J. Phys. Chem. 1984,88, 5653-5656
Figure 6. Most of the parameter values were taken from work already ~ i t e d . ~The . ' ~ pressure dependence of the density of water was obtained from empirical data;28that for pyridine was estimated from the Birch-Murnaghan equation of state38using parameters (KO= 10.33 kbar, KO' = 9.39) obtained by fitting the Tait to compressibility data for benzene.40 Table I11 gives for three pressures the corresponding values for the bond length compression Ar/re and the repulsive frequency shift AvR obtained from the hard-sphere model. These shifts pertain to the normal isotope; however, the ratio AvR/vois isotopically invariant. The magnitudes and pressure dependence of the shifts are quite similar for pyridine and water as the solvent, despite the large difference in size of the solvent molecules. The nearly twofold increase in u/uS for water is offset by the concomitant decrease in psu2 and by the twofold larger compressibility of pyridine (assumed to be the same as benzene40). We thus find that the hard-sphere result for dv/dP of the vl mode of pyridine is 0.8 and 0.6 cm-'/kbar, respectively, for pyridine and water as the solvent. With otu approximations, dv/dP for liquid pyridine should be the same as for benzene. Our value of 0.8 cm-I/kbar indeed agrees well with a recent measurement for u1 of benzene,41which finds 0.75 cm-'/kbar, and also with a theoretical estimate of 0.7 f 0.5 cm-'/kbar, obtained from a quite different procedure.42 Registry No. TTF, 31366-25-3;TCNQ, 1518-16-7;4-PVPYR (homopolymer), 9003-47-8; gold, 7440-57-5; pyridine, 110-86-1.
with
AQ = -FQ/fQ
(A 10)
Here the subscript on the force constants indicates derivatives with respect to the normal mode; these derivatives usually will differ for each mode. The three force constant ratios which determine Av/u0 can readily be expressed in terms of derivatives with respect to the bond lengths or angles, since in any specified mode the displacements of the bond lengths and/or angles are in fixed ratios. For the totally symmetric ring stretching mode
AQ, = ( m / 6 ) ' l 2 C A r i= (6m)'IzAr
(A1 1)
I
since all the Ar, are equal. The formula for Av/vo thus reduces to the same result obtained for the diatomic oscillator. In particular, for comparable bonds in polyatomic molecules, Badger's rule gives the same value for the dimensionless ratio r g / f in eq A5. For the trigonal ring distortion mode
AQ12= (Z/6)'/2cAcu, i
0
5653
(A 12)
Although no relation like Badger's rule is available to evaluate the ratios of angular derivatives in eq 9, this factor is suppressed because AQ12is practically zero. The model simply predicts that, since AQ12 0, the v 1 2mode will show no appreciable solventor pressure-induced frequency shift. Numerical Results. The six dimensionless quantities ( r g / J reG/F, z, 19, u/us, psus3)which enter into calculation of the fractional frequency shift, Av/vo,depend upon four properties of the solute molecule (re,u,J g ) , two properties of the solvent (us, ps), and three mutual properties (F, G, 7'). These quantities are listed in Table 11, except for F, which in effect is provided by
-
(38) Birch, F. Phys. Rev. 1947, 72, 809. (39) Broecker, A.; Oversby, B. "Chemical Equilibria in the Earth"; McGraw-Hill: New York, 1974: PD 26-28. (40) Gibson, R. E.; Kincaid, j.*F. J . Am. Chem. SOC.1938, 60, 511. (41) Schmidt, S. C.; Moore, D. S.; Schiferl, D.; Shaner, J. W. Phys. Rev. Lett. 1983, 50, 661. (42) Pucci, R.; March, N. H. J. Chem. Phys. 1984, 80, 3919.
Hypersonic Sound Attenuation in Benzonitrile M. A. Goodman+ and S. L. Whittenburg* Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 (Received: December 19, 1983; Zn Final Form: June 21, 1984)
The attenuation of thermally induced sound waves in benzonitrile has been measured with Brillouin light scattering. The attenuation in solutions of benzonitrile with carbon tetrachloride has also been measured as a function of temperature. Neat benzonitrile and the solutions display a maximum in the Brillouin line width. The spectra are analyzed in terms of an extended hydrodynamic theory which includes the effect of orientational anisotropy on the polarized Rayleigh-Brillouin spectrum. The dispersion in benzonitrile appears to be due to translational-vibrational energy transfer.
