GENERAL DISCUSSION Prof. A. D. Buckingham (Cambridge University) said Deutch has drawn our attention to theoretical difficulties in obtaining reliable single-molecule orientation correlation functions from dielectric dispersion measurements on polar fluids. Similar problems have been encountered in the determination of dipole moments of molecules in condensed phases but these are significantly reduced by studying dilute solutions in a non-polar solvent. For this case E(W) differs from ~(0) by a small number proportional to the concentration of the polar solute and Deutch's eqn (2.10) and (2.11) become equivalent at infinite dilution. Does he believe that dilute solutions of polar compounds in non-polar solvents are suitable systems for measuring single-molecule orientation-correlation functions ? And could he be enticed into giving us some quantitative estimates of how serious the fundamental difficulties may be ? Prof.A. Gerschel (Orsay)said In response to Deutch I wish to make three points in favour of the dipolar absorption method. The first point deals with the choice between the Cole-Glarum or the Fatuzzo-Mason expressions. We remark that for computing statistical functions in the time domain representation only under certain conditions is there a significant departure between the results of both relationships which exceeds the experimental uncertainties. Such is the case with highly polar liquids possessing a large zero-frequency value co and intense absorption-dispersion features. In such liquids as recently noted with CH3F CH3Cl and CHF3' differences show up in the decay of correlation functions and memory functions depending on which of the theories was applied.I want to point out however that for the vast majority of liquids not possessing such very intense absorption features only minor differences appeared in the computed statistical functions (this was checked with liquids OCS and CHC13) still well within the experimental uncertainties. A second remark deals with the relationship between many-particle and single- particle correlation functions. One may agree that the search for a single-particle information is hopeless when one starts with the mixed information that is provided by dielectric relaxation. But since it is actually multimolecular information in- corporating both self and collective motion it is wise to keep it in this form and to complete the information from other " monomolecular," sources such as spectro-scopic studies of rotational broadening.Then one may gain by comparison information on the relative importance of collective motions. Taken from this point of view the useful and genuine character of dielectric relaxation is precisely to incor- porate both the effects of self and of cross correlations. Finally dielectric measurements may be useful in selecting models of molecular motion. Only if one restricts the measurements to dielectric relaxation are the pro- cesses insensitive to the details of the motion as a consequence of being essentially Markovian. But if dipolar absorption is considered as a whole it is seen to incor- porate the high frequency end that corresponds to damped librational motion.This latter gives information on short-time behaviour when the statistical functions are computed-correlation functions and memory functions-and it is a very sensitive test A. Gerschel C. Brot I. Dimicoli and A. Riou Mol. Phys. 1977 33 527. GENERAL DISCUSSION for any model to check its behaviour at any time against the actual time dependence extracted by Fourier inversion of the total dipolar absorption features. Typical examples of models not giving simultaneously acceptable agreement at short times and long times are the so-called "extended diffusion " models (after Gordon's J and A4 models).1*2 Models of the "itinerant oscillator " type3p4 give a much more satis- factory description on these grounds.Dr. G. Wyllie (University of Glasgow) said Although the qualifications set out by Deutch are important it may still be worth while to see whether there exist systems reasonably described by available theories. But one further qualification is that the dielectric friction term included in Deutch's eqn (3.3) is correct for small angle libration the case discussed by Fatuzzo and Mason wrong for free rotation even with a fixed axis (in which case successive rotations commute) and probably nearly correct for a diffusive motion with a small mean free angle of rotation. If then we combine Deutch's eqn (3.3) and (2.10) the function Eo -1 E2 + EoE + Eo 1 + icoz = -&o -(2E + l)(&-1) contains our information about the molecular mechanics with the dipole-dipole interaction more or less subtracted out.In the particular and probably rare situation where the dipole-dipole random force is uncorrelated with the residual random force acting on a molecule in small-angle diffusive rotation the related function should be the transformed dipole autocorrelation function for the (not realised) motion with the dielectric friction switched off and nothing else altered. Dr. W. Alexiewicz Dr. J. Buchert and Prof. S. Kielich (Poznari) (communicated) Had any of us been able to attend the Symposium we would have presented the fol- lowing material to supplement our paper read at this Symposium. The time-variations of the quadratic variations in electric permittivity in liquids take a simpler form if the analysing field is not time-variable or if the frequency of its vibrations is very low since now the dispersional factors R(uabc)behave as follows Eqn (17) now leads to the following simpler expressions A.Gerschel C. Brot I. Dimicoli and A. Riou,Mol. Phys. 1977,33 527. * J. O'Dell and B. J. Berne J. Chem. Phys. 1975,63,2376. N.E.Hill Proc. Phys. Soc. 1963,82,723. 'G.Wyilie J. Phys. C. 1971,4 564. GENERAL DISCUSSION which are especially well adapted to numerical analysis. In the approximation of Debye rotational diffusion one has r1 = 3r2,where 2, the relaxation time of electric birefringence,l can be used for the determination of the evolution in time of the various temperature-dependent contributions to dielectric saturation by a procedure similar to that applied with respect to the electric birefringence of liquid~.l-~ The curve shapes of the time-evolution of the temperature-dependent contributions reflect the competition between the purely dipolar term and the terms related with the aniso- tropy in electric polarisability of the molecule.This competition is the result of the differences in rise-time and sign of the various terms. The rise in time of the polarisa- tion due to reorientation of the permanent dipole moment is slower than the variations in time due to reorientation of polarisability anisotropy. In order to plot the time-evolution of dielectric saturation which sets in when ex- ternal electric fields are switched on to a system of non-interacting dipolar linearly polarisable molecules (m# 0 y # 0 b = 0) we introduce as in ref.(3) the following dimensionless molecular parameter r = (K) - (3) 1 m2 k3T3 k2T2 kT y ' Whereas for molecules with weak permanent dipoles (and non-dipolar ones) one has r !z 0 in the case of strongly dipolar molecules r differs considerably from zero. Obviously the sign of r depends on that of the anisotropy of electric polarisability of the molecule y = a, -axx. Numerical analyses of the time-evolution of a system of molecules carried out on the basis of eqn (19) are shown in fig. 1 (a) for some values FIG.1.-Time-dependence of the quadratic variations in electric permittivity in liquids calculated 1 m2 from eqn (19) for some values of the molecular parameter r = kT -Y .(a) r> 0,(b)r> 0. of r > 0 and in fig. 1 (b) for r < 0. One notes that competition between the molecular effects leads to large differences in shape between the curves. From eqn (19) the H. Benoit Ann. Phys. 1951,6,561. C. T O'Konski K. Yoshioka and W. H. Orttung J. Phys. Chem. 1959,63,1558. M. Matsumoto H. Watanabe and K Yoshioka J. Phys. Chem. 1970 74 2182; Kolloid-2 1972,250,298. M. Gregson G. P. Jones and M. Davies Trans. Faraday Soc. 1971 67 1630; B. L. Brown G. P. Jones and M. Davies J. Phys. D :AppI. Phys. 1974,7,1192. GENERAL DISCUSSION n saturation value attained by the system after a sufficiently long time (t z,) amounts to 4 Ae(0; t z,) -1 N m4 1_-_-(21) 45 Y (kT)3( Y Y’)* E2(0) Eqn (19) and (20) show moreover that for the two values of Y the steady state dielectric saturation vanishes.Fig. 1 (a,b) moreover shows that experimental determinations of the time-evolution leading to a steady state of dielectric saturation in a liquid can permit the clarification of its electrical nature. For a substance with known values of the molecular para- meters m and y an exact numerical analysis of the time-evolution of saturation can be made by having recourse to eqn (19). Other nonlinear effects can be analysed along similar lines. The latest experimental results achieved in the study of dielectric saturation in liquids1S2 stimulated us to concentrate on this effect as it now appears feasible to determine its evolution in time leading to the steady state.Dr. G. Williams (Aberystwyth) said In response to Wegdam’s comments the theory of the dynamic Kerr-effect was first formulated for the special case of small- angle rotational diff~sion,~~ when for the permanent dipole reorientation of an op- tically anisotropic molecule it was found that the rise-function for the birefringence is a weighted sum of decay-functions* exp-6Dt and exp-2Dt while the decay-function only involves exp-6Dt. Thus the decay-function is faster than the rise-function for this model of reorientation. In contrast a model of “fluctuation-relaxation ” yields5 M. Gregson G. P. Jones and M. Davies Trans. Furuday SOC.,1971 67 1630; B. L. Brown G. P. Jones and M. Davies J. Phys. D:Appf.Phys. 1974,7,1192. L. Hellemans and L. De Meyer J. Chem. Phys. 1975,63,3490. H. Benoit Ann. Physique 1951,6 561. ‘E. Fredericq and C. Houssier Efectric Dichroism and Electric Birefringence (Oxford U.P. London 1974). M. S. Beevers J. Crossley D. C. Garrington and 0.Williams J.C.S. Furaduy 11 1976 72 1482. D is the rotational diffusion coefficient. GENERAL DISCUSSION a rise and decay transient characterised by the same time-function which is not necessarily an exponential function of time. Thus a comparison of rise and decay transients for the Kerr-effect may give information on the mechanism for reorienta- tion. More generally the decay of birefringence may yield (Pz(cos 8 t)) while di- electric relaxation may yield (Pl(cos 6 t)).Comparison is made in the paper of these quantities for relaxation in the supercooled liquid state in order to elucidate the mechanism for reorientation of dipolar solute molecules. Although our data were obtained for fairly concentrated solutions so that internal field factors and cross- correlation terms may be important we do not think our present conclusions would be any different for more dilute solutions. Note that the permittivity and dielectric relaxation behaviour of fluorenonelo-terphenyl and tri-n-butyl ammonium picratelo- terphenyl solutions do not appear 1* to be made complicated by internal field and cross- correlation terms. We emphasize that In certain systems such factors are extremely important and must