3 Molecular Acoustics By A. J. MATHESON Department of Chemistry University of Essex Colchester Molecular acoustics is the study of molecules and their interactions by means of ultrasonic shear or longitudinal waves. When a shear wave propagates through a medium there is no temperature variation in phase with the displacement of the medium which may respond by viscous flow (i.e. a liquid) elastic deformation (solid) or some combination of these two (viscoelastic body). The change from viscous to elastic response (viscoelastic relaxation) occurs when the period of the shear wave becomes comparable to the time required for the elementary molecular diffusive motion. In principle times ranging from many seconds in polymers to s in low-viscosity liquids may be investigated with shear waves.An ultrasonic longitudinal wave contains both a pure shear and a pure com-pressional component. Since the period of the alternating compression is short, a longitudinal wave will propagate adiabatically and the local temperature of the medium will alter in phase with its changing volume. Hence any equilibria which are sensitive to temperature or pressure will be disturbed by the passage of a longitudinal wave. These include not only chemical equilibria but also equilibria involving rotational isomers and the distribution of energy among the translational vibrational and rotational degrees of freedom in fluids. The flow of liquid molecules between different local ‘structures’ can also be studied in this way. In this review the information which has recently been derived from studies of the propagation of low-amplitude ultrasonic waves is considered.Such waves gently perturb an existing equilibrium; they do not have sufficient intensity to induce additional chemical reactions. Two books on molecular acoustics have appeared recently one covering the more physical aspects of the subject2 and the other dealing with those topics considered here.3 The viscoelastic behaviour of polymers has been the subject of a definitive as have the ultrasonic properties of solids :’ neither topic is discussed further here. ’ L. D. Rorenberg ‘High Intensity Ultrasonics,’ Plenum New York 1971; L. A. Spurlock and S. B. Reifsneider J . Amer. Chem. SOC. 1970 92 61 12. * R . T. Beyer and S. V. Letcher ‘Physical Ultrasonics,’ Academic Press New York 1969.A. J. Matheson ‘Molecular Acoustics,’ Wiley London 1971. J . D. Ferry ‘Viscoelastic Properties of Polymers,’ 2nd edn. Wiley New York 1970. R. Truell C. Elbaum and B. B. Chick ‘Ultrasonic Methods in Solid State Physics,’ Academic New York 1969 28 A . J . Matheson 1 Molecular Energy Transfer in Gases When an ultrasonic longitudinal wave passes through a gas the molecular translational temperature oscillates about its equilibrium value. If the sound frequency is low the vibrational rotational and electronic degrees of freedom are able to remain in equilibrium with the translational temperature as a result of molecular collisions. As the frequency of the sound wave increases however, its period may become shorter than the translational-vibrational relaxation time : a given translational temperature is maintained for a time that is so short that insufficient molecular collisions occur to allow the vibrational modes to equili-brate with translation.The sound wave then 'sees' a gas which has no vibrational heat capacity and hence the ultrasonic velocity increases and the absorption falls. A similar effect is observed at higher frequencies when the period of the sound wave becomes comparable to the translational-rotational relaxation time while translational-electronic energy transfer has been observed in NO., Studies of molecular energy transfer in gases have taken place ever since the development of the ultrasonic interferometer in 1925 a perusal of the Zeitschrijit f i r physikalische Chemie shows that the 1930's were a particularly fruitful period.Energy transfer in most pure gases has now been investigated especially around room temperature. The ultrasonic technique is no longer pre-eminent in the field and the shock tube the spectrophone and the laser fluorescence method all yield complementary information. Improvements in acoustic techniques now permit the study of gases having small vibrational heat capacities. An example of this is H2S where the vibrational relaxation time Tvib is 3 x s at 298 K and the average number of collisions required for energy transfer Z is 290.7 In D,S despite the lower fundamental vibration frequency Tvib is longer than in H,S being 4.8 x s at 300 K.' This is the result of the high rotational velocities of these molecules.Energy transfer occurs in the sequence trans rot * vib the translational-rotational collision-number Z,, of H,S being only 8.7 A maximum in the vibrational collision-number at 500 K is also in agreement with vibrational-rotational energy transfer. The ultrasonic interferometer has also been adapted to cover a wide range of temperature. Using a continuous-flow system the vibrational relaxation of CO, has been measured up to 1300 K9 SF has been investigated down to 253 K : at high temperatures the Landau-Teller plot of log Z us. T - ' / 3 is linear but at lower temperatures where the attractive intermolecular forces become important, the vibrational relaxation time is shorter than expected." Similar effects have been observed in the vibrational fluorescence of CO at temperatures down to 100 K.' ' Vibrational relaxation at low temperatures appears to be very sensitive ' H.J. Bauer and K. F. Sahm J . Chem. Phys. 1965 42 3400. ' H. J. Bauer A. C . C. Paphitis and R. Schotter Physica 1970,47,58 109; T. G. Winter and H. E. Bass J . Acoust. SOC. Amer. 1970 48 1 1 19. F. D. Shields and G. P. Carney J . Acoust. SOC. Amer. 1970 47 1269. E. H. Carnevale C. Carey and G. Larson J . Chem. Phys. 1967 47 2829. D. J. Miller and R. C. Millikan J . Chem. Phys. 1970 53 3384. l o K. W. Beste Acustica 1970 23 121 Molecular A cous t ics 29 to the attractive part of the intermolecular potential and further investigations of this should prove fruitful. In molecules where the lowest fundamental vibrational frequency is less than half the frequency of the next lowest vibration double relaxation is expected : rapid energy transfer to the lowest vibration occurs in parallel with the slower energy transfer to the other vibrational modes.Such behaviour is observed by the acoustic technique in C2N and CF,CN.12 Mixtures of the doubly relaxing SO and the singly and more rapidly relaxing CH,F have also been studied : a single relaxation time is found for the whole vibrational-energy content of both molecules on account of the rapid near-resonant vibrational-vibrational energy transfer between the upper modes of the two molecules which enables CH2F2 to act as an energy transfer catalyst for SO . 1 2 The rapidly relaxing D,S simi-larly promotes energy transfer to C02.8 An interesting study of vibrational-rotational energy transfer has been carried out on mixtures of C02 and H it is found that the vibrational relaxation of CO, by ortho-H is about twice as fast as that by para-H,.The energy required to excite the bending mode of CO is similar to the energy of the J = 1 to J = 3 transition of ortho-H but very different from the energies of the J = 0 to J = 2 or J = 2 to J = 4 transitions in para-H .’ A number of good reviews of vibrational-translational energy-transfer theory have appeared. l4 Provided that no complications arise from vibrational-rotational or vibrational-vibrational exchanges the probability of vibrational-translational energy transfer can be calculated to within a factor of three over a wide range of temperature once the intermolecular potential is known.In prin-ciple results of vibrational relaxation experiments can be used to deduce this potential ; for example the greater efficiency of cyclopropane (mass 42) relative to argon (mass 40) in deactivating vibrationally excited cyclopropane could be attributed to a steeper intermolecular p0tentia1.l~ However the possibility of vibrational-rotational energy transfer in cyclopropane renders any quanti-tative conclusions suspect. A detailed theory of vibrational-rotational energy transfer has appeared which considers both the translational and the rotational motions of the colliding species.16 The calculated values of r,ib of HF,I7 HCl, DCl HBr and HI agree well with experiment over the range 800-2000K, while the slower vibrational relaxation of DCI relative to HC1 is also explained.The theory predicts that up to ca. 2500 K DF will relax more slowly than HF, but that at higher temperatures DF will have the shorter relaxation time this l 2 J. D. Lambert D. G. Parks-Smith and J. L. Stretton Trans. Faraday SOC. 1970 66, l 3 S. W. Behnen H. L. Rothwell and R. C. Amme Chem. Phys. Letters 1971 8 318. l 4 A. B. Callear and J. D. Lambert in ‘Comprehensive Chemical Kinetics,’ Vol. 3 , ed. C. H. Bamford and C. F. H. Tipper Elsevier Amsterdam 1969; D. Rapp and T. Kassal Chem. Rev. 1969 69 61 ; J. L. Stretton in ‘Transfer and Storage of Energy by Molecules,’ Vol. 2 ed. G. M. Burnett and A. M. North Wiley London 1969. 2720. l 5 A. G. Welsh and J. E. Taylor J . Acoust. SOC. Amer. 1970 47 1274. l 6 H. K. Shin J . Phys. Chem.1971 75 1079. J. F. Bott and N . Cohen J . Chem. Phys. 1971 55 3698 30 A. J. Matheson arises because of the increased efficiency of translational motion in removing vibrational energy at high temperatures in DF-DF collisions.'* The acoustic technique is again finding favour for studying translational-rotational energy transfer now that the calculation of rotational collision num-bers from thermal conductivity data is considered s ~ s p e c t . ' ~ Two major dis-advantages of the ultrasonic technique are that the interpretation of the results is difficult when the sound period is comparable to the time between collisions and that the study of specific rotational energy levels is rarely possible. The former effect is reasonably well understood in pure gases but is more complicated in gas mixtures.,' The latter effect leads to an increase in the observed rotational relaxa-tion time with temperature.,l Only in H at low temperatures is it possible to study specific rotational tran-sitions by the ultrasonic method.The large energy difference between the rota-tional levels of H permits only the ground and the first-excited states to be occu-pied ; in addition the large values of the rotational collision-numbers permit easy interpretation of the results as translational dispersion is not important. In HD, Zrot x 10 and is independent of temperature in the range 20-43 K whereas for HD-He collisions Z,, = 17. These collision numbers refer to the J = 0 to J = 1 transition. They are considerably smaller than the values for para-H,, where at 77 K Z,, = 715 for the J = 0 to J = 2 transition.,, An interesting study of the rotational relaxation of CO and N has shown that at 307.5 K Z,, = 3.9 for I4N2 4.1 for l4NI5N 4.5 for I5N2 2.8 for 12C160, and 2.7 for '2C'80.The symmetry of N has no influence on Z,, . The reasons for the shorter relaxation time in CO are not clear.23 There has recently been a revival of interest in the optic-acoustic effect and in the spectrophone as a means of studying vibrational-translational energy transfer. 1.r. radiation is directed on to a constant-volume cell containing a gas with i.r.-active vibrations. The resulting excess vibrational energy is degraded into translation by molecular collisions after the vibrational relaxation time has elapsed and the increase in pressure may be detected by a sensitive microphone.Modulation of the i.r. produces a sound wave. The vibrational relaxation time may be calculated from the phase difference between the incident radiation and the sound wave from the change in sound amplitude with the frequency of modulation or by a fluorescence competition method.24 The theory of the spec-trophone has now been investigated in detail.25 For the bending vibration of CO, H. K. Shin Chem. Phys. Letters 1971 10 81. 3 619; F. J. Zeleznik and R. A. Svehla J . Chem. Phys. 1970 53 632. l 9 A. K. Barua A. Manna P. Mukhopadhyay and A. Das Gupta J . Phys. (B) 1970, 2 o G. J. Prangsma R. M. Jonkman and J. J. M. Beenakker Physica 1970 48 323. 21 L. M. Raff and T. G. Winter J . Chem. Phys. 1968 48 3992.2 2 R. M. Jonkman G. J. Prangsma R. A. J. Keijser R. A. Aziz and J. J. M. Beenakker, Physica 1968 38 451; G. J. Prangsma J. P. J. Heemskerk H. F. P. Knaap and J. J. M. Beenakker Physica 1970 50 433. 2 3 P. G. Kistemaker A. Tom and A. E. De Vries Physica 1970,48 414. 2 4 A. W. Read Adv. Mol. Relax. Prccesses 1968 1 257. 2 5 L. Doyennette Ann. Physique 1969,4 253; B. L. Lavercomb and R. W. B. Stephens, Acustica 1971,24,322; R. Tripodi and W. G. Vincenti J . Chem. Phys. 1971,552207 Molecular Acoustics 31 the spectrophone value of the vibrational relaxation time of 6-7ps at room temperature is in good agreement with the ultrasonic value.26 The major advan-tage of the spectrophone however is that it can be used to study any i.r.-active vibration. For example a figure of 4 p s is quoted for the vibrational relaxation time of the asymmetric stretching vibration of C02 .26 An impulsive optic-acoustic effect has also been intr~duced.~' The gas under investigation is irradiated with a pulse from an i.r.laser and the resulting change in pressure observed. The vibrational relaxation time may be calculated directly from the rate of increase of pressure and the method is claimed to be superior to that of the conventional spectrophone. This technique should be particularly useful when combined with vibrational fluorescence experiments.28 The propagation of ultrasonic waves in gases is occasionally used to determine their thermodynamic properties at high temperatures or and it has also been suggested as a method of gas analy~is.~' The use of molecular acoustics in studying equilibria in gases was first suggested in 1920.3 The method is now little used although a further determination of the position of equilibrium in gaseous N20 has been made.32 A theoretical treatment of ultrasonic propa-gation when a large number of equilibria are present has been outlined.33 2 Molecular Energy Transfer in Liquids The passage of an ultrasonic longitudinal wave through a liquid promotes molecular energy transfer between the translational and the vibrational and rotational modes.As in the gas phase energy transfer appears to take place largely as the result of binary collisions between molecules which momentarily have a high relative translational velocity. Since there are typically lo3 times as many collisions per second in a liquid as in a gas at atmospheric pressure and at the same temperature the vibrational relaxation time of an unassociated liquid should be about 10- times that in the gas.In associated liquids the translational and vibrational motions will be more strongly coupled and the vibrational relaxation times will be much shorter. Only a few simple liquids have sufficiently long vibrational relaxation times for them to be observed with ultrasonic frequencies below 1 GHz. A study of liquid CHCl between 213 and 293 K showed that at high temperatures the whole of the vibrational heat capacity relaxed with a single relaxation time; at lower temperatures however a discrepancy between the observed and calculated heat 26 M. Huetz-Aubert and P. Chevalier Compt.rend. 1953 268 B 1068; F. Cannemeijer, M. H. de Vasconcelos and A. E. de Vries Physica 1971 53 77. 