Introduction Rayleigh-Brillouin scattering is a useful method for probing structural relaxation phenomena and motion in viscoelastic liquids composed of small molecules. The width of the depolarized peak of a Rayleigh-Brillouin spectrum is related to the reorientation rate of the molecule. The polarized spectrum consists of a Rayleigh peak and a pair of symmetrically displaced peaks, referred to as the Brillouin doublet. The Rayleigh peak is dominated by the instrumental line width of the laser. The Brillouin frequency shift and line width contain physical information about the structure and dynamics of the fluid.' Patterson et al. studied the attenuation in acetic acid2 using Brillouin light scattering. Acetic acid displayed a maximum in the Brillouin line width around room temperature. The data were analyzed with the macroscopic theory due to Rytov3 and the Present address: Weizmann Institute of Science, Chemical Physics Dept., Rehovot 76100, Israel.
0022-3654/84/2088-5653$01.50/0
mechanism giving rise to the attenuation was shown to be related to the breaking of the hydrogen-bonded network in the acid. Attenuation was observed in several of the simple carboxylic acids by Keegan and W h i t t e n b ~ r g . ~Again, a maximum was observed in each of the acids and the mechanism responsible for the attenuation was related to the breaking of the hydrogen-bonded network. A maximum in the Brillouin line width has also been observed in several of the substituted ben~enes.~ In the substituted (1) Berne, B. J.; Pecora, R. "Dynamic Light Scattering"; Wiley: New York, 1976. (2) Patterson G. D.; Alms, G. R.; Lindsey, C. P. J . Chem. Phys. 1978,69, 4802-6. ( 3 ) Patterson, G. D.; Latham, J. P. J . Polym. Sci., Macromol. Rev. 1980, 15, 1-27. (4) Keegan, P. F.; Whittenburg, S.L. J . Phys. Chem. 1982, 86, 4622-6. (5) Dorfmuller, Th.; Fytas, G.; Mersch, W.; Samios, D. J . Chem. SOC., Faraday Discuss. 1977,11, 106-14. Inoue, N.; Ishigufo, M. Phys. Lett. 1979, 71A, 496-8.
0 1984 American Chemical Society
5654
benzenes the attenuation appears to be due to relaxation of the specific heat, that is, relaxation of the translational energy into the vibrational modes of the molecule. This form of relaxation has been termed T-V relaxation. T-V relaxation in the hypersonic frequency region has also been studied by Brillouin light scattering in carbon tetrachloride.6 Studies have been carried out on anisaldehyde and aniline which also display attenuation in the hypersonic frequency r e g i ~ n . The ~ relaxation mechanism in both of these substituted benzenes also appears to be due to T-V rela~ation.~ We have observed an attenuation in benzonitrile and in solutions of benzonitrile in carbon tetrachloride. To understand the microscopic mechanism for this relaxation we have analyzed the data in terms of the general viscoelastic theory of Lipeles and Kivelson .* Theory It is possible to calculate the polarized Rayleigh-Brillouin spectrum by using the linearized hydrodynamic equations. For orientationally isotropic molecules the set of variables including the number density, the linear momentum, and the local energy is sufficient to describe the experimental spectrum. If we neglect the contribution of the thermal conductivity, the classical Brillouin line width is given by where rl is the line width, q is the scattering wave vector, qs and qv are the shear and bulk viscosity, respectively, and p is the density. The amplitude of the scattered wave vector is given by q = (4?m/X) sin 0/2 (2) where n is the refractive index and 0 is the scattering angle. The classical line width ignores the fact that the viscosity is frequency dependent and therefore fails to