be taken into account in any comparison of dielectric and Kerr- effect data.Examples are (a)hydrogen-bonded liquids ;(6)flexible-chains in the liquid and solid states and (c) liquid-crystal phases. For (a)the equilibrium and dynamic aspects of cross-correlations between molecules is well known for the dielectric case3g4 but not for the Kerr-effect. For (b)the equilibrium aspects of dipole-correla- tions along a chain are well leading to an understanding of the static permittivity and Kerr-constant but the dynamical situation has received less atten- tion.8 For (c) the extensive angular correlations between molecules both in the liquid-crystal phase and above the clearing temperature lead to distinct differences (e.g. in relaxation time) between the dielectric and Kerr-effects (static and dynamic) which must be interpreted in terms of the long-range angular-correlations between molecules [see e.g.ref. (9) and ref. therein]. Dr. J. Yarwood (Uniuersity of Durham) said There are two possible effects on the measured absorption (and birefringence) which have been hardly mentioned (i) the effects of solvent polarisation caused by ion- or dipole-induced dipole interactions. Do such effects not contribute significantly to the dielectric absorption and if so is it possible to separate the different relaxation processes ? (ii) the effects of translational motions (i.e.,collisions) of the ion pairs or ion clus- ters. Models have been described by other authors lo which explicitly include linear Brownian motion between collisions. Can I ask why it is that such motion is not considered important for the systems considered here ? Dr.G. Williams (Aberystwyth)said The dielectric behaviour of solutions of tri- G. Williams and P. J. Hains Furdy Symp. Chem. SOC.,1972,6,14. * M. Davies P. J. Hains and G. Williams J.C.S. Faraday 11 1973,69 1785. N. E. Hill W. Vaughan A. H. Price and M Davies Dielectric Properties and Molecular Behaviour (Van Nostrand New York 1969). A. Rahman and F. H. Stillinger,J. Chem. Phys. 1971,55,3336. M. V. Volkenstein Configurational Statistics of Polymeric Chains-(Interscience New York 1963). P. J. Flory Statistical Mechanics of Chain Molecules (Interscience New York 1969). 'K. Nagai and T. Ishikawa J. Chem. Phys. 1965,43,4508. 'G. Williams and M. Cook Trans.Faraduy Soc. 1971,67,990. 9 M. S. Beevers and G. Williams J.C.S. Furuday 11 1976,72,2171. lo J.-C. Lestrade J. P. Badiali and H. Cachet Dielectric and Related Molecular Processes ed. M. M. Davies (Spec. Period. Rep. Chem. SOC. London 1975) vol. 2 pp. 106-150. GENERAL DISCUSSION 153 n-butyl ammonium picrate in non-polar solvents appears to be1-4 consistent with the majority of the solute being present as unassociated ion-pairs which undergo reorienta- tional motions. Thus for moderate concentrations (as studied in our paper) the dielec- tric relaxation for solvents of low and high viscosity may be considered to arise primarily from the vector dipole time-correlation function (p(0). p(t)> for the re- orientation of the ion pairs. Such an interpretation may not be applicable for the solute in solvents of high permittivity (polar solvents) where the solute ion-pairs may be partially dissociated into ions leading to dielectric relaxation involving ion-ion ion-dipole and dipole-dipole correlation function^.^ Clearly the mechanism for the reorientational motions of an ion-pair may involve an accompanying translational motion of the ion-pair.Put in another way the translational and reorientational motions are really coupled in a general equation of motion which cannot be separated into independent translational and rotational parts (e.g.,translational and rotational diffusion) since the elementary steps of both processes may occur on similar time-scales. For our present work the "fluctuation-relaxation" model does not exclude translational motion of a dipole when the dipole reorientates as a result of a local density fluctuation.Translational motions of dipoles with the exclusion of an accompanying rotational motion obviously cannot relax (~(0).~(t)). Thus in answer to (i) there may be a contribution from ion or dipole-induced dipole interactions but we would suggest that in our systems the major-part of the low frequency behaviour arises from (p(0). ~(t)) for the ion-pairs; and for (ii) translational motions are almost certainly involved in the reorientation process for ordinary dipoles and ion-pairs but the dielectric experiment yields the angular function (~(0). p(t)) = p2(cos 8 (2)). These comments relate to the presentation of dielectric data as ~"(w).For data presented as attenuation Nu) the features at higher frequencies than the dispersion of &(a)will be emphasised (since a(m) K &"/a).Thus information from a(co) will in practice relate to a shorter time-scale than information from &(a). a(m) yields (G(0) Xt)) while ~(m) where the former time-function yields (~(0).~(t)) Prof. J. S. Rowlinson (Oxford)asked Berne about the way in which the amplitudes of the long-time "tails " of the rotational velocity auto-correlation functions depend on the density of the fluid. Alder found that the tails on the corresponding transla- tional functions were most pronounced at densities intermediate between those of gas and liquid. S. M. Thompson G. Saville and I have made some molecular dynamic simulations of the gas-liquid surface of a Lennard-Jones fluid in which we find simi- larly enhanced amplitudes at long times for the translational motion of those molecules that start in the interfacial zone that is at an intermediate density and which move parallel to the surface.The densities in Berne's table 2.1 are also in this intermediate range and it would be of interest to know if this enhancement of the amplitude of the tail of the rotational function is also a characteristic of this range of density. Prof. 3.J. Berne (Columbia University) said In the rough sphere fluid as well as in fluids containing anisotropic molecules the correlation functions of the linear velocity M. Davies and G. Williams Trans.Faraday SOC. 1960,56 1619. E.A. S Cave11 and M. A. Sheikh J.C.S. Faraday II,1973,69,315. J.-C. Lestrade J P. Badiali and H. Cachet in Dielectric and Related Molecular Processes ed. M. Davies (Spec. Period. Rep. Chem. SOC. London 1979 vol. 2 p. 140. M. Davies P. J. Hains and G. Williams J.C.S. Faraday 11,1973,69 1785. ref. (3) p. 127. GENERAL DISCUSSION and angular velocity have the long time tails where d is the dimensionality and where av,dand are the amplitudes of the tails given by where n I D and v are respectively the number density moment of inertia Enskog translational diffusion coefficient and Enskog kinematic viscosity. These two ampli- tudes are related by aw,d = Ad(nav,d)2'd av.d where kid is a constant. For d = 3 Dorfman and Cohen have shown that n&,d as well as go through a maximum at intermediate densities.It follows that also goes through a maximum-albeit at a slightly different density than for av,d. In two dimensions the same reasoning is valid. It should be noted that the amplitudes above refer to time in units of the collision time to. This answers Rowlinson's question. Nevertheless I would like to take this oppor- tunity to draw certain distinctions between the behaviour of CV(t)and Cw(t). In the rough sphere fluid these two functions behave quite differently. At times short com- pared with the collision time both functions decay exponentially with time constants determined from the Enskog equation. For intermediate times that is for times longer than a mean collision time but shorter than the time at which the long time tails have set in C'(t) decays exponentially but more slowly than that given by the Enskog equation.This is what we mean when we say that Co(t)deviates positively from the Enskog correlation function. When In Cw(t)is plotted against the time in units of the mean collision time it is found that this positive deviation increases with density. This should be contrasted with the behaviour of CV(t). For intermediate times In Cv(t)always deviates negatively from the Enskog result. In the very dense fluid CV(t)displays a negative region. The negative deviation in CV(t)has been at- tributed to backscattering collisions. Recent mode-mode calculations (Desai et al.) show that these events do not effect CJt) and attribute the positive deviation in this function even at early times to the hydrodynamic coupling between spin and vortici ty .One way to compare the two functions is to compare the areas under CV(t)and Cw(t).These are DIDEand DR/DR,E respectively where D and DR are respectively the translational and "rotational diffusion " coefficients and DE and DR,E are the corresponding properties predicted by the Enskog theory. D/ DE increases with den- sity until it reaches a maximum at approximately a density equal to + the closest packed density. It thereafter diminishes to a value considerably below 1. This decrease springs directly from the backscattering events. At high densities the long time tails are too small to reverse this trend. DR/DR,E on the other hand should con- tinue to increase with density despite the fact that the asymptotic long time tail becomes progressively a smaller contribution.Prof. B. J. Berne (Columbia Uniuersity)said Deutch has raised a very interesting GENERAL DISCUSSION question concerning mode-mode coupling. There seems to be disagreement over the long-time tail in the orientational correlation functions Several calculations using mode-mode coupling schemes are in disagreement with each other. Noteworthy in this regard are the papers of Keyes and Oppenheim Garisto and Kapral and Pomeau among others. In all of these calculations the asymptotic behaviour is given by a power oft-’ which depends on the rank of the process. On the other hand the generalised hydrodynamic equations which successfully account for the splitting of the depolarised band in light scattering experiments can be used in conjunction with the asymptotic theory of Ernst et al.giving the result that for all (d+2) values of I these orientational functions behave asymptotically as t 2 . In addition if one uses a generalised rotational diffusion equation (Berne) one also arrives at this result. Deutch’s recent work with Hill applying the methods of Bedaux and Mazur raises the interesting possibility that this latter result arises from the hydro- dynamic field generated by a particle of finite volume whereas the mode-mode results have implicitly assumed velocity fields that are created by point particles. Clearly further work is required to resolve these differences.Dr. D. Frenkel (Amsterdam) said In the rotational relaxation of rough spheres angular momentum that is associated with the rotation of a given rough sphere may be transferred to two distinct (though coupled) angular momentum reservoirs in the fluid. Partly the angular momentum will be stored in the translational motions of the rough spheres (vortex currents) partly in the internal rotations. From both reservoirs angular momentum may leak back to the rough sphere under consideration thus slowing down its angular momentum decay rate with respect to the decay rate one would predict using Enskog’s theory. Could Berne please assess the relative import- ance of these two