2 7 T. Aoki and M. Katayama Japan. J. Appl. F-hys. 1971 10 1303. 2 8 C. B. Moore Accounts Chem. Res. 1969 2 103; J. C. Stephenson R. E. Wood and C. B. Moore J . Chem. Phys. 1971 54 3097; H. L. Chen and C. B. Moore J . Chem. Phys. 1971 54 4072. 2 9 L. L. Pitaevskaya A. V. Bilevich and N. B. Isakova Russ. J. Phys. Chem. 1969,43, 1197; G. E. Goring J. Chem. Phys. 1971 54 4514. 30 P L. Thorpe J. Phys. ( E ) 1969 2 1073. 31 A. Einstein Preuss. Akad. Wiss. Berlin Ber. 1920 24 380. 32 H. Blend J . AcouAt. SOC. Amer. 1970,47,757; H. Blend J. Chem. Phys. 1970,53,4497. 3 3 D. Tabuchi .j. Chem. Phys. 1971 55 2218 32 A . J . Matheson capacities suggests that energy transfer to the lower-frequency vibrations of CHCl occurs too rapidly to be observed below 2 G H z .~ ~ In contrast to this a number of binary mixtures of CS, CH,Cl, CH,Br, C6H6 and Cc1 at various concentrations all showed a single relaxation in the available frequency range below 800 MHz although some of the pure liquids have two vibrational relaxation times. The concentration dependence of the ultrasonic absorption and vibrational relaxation times in these mixtures may be explained if it is assumed that intermolecular transfer of vibrational energy occurs readily in a collision and that collisions of unlike molecules are more effective than collisions of like molecules in promoting vibrational-translational energy transfer.35 The Brillouin scattering technique permits the investigation of ultrasonic propagation at frequencies from 1-10 GHz and allows vibrational relaxation to be studied in many unassociated liquids.Thus thiophen has z ~ ~ = 6 x 10- lo s at 293 K while fluoro- chloro- bromo- and iodo-benzene have vibrational relaxation times between 0.6 and 1.0 x 10-'Os at 298 K in these benzene derivatives only part of the vibrational heat capacity relaxes and the same is true of nitrobenzene where Z,ib = 3 x lo-" A number of studies of Brillouin scattering in liquid benzene have been reported although it is agreed that the vibrational relaxation time is ca. 3 x 10- l o s opinions differ on whether the entire vibrational heat capacity relaxes or whether a shorter relaxation time is required for the lowest vibrational mode.,' There is no such controversy in the case of CC14 where the total vibrational heat capacity relaxes in 6 x lo-" s at 293 K.38 Similarly CS has a single vibrational relaxation time of 1.8 x lop9 s at 293 K this value obtained by Brillouin scattering is in excellent agreement with the ultrasonic value of 2.0 x s at 298 K.39 No vibrational relaxation is observed in diethyl ether39 or liquid N :40 in the former the vibrational relaxa-tion is likely to be too rapid to be observed while in the latter the vibrational heat capacity is so small that vibrational relaxation would not be observed because of small experimental inaccuracies.3 Ultrasonic Propagation in Non-relaxing Liquids Measurement of ultrasonic velocities in liquids to an accuracy of one part in lo3 is easily achieved and with care an absolute accuracy of better than one part 3 4 P.K. Khabibullaev M . G . Khaliulin and K. Parpiev Russ. J . Phys. Chem. 1970,44, 3 s J. L. Hunter J. M. Davenport and D. Sette J . Chem. Phys. 1971 55 762. 3 6 S. S . Aliev L. E. Kvasova L. V. Lanshina K. Parpiev and P. K. Khabibullaev, Sou. Phys. Acoust. 1970,16,250; K. Parpiev P. K. Khabibullaev and Y. G. Shoroshev, Sou. Phys. Acousr. 1971,16 531 ; P. K. Khabibullaev K. Parpiev and L. V. Lanshina, Russ. J . Phys. Chem. 1971 45 944. 3 7 W. H. Nichols C. R. Kunsitis-Swyt and S . P. Singal J. Chem. Phys. 1969 51 5659; J. L. Hunter W. H. Nichols and J. W. Haus Abs. Papers 162nd National Meeting Amer. Chem. SOC. 1971 COLL 44; E. Kato and Y . Saji Japan. J . Appl. Phys. 1971, 10 1472.3 8 G. I. A. Stegeman W. S. Gornall V. Volterra and B. P. Stoicheff J . Acoust. SOC. Amer. 1971 49 979. 39 S. Gewurtz W. S. Gornall and B. P. Stoicheff J . Acoust. SOC. Amer. 1971 49 994. 4 0 A. S. Pine J . Chem. Phys. 1969 51 5171. 717 Molecular Acoustics 33 in lo5 can be attained. Wide ranges of temperature and pressure can easily be covered and hence ultrasonic velocities are widely used to obtain accurate thermodynamic data for liq~ids.~’ For example the compressibilities and heat capacities of liquid argon have been determined along seven isotherms in the range 1&150 K at pressures up to 500 atmosphere^.^^ Other liquids investi-gated include mixtures of neon with hydrogen and propane and butane,43b The ultrasonic technique can also be adapted to determine the density of a liquid as a function of temperature and pressure and a wide range of thermodynamic data for liquid mercury has been reported.44 Ultrasonic studies of liquid mixtures are also used to determine excess proper tie^.^' It is important that all such measurements are made at sound frequencies at which no relaxation effects are present.Attempts continue to correlate the ultrasonic velocity with the molecular structures of liquids and investigations are now being conducted over wide ranges of temperature and pressure. Typical recent studies have included liquid metals,46a deuteriated organic nitro- and amino-comp~unds,~~~ and hydrocarbons.46d Although such correlations are useful for providing esti-mates of ultrasonic velocities for engineering purposes they do not throw much light on the intermolecular interactions in liquids.There are recurring reports of anomalies in the physical properties of water and this liquid is so unusual that these cannot lightly be dismissed. Accurate measurements have now been made of the velocity of 9.9 MHz ultrasonic waves in water at 2300 temperatures between 279 and 354 K. The variation of velocity with temperature is a smooth function and there is no evidence of any discon-tinuities or anomalous beha~iour.~’ Negative dispersion of the ultrasonic velocity has been reported in liquid argon and neon the hypersonic velocity obtained from Brillouin scattering being slightly lower than the ultrasonic velocity. It is suggested that at sufficiently high frequencies sound waves propagate non-dissipatively and negative dis-persion occurs.The observed dispersion is small however and is possibly no greater than the variation in the results that is normally obtained in different ultrasonic experimen ts.48 and n-propanol at pressures up to 10 OOO 4 1 J. S. Rowlinson ‘Liquids and Liquid Mixtures,’ 2nd edn. Butterworths London 1969. 42 J. Thoen E. Vangeel and W. Van Dael Physica 1969 45 339. 4 3 ( a ) D. Giisewell F. Schmeissner and J . Schmid Cryogenics 1970 10 150; ( h ) M. G . S. Rao Ind. J. Pure Appl. Phys. 1971 9 169; (c) L. Leibowitz M . G. Chasanov and R. Blomquist J. Appl. Phys. 1971,42,2135; (4 M. P. Hagelberg J. Acoust. SOC. Amer., 1970 47 158. 4 4 J. M. Stallard I. J. Rosenbaum and C. M. Davis J . Acoust. SOC.Amer. 1969,45 583. 4 5 0. Kiyohara and K. Arakawa Bull. Chem. SOC. Japan 1971 44 1224. 4 6 ( a ) S. Rajagopalan J . Phys. Sac. Japan 1969 27 735; (b) W. Schaaffs and F. B. Shenoda Acustica 1970 23 38; (c) M. V. Kaulgud and V. K. Tarsekar Acustica, 1971 25 14; M. V. Kaulgud Acustica 1971 25 22; (6) S. Rajagopalan J. Phys. SOC. Japan 1969 26 584; P. N. Gupta and S. C. Sinha Acustica 1971 25 146. 