1634
J . Phys. Chem. 1987, 91, 1634-1638
required to associate an equivalent amount of bile salt into the mixed micelles. The prevalence of vesicle structures to much higher bile salt content for TC, as observed in the data in Figure 9, is a manifestation of the tendency for TC to associate less readily. That is, the total concentration of T C must be higher than TDC to break up the vesicle structures to form mixed micelles. While one might expect other factors than just composition of the mixed micelles to affect the nature of structures that prevail, the similarities of the F,,,/F, curves for T C and TDC suggest that the two systems behave alike when account is taken of the actual compositional differences. Thus, the maximum in F,,,/F, in the 15 OC data at about 4.5/1 mole ratio corresponds to the changes which we associate with lateral phase separation in the TDC case. Although the DSC data for the TC/DPPC micelles are more complex, there are changes in the enthalpies of the transitions which occur again near the 4.5/1 mole ratio,6 which seems to confirm our hypothesis that at lower temperatures a reorganization of the mixed micelles occurs that provides for thermal activity even to rather high mole ratios of bile salt to lecithin. Note that the monomer/excimer ratios for the T C mixed micelles at 25 and 15 OC are significantly larger than for the TDC mixed micelles, while at 35 OC the fluorescence curves are very similar. (Compare Figures 1 and 6.) The implication of these differences at lower temperatures is that the T C micelles are more ordered (higher F,/F, ratio) at all compositions at 15 and 25 OC. This factor could be a result of larger lecithin domains within the micelles, yielding somewhat more extensive hydrocarbon chain packing than for the TDC micelles. Since the fluorescence ratios
are rather larger for TC, it does seem that the internal characteristics for the micelles are somewhat different even when account is taken for compositional differences. Conclusions. The results of this study have demonstrated that mixed micelles of bile salts and lecithin show complex changes in properties that are dependent on the temperature and on the bile salt structure. A reasonable interpretation of the changes in properties is that (1) there is a sort of lateral phase separation within the micelles at lower temperature and higher mole ratios of bile salt to lecithin and that (2) there are differences in behavior of micelles formed from typical dihydroxy bile salts as compared with trihydroxy derivatives both with respect to the compositional changes that affect the behavior and with respect to the internal characteristics of the micelles. It should be emphasized that these studies are in general at low total lipid content relative to some other studies in the literature, so that the observations made here may not apply at higher total lipid. However, based on some preliminary results at higher total lipid, the trends found here seem to be continuing to higher concentrations. Because the systems are so complex, it seems important to be careful not only to make comparisons of measurements on the mixtures at similar compositions but also to make certain that the bile salt components used are comparable.
Acknowledgment. This work was supported by a grant from the National Institutes of Health, Grant No. AM20946. Registry No. DNP, 14564-87-5; TC, 81-24-3; TDC, 516-50-7; DPPC, 2644-64-6.
Hypersonic Attenuatlon in the Simple Amides M. A. Goodman, V. K. Jain, S. J. McKinnon, and S. L. Whittenburg* Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 (Received: April 21, 1986; In Final Form: September 17, 1986)
The attenuation of thermally induced sound waves in formamide has been measured by Brillouin light scattering. Solutions of formamide in water, methanol, and ethanol as well as acetamide in water have also been measured as a function of temperature. The spectra are analyzed in terms of an extended hydrodynamic light scattering theory. The bulk viscosity of formamide in the hypersonic frequency region is significantly greater than the shear viscosity.
Introduction The amides have been the subject of extensive spectroscopic and theoretical investigation^.'-^ Despite this vast amount of research the bonding, structure, and relaxation of the amides are still not well understood. The purpose for studying these systems is that formamide and acetamide represent some of the simplest systems for understanding hydrogen bonding. The amides exhibit the smallest peptide bonds and serve as model compounds for understanding the hydrogen bonding in more complex biologically active peptides. Several experimental studies probing the hydrogen bonding in amides have employed NMR.' However, Rayleigh-Brillouin scattering is also a useful method for probing structural relaxation and motion in viscoelastic liquids composed of small molecules. The Brillouin spectrum consists of a central Rayleigh peak and (1) Weingartner, H.; Holtz, M.; Hertz, H. G. J. Solution Chem. 1978, 7, 689. Burger, M. I.; St. Amour, T. E.; Flat, D.J . Phys. Chem. 1981, 85, 502. Hinton, J. F.; Ladner, K. H. J. Magn. Reson. 1972, 6, 586. (2) Spencer, J. N.; Berger, S. K.; Powell, C. R.; Henning, B. D.; Furman, G. S.; Loffrendo, W. M.; Rydberg, E. M.; Neubert, R. A,; Schoop, C. E.; Blauch, D. N. J. Phys. Chem. 1981,85, 1236. (3) Kollman, P. A.; Allen, L. C. Chem. Reu. 1972, 72, 283. Kollman, P. A.; Johansson, A. J . Am. Chem. Soc. 1972, 94, 6196. Hinton, J. F.; Harpool, R. D. J. Am. Chem. SOC.1977, 99, 349.
