terms of RRK theory. The rate constant of the elimination is related to the energy content ( E ) of the molecule by the equation : k = A [ ( E - E,)/E]"-' where A and E are the Arrhenius parameters for the thermal-elimination re-action and n is the number of effective oscillators.On the assumption that stabilisation occurs in a single collision the rate constant can be expressed as k = Z where Z is the number of collisions and the probability of complete deactiva-tion on collision is assumed to be unity. It follows that ks/ke = Z / A . ( E / E - E,)"-l Owing to experimental difficulties values of E for the thermal elimination of HF from alkyl halides have not been measured and hence the above rela-tions can be applied to obtain E from the data on the activated alkyl fluorides. Benson and Haugen"' have shown that the energy content ( E ) at different temperatures can be calculated from the equation E = E + ACg'b(T- 298) where E is the energy change on the recombination of the radicals taken to be 85.4 kcal. mole- at 2 9 8 " ~ for fluoralkyl radicals and ACVb is the difference in vibrational specific heat of the two radicals and the activated molecule.The A-factor of the HF elimination reaction is assumed to be 1013*5 set.-' in line with other HX eliminations from alkyl halides and the number of effective oscillators n is usually taken to be two-thirds of the total number of vibrational modes or it can be estimated by comparison with similar rea~ti0ns.l'~ For one particular type of activated molecule formed say from the combination of radicals k,/k is measured over a range of temperatures and the results are interpreted in terms of a plot (see Figure). Theoretical values of k,/k, calculated from Z / A . ( E / E - I?,)"- ' are plotted against temperature resulting in a serie Gas Kinetics 115 of lines one for each of the selected values of E,.By comparing the experimental values of k$k, from plots of halide/olefin versus P with the theoretical lines it is possible to select the value of E which gives the best fit. Benson and Haugen'" and Pritchard and c o - ~ o r k e r s ~ ~ have thus deduced activation energies for HF elimination from alkyl fluorides in the range 5 3 - 6 2 kcal. mole-'. -0.8, 54 53 \ 52 \ 51 '0 -28 300 i 400 5 0 0 6 0 0 700 T O K FIGURE Results for reactions CH2FCH2F* + M + CH2FCH2F + M (s) and CH2FCH2F* + CH2=CHF + HF ( e ) re$ 110). Lines are calculated from log (kJk,) = log (Z/A. (E/E-EJ- ' ) f o r activation energies (E,) between 49 and 54 kcal. mole-' assuming A = set.-' n = 14 and E29 = 85.4 kcal.mole-'. Experimental pointsfrom log (k,/k,) = log ((l/P) (CH2FCH2F/CH2=CHF)} open circles ref 110 filled circles ref 108. An alternative approach involves measuring k,/k values at room tempera-ture for a chemically-activated alkyl fluoride with different energy contents, formed by the three previously described methods. The RRK equation can again be applied to determine which value of E gives the best agreement between calculated and observed kJk; values with assumed values of A and n and estimated values of the different energy contents E. In this way the acti-vation energy for the elimination of HF from EtF has been c a l ~ u l a t e d ' ~ ~ to be 51 kcal. mole-' which is considerably lower than the other estimates. It has been pointed out however that the use of the non-quantised RRK model for a unimolecular reaction leads to an underestimate of E,.Subsequent treatment of more extensive data'" according to the RRKM theory supports a value of 110 J A. Kerr A. W. Kirk B. 1'. O'Grady D. C. Phillips and A. F. Trotman-Dickenson Discuss. Faraday SOC. 1967,44,263 116 J . A. Kerr about 60 kcal. mole-' for HF elimination from alkyl fluorides which is in agreement with the value predicted by the quasi-heterolytic approach.'" The formation of vibrationally-excited molecules by photochemical reac-tions offers some advantages over the chemical-activation approach in that the range of energies is more controllable and.may be more extensive. Thomas, Sutin and Steel112 have carried out an elegant study of the distribution and exchange of vibrational energy in the products of the photolysis of 2,3-diazo-bicyclo[2.2.l]hept-2-ene (I) The primary photochemical split gives activated bicyclo[2.1.O]pentane (11) which can either be collisionally stabilised or rearranges to cyclopentene and penta-1,4-diene.The effects of wavelength pressure and added gases on the relative yields of the hydrocarbon products have been studied in detail. The energy-dependence of the rate constants for the reactions of the activated molecule (11) as determined by wavelength variations were treated success-fully by RRK theory. It was further deduced that the activated molecules were produced with a distribution of energies having a standard deviation of 6-7 kcal. and in consequence the photochemical production of activated molecules may not prove to be a very sensitive test of theories of unimolecular reactions.4. Molecule-molecule Reactions.-There are two general types of reaction, addition and transfer. Addition reactions are the reverse of molecule-elimina-tion reactions e.g. Olefin + HX = RX Since the equilibrium constants tend to favour the elimination reactions, addition reactions are not easy to study although Benson and his collabora-tors,21,113 have made a systematic study of the additions of HI to olefins. Transfer or disproportionation reactions of molecules e.g. 2C2H4 = Et + C2H3 are equally difficult to study being the reverse of radical-radical reactions and highly endothermic. It has become increasingly apparent that molecule-molecule transfer reactions can be important in the initiation of complex high-temperature pyrolyses.'I4 Recent data on molecule-molecule and misiellaneous radical-molecule reactions are given in Table 16. Benson1'6 has made a kinetic analysis of the Diels-Alder reactions of buta-'I1 A. Maccoll Discuss. Faraday SOC. 1967,44,274. Ii2 T. F. Thomas C. I. Sutin and C. Steel J . Amer. Chem. SOC. 1967,89 5107. 'I3 K. W. k g e r and S. W. Benson J . Phys. Chem. 1967,71,1933. S. W. Benson and G. R. Haugen J . Phys. Chem. 1967,71,1735. R. M. Marshall J. H. Purnell and B. C. Shurlock Canud. J . Chem. 1966,44 2778. 116 S. W. Benson J . Chem. Phys. 1967,46,4920 TABLE 16 M olecule-molecule and miscellaneous Reaction Temp log ( O K ) (mole-sec. CO + NO = C 0 2 + NO COCl + NO = C 0 2 + NO + C1 0 + 2N0 = 2N02 HNO + HNO = N20 + H 2 0 SO + NO2 = SO3 + NO SO + 0 = SO2 + O2 MeCHO + NO = MeCO + HNO, CH CHOEt + HCI = MeCH(0Et)Cl Pr‘OH + HI = C3H + H,O + HI trans-but-2-ene + HI = BuI but-1-ene + HI = BuI pent-1-ene + HI = C5H,,I penta-1,4-diene + HI = C5H91 penta-1,3-diene + HI = C5H91 666-746 666-746 478 298 298 223-300 3 8 3 4 5 3 4 3 7 4 9 4 3 5 6 4 5 7 46 1 483 46 1 4 2 1 4 6 1 432 9.5 12.7 * Units mole-’ c.c.’ sec-’; t estimated A-factor; * J.H. Thomas and G. R. Woodman, J. Morecroft and J. H. Thomas J . Phys. Chem. 1967,71 1543; F. C. Kohout and F. A. A. Clyne C. J. Halstead and B. A. Thrush Proc. Roy. SOC. 1966 A 295 355; C. M. I. Christie and M. A. Voisey Trans Faraday SOC. 1967 63 2702; f R. L. Failes 1553; @ R.L. Failes and V. R. Stimson Austral. J. Chem. 1967,20 1143; ’ ref. 113 118 J. A. Kerr diene. It is proposed that the reactions involve a common biradical intermediate and the following competing systems have been considered The results of the kinetic analysis are consistent with independent studies of the rates of individual reactions in the above scheme (i) the pyrolysis of cyclo-octa-l$diene to 4-vinyl cyclohexene and butadiene (ii) the dimerization of butadiene to 4-vinyl cyclohexene (iii) the reverse pyrolysis of 4-vinyl cyclo-hexene to butadiene and (iv) the reaction of 1,4-divinyl cyclobutane in solution to give 4-vinyl cyclohexene cyclo-octa-1,5-diene and lesser amounts of butadiene. Benson's treatment of the data is based on steady-state approxi-mations and the application of thermodynamics to kinetics.Equilibrium constants and rate constants are derived from the thermodynamic expression : log K = log (kf,/k,) = AS12.3 R - AH12.3 RT Where experimental enthalpies and entropies are not available or are con-sidered to be unreliable they are calculated by the group-additivity method,' l7 which is estimated to give A H f to f 1 kcal. mole- ' and So and Ci to f 1 cal. mole-' deg-'. For the reaction scheme or mechanism to be considered valid, there should be good agreement between the observed rate constants and those calculated from the equilibrium constants. 5. Biradicals and Related Species.-The most studied biradical is methylene, CH, and although its reactions and properties are well d o ~ u m e n t e d ' ~ ~ ~ '18 several recent papers have considerably clarified and extended our knowledge.It has been accepted for some time that the ground state of CH is the triplet state (3E,) and that there is a low-lying singlet state ('Al). The commonest sources of CH are the photolyses of ketene (CH,CO) and diazomethane (CH,N,) and it now appears that both give rise to mixtures of 3(CH2) and '(CH,). As a general rule the proportion of '(CH,) increases as the wavelength of the photolysis is decreased and there have been many attempts to determine the exact proportions of '(CH,) and 3(CH,) for given conditions of photolysis. 'Chemical' evidence for the existence of '(CH,) came from a study of the stereo-chemistry of the CH addition reactions to cis- and trans-butene,"9 where it was argued that the stereospecific additions were due to '(CH,) adding across 11' S.W. Benson and J. H. Buss J . Chem. Phys. 1958,29 546. I t * W. B. De More and S. W. Benson Adu. Photochern. 1964 2,219. P. S. Skell and R. C. Woodworth J . Amer. Chem. Soc. 1956 78 4496; R. C. Woodworth and P. S. Skell ibid. 1959,81 3383 Gas Kinetics 119 the double bond in a concerted manner without formation of an intermediate biradical. The additions of 3(CH2) on the other hand have been shown to be non-stereospecific presumedfo arise from the formation of a biradical with rotation around the original double bond.',' It should be pointed out that Benson and De More2' have put an entirely different interpretation on the above experiments based on the different energy contents of '(CH,) and 3(CH2), although the original interpretations are still widely accepted.The reactions of CH with CO',' and with C3H,"2 have both been studied to determine the proportions of '(CH,) and 3(CH,) from the photolysis of CH,CO but the most encouraging results have been derived from the reactions of CHT with C2H4.123 The CHT biradicals were generated from the 3120 A photolysis of CHTCO in the presence of C2H4 with and without added oxygen and over ranges of pressure. From the analysis of the [3H]cyclopro-pane and the C3H]propene it was deduced that the following reactions occurred with the percentages of 3(CHT) and '(CHT) as shown: '(CHT)(17%) + CH2=CH2 = CH2TCH=CH2 CHT / \ '(CHT)(54%) + CH2=CH = CH,-CH, 3(CHTX29%) + CH,=CH2 = CH,-CH2 There was also subsequent isomerisation of the [3H]cyclopropane to [3H] propene.In these as in other experiments use was made of the fact that oxygen suppresses the formation of products from 3(CH,) reactions thereby making it possible to study the '(CH,) reactions alone. NO has been used for the same purpose.' 24 '(CH,) radicals react with alkanes mainly by insertion reactions : '(CH,} + MeCH,Me = MeCH,CH,Me MeCHMe, and it has now been shown that the insertion occurs indiscriminately the rates for primary secondary and tertiary C-H bonds being equal for '(CH,) produced from CH2C0'24 115 and from CH2N2.125 3(CH,) radicals react with alkanes mainly by abstracting hydrogen atoms : 3(CH2) + MeCH,Me = Me + MeCHMe lZo F. A. L. Anet R. F. Bader and A. M. Van der Auwera J.Amer. Chem. SOC. 1960,82 3217; H. M. Frey ibid. p. 5947. B. A. De Graff and G. B. Kistiakowsky J. Phys. Chem. 1967.71 1553. 12' Shih-Yeng Ho and W. A. Noyes J. Amer. Chem. SOC. 1967,89 5091. lZ3 C. McKnight E. K. C. Lee and F. S. Rowland J. Amer. Chem. SOC. 1967,89 469. lZ4 M. L. Halberstadt and J. R. McNesby J. Amer. Chem. SOC. 1967,89 3417. 12' R. W. Carr J. Phys. Chem. 1966,70 1970; B. M. Herzog and R. W. Carr ibid. 1967,71 2688; G. Z. Whitten and B. S. Rabinovitch. ihid 1965 69. 4348 120 J. A. Kerr and while there is no data on the relative reactivities of C-H bonds the usual order of reactivities tertiary > secondary > primary appears to prevail. Both 3(CH,) and '(CH,) add to olefins to give activated cyclopropanes. As previously mentioned the additions of 3(CH,) are believed to proceed via the formation of biradical intermediates and a recent study of the addition of 3(CD,) (from the mercury-photosensitised decomposition of CD,CO) has confirmed this mechanism and further revealed that there is some decomposition of the trimethylene biradical to give ally1 radicals.' 26 Krzyzanowski and CvetanoviC' 2 7 have determined the relative rates of reaction of 3(CH,) (mercury-photosensitised decomposition of CH,CO) and '(CH,) (direct photolysis of CH2C0 at 2660 A) with a series of olefins at room temperature.With 3(CH,) the rate of the principal reaction of addition to give the cyclopropanes depends relatively little on the structure of the olefin, although the addition to butadiene was somewhat faster than to mono-olefins.The additions of '(CH,) to olefins were complicated mainly by insertion but when this was taken into account the relative rates of addition were again essentially equal throughout the olefin series. CH from the photolysis of CH2C0 has been shown to react with MeCl by abstraction,'06' 128 while CH from CH,N2 is believed to react with SiH4 both by abstraction and insertion.'" It was not entirely clear from these systems whether 3(CH,) or '(CH,) was taking part in the reactions. The above summary of the reactions of CH is intended to describe the broad features of the radical although it undoubtedly presents an over-simplified picture. Rate constants for the reactions of methylidene CH with CH, H, and N2 have been determined by flash photolysis of CH4 with vacuum U.V.radiation.' 30 The concentrations of CH radicals were determined by kinetic spectroscopy involving the absorption by CH at 3143 A. From the product analyses and kinetics of the reactions it is proposed that CH radicals react by insertion reactions : CH -!- H,=Me CH + CH4 = C2H4 + H with rate constants of 1.5 x 10' and 6.2 x 10' ' mole- ' C.C. set.- ' respectively. Carbonyl carbene (CCO) has been generated from the photolysis of carbon suboxide (C302) and shown to react with olefins to yield allenes and lesser amounts of alkynes. ' '- ' With ethylene the products are allene and propyne : R. J. CvetanoviC H. E. Avery and R. S. Irwin J . Chem. Phys. 1967,46 1993. lZ7 S. Krzyzanowski and R. J. CvetanoviC Canad. J . Chem. 1967,45 665.lZ8 R. S. B. Johnstone and R. P. Wayne Photochem. and Photobiol. 1967 6 531. l Z 9 J. W. Simons and C. J. Mazac Canad. J . Chem. 1967,45 1717. 13' W. Braun J. R. McNesby and A. M. Bass J . Chem Phys. 1967,46,2071. lJ1 K. D. Bayes J . Amer. Chem. SOC. 1961,83 3712; 1962,84,4077; 1963,85 1730. 132 R. T. K. Baker J. A. Kerr and A. F. Trotman-Dickenson J . Chem. SOC. (A) 1966,975; 1967, 1641 Gas Kinetics 121 CCO + C2H4 = C H 2 X X H 2 + CO = M e C d H + CO so that CCO radicals function effectively as carbon atoms. The relative rates of reaction of CCO radicals with a series of methyl-substituted ethylenes have been determined by Baker Kerr and Trotman-Dickenson 132 by comparison with the reaction: CCO + C302 = polymer + CO These results showed that methyl substitution on the double bound reduced the reactivity of the alkene regularly.Willis and Bayes', have found exactly the opposite effect for CCO adding to methyl-substituted ethylenes using a different method based on comparisons of the efficiency of oxygen quenching of the allene yields. A major discrepancy obviously exists and until it is resolved the effect of olefin structure on the reactivity of CCO is uncertain. 6. Theory.-Aromic Recombinations. The question of non-attainment of a Boltzmann distribution of energy states in atomic recombination and diatomic-dissociation reactions has received further theoretical consideration. ' 34 For the general system A + A + M $ A + M k d it has been demonstrated that provided the concentration of atoms is small it is valid to apply the phenomenological equation dn,,/dt = -&dn,/dt) = -kdnA2nM + k,nA 2nM which implies an equilibrium distribution of internal states.It appears that all the systems so far studied have sufficiently low concentrations of atoms to fulfil this condition. The temperature-dependence of the rate of termolecular atomic-recombina-tion reactions has been calculated on the basis of the 'radical-molecule complex mechanism' ' A + M + A M (33) A M + A + A 2 + M (34) The equilibrium constant K,, was calculated assuming a Lennard-Jones (12-6) potential between A and M and the rate of reaction (34) was calculated from the collision rate between A and AM. For the reaction I + I + Ar = I2 $- Ar (35) the rate constant was deduced to be log k, = 14.5 + 1400/2.3RTmole-2 C.C.sec. - ' in good agreement with experimental values. 1 3 3 C. Willis and K. D. Bayes J . Amer. Chem. SOC. 1966 88 3203; C. Wiliis and K. D. Bayes, 134 N. S. Snider J . Chem. Phys. 1966,45 3299. 13' Shoon Kyung Kim J . Chem. Phys. 1967,46 123. J . Phys. Chem. 1967,71 3367 122 J . A. Kerr Unimolecular Reactions. O’Neal and B e n ~ o n l ~ ~ have described a method for estimating A-factors for four- and six-centre unimolecular reactions based on transition state theory: A = (ekT/h) exp(ASz/R) The problem is to calculate ASz the entropy of activation. For a unimolecular reaction contributions to ASz arise from changes in the vibrational frequencies, internal rotations and from symmetry changes. In forming the transition-state transitional entropy is unchanged rotational entropy changes are small, and it is assumed that there is no change in electronic degeneracy.By drawing up rules for assigning bending stretching and torsional frequencies A-factors have been calculated with an estimated uncertainty of +O-3 in log A(sec.-’). It was deduced that the most important factors in determining AS$ are the losses in hindered internal rotations in forming the cyclic transition states which are ‘looser’ than the analogous cyclic compounds. A-factors have been calculated for a large number of unimolecular reactions and good agree-ment obtained with experimental values. Experimental A-factors for four- and six-centre unimolecular reactions can now be examined for ‘reasonableness’ by comparison with the values calculated by the application of the empirical rules to transition-state theory.The problems of intermolecular and intramolecular energy transfer in unimolecular reactions have been considered. Current theories of thermal unimolecular reactions have overcome the difficulty of inefficient intermolecular internal-energy transfer either (i) by making the Lindemann strong-collision assumption that all inelastic collisions of the activated molecules lead to deacti-vation or (ii) by making the equilibrium-assumption that the distribution of states with insufficient energy to react is given by the equilibrium Boltzmann distribution at ambient temperature. Tardy and Rabin~vitch’~ have made calculations based on a number of different models for deactivation to test these assumptions in the second-order pressure region for five simple uni-molecular reaction systems.Intramolecular energy-flow is a necessary postulate of the RRK theory of unimolecular reactions whereas in Slater’s model vibrations are assumed to be strictly harmonic and there is no transfer between them. solc has extended Slater’s theory by considering the effect on the unimolecular rate constant of allowing rapid intramolecular-energy transfer between some of the normal vibrational modes of the m01ecule.l~~ Theories of unimolecular reactions usually make the assumption that the time scale for reaction is controlled by vibrational processes and that other degrees of freedom reach a rapid equilibrium. In the RRKM theory since the H. E. O’Neal and S.W. Benson J. Phys. Chem. 1967,71,2903. 13’ D. C. Tardy and B. S. Rabinovitch J . Chem. Phys. 1966 45 3720. B. S. Rabinovitch D. C. 138 M. solc Mol. Phys. 1966 11 579; 1967 12 101; M. solc Chem. Phys. Letters 1967 1 160; Tardy and Y. N. Lin J . Phys. Chem. 1967,71 1549. N. B. Slater Mol. Phys. 1967 12 107 Gas Kinetics 123 reaction time is long compared with the time to reach vibrational equilibrium, the reaction is considered as being only a function of the total vibrational energy so that the total unimolecular rate constant has a simple additive con-tribution from all the initial vibration states. Valence and Schlag have now derived a theoretical rate constant for thermal unimolecular reactions in a multi-quantum-level system. 13' It has been shown that the unimolecular rate constant is the lowest eigenvalue of a relaxation matrix that describes all microscopic processes occurring in the reaction system. In a second paper the eigenvalue problem has been solved without the usual assumption of uni-molecular reaction-rate theory that there is an equilibrium distribution of non reactive states. BimoZecuZar Reactions. These will be only briefly mentioned since there have been several comprehensive reviews.140 Theoreticians in this field have received a considerable stimulus from the detailed information on the molecular dynamics of bimolecular processes that has been obtained from molecular-beam studies. Light and co-worker~'~' have developed a statistical or phase-space theory of chemical reactions which was initially applied to ion-molecule reactions re-quiri'ng no activation energy e.g. A+ + BC = AB' + C A + BC+ = AB+ + C Each reaction path was allotted a probability proportional to the amount of phase-space available to it. The theory has subsequently been extended to three-body reactions with activation energies. For systems such as K + HBr, H + C12 and H + HX (X = C1 Br and I) excellent agreement has been ob-tained between calculated and experimental rate constants reaction cross-sections isotope ratios and product excitations. The theory of chemical-reaction cross-sections as applied to molecular-beam studies has been extended by Marcus.142 A statistical-dynamical model has been formulated for total chemical-reaction cross-section as a function of the relative velocity and the vibrational and rotational state of the reactants. The model has been applied to the H + H2 reaction and the reaction cross-sections shown to agree reasonably well with those derived from three-dimen-sional classical-mechanical computer calculations. Marcus has also considered the analytical mechanics of chemical reactions dealing with both the classical and quantum mechanics of linear collision^.'^^ 139 W. G. Valence and E. W. Schlag J . Chem. Phys. 1966,445,216; 1966,45,4280. 140 K. J. Laidler and J. C. Polanyi Progr. Reaction Kinetics 1965,3 1 ; D. L. Bunker 'Theory of Elementary Gas Reaction Rates' (Internation-a1 Encyclopaedia of Physical Chemistry and Chemical Physics Topic 19 Vol. 1) Pergamon Press New York 1966; J. Ross ed. Adv. Chem. Phys. 1966 10, J. Lin and J. Light J . Chem. Phys. 1966,45,2545; and references therein. 142 R A. Marcus J . Chem Phys. 19645,2630; 1967,46,959. 143 R. A. Marcus J . Chem Phys. 1966,45,4493,4500.

ISSN:0069-3022    

DOI:10.1039/GR9676400073

出版商:RSC    

年代:1967

数据来源: RSC

摘要:

7. COLLOID AND INTERFACE SCIENCE By G. D. Parfitt (University of Nottingham) THIS review of the 1967 literature is not comprehensive because of the in-evitable delay in receiving translations of papers from the Soviet Union and of delays in receiving certain important journals e.g. the Journal of Colloid and Interface Science. The following topics are not considered in detail: chemistry at electrode surfaces (polarography electrocapillarity etc) ion-exchange chemisorption and heterogeneous catalysis biological interfaces, and polymers biocolloids or polyelectrolytes in solution. Attention is drawn to the papers from four scientific meetings which were published in the literature in 1967; selected papers are included in this review. The meetings were (1) Symposium on ‘Ice’ Pittsburgh U.S.A.March 1966;’ (2) Symposium on ‘Wetting’ Bristol England September 1966 ;2 (3) Dis-cussion on ‘Colloid Stability in Aqueous and Non-Aqueous Media’ Notting-ham England September 1966 ;3 (4) Symposium on ‘Structure of Surfaces’, Durham North Carolina U.S.A. November 1966.4 Characteristics of Solutions of Soaps and Detergents.-The argument as to whether micelle formation should be considered by the law of mass action or as a pseudo-phase change still continues to attract attention. The latter approach has the great merit of simplicity and has been supported by certain experiments. In the phase-separation model the activity of the monomers should be constant above the critical micelle concentration (c.m.c.). Mysels has claimed that recent and more carefully executed ultrafiltration and surface-tension experiments show an increase in monomer activity above the c.m.c.and supports this with dialysis experiments on sodium dodecyl sulphate (SDS) solutions in his paper with Abu-Hamdi~yah.~ The cell they used per-mitted continuous monitoring of the composition of the dialysate and ex-periments were carried out to answer the criticism of their earlier data that the behaviour was concerned with impurities. Dialysis continues at all con-centrations although slower when micelles are present on both sides of the membrane. The data are considered in terms of a simplified mass-action model and fair agreement found. Further evidence in favour of the pseudo-phase separation model is presented ‘ J . Colloid interface Sci.1967,25 129. ’ SOC. Chem. Ind. Monograph 1967 No. 25. Discuss. Faraday SOC. 1966,42 7. Surface Sci. 1967 8 1. M. Abu-Hamdiyyah and K. J. Mysels J . Phys. Chuti. 1967,71 418. E 126 G. D. Parfitt by Nakayama and Shinoda.6 According to this model the Krafft point is the melting point of the hydrated solid surface-activity agent. Furthermore the solubility curve below the Krafft point (the solid-solute equilibrium curve) must intersect with the c.m.c. curve (the liquid-solute equilibrium curve) at the Krafft temperature. In this paper data are presented on the solubility of SDS and potassium perfluorooctanoate as a function of temperature ill the presence of added salts. The solubility is shown to decrease below the Krafft point in accordance with the solubility-product principle in the presence of salt.The c.m.c. decrease is inversely proportional to the 0.6 power of the gegenion concentration (approx.) and the point of intersection of the two curves shifts to a higher temperature on addition of salt as does the Krafft point. The data, the authors conclude therefore support the phase model. Further progress has been made in establishing values of the thermodynamic parameters involved in micelle formation. Emerson and Holtzer7 have estimated the contribution AG& of the hydrocarbon portion of the molecule to the standard free-energy charge AG," for the addition of one more detergent molecule to a micelle which already contains that number of monomers N most probable at the c.m.c. using the relation RTln(c.m.c.) = AG," = AG," + No is Avagadro's number E the magnitude of charge and IJJb the electrostatic potential at the surface of the micelle.Using light-scattering methods the c.m.c. and micellar weight were determined for SDS in NaCl solutions and for the cationics dodecyltrimethylammonium bromide DTAB (in NaBr), chloride DTAC (in NaC1) and nitrate DTAN (in NaNO,). The evaluation of IJJb using the Poisson-Boltzmann equation involved N from light scattering, the micellar radius (from published X-ray data) and the distance of closest approach of the ions to the micelle. Having thus estimated the electrostatic contribution the part played by the hydrocarbon chain was assessed and found for cationics to be independent of ionic strength and approximately independent of supporting electrolyte.For SDS a small dependence of ionic strength was found and the value for AG& (ca. 11 kcal. mole- ') is about 20% higher than that for the cationics. In another paper Emerson and Holtzer' have studied the effects of various additives on the stability of micelles of SDS and DTAB. The additives chosen were materials known to denature proteins (also compounds closely related to these denaturants) so that with the simpler micellar systems it might be possible to obtain information relevant to the disruption of protein structure which is assumed to be asso-ciated at least in part with the breaking of hydrophobic bonds. The tempera-ture-dependence of the c.m.c. in the presence of urea and substituted ureas, dioxan methanol ethylene glycol glycerol and sucrose has been evaluated, from which enthalpy and entropy changes were calculated.Qualitatively a ' H. Nakayama and K. Shinoda Bull. Chem. SOC. Japan. 1967,40 1797. ' M. F. Emerson and A. Holtzer J. Phys. Chem. 1967,71 1898. * M. F. Emerson and A. Holtzer J. Phys. Chem. 1967,71 3320 Colloid and Interface Science 127 correlation was observed between the hydrophobic nature of the additive and its micelle-breaking power but difficulties in interpretation arise when the additives penetrate the micelle i.e. structural changes as well as hydrophobic interactions and dielectric effects must be considered. Some indirect means of distinguishing penetrating from non-penetrating additives are proposed. It was concluded that it is not possible to take the numerical value of the c.m.c.as a single criterion for the hydrophobic bond strength in micelles. The c.m.c. is directly related (as mentioned above) to the standard free-energy change AG," and N is expected to vary with the additive through changes in the electrostatic as well as the hydrocarbon contributions. Qualitative conclusions could be drawn about hydrophobic bonds in micelles but some reservation was expressed about extension to protein denaturation. The effect of urea on the thermodynamics of micellisation of a series of octylsulphinylalkanols (C18H17SO(CH2)n OH with n = 2 3 4) and of alkyl trimethylammonium alkyl sulphates (C,C,SO with x = 10 8 and y = 10 8) has been reported by Corkill et aL9 The first series was used to study the effect of increasing the distance between the two hydrophilic centres while the second series permitted the effect of increasing chain length to be assessed.From surface-tension measurements (for the c.m.c.) and calorimetric data (for the heat of micellisation) the thermodynamic parameters AGO AH" and TAS" were calculated based on a standard state of unit mole fraction. It is shown that urea affects micellisation in two ways the interfacial energy between hydrocarbon and water is lowered thus reducing the free-energy differences between the alkyl chains in the solvent and those in the micelles thereby raising the c.m.c.; also by changing the degree of solvation of monomer it lowers the compensating heat and entropy terms associated with the solvent reorientation accompanying micellisation.The change in the environment of the hydrocarbon chain of a surface-active agent on micelle formation is considered in two papers which adopt rather different approaches to the subject. From measurements reported by Corkill, Goodman and Walker1' of the partial molar volumes above and below the c.m.c. of three series of compounds (n-alkyl trimethylammonium bromides [RN(Me),Br R = 8 10 12 14 and 161 sodium n-alkyl sulphates [RSO,Na, R = 10 12 and 141 and n-alkylsulphinyl alkanols [RSO(CH,),OH R = 6, 8 and n = 2,3 and 41 it was concluded that in the process of micelle formation the hydration of the methylene groups adjacent to the hydrophilic group is retained. Muller and Birkahn" have made use of the significant chemical shift in the I9F n.m.r. spectra when a molecule is transferred from an aqueous to a non-aqueous environment (the shift for hydrogen is much smaller).With a series of fluorinated soaps (CF,(CH,),CO,Na n = 8 10 and l l ) which judged by the c.m.c. are essentially similar to the ordinary alkyl carboxylates, the shifts in the fluorine n.m.r. signal on micelle formation is compared with J. M. Corkill J. F. Goodman S. P. Harrold and J. R. Tate Trans. Faraday SOC. 1967,63,240. l o J. M. Corkill J. F. Goodman and T. Walker Trans. Furaduy SOC. 1967,63 768. l 1 N. Muller and R. H. Birkhahn J . Phys. Chem. 1967,71,957 128 G. D. ParJitt those for CF,(CH,),CF3 in various solvents and show that the CF group in a micelle has characteristics about midway between that in water and hydro-carbon. This suggests considerable penetration of water into the micelle.The data also indicate that the shift is virtually independent of micelle size and added electrolyte. The density hydration shape and charge of micelles of SDS and dodecyl-ammonium chloride (DAC) have been considered by Stigter' in the light of published viscosity light scattering conductance self-diffusion and electro-phoresis data. This paper is an elaboration of a previous suggestion by the author (with Mysels 1955) that micelles have a rough surface. The model of liquid micelles is characterised by four parameters micellar weight micelle density hydration and electric charge (or surface potential). Considering these parameters and existing data Stigter concludes that (1) the shear surface coincides within 1"A with the surface enveloping the heads of the micellised ions (2) about half the total number of counterions are located inside the shear surface and (3) spherical micelles may grow into flexible rods.Further evidence on the binding of counterions to micelles has been obtained from e.m.f. measurements on a number of surface-active materials (potassium caprate laurate and myristrate; sodium caprate and SDS) by Feinstein and Rosano.' Using a cell combining a standard calomel electrode and a cationic glass electrode the activities of K+ or Na' were measured above and below the c.m.c. Assuming that the number of micelles only increased above the c.m.c. and that the number of anions per micelle remained constant values of the apparent degree of dissociation of cations from the micellar unit just above the c.m.c.were estimated and are as follows KClo 0-79 KC, 0.69 KCI4 0.24 Na Cl0 0-57 and SDS 0-14. Doubt still exists about the dependence of micellar weight of ionic surface-active agents on ionic strength as indicated by light-scattering data. Schott's earlier work (1966) with anionics (sodium decane sulphonate and SDS) and non-ionics (two C, ethylene oxide condensates) showed that the dye solubili-sation method gave good agreement with light-scattering and ultracentri-fugation data for the non-ionics and for the SDS in the presence of swamping electrolyte. Apparently one dye molecule was solubilised by each micelle and since in the absence of electrolyte the micellar weight (by light scattering) of SDS is significantly smaller than in excess electrolyte some doubt was cast on the value of the former and on the use of light scattering to determine micellar weight.Now this work has been extended14 to cationics (DTAB and cetyl pyridinium chloride) and to non-ionics with a larger hydrocarbon core [nonylphenol(EO), and C, (EO)18]. The same micellar weights were obtained by light scattering and dye solubilisation (assuming one dye molecule per micelle) for nonylphenol (EO), and DTAB but for the others the light-scattering value was a factor of three larger i.e. these detergents solubilise l2 D. Stigter J . Colloid Interface Sci. 1967 23 379. l 3 M. E. Feinstein and H. L. Rosano J . Colloid Interface Sci. 1967 24 73. l4 H. Schott J . Phys. Chern. 1967,71,3611 Colloid and Interface Science 129 three dye molecules per micelle.Schott therefore concludes that the dye solubilisation method is not an absolute method for determining micellar weights but it can be used to show relative changes on addition of solubilised impurities or electrolytes and provides the lowest possible value for the. micellar weight. Again the results showed little or no effect of added electrolyte on the micellar weight of ionic detergents in contradistinction to light-scattering data. In the light-scattering method for micellar-weight determination of non-ionic systems it is often possible to interpret the data in terms of the formation of micelles whose average molecular weight is independent of concentration and temperature. However the turbidity data at 22 32 and 42" for the octylsulphinylalkanals (the same compounds as discussed earlier) obtained by Corkill Goodman and Walker" show large deviations from ideal behaviour and the Debye plots are such that reliable micellar weights cannot be obtained from the intercepts.Two limiting cases are considered by the authors in their interpretation. The first involves the interactions in a system containing micelles whose size is concentration independent; this is treated using the Flory-Huggins model for a solution in which there is a large difference in the size of the solvent and solute molecules but is not very successful although the possibility of a concentration-independent size is not excluded. However, more success is achieved with a model in which the spherical micelles are assumed to undergo reversible association similar to that of a protein (the Debye plots for these systems and insulin are similar) and some viscosity data show best agreement with this model.Confirmation of the validity of the aggregation model requires further information from transport processes, which are thermodynamically irreversible and therefore do not depend directly on solution non-ideality. Some related information is reported by Ottewill Storer and Walker.16 The micellar weight of dodecyl hexa-oxy-ethylene glycol monoether in D,O has been determined by the Archibald method of approach to sedimentation equilibrium as a function of temperature. The apparent micellar weight remains constant at 5-1 5" at about 50,000 and then increases rapidly with temperature up to 840,000 at 35" in good agree-ment with published results using the light-scattering method.Examination of the system by sedimentation velocity and viscosity experiments suggest that the kinetic unit changes in size with changes in concentration and temperature. It is concluded that the evaluation of true micellar weights requires a know-ledge of the dependence of activity on concentration and temperature. Some comments on the use of dyes to tag micelles for the measurement of transport properties (electrophoresis diffusion and dialysis) have been made by MyseIs.l7 Since the concentration of dye used is so small that micelles seldom contain more than one dye molecule then in principle the tagged and untagged micelles are essentially the same size and have the same transport J.M. Corkill J. F. Goodman and T. Walker Trans. Faraday SOC. 1967,63 759. l6 R. H. Ottewill C. C. Storer and T. Walker Trans. Faraday SOC. 1967,63,2796. I' K. J. Mysels J . Colloid Interface Sci. 1967,23 474 130 G. D. Parfitt properties. But the micelle might swell says Mysels and if the micelles are heterodispersed the effect will be more significant. The thermodynamics of introducing only one dye molecule per micelle is examined and it is shown that the tagged distribution is skewed towards larger micelles so that the number-average micellar weight of the tagged distribution equals the weight-average value for the untagged one. The probability of finding a dye molecule in a micelle is proportional to the number of molecules in the micelle hence larger micelles are more likely to be tagged in proportion to their size and are more frequent in the tagged distribution.Tagging means that diffusion and dialysis will be apparently slower but the effect on electrophoresis depends on whether the zeta potential or the degree of ionisation tends to be constant with size. The entropy change associated with micelle formation in aqueous media is normally associated with the changes occurring in the solvent. Hence it is to be expected that significant effects are observed when the thermodynamic parameters are evaluated in alcohol-water mixtures. Such is the case for dimethyl dodecyl phosphine oxide in ethanol-water mixtures reported by Herrrnann and Benjamin.'* Light scattering is used to determine the c.m.c.and micellar weight and calorimetric data for AH" so that changes in AS" may be evaluated. The c.m.c. increases slightly as the ethanol concentration is changed from %20% (by volume) and then increases markedly at higher ethanol concentration while becoming increasingly less well defined. A significant decrease in micellar weight (550,000-44,000) occurs from 0-10 % ethanol beyond which the decrease is less marked until the value is 170 in pure ethanol (the molecular weight of the monomer is 246). AHo and ASo values decrease considerably over the range %20% ethanol and then at higher concentrations remain almost constant. These data indicate a reduction in the amount of ordered water that is released during micelle formation when ethanol is present and represent weakened hydrophobic bonding.A change in micelle shape is proposed (rodlike or cylindrical to spherical) as the ethanol concentration is increased. These results are consistent with the current picture of the part played by the water in micelle formation. Data on micelle formation of detergents in hydrocarbon solutions are few, and their reliability is a function of the amount of water present. Sharma, Cowie and SiranniI9 have examined the behaviour of a poloxyethylated nonylphenol ether (about 10 moles ethylene oxide per mole of hydrophobe) in hydrous and anhydrous cyclohexane at -45" by light scattering and by vapour pressure in dry solvent at 39.1". Complex behaviour was observed dependent on the relative proportions of detergent and water.Water appears to have a marked effect on the aggregation of the non-ionic in cyclohexane; the aggregation number rises from about 4 (difficult to be accurate with dry solutions) to 8 as the mole ratio of added water is increased to about 0.28 and K. W. Herrmann and L. Benjamin J . Colloid Interface Sci. 1967 23,478, l9 R. K. Sharma J. M. G. Cowie and A. F. Sirianni J . Amer. Oil Chemists' SOC. 1967,44 488 Colloid and Interface Science 13 1 then rises more steeply until phase separation occurs beyond a mole ratio of 2.4. The difference between the weight and number averages is very small in the dry solvent. The relationship between the cloud point and the micellar properties (c.m.c. and micellar weight) of aqueous solutions of polyoxyethylene nonylphenol ethers (n = 10 15 and 20) has been investigated by Arai2' using light-scattering and surface-tension methods.The c.m.c. increases and the micellar weight decreases as the cloud point rises with growing chain length increasing amounts of ethanol or decreasing amounts of sodium sulphate. In the case of the c.m.c. the relationship is almost linear. There has been some discussion in the literature as to whether certain detergents form dimers below the c.m.c. but the evidence has been conflicting and to some extent a function of the technique used. Clunie Goodman and Symons2 have analysed their conductance data for aqueous solutions of members of the homologous series of sodium n-alkyl sulphonates [alkyl chain length n = 2-14 (even nos.)] in terms of the Onsager theory and conclude that only in the case of the tetradecyl salt is their any deviation that might be ascribed to dimerisation of the long-chain ions.The protection provided by organic compounds (in particular n-hexanol) when solubilised in SDS micelles to the precipitation of the detergent by calcium ions has been demonstrated by Pearson and Lawrence.22 A 2% SDS solution containing hexanol in the mole ratio (hexanol):(SDS) of 1.25 can tolerate 0.018~ CaCl without precipitation at 25" but without hexanol the concentration is 0.006~. Measurements of sodium-ion activity in the various systems allowed the contribution of each species to be determined and a mechanism is proposed involving exchange of the sodium ions with calcium at the surface of the micelles which is enhanced when the micelles contain solubilised hexanol.Hexanol is assumed to cause increased ionisation of the micelles leading to salting-in of the sparingly soluble calcium dodecyl sulphate. A second paper by the same describes a study of the relationship between changes in the electrical conductivity of soap solutions on addition of organic additives and the changes in the ionic activity of the detergent. The increases in equivalent conductance with additive (n-aliphatic alcohols with n = 2-7) concentration are correlated with increases in counter-ion activity ; as n increases there is a greater tendency for the alcohol to penetrate into the micelle causing separation of the head groups decrease in repulsion and release of counter-ions. There has been little published on the solubilisation of water in non-aqueous solutions of non-ionic surfactants and in particular the effect of temperature.Shinoda and O g a ~ a ~ ~ describe a study of the solubilisation of water in solu-tions of poloxyethylene nonylphenol ethers ( n = 5.2,6.0,7.4,9.6 and 14.0) in a '() H. Arai J. Colloid Interface Sci. 1967,23 348. " J. T. Pearson and A. S. C. Lawrence Trans. Faraday SOC. 1967,63,488. 23 A. S. C. Lawrence and J. T. Pearson Trans. Faruday SOC. 1967,63,495. 24 K. Shinoda and T. Ogawa J . Colloid Interface Sci. 1967,24 56. J. S. Clunie J. F. Goodman and P. C. Symons Trans. Faraday SOC. 1967,63,754 132 G. D. ParJitt variety of hydrocarbon and halogenocarbons. Solubilisation of water is large at the optimum temperature (when the solubility and cloud-point curves meet) for solutions containing 2-15 % wt.% of detergent in which micelles exist. The effect of chain length and type of solvent and the effect of temperature are reported providing a useful correlation for the selection of a suitable non-ionic surfactant for the solubilisation of water in various solvents. Thermodynamic data for water solubilisation in non-aqueous solutions of polyoxyethylene nonylphenol ethers (n = 6 7 and 8) or Aerosol OT are provided in the paper by Kitahara Ishikawa and Tanim01-i~~ (such data have not been reported previously). By measuring the vapour pressure of water at different tempera-tures the heat of solubilisation (AH,) was determined using cyclohexane, perchloroethylene and benzene as solvents. With increasing solubilisation in the first two solvents AHs decreased for Aerosol OT and increased for non-ionics while in benzene the curves for the non-ionics show a minimum.All the AHs curves approach the latent heat of vaporisation of water and the data explained qualitatively in terms of the forces (non-dipole and hydrogen bonding) involved. The Liquid-Liquid Interface.-An investigation on the effect of molecular structure and unsaturation on the initial spreading pressure (Fh) and initial spreading coefficient (Sb,) on water of numerous pure low-boiling members of the n-alkane 1-alkane n-alkyl benzene and acetylene hydrocarbon series has been reported by Pomerantz Clinton and Zisman.26 It is shown that from F b and the surface tensions of water (y,) and the organic liquid (yb) it is possible to calculate the initial value of the reversible work of adhesion (wba) and the initial interfacial tension (yab) using the relations (derived) The effect of unsaturation and isomerism on Fb (obtained using the piston monolayer method) W and yab is determined and from the data the molar free energy of adhesion of hydrocarbons to water arising from the hydrophilic nature of unsaturated carbon-carbon bonds is assessed.Although the data are not comprehensive values for the molar free energies for the terminal olefinic group (CH2=CH-) and the aromatic double bond of 1030 and 393 cal./mole respectively have been estimated. Such comparisons are not possible with hydrocarbons from surface pressure versus area measurements. A more convenient method of measuring the value of the critical surface tension yc of a liquid a based on a plot of Sb of liquid b on liquid a versus Yb is discussed by Shafrin and Zi~man.~’ The method has two advantages over the preceding methods first it eliminates measuring the contact angle (which presents difficulties) and second it does not require that yc should fall within a range of surface tensions exhibited by the collective members of the series of homologous spreading liquids.A rapid and reliable method for measuring 2 5 A. Kitahara T. Ishikawa and S. Tanimori J . Colloid Znterfnce Scz. 1967,23 243. 26 P. Pomerantz W. C. Clinton and W. A. Zisman J . Colloid Interface Sci. 1967,24 16. 2’ E. G. Shafrin and W. A. Zisman J . Phys. Chem. 1967,71 1309 Colloid and Interface Science 133 S is discussed in the paper mentioned above.25 The value of yc for the water-air interface has been determined using several homologous series of pure hydro-carbon liquids (normal and branched alkanes and alkenes) and the loyest value found was yc = 21.7 dynes/cm.at 20". Since the results are analogous to those already published for solid surfaces it is concluded that the clean surface of water behaves as a low-energy surface with respect to low-polarity liquids, as expected if only dispersion forces are operative between each alkane and water. High resolution n.m.r. spectroscopy has been used to study the molecular interactions and mobility at liquid-liquid interfaces by Zlochower and Schulman.28 Spectra were taken of the various phases (isotropic viscous birefringent and a low-viscosity second isotropic) formed when a concentrated aqueous solution of DTAB is titrated with chloroform.The changes in line width of the long-chain methylene resonance in DTAB reflect the mobility of the chain in the various phases while the broadening of the H,O resonance provides evidence for the binding of the water at the interface. Ion-dipole association between CHC1 and DTAB is indicated by the large downfield shift of the CHC1 resonance. The theory of Vonnegut for the measurement of interfacial tension from the shape of a fluid drop in a horizontal rotating tube filled with a liquid of higher density has been extended by Princen Zia and Mason.29 Numerical solutions based on exact equations are presented from which it is possible to calculate the interfacial tension from the length of the elongated drop along the axis of rotation knowing the values of drop volume speed of rotation and difference in density between the two phases.Previous attempts were seriously limited by the optical correction involved in measuring the drop shape. The authors have developed an experimental method based on the measurement of drop length without the need for optical correction. Results for the system n-hexadecane-glycerol heptane-glycerol (and air-glycerol) show good agreement (within 3 %) with other methods (pendant drop ring tensiometer). Two papers deal with the interfacial tension at the hydrocarbon-water interface. Using the pendant-drop method and an apparatus of new design capable of measuring 0.001 dyne/cm.at high temperature and pressure, Jennings,' has measured the interfacial tension of benzene-water and n-decane-water in the intervals 25-1 76" and 1-8 17 atmospheres. The effect of temperature is much greater than that of pressure and the general equation for the interfacial tension is y = a + a,P + a (t - 25) where t is in degrees centigrade. Values of the constants for the two systems are given. These data are of practical interest because of the increasing depths of new oil discoveries and the injection of heat in low-temperature reservoirs to assist oil recovery. In the second paper Gillap Weiner and Gibaldi consider the linear increase I. A. Zlochower and J. H. Schulman J . Colloid interface Sci. 1967,24 11 5. 29 H. M. Princen I.Y.Z.Zia and S.G. Mason J . Colloid Interface Sci. 1967,23,99. 'O H. Y. Jennings J . Colloid Znterface Sci. 1967,24 323. 31 W. R. Gillap N. D. Weiner and M. Gibaldi J . Amer. Oil Chemists' SOC. 1967,44 71. 134 G. D. Parfitt in interfacial tension at 25" of n-alkane-water [chain length n = 6-16 (even nos.)] systems with the log of the chain length. Contrary to previously published data it is found that the values of @ in the Girifalco and Good equation of yiz0 the dispersion force component for water are not constant but vary in a regular manner with the log of the hydrocarbon chain length. Furthermore the relationship between chain length and interfacial tension is opposite to that predicted by Antonow's rule y12 = /yl + y2/. A model for the interface involving water structure is devised to explain the chain-length dependency of the interfacial properties of the hydrocarbons.A comprehensive set of interfacial-tension data for the adsorption of highly purified SDS from aqueous solutions at the air-water and water-hexane, octane nonane decane heptadecane hexene octene cyclohexane cyclo-hexane benzene butylbenzene and carbon tetrachloride interfaces at 25" is reported by Rehfeld3* (previous data were limited to decane heptane and petroleum ether). The interfacial tension versus log concentration data below the c.m.c. were fitted to a polynomial of the second degree. Organic molecules containing x-electrons give much lower interfacial tensions than the n-alkanes, whereas molecules with dipoles give only slightly lower tensions.The effect of the organic liquid on the c.m.c. and the free energy of micelle formation and the concentration of SDS (evaluated using the Gibbs equation) at each of the organic liquid-water interfaces when the bulk concentration is the c.m.c. are qualitatively correlated with the solubility of the hydrocarbon in the micelles. Electrocapillary curves of oil-water systems containing surface-active agents have been discussed in two papers by Watanabe et a1.,33? 34 using KCl in the aqueous phase and ionic detergents (anionic and cationic) in the oil phase (various polar organic solvents). The interfacial tension was suppressed over the cathodic or anodic polarization range by cationic or anionic agents respectively and using the Lippmann-Helmholtz equation it was concluded that the water side of the interface was charged positively or negatively for the two cases.This charge is assumed to be due to the counterion layer associated with the adsorbed agent on the oil side. In the second paper the effect of cation (or anion) valency of the electrolyte in the aqueous phase is discussed. Over the cathodic branch the suppression of the interfacial tension is greater the larger the crystal radius of the anion and the reverse for the anodic branch. The data demonstrate the applicability of the technique to the study of the oil-water interface under controlled electrical conditions which should lead to a better understanding of the adsorption mechanism at this interface. An investigation of specific adsorption at the mercury-methanol interface is reported by Garnish and parson^.^' The marked difference in behaviour of " S.J. Rehfeld J . Plrys. Chem. 1967,71 738. 3 3 A. Watanabe M. Matsumoto H. Tamai and R. Gotoh Kolloid-Z. 1967. 220 152. 34 A. Watanabe M. Matsumoto H. Tamai and R. Gotoh Kolloid-Z. 1967,221,47. 35 J. D. Garnish and R. Parsons Trans. Faraday SOC. 1967,63 1754 Colloid and Interface Science 135 methanol and water in the capacity curve for the inner layer in the absence of specific adsorption had not previously been adequately explained. By studying the temperature coefficient of the potential at the zero point of charge and the adsorption of di-n-butyl ether it was concluded that when the mercury is uncharged the methanol dipole is oriented with its negative end towards the mercury.From capacity and electrocapillary curves the adsorption isotherms of iodide ions and of thiourea from methanol solutions were determined and found to be associated with a free energy of adsorption which is a linear function of the charge on the metal and a charge-dependent interaction co-efficient. Certain similarities exist in the behaviour of thiourea in methanol, water and formamide ; the two-dimensional second virial coefficients are similar suggesting similar properties of the inner layer in the three solvents, i.e. the effective dielectric constant is similar. Larger differences were found with the iodide ion; the virial coefficient is very large and this is the cause of the absence of adsorption humps in the capacity curves with methanol.The study of the structure and properties of black lipid membranes leads to useful information on various phenomena of biological and technological importance (adsorption colloid stability cell biology etc.). Tien36 has measured, using a new technique (described) the interfacial free energy of black lipid membranes of less than 100 in thickness separating two aqueous solutions, and prepared from cholesterol dissolved in n-dodecane with dodecyl acid phos-phate dioctadecyl phosphite and hexadecyl trimethylammonium bromide (HTAB) as stabilising agents. The ability to form a stable black film is shown to depend on both the interfacial free energy and the c.m.c. of the agent; the forma-tion of stable films is not limited to the use of chemical phospholipids. The electrical properties of cholesterol-n-dodecane-aqueous HTAB system is reported by Tien and Diana,37 and also includes measurements with various neutral electrolytes in addition to the HTAB in the aqueous phase.The trans-verse membrane resistance is dependent both on the electrolyte and the anionic species used the order of the effect of the anion on the decrease in resistance observed being I- > Br- > SO:- > C1- > F-. A qualitative explanation of the effect is proposed in terms of an interaction between the HTA’ and anion at the membrane-water interface. Membrane capacitances were also measured as a function of salt concentration and type and considered qualita-tively in terms of the electrical double layer at the interface. Emulsions. An exact method of solution of Smoluchowski’s equations for the kinetics of the rapid coagulation of emulsions is given by Rice and White-head.38 Smoluchowski’s original theory based on diffusion of the dispersed particles makes a number of assumptions (spherical particles no attractive forces except on contact etc.) and readily gives an expression for the collision rate.The simplifying assumption of Smoluchowski that the product (ri + rj) (r; + r, ’) may be replaced by 4 ri and rj being the radii of any pair of co-36 H. T. Tien J . Phys. Chem. 1967,71,3395. 37 H. T. Tien and A. L. Diana J . Colloid Interface Sci. 1967 24 287. C. L. Rice and R. Whitehead J . Colloid Interface Sci. 1967,23 174 136 G. D. Parfitt agulating particles is discarded in this treatment for emulsions and an exact solution is obtained for the case of particles which on collision coalesce into a third spherical droplet.The time-dependence of the intensity of light scattered by a coagulating emulsion is also analysed. The deviations from Smoluchowski’s original expressions are found to be surprisingly small because the low degree of polydispersion associated with times less than the half-life for the emulsion. It is also indicated how the theory may be modified to take into account mutual forces between droplets incomplete adhesion on collision orthokinetic coagu-lation due to sedimentation delayed coalescence and the breaking up of uncoalesced aggregates. A quantitative study of the role of pepsin as emulsifier in the stability of Niijol in water emulsions has been reported by Prakash and Sri~astava.~’ Particle counts were made haemocytometrically to study the coagulation of the emulsions as a function of pH electrolyte concentration and emulsifier concentration ; the electrophoretic mobility was also measured.Using the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory of stability of lyo-phobic colloids the interaction energies have been calculated for different surface potentials and ionic strengths and with classical double-layer theory the charge densities in the Stern and Gouy layers were estimated. The assumption is made that the coagulation sets up a temporary singlet-doublet equilibrium after a time t > a2/D (a = particle radius D = diffusion coefficient). By counting the singlets and doublets the experimental degree of aggregation was calculated and compared with those calculated theoretically using various values of the Hamaker constant A.It is concluded that coagulation into the secondary minimum occurs with A = 6 x erg; the energy barriers are too high for primary minimum coagulation. The factors responsible for the formation of micro-emulsions are considered by Prince.40 Schulman’s theory (1959) for the formation of emulsions stabilised with oleate soaps and long-chain alcohols indicates that the condition for the formation of these small particle (8&800 A diameter) emulsions is that x > yo/w whereas when x c only a macro-emulsion (particles ca. 1 p diameter) would form. Here n is the spreading pressure (n = yo,w - y where y is the total interfacial tension and yo,w that of the oil-water interface in the absence of stabilising agents) in the monolayer of adsorbed species.When n 3 yo,w energy - y dA ( A = surface area) would be available to increase the total surface area hence a micro-emulsion would form. However recent data with mixed films of soaps and alcohols suggest the need for a re-assessment of these factors which Prince has carried out in his paper. The initial negative interfacial tension is now assumed to be due to a large depression of yo, rather than a high x the depression arising from the spontaneous distribution of alcohol molecules between the interface and the oil phase. Rehfeld4’ describes a new method of studying the particle-size distribution 39 C. Prakash and S. N. Srivastava Bull.Chem. SOC. Japan. 1967,40 1756. 40 L. M. Prince J. Colloid Interface Sci. 1967,23 165. 41 S. J. Rehfeld J . Colloid Interface Sci. 1967 24 358 Colloid and Interface Science 137 of mechanically prepared hydrocarbon in water emulsions. This technique has been developed to overcome the problems associated with handling and dilution in the normal microscopic method. A small amount of polymer is dissolved in the hydrocarbon to be emulsified and the hydrocarbon is subse-quently removed by thermal distillation or dilution leaving a polymer dispersion which is counted in a Coulter Counter. The technique was used to study the particle size of benzene in water emulsions as a function of the initial surfactant (SDS) concentration and emulsification time. It is shown that the steady-state particle size decreases with increasing concentration of SDS up to the c.m.c., above which it remains constant.The time to reach the steady-state value increases linearly with increasing surfactant concentration. S h i n ~ d a ~ ~ has correlated the dissolution state of a non-ionic surfactant with the curvature of the adsorbed monolayer of surfactant at the hydrocarbon-water interface and the stability and type of emulsion as a function of tempera-ture. In his analysis he has used such experimental facts as micellar dispersion, the clouding phenomena and the temperature-dependence of the solubilisation of the hydrocarbon (or water) in aqueous (or non-aqueous) surfactant solutions. It is found that the phase-inversion temperature in emulsions corresponds to the temperature at which the hydrophilic-lipophilic property (HLB value) of the surfactant balances for a given hydrocarbon-water system.Hence phase-inversion temperature data are useful in interpreting emulsion behaviour and as a guide for the selection of an emulsifier. The Liquid-Vapour Interface.-A knowledge of the concentration profile of a system containing two fluid phases in direct contact enables the surface excess thermodynamic properties of the system to be determined. Lattice models have been used with a plane interface of several molecular diameters in thickness and the concentration profile is given by the solution of a non-linear second-order difference equation but the computations are laborious and few data are available. Using a computer Lane and Johnson43 have attempted to obtain an exact solution assuming it to be symmetric using a method described by Ono (1947) but without success and propose a method of successive approximations which is an extension of the two-layer interface calculations of Defay and Prigogine.This method provides a well-defined, self-consistent approximate solution without assuming that the final solution is symmetric. By interpreting the internal latent heat (Li) of a liquid as the excess of energy which the surface layer of a liquid removed from the parent liquid possesses over that possessed by an equal mass of the liquid Ramanadha~n~~ has ob-tained the following relation for the thickness of the surface layer 42 K. Shinoda J. Colloid Interface Sci. 1967 24,4.43 1. E. Lane and C. H. J. Johnson Austral. J . Chem. 1967,20,611. 44 M . Ramanadham Indian J. Pure Appl. Phys. 1967,5,369 138 G. D. Parfitt where p" is the density of the surface layer and z its thickness and y is the surface tension of the liquid. The calculated values of z for various liquids are of the order of magnitude usually associated with the dimension of molecules (at 20" z 7-6 A for benzene 1.9 A for water 2.3 A for methyl alcohol etc.) and increase with temperature. Surface tension. Several theories of surface tension of liquids have been published and that of Ree Ree and Eyring (1964) using significant-structure theory gives a simple equation which is approximate but yields good results. However it includes the Lennard-Jones 6-12 potential whose characteristic constants are available only for simple liquids and hence the application of the equation is limited.Lu et aL4' have derived another simple equation of surface tension using significant-structure theory by introducing the approximation that the surface of liquids consists of a monomolecular layer in which the molecule has a sublimation energy different from that for a bulk-liquid mole-cule. The agreement between calculated and observed values for a variety of liquids of monatomic diatomic and polyatomic molecules including liquid metals is overall satisfactory although there are marked exceptions e.g. A controversy has existed as to whether water has a dynamic surface tension, and this has stemmed from the fact that certain dynamic methods notably the oscillating jet leads to a time-dependent surface tension.Either the technique gives erroneous values or water does have a dynamic surface tension and Vandegrift46 has shown which is correct. He measured the surface tension, using the oscillating jet of a liquid having the same physical properties as water but with no association and having nearly the same velocity character-istics (carbon tetrachloride was chosen) and found similar time effects. From this and experiments with different size orifices he concluded that water has no dynamic surface tension in the millisecond range and that any time-dependent effects in this region are probably due to an inadequate mathematical descrip-tion of the process and not to liquid structure effects. The surface tension-temperature relationship for water is described by C l a ~ s s e n .