4’ W. Senghaphan G. 0. Zimmerman and C. E. Chase J. Chem. Phys. 1969,51 2543. 4 8 P. A. Fleury and J. P. Boon Phys. Rev. 1969 186 244; E. V. Larson D . G. Naugle, and T. W. Adair J. Chem. Phys. 1971 54 2429 34 A . J. Matheson Ultrasonic propagation is also being used to study the structure of liquid metals. The temperature dependence of the ultrasonic absorption in Sn suggests that traces of a solid-like structure persist to high temperatures and pressure^.^^ In solutions of K in liquid NH, the temperature dependence of the ultrasonic velocity changes in the region where the solutions undergo a metal-non-metal transition this change occurs at a lower molar concentration of K than of Li, the latter ion being smaller.s0 Mixtures of K and Rb show no anomalous ultra-sonic absorption which suggests that there is no tendency towards the formation of molecular complexes.In Na-Cs solutions however the absorption has a large maximum in mixtures containing 75 atomic percent Na. This decreases with increasing temperature indicating the disappearance of some molecular associ-ation presumably this is Na,Cs although there is no evidence for this in the solid phase.51 Measurements of ultrasonic absorption provide the only means of determining the volume viscosity of liquids.This represents the energy loss associated with the compressional component of the longitudinal wave when molecules flow between packings of high and low density in the liquid. Theoretical treatments of simple liquids whose molecules interact with pairwise central additive inter-molecular forces suggest that the ratio of volume to shear viscosity should be 5 :3.52 The calculation from first principles of the volume viscosity of molecular liquids is not yet possible and indeed even experimental estimations are difficult when a number of relaxation processes contribute to the ultrasonic absorption. Determinations of the volume viscosities of liquid Ne,s3a of the alkali metals,536 and of Bi and PbS3' have been reported.An extensive tabulation of the volume viscosities of H20 five alcohols CCl, and two hydrocarbons at pressures up to 5000 atmospheres has also been given.s3d The ultrasonic absorption and bulk viscosity of water have been calculated using a two-state model. Each molecule is assumed to have two states available, the one characterized by a higher volume and lower energy (ice-like structure) and the other by a lower volume and higher energy (close-packed structure). The periodic pressure changes in an ultrasonic wave causes the molecules to move between these states and ultrasonic absorption results.54 This simple model with various auxiliary assumptions gives a good description of the ultra-sonic absorption in D20,5sa methanol,ssb and ethanols5' in the case of the 4 9 M.B. Gitis I. G. Mikhailov and S. Niyazov Sov. Phys. Acoust. 1970 16 113; V. K. Ablordeppey Phys. Rev. ( A ) 1971 3 1680. D. E. Bowen J . Chem. Phys. 1969 51 1 1 15. 5 1 M. G. Kim and S. V. Letcher J . Chem. Phys. 1971 55 1164. 5 2 R. D. Mountain J . Chem. Phys. 1968 48 2189; A. V. Narasimham I.E.E.E. Trans. Sonics Ultrasonics 1969 16 182. 53 ( a ) E. V. Larson D. G. Naugle and T. W. Adair Phys. Letters ( A ) 1970 32 443; (b) M. G. Kim K. A. Kemp and S. V. Letcher J . Acoust. SOC. Amer. 1971 49 706; ( c ) J. M. Flinn J. Jarzynski and T. A. Litovitz J . Chem. Phys. 1971 54 4331; (4 S. Hawley J. Allegra and G. Holton J . Acousr. Soc. Amer. 1970 47 137. 5 4 L. Hall Phys.Rev. 1948 73 775; T. A. Litovitz and C. M. Davis in 'Physical Acoustics,' Vol. 2A ed. W. P. Mason Academic New York 1965. 5 5 ( a ) S. K. Kor G. Rai and 0. N . Awasthi Phys. Rev. 1969 186 105; (6) S. K. Kor, 0. N . Awasthi G. Rai and S. C. Deorami Phys. Rev. ( A ) 1971 3 390; S. K. Kor Molecular Acoustics 35 alcohols however there is no evidence that the temperature changes accom-panying the passage of an ultrasonic wave do not also perturb the equilibrium. In considering the pressure dependence of the ultrasonic absorption in water, the unlikely assumption is required that the ice-like structure has a higher energy than the close-packed form. This dlffculty can be overcome by assum-ing a hollow cluster of about eight water molecules in the ice-I structure with non-hydrogen-bonded molecules within the cavities of the structure.This model gives a good description of the pressure dependence of the ultrasonic absorption in water.56 A two-state model using experimental co-ordination numbers has also been applied to ultrasonic absorption in Bi and Pb.53‘ 4 Ultrasonic Propagation near Critical Points Anomalous ultrasonic velocities and absorption coefficients are often observed in liquid mixtures which show non-ideal thermodynamic beha~iour.~’ It is now accepted that the excess ultrasonic absorption is caused by fluctuations in the local composition of the solution. When the system is perturbed by the passage of a sound wave a new equilibrium distribution of fluctuations is required and the rate of attainment of this is governed by the rate of molecular diffusion.At low ultrasonic frequencies diffusion may be sufficiently fast to allow the local composition to remain in equilibrium with the perturbation but at higher frequencies the attainment of equilibrium lags behind the pert~rbation.~’ This theory gives a good description of the ultrasonic absorption in aqueous solutions of CH3CN,59a alcohols,59b propylene oxide tetrahydrofuran and d i ~ x a n . ~ ’ ~ The heat capacity at constant volume of a one-component system has a sharp maximum at the critical point and a corresponding minimum in the ultrasonic velocity has been observed in argon6’“ and propane6” ; similar minima have been reported in critical mixtures.60c Brillouin scattering is particularly useful for determining the sound velocity near the critical point since the high sound absorption precludes the application of conventional techniques at frequencies above a few MHz.~’ This absorption has been attributed to a coupling of the S.C. Deorani and B. K. Singh Phys. Rec. ( A ) 1971 3 1780; (c) S. K . Kor B. K. Singh and R. Prasad Phys. Letters (A) 1971 35 100; G. Rai B. K. Singh 0. N. Awasthi and U. S. Tandon Phys. Letters (A) 1971,36 319; S. K. Kor S. C. Deorani, B. K. Singh R. Prasad and U. S. Tandon Phys. Rev. ( A ) 1971 4 1299. 5 6 0. Nomoto and H. Endo Bull. Chem. SOC. Japan 1971 44 1519. 5 7 M. J. Blandamer and D. Waddington Adv. Mid. Relax. Processes 1970 2 1 . 5 8 V. P. Romanov and V. A. Solovyev Sou. Phys. Acoust. 1965 11 68 219. 5 9 ( a ) M. J. Blandamer M. J. Foster and D.Waddington Trans. Faraday SOC. 1970, 66 1369; (b) F. Garland J. Rassing and G. Atkinson J. Phys. Chem. 1971,75 3182; W. M. Madigosky J . Acoust. SOC. Amer. 1970 47 98; (c) E. K. Baumgartner and G. Atkinson J. Phys. Chem. 1971 75 2336. 6 o ( a ) J. Thoen E. Vangeel and W. Van Dael Physica 1971 52 205; (b) L. Guengant and A. M’Hirsi Compt. rend. 1971 273 B 702; (c) G . D’Arrigo D. Sette and P. Tartaglia Phys. Letters (A) 1971,35 133 ; V. F. Nozdrev and F. Tashmukhamedov, Sou. Phys. Acoust. 1971 17 142. 