describe the line width. In real fluids there is a time delay in the response of the fluid to the applied stress, which means, in frequency space, that the modulii and transport coefficients are functions of the frequency of the applied stress. For anisotropic molecules one must also include orientational variables in an extended hydrodynamic theory. In the extended hydrodynamic equations the shear modes are coupled to the orientational modes. The hydrodynamic equations of Lipeles and Kivelson couple the Fourier transformed densities of orientation Oxx-uv with the reduced momentum divergence (d = vp) and the number density n. n and d are conserved variables, while 0 is slowly varying. The theory of Lipeles and Kivelson describes the frequency dependence of the shear viscosity due to translation-rotation coupling. The theory is an extended hydrodynamic theory due to the addition of the slowly varying orientation variable. It cannot be considered as a generalized hydrodynamic theory since it does not include the coupling to the local energy density. A generalized hydrodynamic theory has been given by Lin and Wange9 The coupled equations of motion for the set of variables of Lipeles and Kivelson is given in matrix form as
a
/~5x-yy\
iq [ Rri ~
II P
- ( ~ P W ' l p p l q2[riv + 4/3ris(l -R)llp
iqh
0
where r is the orientational line width, R is the translationalrotational coupling constant, m is the mass of the molecule, and C,is the sound velocity in the low q limit. Also, p = ( N / V ) ( l Nf)/lSpk,T, where f is a measure of the orientational pair correlation. The density fluctuation can be expressed as where do is the sound wave frequency at x = 0, and x is the direction of propa-
+
~~
Goodman and Whittenburg
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
~
(6) Fleury, P. A.; Chiao, R. Y. J. Acousl. SOC.Amer. 1966, 39, 751-6. Litovitz, T.A.; Davis, C. M., Jr. J. Chem. Phys. 1966, 44, 840-5. Stegeman, G. I. A.; Gornall, W. S.;Volterra, V.; Stoicheff, B. P.J . Acoust. SOC.Amer. 1971, 49, 979-93. (7) O'Sheen, B. L.; Wang, C. H.; Fytas, G. J. Chem. Phys., in press. (8) Rytov, S. M. SOU.Phys. JETP 1970, 31, 1163-71. (9) Lin, Y.-H.; Wang, C. H. J . Chem. Phys. 1979, 70,681-8.
gation. Expanding eq 4 in a Taylor series and substituting into eq 3 gives q=
w2/vs- ia
(5)
where V, = C,[1
+ w2RI'q/2Csp(w2+
r12)]
(6)
and the sound absorption coefficient is a = rl2/2C3p[qV
+ 4/3vs(1- R ) + r2qsR(wZ+ TI2)]
(7)
The resulting expression for the Brillouin line width is
rl = (q2/2p)[sv + 4/33as(l - R ) + r211sR/(r2+ w2)1 (8) The magnitude of the Brillouin line width is proportional to the viscosity. The total viscosity is composed of both bulk and shear terms. The first term in eq 8 is the line width contribution due to the bulk viscosity. The bulk viscosity is dependent on structural and translation-vibration relaxation. The shear viscosity contains a contribution due to the unrelaxed structure of the fluid, 4/3qs(1 - R ) , and the coupling of translation to orientation, the last term in eq 8. Because Lipeles and Kivelson did not include the local energy conservation they did not obtain an exact expression for the bulk viscosity. However, by including the orientational variables Lipeles and Kivelson did obtain an exact expression for the fraction of the total shear viscosity that is due to structural contributions, qs(l - R ) , and the fraction that is due to orientation, qsR. Experimental Section Benzonitrile and carbon tetrachloride were both distilled and solutions of 100,90, 80, and 60% (V/V) benzonitrile in carbon tetrachloride were prepared. In order to remove dust the solutions were filtered through a 4-5-pm fritted glass filter into a fluorescence cell. Rayleigh-Brillouin spectra were obtained as described previ0us1y.