~ ~ Data have been analysed by the method of Eotvos (1886) which permits the calculation of extensive surface properties as a function of temperature for an amount of surface that always contains the same number of molecules; the surface layer of molecules is assumed to expand with temperature in the same ratio as does the interior liquid. Thus the extensive surface property of surface free energy AGs of a fixed number of molecules (comprising 1 cm. of surface at 4") is calculated by dividing the surface tension by of the density allowing enthalpy and entropy data to be evaluated. The corrected surface tension is a linear function of temperature and the derived values of the extensive thermodynamic properties (based on 1 cm.2 of surface at 4") are : AGs = +75.74 erg (at O O ) AHs = + 115.42 erg and ASs = +0.1453 erg/% Hg NH,,C6H,.45 Wei-Chen Lu Mu Shik Jhon T. Ree and H. Eyring J . Chem. Phys. 1967,46 1075. 46 A. E. Vandegrift J . Colloid Interface Sci. 1967 23,43. 47 W. F. Claussen Science 1967 156 1226 Colloid and Interface Science 139 which become +2120 cal./mole of surface +3231 cal./mole of surface and + 4-067 entropy units/mole of surface respectively when a hexagonal surface structure is assumed. For binary liquid mixtures a theory of surface tension is proposed by Shere~hefsky~~ leads to a general expression of the form where y yl and y2 are the surface tensions of the mixture and of pure com-ponents 1 and 2 respectively x2 the mole fraction of 2 in the bulk region and AG is the free-energy change in the surface region when solvent (1) is replaced by a mole of solute (2) occupying an area A2/t with t = molecular thickness of the surface region.The equation is applied to seventeen binary liquid mixtures of organic liquids (over the whole range of mole fraction) and the agreement is shown to be good. Values of t derived from the data assuming values of A, are unity in most of the cases (unity corresponds to one molecular diameter of component 2). Those which deviate from unity are interpreted in terms of molecular orientation in the surface layer. Sprow and P r a ~ s n i t z ~ ~ have demonstrated that the surface tensions of mixtures of simple liquids can be predicted satisfactorily from a model based on a regular surface solution with molecules of similar size and dispersion forces predominating.The agreement for such mixtures as carbon tetrachloride-chloroform and neopentane-benzene is within experimental error. For com-plex systems the use of a parameter 01 reflecting the difference in characteristic energy between the bulk liquid and the surface leads to a good fit of the data for a number of associated systems e.g. ethanol-water acetone-chloroform etc. Eberhart’s (1966) equation for the surface tension of liquid mixtures has been shown to fit the data for a variety of systems. The equation involves an empirical constant which Ramakrishna and Suri” show is given by s = exp(y1 - ./2)A2/RT and values of S calculated from the two equations are compared for various liquid mixtures including molten electrolytes and metals.A similar conclusion is reached by S~hmidt.~ The success of the equation is probably because of the validity of the assumption that (f3‘fI)/(f;1,) = 1 where f = activity co-efficient and superscript s refers to the surface phase. Although many values of surface tension of surfactant solutions are reported it is rare that various methods of measurement are compared for one system. Boucher Grinchuk and Zettlem~yer~~ have measured the static surface 48 J. L. Shereshefsky J . Colloid interface Sci. 1967 24 317. 49 F. B. Sprow and J. M. Prausnitz Canad. J. Chem. Eng. 1967,45 25. 5 1 R. L. Schmidt J. Phys. Chem. 1967,71 11 52. 5 2 E. A. Boucher T. M. Grinchuk and A. C. Zettlemoyer J. Colloid Interface Sci.1967 23 600. V. Ramakrishna and S. K. Suri. lndian J. Chem. 5,310 1967 140 G. D. ParJitt tension at 25” of aqueous solutions of sodium chloride and sodium hexyl a-sulphopelargonate using the Wilhelmy plate drop-volume and pendant-drop methods. They conclude that the first two methods give reliable results which differ by no more than 1 5 % . Their pendant-drop apparatus lacked precision but gave values in accord with those of the other methods. For dynamic surface tension the technique used depends on the age of the surface; up to 30 milliseconds old the jet methods are used and for surfaces older than 200 milliseconds the excess bubble-pressure apparatus is convenient. However, for surfaces of ages 30-200 milliseconds there had been no useful method published until Austin Bright and S i m p ~ o n ~ ~ reported their extension of the maximum bubble-pressure technique by use of stroboscopic counting since the limitation in the normal method is the rate at which the bubbles can be counted visually (the limit is about 5 per second).Using the stroboscopic method rates of up to 50 per second were successfully determined. The dynamic surface tensions of Manoxol OT (Aerosol OT) in aqueous and aqueous NaCl solutions are reported. A new equation of state of mixed adsorbed spread or penetration mono-layers is presented by J 0 0 . s ~ ~ and tested for the system sodium laurate and sapoalbin which have very different saturation-adsorption values (previous attempts are applicable to systems for which the saturation values are equal).Agreement between theory and experiment is considered satisfactory. Soapfilms. One method of investigating the properties of the aqueous core of a foam film is the measurement of film conductance parallel to the surface and interpretation of the results in terms of surface conductivity although this method has received little attention. In their paper Clunie et u E . ~ ~ describe simultaneous measurements of thickness and conductivity on foam films drawn from aqueous solutions of the neutral surfactant C,6H33N+Me, (CH2)3SO; (C 6 sultaine) containing NaBr. The surface monolayers are formally uncharged and adsorb inorganic ions to produce an electrolyte excess in the core; the film ruptures when the thickness falls below that cor-responding with the secondary minimum (of the DLVO theory) arising from double-layer overlap between the two monolayers.The zeta potential calcu-lated using Bikerman’s theory of surface conductance decreases with in-creasing electrolyte concentration. Mysels and Joness6 have described a method using soap films for the direct measurements of the double-layer repulsion with distance hence forming a qualitative test of the DLVO theory. A soap film is formed in a ring of porous porcelain whose pores communicate to the outside with the film in an enclosure in which the air pressure can be varied. By applications of large pressure differences between air contacting the free surfaces of the film and the bulk liquid in the pores of the solid the film can be subjected to stresses exceeding ’’ M.Austin B. B. Bright and E. A. Simpson J . Colloid Interface Sci. 1967 23 108. 54 P. JOOS Bull. Soc. chim. belges. 1967 76 591. ’’ J. S. Clunie J. M. Corkill J. F. Goodman and C. P. Ogden Trans. Faraday SOC. 1967,63,505. ’‘ K. J. Mysels and M. N. Jones Discuss. Faraday Soc. 1966,42,42 Colloid and Interface Science 141 one atmosphere. The applied pressure is balanced primarily by the double-layer repulsion between the monolayers of the film so that as the pressure is increased the thickness decreases indicating how the double-layer repulsion varies with distance. SDS and sodium tetradecyl sulphate solutions were used and satisfactory agreement with theory was obtained for the region of low potentials which determined the slopes of the distance function.Reasonable agreement is found in the absolute values the calculation of which make certain assumptions about the high-potential region and film structure. In the thinning of soap films at short distances (10-20 A) the stability is governed by the interaction between solvation layers and any closer approach entails desorption which manifests itself as a rapidly increasing repulsive force as successive solvation layers are removed. This implies that primary-minimum (or Perrin) films are subject to very large pressure differences before they can be further thinned. In an investigation of this effect Clunie Goodman, and Symons5’ have measured film thickness of films from decyl trimethyl-ammonium decyl sulphate solutions containing NaBr as a function of relative water-vapour pressure.The results indicate that a strong repulsive force indeed exists which prevents film collapse at a limiting equilibrium thickness of 40 A corresponding to a thickness of the aqueous core of 12A. The magnitude of this force is of the order of that required for desolvation. A study of the stability of black films drawn from aliphatic hydrocarbon (n = 6 10 12 and 14) solutions of normal alkyl chain esters (n = 14 16 18, and 22) has been made by Taylor and Haydon.’* The film thickness is not determined by the chain length of the hydrocarbon solvent but the hydro-carbon part of the film is equal to twice the chain length of the ester molecules. Theoretical consideration of the force associated with the steric interference of the alkyl chains at the two interfaces on thinning indicates that a repulsion sufficient to stabilise the film comes into operation immediately the film becomes thinner than twice the chain length of the stabiliser.This study provides convincing evidence that interaction between the alkyl chains adsorbed on two approaching surfaces is responsible for the stability. It is generally assumed that the permeation of gases through insoluble monolayers is best described by an energy-barrier theory. The work of Princen, Overbeek and Mason59 suggests that for soluble monolayers the transport is governed by a simple diffusion mechanism which may be through aqueous pores between the surfactant molecules. Previously reported data of the authors on the permeability of very thin soap films (HTAB and NaBr) to various gases (He Ne Ar O, N, H, CO, and N,O) have been re-analysed, and the simple theory explains the results.A new technique for measuring film elasticity is described by Prins Arcuri, and van den Tempel,60 which involves simultaneous measurement of the ’’ J. S. Clunie J. F. Goodman and P. C. Symons Nature 1967,216 1203. ’* J. Taylor and D. A. Haydon Discuss. Faruday Soc. 1966,42 5 1. ” H. M. Princen J. Th. G. Overbeek and S. G. Mason J. Colloid Interface Sci. 1967 24 125. ‘* A. Prins C. Arcuri and M. van den Tempel J . Colloid Interface Sci. 1967 24 84 142 G. D. Parfitt increase in surface tension and the corresponding change in thickness. The measured elasticity of films drawn from aqueous solutions of SDS sodium decyl sulphonate and cetyl trimethylammonium bromide (CTAB) above and below the c.m.c.is compared with the composition and thickness of the films. As predicted by theory the Gibbs elasticity decreases with increasing film thickness and the agreement with theory of the relation between elasticity and composition is satisfactory provided the surfactant is pure. Insoluble monolayers There has been no systematic research published on the retardation of water evaporation by monolayers spread on the water surface of members of the series ofnormal fatty alcohols C 2-C20 which includes the odd members of the series. Noe and Dressler6' have measured the retarda-tion by the nine pure alcohols. A linear relationship exists between per cent evaporation retardation and chain length from 18 % for C12 to 65 % for C,O, with both odd and even alcohols fitting on the same straight line.A theoretical equation of state for monolayers of fatty acids on water has been developed for the liquid expanded state by Smith.62 Previous attempts at describing this state had met with little success. Smith's equation is where II is the surface pressure A the area per molecule n the number of carbon atoms in the chain d the chain diameter and E the minimum Lennard-Jones potential energy. It is based on a simple model with the CH groups acting as a stack of hard discs and the theoretical term for van der Waals cohesion between CH groups is combined with a co-area term developed for two-dimensional hard-disc fluids. The equation is tested with experimental data for a large number of saturated fatty acids.Although there are no adjustable paramerers the equation predicts the experimental variables A n and T to within about 15 % at a given value of II. The equation is also approximately valid for unsaturated fatty acids if n is replaced by 2.5 n where n is the number of carbon atoms to the double bond counting from the ninth carbon atom in the chain. Some attention has been paid to mixed monolayers. Lomonosova and Trape~nikov~~ have studied the temperature variation of the equilibrium surface pressure in monolayers on water of mixtures of straight-chain alcohols with odd numbers of carbon atoms (C and C ,). The mixtures were prepared either by fusing together the components or by normal mechanical mixing. The pressure-temperature curves exhibit breaks which are associated with phase changes.Of particular interest is the behaviour in the temperature range adjacent to the melting point in which 'dips' had been previously observed for the certain single alcohols and substituted alcohols and presumed due to the presence of homologues. Differences were observed between the melts and 6 1 E. R. Noe and R. G. Dressler Ind. and Eng. Chem. (Product Res. and Develapmenr) 1967,6 132. 6 2 T. Smith J . Colloid InterfQce Sci. 1967 23,27. 63 T. A. Lomonosova and A. A. Trapeznikov Zhur.fiz. Khim. 1967,41 384 Colloid and Interface Science 143 mechanical mixtures but no 'dips' were found indicating that these are associ-ated with structural effects. A theory is developed by Joos Vochten and R ~ y s s e n ~ ~ which permits calculation of the surface shear viscosity of a mixed film if the flow parameters of each single component are known.It is assumed that the free energy of viscous flow for the mixture is proportional to the mole fractions of the com-ponents in the surface and to the free energy of viscous flow of the single components. The surface viscosity of mixed adsorbed films of two saponins, digitonin and senegin is measured and used to test the equation; a good fit is achieved. Large deviations were found for the cholesteroldigitonin system suggesting interaction between the two components. The transfer of Langmuir-Blodgett monolayers of 4C-labelled stearic acid on to mica silica glass silver copper platinum and iron has been determined at surface pressures of 30 17.5 and 10 dynes/cm.by S ~ i n k . ~ ~ Using Geiger counting autoradiography electron microscopy and reflection electron diffraction the activity and the nature of the transferred films were determined. Particular interest was shown in the influence of the chemical nature of the substrate on the deposition process ; large-grained polycrystals of silver were used to study the anisotropy of deposition and the influence of surface roughness and lattice defects investigated on thin (1 11) crystals and polycrystalline films of silver condensed on mica and glass. Also the dependence on piston oil pressure pH of the aqueous substrate and the rate of withdrawal of the specimen was examined. The paper contains a number of electron micro-graphs of the deposited layers.The transfer ratio (fraction of close-packed stearic acid monolayer that can be transferred from a water surface) is found to be uninfluenced by the pH between 2 and 6 the piston oil pressure between 10 and 30 dynes/cm. and the rate of transfer between 2.5 and 12.5 mm./min. The stability of the transferred films reflect the competition between water and the acid for the solid surface e.g. they are stable on mica but collapse on silica and glass. For atomically-smooth silver surfaces the transfer ratio may be as low as 0.5 and depends on rate of transfer and crystal orientation; it is least for crystal faces close to (1 11). Further work by the same author66 concerns the rate of desorption of l4C-labe1led stearic acid from Langmuir-Blodgett monolayers in vacuum over the temperature range 2142.5" for mica substrates and 38-80" for thin (1 11) epitaxial silver films on mica (an examination of the stability of the layers is important since these layers are used in studies on lubrication flotation and adhesion).Activation energies of 43.3 and 10 kcal./ mole respectively were obtained. The process is largely zero-order. Again the sensitivity of the process to the structure of the surface on an atomic scale is demonstrated. The Solid-Liquid Interface.-The nature of the liquid phase adjacent to the solid surface continues to be controversial in particular with water. For some 64 P. Joos R. Vochten and R. Ruyssen Bull. SOC. chim. belges. 1967,76,601. 66 J. A. Spink J . Colloid Interface Sci. 1967 24 61. J. A. Spink J . Colloid Interface Sci.1967 23,9 144 G. D. Parfitt years Deryaguin has maintained that surfaces of glass and quartz have the ability to change the physical properties of water and other polar liquids over a relatively large distance. If this is the case then the implications in colloidal problems as well as in biology and medicine are far-reaching. In his most recent paper in English on the subject in relation to the stability of colloidal dispersions Deryaguin6’ has presented experimental evidence for the existence at lyophilic surfaces of thick (500-1000 A) boundary layers of polar liquids that have properties which differ from those of the bulk. He discusses his blow-off method for viscosity measurement the evaluation of shear elasticity modulus of a variety of liquids using piezoquartz the expansion of water in glass capillaries and the formation of ‘anomalous’ water of density and viscosity some 1-2-1-5 times higher than normal water.The paper is basically a review of the work already published in the Russian literature. Some n.m.r. studies of adsorbed water molecules in amounts from 1-15 monolayers on silica surfaces have been made by Clifford and Lecchini68 with particular reference to the effect of porosity surface coverage and temperature on the spin-spin and spin-lattice relaxation times of the water protons. The presence and size of micropores is shown to dominate the effect of silica surfaces both on the freezing behaviour and on both the relaxation times of adsorbed water. The effect of the surface on the spin-lattice relaxation is largely due to a reduction in molecular motion of the adsorbed water while the spin-spin relaxation is dominated by slow exchange with surface hydroxyl groups.The authors review the general principles but conclude that the lack of a satisfactory theory prevents firm conclusions about molecular mobility being drawn from the n.m.r. results. A model system for the study of hydrophobic interactions between water and hydrocarbon is proposed and investigated by with the mechanism of stabilisation of protein structures in mind. Small glass beads treated with dichlorodimethyl silane behave as uniform particles of solid hydrocarbon but with effectively zero solubility in non-polar solvents. In non-polar solvents they remain as individual beads but in ‘ordered’ liquids such as water or formamide they undergo normal hydrophobic interactions and consequently aggregate into clusters.Experiments were carried out to determine the con-centration of additive which must be added to water to cause the change over from clusters to individual beads i.e. to reduce the interfacial tension appropri-ately. The additives include the short-chain alcohols formamide urea SDS, dimethylsulphoxide etc. and form a useful series for comparing the effect on hydrophobic interactions with that on liquid structures. Bailey and Kay7’ have carried Jut a detailed investigation of the influence of vapour liquid and oriented monolayers on the interfacial energy of mica. Using a cleavage technique solid-fluid interfacial energies were measured.In 67 B. V. Deryaguin Discuss. Faraday SOC. 1966,42 109. 6 8 J. Clifford and S. M. A. Lecchini SOC. Chem. Znd. Monograph 1967,25 174. 69 R. Cecil Nature 1967 214 369. ’O A. I. Bailey and S. M. Kay Proc. Roy. SOC. 1967 A . 301,47 Colloid and Interface Science 145 this method the work done to cleave a thin strip of mica is determined by measuring the forces required to maintain given separations at the ends of the mica strip. High resolution multiple-beam interference fringes were used to determine the area. The mica was cleaved first in an atmosphere of vapour and then in the corresponding liquid to give the solid-vapour and solid-liquid interfacial energies. Using water and hexane Young’s equation was verified for systems with zero contact angle.For the first time it has been possible to make independent measurements of each of the interfacial energies involved in the equation. The interfacial energies obtained were cleavage in water vapour 182.8 & 0.3 erg/cm.2 in liquid water 107.3 & 1.1 erg/cm.2 in dry hexane vapour 271 f 1 erg/cm.2 and in dry hexane liquid 255 f 1 erg/cm.2 The technique was also used to determine the work done in separating mica surface covered with an adsorbed monomolecular layer of lauric acid ; a value of 37 erg/crn.’ for the surface energy of the acid monolayer on mica was obtained. The interface between ice and silica surfaces is according to Anderson,71 separated by an essentially liquid-like unfrozen interfacial layer of water, the thickness of which varies with temperature.Between 0 and - 5” the thick-ness ranges from 15-45 A but below - 5” to liquid nitrogen temperature the thi’ckness decreases only from 6-3 A. At low temperatures it appears that the mobility of the interfacial water is much reduced and it may assume properties approaching those of the solid. The evidence is obtained from published work on frozen montmorillonite-water systems and from other related observations ; the work of Deryaguin and his collaborators is not discussed. In a second paper by the same author72 the nucleation of ice on clay mineral surfaces is considered with particular reference to the liquid layer discussed above. The conclusion is drawn that it is not ne-cessary for embryos to form by direct attachment to the surface but may originate some distance away in the unfrozen region adjacent to the surface.It is envisaged that various kinds of ordering are brought about in water by interaction with a substrate and one form of the icelike structures might lead to an embryo. Anderson claims that the theory accounts for all the experimental observations so far reported. The effect of liquid in the region between two identical wetted solid spheres in contact on the force of adhesion has been estimated theoretically by Gillespie and S e t t h ~ e r i ~ ~ from the equations of Radushkevich and Melrose for the capillary pressure. Calculated data are presented relating the force of adhesion resulting from the capillary action to the amount of liquid the particle radii, the surface tension and the contact angle.Some experimental data with glass spheres and mineral oil or water are compared with the theoretical results and the agreement is reasonable. Contact ungle. The methods for the measurement of contact angles of liquids on solid surfaces are well known and lead to numerous problems of ’’ D. M. Anderson J . Colloid Interface Sci. 1967 25 174. ” D. M. Anderson Nature 1967,216,563. ” T . Gillespie and W. J. Settineri J . Colloid Interface Sci. 1967 24 199 146 G. D. Parfitt interpretation. Longman and Palmer74 describe two new microscopic methods for determining the contact angle of small droplets of liquid deposited on a surface which involve interference microscopy and either reflected or trans-mitted light. Both methods rely on the resolution of interference fringes and thus the contact angle that enables the fringes to be resolved to the edge of the drop is normally the largest angle that may be measured.These are estimated as 15 and 30" for the reflected and transmitted light methods respectively. The time involved in the experiments is rather longer than for the more usual methods but the accuracy is greater particularly for small angles. For fibres a new technique has been described by Jones and Porter75 which involves a refinement of the light-beam reflection technique for use with filaments and microscope equipment. Previously contact angles were determined from photo-graphs of the liquid-surface silhouette near the point of contact. It is claimed that the new method is rapid and more accurate particularly when small angles are involved.In the measurement of contact angle very little has been said on the way in which the angle changes when the three-phase line of contact moves or is caused to move over the solid surface. Dynamic studies of contact angle bear the same relationship to static equilibrium measurements as does any other kinetic-rate study to the corresponding state of equilibrium and hence they provide information which cannot be obtained from static measurements. Elliott and R i d d i f ~ r d ~ ~ have described an apparatus and procedure for growing a bubble of one fluid with constant radial velocity between parallel solid plates, so displacing a second fluid. By reversing this process both advancing and receding angles can be studied as a function of interfacial velocity.Results are given for the displacement of air by water between two siliconed glass plates at 22 and 42" and between polythene plates at 22". Also of a water-saturated hydrocarbon oil (Bayol D) between siliconed glass plates by oil-saturated water and by an aqueous potassium laurate solution at 22". In all the systems they found a definite dependence of the advancing and receding contact angles on the interfacial velocity except at very low speeds. The contact angle of water on ice has been measured by Knight;77 this is the first reported measurement of the contact angle between the molten and crystalline states of the same material. The experiment was carried out by pouring boiling distilled water onto a copper plate previously cooled to - 70" with dry ice and successive photographs taken of the puddle for a period of several seconds.The intersection lines traversing the surface of the puddle, were observed; the water was forced back by the advancing intersection line (suggesting ysv < ysl + ylv) and maintained a sharp angle with the ice surface. Photographs illustrate the effect. The apparent intersection angle decreases with decreasing freezing rate and a minimum value for the receding contact 74 G. W. Longman and R. P. Palmer J . Colloid Interface Sci. 1967 24 185. 7 5 W. C. Jones and M. C. Porter J . Colloid Interface Sci. 1967 24 1. 76 G. E. P. Elliott and A. C. Riddiford J . Colloid Interface Sci. 1967,23,389. 77 C . A. Knight J . Colloid Interface Sci. 1967,25 280 Colloid and Interface Science 147 angle of water on ice is 12 1” at slightly below 0” at a receding rate of about 1 cm./sec.on a somewhat rough surface. The old problem of contact-angle hysteresis is considered by Dettre and Johnson78 in some studies on the wettability of porous surfaces. An ‘idealised’ model porous surface was generated on the computer and the wettability compared with water contact angles measured on specially prepared porous surfaces of polyethylene polypropylene paraffin wax and a fluoro-carbon polymer using the sessile-drop profile method. The theoretical curves using one adjustable parameter are consistent with the experimental results. This parameter is the ‘drop energy’ which is the smallest energy barrier which the liquid drop is unable to cross. This energy barrier is between any two meta-stable configurations (of which there are many) of the drop on the porous surface i.e.between regions of different contact angles as when the liquid periphery crosses air spaces between the solid regions. Under such circum-stances the familiar equation of Cassie and Baxter does not apply. Wetting. Equations which describe the shape of a bubble or drop resting on an inclined surface have been derived by Larkin” using the capillary equations of Bashforth and Adams (1883) and the solutions tabulated. Application of the results requires a definition of contact angle for interfaces resting on an inclined plane. Experimentally the contact angle varies around the line of solid-liquid-vapour contact and this is shown by the calculations.It is suggested that there is a point on the three-phase line at which the Dupre equation would apply. This point is selected such that the normal to the three-phase line which lies in the inclined surface is perpendicular to the local gravity vector. Drop weights were predicted from advancing and receding contact angles and showed reasonable agreement with experimental values. The free-energy changes associated with wetting and displacement are considered by Melrose.80 The duplex-film hypothesis of Harkins which for spreading conditions is equivalent to both Antonoffs rule and Young’s equation is shown to follow from the analysis due to Gibbs of the stability conditions governing the film adsorbed from the vapour phase. The associated free-energy changes are discussed.A modified form of the Bartell-Osterhof equation is then developed which provides a relationship between the observed wetting parameters displacement and adhesion tensions. This relation is applied to available data for water and n-decane in contact with polytetra-fluorethylene and polyethylene but the problems of contact-angle hysteresis make interpretation difficult. The fundamentals of wetting phenomena in capillary systems are re-examined by Blake Everett and Haynes,8 ’ with particular reference to the use of the Washburn equation to describe two-phase capillary flow and illustrated by some experiments using. a water-benzene interface in a hori-R. H. Dettre and R. E. Johnson SOC. Chem. Ind. Monograph. 1967,25 144. ’’ B. K. Larkin J . Colloid Interface Sci.1967,23 305. 8o J. C. Melrose SOC. Chem. Ind. Monograph 1967,25 123. 81 T. D. Blake D. H. Everett and J. M. Haynes SOC. Chem. Ind. Monograph. 1967,25 164 148 G. D. ParJitt zontally-mounted glass capillary to investigate the velocity-applied pressure behaviour. The results depend strongly on the state of the glass surface. The rate of approach to the equilibrium capillary rise in a vertical uncoated glass capillary using di-n-butyl phthalate against either vacuum or dry argon was also studied. The results demonstrate that the Washburn equation is valid (with exceptions) if it is accepted that the derived dynamic contact angles used are reasonable; The point is made that a complete study of the Washburn equations should be carried out with all the observable parameters studied in the same experiment.Bernett and Zisman82 have discussed the effect of terminal branching and chlorine substitution on the critical surface tension yc of fluorinated carboxylic acids. It had previously been shown by Zisman that a surface rich in covalent florine atoms has a yc which is lower than that containing any other chemical constituent. The lowest value was achieved with a smooth solid surface coated with a condensed monolayer of perfluorododecanoic acid but small departures from adlineation by modifying the structure to prevent close-packing caused significant changes in yc. In this paper the effect on yc of terminal branching and of replacing the terminal fluorine with chlorine is studied for two homologous series of acids (CF3)2CF(CF2),C02H and CF2Cl(CF,)CF(CF2),C02H with n = 11-1 and 9-1 respectively adsorbed on discs of chromium and platinum.Contact-angle measurements on homo-logous series of n-alkanes open-chain polydimethylsiloxanes and various other liquids were carried out to give yc values. In every case yc was increased significantly by branching or terminal chlorine substitution and in most cases (except for the lower homologue acids) the results were independent of the surface. The effect of adsorbed water on the spreading of organic liquids on soda-lime glass is reported by Shafrin and Zi~rnan.'~ Increasing the relative humidity increased the contact angle for many non-hydrophilic liquids on glass; the high-energy glass surface is converted into one that behaves as a low-energy surface i.e.one with a low yc towards non-hydrophilic liquids. Increasing the thickness of the adsorbed water layer leads to a surface with decreasing yc approaching that of bulk water. This work relates to the adhesion of the fibres and the resin binder in the manufacture of glass-fibre-reinforced plastics and is particularly pertinent because of the paucity of experimental data on the effect of thickness of an adsorbed water film on the ability of organic liquids to spread on a hydrophilic solid surface. The thickness of a wetting film which is left when a liquid drains from a smooth plate is discussed by Read and Kit~hener,'~ with experiments carried out on the silica-water system and a theoretical treatment based on Deryaguin's 'disjoining pressure' concept.They explain that disjoining pressures may be calculated by considering four types of physical force namely Born repulsion 8 2 M. K. Bernett and W. A. Zisman J . Phys. Chem. 1967,71,2075. '' E. G. Shafrin and W. A. Zisman J . Amer. Ceram. SOC. 1967,50,478. 84 A. D. Read and J. A. Kitchener SOC. Chem. Ind. Monograph 1967,25,300 Colloid and Interface Science 149 forces permanent-dipole interactions London dispersion forces and electrical double-layer forces. Although the first two may often be neglected this is not the case when dipolar molecules are oriented at the surface leading to ‘auto-phobism’ or when surfaces are ‘hydrophobic’ to highly associated liquids. In the case of thick layers of dilute electrolyte solution (as in this work) the disjoining pressure may be calculated by summing the long-range repulsion with the London energy.An apparatus is described for the measurement of the thickness of the wetting films and compared with that predicted by the theory using the zeta potential and assuming that no electric field passes through the air-water interface i.e. the double-layer structure between the plate and air is exactly equivalent to that in one-half of a plate-water-plate system having double the thickness and the same potential on both plates. The thickness of the wetting films obtained were of the correct order of magni-tude ( lo3 8 and decreasing with electrolyte concentration). Heats of wetting. The thermodynamic relations between quantities obtained from an immersional heat curve and the heats derived from adsorption iso-therms have been examined by Melr~se.~’ It is verified that the immersional heat decrement is an integrated isosteric heat and not related to the film pressure and its temperature coefficient by means of an equation of the Gibbs-Helmholtz type.The interpretation of gas-adsorption data on homogeneous surfaces (e.g. graphitised carbon black) has been successfully carried out but no immersional heat-coverage data have been reported. This paper predicts the form of relationship between heat and coverage namely that a maximum can be expected in the curve prior to the completion of the first layer. Using the theory of additivity of intermolecular forces proposed by Fowkes (1963) the contributions due to dispersion forces polarisation forces and hydrogen bonding to the interaction between Graphon and rutile with organic liquids of varying polarity (n-butyl derivatives) are estimated by Lavelie and Zettlemoyers6 from heats of wetting data.For Graphon the average dispersion-force contribution to the heat of wetting is 110 erg/cm.2 and for rutile 146 erg/cm’. Dispersion forces alone account for the heat liberated in forming the Graphon-organic liquid interface but the rutile value involves a minor contribution due to polarisation of the liquid by the electrostatic field of the solid. Approximately 70% of the interaction energy for heptane on rutile is due to dispersion forces and the remaining 30% due to polarisation of the hydrocarbon by the rutile. For butanol on rutile the major contributor is dipole-dipole interaction with less than 10 % due to hydrogen bonding.An attempt has been made by the Whalen and Wades7 to verify the thermo-dynamic relationships proposed by Melrose (1969 which relate the adhesion energy between a liquid and a solid to the heats of immersion and spreading pressure or to the contact angle and its temperature dependence. In principle a comparison of measured contact angles with adsorption data and/or im-*’ J. C. Melrose J . Colloid interface Sci. 1947 24,416. 86 J. A. Lavelie and A. C. Zettlemoyer J . Phys. Chem. 1967,71,414. ” J. W. Whalen and W. H. Wade J . Colloid Interface Sci. 1967,24 372 150 G. D. Parfitt mersion heats obtained on analogous systems can resolve questions related to the operational validity of contact angles and test the relationship.However, there are uncertainties involved in establishing values for the spreading pressure and immersion heat associated with an adsorbed film at saturation pressure and also in the measurement of the contact angle-temperature relationship. Nevertheless Whalen and Wade considered it worthwhile to establish signs and limited values of magnitudes for the pertinent parameters, and in their study used the low-energy material Teflon-6 and alternate members of the homologous series of n-alkanes from hexane to hexadecane. Because the heat evolved is so small a large number of immersion heats were determined for each hydrocarbon. For the series the adhesion energy is constant at 32 f 2 ergs/cm.’ for Clo and higher and for the lower members the energy increases sharply approaching the liquid-surface energy as a limiting value.It is estimated that the temperature-dependence of the contact angle is negative spreading-pressure terms are negligible for C, and higher and where significant ad-sorption occurs the temperature derivative of spreading pressure is negative. The authors also demonstrate that for many interfacial systems the contact angle can be obtained from a single heat of immersion value. Adsorption at the solid-liquid interface. Two papers have reported potentio-metric studies at the ferric oxide-aqueous solution interface. The work of Atkinson Posner and Quirk88 assumes that the surface charge is determined by the transfer of H+ and OH- ions across the interface. From data in solutions of high ionic strength of indifferent electrolyte (KC1) equations are derived for the net adsorption density ( r H + - r o H - microequivalents per gram) by equating the electrochemical potentials of potential-determining ions and indifferent counterions in the solution and surface phases and neglecting counterions in the diffuse layer.The equations contains interaction constants, and the dependence of these or the parameters on the particle surface area of the various precipitates used is not satisfactorily represented by the Brunauer-Emmett-Teller (BET) nitrogen area. It is concluded that the adsorbed counterions remain solvated and form ion-pairs with only a small proportion dissociating into the diffuse layer. A quantitative study of the time-dependent abstraction of H + and OH- ions from solution by crystalline ferric oxide precipitates is reported by Berube, Onoda and de B r ~ y n .~ ’ The experiment involved potentiometric titration of oxide suspensions with observations of pH drift with time after rapid displace-ment of the pH of the solution initially equilibrated with the solid at the zero point of charge. Also tritium exchange with the tritiated oxide was followed. The pH-drift experiments yielded a diffusion coefficient for protons into or out of the hydrated surface region of cm.2/sec. and an activation energy of 20 kcal./mole. The tritium-exchange experiments also yield a diffusion coefficient of cm.’/sec. and confirm the presence of a hydrated surface layer of thickness not exceeding 26 A (equivalent to four layers of chemisorbed 88 R.J. Atkinson A. M. Posner and J. P. Quirk J . Phys. Chem. 1967,71 550. 89 Y. G. Berube G. Y. Onoda and P. L. de Bruyn Surface Sci. 1967,7,448 Colloid and Interface Science 151 surface water). Comparison with published experimental data on Ti02, ZnO and A1,0 suggests that the diffusion model proposed earlier by the authors is to be augmented by a surface anion exchange between OH- and other univalent inorganic anions derived from the supporting electrolyte to account for the experimental facts. The properties of the zinc oxide-aqueous solution interface have been studied by Healy and Jellett.go Zinc oxide differs from the 'insoluble' oxides that owe their charge to the exchange of H+ and OH- ions in that it is partially soluble in aqueous media yielding hydrolysed species which in turn adsorb the over-all equilibrium again being determined by the activity of the Hf and OH- ions.This paper examines in detail the interfacial reactions of ZnO in water. Coagula-tion and electrophoresis techniques were used to examine the properties of the system as a function of pH and ionic strength. The surface charge at each pH is determined by the concentration and adsorption potential of each hydrolysed (charged and uncharged) 'Zn (11) species. Maximum aggregation occurs at a pH where the electrophoretic mobility is large and negative and this is assumed due to flocculation by polymeric zero-charged Zn (11) hydrolyzed species. No direct correlation between mobility and coagulation was observed. At no pH is the mobility reduced to zero in contrast to the insoluble oxides which exhibit a well-defined zero point of zeta potential.Aleksandrova and Kiselevg' have shown that it is possible to predict with reasonable accuracy for certain cases the adsorption isotherm for a binary liquid mixture on a solid surface. The requirement is strong specific adsorption of one component and non-specific adsorption of the other and the estimate is made in terms of the heats of adsorption of the individual vapours of the components. The equilibrium constant for the system n-octene n-octane, zeolite NaX is estimated using the equation K = exp[Hzr" - H,"~~""]/RT where Ha is the heat of adsorption from the vapour at low coverage and from it the Gibbs adsorption isotherm is determined.Agreement between the pre-dicted and experimental curves is good. Using the thermodynamic treatment of Everett (1964) an analysis of adsorp-tion and heat of immersion data of binary liquid mixtures of benzene and cyclohexane on silica gel was carried out by Lu and Lama.92 The adsorbates were chosen as they are of approximately the same size. Using activity-coeffi-cient data for the bulk phase the activity coefficients for the molecules in the adsorbed phase were determined. For both components the surface-activity coefficients are close to unity over the entire mole-fraction range except for the cyclohexane at low bulk and surface mole fractions. A value of 10.47 was calculated for the thermodynamic equilibrium constant. From published 90 T. W. Healy and V.R. Jellett J . Colloid Interface Sci. 1967 24 41. 