6 1 R. D. Mountain J. Res. Nut. Bur. Stand. ( A ) 1969 73 593; M. A. Anisimov I. M. Arefiev A. V. Voronel V. P. Voronov Y. F. Kyachenko and I. L. Fabelinskii, Zhur. eksp. teor. Fiz. 1971 61 1526; R. Mohr K. H. Langley and N. C. Ford J . Acoust. SOC Amer.1971 49 1030 36 A . J Matheson ultrasonic wave to the density fluctuations which exist in the liquid and also to the composition fluctuations in liquid mixtures. Theories derived on this b a d 2 give a satisfactory account of the ultrasonic absorption at the critical points of Xe,63" and nitrobenzene-n-hexane and aniline-~yclohexane~~~ mixtures. If ther-mal relaxation processes are also present however it is not possible to disentangle the various contributions to the ultrasonic absorption in the critical region.63c Similar behaviour is shown by liquid crystals. There is an abrupt minimum in the ultrasonic velocity and a maximum in the ultrasonic absorption at the transition from an isotropic liquid to the cholesteric phase.64 If nematic liquid crystals are oriented by a magnetic field the ultrasonic absorption is markedly anisotropic but the velocity is independent of the direction of p r ~ p a g a t i o n .~ ~ 5 Rotational Isomeric Relaxation in Liquids The temperature and pressure fluctuations which accompany the passage of an ultrasonic wave through a liquid perturb the equilibrium distribution of mole-cules among their rotational isomeric states. If the period of a sound wave is sufficiently long energy is abstracted from the wave to promote molecules to a higher energy conformation ; as the sound frequency increases the conformational equilibria become unable to follow the rapid temperature and pressure changes, and the ultrasonic absorption per unit of distance falls. The relaxation time of this process can be related to the rate of conversion of the higher energy isomer into its lower energy conformation and the temperature dependence of the relaxation time gives the barrier to the interconversion.The energy difference between the two conformations can also be found. It has been observed on many occasions however that the ultrasonic technique gives incorrect values for this difference owing to the number of unjustifiable assumptions which must be made chief of which is that the volume difference between the two conformations is negligible. This has been well demonstrated by a comparison of ultrasonic n.m.r. and equilibration studies although the volume difference between the conformations of molecules such as 1,1,2-tribromoethane is only of the order of 2 % this is sufficient to introduce unaccept-able errors into the ultrasonic values of the energy differences.66 To establish energy differences reliably the pressure dependence of the ultrasonic absorption will also be required.Fortunately no such doubts attend the ultrasonic deter-mination of energy barriers. One of the classic groups of compounds to be studied by ultrasonics is the crj-unsaturated aldehydes. A recent reinvestigation of ultrasonic relaxation in 6 2 M. Fixman J. Chem. Phys. 1962,36 1961 ; K. Kawasaki Phys. Rev. (A) 1970,1 1750. 6 3 ( a ) C. W. Garland D. Eden and L. Mistura Phys. Rev. Letters 1970 25 1161; (b) G. D'Arrigo L. Mistura and P. Tartaglia Phys. Rev. ( A ) 1971 3 1718; ( c ) V. P. Gutschick and C. J. Pings J. Chem. Phys. 1971 55 3845. 64 C. G.Kartha and A. R. K. L. Padmini J. Phys. SOC. Japan 1970 28 470; C. G. Kartha A. R. K. L. Padmini and G. S. Sastry J . Phys. Soc. Japan 1971 31 617. 6 s K. A. Kemp and S. V. Letcher J. Acoust. SOC. Amer. 1971 50 125. 6 6 K. R. Crook E. Wyn-Jones and W. J. Orville-Thomas Trans. Faraday Soc. 1970, 66 1597 Molecular Acoustics 37 cinnamaldehyde gave an energy barrier of 24 kJ mol- ' for rotation about the C-C single bond adjacent to the carbonyl this figure is identical to the earlier value.67b This barrier has been compared with the I3C-H coupling constant of the C atom in the aldehyde group a reasonable correlation does exist between these parameters in a number of compounds confirming the role of conjugation in determining the energy barriers in these molecules.68 Confirmation of the barrier of 28 kJ mol- ' in triethylamine has also been reported.69" The conclusions from the ultrasonic investigations about the nature of the rotational isomerization in this molecule have been borne out by i.r.The absence of ultrasonic relaxation in cyclohexene and its 2-methyl derivative has also been ~onfirmed.~' In the 3- and 4-substituted compounds relaxation is observed however the backwards barriers to the interconversion of the rotational isomers ranging from 14 to 22 kJ mol- in 3-methyl- and 4-bromo-cyclohexene respectively. This relaxation is attributed to a perturbation of the equilibrium between the axial and equatorial half-chair i~orners.~' In some 2-halogenomethyl- 1,3-dioxans two relaxation processes are found the lower frequency process arises from ring inversion while internal rotation of the halogenomethyl group occurs at higher frequencie~.~' A number of further investigations of rotational isomerization abou# the C-0 bond in esters have been carried out.Because the relaxation frequencies of most esters lie in the range 100 kHz-10 MHz where experimental accuracy is poor a number of discrepancies are found between the results of various workers. In ethyl formate a careful investigation covering the frequency range from 100kHz to 130MHz confirms an activation energy for the backwards reaction of 34 kJ mol- 1.72a Rotational isomerization of ethyl formate has also been studied in thirteen solvents the relaxation frequency is independent of ester concentration in polar solvents but decreases as the concentration of ethyl formate increases in non-polar solvents.72b The relaxation frequencies of the alkyl acetates increase with increasing size of the alkyl group from methyl to ~ e n t y l ~ ~ " this favours the theory that the backwards barrier is determined primarily by steric repulsion of the ester alkyl The origin of the ultrasonic relaxation processes observed in dilute polymer solutions remains controversial.Despite the large experimental uncertainties in determining the small relaxational absorption previous workers have found h 7 ( a ) P. K. Khabibullaev S. S. Aliev and K. Parpiev Russ. .I. Phys. Chem. 1969 43, 1066; ( b ) M. S. de Groot and J. Lamb Proc. Roy. Soc. 1957 A242 36. '' R. A. Pethrick and E. Wyn-Jones Trans. Faraday Soc.1970 66 2483. 6 9 ( a ) S. S. Aliev K. Parpiev and P. K. Khabibullaev Sou. Phys. Acousf. 1970 15 444; (b) K. Kumar Chem. Phys. Letters 1971 9 504. 7 0 K. R. Crook and E. Wyn-Jones Trans. Faraday SOC. 1971 67 660. 7 1 G. Eccleston B. Walsh E. Wyn-Jones and H. Morris Trans. Faraday Soc. 1971, 67 3223. '' ( a ) Y. Tannaka Acustica 1970 23 328; (b) M. S. Martynov and V. F. Nozdrev, Russ. J . Phys. Chem. 1971 45 1013. 7 3 ( a ) K. M. Burundukov Russ. J . Phys. Chem. 1970 44 616; ( 6 ) J. Bailey S. Walker, and A. M . North J . Mol. Structure 1970 6 53 38 A . J. Matheson that a single relaxation process was sufficient to account for the results and attributed this to a crankshaft motion of the polymer chain.74 A further investi-gation with a more extended frequency range has now revealed two relaxation processes which are independent of polymer concentration and almost inde-pendent of temperat~re.'~ Although the ultrasonic technique should prove a powerful means of investigating the dynamics of local conformational changes in polymers much further work is required to permit an unambiguous interpre-tation of the results.6 Solution Kinetics The temperature and pressure variations which accompany the passage of an ultrasonic wave through a solution disturb any equilibria which are present, and from the chdnge in ultrasonic absorption with frequency the relaxation time and rate constants of a reaction may be deduced. The ultrasonic technique is applicable to reactions with half-lives covering about five decades of time (10-5-10- lo s).Acoustic techniques can determine relaxation times and activation energies with great precision. Unfortunately it is rarely a simple matter to relate an observed relaxation process unambiguously to a particular equilibrium. Although ultrasonic relaxation in carboxylic acids was first observed in 1936,76 the molecular origin of this is still being investigated. The available evidence now favours an equilibrium between an open and a closed dimer: \ k /p /p . - O C-R 7L R-C R-C kb \ O-H.O 4 0 -H . 