~The exciting source was a single frequency argon ion laser operated at 514.5 nm, and the scattered light was observed at 90". The fluorescence cell was thermostated and the temperature controlled to within *O.l "C. Spectra were taken in the temperature range from 25 to 100 "C. The scattered light was collimated through a Fabry-Perot interferometer by a long focal length lens. Output of the interferometer was focused through a pinhole and onto a photomultiplier tube. Any Raman scattering was eliminated by a narrow-band-pass filter centered at the laser frequency. The digital output of the photomultiplier tube was connected to a Burleigh DAS-10 stabilizer and ramp generator, and then to a Digital Equipment Corporation LS1-11/03 minicomputer. The data files were transferred from the minicomputer to a DEC- 10 computer for analysis. One thousand data points were collected over two orders of Brillouin spectra. The free spectral range was optimized to avoid overlap of adjacent orders and was 17.98 GHz for the neat and 80% solutions and was 18.86 GHz for the 90% and 60% solutions. The finesse, which is a measure of the line width of the instrumental peak, was typically 50-60. All spectra were deconvolved by using the experimentally measured instrumental function. The deconvolving procedure was a modification of the van Cittert method.l09" This method has the advantage that the deconvolving can be done with the actual experimental instrumental spectrum and does not assume any functional form for the line shape. The deconvolved spectra were fit with a nonlinear least-squares fit to a series of Lorentzian peaks and a base line. For liquid benzonitrile the VV scattering contains a large contribution from the anisotropic component. The scattered light was collimated through a Glan-Thompson polarizer to reject the VH component. The functional form used by the fitting routine contained four Lor(10) Burger, C. H.; Van Cittert, P. H. Z. Phys. 1932, 79, 722-6;1933, 81, 428-3 1. (1 1) Jones, R.N.;Venkataraghavan, R.; Hopkins, J. W. Spectrochim. Acta 1967, 23, 925-39.
Sound Attenuation in Benzonitrile
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5655
TABLE I: Brillouin Line Width and Frequency Shift (GHz) for Benzonitrile 100% 90% 80% 60%
T , O C ~ , 25.6 27.2 30.6 33.8 36.8 40.0 43.7 46.4 49.6 53.8 59.0 63.0 66.0 69.1 72.0 75.4 80.0 83.0 86.2 89.8 92.8
r,
6.56
0.15
6.46 6.45
0.14 0.18
6.24 6.18 6.14 6.09 6.01 5.87 5.86 5.79 5.75 5.69 5.59 5.52 5.45 5.42 5.34 5.26
0.18 0.18 0.21 0.22 0.29 0.30 0.35 0.40 0.37 0.40 0.32 0.36 0.34 0.35 0.33 0.34
TABLE II: Contributions to the Longitudinal Brillouin Line Width for Neat Benzonitrile
w,
rl
w,
r,
a,
r,
6.06 6.03
0.24 0.27
5.79
0.35
5.72
0.39
5.49 5.42 5.33
0.42 0.38 0.37
5.98 5.90
0.29 0.31
5.65
0.40
5.78 5.72 5.67 5.56 5.52 5.46 5.44 5.40 5.33 5.30 5.22 5.18 5.12 5.05
0.31 0.31 0.31 0.31 0.30 0.34 0.35 0.37 0.38 0.38 0.35 0.37 0.35 0.34
5.51 5.49 5.35 5.32
0.37 0.36 0.30 0.32
5.26 5.27 5.21 5.15 5.13 5.02
0.34 0.32 0.32 0.28 0.29 0.32
5.16 5.10
0.31 0.28
4.90
0.27
4.94
0.24
T, OC
r,
25.6 30.6 33.8 40.0 43.7 46.4 49.6 53.8 59.0 63.0 66.0 69.1 72.0 75.4 80.0 83.0 86.2 89.8 92.8
0.16 0.14 0.18 0.18 0.19 0.19 0.21 0.29 0.30 0.35 0.40 0.37 0.40 0.32 0.36 0.34 0.35 0.33 0.38
Fa 0.022 0.022 0.022 0.021 0.021 0.021 0.020 0.020 0.018 0.018 0.018 0.017 0.016 0.016 0.015 0.014 0.014 0.013 0.012
re-, 0.057 0.052 0.050 0.044 0.043 0.041 0.038 0.036 0.033 0.031 0.030 0.028 0.027 0.026 0.024 0.023 0.022 0.021 0.020
rT-" 0.05 0.06 0.08 0.10 0.12 0.14 0.16 0.19 0.22 0.25 0.26 0.27 0.28 0.28 0.37 0.26 0.25 0.23 0.21
(9)