91 G. Ya. Aleksandrova and A. V. Kiselev Zhur.fiz. Khim. 1967,41 1197. 92 B. C. Y. Lu and R. F. Lama Trans. Faraday Soc. 1967,63,127 152 G. D. Parfitt heats of mixing data the heats of mixing in the surface phase were evaluated and found to be significantly higher than those for the bulk liquid. A similar study to that just described has been reported by Wrightg3 using benzene + cyclohexane benzene + carbon tetrachloride and carbon tetra-chloride + cyclohexane mixtures with two charcoals as adsorbents. Adsorp-tion and heats of wetting data are reported and the data treated using Everett’s thermodynamic theory to see how far these real systems conform with or deviate from the requirements of perfect and regular surface behaviour.In general these systems approximate to regular surface behaviour (with some exceptions) and also to perfect surface behaviour over a wide concentration range despite the intrinsic non-ideality of the system. It is suggested that the equations may not be sensitive enough to distinguish between regular and perfect behaviour or the systems chosen are intermediate in character and satisfy both situations to some extent. One of the primary difficulties in analysing composite adsorption isotherms for the adsorption of binary liquid mixtures on solid surfaces to obtain isotherms for the individual components is the evaluation of the monolayer values for each component. Using molecular models or vapour-adsorption data is satisfactory when both components adopt the same configuration on the surface, but as Day and Parfittg4 point out difficulties arise in describing the surface layer when the molecules take up different orientations.Using data for alcohol-xylene (or heptanekrutile systems in which it is assumed that the hydrocarbon lies flat and the alcohol adopts a perpendicular orientation it was found neces-sary to include multilayers of hydrocarbon to define the mixed ‘monolayer’ thick film and successful interpretation of the composite adsorption data was then achieved. Comparison between adsorption from liquid mixtures at the liquid-vapour and liquid-solid interfaces is the subject of two papers. Aveyard’Sg5 paper is primarily concerned with the former interface and concerns binary n-alkane mixtures(6 + 16,6 + 14,6 + 12,7 + 16,8 + 16,lO + 16,and 10 + 14)and the applicability of the surface-tension data of the equation of Butler of Hoar and Melford and of Prigogine and Morechal.The equations fit the data well if it is assumed that the molecules lie flat at the surface. Adsorption of the 8 + 16 mixture on Graphon was compared with that derived from the surface-tension data. Octanol is preferentially adsorbed at the vapour interface but on Graphon hexadecane is preferred i.e. the component with the lower surface tension is adsorbed preferentially at the liquid-vapour interface. Nagy Schay and Szekrenyesyg6 classify composite adsorption isotherms for binary liquid mixtures on solid adsorbents into five basic types according to the degree of preferential adsorption of each component.Using the Gibbs adsorption isotherm they have shown that surface-tension data lead to all the five types 93 E. H. M. Wright Trans. Faraday Soc. 1967,63 3026. 94 R. E. Day and G. D. Parfitt J . Phys. Chem. 1967,71,3073. 95 R. Aveyard Trans. Faraday SOC. 1967,63,2728. 96 L. G. Nagy G. Schay and T. Szekrenyesy Acta. Chim. Acad. Sci. Hung. 1967 53,145; Magyar Ktm. Folydirat 1967,73,299 Colloid and Interface Science 153 being encountered at the liquid-vapour interface although there is an essential difference between the adsorption process at the two interfaces. An analysis is made of the conditions which determine each type of isotherm at the liquid-vapour interface in terms of the thermodynamics of the adsorption process. By careful choice of three different adsorbate solutions the total surface area, and the individual contributions of the carbon and hydroxyapatite components of bone char have been determined by Bennett and Abram.97 The total surface was measured by adsorption of Manoxol OT (Aerosol OT) from aqueous solution the carbon surface by CTAB from aqueous solution and the hydroxy-apatite by Manoxol OT from benzene solution.The adsorbates have very different interactions with the hydrophobic and hydrophilic regions according to the solvent used. Samples of bone char were progressively decarbonised to nearly zero and the changes in the individual surface areas measured; in all cases the sum of the carbon and hydroxyapatite areas remained equal to the BET nitrogen area. Based on the diffuse double-layer theory van den Hul and Lyklema'' have demonstrated that the specific surface areas of suspended charged particles may be derived from the measurement of the negative adsorption of co-ions.The advantage of this method is that it requires no molecular cross-section of an adsorbing molecule or ion. The method is illustrated with AgI suspensions with areas between 1 and 5 m.2/gm. and prepared by different methods. The relationship between area and negative adsorption is based on isolated flat double layers (no solution for spheres is available) the deviations from these criteria in the experimental system is shown to be small and the areas calculated are in good agreement with those estimated from double-layer capacity measurements. The Characterisation of Solid Surfaces.-Chemical structure.Investigations of the nature and quantity of hydroxy groups on the surface of oxidic substances continue to make progress as new techniques and more instrumental precision become available. Boehm and Herrmann99 used three methods (deuterium exchange acetylation and reaction with thionyl chloride) for estimating the concentration of surface hydroxy groups on a non-porous anatase sample of area 56 m.2/gm. After outgassing at 150" there are 4.9 hydroxy groups/100 A2 compared with the estimated average of 12-14 for a fully-hydroxylated surface. Thermal decomposition of the surface hydroxy groups occurred at outgassing temperatures below 200" and was apparently complete at 350". On exposure to water vapour at various temperatures up to 290" only half the original number of hydroxy groups were reformed but under liquid water the surface was completely rehydroxylated.For silica surfaces the adsorbed water and the silanol and siloxane were estimated by Kellum and Smith1'' using various techniques. The silicas used included pyrogenic (Cabosils) precipitated and 97 M. C. Bennett and J. C. Abram J . Colloid Interface Sci. 1967 23 513. 98 H. J. van den Hul and J. Lyklema J . Colloid Interface Sci. 1967 23 500. 99 H. P. Boehm and M. Herrmann Z . anorg. Chem. 1967,352 156. loo G. E. Kellum and R. C. Smith Analyt. Chem. 1967 39 341 154 G. D. Parfitt wet-process samples with surface areas 200-600 m.2/gm. A modified Karl-Fischer titration gave rapid and precise determination of adsorbed molecular water in the presence of hydroxy and siloxane groups and compared favourably with results using azeotropic distillation and thermogravimetric analysis.The method of catalytic condensation with boron trifluoride acetic acid and pyri-dine gave values for the water and silanol which compared with those from the thermogravimetric and thermal-condensation (at lO00") methods. Estima-tion of the sum of adsorbed water and strained siloxane rings with reactivity greater than that of hexamethylcyclotrisiloxane was possible by reaction with methanol and conventional Karl-Fischer reagent using a recording biampero-metric apparatus to follow the reaction. The results indicate that a marked decrease in silanol group population with a quantitative increase in strained siloxane occurs at temperatures of 150" and below.Complete removal of surface water (molecular and hydroxy) is only achieved at temperatures in excess of 400". Strained siloxane bridges are stabilized by thermal effects above 150". The surface hydroxy groups on silica alumina and silica-alumina catalysts were determined using a variety of organometallic compounds by Sato et ~ 1 . ' ~ ' Experiments were carried out in a closed system under a nitrogen atmosphere and the volume of ethane produced was measured. To determine the total hydroxy content triethylaluminium is the most convenient ; other compounds show varying reactivity according to the nature of the hydroxy site e.g. tri-ethyl borane does not react with silica-alumina containing a strong Bronsted acid site.The hydroxy groups on the surface of various samples of magnesium oxide (from thermal decomposition of the corresponding hydroxide) have been studied by Faure Fraissard and Imelik,lo2 using diborane trimethylchloro-silane methyl magnesium iodide and by deuterium exchange the latter being the most successful. 1.r.analysis shows a sharp band at 3690 cm.- ' and a less intense band at 3640 cm.-' due to OH-stretching after outgassing at 150"; at higher temperatures a band appears at 2740 cm.-' as a result of some dehydroxylation. Deuterium exchange did not go to completion and indicated that the major part of the total water exists in the bulk of the solid. Hughes and White'03 report a study of the surface structure of decationised Y zeolite by quantitative i.r.spectroscopy. The integrated absorption in-tensities accessibilities relative acidities and hydrogen-bonding characteristics of the hydroxy groups giving 3650 cm-' and 3550 cm-' bands in the i.r. spectrum were studied. These bands are assigned to the hydroxy groups associated with the aluminosilicate portion of the zeolite. Adsorption of piperidine demonstrates that both hydroxy groups are protonic acids and are accessible to molecules in the large intercrystalline channels but the concentration of these sites is much smaller than the ion-exchange capacity. Using pyridine the hydroxy group with a band at 3650 cm-' is shown to be a stronger Bronsted acid than that with 3550 cm-' and experiments with M. Sato T. Kanbayashi N. Kobayashi and Y . Shima J . Catalysis 1967,7 342.T. R. Hughes and H. M. White J . Phys. Chem. 1967,71,2192. lo* M. Faure J. Fraissard and B. Imelik Bull. Soc. chim. France 1967,2287 Colloid and Interface Science 155 t-butanol indicate the lower frequency hydroxy group is strongly hydrogen bonded to other oxygen atoms of the zeolite whereas the other hydroxy group is not. Dehydration at elevated temperatures convert the Bronsted sites to Lewis sites and exposure to water converts some of the Lewis sites to Bronsted sites but not necessarily to the original hydroxy groups. The study of physical adsorption of non-polar gases by decationated zeolites permits a more precise hydroxy band assignment since hydroxy groups on lattice points where they cannot interact with the surroundings will not be affected.White et al.lo4 have determined the shift and change in intensity of the OH-stretching bands of decationated Y zeolite following adsorption of N, O, CH4 Ar and Kr. Bands at 3677 cm-' and 3567 cm-' are assigned to hydroxyls in the supercage and in the cubo-octahedron respectively. The frequency of the shifted bands is almost unaffected by the amount adsorbed suggesting that the hydroxy environment in zeolites is homogeneous (as opposed to silica) hence with a simple electrostatic model it was possible to correlate the shift and intensity change of the 3677 cm- ' band to the dielectric constant of the polarisable adsorbed molecules. Low-energy electron diffruction andfield ion microscopy. Low-energy electron diffraction (LEED) has been widely adopted as a means of studying crystal surfaces but the mechanism of the interaction of low-energy electrons with crystals is not yet well defined.McRae"' has considered the central problem in diffraction theory as approached from the self-consistent multiple-scattering viewpoint of determining the effective wave field incident on each atom in the crystal. In his theory the author treats each atom layer of a model crystal explicitly and shows that the properties of the effective Geld imply the existence of two specific dynamical effects in LEED intensities namely the occurrence of fractional-order peaks in intensity curves and multiple-scattering resonance effects. Experimental evidence for both effects is cited. Future applications of the multiple-scattering approach to the effects of adsorption on intensities to thermal diffuse scattering to Kikuchi effects and to the effect of crystal size are discussed.The most complicated LEED patterns have commonly been explained in terms of single scattering leading to complex two-dimensional surface structures commensurate with the complexity of the diffraction patterns. Bauer1O6 considers this to be a result (in part) of a misconception of the diffraction process and is part of a consequence of the expectation that surfaces have a tendency to form two-dimensional structures. He demonstrates that the certain complex LEED patterns (Ag on Cu C on W etc.) can be interpreted in terms of multiple scattering by superimposed well-known structures. A LEED study of the structures of the clean (lOO) (1 1 l) and (1 10) faces of platinum is reported by Lyon and S~morjai,'~' experiments being carried out J.L. White A. N. Jelli J. M. Andre and J. J. Fripiat Trans. Faraday SOC. 1967 63 461. lo' E. G. McRae Surface Sci. 1967,8 14. E. Bauer Surface Sci. 1967 7 351. lo' H. B. Lyon and G. A. Somorjai J . Chem. Phys. 1967,46 2539 156 G. D. ParJitt in the range 300-1769" (melting point). Two types of surface structure, ordered and disordered were found and both types appear to be the property of the clean platinum substrates. The ordered structures appear during annealing after ion bombardment at <900" and are believed to be due to ordered arrays of vacancies in the substrate plane. The disordered structures appear at high temperatures they are irreversible and can only be removed by ion bombardment.The ratio of lattice parameters assigned to the diffraction rings on each substrate indicate that they can be due to domains of (111) surface structure and this disordered close-packed-hexagonal structure seems to be the stable high-temperature surface phase of platinum. Energy distributions of the electrons 'inelastically' scattered from the tungsten (1 10) surface for primary energies of 5&-250 ev have been obtained by Tharp and Scheibner'08 using a modified LEED system. The information obtained by examining both elastic and inelastic processes rather than from studying diffraction phenomena alone is discussed. In addition analysis of the mass spectra of desorbed species and the Auger peaks in the secondary electron-energy distributions have been used in addition to LEED to study the contamination on and near the surface demonstrating the usefulness of the combination of techniques to detect and identify impurities and to deter-mine their probable surface structures.have demonstrated with a variety of adsorbates (C6H3Br3 GeI, FeCl, ZnI, Br, C, Xe etc.) physically adsorbed on a graphite single crystal that LEED provides a powerful means of studying physisorption and related phenomena. Good patterns however were not obtained with C6H6 eel, C14H10 C6H4(OH) etc. Ordered structures are revealed with evidence for lattice gas and two-dimensional liquid and crystal phases the structure formed depending on the lateral forces. Desorption by the electron beam waiobserved but it was not a serious factor.Muller' lo reports that while ordinarily field ionization of helium in a field-ion microscope ocurs at a field of 450 mv/'cm. only 300 mv/cm. need to be applied when a small amount of hydrogen has been admitted. This promotion effect is shown to be due to adsorption of hydrogen and is explained by a rearrangement of surface charge transferring about to of an electronic charge from a protruding tungsten atom to an adjacently-adsorbed hydrogen atom to form a hydride-like bond. The introduction of hydrogen promotion reduces in many cases the evaporation field so much that the metal no longer yields to the field stress which previously arose because of the extremely high electric field necessary to operate a field-ion microscope. Now it is possible to use the microscope to study Fe Ni and Co and an extensive study of cobalt is reported by Nishikawa and Muller.'" The image quality was found to be satisfactory for viewing stacking faults twin boundaries and phase boundaries between hcp cobalt and fcc cobalt in atomic dimensions.Lander and lo8 L. M. Tharp and E. J. Scheibner J . Appl. Phys. 1967 38 3320. log J. J. Lander and J. Morrison Surface Sci. 1967 6 1 . ' l o E. W. Miiller Surface Sci. 1967 7,462. ' 0. Nishikawa and E. W. Miiller J . Appl. Phys. 1967 38 31 59 Colloid and Interface Science 157 Physical structure. The evaluation of pore-size distribution has attracted attention. Viswanathan and Sastri' '* suggest a simple method for computing the distributions in terms of surface areas instead of pore volumes directly from the low-temperature desorption isotherms of nitrogen.The equation, deduced from a model of the desorption process originally proposed by Wheeler (1955) is simple and does not require the use of a computer. The method when applied to published data obtained on a variety of porous solids gives results which are generally in good agreement with those found by the Brunauer-Emmett-Teller (BET) and Barrett-Joyner-Halenda (BJH) methods as are the distribution plots. The authors suggest that the distribution obtained directly in terms of the surface area is more relevant to catalysts and catalytic activity than the more usual volume-distribution functions. Another simplified approach this time using a modified form of the BET equations, has been proposed by Medema and C~rnpagner.''~ The method is not intended to be a substitute for the more refined methods but is considered to be of value as a quick first-approximation for technological purposes.The adsorption equation is simplified by assuming that the accessible surface areas are taken to be equal only for the first n adsorbed layers and from layer n on they are taken to decrease with a constant factor s < 1 such that = V for i < n and V;. = V si-" for i > n Here 6 is the amount of gas that can be adsorbed in layer i. A general isotherm equation is obtained which involves besides the volume adsorbed and the C constant the two parameters n and s. The capacity of the first layer agrees well with the BET monolayer capacity and the pore-size distributions are in qualita-tive agreement with the results of the more involved procedure associated with the Kelvin equation.All methods employed for pore-structure analysis were based on idealised models for the pore shapes (most assume cylindrical some parallel plate) until Brunauer Mikhail and Bodor' l4 published their analysis for pore volume and surface distributions without assuming any shape. The analysis is made in terms of hydraulic radii instead of Kelvin radii ; the hydraulic radius is defined as V / S where V is the volume of a group of pores and S the surface area of the pore walls. V is obtained in a conventional manner from adsorption or desorption isotherms while S is also obtained from the isotherms but by a new method based on Kiselev's (1958) method of surface-area determination.The volumes surfaces and hydraulic radii thus obtained are properties of the cores of a group of pores the core being defined as the empty part of a pore that contains an adsorbed film on its walls. In fact it is necessary in the calcula-tion to make corrections for the desorption from the walls of the empty pores and in this a shape is required. The authors claim that the corrections add little significant information to that obtainable from the uncorrected values. B. Viswanathan and M. V. C. Sastri J . Catalysis 1967,8 312. J. Medema and A. Compagner J . Catalysis 1967,8 120. 'I4 S. Brunauer R. Sh. Mikhaii and E. E. Bodor J . Colloid Interface Sci. 1967,24,451 158 G. D. ParJitt By small sacrifices in accuracy Lester"' has demonstrated that the time required (ca.40 hours) for the experiments and calculations in the determina-tion of pore-size distributions of catalysts from nitrogen-adsorption isotherms, may be reduced by about one-third. Only 12-15 experimental points are taken (usually 40 or more) and the regions between data are analysed using a modified form of the Halsey equation log (p/p,,) = - A / f l ; A and n are deter-mined by the two adjacent real data points. The agreement between computed and actual points is within experimental error. The calculation of the pore-volume size distribution then follows the method of Cranston and Inkley (1957) assuming cylindrical pores. Little accuracy is lost considering the time and effort saved. The evaluation of physical structure of the surface of porous solids using the t method (based on a standard adsorption isotherm for a non-porous surface) proposed by de Boer (1965) has been extended by Broekhoff and de Boer'16 to include open cylindrical pores.A combination of the t plot and characterisation of the hysteresis loop in the nitrogen-adsorption isotherm often leads to a clear picture of the pore system present. However there is some ambiguity with respect to the calculation of pore distributions from the adsorption branch. For isotherms exhibiting the A type of hysteresis loop, open cylindrical pores may be assumed but here the adsorption branch is only metastable with respect to the desorption branch and the Kelvin equations may not be applied. The authors have used simple thermodynamic arguments to show that the equation of Cohan (1938) for capillary condensation in open cylinders is not suitable for quantitative work.By introducing the universal t curve a model for the occurrence of hysteresis is given and quantitative relations are derived for the spontaneous filling of pores during adsorption as well as for the evaporation of capillary condensate on desorption in terms of the pore radius. It is shown that the thickness of the adsorbed layer in a cylindrical pore is expected to be different from that on a flat surface at the same pressure. With increasing pressure the adsorbed film in an open cylindrical pore becomes unstable at a certain pressure leading to spontaneous filling of the pore by capillary condensation. After filling hysteresis is found during desorption by the presence of a different form of meniscus capillary evapora-tion during desorption taking place at a lower relative pressure.Application of the equations requires a mathematical expression for the t curve in terms of RT In (pdp) as a function of t and this is derived in the second paper by Broekhoff and de Boer."' Numerical values for the radii of pores spontane-ously filling with capillary condensate at a given relative pressure are given, with which the pore distribution may be calculated. The results are shown to be a major improvement over the results obtained using the Cohan equation for capillary condensation. G. R. Lester J . Catalysis 1967,8,283. J. C. P. Broekhoff and J. H. de Boer J . Catalysis 1967,9 8.J. C. P. Broekhoff and J. H. de Boer J . Catalysis 1967,9 15 Colloid and Interface Science 159 Use has been made of the t plot by other workers. Day and Parfitt'18 show that the t method reveals the presence of micropores (cracks) in the surface of a pure rutile of surface area of about 30 m.2/gm. and that the standard BET method is not applicable for the determination of the specific surface for such material. Horlock and Anderson' l9 have studied beryllium oxide powders prepared by the thermal decomposition of P-Be(OH) in vacuo and contain a substantial volume of pores < ca. 6 A and < ca. 3 A. t plots give information on the micro-structure which is amplified by adsorption of molecules of various sizes and nature (He H20 and CCI,). With aluminium hydroxide gels Bye, Robinson and Sing'20 suggest that the t plot is a useful way of recognising the onset of reversible capillary condensation but emphasise that caution must be exercised in the applications to microporous solids and this is also illustrated in papers by Bye and Sing,'" and by Sing.'22 Surface area.The surface area and structure of a commercial activated alumina has been examined by Bowen Bowrey and Malin'23 by direct observa-tion using an electron microscope. From electron micrographs (shown in the paper) it was concluded that the sample contained regions of well-ordered pores approximately cylindrical in cross section with a mean diameter of 27 1 A and arranged hexagonally and other regions of random pores without characteristic size or shape between the particles.Some estimates of the proportion of the total BET surface (of 275 m.2/gm.) due to pores is given. A t plot suggests the existence of large macropores in which no condensation occurs and contributing an area of 18 m.2/gm. and these are assumed to lie between particles in the granules. Surface areas of 0.1-0.5 m.2/gm. have been determined using Kr-85 by Beurton Bussiere and Imelik.I2 Using a scintillation counter the pressure of the gas was determined as well as the amount adsorbed by direct measure-ment of the radioactivity of the sample and the area estimated by the BET method. A reproducibility of 10 % is claimed using various solid materials. Rootare and Pren~low'~' consider that no previous serious effort had been made to use the mercury porosimeter as a reliable surface-area measuring device and they show that surface areas can be calculated directly from stand-ard porosimeter pressure-volume curves without assuming a particular pore geometry.The results for 20 different powders with areas in the range 0-1-1 10 m.'/gm. compare favourably with those from BET measurements provided porosimeter pressures are high enough to force mercury into the smallest pores and that the mercury does not wet the powder (low-energy surfaces). The surface area and particle structure of Teflon-6 has been studied by 1 1 * R. E. Day and G. D. Parfitt Trans. Faraday Soc. 1967,63,708. lZo G. C. Bye J. G. Robinson and K. S. W. Sing J . Appl. Chem. 1967,17 138. lZ2 K. S. W. Sing Chem. and Znd. 1967 829. I f 3 3. H.Bowen R. Bowrey and A. S. Malin J . Catalysis 1967 7 209. lZ4 G. Beurton P. Bussiere and B. Imelik Bull. SOC. chim. France 1967 1793. 125 H. M. Rootare and C. F. Prenzlow J . Phys. Chem. 1967,71,2733. R. F. Horlock and P. J. Anderson Trans. Faraday SOC. 1967,63 717. G. C. Bye and K. S. W. Sing Chem. and Znd. 1967 1139. 160 G. D. Parfitt Whalen Wade and Porter'26 using nitrogen and argon isotherms. No linear BET region was observed for this low-energy surface and areas estimated from the isotherm show considerable discrepancy depending on the adsorbate and isotherm region selected. Electron-microscope areas were found to be significantly greater than the estimated maximum nitrogen BET area but in reasonable agreement with that using argon. It appears that Teflon-6 granules consist of fundamental particles connected by a filament network each particle being a two-phase system.The interior phase may consist of ordered polymer chains while the surface phase of lower density may consist of disordered, random-length polymer chains. The availability of a large number of data on the cross-sectional areas of molecules adsorbed on solid surfaces which have appeared since the last examination carried out by Livingston in 1949 have led McClellan and Harn~berger'~~ to re-examine the subject. Data for the adsorption of two or more gases measured on the same solid are collected and these values for 106 compounds (1 88 references) are tabulated as are cross-sectional areas calculated from molecular models critical constants or liquid density.It is concluded that the size of the adsorbed molecule is not constant but varies with the adsorbent temperature of adsorption and choice of reference sub-stances. Recommended values for cross-sectional areas are N (- 195") 16-2A2, n-C,H, (0') 44.4 81'. The calculated values tend to be lower than those from adsorption measurements. Surfaceenergy. Using published contact angles of water drops on solid noble-metal plates ThelenI2* has calculated using Fbwkes' theory (1964), the dispersion energies of the metals with the following results Ag 84.95, Au 121.63 Pd 129.86 and Pt 18956 ergs/cm.'. These values are shown to correlate with cohesive energy densities (C.E.D.) (hence to the energies of vaporisation) and with total surface free energy calculated from Cottrell's approximate equation (1964), Ar ( - 195 - 183") 13.8 .8L2 Kr (- 195") 20.2 A' C6H6 (20") 43.0 A' and ys = r (C.E.D.) - TS where r is the atomic radius and S the surface entropy (taken as 0.4 erg/cm.' deg.).Application of fundamental and statistical-mechanical principles to the terrace-ledge kink model of crystalline surfaces leads to a two-parameter theory of the anisotropy of surface tension (specific surface free energy) reports Gruber and M~llins.''~ Previous treatments of the surface free energy as a function of crystallographic orientation has been confined to absolute zero and the effect of a finite temperature on the free energy arising from configura-J. W. Whalen W. H. Wade and J. J. Porter J . Colloid Interface Sci. 1967 24 379. ''' A.L. McClellan and H. F. Harnsberger J . Colloid Interface Sci. 1967,23 577. ''* E. Thelen J . Phys. Chem. 1967 71 1946. E. E. Gruber and W. W. Mullins J . Phys. and Chem. Solids 1967,28 875 Colloid and Interface Science 161 tional entropy has been little discussed. The authors take into account this entropic effect and thus calculate the energy at a finite temperature ; the entropy term is shown to contribute significantly to the ledge free energy. Examples of the predicted anisotropy of surface tension are given for copper. Adsorption of Gases on Solids.-A generalised potential theory of adsorption is developed by Kuhn13' by deriving first the expression of the possible course of adsorption without the pressure variable and then completing this for the pressure-dependence of equilibrium by applying Polanyi's adsorption potential concept.The equation derived is when k and 6 are constants for a given temperature y is the power of the variation of potential with distance from a given adsorption site and p is provisionally the pressure corresponding to a supposed static-adsorption equilibrium with points of maximum surface potential. A different adsorption potential is assumed for each site and also a hemispherical loop is assumed to be formed on each site as the relative pressure increases. The equation is capable of representing all general forms of adsorption isotherms and contains four adjustable constants. Conventionally the calculation of the thermal-accommodation coefficient a associated with the energy transfer between a beam of gas molecules and a solid is based on the model of harmonic oscillation of the surface atoms and usually studies based on this model lead to a values much smaller than the observed data.Interaction-potential parameters are then adjusted rather than applying a more realistic model. Shin13 has assessed the effect of removing the approxima-tions of harmonic oscillation and using data for helium and neon on tungsten, nickel and iron shows that there is a large range of values of the ratio of the a values calculated with and without assuming harmonic oscillation. The author concludes that the logical step to improve the theory is to consider the an-harmonic behaviour of the surface atom. In general anharmonicity increases the probability of energy transfer over the model for simple-harmonic oscilla-tion.The dependence of adsorption properties on surface structure for bcc substrates is considered by Neustadter and Ba~igalupi,'~~ by applying the Lennard-Jones 6-12 atom-interaction potential to the calculation of the adsorption energy of an atom on to as many as 132 sites on a unit-cell surface area for each of the eight highest surface-density planes of a bcc substrate. A normalised adsorption energy is plotted as a function of position on a unit-''' I. Kuhn J. Colloid interface Sci. 1967 23 563. 131 H yung Kyu Shin J. Phys. Chem. 1967,71 1540. ''' H. E. Neustadter and R. J. Bacigalupi Surface Sci. 1967,6,246 162 G. D. Parfitt cell area of each plane for various adsorbate-adsorbent combinations and normalised values of maximum adsorption energies and minimum-surface diffusing-activated energies are obtained.The results are compared with data for the adsorption for variety of adsorbates (inert gases alkali metals and alkaline-earth metals) on transition-metal substrates and found to be in good agreement. The (1 10) surface is found to be the lowest energy configuration for the bcc crystal. Such a study of adsorption on an atomic scale is considered essential now that the field-ion microscope and the field-emission microscope have shown that the adsorption properties are strongly dependent on the atomic arrangement of the substrate. Adsorption in micropores is discussed by Dubinin. 133 Radical differences between adsorption phenomena taking place in micropores (effective radius from 5 4 to 13-14 A) and those on the surface of intermediate pores (15-16 to 1000-2000 A) or on non-porous adsorbents demand different theoretical approaches to describe and interpret the behaviour.Dubinin discusses the basic principles of adsorption in micropores associated with his 'theory of volume filling of micropores' and the new trends which involve empirical methods for calculating adsorption equilibria. Two extensions to the Ross and Olivier (1964) theoretical model for physical adsorption on heterogeneous surfaces are suggested by Hoory and Prausnitz. 134 In this model the surface is visualised as a collection of homogeneous patches, and variation in the adsorption potential from patch to patch are taken into account. However the model neglects possible variations in translational, rotational and vibrational energies and entropies of the molecules at the different patches.In this paper the effect of the variation of vibrational energy on the adsorption isotherm at low coverage is analysed. Furthermore the statistical distribution function of the adsorption potential over the different patches is considered not as previously with a Gaussian distribution but the log-normal distribution is proposed. Both extensions are tested on published data for adsorption of argon on a heterogeneous carbon black (black pearls). Apparently the effect of including vibrational-energy changes is small and no significantly large effects are caused if the complete Gaussian distribution is replaced by log-normal distribution.Hoory and P r a ~ s n i t z ' ~ ~ have also derived a systematic treatment for mobile monolayer adsorption of gas mixtures on homogeneous surfaces. By defining a surface fugacity for each component non-ideality of mixing in the monolayer is related to constants in the two-dimensional equation of state. The results are extended to heterogeneous surfaces using the surface-patch concept of Ross and Olivier; the theory is a generalisation to mixtures of the Ross and Olivier theory for pure gases. For this system three heterogeneity parameters were required two being the variances of the adsorption potential distributions for the pure components while the third is their covariance. 133 M. M. Dubinin J . Colloid Interface Sci. 1967,23,487. 134 S . E.Hoory and J. M. Prausnitz Surface Sci. 1967,6,377. S. E. Hoory and J. M. Prausnitz Chem. Eng. Sci. 1967,22 1025 Colloid and Interface Science 163 For non-polar chemically-pure gases good estimates of mixed-gas adsorption on heterogeneous surfaces using only data for the pure component are shown to be possible. Computed results for adsorption of ethane-ethylene mixtures on charcoal agree well with experimental data. Adsorption on oxides. The displacement of the i.r. absorption band due to free surface hydroxy groups as a result of their interaction with adsorbed molecules is associated with the energy of this interaction and the change in intensity gives further information on the effect. Galkin Kiselev and L ~ g i n ' ~ ~ report data on the interaction of a variety of molecules with Degussa Aerosil.The intensity ratio of the bands due to perturbed and free hydroxyls increases until a monolayer is reached. For a series of molecules of similar electronic structure (benzene and its alkyl derivatives) there is a linear frequency shift and intensity ratio with increase in total heat of adsorption and decrease of ionisation potential. A simple relationship of this kind does not exist for mole-cules of different electronic structure because of the different contributions of specific and non-specific interactions to the total heat of adsorption. An approximately-linear relation exists for such molecules when the difference between the heats of adsorption on hydroxylated and dehydroxylated surfaces is taken as the energy of the specific interaction with the surface hydroxyls.Precise gravimetric data extending down to p / p = 10- has been obtained by Whalen137 for nitrogen and benzene on two characterised silica surfaces, with a view to establishing the applicability of the BET method to both weakly and strongly interacting adsorbates on variable-structure surfaces of constant area. Both adsorbates are shown to interact with the surface in a manner dependent upon the substrate structure which was varied by outgassing at temperatures up to 400". The surface areas derived from nitrogen-adsorption data using the BET equation depends only slightly on the nature of the surface, and justifies the value of nitrogen for routine surface-area measurement (although gross differences may lead to larger variations).Benzene does not form complete monolayers or statistically-equivalent multilayers in the region of BET applicability and the adsorption is strongly dependent on the detailed chemical nature of the surface. Apparent compliance of the benzene data to the BET model is considered fortuitous. The Adamson-Ling treatment (1961) is used to obtain site energy-distribution functions from the adsorption isotherms. For nitrogen two peak functions are obtained which vary in accord-ance with the established oxide-hydroxide character of the surface but in contrast the spectrum of interaction energies for benzene is quite wide. These results are consistent with the known surface structures and with specific adsorbate interaction. The decrease 0 in surface free energy for adsorption of a gas on a solid surface is usually evaluated by application of the Gibbs adsorption equation to the observed isotherm such that 136 G.A. Galkin A. V. Kiselev and V. I. Lygin Zhur.jz. Khim. 1967,41 40. 137 J. W. Whalen J . Phys. Chem. 1967,71 1557 164 G. D. ParJitt P c$ = RTSn,dlnp 0 where n is the number of moles of gas adsorbed at pressure p. The evaluation of this integral presents a number of problems and since no general relation exists between n and p for more than a limited range of the isotherm it is usual to evaluate the integral by graphical methods involving different extrapolations. Glossman and Corrin' 38 have used the Dubinin-Radushkevich approach (1947) to describe data in the very low-pressure region as an aid to the extra-polation to zero pressure for their data on the adsorption of argon on anatase (the Harkins and Jura sample) at 76-91 and 89.39"~ down to relative pressures of ca.lop7. The data fit the Dubinin-Radushkevich equation at adsorption potentials greater than 2-2 x lo3. Differential and integral thermodynamic-adsorption functions were calculated and show that at a coverage of about 12 % of the BET monolayer a pseudo-monolayer effect is observed (maximum in the enthalpy functions and a minimum in the entropy functions). It is concluded that the anatase sample is composite with patches of high-energy sites occupying about 12 % of the total area. It is not often that the rate of physical adsorption or desorption of gases on solids is studied partly due to experimental difficulties and partly to a lack of theoretical basis (this is not the case with chemisorption).Micale and Zettle-moyer'39 have measured the rate of desorption of water from the rutile surface at 25 40 80 and loo" and using the Elovich equation modified so that the rate approached zero as the reversible water on the surface approached zero, obtained values of the rate constants. The modified form where b and P are constants q the amount adsorbed or desorbed at time t and A is the initial concentration of desorbable gas on the surface is empirical and the physical significance of the constants is not clear. The heat of desorp-tion varied from 8.0 to 5.9 kcal./mole with decreasing surface coverage but the small decrease does not appear to be significant and the values cannot be explained at the present time.The physical adsorption of nitrogen on ice powder prepared at 7 7 " ~ , reported by Adamson Dormant and Orem,14' indicates a fairly uniform and not highly polar surface. Annealing at - 70" leads to adsorption behaviour characteristic of a non-polar surface such as Teflon and surface inertness towards nitrogen reaches an extreme in the case of snow samples collected from two locations in California and Colorado. Ideas on the surface structure which follow from the data are discussed and the authors suggest that water and probably ice near its melting point exhibit an apparently heterogeneous surface the molecules in the surface rearranging to permit strong interactions 13* N. Glossman and M. L. Corrin J .Colloid Interface Sci. 1967,23 237. 