0 \ 'C-R / H- 0 At 298 K ks = 3.5 x lo's-' and k b = 3.4 x lo6 s-' for acetic acid solutions in acetone.77" Similar values are obtained for solutions of acetic acid in CCl,77b and The rates of dissociationof the dimers formed from some substituted benzoic acids in NN-dimethylformamide have been correlated with the Hammett substituent constants which relate reactivity to electron den~ity.'~" A more rapid reaction has also been observed in glacial acetic and in aqueous propionic valeric and butyric The relaxation time of this process 7 4 H.Hassler and H. J. Bauer Kolloid-Z. 1969 230 194; H. Nomura S. Kato and 7 5 0. Funfschilling P. Lemarechal and R. Cerf Compr. rend. 1970 270 C 659. 7 6 P. Bazulin Cornpt. rend. Acad. Sci. U.R.S.S. 1936 3 285. 7 7 ( a ) R. D. Corsaro and G. Atkinson J. Chern. Phys. 1971,54,4090; (b) V. N. Zalivchii, V. I. Moklyak and V. N. Avramenko Russ. J . Phys. Chern. 1969,43 1049; ( c ) R. D. Corsaro and G. Atkinson J . Chem. Phys. 1971 55 1971. 7 8 ( a ) T. Yasunaga S .Nishikawa and N. Tatsumoto Bull. Chern. SOC. Japan 1971, 44 2308; (b) F. Bader and K. G. Plass Ber. Bunsengesellschaft Phys. Chem. 1971, 75 553; ( c ) L. V. Lanshina M. I. Lupina and P. K. Khabibullaev Sou. Phys. Acoust., 1971 16 343. Y. Miyahara J . Chern. Sac. Japan 1969 90 250 Molecular Acoustics 39 is ca. 2 x 10- lo s at 293 K and it is attributed to an equilibrium between mono-meric and dimeric forms of the acid. The association of N-methylacetamide in CCl by hydrogen bonding has been investigated. A single relaxation time is observed in the concentration range 0.024.1 mol l-' and the concentration dependence of this is in agreement with the assumption that only a monomer-dimer equilibrium exists. This simple picture is contradicted by i.r. studies however and it can be shown that the ultrasonic data are also consistent with an association model involving several polymeric species : A, 4 N * N,-l f N k b is 3.1 x lo7 s-l at room temperature.79a Similar association is observed in solutions of benzyl alcohol in c y c l o h e ~ a n e .~ ~ ~ Ion-pair formation is now the accepted mechanism for explaining ultrasonic relaxation in aqueous electrolyte solutions." Relaxation has been observed in a range of aqueous lanthanide nitrates at 298 K a single relaxation process is sufficient to describe the results within the range of frequency covered (5-290 MHz). This has been attributed to the equilibrium between a solvated ion-pair and a contact ion-pair : La3+(H,0)N03- La3+ N Q - + H,O The dependence of the relaxation time upon the cation can be rationalized in terms of the change of solvation along the lanthanide series." A number of studies of ultrasonic relaxation in solutions of the tetra-alkyl-ammonium salts have been reported.A study of seven such salts in acetone revealed a single relaxation process which was attributed to the diffusion-controlled formation of ion-pairs.82" A similar process is observed in solutions of some transition metal rn-benzene disulphonates in methanol.82b Two relaxa-tion processes have been observed in aqueous solutions of the tetra-alkyl-ammonium salts. The higher-frequency relaxation is again the result of a dif-fusion-controlled process. The lower-frequency process is particularly marked with salts containing large alkyl groups at high concentrations it can be attri-buted to an equilibrium between free water molecules and water molecules in the destructured region around the ~ a t i o n .' ~ The ultrasonic technique is finding increasing application in the study of biological materials. The wide variety of possible equilibria makes the interpre-tation of the results difficult but conversely a complete understanding of the l 9 ( a ) J. Rassing and 0. Osterberg Acta Chem. Scand. 1969 23 693; J . Rassing and F. Garland Acta Chem. Scand. 1970 24 2419; J. Rassing Acta Chem. Scand. 1971, 25 1418; (b) J. Rassing and B. N. Jensen Acta Chem. Scand. 1970 24 855. 8 o M. Eigen and K. Tamm Z. Elektrochern. 1962 66 93. G. S. Darbari F. Fittipaldi S. Petrucci and P. Hemmes Acustica 1971 25 125. *' ( a ) G.S. Darbari and S. Petrucci J . Phys. Chem. 1970 74 268; (b) A. Fanelli and S. Petrucci J . Phys. Chem. 1971 75 2649. M. J. Blandamer and D. Waddington J. Chem. Phys. 1970,52,6247; J. Marchessault, J . Broadhead and E. Yeager J. Acoust. Soc. Amer. 1970,47 98 40 A . J . Matheson relaxation processes observed would give a detailed picture of the behaviour of such materials.84 Proton transfer at side-chain groups has been proposed as a source of ultra-sonic absorption in aqueous proteins and polypeptides. Glycine is a useful model compound for investigating this proposal since it has two possible proton-transfer mechanisms at high pH reaction of OH - with NH + occurs whereas at low pH there is protonation of C02-. Each of these mechanisms gives rise to a single relaxation in the appropriate pH range of aqueous glycine.At physio-logical pH values near 7 however ultrasonic absorption from proton-transfer reactions is The ultrasonic relaxation observed in aqueous arginine and lysine solutions is less simple. These compounds have amino-side-chains with pK values greater than 11.0 the ultrasonic results do not satisfy a model based upon independent reaction of OH- with the two NH,’ groups however but require some inter-action between the two proton-transfer processes.86 The relaxational behaviour of bovine serum albumin fl-lactoglobulin and lysozyme is very similar to that of the amino-acids. Proton transfers to side-chain groups are the dominant cause of ultrasonic absorption at high and low pH. At intermediate pH values a number of processes could contribute to the ultrasonic absorption including solvation equilibria conformational changes, and keto-enol equilibria attempts to distinguish among these processes is greatly hindered by the proton transfers.87 The ultrasonic absorption of aqueous haemoglobin solutions at intermediate pH values is independent of the prepara-tive procedure and of the long-range molecular structure local processes are involved but the molecular mechanisms of these are uncertain.88 Ultrasonic measurements show that a relaxation process occurs in the time range 10-7-10-8 s in phosphatidylserine and to a lesser extent in phosphatidyl-choline dispersions.The absorption is modified by changes in the phospholipid concentration pH and the cholesterol and bivalent-metal-ion content.Confor-mational changes and solvation are probably involved.89 In biological tissues the protein content is largely responsible for the observed absorption although contributions from the structural features of the tissue are also apparent.” 7 Viscoelastic and Structural Relaxation in Liquids When a high-frequency shear (transverse) wave propagates in a liquid the response of the liquid depends on whether the time for the elementary diffusive motions 8 4 G . G . Hammes Accounts Chem. Res. 1968 1 321. 8 5 M. Hussey and P. D. Edmonds J . Acoust. Soc. Amer. 1971 49 1309. 8 6 M. Hussey and P. D. Edmonds J . Acoust. Soc. Amer. 1971 49 1907. 