reservoirs for the slowing down of angular momentum relaxation? Prof. B. J. Berne (Columbia Uniuersity) said The total angular momentum of a fluid consists of two parts a part due to the translational motion of the molecules which gives rise to orbital angular momentum and a part due to the tumbling of the individual molecules which we call the spin angular momentum.The spin angular momentum of a molecule can relax only by exciting the orbital and spin angular momentum of the remaining degrees of freedom. This is required by angular momentum conservation. The orbital angular momentum created can be regarded as a vortex field. A relaxing particle therefore creates a vortex field which in a dense fluid diffuses away with a “ diffusion ” coefficient given by the kinematic viscosity. Some years ago Ailawadi and I showed that the long time tail is governed by this slow “ hydrodynamic ” diffusion of the vortex field and not by dissipation into the remain- ing spin field.This conclusion is strongly affirmed by recent mode-mode calculations. A striking example of this is that of a molecule relaxing in a solvent in which there are no spin degrees of freedom so that there can be no dissipation into the spin field. We have computed the correlation function for a non-uniformly rotating sphere with stick boundary conditions in a viscous continuum fluid. The long time tail in the angular velocity correlation function is identical to that calculated for a fluid with a spin field. Prof. Th. Dorfmiiller (Bielefeld)said The shear viscosity of liquid crystals as measured in a capilIary viscometer near the transition temperature exhibits a shape GENERAL DISCUSSION as shown in the figure.When the isotropic liquid is a few degrees above the transi- tion temperature it has a viscosity which is higher than the viscosity of the nematic liquid at lower temperatures. As the rotation of the molecules around the long axis is strongly hindered in the nematic phase as compared to the isotropic phase the viscosity does not seem to be simply a monotonic function of the single particle reorientational times. Thus we are faced with the situation that the single particle reorientation is faster in a high viscosity than in a low viscosity liquid. It seems that we have to accept that with a capillary viscometer we measure a collective reorientation time which under some circumstances (highly anisotropic molecules in an ordered state) does not behave as the single particle reorientation time.Photon correlation spectra of light scattered in many supercooled associated liquids show that in such systemsthe relaxation ought to be described in terms of a distribution of relaxation processes. Hence the question arises as to whether we can speak of a single relaxation time as in eqn (2) when dealing with the narrow central line at Our measurements on polarized and depolarized light scattering of supercooled polyalcohols always show a broad distribution of relaxation times conforming to a distribution function obtained by Lit0vitz.l According to Isakovich and Chaban2 we have to consider the light scattered from such systems as due to the fluctuation of a local order parameter.The time depend- ence of this is due to a simultaneous appearance of two coupled mechanisms a diffusional contribution to the correlation function P(r t) and a relaxational process both being governed by the equation P(r t) = DV2P(r t) -1 P(r t). TO Under certain realistic conditions this leads to a distribution function of relaxation times depending upon two parameters a characteristic relaxation time zoand a width parameter B. B has been shown to be extremely wide. The frequently used Cole/ Davidson distribution function less accurately describes the experimental results. Furthermore the temperature dependence of z is of the non-Arrhenius type and is practically identical to the temperature dependence of the macroscopic shear viscosity.C.J. Montrose and T.A.Litovitz J. Acuusf. SOC.Amer. 1970,47 1250. * M.A. Isakovich and I. A. Chaban Sou. Phys. JETP 1960,23,893. GENERAL DISCUSSION Dr. G. Searby (Nice)said We are of course quite aware that supercooled liquids show a distribution of relaxation times and Dorfmuller's query on the validity of the analysis used in our paper (and elsewhere) is quite legitimate. It is important how- ever to realise that in such liquids the width of the distribution decreases as the melting point is approached from below and can be quite narrow in the normal liquid state with a consequent nearly Arrehnius type of behaviour for z and q. Light scattering spectra in the HH geometry show a weak fine structure at the Brillouin frequency (arising from coupling between reorientation and longitudinal sound waves) but since this structure is displaced in frequency very localised and also very weak it may easily be ignored and the profile of the HH lines can be used to measure the average reorientation time and to estimate the distribution parameter p.We have analysed a number of HH spectra of different viscous liquids assuming a Cole-Davidson distribution of relaxation times. On the whole the results are as fol- lows (a)k2rl < 1 (generally above and away from the melting point). The distribution pr of relaxation times is too narrow to be evident over the limited frequency range covered by the interferometer. (b).%' > 1 (generally around the melting point).In some cases a distributed Pr spectrum provides a slightly better fit than a Lorentzian spectrum. For example for ethyl benzoate close to the melting point we found /I= 0.9. So the linewidths quoted at the lowest temperatures may indeed need to be interpreted with a little caution. The important point however is that in this region of 3the HH lineshape is nearly Pr Lorentzian wheras the VH lineshape is very different-see our fig. 7 for example. The small distribution of z therefore has no direct effect on the shape of the VH spectra. 2B 1 (supercooled liquids far below the melting point). In this region the Pr reorientation line is accessible to light beating techniques but is orders of magnitude narrower than the interferometer instrumental function.It is not possible to knalyse the spectra in terms of z q or R,nevertheless there re- mains an important difference between the observed VH spectra and the spectrum predicted by eqn (2). This difference is the integrated intensity of the propagating doublet which according to eqn (2) is equal to the integrated intensity of the reorienta- tion line independent of z q or R. It is probable that a more complete theory includ- ing the effect of one (or more) relaxing variables would account for the observed spectra. Prof. M. Davies (Aberystwyth)said Why did you heat your liquid crystal 140 "C above the clearing point before taking a spectrum? Dr. G. Searby (Nice) said The reason is very simple we wanted to verify that a liquid crystal in the isotropic phase shows the same coupling (between reorientation and the hydrodynamic modes) that is found in other liquids.The value of the coup- ling parameter in this case is also of great interest. We therefore chose the tempera- ture for which I? for the liquid crystal was around 1 GHz as for other liquids studied. k2r This would also give -a value of around 0.3 where the VH dip is most easily seen. Pr GENERAL DISCUSSION Because of the strong correlations that exist even in the isotropic phase the re- orientational motion is very slow and a very high temperature was necessary in order to obtain a motion sufficiently rapid. It also follows that at more moderate tempera- tures the ratio k2V -is very high as in supercooled liquids but in this case the vis- Pr cosity is very much lower and there should not be the complication of other slow variables affecting the spectrum.We would expect therefore that eqn (2) would accurately describe the VH lineshape for all values of % contrary to the case of Pr supercooled liquids. Dr. J. M. Vaughan (Maluern) said I would like to compliment the two previous speakers Searby and Pecora on their contributions which I have much enjoyed reading. While we are dealing with laser scattering studies it is perhaps appropriate to consider some developments in Fabry-Perot interferometry which will I think make a useful contribution to our subject over the next few years. In particular I am referring to the use of multi-pass instruments; these comments arise from collabora- tion with G.W. Bradberry of Exeter University. The instrumental form due to a single pass Fabry-Perot interferometer is given by the well-known Airy formula which is modified in practice by departures from plate parallelism flatness and the finite size of pinhole aperture etc. The extinction (ratio of instrumental peak height to mid order background) rarely exceeds lo3. With the technique of passing the light two or more times through the etalon the instrumental width near the line centre is made somewhat narrower but most importantly the inter-order background is greatly reduced. Extinctions greater than lo6are routinely obtained in for instance triple-pass use. So much is well known and the obvious applications have been made to the study of very weak spectrally-shifted features in the presence of for example strong elastic scattering.This is illustrated by fig. 1 and 2 which are taken from some recent investigations of ours on Brillouin scattering in bulk and thin film samples of cyanobiphenyl liquid crysta1s.l. -1.5 GHz ln 4 3 V I 00 frequency FIG.1.-Quasi-elastic light scattering spectrum of a thin film sample of 5 CB at 32.5 "Cin the ne- matic phase; the interferometer recording shows channel contents (photon counts) plotted against frequency. The Rayleigh peak has been reduced on the diagram by a factor of lo5. The Brillouin peaks are shifted rt4.76 GHz and the scattering vector is of magnitude 1.82 x lo5cm-' However the point of my comment is not so much concerned with these Brillouin scattering studies it is rather to draw attention to the possibilities opened for the study of Rayleigh lines by exploiting the high extinction properties of the multipass instru- ment.With suitable choice of experimental parameters we believe that very sensitive analysis of the line shape is possible. In particular for lines of a Lorentzian charac- G. W. Bradberry and J. M. Vaughan. J. Phys. C:Solid State Phys. 1976,9,3905. * J. M. Vaughan Phys. Letters 1976 58A,325. GENERAL DISCUSSION temperature / 'C FIG.2.Brillouin shift hypersonic speed and attenuation in the region of the nematic-isotropic transition (dotted line) for 5 CB at a constant scattering vector of magnitude 1.82 x lo5 cm-'. ter or having appreciable wing intensity while the profile near the line centre may be extensively modified by the instrumental form because of the very high extinction the shape away from the centre is very little changed over a wide range of frequency.If a simple Lorentzian form can reasonably be assumed then an experimental measure- ment of its width r (half width half height) may readily be determined from the expression k2 r=nA.