orientational relaxation time has been measured. This has been measured for neat benzonitrile by using depolarized Rayleigh light scattering. Typically, however, the reorientational relaxation time measured by depolarized Rayleigh light scattering is a collective reorientation time. That is, it also depends on the static and dynamic pair correlation factors. In the theory of Lipeles and Kivelson the orientational relaxation entering the VV spectrum is the same as in the VH spectrum. Thus, the measured value for the reorientation time, 7,at 293 K is 21.6 ps.13 With this value it can be seen that the term a17 is not unity, but is large enough to affect the shear viscosity. The contribution of the orientational contribution to the shear viscosity also depends on the size of the translation-rotation coupling. The translationrotation coupling constant is also measured by depolarized Rayleigh light scattering. For benzonitrile it is roughly 0.4, that is, 40% of shear viscosity (at zero frequency) is due to reorientation.12 Combining these results with eq 7 and eq 9 we can evaluate the contribution of the reorientational part of the shear viscosity to the Brillouin line width. The reorientational contribution to the line width is given in Table 11. As can be seen from the tabulated values, the reorientational contribution is small. This is generally observed. As was pointed out for anisaldehyde and aniline,' and is true for benzonitrile, even for very optically anisotropic molecules where there is a large coupling between orientation and the hypersonic longitudinal wave, orientational relaxation of the shear viscosity is not important. This implies that orientational relaxation of the shear viscosity is not important in the hypersonic frequency region. We must still subtract out the contribution due to structural relaxation. Since the structural relaxation time above the melting point of the liquid remains short relative to the inverse of the hypersonic frequency, the structural contribution increases as the liquid is cooled toward its melting point. We can therefore assume that the structural contribution to the shear line width is just its unrelaxed value, os(l - R ) . With this assumption the shear contribution to the line width is identical with that given in eq 8. Again, taking R to be temperature independent and equal to 0.4 and using the measured shear viscosities at each temperature we have calculated the structural contribution to the shear line width given in Table 11. From Table I1 we can see that neither the orientational nor the structural contribution to the shear line width display a maximum. Thus, the maximum in the line width must be due to the contribution of the bulk viscosity. The bulk viscosity can also be written as a sum of two contributions: a dilational structural relaxation and a specific heat
where 7 is the reorientational relaxation time which is related to the depolarized Rayleigh line width, r,via 7 = (2rI')-'. The structural contribution gives rise to a line width that increases as the liquid is cooled toward its melting point. The magnitude of the reorientational contribution can be evaluated if the re-
(12) Whittenburg, S. L.; Wang, C. H. J . Chem. Phys. 1977, 66, 4995-5000. (13) Alms, G. R.; Patterson, G . D. J . Chem. Phys. 1978, 68, 3440-4. Whittenburg, S. L.; Wang, C. H. J . Chem. Phys. 1979, 71, 561-2. Alms, G. R.; Patterson, G. D. J . Chem. Phys. 1979, 71, 563-4.
a Concentration given as volume percent benzonitrile in carbon tetrachloride.
entzians for each spectral order, two shifted Lorentzians for the Brillouin doublet, and two unshifted Lorentzians for the Rayleigh peak and the anisotropic component.