8 7 S. K. Sadykhova and I. E. Elpiner Sou. Phys. Acoust. 1970 16 101 ; R. Zana and J. Lang J .Phys. Chem. 1970,74 2734; 0. M. Zorina K. P. Fursov and I. E. Elpiner, Sou. Phys. Acoust. 1971 17 129. ’* P. D. Edmonds T. J. Bauld J. F. Dyro and M. Hussey Biochim. Biophys. Acta, 1970 200 174; W. D. O’Brien and F. Dunn J . Acousf. SOC. Amer. 1971 50 1213. *’ G. G. Hammes and P. B. Roberts Biochim. Biophys. Acta 1970 203 220. ’ O W. D. O’Brien and F. Dunn J . Acoust. SOC. Amer. 1971 50 99; H. Pauly and H. P. Schwan J . Acoust. Soc. Amer. 1971 50 692 Molecular Acoustics 41 of the liquid molecules is shorter or longer than the period of the shear wave. In the former case the liquid responds as a Newtonian viscous liquid and in the latter as a Hookean elastic solid having a rigidity modulus G,. Current interest centres on the molecular factors which determine G of liquids and also on their viscoelastic-relaxation regions in which the transition from viscous to elastic response occurs.An ultrasonic longitudinal wave contains both shear and compressional components. The interpretation of the results of longitudinal-wave experiments alone is difficult but if the viscoelastic behaviour of liquids is understood from shear-wave experiments then the compressional or structural behaviour can be elucidated. A new edition of the ‘viscoelastician’s bible’ has a ~ p e a r e d ~ while viscoelastic and structural relaxation in non-polymeric liquids has been reviewed.” The modulus G and its temperature dependence is known for many liquids. Unfortunately these liquids tend to have complex molecular structures and only a modest range of temperature can be studied with present experimental tech-niques.Although many empirical relations have been proposed the most satis-factory description of the available results is given by a linear increase of 1/G, with temperat~re.~ Calculations of G are restricted to the simplest liquids such as Ar for which no experimental data are available for example a combination of the Bernal-Scott model with the Lennard-Jones potential gave G of Ar to be 1.2 x lo9 N m-’ in the vicinity of the triple point.92 Information on the bulk modulus K of liquids is even more sparse the ratio Km G is between three and four in most molecular liquids and within the considerable experimental uncertainty the temperature dependences of K and G are the same.91 Further experimental and theoretical work on the elastic moduli of liquids is clearly desirable.The viscoelastic-relaxation region of a liquid is usually determined experimen-tally by applying the time-temperature superposition principle measurements with shear waves at a small number offrequencies ovei a wide range oftemperature are used to simulate a wide range of frequency at constant temperature. It should be emphasized that the experimental evidence in support of this procedure covers only modest ranges of frequency and temperature and that a similar procedure cannot be applied in the related area of dielectric r e l a ~ a t i o n . ~ ~ The most successful description of the viscoelastic relaxation of supercooled liquids is the empirical BEL model which represents the shear mechanical impedance of a viscous liquid as a parallel sum of the impedances of a Newtonian liquid and a Hookean solid;94” an adaptation of this model describes the unexpected behaviour of liquid mixtures.94b This model implies that there is no dependence of viscoelastic behaviour on molecular factors except in so far as these determine the shear viscosity and G of the liquid.Although this model 9 1 9 2 A. R. Dexter and A. J. Matheson J . Chem. Phys. 1971 54 203. ’’ J. G. Berberian and R. H. Cole J . Amer. Chem. Soc. 1968 90 3100. 94 ( a ) A. J. Barlow A. Erginsav and J. Lamb Proc. Roy. Soc. 1967 A298,481 ; (6) A. J. A. R . Dexter and A. J. Matheson Adc. Mol. Relax. Processes 1972 in the press. Barlow A. Erginsav and J. Lamb Proc. Ro-v. Soc. 1969 A309 473 42 A .J. Matheson fails at long times and low frequencies it provides a useful first approximation to the viscoelastic behaviour of liquids. A number of liquids do not agree with the predictions of the BEL model and various empirical distributions of viscoelastic relaxation times have been intro-duced to represent the observed viscoelastic behaviour these distributions have mostly been borrowed from dielectric relaxation.” A common errm in this procedure is to equate viscoelastic relaxation with dielectric relaxation in fact the latter should strictly be called dielectric retardation and the dielectric distribution functions should be used to represent the distribution of viscoelastic retardation times which describe the behaviour of the compliance (reciprocal of the rigidity modulus).g5 The Davidson-Cole distribution has been successfully applied in this way to the viscoelastic retardation of a nitrate melt and the be-haviour of many other liquids may be adequately represented by this function.96 A disadvantage of this distribution is that it contains at least two unknown constants which have not yet been related to molecular parameters although one of these constants can be determined from creep-recovery experiments.” An interesting comparison of viscoelastic and conductivity relaxation in concentrated aqueous LiCl solutions has been reported.At low viscosities (< lo3 N s m-2) the average shear and conductivity relaxation times are within 30% of each other but at higher viscosities the ratio of the shear to the con-ductivity relaxation times becomes equal to two or three at high viscosities ionic conductivity does not require simultaneous structural rearrangements when one ion is much more mobile than the ~ t h e r .’ ~ A wide variety of results has been obtained for the longitudinal and structural relaxation of liquids. Measurements have been reported of the ultrasonic velocity and absorption in a number of alcohols ranging from the butanols to heptanol at viscosities below 1 N s m-2 and with frequencies up to 2 x lo’ Hz. In every case the data are described by a single relaxation time to within & 5 %. This suggests that both the structural and viscoelastic processes have the same re\axation time ; mbreover the activation entropy and enthalpy of the acoustic relaxation are the same as those for viscous flow in the range of temperature investigated.” A single relaxation process is also observed in hydrated calcium nitrate melts.100 Most investigations of structural relaxation are made with lower ultrasonic frequencies and the effective frequency range is extended by a time-temperature superposition principle despite the fact that Brillouin scattering measurements of glycerol show a narrowing of the distribution of relaxation times with increasing 9 5 F.R. Schwarzl and L. C. E. Struik Ado. Mol. Relax. Processes 1968 1 201. 96 G. M. Glover and A. J. Matheson Trans. Furaday Soc. 1971 67 1960. 9 7 D. J. Plazek and J. H. Magill J . Chem. Phys. 1966 45 3038. 9 8 C. T. Moynihan N. Balitactac L. Boone and T. A. Litovitz J . Chem. Phys.1971, 55 3013. 99 P. K. Khabibullaev and T. Mamanov Russ. J . Phys. Chem. 1970 44 1499; T. Mamanov K. Parpiev and P. K. Khabibullaev Sou. Phys. Acoust. 1970 15 537; S. S. Aliev K. Parpiev and P. K. Khabibullaev Sou. Phys. Acoust. 1971 16 387; U. Gadaibaev T. Mamanov and P. K. Khabibullaev Sou. Phys. Acousr. 1971,16,522. l o o G . S. Darbari M. R. Richelson and S. Petrucci J . Chem. Phys. 1971 55 4351 Molecular Acoustics 43 temperature."' The distribution of structural-relaxation times which results isgenerally not the sameas that for viscoelastic rela~ation.