-T.Av where in an experimental spectrum A is the signal content within a small frequency interval Av at a distance kfrom the line centre and Tis the integrated signal within the whole spectrum. The fit to a single Lorentzian can obviously be examined by com- paring values of r obtained at different values of kin the same spectrum.By varying temperature / 'C FIO.3.Lorentzian line width r of the Rayleigh peak plotted against temperature for 5 CB in the isotropic phase. The clearing temperature of the sample is indicated by the arrow. The error bars are approximateIy f3%. GENERAL DISCUSSION the etalon plate separation the shape may be examined over an even larger range of frequency. The precision that may be realised is very high-for example the con- ventionally defined resolving limit of spectroscopic instruments is rarely smaller than 10 MHz. Problems of deconvolution near the line centre ensure that intrinsic Ray- leigh line widths less than this can be obtained only with very limited accuracy. However by applying the technique outlined to analysis of the wing intensity these limitations are overcome.Fig. 3 shows data obtained on depolarised Rayleigh spectra of 4’-n-pentyl-4-cyanobiphenyl(5 CB) in the isotropic phase close to the isotropic- nematic transition. Each value of r has been obtained from the intensity at twelve points in the frequency range 0.45-0.9 GHz. Within experimental error these values were the same showing a good fit to a single Lorentzian over this range; the statistical error in l? amounts to about &3%. The conventionally defined resolving limit (full width at half height) for the spectrometer was -100 MHz nearly two orders of mag- nitude greater than the smallest line width measurement. The technique is described in greater detail in a paper of Bradberry and myself.’ In conclusion there seems a good prospect that the multipass interferometer will be as fruitful in the precision analysis of Rayleigh lines as it has been in the study of Bril- louin scattering.Prof. B.J. Berne (Columbia University) said To take up a point raised by Manse1 Davies it now appears that hydrodynamic models can be applied with great success to the motion of molecules in solvents where the solvent molecules are not large com- pared to the molecule in question. The evidence for this springs from several sources. Zwanzig and Bixon have computed the velocity correlation function of a sphere moving in a compressible viscoelastic fluid. This agrees well with molecular dynamics studies of the smooth hard sphere liquid and of the Lennard-Jones liquid when slip boundary conditions are used.Perrin calculated the translational and rotational diffusion coefficients for ellip- soids with stick boundary conditions. When applied to the tumbling of small mole- cules like benzene the rotational diffusion coefficients disagreed with experiment by as much as one and two orders of magnitude. Recently Zwanzig and Hu using a variational principle have calculated these quantities for ellipsoids with slip boundary conditions. Their results are in close agreement with the depolarised light scattering measurements of Pecora et al. on several small molecules. Acrivos et al. have im- proved on the agreement by introducing a more detailed model of benzene in which six slippery spheres are placed at the vertices of a hexagon.Thus it appears that for small molecules hydrodynamics with slip boundary conditions is quite successful. In hydrodynamic calculations the fluid is treated as a continuum. The important physical assumptions are connected with the boundary conditions. One of the im- portant remaining problems is to show how the boundary conditions spring from the intermolecular forces. This is actually a subtle problem. The rough sphere fluid is a good case to consider. We find that although the spheres are microscopically rough stick boundary conditions are not applicable. It appears that the velocity field produced by a rotating sphere outside of its boundary layer is much more like that of a sphere with slip boundary conditions that that of a sphere with stick boundary conditions.Much remains to be done before we under- stand the underlying molecular mechanism. G.W.Bradberry and J. M.Vaughn Opt. Comm. 1977,20,307. GENERAL DISCUSSION Prof. R. Pecora (Star3ford Uruirersity) said In response to remarks by Mansel Davies The viscosity used in our studies is the macroscopic solution viscosity as measured by an Ostwald viscometer. There is in fact a great deal of evidence that hydrodynamic type theories (" general-ised hydrodynamics ") are applicable to phenomena at the molecular level. One strik- ing example of this is the molecular dynamics calculation of Alder et aZ.l These authors calculated both the translational self-diffusion coefficient and the viscosity of a hard sphere liquid and showed that the Stokes-Einstein relation between these quanti- ties calculated with dip boundary conditions was obeyed.We have performed measurements of rotational relaxation times of molecules in the liquid state as a function of solution viscosity. For classes of these liquids which satisfy the conditions (1) the solute and solvent molecules are roughly the same size (2) there are no strong intermolecular interactions (e.g. dimer formation hydrogen bonding) it is found that the single-molecule reorientation time has a vis- cosity dependence whose slope can be predicted by hydrodynamics with slip boundary conditions to within about &15%. The Stokes-Einstein expression with stick boundary conditions predicts much too much friction and is as you point out useless for predicting rotational relaxation times in this class of liquids.The Stokes-Einstein relation with stick boundary con- ditions is however valid for the rotational relaxation times of solute molecules which are much larger than the solvent molecules. The example you give of some extra polymer dissolved in a solution of rotating smaller molecules does not fit into either of the above categories. I would certainly not expect the rotational relaxation time to follow the macroscopic solution viscosity in this case. Rotational relaxation times of molecules near a gas-liquid critical point or a solution consolute point would probably not have simple relations to the macro- scopic solution viscosity either. Prof. D. Kivelson (Uniuersity of California) said In answer to the question of Mansel Davies concerning the use of solvent solution or microviscosities in making use of the Debye expression I would like to refer to and expand upon the discussion below eqn (25) in my introductory article.I for one shy away from the use of microviscosity (vmicro)because it cannot be measured independently of the Debye relationship-it is essentially a quantity with the dimensions of viscosity which ensures that the expression works exactly. As I have indicated I prefer to substitute tpc for qmicra where q is the independently measured macroscopic viscosity and K is the dimensionless coupling of rotational to translational modes discussed near eqn (23)-(25) of my introductory article. For small molecules that are not too asymmetric or interactive such as the xylenes discussed by Pecora K is small independent of Tand q and has values close to the hydrodynamic slip values.In dilute solutions of larger more interactive probe molecules K is still relatively independent of T,q and pressure but has values between the slip and stick values values that vary with solvent. If the solvent consists of two components for many solvents the macroscopicsolution viscosi$y can still be used with the Debye expression provided an appropriately weighted K,such as ([dA)-IC(~)]X~ + B. J. Alder D. M. Gass and T. E. Wainwright J. Chem. Phys. 1970,53 3813. * J. R. Bauer J. I. Brauman and R. Pecora J. Amr. Chem. SOC.,1974,96,6840. GENERAL DISCUSSION dB)) are the K'S for the probe molecule in pure A and pure is used where dA)and dB) B respectively and X is the mole fraction of the A constituent in the solvent.Once again this effective K is independent of T and q. Davies has pointed out that if small amounts of polymer are added to certain solu- tions the solution viscosity changes by orders of magnitude but the rotational correla- tion time q is relatively unaffected. Of course as he maintains the Debye expression is not useful in this case since the solution viscosity appears to have little connection to zi. As indicated in my introductory article I would propose the following explana- tion of the various situations mentioned. Coefficients of shear viscosity are macro- scopic in the sense that they depend upon the interactions and structure over a distance of many molecular radii; however computer calculations seem to indicate that this distance may not be much greater than ten or so radii.Similarly the rotational relaxa- tion of a molecule depends upon more than its interactions with its nearest neigh- bours since in turn the nearest neighbours are severely constrained by their neigh- bours. It is not unreasonable to assume that for rotational relaxation the structure and interactions over a distance of many molecules a distance comparable to that characteristic of viscosity determines the actual behaviour. However if the viscosity is enhanced by the addition of polymer one would find that the viscosity increases with wavelength up to wavelengths of several hundred Angstroms while the rotations of small molecules in fluid cavities are still relatively independent of wavelength for wavelength above about 20 A.This dependence upon wavelength was emphasized by Deutch in his comments. The coefficient of shear viscosity is normally measured at very large wavelengths. In summary we can assume rl(Ar) and q(A,) where Ax and Av are wavelengths above which zi and q respectively are independent of wavelength. The Debye relation states that zi(A,) is proportional to q(A,); if A,, 5 AT the solution viscosity ~(oo) may be used but if Aq A, a microviscosity q(&) must be used. In " normal " situations A,, E & but with the addition of polymer it is likely that A is very large. Dr. P. S. Y. Cheung (University of Kent) said I would like to suggest an alternative method to interpret Pecora's results for the neat liquids.The comment is however directed to Kivelson since it concerns the general usefulness of eqn (2) in the text Eqn (2) is derived from the Mori projection operator method and applies when the orientational variables are " slow ".I When applying eqn (2) two questions arise (1) " When are the relevant variables ' slow ' enough?" and (2) " How does one interpret the dynamic factor gN,which is formally defined in terms of a projection operator in terms of microscopic processes?'' (In other words what information can be gained from a knowledge of gN?). By recasting eqn (1) into a slightly different form it is possible to interpret the z,/z, data outside the projection operator scheme.We define the normalised correlation function for light scattering as and those for the single-particle and distinct contributions as T.Keyes and D. Kivelson J. Chem. Phys. 1972,56,1057. GENERAL DISCUSSION wherefN = (N -1)(~(’)(0)~(2)(0)) is the same as theflv in (2). Now if we define the correlation time z of a normalised correlation qx(t)as then where h is the ratio zd/zSpand contains information relating to correlated motion. Thus eqn (B) allows one to interpret the experimental data for zLsand zspin terms of two well-defined microscopic parameters fN and h. The equation is quite general and does not depend on any model or theory of reorientation. A corresponding equation applies for dielectric relaxation and the present view of experimental data is close to comments made by Williams in his paper presented earlier in the meeting.Using Pecora’s results for zLs zspand fN for the neat liquids one finds 0-P-m-xylene. h 15 & 65 0.4 & 0.2 3.0& 1.5. On general grounds one does not expect Td to differ from zspby a factor larger than 10 or less than 0.1 so the value for o-xylene is probably too large-the large un- certainty arises because f N as quoted carries a large experimental error. The interpretation of h is by no means straightforward and is too complex a problem to enter into in detail here. One approach would be to evaluate typical values for specific types of correlated motion or by computer simulation for general molecu- lar types classified according to shape or the interaction potential so as to facilitate interpretation of experiment.Incidentally a computer simulation of a nitrogen like diatomic by Levesque and Weisl gives fN = -0.09 and h -4. It is interesting to note that for the nitrogen simulation eqn (2) is invalid because the correlation functions are non-exponential with a corresponding non-Lorentzian Rayleigh spectrum. Indeed if one goes far enough out into the “ wings ” the light scattering spectrum of benzene is non-Lorentzian showing significant free-rotation even at room-temperature.2 Thus for xylene one should be careful to include the wings to obtain zLs as defined by eqn (A)-this necessitates of course considerations of induced ~cattering.