Results and Discussion The experimentally measured values for the frequency shift and line width of the benzonitrile solutions obtained from the fits to a series of Lorentzians are listed in Table I. From the tabulated data it can be seen that the maximum in the line width occurs at approximately 70 "C for the neat benzonitrile. The maxima occur at about 75 and 35 "C for the 90 and 80% solutions, respectively, and well below 20 "C for the 60% solution. In general, the line width maximum shifts to lower temperatures as the benzonitrile is diluted with carbon tetrachloride. This is usually observed. The apparent shift of the maximum toward higher temperature for the 90% solution is within the error of the measurement. An approximate value for the characteristic time of the relaxation can be obtained by noting the value for the frequency shift at the maximum in the attenuation. The characteristic time is roughly equal to (2rw)-'. This only gives an estimate, however, since it assumes that the maximum in the line width occurs where w 7 = 1. This was shown to be only approximately true in previous work. The characteristic time is roughly 30 ps for benzonitrile. In a typical ultrasonic measurement the frequency is scanned to find a frequency at which the absorption is a maximum. From the frequency of the maximum absorption the relaxation time can be calculated. The Brillouin experiment is very similar. The frequency of our measurement, wlr is a rather linearly decreasing function of temperature. Thus, by changing the temperature we are in essence scanning frequency in addition to changing the relaxation time. The process giving rise to the attenuation can be determined by discussing the various contributions to the shear and bulk viscosities. For simple, anisotropic liquids the shear viscosity contains only two contributions, a structural term and one due to reorientation. This can be seen from both the Rytov theory, as well as from the extended hydrodynamic theory. Thus, the frequency-dependent shear viscosity can be written as 9s(w)
= a ( 1 - R) + R % / ( l
+ WZ72)
Goodman and Whittenburg
5656 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
relaxation. Little is known about the structural contribution to the bulk viscosity. Without assuming any mechanism for the relaxation of the bulk viscosity we can write the relaxing part of the line width as
rv= ( R f -
+
1)w2~,/(1 &,2)
(10)
where R’is the relaxation strength of the mechanism responsible for the relaxation of the bulk modulus. In general, the relaxation strength is given by R’ = u,z/u2, where u, and uo are the limiting sound velocities at high and low frequencies, respectively. In eq 10 w is the frequency of the measurement and rv is the relaxation time. We have fit the residual line width to eq 10. The fit value of the relaxation strength is R‘= 1.10. This value is very close to the relaxation strength reported for other substituted benzenes in which the relaxation is thought to proceed through relaxation of the specific heat.5.7 Therefore, we assign the relaxation mechanism in benzonitrile to be due to relaxation of bulk viscosity due to relaxation of the specific heat. Although the residual line width can be entirely described by T-V relaxation, this does not rule out the possibility of a small structural contribution to the bulk viscosity. The result of the fit of the residual line width to eq 10 is given in Table 11. The specific heat relaxation is a measure of translation-vibration coupling, that is, it is a relaxation of the translational energy into the vibrational modes of the benzonitrile molecules. We can calculate the relaxation strength for T-V relaxation by noting that it is defined by R’ = (y - l)CI/C, - CI. In this expression for the relaxation strength, C, is the internal contribution to the specific heat from vibrational modes of the molecule. The internal contribution can be calculated from the Planck-Einstein relation CI = R C ( h v , / k T ) 2 ( e x p [ - h v i / k T I ) / ( 1- exp[-hui/kU) i
+R (1 1)
if the vibrational frequencies are known. The vibrational frequencies have been measured for benzonitrile by Green and H a r r i ~ 0 n . I ~In the relation for the relaxation strength C, is the measured specific heat capacity. The experimental value for the heat capacity at 20 “ C is 190.4 J/(K mol),15 however, a survey of the literature failed to give the heat capacity as a function of temperature. This value is approximately true over the range from 20 to 100 OC. In the above equation for the relaxation strength y is the ratio of specific heats. This ratio can be determined from the tabulated equation of state16or from the experimental Brillouin spectra.I7 By using the Rayleigh and Brillouin peak areas at 70 “C we have found y to be 1.4. Using these results we can calculate the relaxation strength for benzonitrile for relaxation into the various vibrational modes. If we neglect the temperature dependence of the specific heat, the calculated value for the relaxation strength is 1.098 if we assume relaxation into the four lowest-lying vibrational modes. Because of the error in the measured line width we cannot determine whether the relaxation is into between three and six vibrational modes. It is apparent that the relaxation is into only a few of the lowest vibrational modes. This is consistent with what has been observed in other substituted benzene^.^,^ Such vibrational relaxation in the hypersonic frequency region has been observed in the halogenated benzenes5 The halogenated benzene closest in size to benzonitrile is the chloro derivative. The measured value for the relaxation time in chlorobenzene is 28 ps, which is the same as for benzonitrile. Also, the measured value for the relaxation times of p-anisaldehyde and aniline are 25 and 22 ps, re~pectively.~ This suggests that the vibrational relaxation in benzonitrile is not due to the nature of the nitrile group but rather the fact that it is a substituted benzene. This is not suprising since the low-frequency (14) Green, J. H. S.; Harrison, D. J. Spectrochim. Acta, Part A 1976,32, 1279-86. (15) Lange, N. A. “Handbook of Chemistry”; McGraw-Hill: New York, 1961; 10th ed. (16) “International Critical Tables of Numerical Data, Physics, Chemistry and Technology”; McGraw-Hill: New York, 1933. (17) Landau, L.; Placzek, G. Phys. Z . Sowjetumion 1934, 5 , 172-6.