~ ' In bis[m-(m-phenoxy-phenoxy)phenyl] ether however both shear and structural relaxation can be described by the BEL model."' In several liquids at temperatures below the main structural relaxation region an additional relaxation process is observed.This has been attributed to an unspecified hysteresis-loss mechanism or to non-Hookean behaviour in glassy liquids. The most probable explanation however, is that it is the result of local conformational changes,'03" and this is borne out by dielectric studies. lo3' Thus the large number of relaxation processes observed in the study of ultrasonic propagation in viscous liquids makes a detailed inter-pretation of the results difficult. Many attempts have been made to devise a theoretical treatment of viscoelastic and structural relaxation in liquids. Early attempts related the distribution of relaxation times to the distribution of molecular environments such models give a useful qualitative description of the experimental results but do not provide a quantitative explanation of the relaxation proces~es.~' The most successful of these models has been applied to the viscoelastic relaxation of some molten oxides and the longitudinal relaxation of a nitrate melt there environ-mental dissimilarities arise from local concentration fluctuations.' O4 Changes in the molecular environment are often assumed to occur as a result of both spontaneous molecular motion in response to an applied stress and of small diffusional motions. Various combinations of these two motions have been used to describe molecular relaxation processes in viscous liq~ids,'~' but a complete prediction of the time-dependent properties of liquids is not yet possible. 8 Instrumentation A major limitation of acoustic techniques is the comparatively narrow range of frequency available.This may be contrasted with dielectric techniques where frequencies from d.c. to co are available using no more than three black boxes.'06 In the gas phase an adequate range of ultrasonic frequencies is available and this is supplemented by the variation in the effective time-scale provided by changing the pressure. The ultrasonic interferometer remains the most important experimental technique above 100 kHz atm- I . In the continuous wave inter-ferometer high accuracy in the ultrasonic velocity and absorption is difficult to achieve particularly at low frequencies because of the occurrence of various radial waves in the interferometer chamber ; methods for minimizing the l o ' l o ' A.J. Barlow J. Lamb and N. S. Taskopriilii J . Acoust. SOC. Amer. 1969 46 569. D. A. Pinnow S. J. Candau J. T. LaMacchia and T. A. Litovitz J. Acoust. SOC. Amer., 1968 43 131. (a) A. R. Dexter and A. J. Matheson J. Chem. Phys. 1971 54 3463; ( b ) G. P. Johari and M. Goldstein J. Chem. Phys. 1971 55 4245. l o 4 R. Weiler R. Bose and P. B. Macedo J. Chem. Phys. 1970,53 1258; J. H. Simmons and P. B. Macedo J. Chem. Phys. 1970,53,2914; J. H. Simmons and P. B. Macedo, J. Chem. Phys. 1971 54 1325. l o 5 J. E. Anderson and R. Ullmann J. Chem. Phys. 1967 47 2178; C. J. Montrose and T. A. Litovitz J. Acoust. SOC. Amer. 1970 47 1250. M. Davies Ann. Reports ( A ) 1970 67 65 44 A . J . Matheson importance of these have now been outlined. '07 An improved tube-technique for use at lower frequencies has also been reported.'08 Brillouin scattering has been used to determine the ultrasonic velocity in gases in the GHz region but the experimental difficulties are considerable.'0g Two transducers with a continuously variable range of frequency have become available.An electrostatic transducer operates from 200 kHz to 15 MHz,' lo' while a capacitance microphone can generate longitudinal waves in solids or aelay lines between 1 and 1 0 0 M H ~ . " ~ ~ A novel electrode configuration has been devised for eliminating diffraction lobes from conventional piezoelectric transducers."' The use of Bragg diffraction of light from an ultrasonic beam passing through a liquid is claimed to yield values of the ultrasonic velocity of accuracy comparable to the conventional pulse technique,' ' 2' while in the range 0.5-2 GHz light diffraction is probably superior to all other techniques for studying ultrasonic propagation.' ' 2b Simple logic circuitry has been devised for coherent detection of ultrasonic pulses which gives up to 25 dB improvement in the minimum useful ultrasonic signal.' l 3 An absolute accuracy of k0.15 m s- ' is claimed for a system in the MHz range which involves standing longitudinal waves between a transmitting and a receiving transducer.' l4 Improved methods of bonding transducers to delay lines have been suggested including indium metal,' 15' supercooled liquids,' ' 5 b or silicone oil containing finely dispersed Methods of studying ultrasonic propagation at temperatures in excess of 3000 K have been devised.' ' Brillouin scattering is now an accepted technique for studying the propaga-tion of ultrasonic longitudinal waves in liquids and useful reviews of this and of stimulated Brillouin scattering have appeared.'I7 More recently the fine structure of the Rayleigh wing has been associated with hypersonic shear waves in liquids this should provide an invaluable extension of the frequency range available for viscoelastic studies.' l 8 l o ' A. R. Colclough Acustica 1970 23 93; I . Vasilyus V. Ilgunas and 0. Kubilyunene, Sou. Phys. Acoust. 1971 17 189. F. D. Shields and B. Anderson J . Chem. Phys. 1971 55 2636. l o g A. M. Longequeue and P. Lallemand Compt. rend 1969 269 B 1173. ' l o ( a ) P. Alais and M. T. Larmande Compt. rend. 1971 272 B 185; (b) E.L. Meeks, R. D. Peters and R. T. Arnold Rev. Sci. Instr. 1971 42 1446. F. D. Martin and M. A. Breazale J . Acoust. Soc. Amer. 1971 49 1668. 1 1 2 ( a ) E. W. Taylor and S. S. Alpert J . Acoust. Soc. Amer. 1970,48 1287; ( 6 ) F. Rheault and E. L. Adler J . Acoust. SOC. Amer. 1971 49 1448. R . A. Leskovec J. L. Hunter and J . M. Davenport Rec. Sci. Instr. 1970 41 1426. ( a ) P. A. M. Stewart J . Phys. ( E ) 1970 3 740; (b) A. J. Matheson J . Phys. ( E ) 1971, 4 796; (c) V. E. Sorokin and I. I. Perepechko Cryogenics 1971 11 406. 11' K. M. Burundukov and A. M. Lobanov Sou. Phys. Acoust. 1970 16 259. l 6 0. D. Slagle and R. P. Nelson Rev. Sci. Instr. 1970 41 1676. ' l 7 V. S. Starunov and I . L. Fabelinskii Scv. Phys. Uspekhi 1970,12,463 ; I . L.Fabelinskii, Izvest. Akad. Nauk S.S.S.R. 1971 35 874; R . Figgins Contemp. Phys. 1971 12 283. 'I8 A. A. Berdyev and I. B. Lezhnev,.Sou. Phys. JETP Letters 1971 13 32; A. B. Bhatia and E. Tong J . Acoust. SOC. Amer. 1971 49 1437; C. H. Chung and S . Yip Phys. Rev. ( A ) 1971 4 928; V. S. Starunov Zhur. eksp. tear. Fiz. 1971 61 1583 Molecular Acoustics 45 9 Conclusions The main use of the acoustic technique in chemistry is in obtaining kinetic infor-mation for reactions having half-lives between and lO-'Os. The experi-mental techniques for studying ultrasonic propagation are well established and reliable and of much less complexity than many other techniques currently employed by chemists. Although rate constants and activation energies may be measured with great precision a drawback of this method of studying fast reac-tions is the difficulty of attributing the observed relaxation process to a particular reaction when several possibilities exist. Acoustic techniques are also of great use in structural studies of liquids and are complementary to the many other available techniques such as dielectric or nuclear magnetic relaxation and neutron or light scattering