~ We note that Pecora’s zLsis deduced from the Lorentzian part of the spectrum which is correct only within the framework of eqn (2).In view of the above comments the usefulness of eqn (2) in analysing experimental results is questionable. My view is that the most important result of Kivelson’s paper is not eqn (2) but lies in the explanation it gives for the occurrence of a Lorent- zian in the centre of the Rayleigh spectrum even in the presence of correlation of orientation and correlated motion. D. Levesque and J. J. Weis Phys. Rev. A. 1975 12,2584. * H. D. Dardy V. Volterra and T. A. Litovitz J. Chem. Phys. 1973,59,4491. P. E. Schoen P. S. Y. Cheung D. A. Jackson and J. G. Powles Mul. Phys. 1975,29 1197. GENERAL DISCUSSION Prof. D. Kivelson (Uniuersityof California)said In response to Cheung's ques- tions we can of course write the many particle rotational correlation time zl as 21 =zpq1 +X] where z~(~) is everything else that enters is the single particle correlation time and XZ~(~) into zZ.However this expression merely states that zl and zl(s)differ and it does not relate the difference to quantities that can be measured by other methods. The statement becomes particularly useful if Ng z 0 because 1 +Nf can be determined inde- pendently; furthermore the dynamic quantity g in the diffusion limit is related to a physically significant rapidly decaying correlation function. Prof. B. J. Berne (ColumbiaUniversity)said The problem discussed by Keyes and Kivelson is the following Given that CI@)(t), the self-orientational correlation func- tions decay exponentially with time constants z~(~), how do the collective correlation functions Cl")(t) decay.Their solution to this problem is now well known to be The collective correlation function is also an exponential with a time constant related to the time constant appearing in the self motion Here g is a dynamic contribution arising from the cross correlation function of the angular velocities (weighted by orientational terms) andfis a static orientational struc- ture factor. It is tempting to subdivide CltN)(t)into two terms with different time constants one arising from the self motion and one arising from the distinct motion. In my opinion this would lead to certain difficulties. The self term is always positive whereas depending on molecular shape the distinct term might be negative for certain ranks 1.This leads to the possibility of negative power spectra. Aside from this we should take our cue from the vast literature in hydro- dynamic and generalised hydrodynamic fluctuation theory which deals with the trans- lational analogues Fs(k,t) and F(k t). The pole structures of these two functions are quite different. Only at very large values of k does F(k t) behave like F,(k,t). Moreoever at small and intermediate values of k the poles in the Laplace transforms of these functions are totally unrelated. At small k,Fs(k,t) is a single exponential and F(k t) consists of three exponentials. The damping rates in F(k,t) are unrelated to those in F,(k,t). Decomposition of F(k,t) into a self and distinct term would be fruitless.Consider the simple case of N solute molecules moving in a solvent. Then let GENERAL DISCUSSION @>,(k,t) and @(k t) be the translational self and collective correlation functions. Then using irreversible thermodynamics one can show that at small k OS(k,t) decays exponentially with time constant l/z = k2Dswhere D is the self diffusion coefficient whereas @(k,t) decays exponentially with time constant l/zN = k2L($) where L T’P is a kinetic coefficient and ap/acis a thermodynamic derivative of the chemcal poten- tial with concentration. At sufficient dilutionL 2i 0,but in general L = (1 + Ng)D where Ng represents a dynamical correction to the self diffusion coefficient.Also 5= lim S(k) afl k+O where S(k)is structure factor of the solute. It is the analogue of 1 + Nfin the orienta- tional problem. Thus there is a one to one correspondence here to the orientational problem. Dr. J. M. Vaughan (MaZvern)said I agree with Kivelson that the strong scattering close to the isotropic-nematic transition makes the spectroscopic task easier; and in the present work we have been able to employ low laser power to avoid heating the sample. However we have used the multipass technique quite successfully well away from the transition where the scattering is greatly reduced (and incidentally we have also observed the central dip in the V-H spectrum of 5 CB referred to by Searby). With a good stable interferometer and suitable choice of instrumental parameters such as laser power etalon aperture etc.I would say the technique can be employed with a wide range of scattering systems. Dr. J. Yarwood (University of Durham) said In connection with the dependence of vibrational band width on the upper state quantum number n,we have recently meas- ured the ratio of isotropic Raman band widths of fundamental and first overtone for three simple (polar) liquids and their dilute solutions in carbon tetrachloride. The results shown in the table,l p2 clearly indicate that this band width ratio has neither n nor n2 dependence. Furthermore it is clear that different modes have different ratios and also show different degrees of narrowing on going to a dilute solution. Thus for polar molecules it appears that the:situation may be more complex and this is of course not unexpected since in both Madden’s treatment and in that of Bratos et aL3 the effects of induced moments are neglected.It should also be noted that for acetonitrile and for nitromethane the effects of resonance energy transfer (i.e. coupling of transition moments of different molecules in the liquid) as shown4 by isotropic dilution experiments are very small. I would also like to present the results of some neutron quasi-elastic scattering data which we have recently made for acetonitrile and its solution in carbon tetrachloride. These results (obtained in collaboration with T. C.Waddington and P. G. Woodcock) were collected at low momentum transfer (Q I I A-l) and high energy resolution (180 peV) on the 4H5 spectrometer at A.E.R.E.Harwell. A plot of the quasi- elastic peak half-width (after removal of the ‘‘instrument ’’ width) against Q2 at A more complete table is given in J. Yarwood and R. Amdt Chem.Phys. Letters 1976,45 155. G. Doge 2. Naturforsch. 1973,28A 919; R. Amdt G. Doge and A. Khuen Chem. Phys. in press. S. Bratos and E. Marechal Phys. Reu. 1971 A4,1078. J. Yarwood R. Arndt and G. Doge Chem. Phys. (submitted for publication) and unpub-lished data. GENERAL DISCUSSION TABLE SHOWING COMPARISON OF FUNDAMENTALAND OVERTONE BAND WIDTHS FOR SOME SIMPLE LIQUIDS. (293 K). 1.41 1.30 2.48 1.61 CHJ v,/~v 2.88 3 .OO ~~ CH3N02 ~212~2 2.40 2.38 v3/21.'3 v4/2v4V5/21.'5 1.89 2.63 2.82 1.70 2.33 3.17 Concentration is 0.25 mole fraction of solute.low Q values gives a value of the translational diffusion coefficient D according to AE+(Q. E) =2hD;Q2. The data when plotted this way (see diagram below) show that D decreases drastic- ally on diluting with carbon tetrachloride (the data give 0;= 3.1 x cm2s-l for -_-__ FIGuRE.-comparison of Quasi-elastic peak width against Q2plots for CH3CN CH3CN in CD3CN and a 40% (by volume) solution in carbon tetrachloride. (Resolutionis about 180-200 peV at 1220 ps rn-l incident time of flight). GENERAL DISCUSSION the liquid at 295 K and D = 1.9 x low5cm2s-' for a 40% solution in carbon tetra- chloride). These data show that the collision rates increase on dilution with CC14 giving a slower rate of translational motion.This is entirely in accord with recent results we have obtained from the isotropic Raman scattering of the v band in the same systems. Here the values of the correlation time 2 obtained by fitting the ob- served vibrational correlation functions to the expression Y"(t) = exp -W">CtG + 2 (exp (-m-113) show a considerable decrease on diluting with CC14 (from 0.4to 0.25 ps). Such cor- relation times support the idea of an increase in the rate of hard collisions producing an increase in the rate of vibrational relaxation. It remains to be shown whether or not such changes in the dynamic properties of the acetonitrile molecules may be correlated with macroscopic viscosity changes or whether microscopic changes (due to changes in intermolecular potential) dominate the picture.Dr. P. A. Madden (Cambridge Uniuersity) said One of the reasons for developing the resonance Raman technique for vibrational dephasing studies was that spectra of very dilute solutions of non-polar diatomics can be obtained. For such systems the term in the Hamiltonian responsible for dephasing should be of the form Gq2(see the paper) the consequences of this term for the bandwidths can be evaluated in the slow and fast motion limits. For concentrated solutions of diatomics additional terms of the form Gi,Jqiqj(i # j) arise in which i andj label molecules for concentrated solu- tions of polyatomics the general term will be Gal:,pjqarqpj (i # j i =j) in which qai is the normal coordinate for the uthnormal mode of the ithmolecule.A recent study' (see also the comment by Lynden-Bell at this Symposium) shows that the effects are often non-additive. Complex interference effects may occur. It may be expected that when several of these terms are important the simple n and n2relationships will not hold. Similar relationships to those reported here by Yarwood have been found for other polyatomic systems.2 Dr. R. M. Lynden-Bell (Cambridge University) said I should like to amplify the refer- ence to work on vibrational dephasing3* that Madden made.5 In a neat liquid in the rapid motion limit where fluctuations in the intermolecular potential are fast com- pared with the vibrational dephasing time there are two types of term which contribute to dephasing. These are self terms such as and for an anharmonic oscillator and exchange terms where the vibrational quantum is exchanged between identical molecules 1 and 2.R. M. Lynden-Bell Mol. Phys. to be published. C. Brodbeck I. Rossi Nguyen-Van-"hanh and A. Ruoff Mol. Phys. 1976,32,71. P. A.Madden and R. M. Lynden-Bell Chem. Phys. Letters 1974,38,163. R. M.Lynden-Bell Mol. Phys. 1977,in press. P.A. Madden this Symposium. 