13' F. J. Micale and A. C. Zettlemoyer J . Colloid interface Science 1967,24,464. I4O A. W. Adamson L. M. Dormant and M. Orem J . Colloid Interface Sci. 1967,25 206 Colloid and Interface Science 165 with the adsorbate. Freezing a clean surface at liquid-nitrogen temperatures so that no rearrangement can occur means that the surface retains its non-polar and essentially homogeneous nature. Measurement of the dielectric behaviour of gas molecules adsorbed on a solid surface by measuring the capacitance change of a test condenser filled with the adsorbent leads by application of the Clausius-Mosotti equation (or other equations) to the polarisability of the molecules in the adsorbed phase. However there are difficulties in the application of the equation but GrObnerl4l has demonstrated a method for the evaluation of relative polarisabilities for two gases by comparing the appropriate capacity changes and these relative values are shown to yield valuable information.His study includes N2 COz C2H2 CC12F2 and l,l-F,C,H on alumina (120 m.2/gm.). The capacitance change was non-linear for large surface con-centrations and it is considered that the polarisability a depends on the number of molecules adsorbed per unit surface i.e. a = A[1 - (N/S)B] where A and B are constants N is the number of molecules and S the surface area. B has the dimension of a surface area per molecule and defines an average distance at which the interaction of neighbouring molecules affects their polarisability.Adsorption on carbons. Graphite and the graphitised carbon blacks are popular adsorbents because of their characteristic surfaces and in particular the graphitised blacks provide ‘homogeneous’ surfaces for fundamental studies. Harris Hudson and Ross’42 describe a technique for the measurement of physical adsorption of gases at pressures as low as 10- lo torr on small solid samples of very low surface area (a few cm.2) whose structure can be charac-terised independently by X-ray diffraction and electron microscopy. The method is a variation on the ‘flash-filament’ technique and was used to study the adsorption of krypton (at liquid nitrogen and oxygen temperatures) on annealed pyrolytic graphite the surface of which was studied by means of electron microscopy.Over the pressure range 10- torr the isosteric heats vary from 5-6-3.5 kcal./mole. The results suggest a high degree of surface heterogeneity and that adsorption at low coverage takes place in interlamellar crevices less than 10 8 wide. In view of the strongly anisotropic properties of graphite the boundary surfaces of graphitic solids should present two arrays of adsorption sites one in the basal planes and the other in the prism faces of the graphite crystal. Different specimens of graphite should vary in surface properties according to the proportion of basal plane and prism faces that are present. This assumes that the anisotropic properties of the crystal extend into the boundary surface. D e i t ~ ’ ~ ~ has suggested that the high-temperature (OO) physical adsorption of C02 at low pressure (below 1 torr) provides sufficiently low coverage to discriminate between the adsorption sites.The adsorption isotherms presented 0. Grobner J . Chem. Phys. 1967,46,4381. L. B. Harris J. B. Hudson and S. Ross J . Phys. Chem. 1967,71 377 143 V. R. Deitz J . Phys. Chem. 1967,71 830 166 G. D. Parfitt in the paper for mineral graphite and annealed pyrolytic graphite a graphitised carbon black and a heat-treated coconut charcoal show two distinct regions of surface coverage separated by a wide plateau. At very low pressures (<Om01 torr) the adsorption is compatible with high-energy adsorption on one array of carbon atoms in the prism faces and at higher pressures the adsorption is on the more abundant basal planes. The similar behaviour for graphite graphitised carbon black and charcoal is significant.Some calculations based on the different electronic environment to which the adsorbed molecules are subjected (dispersion interaction) on the two types of sites leading to different interaction energies are published by Meyer and D e i t ~ ' ~ ~ and show that anisotropy has a definite influence on the adsorptive properties of graphite. Low-pressure isotherms (down to lop4 torr) for benzene toluene thiophene, cyclohexane and n-hexane are reported by Pierce and E ~ i n g ' ~ ' for graphitised Sterling MT (3100"). Usually isotherms are concave to the pressure axis at low coverage for a non-uniform surface and convex for a uniform surface; the convex shape is due to lateral interactions which cause an increase in the beat of adsorption as the coverage increases.Benzene isotherms below the freezing point are concave to the pressure axis at low coverage have a heat of adsorption equal to the heat of vaporisation during filling of the first layer show no change in V (monolayer volume) with temperature and show no lateral interactions at any coverage. These properties are explained in terms of strong localisation of benzene at lattice sites due to similarity of the aromatic nucleus hexagon to lattice hexagons of graphite. Toluene shows the same effect but the other adsorbates give normal convex isotherms. Concave isotherms for benzene on a graphitised carbon black (and convex for water) over the range 30-100" are reported by Beldjakova Kiselev and K0va1eva.l~~ Gas phase chromatography was used based on the method of Glueckauf (1945).Isosteric heats of adsorption were calculated and the results show good agreement with those obtained by static methods. Xenon adsorption isotherms (using Xe-133) for Sterling MT (3100") and Grapkon at surface coverages ranging from 10-'o-0.9 are reported by Cochrane et aE. 147 The small degree of heterogeneity associated with both adsorbents is confirmed. For Sterling MT Henry's law is closely obeyed for coverages 10-10-10-6 and for both carbons the adsorbed phase at high coverages is interpreted as a two-dimensionally mobile layer with adsorbate-adsorbate interactions. The homogeneity of the surface is considered the cause of the difference between the surface area from t plots and the BET values for graphitised carbon blacks and the former is considered to be correct by de Boer and co-workers.148 Stepped isotherms are normally obtained with graphitised carbon blacks, 144'E. F. Meyer and V. R. Deitz J . Phys. Chem. 1967,71 1521. 145 C. Pierce and B. Ewing J . Phys. Chem. 1967,71,3408. 146 L. D. Beldjakova A. V. Kiselev and N. B. Kovaleva Bull. SOC. chim. France 1967 285. 147 H. Cochrane P. L. Walker W. S. Diethorn and H. C. Friedman J . Colloid InterfuceSci., 148 J. H. de Boer J. C. P. Broekhoff B. G. Linsen and A. L. Meijer J . Catalysis 1967,7 135. 1967 24 405 Colloid and Interface Science 167 the steps corresponding to the filling of successive layers. In addition to the need for a homogeneous surface it is considered necessary that there must be strong lateral interactions between adsorbed molecules and that the tempera-ture must be such that thermal agitation of the adsorbed molecules does not erase the discontinuities between the filling of adsorbate layers.The work of Bassett Boucher and Z e t t l e m ~ y e r ' ~ ~ confirm that stepped isotherms are possible at room temperature if the saturation pressure is in the range 1-10 torr (as predicted by Pierce 1966). Isopropyl alcohol adsorption on Graphon at 0 and 25" has been investigated and it is concluded that the temperature needed to show steps is related to the characteristics of the adsorbate. The reduced temperature is a better guide. Strong lateral interactions coupled with relatively weak adsorbate-adsorbent interactions enhance step-wise adsorption and alcohols on carbon fit these requirements.Adsorption of gases on other surfaces. Some difficulties have been experienced in the past in the characterisation of the surface of silver iodide in terms of its interaction with water vapour partly because of contamination resulting from the preparation (aqueous precipitation) and partly because interpretation is made difficult by three-dimensional clustering of the adsorbate molecules in the adsorbed phase. In the investigation reported by Edwards and Corrin"' these difficulties have been removed by using methanol as adsorbate and a sample of AgI (surface area about 1 m.2/gm.) prepared by direct reaction between metallic silver and iodine followed by treatment with ammonia. The isotherms did not fit the Brunauer classification and their shapes indicate absence of three-dimensional clustering.Isosteric heats calculated from measurements at 9.77,19.79 and 30.02" over the pressure range 0.24-10.8 mm., indicate that the surface has a dual nature. About 12% of the heterogenetic surface consists of high-energy sites located patchwise over the surface. The adsorption of n-pentane by a NaX zeolite at 180 200 230 250 and 270" has been studied by Garkavenko and c o - ~ o r k e r s . ' ~ ~ (At temperatures lower than 180" the adsorption is so strong that reversibility etc. at low coverage when the voids of the zeolites are filled is difficult to assess). The isotherms are Langmuirian and log K varies almost linearly with the reciprocal of the temperature ( K is the equilibrium constant).Theoretical isotherms calculated from the Langmuir equation using this temperature-dependence of K agree well with the experimental curves. Isosteric heats are practically independent of the amount of pentane adsorbed and are close to the 12-3 kcal./mole calculated from the temperature-dependence of K and also to published calorimetric data. Entropy calculations indicate that as the voids become filled the mobility of the n-pentane molecules decreases and over a wide range is less than in the liquid state. The surface of cavities in X-type zeolite cationated by small-radius covalent D. R. Bassett E. A. Boucher and A. C. Zettlemoyer J . Phys. Chem. 1967,71,2787. H. W. Edwards and M. L. Corrin J . Phys. Chem. 1967,71,3373. L.G. Garkavenko 0. M. Dzhigit A. V. Kiselev K. N. Mikos and G. G. Muttik Zhur.Jiz. Khim. 1967,41. 244 168 G. D. Parfitt cations is homogeneous to non-specific adsorbates due to the crystalline struc-ture and on such surfaces adsorbate-adsorbate interactions are clearly defined. Adsorption isotherms have a wave-like form first convex to the pressure axis and an inflection point near half-monolayer coverage; heats of adsorption increase with coverage cf graphitised carbon blacks. For the zeolites Kr Xe, C2H6 n-C5Hl, and n-C6Hl show this behaviour. The adsorption of krypton and xenon at temperatures in the range - 30 to - 90” is discussed in detail in a paper by Aristov Bosacek and Kiselev.lS2 Simple equations are deduced to take approximate account of adsorbate-adsorbate interactions in the adsorbed phase and adsorption values and isosteric heats are predicted which are in agreement with the experimental data.The electrical coriductivity of a semiconductor may increase or decrease according to the nature of the gas adsorbed on the surface as demonstrated with copper and zinc oxides. The reverse of this process in which the quantity of adsorbed substance might be influenced by appropriate manipulation of the density of electrons within the solid is considered by R o ~ h o w ’ ~ ~ and if an alternating field is applied he defines the possibility of alternately seizing and releasing the adsorbed gas as ‘alternosorption’ which is shown to be reversible in principle. Application to heterogeneous catalysts is discussed. Spectra of adsorbed species.Although LEED and field emission studies give information on the form of the adsorbed phase on a single crystal of a metal or semiconductor they give only very indirect evidence as to what species are present. The application of i.r. spectroscopy has obvious merits, but there are certain difficulties both experimental and in interpretation. It is necessary to optimise the experimental parameters and to have a theory for the interpretation of the vibrational spectrum for a regular moiiomolecular film chemisorbed on clean oriented single-crystal metallic or semimetallic sub-strates. The spectrum is discussed in the harmonic-oscillator approximation by Smith and Eckstrom,’ 54 and it is concluded that optical modes must be totally symmetric with respect to translation and be of an appropriate symmetry species under the unit cell ( N factor) group.The implications of anharmonicity, quadrupolar-induced transitions and non k = 0 processes are discussed and the theory applied to the case of CO and H (or D2) adsorbed on the (loo), (110) and (111) surfaces of nickel. Some agreement is found although present experimental data were not obtained under optimum conditions. An e.s.r. study of chlorine atoms adsorbed on a silica-gel surface at 77”K, reported by Gardner,”’ indicates that the orbital degeneracy has been re-moved as a result of the electrostatic interaction with the surface. The author states that this is the first example of detection of trapped halogen atoms. An estimate of 2.7 x 1017 v/cm.2 has been made for the electric-field gradient at the position of the chlorine atom.1 5 2 B. G. Aristov V. Bosacek and A. V. Kiselev Truns. Faraday SOC. 1967 63 2057. l S 3 E. G. Rochow J . Inorg. Nucleur Cheni. 1967,29,65. 155 C. L. Gardner J. Chem. Phys. 1967,46 2991. W. H. Smith and H. C. Eckstrom J . Chem. Phys 1967.46. 3657 Colloid and Interface Science 169 Substrate absorption limits the use of i.r. spectroscopy to the high-frequency modes of vibration of the adsorbate whereas Raman spectra should provide an effective alternative method for covering a wide frequency range. The use of a conventional laser Raman spectrometer has been investigated by Hendra and Loader,156 using CCl, Br, CS, and trans-C,H,Cl adsorbed on silica gel and spectra recorded over the range 150-3400 cm- '.This is a preliminary investigation which looks promising. The i.r. and e.s.r. spectra of silica (Aerosil) y-alumina rutile titanium dioxide, and of these oxides with adsorbed gases have been studied by Kiselev and Uvarov.lS7 On the clean oxide e.s.r. signals were only detected with alumina and rutile. Adsorbed n-hexane benzene diethyl ether acetone diethylene-triamine pyridine and acetic acid were studied by i.r. and anthracene by e.s.r. spectroscopy. In addition to the specific interactions of the oxygen and nitrogen containing molecules on all three oxides there is chemical interaction with the aprotonic acid centres of alumina and rutile. Similarly with anthracene for which charge transfer takes place and ion radicals emerge. Such effects were not observed with silica suggesting the absence of aprotonic electron-acceptor centres on the silica surface.In the characterisations of solid surfaces and adsorbed species by i.r. spectro-scopy almost no spectra have been obtained at elevated temperatures yet most catalytic reactions of practical importance occur at high temperatures. The paper by EberlyI5* describes a new high-temperature i.r. cell which he has used to record spectra at temperatures up to 650" and pressures from lo-' mm.-760 mm. A study of the interaction of the various ion-exchanged faujasites (Y zeolites) with hexene-l and other olefins at 90-427" is described. Three different hydroxy groups were found with hydrogen faujasite at 427" and these groups readily exchange with deuterium gas.Hexene-1 adsorbed at 93" with the loss of double-bond character; at higher temperatures polymer-isation and dehydrogenation processes occur. On other ion-exchanged forms the main reaction involved the loss of double-bond character. Sols.-Particle size. The use of a simple small-angle scattering device attached to a commercial X-ray diffractometer (Philips) for determining particle size distribution of thoria sols is described by Stoecker,lS9 and shows that simple equipment of low resolution is adequate for a system of particles having a scattering curve that can be approximated by a Gaussian distribution (or by a composite of several Gaussian distributions). Each thoria sol investi-gated had its own characteristic scattering curve the shape of which was un-changed by dilution and the average particle diameter agreed with that deter-mined by line broadening.Besides the inherent difficulties in the electron-microscopic examination of sols that are associated with the preparation of the sample for analysis there 156 R. J. Hendra and E. J. Loader Nature 1967,216,789. l S 7 A. V. Kiselev and A. V. Uvarov Surface Sci. 1967,6,399. lS8 P. E. Eberly J . Phys. Chem. 1967,71 1717. W. C. Stoecker Analyt. Chem. 1967,39,628 1 70 G. D. Parfitt always arises the uncertainty of defining exactly the shape and character of particle aggregates from electron micrographs. A new geometrical method of analysis has been described by Medalia.16' The silhouette is treated as a plane figure from which are calculated the radii of gyration about the two central principal axes in the plane.The ratio of these radii is taken as the anisometry of the figure and other parameters are also calculated including the area and bulkiness as well as a 'structure factor' which expresses the excess area swept out by the figure as it rotates. To relate the two-dimensional projection to the three-dimensional aggregate flocs are generated by computer simulation. Similarity is demonstrated between the appearance of the simulated flocs and of actual electron micrographs of carbon blacks. Using recent values of the refractive index of selenium Danchot and Watillon16' have computed with the Mie equations the extinction coefficients of selenium sols as a function of wavelength (240-1100 mp) for particle diameters in the range 0 ( x 20)-500 mp.The computation was limited when the contributions of both the nth electric and magnetic partial waves were smaller than the 10-4th part of the extinction coefficient. The maxima appearing in the extinction curves are related to the contribution of various electric and magnetic partial waves and all the maxima shift towards the i.r. with increasing particle size. The influence of a normal particle-size distribution on the extinc-tion coefficients is analysed and the data afford a simple and accurate method for the simultaneous determination of particle diameter and size distributions. The first comprehensive study of the optical behaviour of dilute aqueous dispersions of carbon black has been carried out by Donoian and Medalia.I6' Both absorption and scattering (Zimm plot and angular-dependence) were studied and the relative importance of each to the extinction of light through the suspensions assessed.For most blacks the extinction is due mainly to absorption with subsequent conversion into heat but for the less-jet furnace blacks extinction due to scattering contributes at least 20% of the total. Both forward and total scattering increasz monotonically with particle size in the larger particle size range of blacks as does the diffuse reflectance from opaque pastes. Using the optical parameters obtained from measurements on the dilute sols the diffuse reflectance of concentrated systems was estimated but quantita-tive agreement with experiment is poor but a qualitative correlation is evident.Stability. Much fundamental work has been done on the stability of silver halide sols prepared by the 'classical' method of mixing reagents in a controlled manner ; however such sols are not monodisperse and the desirability of using sols with narrow particle-size distributions for comparison with theory is obvious. Methods of preparation involving homogeneous precipitation or decomposition of soluble complexes lead to sols of too low concentration to be useful but Weiss Ericson and her^'^^ have developed a procedure for 160 A. I. Medalia J . Colloid Interface Sci. 1967 24 393. 16' J. Dauchot and A. Watillon J . Colloid Interfuce Sci. 1967 23 62. 16' H. C. Donoian and A. I. Medalia J . Paint Technology 1967,37 716. 163 G. R. Weiss R. H. Ericson and A. H. Herz J .Colloid Interface Sci. 1967 23 277 Colloid and Interface Science 171 producing concentrated dispersions of monodisperse AgBr crystals. Using gelatin solutions monodisperse halide dispersions were formed by controlled mixing of reagents and then the gelatin was destroyed with enzymes. The zero point of charge of these and the classical sols is at pAg 5.3 f 0-2 and this is independent of crystal size and size distribution. Mere dilution of the sols to lo-% AgBr lowered the zero point of charge to pAg 2-4. The Smoluchowski theory of rapid coagulption does not take into account the attractive forces between the particles and therefore values of the stability ratio W calculated using the Fuchs theory (1934) may be less than unity i.e. the actual rate of coagulation is greater than the theoretical rapid rate.For adequate comparison with experiment W c 1 is untenable. McGown and Parfitt'64 have derived a simple equation to take account of the attractive forces in the derivation of a theoretical value for W Deryaguin and M ~ l l e r ' ~ ' have estimated the effect of the viscous resistance of the aqueous medium between coagulating particles which is normally assumed to remain constant and is expressed by the Stokes formula. They conclude that including a term to allow for changes in viscous resistance leads to a negligible effect on W and therefore differences between theory and experiment cannot be explained in this way. The successful application of the Deryaguin-Landau-Verwey-Overbeek (DLVO) theory of colloid stability to dispersions in non-aqueous media has been demonstrated by several workers.The coagulation kinetics of rutile in hydrocarbon solutions of Aerosol OT reported by McGown and Parfitt'66 show excellent agreement with the theory over a wide range of zeta potential. The magnitude and sign of the charge on the rutile particles is a complex function of the concentration of surfactant and the quantity of water in the system. Provided the water content of the solution is below 60 p.p.m. the ionic mechanism is operative and experiment agrees with theory. At higher water concentrations deviations are observed as shown in a further paper by the same a ~ t h 0 r s . l ~ ~ An increase in the amounts of water added leads to an increase in stability but a maximum in zeta potential.It is suggested that water adsorbed on the rutile surface leads to an increase in the effective particle (aggregate) size which compensates for the decrease in potential and maintains the stability. A similar correlation between the zeta potential and dispersion stability is demonstrated by Romo'68 for alumina and aluminium hydroxide in n- and iso-C, C, and C5 alcohols. Changes in sign of charge (negative to positive) were observed on addition of small quantities of water to alumina dispersions but the correlation was maintained. For the positively-charged hydroxide dispersions the stability increased with addition of water with no reversal of charge. Crowl' 69 has studied the stability of dispersions of mixed pigments (phthalo-16' B. V. Deryaguin and V.M. Muller Doklady Akad. Nauk. S.S.S.R. 1967,176,869. D. N. L. McGown and G. D. Parfitt J . Phys. Chem. 1967,71,449. D. N. L. McGown and G. D. Parfitt Discuss. Faraday SOC. 1966,42,225. D. N. L. McGown and G. D. Parfitt Kolloid-Z. 1967,220 56. L. A. Romo Discuss. Farad. SOC. 1966,42 232. 'Iy V. T. Crowl J . Oil Colour Chemists' Assoc. 1967,50 1023 172 G. D. Parfitt cyanines and titanium dioxide) in non-aqueous solutions of alkyd resins and similar media in an attempt to explain the flocculation flotation and flooding behaviour of alkyd and alkyd/amino paints. The degree of flocculation of the phthalocyanine pigments correlated with differences in particle-size distribu-tions of the pigments those with the greatest amount of fine particles showing the least flocculation.In general the stability was related to the nature and thickness of the adsorbed layer and although by electrophoresis a surface charge was found in some cases the effect of this charge was shown to be insufficient to explain the behaviour. Flotation effects are most pronounced with the finer sized pigments except where co-flocculation of the two pigments occurred. Flooding of the oxide pigment is associated with polar material in the alkyds. The removal of colloidal particles adhering to a solid surface by a non-aqueous surfactant solution has been studied by Clayfield and Lumb.”’ Particles of carbon black were deposited from a dispersion in a non-polar hydrocarbon oil surface of a metal powder bed and the removal attempted with hydrocarbon solutions of polyisobutene-succinic anhydride/tetraethylene-pentanine block copolymers of molecular weights in the range 600-120,000.Considerable detachment on the solid particles occurred with minimum hydrodynamic-displacement action and is explained in terms of the ‘secondary minimum’ adhesion concept and an entropic mechanism of polymer detergent action. The mechanism of flocculation by various water-soluble polymers (non-ionic anionic and cationic) has been investigated by Slater and Kitchenerl’l using aqueous fluorite suspensions. The influence of molecular weight the open structure of the flocs in contrast to those resulting from electrolyte coagulation and other data are accounted for qualitatively by the ‘bridging’ mechanism but the quantitative theory of Smellie and La Mer (1958) of refiltration curves is shown to be invalid.The adsorption of polymer on the ionic fluorite crystal surface is considered to be non-ionic and associated with a dipole interaction of non-ionic groups with the electrostatic field of the lattice. The part played by water structure around colloidal particles is considered by Johnson et in an attempt to explain marked deviations from the DLVO theory which the authors had observed with arachidic acid sols e.g. they are stable at zero zeta potential. The experiments reported are of measure-ments of the most rapid rate of coagulation of monodisperse polyvinylacetate sols at different temperatures and the rates compared with those predicted by the classical Smoluchowski theory based solely on diffusion.The experimental rates are lower than the theoretical values supporting the water-structure postulate and further evidence is provided from relaxation times of the water 170 E. J.Clayfield and E. C. Lumb Discuss. Faraday SOC. 1966,42,285. ”’ 172 G. A. Johnson S. M. A. Lecchini E. C. Smith J. Clifford and B. A. Pethica Discuss. Farday R. W. Slater and J. A. Kitchener Discuss. Faraday SOC. 1966,42 267. Soc. I966,42 120 Colloid and Interface Science 173 in the system as a function of temperature and particle concentration using spin echo n.m.r. techniques. The evidence presented would appear to support the views of Deryaguin on the long-range structuring of boundary layers of water. have studied the kinetics of coagulation by barium nitrate of a series of monodisperse polystyrene latex dispersions (600-4230 A) and compared log W versus log electrolyte-concentration curves with those predicted by the DLVO theory.The theory predicts an increase of slope with particle size but the experimental slopes showed little change with an increase in particle radius over nearly an order of magnitude a discrepancy yet to be explained. Estimated values of the Hamaker constant range from 1.03 x 10- l4 -1.10 x 10- l 3 erg. Similar experiments by Watillon and Joseph-Petit' 74 lead to a constant between 4 x and 7 x erg. Using a turbidity technique for the evaluation of stability ratios Daluja and Srivastava'75 have carried out a quantitative study (the first ever) of the coagulation of negative antimony sulphide sols on addition of mono-(Na' , K') di-(UOi + Mn2+ Ba2 +) tri-(A13 +) and tetra-(Th4+) valent cations.The critical electrolyte concentrations decrease in the order Na+ > K+ > UO;' > Th4+ > Mn2+ > Ba2+ > A13+ and show a marked deviation from the Schulze-Hardy rule. Using the DLVO theory with the zeta potential the authors have estimated values for the effective Hamaker constant varying from 2.4 x 10-l2 and 1-8 x erg according to the method of analysis. Rapid rate constants are lower than the theoretical (Smoluchowski) values by a factor of ca. 20. It is generally assumed that the effect of similions (those ions of the same sign of charge as the particles) on colloid coagulation is small and very little work has been done on the magnitude and nature of the effect.Lindfors and co-w o r k e r ~ ' ~ ~ have used the 'in statu nascendi' technique to investigate the critical electrolyte concentration of sodium counterions associated with various anions for negatively-charged silver bromide sols. The critical con-centration shows a linear dependence on the Stokes radius of the anion and there is a marked dependence on the charge of the similion the concentration being considerably larger for di- and tri-valent anions. The effect is still small compared with that of the counterion. Large organic cations (strychnine quinine etc.) are known to coagulate negative lyophobic colloids at concentrations considerably lower than simple inorganic ions of the same charge but before the work reported by Matijevic and K01ak'~~ there had been no previous studies containing sufficient in-formation to correlate the charge size configuration and chemical composition of the complex counterion with its effect on colloid stability.Their paper contains the results on the interactions of silver bromide sols with a number of Ottewill and 173 R. H. Ottewill and J. N. Shaw Discuss. Faraday Soc.,'l966,42 154. 174 A. Watillon and A. M. Joseph-Petit Discuss. Faraday SOC. 1966,42 143. 175 K. L. Daluja and S. N. Srivastava Indian J . Chem. 1967,5 262. 176 K. R. Lindfors D. X. West G. L. Blackmer and L. M. Carson J . Phys. Chem. 1967,71,3057. 177 E. Matijevic and N. Kolak J . Colloid Interface Sci. 1967,24,441 174 G. D. Parfitt metal (Ni Co Cr) chelates which permit variations in the size and nature of ligand and also with the same ligands variation of central ionic charge.The ‘in statu nascendi’ method was used to determine the critical stabilization concentration or critical coagulation concentration and significant enhance-ment of the coagulation power and charge-reversal ability of the metal ions by chelation is demonstrated. The remarkable effects are discussed in terms of the stability size and hydration of the chelate counterions. Electric double-layer and electrokinetic phenomena. In their paper on the discrete-ion effect in ionic double-layer theory Levine Mingins and Bell178 have reviewed the present state of the theory and concluded that only the hexagonal lattice model the cut-off disc approach and the Buff-Stillinger model are self-consistent. However the Buff-Stillinger model can break down at non-metallic interfaces and the lattice model is only valid at high surface charge densities.To cover all cases the authors suggest a ‘middle-of-the-road’ approach which might be provided by a cut-off disc of varying radius or by a more elaborate model based on a lattice liquid theory of the adsorbed phase, or by a calculation of the correlation function for relative ionic distributions on the inner Helmholtz plane. The paper also includes a discussion of certain experimental ‘anomalies’ in terms of the discrete-ion effect namely the Esin-Markov effect the maximum in the potential at the outer Helmholtz plane, certain aspects of colloid stability (e.g. the slope of log W versus log electrolyte-concentration plots) mutual antagonism of electrolyte mixtures in coagulation behaviour and certain effects at the mercury-electrolyte solution interface and with ionized monolayers.The relation between the surface charge density of stabilising ions and surface potential for a model which represents the silver iodide-aqueous 1 1 electrolyte solution interface with or without specific cation adsorption is examined by Levine and Matije~ic”~ in connection with the criticism of Mirnik of current electric double-layer theory. It is shown that the general behaviour can be reproduced by the theory and the authors claim than Mirnik’s proposal that the condition of thermodynamic equilibrium between AgI and the aqueous phase with respect to stabilising (I-) ions implies log charge density being proportional to surface potential is essentially incorrect.Mirnik’s ion-exchange theory of coagulation is also discussed and arguments given which are claimed to show that the theory is invalid. Mirnik,I8’ however, suggests that the derivation of Levine and Matijevic does not assume equality of the chemical potentials of the I- ions in the double layer and in solution, and claims that their approach is not physically significant. Furthermore he suggests that the objections to his ion-exchange theory are not valid. Corrections to the Poisson-Boltzmann equation for the potential distri-bution in the diffuse part of the electric double layer are considered by Levine ”’ S. Levine J. Mingins and G. M. Bell J . Electroanalyt. Chem. Interfacial Electrochem., 1967, 17’ S .Levine and E. Matijevic. J . Colloid Interface Sci 1967. 23. 188. 13 280. 180 M . M. irnik J . Colloid Interface Sci. 1967 24 282 Colloid and Interface Science 175 and Bell" in terms of ion-size variation in dielectric constant self-atmosphere effect the effect of medium compressibility and cavity potentials. Some numerical solutions of the modified equation for a single charged plate and for two equally charged parallel plates immersed in large volumes of aqueous 1 1 electrolyte are presented. No account is taken of the Stern layer containing adsorbed counterions. The potential drops more rapidly with distance from the surface than predicted by the unmodified equation but the corrections even at 0 . 1 ~ and potentials ca. 50-75 mv are not excessive.For two double layers the correction is such as to lead to a decrease in repulsion but the magnitude of the effect is not sufficient to affect the currently accepted stability theory of hydrophobic colloids. The influence of temperature on the electric double layer at the silver iodide-aqueous solution interface and the application to sol stability has been reported by Lyklema. 182 The technique involved a potentiometric titration of suspended AgI with potential-determining electrolyte and experiments were carried out at 5-85". At 25" alkali ions adsorb specifically on negative AgI, which gives rise to marked ion specificity in the double-layer capacitance leading to the lyotropic sequence in coagulation concentrations. With in-creasing temperature charge and capacitance decrease with a concurrent decrease in specificity and at 2 65" the double layer is predominantly diffuse and non-specific with absence of lyotropic sequence.Some evidence is presented (definite point of inflection in the differential capacitance versus temperature plot) for a phase transition at about 50" in the water layer adjacent to the particles. It is usual to describe the electrical behaviour of the non-polarisable interface between solids such as AgI and electrolyte solutions with the assumption of permanent equilibrium conditions i.e. of surface charge and potential difference between solid and solution being completely determined by the solution composition. However when rapid changes occur such as in collisions between particles in Brownian motion or changes in the double layer due to sudden changes in electrolyte concentration the assumption must be only an approxi-mation.Frens Engel and O ~ e r b e e k ' ~ ~ have considered the situation that arises when the inert electrolyte is added to a AgI surface in contact with an electrolyte solution. The double-layer capacity is changed and since double-layer capacities are adjusted in short times (ca. 10- ' sec.) it takes high exchange currents (10 A/cm.2) to maintain equilibrium. Exchange currents depend on the potential-determining ion concentration and conditions may be such that they are of the order of pA/cm.2 when equilibrium would be restored seconds after addition of inert electrolyte. Experiments are described in which the transient changes in e.m.f.of a galvanic cell containing a AgI electrode and reference electrode after adding the inert electrolyte. The effect vanishes at the zero point of charge. It is concluded that the exchange current fails to S. Levine and G. Bell Discuss. Faraday SOC. 1966,42,69. J . Lyklema Discuss. Faraday Soc. 1966,42 81. lE3 G. Frens D. J. C. Engel and J. Th. G. Overbeek Trans. Faraday Soc. 1967,63,418 176 G. D. Parfitt maintain equilibrium conditions during the rapid process even at the non-polarisable AgI-solution interface. The technique provides a new method of establishing the zero point of charge. Electrokinetic studies on oxidised aluminium surfaces by Morfopoulos and Parreira18 show that the behaviour of aluminium oxidised in air or water is intermediate between that of aluminium metal and pure alumina.The zero points of zeta potential obtained at constant ionic strength range from pH 6-9 depending on the extent of surface oxidation and permit correlation of electrokinetic parameters with corrosion phenomena. Adsorption isotherms for simple and complex ions were deduced from the measurements. Aerosols.-The work reported by Matteson and Stober' 8 5 was initiated to determine how the particle size distribution and quantity of dispersed material in aerosols generated from salt solutions varies with the concentration of the solution and the nature of the electrolyte. Several strong electrolytes (CuSO,, MnSO, ZnSO, MnCl, NaC1 and Th(NO,),) were dispersed from 0.1-10.0 weight per cent solutions with a modified Dautrebande-type generator and the particles examined by electron microscopy and the aerosol concentration determined by drawing through a membrane filter and analysing titrimetrically.For a given dispersant concentration in solution the concentration of electrolyte in the aerosol and the mean-volume diameters (from log normal size distri-bution) increased approximately in the same order namely Th(NO,), NaCl, CuCl, ZnSO, MnSO, and CuSO,. This is attributed to the variation in resistance to particle agglomeration by surface charges on the mist droplets. Estimated electrical field intensities at the external drop surface are in quali-tative agreement with the order of particles sizes. For a given electrolyte the mean-volume particle size increased with an average of 0.45 power of dis-persant concentration for electrolytes with polyvalent cations and with the 0.28 power for NaCl.A constant size was achieved at a certain concentration according to the electrolyte and above this concentration the number of particles increased. Some experiments were carried out with methanol solu-tions ; these gave relatively higher aerosol concentrations an effect related to the solvent surface tension. By analysis of the angular distribution of the polarisation of the scattered light from aerosols of solid spheres of vanadium pentoxide Jacobsen Kerker, and Matijevic' 8 6 have compared the particle size distributions at different wavelengths; this aerosol has a high optical absorption in the lower wave-length part of the visible spectrum comparable to that of metals but at higher visible wavelengths there is very little absorption (comparable to dielectrics).Hence the characteristics of the scattered light depend on the wavelength. The very different scattering data were analysed to give size distributions which agreed with each other and the uniqueness of the results was established with the aid of error contour maps. la4 V. C. P. Morfopoulos and H. C. Parreira Corrosion Sci. 1967,7 241. Ins M. J. Matteson and W. Stober J . Colloid Interface Sci. 1967,23,203. R. T. Jacobsen M. Kerker and E. Matijevic J . Phys. Chem. 1967,71,514 Colloid and Interface Science 177 Sulphuric acid aerosols consisting of droplets of narrow size distributions have been prepared by Coutarel et al.,I8' and the particle size distribution determined by light scattering. Particle size increased with increasing boiler temperature and decreased sharply with flow rate. These aerosols could be grown by passing over dilute solutions of the acid when the droplets absorb water until their vapour pressure reach that of the master solution; the rate of growth is proportional to the particle volume. Takahashi and Iwai188 have calculated the size distribution of various aerosols (linoleic acid triphenylphosphate stearic acid) containing very small particles (0.064.3 p) by means of polarisation ratio and/or dissymmetry of scattered-light measurements at various wavelengths. The values of these parameters were calculated for various size distributions assuming a log normal distribution. Estimated values of geometric mean size and standard deviation were confirmed with values obtained by electron microscopy. The polarisation ratio at 90" is shown to be very sensitive to size and polydispersity, while dissymmetry is essentially insensitive to polydispersity. Using both parameters it is possible to determine the mean size and standard deviation of polydispersed small aerosol particles within an error of about 10 % or less. The reproducible preparation of aerosols and their accurate characterisation by light scattering have been described in the literature and with such progress it should now be possible to follow coagulation by light scattering. Willis, Kerker and Matije~ic'~' have calculated the size distribution at various times of a dispersion of spherical aerosol particles undergoing coagulation as a result of Brownian motion for two initial distributions having a model radius of 0.25 p and zeroth-order logarithmic-breadth parameters of o0 = 0.1 and 0.3. For this distribution the angular variation of the polarisation ratio of the scattered light is calculated for h = 5460 and m = 1-50. Light scattering is shown to be useful for following the coagulation of the narrower of the two distributions up to about 1.4 half-lives. Using the equations of Smoluchowski modified to include a feed term, Mockros Quon and Hjelmfelt ' have calculated the particle size distributions of an aerosol that is being continually reinforced by the introduction of particles while coagulation under Brownian motion is proceeding. The dependence of the size distribution on the coagulation and feed rates and on the nature of the feed is discussed. la' J. Coutarel E. Matijevic M. Kerker and Chao-Ming Huang. J . Colloid Interface Sci. 1961, 24,338. K. Takahashi and S. Iwai J . Colloid Interface Sci. 1967,23 113. E. Willis M. Kerker and E. Matijevic J . Colloid Interfie Sci. 1967 23 182. L. F. Mockros J. E. Quon and A. T. Hjelmfelt J . Colloid Interface Sci. 1967 23,90