TABLE III: Dispersion in the Hypersonic Longitudinal Wave w , GHz T, “C exptl calcd Aw, GHz 2.5.6 30.6 33.8 40.0 43.1 46.4 49.6 53.8 59.0 63.0 66.0 69.1 72.0 75.4 80.0 83.0 86.2 89.8 92.8
6.56 6.46 6.45 6.24 6.18 6.14 6.09 6.01 5.87 5.86 5.79 5.15 5.69 0.59 5.52 5.45 5.42 5.34 5.26
5.93 5.85 5.79 5.69 5.63 5.59 5.54 5.48 5.40 5.35 5.31 5.21 5.24 5.19 5.14 5.11 5.07 5.03 5.00
0.63 0.61 0.66 0.55 0.55 0.55 0.55 0.53 0.47 0.51 0.48 0.48 0.45 0.40 0.38 0.34 0.35 0.31 0.26
vibrational modes of each of these substituted benzenes is very similar to the vibrational spectrum of benzonitrile. The concentration dependence of the vibrational relaxation time was studied both in this work and in a dielectric relaxation study.18 In the dielectric study the relaxation time was found to decrease upon addition of carbon tetrachloride; however, at concentrations above 60% benzonitrile the relaxation time was almost constant. The relaxation times can be determined for our solutions by taking T = (27rwmax)-l. This yields a relaxation time which is constant around 28 ps. The effect of dilution of Kneser liquids, or liquids which have vibrational relaxation, has been d i s c u s ~ e d . l ~Carbon ~~ tetrachloride is also a Kneser liquid, with a vibrational relaxation time due to only a single vibrational mode of 54 pse6 The effect on the relaxation time of mixing of two Kneser liquids has been calculated by Sette.21 Because the relaxation time of benzonitrile is nearly equal to the relaxation time of carbon tetrachloride the effect of including the “average” relaxation time is small. A greater effect is due to the change in density of the solution. Carbon tetrachloride is very dense for a simple fluid. The sound velocity, which is related to the frequency of our measurement through w = qV,, is a function of the density of the sample through Vl = (l/K,p)l/’ (12) where K, is the adiabatic compressibility. Therefore, the addition of carbon tetrachloride increases the density of the sample. This results in a decrease in the adiabatic frequency. Thus, the different solutions simply correspond to a different means of scanning through the maximum by changing the frequency. We have calculated the frequency shift for neat benzonitrile from eq 12 using the adiabatic compressibility measured by PatilZ2from ultrasonic measurements at 3 MHz and the tabulated density.16 The experimental and calculated shifts along with the difference are given in Table 111. As can be seen from the difference, the experimental shift is larger than the calculated value at all temperatures. Thus, the shift displays a positive dispersion as is predicted when frequency-dependent transport coefficients are included. Acknowledgment. The authors thank Dr. G. D. Patterson and Dr. C. H. Wang for several valuable discussions. We also acknowledge support for this research from the Cancer Association of Greater New Orleans, Research Corporation, the U N O Research Council, and the UNO Computer Research Center. Registry No. Benzonitrile, 100-47-0; carbon tetrachloride, 56-23-5. (18) Fischer, V. E.; Fessler, R. Z . Naturforsch. 1953, 8, 177-85. (19) Herzfeld, K. F.; Litovitz T. A. “Absorption and Dispersion of U1trasonic Waves”; Academic Press: New York, 1959. (20) Bauer, E. Proc. Phys. SOC.,London, Sect. A 1949, 62, 141-4. (21) Sette, D. J. Acoust. SOC.Amer. 1951, 23, 359-63, J. Chem. Phys. 1950, 18, 1592-6. (22) Patil, K . J. Indian J . Pure Appl. Phys. 1978, 16, 608-13.