168 GBNERA L-D I S CUSS 10N In these expressions V12is the intermolecular potential of molecules 1 and 2 and qj q2are the vibrational normal coordinates of these molecules. Vibrational dephasing is observed in isotropic Raman scattering (an I = 0 process) and in infrared (I = 1) and depolarized Raman scattering (I = 2).These dephasing times may differ as cross terms between exchange and self terms can con-tribute to I = 0 but not to I = I and negligibly to I = 2 giving T2-I = (Fez+ F2)r; I = 1 or 2 2y1= (F + F$7; I = 0 where Fe and F,are the amplitudes of the frequency changes due to exchange and self terms and z is the correlation time. Evidence for the importance of exchange effects in some normal modes comes from isotopic dilution studies. There are many different terms in the intermolecular potential which may cause vibrational dephasing short range forces dipole-dipole van der Waals etc. which have different angular and distance dependences. These contribute independently to the rate of dephasing and have different correlation times z. In solutions pair interaction of molecules of different types gives self terms but the exchange terms are no longer resonant.In a mixture the vibrational dephasing rate has the form where 7AA and xAB are correlation times for AA and AB intermolecular inter- actions. Tabisz and I1have tested some experimental results to see if they agree with these rapid motion predictions. First the measurements of methyl iodide vibrational line widths (v3(alg))by Campbell Fisher and Jonas2 asl(a function of pressure. Assuming that changes in z are proportional to changes in bulk viscosity and that changes in F2are proportional to changes in density one predicts that T2-l should be proportional to qp. We obtain from the experimental results good straight lines with a non-zero intercept i.e.T2-l = ko + Sqp where the slope S increases with temperature and the intercept ko,(intrinsic line width?) is apparently independent of temperature and is about half the total relaxa-tion rate. Data of Neuman and Tabisz3 on the vibrational dephasing of alg in benzene (992 cm") in liquid mixtures with CC14fit a relationship T2-I = ko 4-A ~AIDAA 4-A$ ~BIDAB where we have used the inverses of the self and mutual diffusion coefficients DAA DAB as measurements of the correlation times and assumed that F2AA and FA,are proportional to the molefractions of A and B MAand MB,respectively. Mr. M. R. Battaglia Mr. T. I. Cox Dr. P. A. Madden and Mr. R. A. Shatwell (Cambridge University) said The experimental results on vibrational dephasing quoted in the paper were obtained by workers not primarily interested in relaxation studies.In order to demonstrate that meaningful relaxation parameters can be ex- R.M. Lynden-Bell and G. C Tabisz 'Ckem.Phys. Letters 1977 in press, 'J. H. Campbell J. F. Fisher and J. Jonas J. Chem.Pks. 1974,61,346. 'M. N. Neuman and G. C. Tabisz Chem. Phys. 1976,15,195. GENERAL DISCUSSION 169 tracted from Resonance Raman lineshapes it is necessary to solve the problems of (a) providing a well defined baseline for the spectrum; (b) defining the medium temperature at the laser focus in an absorbing medium; (c) separating the hot band contribution from the band profiles. To this end we will describe our recent studies on the system I2 + CCl previously studied by Kiefer and Bernstehl The difference system described in the paper has been modified2 to deal with the problem described there of excess solvent scattering from the pure solvent half-cell.The light now passes through a Pockels cell followed by a polarizer (in the plane of the initial laser polarisation). A voltage is applied to the Pockels cell only when the pure solvent half-cell is illuminated; in such a way as to reduce the laser intensity incident on the cell. By varying the applied voltage the solvent bands may be nulled in the difference spectrum and a pure solute Raman spectrum obtained distorted only by (weak broad) fluorescence. The medium temperature was obtained from the ratio of the Stokes to anti-Stokes intensities of the CCl bands of the solution (adjusted for spectrometer response) and assuming efficient V -T relaxation.It was found to be 320 K (consistently for all CC14 bands) when 500 mW of 514.5 nm radiation was focus- sed on the mol dm-3 I2 + CCl solution. The Stokes to anti-Stokes intensity ratio for the I2 fundamental however showed a “ temperature ” of 284 K. The first (-21 1 cm’l) anti-Stokes line is the -1st member of the hot-band overtone pro-gression (Zl +n) and this result shows that the iodine hot-band intensities through- out the spectrum will not take their thermal values. Consequently when fitting a line to obtain the lineshape parameters the hot-band intensities (and their widths) must be allowed to vary freely. Shown in the figure are the square roots of the line widths of the 0 -+ n transi-n FIGuRE.-The square root of the width A,,/cm-I of the 0 3n line against n.The dotted line passes through the most reliable data points. tions obtained by fitting Voigt functions to the overtone profiles plotted against n. Separate Voigt functions were used for the fundamental (Io+n) and hot-band (Zl+n+l) contributions to a band with freely varying position width and height. The spectra were of sufficiently good quality that the positions of the hot-bands as W. Kiefer and H. J. Bernstein 3. Raman Spectr. 1973,1,417. * M. Battaglia T. I. Cox,P. A. Madden and R. A Shatwell in preparation. 170 GENERAL DISCUSSION fitted agreed closely with the values predicted by differencing the appropriate funda- mental positions and the widths agreed with the theoretical relationship to the funda- mental widths,l at least for the lower overtones (n < 5).For small to intermediate n values the widths closely follow the n2dependence discussed in the paper appropriate to the "fast motion " limit. But as the linewidth becomes large (n > 6) the n de-pendence is slower than n2 and is tending to the linear n dependence appropriate to the slow motion limit.2*3 Prof. A. Gerschel (Orsay)said A first remark is made to support the contribution of two-body encounters effects in liquids although we do not pretend to such a com- plete analysis as Litovitz's. We have considered the integrated intensity variations of far infrared absorption in compounds like CSZ4and CC14 that were studied in a range of densities and temperatures extending from the triple point up to the critical point.Analysis of the density dependence of these intensities was carried out and revealed acceptable agreement with a squared densities law. Since in the dense structure the frequency of collisional events also depends on the squared density we thought it reasonable to relate the variation of absorption intensities to that variation in the occurrence of collisions. In this respect a restriction of consideration of two- body collisions appeared satisfactory within the experimental accuracy. At longer times a second remark applies dealing with evidence of many-body effects in the molecular interactions at liquid densities as clearly revealed by far infra- red experiments on polar liquids especially with molecules possessing high permanent dipole moments.It comes as an effect of the local structure to suppress the randomiz- ing character of gas-like bimolecular encounters rather we should speak of corre- lating collisions to account for the persistence of a damped oscillatory librational m~tion.~*~ Narrower spectra are observed a reason for this being that advocated by Litovitz that many-body correlations decay slower than two or three-body correlations; the main reason however is here a consequence of increased coherence in the angular motion. Not surprisingly the measured effects of the many-body correlations were weak in the liquids investigated in this work constituted of atoms or spherical molecules since the advent of these effects depends on the degree of local organization a consequence itself of molecular anisotropy (of either steric or dipolar origin).Dr. G. C. Tabisz and Prof. A. D. Buckingham (Cambridge University) said An aim of the paper of Stuckart Montrose and Litovitz is to compare the collision- induced scattering from inert-gas atoms with that from tetrahedral molecules. We suggest a mechanism which can account for two distinctive features of the scattering from tetrahedral molecules namely the excess intensity of the depolarized scattering over the predictions of the (point) dipole-induced-dipole model and the occurrence of an extremely broad high-frequency tail.'. * This mechanism yields a collision-induced rotational Raman scattering.P. A. Madden and R. M. Lynden-Bell Chem. Phys. Letters 1976,38,163. S. Bratos and E. Marechal Phys. Rev. A 1971,4,1078. G. Doge 2.Naturforsch. 1973 28A 919. I. Darmon A. Gerschel and C. Brot Chem. Phys. Letters 1971,8,454. A. Gerschel I. Darmon and C. Brot Mol. Phys. 1972,23,317. A. Gerschel C. Brot I. Dimicoli and A. Riou MoZ. Phys. 1977,33 527. D. P. Shelton and G. C. Tabisz Proc. Fifth Int. Con$ on Raman Spectroscopy ed. E. D. Schmid (Freiburg 1976) p. 382. * F. Barocchi and M. Zoppi Proc. Fifth Int. Conf. on Raman Spectroscopy ed. E. D. Schmid (Freiburg 1976) p. 386. GENERAL DISCUSSION 171 Tetrahedral molecules lack a centre of symmetry and therefore possess a non-zero anisotropic dipole-quadrupole polarizability tensor A.l To appreciate the signifi- cance of A consider a light beam incident upon a pair of molecules 1 and 2 separated by a distance R.The electric field E associated with the light beam induces a dipole moment p = alE in 1 and the field F due to pl induces a dipole moment aaF in 2. This yields the well-known dipole-induced dipole (DID) contribution in R‘3 to the polarizability of the pair. The field-gradient F‘ due to pl also acts on 2 to induce a dipole moment +Az:F‘; moreoever the external field E induces a quadrupole moment 0 = Al . E in 1 and its field induces a dipole in 2. These two interactions yield a pair-polarizability varying as R‘4 and rotating with the tetrahedral molecules. The following expressions are obtained for the mean-square values of the pair-polariza- bility components a, and ayz,averaged isotropically over all orientations The first term in {a&> gives the polarized Rayleigh scattering; the terms in are the dipole-induced-dipole contributions while those in R-are new and yield the induced rotational scattering.For tetrahedral molecules A is determined by a single parameter A.l For CH, A(4n~J-lhas been estimated by Isnard et aL2 to be 2.35 x cm4. In this case the term in R-8 in <a,”z)is 4% of that in and the depolarized rotational scattering should be observable. If all the excess intensity in the observed depolarized spec- trum is attributed to induced rotational scattering then A(4neJ-l would be (4.9 & 2) x cm4 for CH4 and (5.2 & 3) x cm4 for CF4. .T m 0 L 100 200 300 0 / cm’ FIG.1.