ISSN:0069-3022    

DOI:10.1039/GR9676400125

出版商:RSC    

年代:1967

数据来源: RSC

摘要:

ROTATIONAL VIBRATIONAL AND ELECTRONIC SPECTROSCOPY WE have decided to divide this Report into three separate sections on Micro-wave Infrared and Raman and Electronic spectroscopy. The scope has been limited to a consideration of papers listed in Current Chemical Papers for 1967 and thus contains references to work published in the latter part of 1966. Approximately 4000 titles have been scanned and about 900 papers read; no attempt has therefore been made to make the treatment comprehensive. Only papers of special interest to the reviewers or typical of those involved in major advances have been cited. Some slight overlap with the relevant Reports of 19661*2 has been inevitable under the new framework for Annual Reports. Two books devoted to general spectroscopy have appeared recently one by Whiffen3 and the other a set of problems of interest to organic chemists by Baker et aL4 A. D. Walsh Annual Reports 1966,63,44. * D. B. Powell Annual Reports 1966 63 112. D. H. Whiffen ‘Spectroscopy’ Longmans London 1966. A. J. Baker T. Cairms G. Eglinton and F. J. Preston ‘More Spectroscopic Problems in Organic Chemistry’ Heyden London 1967

ISSN:0069-3022    

DOI:10.1039/GR9676400179

出版商:RSC    

年代:1967

数据来源: RSC

摘要:

Part (i) MICROWAVE SPECTROSCOPY by J. E. Parkin (Department of Chemistry University College London) SINCE the last Annual Report by Shcridan.‘ summaries by Gordy2 on milli-metre wave spectroscopy and by Sheridan3 on microwave spectroscopy have appeared. More recently Flygare4 has published a comprehensive review covering January 1964-1967. A book by Sugden and Kenney’ contains a reference list of work molecule by molecule complete up to 1963. Instrumental advances have been discussed by Gordy2 and She~idan.~ The increasing range of sources and detectors now affords considerable overlap with the i.r. region. Greater sensitivity and stability of detectors including the development of commercial ‘spectrum accumulators’ by which a weak signal is built up with time thus increasing the signal to noise ratio have enabled molecules with very small dipole moments to be studied.The microwave absorption for HC=CD observed by Muenter and Laurie6 with a dipole moment ca. 0.01~ is ample testimony to this. Double-resonance techniques and improved computational procedures have also enabled significant advances to be made particularly in the field of larger molecules. Finally the development of a commercial instrument by the Hewlett-Packard Company,’ with several novel features suggests that the day may be near when microwave spectroscopy becomes a routine chemical research tool. The great sensitivity and selectivity of the technique gives it many advantages over more con-ventional spectroscopic methods for analytical applications as well as for purely spectroscopic investigations.Structure Determinations.-Microwave spectroscopy when applicable, continues to be the most reliable method for the determination of molecular structure and such molecular parameters as dipole moments. quadrupole coupling constants and barriers to internal rotation. During 1967 about eighty papers have appeared dealing in greater or lesser detail with molecules ranging from diatomic free radicals to one molecule with eighteen atoms. Very precise information can be obtained for diatomic molecules including bond lengths accurate to 0.0001 8 or better. It still remains true however that for very few polyatomic molecules have the equilibrium geometrical para-’ J. Sheridan Ann. Reports 1963 160. W. Gordy Pure Appl. Chem. 1965,11,403 J.Sheridan Pure Appl. Chem. 1965,11,455. W. H. Flygare Ann. Rev. Phys. Chem. 1967,18,325. T. M. Sugden and C. N. Kenney ‘Microwave Spectroscopy of Gases’ van Nostrand London, 1965. ‘ J. S. Muenter and V. W. Laurie J . Amer. Chem. SOC. 1964,86,3901. ’ Hewlett-Packard Company. Palo Alto California U.S.A 182 J . E. Parkin meters the so-called re-structure been determined. To do this involves measurement of the rotational constants for several isotopic modifications of the molecule in all the excited vibrational fundamentals. More usually, approximate ro or rs structures are determined. Costain' has discussed in-formally the problems relating to the accuracy of these structures. The critical use of data from electron diffraction and elsewhere will become more important especially when large molecules are considered.Dallinger and Toneman*= report an electron-diffraction study of 1,3-cyclohexadiene in which the micro-wave rotational constants are used as constraints in the structure determination. In dealing with small molecules especially those containing hydrogen, centrifugal-distortion effects become important. Two important papers by Watsong have appeared in which he considers the general problem of deter-mination of centrifugal-distortion constants from rotational energy levels, and the problem of indeterminacy of the constants obtained. He shows in particular that only five quartic distortion constants zapYs are linearly inde-pendent for non-planar molecules rather than six as previously assumed. A few recent analyses have been re-examined" in the light of this finding with significant improvement in the results.No doubt others will follow. Small Molecules and Radicals. Interest in these molecules traditionally the field of the electronic spectroscopist is becoming increasingly apparent see F l ~ g a r e . ~ The S - 0 radical is much studied and Amano Hirota and Morino,' from measurements on the first vibrationally-excited state of 32S-1 60 have determined the equilibrium bond length re to be 1.48108 & 0.00005 A. Recent investigations of Sn0,12 InCl,I3 and GeTe14 (in the latter 19 different isotopic modifications were measured separately) have provided data of similar accuracy. The spectra of KOH and CsOH vapours have been measured by Kuczkowski, Lide and Krisher." The K-0 and Cs-0 bond distances were determined as 2.18 and 2.40 A and the dipole moment of CsOH as 7.1 rf O ~ D favouring a highly ionic bond.A peculiar variation in the rotational constant B with the bending vibration (a ca. 300 cm.-') remained unaccounted for although quasi-linearity (a small potential hump at the linear configuration) and the very large amplitude of the vibration were considered. The combination of microwave data (centrifugal distortion and 1-type doubling constants) and i.r. data (vibrational frequencies and Coriolis coupling constants) in order to provide a reliable force field for the molecule is especially favourable in triatomic molecules where the number of parameters is still C. C. Costain Trans. Amer. Cryst. Assn. 1966 2 157.J. K. G. Watson J . Chem. Phys. 1966,45 1360; 1967,46 1935. G. Dallinger and L. H. Toneman J . Mol. Structure 1967 1 11. l o H. Dreizler 2. Naturforsch. 1966,21a 1719; H. 0. Sorensen J . Mol. Spectroscopy 1967,22,325. l 1 T . Amano E. Hirota and Y. Morino J . Phys. SOC. Japan 1967,22,399. l2 T . Torring 2. Naturforsch. 1967 224 1234. l 3 G. A. L. Delvigne and H. W. de Wijn J . Chem. Phys. 1966,45,3318. l4 J. Hoeft and H. P. Nolting Z . Naturforsch. 1967 224 1121. l 5 R. L. Kuczkowski D. R. Lide jun. and L. C. Krisher J . Chem. Phys. 1966 44 3131; D. R. Lide jun. and R. L. Kuczkowski ibid. 1967,46,4768 Part (i) Microwave Spectr.oscopy 183 small. Work of this kind has been reported on HCN,16 OCSe,17 NSF,18 FCN,I9 and NF, PF, and AsF,.~' Morino and Matsumura2' have deter-mined a new ?-,-structure for o c s rc- = 1.157 A and rcs= 1-5606 8 using measurements on various vibrationally-excited states.Measurements of the 1-type doubling constants enable the Coriolis coupling constants to be deter-mined and a preliminary calculation of the harmonic potential field is given. The variation of these constants in higher vibrational levels will provide data sufficient to determine many of the anharmonic potential constants and work is proceeding along these lines. Other Molecules. Structural and other information for some interesting molecules is summarised in the Table. A number of complete or near-complete structural determinations have been reported. Accurate bond lengths and angles for molecules containing silicon,26-28* 38 germanium,32.and selen-ium23,42 might be noted and some of these papers give interesting correlations with analogous compounds containing carbon and sulphur. Several interesting small-ring compounds4s~ 46 " 9 s 3 9 54 have had their conformation confirmed on the basis of their rotational constants. Internal rotation is a fruitful study with microwave spectroscopy. Molecules can be studied in several excited torsional states from which the torsional frequency and torsional barrier can be determined quite accurately. The methyl torsion in toluenes9 and p-chloro-toluene58 has a six-fold potential and is found to have a barrier of 13.94 cal. mole- '. Flygare4 summarises a large number of methyl torsional barriers and a large amount of theoretical work is currently being carried out on their origin.Kuzckowski and Lide39 report the structure of the interesting molecule PF,BH,. The molecule has a high barrier 3.24 kcal.mole-' and they were able to estimate the dissociation enthalpy of the molecule (2PF,BH3 + 2PF3 + B2H6) as 10.99 kcal. Investigation of the excited states of nitrosobenzeness indicates a barrier of 3.9 k.cal.mole- and the molecule is planar at equilibrium. Thiophenols6 is also planar and demonstrates no torsional splitting. One of the most promising structural determinations recently is the work of Pierce and Beecher61 and Pierce and Nelson62 on the two conformational isomers of cyclohexyl fluoride. This appears to be the first reported microwave study of the cyclohexane ring system. They find the axial fluoride isomer to be more stable than the equatorial fluoride by 400 300 cal.mole-'.The ring geometry is assumed and bond lengths adjusted slightly to fit the observed rotational constants. With such large molecular systems as this there is little likelihood of complete structural determinations but many gross conformational problems of interest to the organic chemist are waiting to be solved. l 6 A. G. Maki and D. R. Lide,jun. J . Chem. Phys. 1967,47,3206. Y. Morino and C . Matsumura h l l . Chem. SOC. Japan 1967,40 1101. '* A. M. Mirri and A. Guarnieri Spectrochim. Acta. 1967,23A 2159. l9 W. J. Lafferty and D. R. Lide jun. J . Mol. Spectroscopy 1967 23,94. *' A. M. Mirri J . Chem. Phys. 1967,47 2823. Y . Morino and C. Matsumura Bull. Chem. SOC. Japan 1967,40,1095.22 M. Lichtenstein V. E. Derr and J. J. Gallagher J . Mol. Spectroscopy 1966,20 381 TABLE. Some Recent Microwave Investigations. Bond lengths rxy are in A; dipole moment p in Debyes; barrier to internal rotation coupling constants determined ; c.d. = centrifugal distortion Molecule Reference Comments H2O SeOF, HCNO HNCO trans-€€NO2 HSiC13 SiF31 SiFC1, CH3F CD3F CHSCN CD3CN CH3Br CD3Br CH31 GeH3CN CF3CH0 CH,FCOF 1,2,5 selenadiazole CH,SiC13 GeH3SiH3 CH3NF2 CF3CHF2 22 23 24 2 4a 2s 26 2 1 28 29 29 30 31 32 33 34 3 5 36 31 26 38 p = 1.884 & 0012 new transitions. rSeO = 1.580 rSeF = 1.727 angles; character. rCH = 1.027 rCN = 1.161 rNo = 1.207, Dipole-moment variation with K. rNo(H) = 1.433 rNO = 1.177 r o H = 0.954, rSiH = 1.4655 rSiCl = 2-0118 p = 0.86, rsI = 2.387 q.c.comparson with other rSiF = 1.520 rSiCl = 2.019 p = 0 4 9 p = 1.8472 1-8682 precise measurement, p = 3.913 3.919 precise measurement, excited states Coriolis interactions. q.c. excited states Fermi resonance. complete structure p = 2-57 V = 4.170, p = 1.65 V = 0.885 double resonance brans = 2.67 pcis = 2-05 V = 19-1.3, p = 1-11 q.c. planar. rCF = 1-335 I, = 1.520 V = 3.51, rGeSi = 2-357 - p = 0.1 c.d. could not TCN = 1.155 rCeC 1*919,.~ = -3.99, p = 1-91 I/ = 0. PF3BH3 CHCS CH3 CH2CHN02 CH SeCH, pyrazole 1-methylcyclopropene bicyclo[ 1,1,0] butane pyridazine 1,3,2-dioxaborolan furfural CH3CH20CH0 3,4-dimethylenecyclo bu tene 1,2 and 1,3 difluorobenzene trans-2,3-epoxybutane spiropentyl chloride nitrosobenzene thiophenol 4-methyl pyridine p-chlorotoluene toluene (CH3)3CCH0 cyclohexyl fluoride CH3CHCHZOH 39 40 4 1 42 4 3 44 4 5 46 47 48 49 5 0 5 1 5 2 5 3 5 4 5 5 5 6 5 1 58 5 9 60 61 rBH = 1.207 rpp = 1.538 rpB = 1.836, rCMeS = 1.815 rcs = 1.680 p = 1.69, p = 3-70 V = 0.3 (nitro) q.c.planar. rCSe = 1-943 rCH = 1.093 p = 1.41, p = 2.214 planar with no symmetry p = 1-55 gauche configuration. structure determined V = 1-39. structure determined p = 0.675. complete structure p = 2.28 q.c. c. complex potential fuction ECis - E,,,, structure p = 0.618 planar. structure p = 2.03 V = 2.444. rotational constants V = 3.9 excited rSH = 1-30 rcs = 1-77 planar no torsional r" = 1.330 rcsc5 = 1.375 p = 4.22, brans = 1.98 pgau&e = 1.81 V = 1.10, p1,2 = 2.59 ~ 1 3 = 1.51 c.d.rCCl = 1.74 rCC = 1.51,q.C. p = 2.70 V6 = 13.51 cal q.c. rCcl = 1.74 v6 = 13.93 cal 9.c. P = 0.374 V = 13.94 cal. p = 2.66 VBut= 1.186 VMe = 2.6 3.5, axial rCF = 1.399 rcc = 1.526 rC 186 J . E. Parkin Analysis of the Stark splittings of favourable lines in the microwave spectrum provides the most accurate method available for dipole-moment measurement. Several erroneous dipole moments still appear in the literature based on solution studies when precise values are available. Analysis of hyperfine structure in the microwave spectrum enables nuclear quadrupole coupling constants to be measured fairly accurately.Here again a large amount of data is accumulating rapidly. Microwave Double-Resonance and Rotational Relaxation.-Double-resonance techniques are proving very useful in several aspects of microwave spectroscopy. By saturating a given transition with microwave power a non-equilibrium population distribution is set up in the two levels involved, and an increase or decrease in intensity in other transitions involving one of 23 I. C. Bowater R. D. Brown and F. R. Burden J. Mol. Spectroscopy 1967,23 272. 24 M. Winnewisser and H. K. Bodenseh Z. Naturforsch. 1967,22a 1724. 24(Q) K. J. White and R. L. Cook J. Chem. Phys. 1967,46 143. *’ A. P. Cox and R. L. Kuczkowski J. Amer. Chem. SOC. 1966,88,5071. 26 M. Mitzlaff R. Holm and H. Hartmann Z. Naturforsch. 1967,22a 1415.27 L. C. Sams jun. and A. W. Jache J. Chem. Phys. 1967,47 1314. R. Holm M. Mitzlaff and H. Hartmann Z. Naturforsch. 1967,22a 1287. 29 P. A. Steiner and W. Gordy J. Mol. Spectroscopy 1966,21,291. 30 Y. Morino and C. Hirose J. Mol. Spectroscopy 1967,24 204. 31 Y. Morino and C. Hirose J. Mol. Spectroscopy 1967 22,99. 32 R. Varma and K. S. Buckton J. Chem. Phys. 1967,46 1565. 33 L. Pierce R. G. Hayes and J. F. Beecher J. Chem. Phys. 1967,46,4352. 34 R. C. Woods J. Chem. Phys. 1967,46,4789. 35 E. Saegebarth and E. B. Wilson jun. J. Chem. Phys. 1967,46,3088. 36 G. L. Blackmann R. D. Brown and F. R. Burden Chem. Phys. Letters 1967,1 379. 37 A. B. Tipton C. A. Britt and J. E. Boggs J. Chem. Phys. 1967,46 1606. 38 A. P. Cox and R. Varma J. Chem. Phys. 1967,46,2007. j9 R.L. Kuscowski and D. R. Lide jun. J. Chem. Phys. 1967,46,357. 40 D. den Engelsen J. Mol. Spectroscopy 1967,22,426. 41 H. D. Hess A. Bauder and H. H. Gunthard J. Mol. Spectroscopy 1967 22 208. 42 J. F. Beecher J. Mol. Spectroscopy 1966 21,414. 43 W. H. Kirchhoff J. Amer. Chem. SOC. 1967,89 1312. 44 A. N. Murity and R. F. Curl jun. J. Chem. Phys. 1967,46,4176. ” M. K. Kemp and W. H. Flygare J. Amer. Chem. SOC. 1967,89,3925. 46 M. D. Harmony and K. Cox J. Amer. Chem. SOC. 1966,88,5049. 47 W. Werner H. Dreizler and H. D. Rudolph Z. Naturforsch. 1967 22a 531. 48 J. H. Hand and R. H. Schwendeman J. Chem. Phys. 1966,45,3349. 49 F. Monnig H. Dreizler and H. D. Rudolph Z. Naturforsch. 1966 21a 1633. ’ O J. M. Roveros and E. B. Wilson jun. J. Chem. Phys. 1967,46,4605.” L. Nygaard E. R. Hansen R. L. Hansen J. Rastrup-Andersen and G. 0. Sorensen Spectrochim. 53 M. R. Emptage J. Chem. Phys. 1967,47 1293. 54 L. M. Woerner and M. D. Harmony J. Chem. Phys. 1966,45,2339. ” Y. Hanyu C. 0. Britt and J. E. Boggs J. Chem. Phys. 1966,45,4725. 56 K. I. Johansson H. Oldeberg and H. Selen Arkiv Fysik 1967 33 313. ” H. D. Rudolph H. Dreizler and H. Seiler Z. Naturforsch. 1967 22a 1738. 58 G. E. Herberich Z. Naturforsch. 1967 22a 761. 59 H. D. Rudolph H. Dreizler A. Jaeschke and P. Wendling Z. Naturforsch. 1967 22a 940. 6o A. M. Ronn and R. C. Woods J. Chem. Phys. 1966,45,3831. 61 L. Pierce and J. F. Beecher J. Amer. Chem. SOC. 1966,88,5406. R. D. Brown F. R. Burden A. J. Jones and J. E. Kent Chem. Comm. 1967,808. Acta. 1967,23A 2813 Part (i) Microwave Spectroscopy 187 the levels is observed.Spectrometers have been d e ~ c r i b e d ~ ~ - ~ ~ incorporating this principle. Unland Weiss and F l ~ g a r e ~ ~ and Cox Flynn and Wilson64 have discussed the application of the technique to problems of assignment and identification. As an example Woods34 in an investigation on fluoral has described a successful search for weak and dispersed R-branch transitions which were connected with known Q-branch transitions. Oka68 has used the technique to demonstrate a ‘forbidden’ AJ = +3 transition 303 t Ooo in ethyl iodide. On pumping at the corresponding frequency with intense microwave power a signal line 404 +- 303 was observed to increase in intensity by some 10%. The weak AJ = 3 transition is allowed by the large iodine nuclear quadrupole.In some even more interesting experiments Oka679 69 has investigated collision-induced transitions in a series of molecules. For ethylene oxide for instance by pumping strongly the 2, t 2, transitions and monitoring the transitions 3, + 31 and 3, t 321 he showed that rotational energy was transferred by collision from the J = 2 levels to the J = 3 levels according to quite strict electric-dipole selection rules. The change in energy was larger at increased pressure due no doubt to the minimisation of wall effects. Similar observations were made with H,CO HCN and H,CCO. In some cases, quadrupole selection rules leading to AJ = 2 transitions appear to be import-ant. In addition he has obtained quantitative rate constants for the various collision processes and demonstrates for instance that for AJ = 1 collision-induced transitions the rate constants are the same order as those for AJ = 0 transitions even though the former involve much more widely-spaced energy levels.He considers this as evidence in support of Anders~n’s’~ theory of rotational resonance proposed to account for pressure broadening in the ammonia spectrum. Unland and Flygare66 have described double-resonance experiments on OCS in which they measured directly the relaxation time between two states. They found that the relaxation times obtained were half as long as those obtained from line-width data also indicating preferred collisional-exchange selection rules. They discuss possible extensions of relaxation experiments in the study of transient species gaseous chemical kinetics and lifetimes of excited vibrational states.Ronn and Wilson’ have confirmed Oka’s findings and have considered several other molecular systems. Gordon7 has contri-6 2 L. Pierce and R. Nelson J . Amer. Chem. SOC. 1966,88 216. 6 3 M. L. Unland V. W. Weiss and W. H. Flygare J . Chem. Phys. 1965,42 2138. 64 A. R. Cox G. W. Flynn and E. B. Wilson jun. J . Chem. Phys. 1965,42 3094. 6 5 R. C. Woods A. M. Ronn and E. B. Wilson jun. Rev. Sci. Instr. 1966 37 927. 66 M. L. Unland and W. H. Flygare J . Chem. Phys. 1966,452421. 6’ T. Oka J . Chem. Phys. 1967,47 13. 6 8 T. Oka J . Chem. Phys. 1966,45752. 6 9 T. Oka J . Chem. Phys. 1966,45,754. ’O P. W. Anderson Phys. Rev. 1949,76647. 7 1 A. M. Ronn and E. B. Wilson jun. J . Chem. Phys. 1967,46,3262. 7 2 R. G. Gordon J . Chem. Phys. 1967,46,4399 I88 J . E. Parkin buted a theoretical study of inelastic collisions between molecules allowing a more quantitative interpretation of these and related experiments. There is no doubt that this technique will provide much more quantitative information on collision processes than has hitherto been available and further results are awaited with interest

ISSN:0069-3022    

DOI:10.1039/GR9676400181

出版商:RSC    

年代:1967

数据来源: RSC

摘要:

Part (ii) INFRARED AND RAMAN SPECTROSCOPY by P. J. Hendra (Department of Chemistry The University of Southampton) THE major experimental advance occurring this year has been the introduction of laser-Raman spectroscopy to Chemical laboratories. Approximately fifty papers have appeared wherein this new technique has been used and four commercial spectrometers are now available. This section is divided into an account of the developments in laser-Raman spectroscopy followed by a survey of the more conventional techniques in vibration and vibration-rotation spectroscopy. Laser Raman Spectroscopy.-As forecast in the last Annual Report, there has been very rapid development in the technique and application of Raman spectroscopy using laser sources. A review by Brandmuller ’ has ap-peared which covers developments until February 1967 whilst an account of Raman spectroscopy edited by Szymanski’ includes a chapter by Koningstein, devoted to the subject.Unfortunately this book seems to have suffered some delay in preparation since it contains few references more recent than 1965. During the period under review the number of laser-Raman spectrometers available to chemists has increased markedly and as a result a number of papers have appeared which demonstrate that many groups are currently applying this new technique to as wide a range of problems as possible. It is now well established that whereas the examination of all but colourless non-turbid liquids or crystals was experimentally difficult using conventional methods the laser source has completely transformed Raman spectroscopy.This transformation has been emphasised recently in a very interesting ~urvey.~ The first field where the laser source showed enormous advantages over the conventional Toronto Arc was in the study of deeply-coloured liquids and solids.’ During the year a number of papers have appeared containing routine spectra of almost opaque solid^,^ and even colorimetric reagent^.^ In fact the renaissance has been so profound that in normal circumstances better spectra can be obtained from many solids than from their solutions. The ease and routine nature with which chemists can use the commercial instruments (appreciable numbers of Perkin-Elmer LR1* Cary 81,T Huet,$ Coderg,§ and Spex(( J. Brandmuller Naturwiss. 1967,21 293.‘Raman Spectroscopy’ Ed. H. A. Szymanski Plenum Press New York 1967. ’ I. R. Beattie Chem. in Britain 1967 3 347. P. J. Hendra J. Chem. SOC. (A) 1967 1298. E. R. Lippincott T. E. Kenney T. R. Nanney and C. K. Weifenbach J. Chem. SOC. (4 1967,32. P. J. Hendra and Z. Jovic J . Chem. SOC. (A) 1967 1127. * Perkin-Elmer Corp. Beaconsfield Bucks. t Cary Instruments Monrovia California U.S.A. Fa. Huet Societe General d’optique Paris France. $ Fa. SociCtC de Conversion des Energies Clichy France. 11 Spex Industries Metuchen New Jersey U.S.A 190 P. J. Hendra instruments have now been delivered) and the various types of sample they are able to examine make Raman spectroscopy a potentially valuable analytical tool. The field which has benefited most from this renewed interest is co-ordination chemistry Here the problems in the measurement and use of vibrational spectra are twofold-firstly; the species are frequently deeply coloured and contain heavy atoms resulting in the need for far i.r.and laser-Raman techniques but having the intrinsic advantage that the Raman intensi-ties are high due to the high polarisability of heavy-atom systems. Secondly, the molecules frequently have a high degree of symmetry with the inevitable result that the observations of i.r. spectra alone give very little reliable and definitive information. This latter limitation is so severe in centrosymmetric square planar and octahedral systems that the Raman spectra if recordable should be an essential part of all studies of the vibrational characteristics of co-ordination compounds in future.A classic example of the limited value of i.r. spectroscopy alone is furnished by a recent study by Hartley and Ware6 of the metal cluster compounds containing the ion [Mo,C1,I4-. Whereas a previous i.r. study' had simply identified two absorptions and a recent study identified a band near 230 cm. ' with a stretching of the Mo-Mo bonds,' this more complete analysis was much more informative. The laser-Raman spectrum contained ten bands and crude force constants were calculable for the Mo-Mo bonds. A similar study of Ir4(C0)129 was equally valuable the Ir-Ir stretching force constant having a value close to 1-3 millidynes per A. Another field where Raman spectroscopy is making great advances is in the study of the vibrational spectra of polymers.Symmetric modes of highly stereoregular species are of course only apparent in the Raman effect yet the technique has contributed little information to date' due to experimental limitations. During the year a report has appeared of the vibrational Raman spectrum of isotactic polypropylene.' ' The spectrum is of superb quality. In addition a new effect has been noted12 in that dichroism in the intensity of the Raman bands of stretched polymers has been observed for polypropylene fibre and tape. Although the effect is related to that familiar in the i.r. the explanation is somewhat complex. It is easy to visualize that the dipole deriva-tive (dp/Lldq) is maximized in the same general direction as the vectors in a given vibrating system but it is by no means certain that (Ja/Jq) should obey this rule.A more recent study of the dichroism in the Raman spectrum of polyethylene fibres13 has shown that it is likely that (aa/aq) is parallel to the vectors in a given vibration and further that the assignment of the Raman ' D. Hartley and M. J. Ware Chem. Comm. 1967,912. ' R. J. H. Clark D. L. Kepert R. S. Nyholm and G. A. Rodley Syectrochim.-Acta 1966,22,1967. * F. A. Cotton R. M. Wing and R. A. Zimmerman Inorg. Chem. 1967,6 11. C. 0. Quicksall and T. G. Spiro Chem. Cornm. 1967,839. l o J. R. Nielsen J . Polymer Sci. Part C Polymer Symposia 1963 19. l 1 R. F. Schaufele J . Opt. SOC. Amer. 1967,57 105. l2 P. J. Hendra and H. A. Willis Chem. and Znd. 1967,2146. l3 P . J. Hendra and H. A. Willis Chem.Comm. 1968,225 Part ( i i ) Infrared and Raman Spectroscopy 191 spectrum to fundamental modes is in error. It is suggested that the bands at 1133 and 1065 cm.- are assigned to B, and A respectively and not the reverse as previously widely thought. As the technique is applicable to thick fibres and sheets and requires no special sample preparation before examination it has great potential as an ancillary to i.r. dichroic measurements and has already been applied to polyethylene terephthalate and Nylon 66. During the later part of the year a report appeared14 describing preliminary experiments on adsorbed species. In many ways the results suggest that Raman spectroscopy may have intrinsic advantages over absorption measurements in this field since the background caused by the substrate material is remarkably unobtrusive.The work described was limited to physically adsorbed molecules but high sensitivity was demonstrated in that layers of bromine on silica gel down to thicknesses of the order of & monolayers gave spectra indicating the presence of bromine. Whereas in the i.r. the lowering of symmetry caused by the adsorption process makes many of the Raman bonds i.r. active the reverse does not seem to be true i.e. physically adsorbed centrosymmetric molecules show Raman spectra similar to those of the non-adsorbed species and mutual exclusion is retained. The demonstration of the effect in chemisorbed systems has appeared recently'' and is of interest since it is in this field that commercially-valuable heterogeneous catalytic problems may be accessible.There seems little reason to doubt that laser-Raman spectroscopy will be applied increasingly in this field since spectra of species adsorbed on silica carbon black and alumina have been recorded. In some cases electronic transitions can give rise to Raman emissions and some of these have been demonstrated and identified during the year by Koningstein.16 The effect is found to be of low intensity but the use of low temperatures and sophisticated optical and electronic design enables excellent spectra to be observed. Care is needed to distinguish the Raman effect from fluorescence but comparing spectra on the Stokes and anti-Stokes sides of the exciting line solves this problem. The trivalent cations of ytterbium europium, and neodymium in yttrium gallium garnet were studied in the first paper of a series.Although the helium-neon laser occupies the most important place in Raman spectroscopy examples are to be found of the use of other sources. Gee and Robinson17 have used an Argon-ion laser to obtain the Raman spectrum of crystalline benzene at 77" and 2 ' ~ . An output from the source of 250 milli-watts at 4880 8 enabled results to be recorded at a resolution of 0-65 cm.-' Brand-muller et have compared the performance of a quasi-continuous and continuous ruby lasers (at 6943 A) with the helium-neon gas laser but found them as yet inferior except for compounds such as p'-dimethylamino-p-nitro-l4 P. J. Hendra and E. J. Loader Nature 1967,216 789. l 5 P. J. Hendra and E. J. Loader Nature 1968,217,637.I' A. R. Gee and G. W. Robinson J . Chem. Phys. 1967,46,4847. J. A. Koningstein J . Chern. Phys. 1967,46 2811. J. Brandmuller K. Burchardi H. Hacker and H. W. Schrotter 2. angew. Phys. 1967,23 112. 192 P. J. Hendra azobenzene which are very deeply coloured. Perhaps the most elegant work in Raman spectroscopy using a laser source is that due to Porto and his co-workers on single crystals. A list of these will be found in ref. 1. A number of reports appeared at the 9th European Congress on Molecular Spectroscopy held in Madrid in September on work by other groups on single crystals. Their results are awaited with interest since the emphasis may then turn towards ranges of chemically interesting compounds. Tentative results on the Raman spectrum of a single crystal of a co-ordination compound have appeared.Ig The Raman spectra of gases are much more easily observed using laser sources than with gas-discharge lamps.It seems particularly advantageous to place the sample cell inside the resonant cavity of an argon-ion laser when vibration vibration-rotation and pure rotation lines can be observed using both photographic and recording spectrometers. The spectra of a number of gases were reported by Bernstein in Madrid (see above) but the most fascinating experiments described were those due to Barrett and Rigden.They examined gaseous CO in a cell within an argon-ion laser and observed the rotation lines. They then exposed the sample to a d.c. discharge and re-examined the spectrum whilst the discharge was in progress.They found prominent new bands in their Raman spectra neatly placed between the 'ordinary' rotational lines. The explanation of the effect was the subject of much discussion at the Conference. Structural Determinations using Infrared and Raman Spectroscopy.-As is always the case a large proportion of the effort in vibrational spectroscopy this year has been supplied to the solution of structural problems. The most thorough investigations are usually those involving an analysis of the complete spectrum followed by a structural diagnosis based on hypothetical models and the application of selection rules. A classical example of this approach was furnished by Clarke and Wood-ward2' who examined the cations of formula [(MeHg)],S+ and (MeHg),O+.The evidence (i.r. and Raman) strongly favours a pyramidal structure for the former but a planar (or nearly so) structure of the oxonium ion seems more probable. Another example of a structural determination typical of the work reported this year includes a far i.r. spectrum and assignment of the hyponitrite ion confirming its trans structure (C2,J.21 The method does have limitations however and on occasions results from other physical methods appear to disagree with the vibrational evidence. An example of this problem appeared during the year. Although trisilylamine is well established as a planar molecule,22 a paper appeared last year2 on the i.r. and Raman spectra of trisylyl phosphine suggest-l9 P. J. Hendra and E. R. Lippincott Nature 1966,212 1448. 2o J.H. R. Clarke and L. A. Woodward Spectrochim. Acta. 1968,23A 2077. 21 C. E. McGraw D. L. Bernitt and I. C. Hisatsune Spectrochirn. Acta 1967,23A 25. 22 K. Hedberg J . Amer. Chem. SOC. 1955,77,6491; E. A. V. Ebsworth J. R. Hall M. J. Mackillop, 23 G. Davidson E. A. V. Ebsworth G. M. Sheidrick and L. A. Woodward Spectrochirn. A k a , D. C. McKean N. Sheppard and L. A. Woodward Spectrochirn. Acta 1958,13 202. 1966 22 67 Part (ii) Infrared and Raman Spectroscopy 193 ing a similar structure and this has come under fire recently. A report appeared during the year on an electron diffraction study of (SiH,),P and (SiH,),As showing that the evidence clearly supported a pyrimidal C structure2, like trigermyl phosphine. However in a paper25 read before the American Chemical Society it was suggested that (SiH3)3P was planar.A further fascinat-ing twist to this story is that Goldfarb and Khare examined trisylamine in an Argon matrix and found that its i.r. spectrum could be interpreted in terms of a C3” structure but that methyldisilylamine is planar and dimethylsilylamine pyramidal.26 Clearly the energy difference between the two forms in these systems is small and crystal forces can distort the structure easily. In many cases it is not necessary to obtain the complete i.r. and Raman spectrum of a compound in order to discriminate between the likely structures. A very large number of examples of this type of work are to be found but there is room only for a few examples here. The selenium and tellurium halides have been repeatedly examined using i.r.and laser-Raman techniques during the year. Adams and suggest that the i.r. evidence is in favour of tellurium chloride and bromide having the TeCllCl- structure in the solid phase but that a molecular species is found in benzene solution. George et also examined the far i.r. spectra of the solids and came to a similar conclusion regarding SeCl, SeBr, TeCl, and TeBr,. The laser-Raman spectra29 of these species have been used as evidence for the existence of molecular species of C, symmetry in the solid phase. A comparison with far i.r. observations on the series SeBr, SeClBr, SeCl,Br, and SeCl seems to lend support to this conclusion. The reviewer who has a vested interest in the argument is not willing to adjudicate. During the year the i.r.spectrum of the P,I molecule was reported3’ and was used as evidence that the molecule did not exist in the ‘gauche’ configura-tion. A report3’ however appeared on the i.r. and Raman spectra of this com-pound the latter being obtained using helium discharge lamps giving an exciting line at 6678-15 A. The experiment was particularly interesting since the deeply-coloured compound was examined in solution and as a solid. The evidence strongly favours a trans PI2-PI structure of C, symmetry both in the solid state and in solution. Eleven spectral features were assigned to funda-mental modes. Attention was not confined to inorganic problems although much of the reports of the spectra of organic molecules was analytical and concerned with the presence of absence of functional groups.Two examples of gross structure determinations are as follows : 24 B. Beagley A. G. Robiette and G. M. Sheldrick Chem. Comm. 1967,601. ” A. H. Cowley and W. D. White Abtstracts 153rd Meeting Amer. Chem. SOC. 1967 L145. 26 T. D. Goldfarb and B. N. Rhare J . Chem. Phys. 1967,46 3379,3388. 27 D. M. Adams and P. J. Lock J . Chem. SOC. (A) 1967,145. 28 J. W. George N. Katsaros and K. J. Wynne Znorg. Chem. 1967,6,903. 29 G. C. Hayward and P. J. Hendra J. Chem. SOC. (A) 1967,643. 30 R. L. Carrol and A. H. Cowley Chem. Comm. 1967 872. 31 S. G. Frankiss F. A. Miller H. Stammreich and T. Texeira Sans Spectrochirn. Acttr 1967,23A. 543 194 P. J. Hendra An investigation of the vibrational and n.m.r. spectra of the isocyanate dimer (CF,*SNCO) by Downs and Haas3 confirms that it has the cyclic uretidine 1 3 dione structure (I) with the CF groups occupying the ‘trans’ configuration whilst a laser-Raman study of hexanitro~obenzene~~ gave some evidence that it occurs as benzotrisfuroxan (11).N-0 The speed of application and convenience of the spectroscopic methods make them particularly valuable tools for structural studies. There have been many examples of the use of these attributes during the year. Thus during the year much interest has been shown in the nature of the chalcogen-chalcogen bond.34 Much of this has been of a theoretical nature and concerned with explaining the approximately 90” anhedral angle charac-teristic of the molecules having such bonds e.g. H,02 Se2(CF,)235 etc. An interesting report by P e d e r ~ e n ~ ~ appeared in the middle of the year in which the anhedral angle in hydrogen peroxide was deliberately altered.In fact i.r. spectra of solid sodium oxylate perhydrate (Na,C20 - H,O,) gave evidence for the hydrogen peroxide molecule having a planar trans structure. On the other hand the caesium salt appeared to contain skew molecules. Two elegant reports have appeared on compounds of xenon. In the first, Nelson and Pimentel,’ reacted the element with chlorine under discharge and condensed the product onto a cooled caesium iodide flat. A very complex absorption band was observed at 310 cm.-’ which they propose could be due to the asymmetric-stretching mode of linear XeCl molecules. As evidence they point out that (a) a 2 1 stoicheometric ratio of gases was used in the discharge (b) they do not observe any absorption attributable to a symmetric-stretching vibration and (c) the band has exactly the right contour for a linear molecule of this type when allowance is made for the proportions and masses of the seven isotopes of xenon and two of chlorine.The relative intensities and frequencies were shown to fit a linear model very closely. In the second investiga-tion Gasner and C l a a ~ e n ~ ~ examined the compound xenon hexafluoride. Although one might anticipate an octahedral structure the i.r. and laser-3 2 A. J. Downs and A. Haas Spectrochim. Acta 1967,23A 1023. 33 N. Bacon A. J. Boulton and A R Katritsky Tr~ins Frrraday SOC 1967,63 833 34 W. H. Fink and L. C. Allen J. Chem. Phys. 1967,46,2261.35 W. E. Palke and R. Pitzer J. Chem. Phys. 1967 46 3948. L. Pedersen and K. Morokuma, 36 B. F. Pedersen Acta. Chem. Scand. 1967,21,801. 37 L. Y. Nelson and G. C. Pimentel Inorg. Chem. 1967,7 1758. E. L. Gasner and H. H. Claasen Inorg. Chem. 1967,6 1937. J . Chem. Phys. 1967,46,3941 Part (ii) Infrared and Raman Spectroscopy 195 Raman spectra of the compound at 40" (solid) 54" and 92" (liquid) and 94" (vapour) suggest otherwise. Although the vapour densities of the system suggest monomeric character the relative intensities of some bands are definitely temperature sensitive. It is possible that the liquid resembles the crystal in containing tetramers. The line at 609 cm.-' in the vapour-phase Raman spectrum is weaker than that at 520 cm.-' and is broad but polarised.In addition the i.r. of the vapour has distinct absorptions at 613 and 520 cm.-' Clearly the structure cannot be centrosymmetric in the vapour phase or some unusual electronic effects must be interfering in this region of the spectrum. It is fascinating to note however that Bartell,' has predicted very recently the occurrence of a pseudo Jahn-Teller effect in XeF6 from theoretical considera-tions and he states that a distorted structure is the most probable. The structure of hydrogen-bonded systems has been a popular subject for study for a long time and three examples will be cited. Waldstein and Blatz4' have recorded Raman spectra of liquid acetic and formic acids whilst Jakobsen et d4' have reported the low-frequency absorption spectrum. The authors agree that acetic acid appears to exist as predominantly cyclic dimers whilst formic acid is polymeric.An investigation of the vibrational spectrum of acrylic acid and sodium a ~ r y l a t e ~ ~ shows that the acid has a 'pseudo' C, type of dimeric ring structure. The enthalpy charge on dimerization was estimated to be about 8; kcal. compared with about 7 for saturated acids. The difference in values is probably associated with the degree of conjugation in the un-saturated acids. The study of charge-transfer complexes using far i.r. techniques has been supplemented this year by the report of the laser-Raman spectra of these species.43* 44 The former paper and one due to Yagi et aL4' are concerned with the effect of a range of acceptor molecules on the vibrational spectrum of a halogen or interhalogen compound.In the familiar benzene-bromine complex Hassel and S t r ~ m m e ~ ~ have suggested from diffraction data that the bromine molecule lies on a centre of symmetry in the system. Person et u Z . ~ ~ have ex-amined the i.r. spectrum of the compound at -200" and have been able to explain their results in terms of a C structure. They explain that the crystal data obtained at -50" may be correct and a structure change occurs with temperature variation or that the crystal form was rhombohedra1 rather than monoclinic. Lively interest has been demonstrated this year in the spectra of the trihalide ions. In the salt NO'ClF the difluorochloride seems linear but in the rubidium jg L. S. Bartell J . Chem. Phys. 1967,46,4530.40 P. Waldstein and L. A. Blatz J . Phys. Chem. 1967,71 2271. 41 R. J. Jakobsen Y . Mikawa and J. W. Brasch Spectrochim. Acta 1967,23A 2199. 42 W. R. Feairheller jun. and J. E. Katon Spectrochim. Acta 1967,23A 2225. 43 P. Klaboe J . Amer. Chem. SOC. 1967,89 3667. 44 G. C. Hayward and P. J. Hendra Spectrichim. Acta 1967,23A 1937. Y . Yagi A. I. Popov and W. B. Person J . Phys. Chem. 1967,71,2439. 46 0. Hassel and K. 0. Stromme Acta. Chem. Scad. 1958,12,1146. 47 W. B. Person C. F. Cook and H. B. Friedrich J . Chem. Phys. 1967,46,2521. 4 196 P. J. Hendra and caesium salts the solid-phase spectra suggest otherwise.48 Two reports on some of the heavier anions have appeared one concerned with the i.r. and Raman (using discharge lamps)49 and the other the i.r.and la~er-Raman.~' Both seem to agree and again it is suggested that crystalline forces can distort an otherwise h e a r ion. The first paper4' is particularly interesting in that a new method of examining dark-coloured solids in the Raman effect using discharge lamps was utilised. It is unfortunate that this technique was not developed sooner from the point of view of the inorganic chemist. The study of the vibrational characteristics of aqueous solutions has always been a popular field amonst Raman spectroscopists. A number of papers have appeared this year of which an example is one due to Hester and Grossmans' where the laser-Raman spectra of In3 + solutions were examined. The tempera-ture-dependence was found to be most interesting since changes in the Raman spectrum at Av values below 500 cm.-' indicated the presence of highly-ordered clusters of water molecules around the cations.The ion In(H,O):+ can be clearly identified due to its production of an emission near Av = 400 cm.-l and this is found particularly in the room-temperature spectrum of the perchlorate. The very high intensity of the band is however used as evidence for ordered cluster formation around this octahedral complex cation. The intensity of this peak in In2(S04) increases rapidly as the temperature of the solution is lowered and is very high in the glass formed by cooling the solution to about -40". Goulden and Mannings2 have made a valuable contribution this year by pointing out clearly that i.r. spectra of aqueous solutions are readily obtainable.They show that 5 % w/v solutions in 50 pm path cells will give useful spectra of such ions as sulphate carbonate and the phosphates. Vibrational Spectra of Small Molecules.-As is always the case a large number of small molecules have been examined. In order to give some idea of the range of species and of the type of analysis typical of the work carried out and reported this year we include a table (Table 1) of about twenty examples of molecules multimers ions etc. Inevitably the largest proportion of molecules studied were inorganic and of particular interest to co-ordination chemists although those interested in organic compounds were not neglected. The thoroughness of study and analysis were varied. Some workers quote results measured on solid liquid, gaseous and even matrix-isolated species whilst others contented themselves with an examination of a single phase.The detailed analysis of lattice modes and interactions in the solid phase is on the increase. Vibrational Analysis and Force Constants.-It is quite impossible to review adequately the scope of systems whose vibrations have been analysed during 48 K. 0. Christe W. Sawodny and J. P. Guertin Inorg. Chein. !967,6 1159 49 A. G. Maki and R. Forneris Spectrochim Acta 1967,23A 867. 5 0 G. C. Hayward and P. J. Hendra Spectrochim Acta 1967,23A 2249. 5 1 R. E. Hester and W. E. L. Grossman Spectrochim Acta 1967 23A 1945. 5 2 J. D. S. Goulden and D. J. Manning Spectrochim. Acta 1967,23A 224 Part (ii) Infrared and Raman Spectroscopy 197 TABLE 1 Molecule Reference Comments C,H,Se 53 Planar selenophene molecule.Full assign-ment given. U.V. data included. Most results unique. 54 Divinyl ether. 1.r. and Raman study. C, rotational isomer most stable. Assignments proposed. c203 55 v q at 63 cm. - '-very flat potential well for this bending mode. Carbon suboxide. C,Hl,O 56 Di-tertiary butyl peroxide. Full assignment of all observed features. ClNF 57 Spectrum of gas trapped in Ar matrix. Full assignment given. NF,O 58 C, symmetry 6 fundamentals observed B = 0.19 cm.-' rNAF = 1.48A FZB-CN 59 1.r. spectrum 400&245 cm.- '. All bands assigned. N0,Cl and NO,F 60 Re-examination of spectra. New assign-ments. Force constants computed AH: (298") FNO = -25.8 kcal. mole-'. ClNO = +3.39 kcal. mole-'. F,P.S 61 C3, confusion in assignment resolved. vWF) 983 and vwc,) 768 cm.-'. 62 Bands in solid HF dimer trimer and chain polymers identified. SeF and WF6 63 Vibrational analysis and Coriolis constants applied to force field. s6 64 D3d chair ring. Raman data incomplete. Full assignment give 198 P. J. Hendra Table 1-continued C2D,Se 65 Complete assignment. Some modes identi-fied by using co-ordination compounds. 66 Discussion on 'interaction constants' to be used in Urey-Bradley Force Field calculations. BaCl - 67 Raman of BaC12/KC1 melt systems. Full assignment of 3 bands. Fourth funda-mental found by quenching melt and examining solid in the i.r. Structure Dlh Ga2CI 68 Approximate force constants calculated after assignment of i.r. and Raman bands.C4HC17 69 Chlorocyclobutane and deuteriated ana-logues. Study of ring puckering (v = 165 cm.- '). Potential neergy function for this mode discussed. sc1; SeCl,+ TeCl; 70 Raman spectra recorded of AsFi-salts. Force constants computed. D2S 71 v1 and v2 analysed. Rotational constants calculated. 72 Re-investigation of i.r. spectrum. Fermi resonance between 2v2 and v1 postulated. 53 A. Trombetti and C. Zauli J . Chem. Soc. (A) 1967,1106. 5 4 A. D. H. Clague and A. Danti J . Mol. Spectroscopy 1967,22,371. 5 5 R. L. Redington Spectrochim. Acta 1967,23A 1863. 5 6 D. C. McKean J. L. Duncan and R. K. Hay Spectrochim Acta 1967,23A 605. 5 7 J. J. Comeford J. Chem. Phys. 1966,45,3463. 't3 E. C. Curtis D. Philipovich and V. H. Moberley J . Chem. Phys.1967,46,2904. 5 9 N. B. Colthup Spectrochim. Acta 1967,23A 2167. 6 o D. L. Bernitt R. H. Miller and I. C. Hisatsune Spectrochirn. Acta 1967,23A 237. 6 1 R. G. Cavell Spectrochim. Acta 1967,23A 249. '* J. S. Kittelberger and D. F. Hornig; ;I. Chem. Phys. 1967 46 3099. 6' S. Abramowitz and I. W. Levin lnorg. Chem. 1%7,6 538. 64 L. A. Nimon V. D. Neff R. K. Cantley and R. 0. Buttlar J . Mol. Spectroscopy 1967,22 105. 6 5 J. R. Allkins and P. J. Hendra Spectrochim. Acta 1967,23A 1671. 66 K. Shimizu and H. Shingu Spectrochim. Acta 1966 22 1999. 67 J. R. Chadwick P. J. Cranmer and H. C. Marsh J . Znorg. Nuclear Chem. 1967,29 1532. '* I. R. Beattie T. Gilson and P. Cocking J . Chem. Soc. (A) 1967 702. J. L. Hollenberg J. Chem. Phys. 1967,47 3271 Part (ii) Infrared and Raman Spectroscopy 199 the year.One field in which significant progress has been made is in the use of the spectra of crystals to support assignments. Thus Sbrana et al.73 were able to show a number of errors in the previous assignments of the spectra of pyrimidine by examining single crystals of the protonated and tetra-deuteriated molecules in polarised i.r. radiation. Similar approaches to the spectra of anthraq~inone,~~ 1,2,5-0xadiazole,~ and some pho~ophonitrilics~~ have enabled the assignments to be corrected and put on a firmer experimental footing. Yamada and S u z ~ k i ~ ~ went a step further and examined a bulk crystal in the i.r. using attenuated total reflectance. Although the spectra of oriented polymers have already been recorded by this method this is the first report of the effect using a single crystal.The previous assignments were by no means unanimous and a new set of proposals are given. Other papers which must be mentioned include ones on the mechanical calculation of force constants by Becker and Mattes,78 Bruton and Wood-ward,79 and a note by Llewellyn Jones" on the transferability of force constants. It has become customary amongst many co-ordination chemists interested in carbonyl compounds to relate force constant and 'bond strength'. Jones points out that this is most hazardous unless the types of system compared are very similar e.g. the K- values in M(CO),L cannot be compared meaningfully with those in M(C0)6. Further one cannot use 'approximate' force constants interactions must be allowed for since these are highly signifi-cant.In another paper Jones discusses the connection between force constants and bond order in the dichalcogenides of carbon.8' In a similar vein Wing and Crockerg2 point out the value of i.r. intensities for structural diagnosis and plea for their use rather than absorption frequencies. One cannot help asking if force constants are nm-transferable and cannot be related to bond strengths of what value are they? If these restrictions apply vigorously then frequencies calculated from 'apparently reasonable' force constants must be suspect in value especially since it remains virtually impossible to forecast interaction constants in most cases. Vibration Rotation Spectra.-The study of rotation vibration is a perennial feature in the i.r.field. An example where detailed structural information was obtained is an account of the spectrum of germyl isothiocyanateg3 and its tri-69 J. R. Durig and A. C. Morrissey J . Chem. Phys. 1967,46 4854. ' O W. Sawodny and K. Dehnicke Z . Anorg. Chem. 1967 349,169. 71 R. E. Miller and D. F. Eggers jun. J . Chem. Phys. 1966,45 3028. 72 J. W. Nebgen F. I. Metz and W. B. Rose J . Mol. Spectroscopy 1966 21 99. 7 3 G. Sbrana G. Adembri and S. Califano Spectrochim. Acta 1966 22 1831. 74 C. Pecile and B. Lunelli J . Chem. Phys. 1967,46,2109. 7 5 G. Sbrana M. Ginannerchi and M. P. Mazocchi Spectrochim. Acta 1967,23A 1757. " U. Stahlberg and E. Steger Spectrochim. Acta 1967,23A 627. 77 H. Yamada and K. Suzuki Spectrochim. Acta 1967,23A 1735. " H. J. Becker and R.Mattes Spectrochim. Acta 1967,23A 2449. 79 M. J. Bruton and L. A. Woodward Spectrochim. Acta 1967,23A 175. 'O L. H. Jones Znorg. Chern. 1967,6 1269. " L. H. Jones Znorg. Chem. 1967,6,429. e.' G. Davidson L. A. Woodward K. M. Mackay and P. Robinson Spectrochim. Acta 1967, R. M. Wing and D. C. Crocker Inorg. Chem. 1967,6,289. 23A 2383 200 P. J. Hendra deuteriated derivative. The i.r. and Raman spectra were recorded and assigned and the Ge-H modes near 2130,870 and 645 cm.-' were examined in detail in the gas phase. The results were interpreted as indicating an angle of ca. 156" between the Ge-N and N - C bonds. In small systems it is possible to record rotational constants. An example of this type of work appearing this year was the molecule 15N180 where values re = 1.507 A o = 1818.94 cm.-', and D = 4.7 x lo- cm.-' were c a l c ~ l a t e d .~ ~ Another example which poses interesting questions is an examination of the spectrum of b ~ t a d i e n e . ~ ~ The analysis of the rotational fine structure lead to the proposition of a carbon-carbon length of 1-464 f 0.003 A and a C = C angle of 123.2 f 0.2". The C-C single-bond length is significantly shorter than the value obtained from electron-diffraction data. Occasionally seemingly anomalous behaviour is noted in these investiga-tions. One sample from this year's work is contained in a paper by Durig and Wertzg6 on the i.r. spectra of HNCS and DNCS. It was observed that large gas-solid shifts occurred on freezing these gases and also that the vibration-rotation results from the N-H stretching band gave rotational constants of 43.45 & 0-5 cm.-' for the ground state but 36-67 & 0.5 for the first excited vibrational state.This fall in value seems very large. An explanation of an apparent anomaly was also offered during the year by Brown and Sheppard and by Sanb~rn.~' They explain the shape of the C=C and C=N stretching bands in gas-phase i.r. spectra of acetylenes and nitriles by invoking the occurrence of a multiple Q-branch structure associated with 'hot bands'. The reason may well be due to interaction of the C-C=X deformation and C=X stretching modes. A similar explanation for v2 in C F C S H was given by Sanborn. Another interesting paper appearing recently concerned the rotation of monomeric hydrogen fluoride in rare-gas lattices.88 There is a low barrier to rotation as demonstrated by the contour of the vibration-rotation band in the i.r.An interesting observation is that the centre of gravity does not co-incide with the centre of a lattice site i.e. there is a low potential maximum at this position. The effect seems to increase from argon to xenon. Also during the year a paper appeared on the pressure induced rotational quadropole spectra of hydrogen ~hloride.~' Intensities of the AJ = 2 lines were observed for HCl and HCl/SF mixtures and HBr and HBr/SF,. The molecular quadropoles were calculated as 5-8 x e.s.u. cm.2 for HCl and HBr respectively. It is claimed that these are unique results. C \ and 5-5 x 84 J. L. Griggs jun. N. K. Narahari Rao L. H.Jones and R. M. Potter J . Mol. Spectroscopy, 8 5 A. R. H. Cole G. M. Mohay and G. A. Oxborne Spectrochim. Acta,,1967,23A 909. 86 J. R. Durig and D. W. Wertz J . Chem. Phys. 1967,46,3069. 87 J. K. Brown and N. Sheppard Spectrochim. Acta 1967,23A 129; R. H. Sanborn ibid. p. 1999. 88 M. T. Bowers G. I. Kerley and W. H. Flygare J . Chem. Phys. 1966,45,3399. 8 9 S . Weiss and R. H. Cole J . Chem. Phys. 1967,46 644. 1967 22 383 Part ( i i ) Infrared and Raman Spectroscopy 20 1 Infrared Intensities.-Perhaps the major development during the year has been the expansion of interest in the intensities of i.r. bands in solids. A typical example of the type of work confined to simple molecular systems is that due to Ross and S~hnepp,~' who examined nitrogen and carbon dioxide as solids, and developed a theory to explain the intensities of the bands.In addition steady progress is apparent in the scope of investigations of gas-phase absorp-tion intensities. The advantage in examining gases is that intermolecular forces do not perturb the molecular motions. One of the major problems however in this field is the necessity of using high pressures to broaden the rotation-vibration lines. This broadening is needed because the slit-width of even the best commercial i.r. spectrometers is quite large and certainly greater than the width of a vibration-rotation band at low pressures. Pressure broaden-ing is of course caused by intermolecular collisions and therefore the use of this technique tends to destroy the advantage of measuring spectra in the gas phase.An example of the pressure-broadening technique was furnished by Morcillo et aL9' who examined CH2F2 CH,Cl, and CF,Cl,. They conclude, from their studies based on a new theory to explain absorption intensities, that (ap/d4) is not directed along the bonds but is strongly deflected towards the most polarisable atom in a molecule. A report appeared during the year in which intensities of the v3 bonds in methane nitrous oxide and acetylene were measured usiag a method which does not require pressure broadening. Hunter92 used a constant-volume gas cell containing the gas and recorded the pressure rise when filtered i.r. rotation was allowed to enter the cell and be absorbed by the gas. The pressure rise was minute but by using a moving diaphragm as half of a condenser he was able to measure the rise accurately.The amount of energy absorbed was measured by using electrical heating until the same pressure rise as before was produced. No corrections for overtones or combinations were included and the band pass of the filters was 3-5 p. The intensity data are probably accurate to within 7 % and are compared with previously published work. Hunter's table is reproduced in Table 2 and is self explanatory. TABLE 2 Intensity data in literature cm.-' atm.-' New results v,-CH 324,326,358 3 70 v3-N,0 1867,1650,1617,997,1850 1760 v~-C~H 590,280,325 420 Using i.r. dispersion and at 2 9 4 " ~ pressure-broadened absorp-tion techniques. 0. Schnepp J . Chem. Phys. 1967,46,3983,3991. . 91 J. Morcillo J. J.Zamorano and J. M. V. Heredia Spectrochim. Acta 1966 22 1969. 92 T. F. Hunter J . Chem. SOC. (A) 1967,374 202 P. J. Hendra Vibrational Spectra of Polymers.-Apart from the reports of the laser-Raman spectra of polymers a considerable number of papers on the i.r. spectra have appeared. A revision in the assignment of the spectral features to the vibrations of polyethylene has been discussed by Snyder93 confirming that the study of polymers and especially the more complex ones is still in its infancy. This statement particularly applies to the identity of the lower-frequency bands. At the International Conference on Molecular Spectroscopy held in September in Madrid these bands in solid polymers were discussed in detail. A paper by Tasumi and Krimmg4 has appeared in which the bands in solid polyethylene are identified dispersion curves produced and solid phase chain-chain interactions discussed.Zerbi et have examined molten polypropylene and solid polyvinylidene fl~oride.’~ The former is considerably different from the solid but still contains helical moieties (normal mode calculations support 5 repeat units per helical section) whilst the fluoride seems to occur in two forms, one planar zig-zag and the other less symmetrical but including a glide-plane. Another typical example of structural determination in polymeric systems was one due to Matsura and Miyazawa” who showed that in polyethylene-glycol (liquid) a random coil structure is likely. Probably the low melting point is connected with this coiling. Yet another field where spectroscopic examination is of value is in the decomposition of polymers and an example has appeared recently.Luongog8 irradiated ?oly-(3-methylbut-2-ene) with electrons of 1 MeV. It is suggested that the decay occurs as follows and since an increase in vinylidene saturation I 6-C-C + 2Me.+H’- CH, H CH,H I II I and a small increase in trans unsaturation is observed coupled with a yield of hydrogen and propene the first mechanism is the most likely. Infrared Spectroscopy of Adsorbed Species-Since numerous papers have appeared in the field and no new developments seem to be apparent it is only possible to select typical examples. In one such a classic system carbon monoxide on palladium was e~amined.~’ Two bands were observed at 4.8 p M groups.This latter 7 - O \ due to M-CEO groups and at 5.2 p from M 93 R. G. Snyder J . Mol. Spectroscopy 1967,23,224. 94 M. Tasurni and S. Krirnrn J . Chem. Phys. 1967,46,755. 95 G. Zerbi M. Gussoni and F. Ciampelli Spectrochim. Acta 1967 23A 301. 96 G. Fortili and G. Zerbi Spectrochim. Acta 1967,23A 285. 97 M. Matsura and T. Miyazawa Spectrochim. Acta 1967,23A 2433. 98 J. P. Luongo J . Polymer. Sci. Part B Polymer letters 1967 5,281. 99 J. K. A. Clarke G. Farren and H. E. Rubalcava J . Phys. Chem. 1967,71,2376 Part (ii) Infrared and Raman Spectroscopy 203 band seems to remain after continued pumping whilst the former is varied in intensity with the coverage of the palladium on its support (in this case silica). The authors suggest that this latter observation may be caused by the crystallite size of the metal on its substrate.In low concentrations of palladium the particles are small and it is suggested this leads to a spacing of the metal atoms unfavourable to the formation of bridges. A further quite typical example of the work published this year is again on the re-examination of a classic system -NH on porous glass."' Examination of ammonia over dehydroxylated fluoridated and deuteriated porous glasses are included but the i.r. spectra are confined to the 3400 cm.- region. Evidence B is put forward for the formation of 'B-NH, \ -SiNH2 \N-H and / B / / physically adsorbed ammonia groups on the*surface. Finally a paper on physically adsorbed species and surface reactions ; Young and Sheppard''' have shown amongst other things that acetaldehyde adsorbed on silica heated to 120" gives a spectrum convincingly identified as that due to crotonaldehyde. Two excellent books have appeared on this subject during the year one by Hare102 and the other by Little.lo3 loo M. J. D. Low N. Ramasubramanian and V. V. Subba Rao J . Phys. Chem. 1967,71 1726. l o 2 M. L. Hare 'Infrared Spectroscopy in Surface Chemistry' Marcel Dekker New York 1967. lo' L. H. Little 'Infrared Spectra of Adsorbed Species' Academic Press New York 1966. R. P. Young and N. Sheppard J . Catalysis 1967,7 223; Trans. Faraday SOC. 1967,63 2291

ISSN:0069-3022    

DOI:10.1039/GR9676400189

出版商:RSC    

年代:1967

数据来源: RSC