-The calculated translationally broadened induced rotational spectrum of CHI at 295 K.Points are shown at 20 cm-’ intervals on the Stokes side. The profile beyond 200 cm-’ is described by an exponential function exp(-w/wo) with wo = 130 cm-’. The line labelled DID represents the profile of the dipole-induced-dipole contribution as estimated from the data in ref. (8). A. D. Buckingham Adu. Chem. Phys. 1967,12 107. P. Isnard D. Robert and L. Galatry Mol. Phys. 1976,31,1789. GENERAL DISCUSSION The rotational selection rules are AJ = 0 &1 &2 -+3 and the relative intensity distribution of the rotational spectrum may be calculated. For tetrahedral molecules the tensor A transforms in the same way as the octopole moment.Theoretical spectra have been generated by accounting for translational broadening with a lineshape this is an approximation as the contributions appropriate to the DID intera~tion;~* to the pair polarizability have a different R-dependence. For CH4at 295 K (fig. 1) the shape of the calculated spectrum beyond 200 cm'l is consistent with an exponential profile whose characteristic frequency coois 130 cm-l; the observed value8 is 138 cm-I. For CF4at 295 K (fig. 2) the slope of the high-frequency wing of the calculated spec- I 1 I i 50 100 200 dCl.6' n~. 2.-The calculated translationally broadened induced rotational spectrum of CF4 at 295 K. Points are shown at 5 cm-l intervals on the Stokes side. The profile beyond 40 cm-l is described by an exponential function exp(-coo/oo) with coo = 19.3 cm-'.The line labelled DID represents the profile of the dipole-induced-dipole contribution as estimated from the data in ref (7). trum corresponds to coo = 19.3 cm-l while the experimental value8 is 32.2 cm-l. The poorer agreement with experiment for CF4 is understandable. Methane has a large rotational constant and the lines are widely spaced at high frequencies (AJ = 3); their distribution essentially determines the shape of this part of the spectrum. How-ever in CF4the rotational lines are closely spaced and the shape of the spectrum de- pends critically on the broadening. Dr. P. A. Madden (Cambridge University) said I would like to describe a theoreti- cal calculation of the depolarized Rayleigh scattering from liquid argon at 85.4 IS which may be compared with the experimental lineshape at 84 K reported in the paper under discussion.The calculation is of interest in the present context for the light it casts on the mechanism controversy. The theory proceeds from the expression,l for the depolarized light scattering spectrum (k is the scattering vector and cr3 the P. A. Madden Chem. Phys. Letters 1977,472174. GENERAL DISCUSSION frequency). nk and Fxz(kf)are the Fourier transforms of the number density and the xz component of the tensor giving the interaction induced polarizability $xz(r). In the calculation a DID interaction was assumed where the sums run over all particles and i,dr denotes that integration extends over all space excluding a sphere of radius 42 at the origin.Then k k j(ka) (3) Fx,(k)a dreik.rFxz(r)tc3 v5 in whichj is a first order Bessel function. The dynamical properties enter through the correlation function for the bilinear number density fluctuations. An expression for this correlation function was developed using the Mori approach and the correlation functions appearing in the theory related to parameters obtained from inelastic neu- tron scattering data on liquid argon by use of the Kirkwood Superposition Approxi- mation. The final expression then contains no adjustable parameters and the cal- culated lineshape is in excellent agreement with the experimental one for frequencies 0-100 crn-l. The relevance of this calculation to the mechanism controversy under discussion is that the whole lineshape here arises from a single mechanism and is a property of the dynamics and not the detailed form of the interaction tensor.This conclusion can be seen from the expression for the intensity within the simplified electrodynamics used here The static correlation function appearing is in the Superposition Approximation (S(k’)-1)2 where S(k) is the neutron scattering structure factor. This factor in the integrand is sharply peaked at k‘ III 2n/a and the factor [k’jl(k’a)/(k’a)12 [see eqn (3)] makes the integrand die for all larger k’. All contributions to the spectrum then are determined by the value of the integrand in (1) at k’ N 2n/a. The functional form of Txz(k’), which enters through the first factor on the r.h.s.of (3) matters little since only the value ?xz(27c/a) is important and then only in determining the intensity. Dr. D. W. Oxtoby (Paris)said Depolarized light scattering intensities and spectra depend on the form of the pair polarizability anisotropy P((R). In the lowest order point dipole (DID) approximation p(R) is given by where R is the interatomic distance and a the atomic polarizability. W. M. Gelbart and I have shown’ that when short range effects due to overlap exchange and finite atomic size are taken into account the resulting P(R)can be represented in the form W.M. Gelbart and D. W.Oxtoby Mol. Phys. 1975,29,1569; 1975,30,535. GENERAL DISCUSSION where Ro z a&. Since the exponential term is of shorter range than the point dipole term Litovitz et al.suggest that it will introduce primarily high frequency Fourier components in the light scattering spectrum. In fact exactly the reverse is true because the short range term is subtracted the resulting p(R)varies less steeply with distance and it is low frequency components which are enhanced. This shows that the short and long range parts must be treated together and their influence on spectral features may not be separated. Prof. K. Singer (Royal Holloway College) said We have applied the continued fraction memory function analysis to rotational self correlation functions obtained in molecular dynamics simulations of linear molecules (F2,C12 Br, C02) based on the two centre Lennard-Jones potential .' For these model liquids under conditions corresponding to the experimental triple point the situation is much simpler than in the systems described by Gerschel; that is the higher memory functions are both shorter lived and simpler than the lower ones.To avoid the numerical difficulties which arise in the calculation of higher memory functions from numerical data we have assumed analytical forms with variable para- meters for the highest memory function and optimised the parameters so as to obtain the best fit to the given correlation functions. In addition the following simplifying assumptions are made the third memory function of the orientational autocorrelation (a.c.f.) functions for PI (C,(t))and P2 (C2(t)) and the second memory function of the angular momentum a.c.f.(CJ(t)) differ only by multiplicative factors i.e. M3(2)(t)= MJ2)(0)F(t) for C2(t) (2) M2(J)(t)= MJJ)(0)F(t) for CJ(t). (3) It follows from (3) that the first memory function of the torque a.c.f. ( CT)is M"T'(t) = hf"T'(O)F(t) + M,'J'(O). (4) The zero-time values of the memory functions are determined by the equilibrium prop- erties of the liquid. The trial functions F(t) included (a) exp (-at2) (b) a exp (-alt2) + (1 -a,) exp (-a2?') (c) exp (-at2) + at2 exp (-bt) (d) aexp(-at)(l + at) + (1 -a)exp (-bt)(l + bt). Table 1 lists the standard deviations over the range 0-2 x s between the molecular dynamics results for the four rotational a.c.f.s. and the correlation functions generated from the optimized memory functions.The results for II(b) are shown in graphical form (fig. 1). In each case the initial decay is faster and the size of the positive or negative tail smaller as one goes from a lower to a higher memory func- tion. On the time scale of Cl(t)and C2(t) the first memory function of CTor the second memory function of CJare nearly delta functions. It should be noted however that even these memory functions have a definite small and not very short lived dip (E -0.02 at 0.2 ps and N -0.01 at 0.6 ps) before the asymptotic value is attained. K. Singer A. J. Taylor and J. V. L. Singer unpublished. The computer program and some of the basic ideas in this approach are due to E. Detyna. GENERAL DISCUSSION TABLE 1 standard deviations.system C20) GO) Cdt) T* = 1.06 0.030 0.029 0.023 p* = 0.608 0.008 0.010 0.003 I* = 0.505 0.005 0.013 0.012 T* = 1.00 0.032 0.030 0.031 p* = 0.539 0.004 0.007 0.004 I* = 0.63 0.006 0.009 0.007 III (CO,) T* = 1.345 0.017 0.012 0.009 p* = 0.422 0.001 0.008 0.004 I* = 0.793 0.4-\\ ‘? 0.2-t, \ \‘*-.-.-.-* -. -. -.-.-.-._._._._._._,_._. -__ - - -------O-‘I ,~-‘L// I I I I I 1 I 1 I -0.2 -0.2I I I 1 I I I I 1 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 t I 10-’z’2s FIG.1(b).-Cz(t) the normalised a.c.f. of P2,--the normalised first memory function of C2(t),-* -the normalised second memory function of C2(f) GENERAL D I S CU S S I ON 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 t 1 10-’2s FIG.l(c).-CJ(t) the normalised angular momentum a.c.f.,- -the normalised first memory function of CJ(t),--the normalised second memory function of CJ(t).t I lo-’ FIG.l(d).-cT(t) the normalised torque a.c.f.,- -the normalised first memory function of CT(f). (The discrepancy between the regenerated and given a.c.f.s. would in these graphs only show up as a thickening of the line in some places and has therefore been omitted.) Dr. D. Frenkel (Amsterdam) said In one respect the memory functions for rota- tional motion differ fundamentally from the corresponding functions for translational motions. In the limit of free rotation the former memory functions do not reduce to any simple form whereas in a dilute gas the velocity memory function tends to zero. To give a specific example the dipole correlation function of a linear free rotor is proportional to <u(O) u(t)) = (I,,kT)/mdwco exp (-Iit1~/2kT) 0 GENERAL DISCUSSION the frequency spectrum of the first memory function corresponding to this correlation function is not just complicated but even singular.My question to Gerschel is whether knowing that translation and rotation memory functions behave qualitatively differently at low densities one should attach much significance to similarities at inter- mediate densities ? Dr. G. Wyllie (University of Glasgow) said I should like to express admiration of the experimental work which has enabled Gerschel and his colleagues to obtain such reliable information about the polarization autocorrelation functions.The discus- sion in terms of the well-known Mori hierarchy of equations is illuminating but the equations quoted by Gerschel as (1.1) and (1.2) are not the only ones possible and may be in a certain sense misleading. Ford Kac and Mazurl derived for a limited class of systems an equation of the form 4t) = -r(t)u(t> + n(t) or g(t>= -y(tlg(t) and Tokuyama and Mori recently gave a general derivation. The form is obviously inconvenient if g vanishes anywhere where 8 does not. The autocorrelation function of n has the neat form It is clear from Gerschel’s (1.2) and (2.7) that the immediate physical function g and the autocorrelation function K,of the “ random ” forcefare not linearly related and it can be easily verified for simple linear systems with well defined normal modes that K,typically contains frequencies with which nothing in the system actually vi- brates.The spectra of (f(O)f(t))or of <n(O)n(t)> should be used with caution in the interpretation of molecular mechanisms. Prof. A. Gerschel (Orsay)said In agreement with Frenkel’s remark a close com- parison of the details of translational and rotational memory functions (or 2nd order memory functions) would be irrelevant. Only those important features such as the relatively slow decay and the presence of obvious positive correlations do deserve discussion. If these are physically meaningful in the sense that I developed in my paper then analogies with the findings of translational dynamics deserve to be em- phasized in so far as they are predictions from numerical simulation while here we deal with the first experimental evidence of the effects.Moreover it is interesting to find out similarities in both dynamics translational and rotational since basically the same processes are responsible for elementary displacements either linear or angular. In this respect I should add that a critical examination of model descrip- tions of the orientational motion have led us to prefer the rotational analogue of the “itinerant oscillator ” model a model that also succeeded in describing translational motion as it was primarily intended to In a sense Wyllie’s remark is of a similar nature pointing out the difficulties in assessing the details of memory functions-or their frequency spectra-as definite molecular mechanisms.Since our K, (t) present long lived correlations it may be significant that a Langevin generalized formalism is not well suited to functions like G. W. Ford M. Kac and P. Mazur J. Math. Phys. 1965,6,504. M. Tokuyama and H. Mori Prog. Theor.Phys. 1976,55,411. A. Gerschel I. Dimicoli J. Jaffrd and A. Riou Mul. Phys. 1976 32 679. 178 GENERAL DISCUSSION g, (t)depicting short-time processes the separation into a generalized friction kernel and a random force is no longer meaningful if the fluctuations of the driving force and those of the random force occur in the same time scale. In other words if fluctua- tions in the rotational velocity and fluctuations in the torques responsible for the velocity changes exhibit comparable time dependence the orthogonality condition is no longer satisfied.For these reasons we confined our analysis to sketching striking similarities with molecular dynamics results refraining from inferring much more detailed motional mechanisms from our second memory function characteristics. Kivelson remarked that a mathematical proof of the identification of functions Kg(t) and grY(t)has been already provided with further identification of both these func- tions with the angular velocity correlation function. Such proofs have been given by many authors including ourselves provided that the orientation correlation functions decay slowly enough in comparison with the angular velocity (or the rotational velocity) correlation functi0n.l It was to test how severe that restriction was that we system- atically computed both functions Kg(t)and g,,(t) under varied physical states of a same liquid resulting in quite satisfactory agreement at high densities and a gradual de- parture for lower densities states.Prof. A. D. Buckingham (Cambridge Uniuersity) asked What is the angle-depend- ent pair potential employed by van der Elsken and Frenkel in their calculations of the rotational line-widths for HCI in compressed Ar and how does it compare with potentials deduced from information about the HClAr "molecule "? Dr. D. Frenkel (Amsterdam) said:In the molecular dynamics calculations described in the present paper the anisotropic perturbation acting on a probe molecule in a dense fluid was computed. In these calculations it was assumed that the r-dependence of the I = 1 and I = 2 part of the anisotropic probe-host interaction was proportional to the Ar-Ar Lennard-Jones (6-12) potential (a = 3.405 A).Clearly this will be an oversimplified description of the HC1-argon anisotropic interaction. For instance the long-range behaviour of the HCI-argon interaction that should go as r-' is described by Y-~. Moreover one may expect the position of the minimum of the I = 1,2 parts of the potential to differ somewhat from rmi 2% for the L.J. (6-12) potential. However it should be realized that the quite detailed investigations of the HC1-argon anisotropic interaction by Neilsen and Gordon,2 Dunker and Gordon3 and Holmgren and Klemperer4 have not yet provided us with a set of anisotropic potential parameters that account for all experimental information on the binary HCl-Ar interaction.In fact the different potentials that have been proposed differ in their estimate of the depth of the I = 1 (I = 2) part by a factor of 2 to 3. In particular it is not known whether the I = 1 or the I = 2 interaction has the deeper minimum. In view of these observations there is little reason to reject the anisotropic potentials that are used in the present M.D. calculations as being inadequate to describe known characteristics of the HCI-Ar anisotropic interaction. It should be mentioned that the values for the depth of the I = 1 and I = 2 part of the anisotropic interaction that yielded the best fit for the linewidths given in table 1; cf.cl = 32.3 cm-l and e2 = 49.1 cm-' fall within the range of values given in ref. (1) and (3). However our estimates for cl and c2 should be treated cautiously because they were obtained by A. Gerschel I. Darmon and C. Brot MoZ. Phys. 1972,23 317. W. B. Neilsen and R. G. Gordon J. Chem. Phys. 1973,58,4131. A. M. Dunker and R. G. Gordon J. Chem. Phys. 1976,64,354. S. L. Holmgren and W. Klemperer personal communication. GENERAL DISCUSSION fitting experimental data on dense gases. Non-pairwise additive contributions to the anisotropic interaction may be of some importance. Hence we may only hope to obtain information about an effective two-body anisotropic interaction. Prof. A. D. Buckingham (Cambridge University) made the following summarizing remarks We have focused our attention in this Symposium on some of the newer techniques for studying the relaxation of molecules.In particular we have heard papers on dielectric polarization and the Kerr effect on polarized and depolarized light scattering on resonance Raman scattering on infrared absorption and on com- puter simulation by molecular dynamics calculations. Other techniques such as inelastic neutron scattering and magnetic resonance spectroscopy would also have been appropriate but were excluded by the organizing Committee who sought to arrange a compact and coherent Symposium. Non-linear polarization and scattering were not excluded but have not featured in our discussion; a paper in this area was not presented owing to the regrettable absence of Professor Kielich.I shall not attempt to summarize the individual papers-the authors have done that for themselves-but shall make some general remarks. The first is to emphasize a point made in one or two of the manuscripts-we should strive to employ several techniques on the same system. Each of the techniques we have heard about has its special virtues but none in isolation provides a full story. The Symposium has been helpful in the way it has brought together several complementary techniques; let us hope that it may lead to joint investigations of the same system in different laboratories. And we should strive to exploit as many variables as possible; density changes are particularly to be recommended and fortunately high-pressure instrumentation is now simple and convenient.It may be useful to divide our subject into three parts the molecules the inter- molecular forces and the bulk phase and for each of us to ask ourselves the awkward question as to where our principal interest lies. If we are chiefly concerned about the structure and properties of isolated molecules then we should direct our efforts to the gaseous or crystalline phases and avoid non-equilibrium phenomena. We may be interested in changes in molecular properties in going from the isolated to the dissolved state; that would compel us to look at liquids and solutions but we should concen- trate on those techniques such as vibrational spectroscopy where the excitation is highly localized and bear in mind that the identity of a molecule may be lost in a condensed medium.Where does one molecule end and another begin? If our main interest is in intermolecular forces we should again try to work with gases at low densities or with crystals and exploit the advantages of different techniques. Thus molecular-beam scattering combined with second-virial coefficients or with calculated long-range interaction energies can give us accurate potentials for simple systems such as the inert gases and HZ.And double-resonance spectroscopy in gases can yield the probability that a collision causes a transition between particular quantum states; tuneable lasers will extend the range of this particular technique. On the other hand if our interests are in the fluid phase itself we shall wish to exploit a number of tech- niques and become involved with models of reality.Information obtained in one area can be fruitful in another-thus knowledge of the properties of isolated molecules provides us with a description of the long-range intermolecular forces and a know- ledge of these and of the short-range forces (where electron exchange renders the integrity of the individual molecules doubtful) illuminates the mechanisms of energy transfer and molecular relaxation. The technique of computer simulation provides us with the opportunity to unravel the complex nature of molecular interactions and relaxation in dense fluids. It should GENERAL DISCUSSION help us to gain a firmer understanding of the relative significance of different micro-scopic contributions to an observable.The technique has already answered some questions and posed some new ones and is bound to grow in importance. As it will soon be Christmas it seems appropriate to end by setting a puzzle con- cerning the rotational motion of a polar body in a fluid. We know that a dipole p in a spherical cavity in a continuum induces in the cavity a reaction field R proportional to p R =gp. In Onsager’s theory of dielectricsi g = 2(~-1)[(2e + 1)47~q,a~]-~ where E~ is the permittivity of free space E is the dielectric constant of the continuum and a is the radius of the cavity. With a dipole inside an ellipsoid of revolution the principal components of the reaction field are R1 = gipi R2 =gzlU2 where g # g2. In general therefore the reaction field is not parallel to p and the dipole experiences a torque p x R of magnitude plp2(g -gl).If the dipole is fixed in the ellipsoid it might be supposed that the whole will rotate and give rise to per- petual motion! Those attending the Symposium were left to solve the paradox. The solution is to be found by seeking an equal and opposite torque on the ellipsoid; its source lies in the asymmetry in the energy density of the continuum in which there is an electric field due to p and to the boundary of the ellipsoid. L. Onsager J. Amer. Chem. Soc. 1936,58 1486.