0022-3654/87/2091-1634$01.50/0
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 shift is equal to the longitudinal phonon frequency and can be related to hypersonic velocity and compressibility of the liquid. The Brillouin line width is a sum of contributions from the bulk and shear viscosity of the fluid. Since the zero-frequency viscosities are not necessarily equivalent to those in the hypersonic frequency region, physical information about the relaxation of the fluid can be obtained. Thus, a symmetric Rayleigh-Brillouin study can yield valuable information not easily obtained by other technique^.^ Some strongly self-associating simple liquids have been studied by Rayleigh-Brillouin spectroscopy. Attenuation has been observed in several of the simple carboxylic acid^.^,^ For each of the acids the mechanism giving rise to the attenuation was shown to be related to the breaking of the hydrogen-bonded network. We have observed attenuation in neat formamide and in formamide and acetamide solutions. To understand the microscopic (4) Berne, B. J.; Pecora, R. Dynamic Light Scarrering, Wiley: New York, 1976. (5) Patterson, G. D.; Alms, G. R.; Lindsey, C. P. J . Chem. Phys. 1978, 69, 4802. (6) Keegan, P. F.; Whittenburg, S. L. J. Phys. Chem. 1982, 86, 4622.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Hypersonic Attenuation in the Simple Amides mechanism for this relaxation, we have analyzed the data in terms of an extended hydrodynamic theory of light scattering of Lipeles and K i ~ e l s o n . A ~ generalized form of these equations has been derived by Wang.8 Theory The polarized Rayleigh-Brillouin spectrum can be calculated by using the linearized hydrodynamic equations, which include the number density, the linear momentum, and the local energy. For orientationally isotropic molecules these variables are sufficient to describe the experimental spectrum. The classical Brillouin line width is given by and the Brillouin shift of the longitudinal acoustic phonons is given by Awl = qV,;(q) (1b) where Awl is the line width, q is the scattering wave vector, vs and qv are the shear and bulk viscosity, respectively, p is the density, and V, is the sound velocity in the fluid. The amplitude of the scattered wave vector is given by q = (4xn/A) sin (8/2) (2) where n is the refractive index and 0 is the scattering angle. For purely viscous fluids the static or zero-frequency sound velocity is given by (3) where KO = PT-' is the static modulus of compression, PT is the isothermal compressibility, and y = Cp/Cuis the ratio of specific heats of constant pressure and volume. Note that the above equations describe the method by which the frequency may be scanned in a Brillouin experiment. In a typical ultrasonic or dielectric experiment the frequency of the probe is scanned until it is in resonance with relaxation frequencies of the sample. In the Brillouin experiment the frequency of the experiment is Awl, which may be scanned by varying either the scattered wave vector, q, or the sound velocity, V,. The scattered wave vector can be altered by changing the scattering angle, 8, or the wavelength of the laser, A. Alternatively, by scanning the temperature, the density of the sample is scanned linearly. Equation 3 shows that this corresponds to a monotonic change in the sound velocity, V,, which, by eq 1b, corresponds to scanning the frequency of our measurement. This is the method used in this study. It has the problem that the relaxation frequency is also a function of temperature. However, it is still possible to find a temperature at which Awl coincides with the relaxation frequency of the sample. The classical line width ignores the fact that the viscosity is frequency dependent, and therefore it 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. The relevant modulus for polarized scattering is the adiabatic longitudinal modulus, M(w), which is related to the modulus of compression, K(w), and the shear modulus, C(w), via
+
M(w) = K ( w ) (4/3)G(o) (4) The fluctuation in the optical anisotropy also contributes to the total scattering intensity and therefore affects the Brillouin line width. The contribution to the total intensity and the optical anisotropy have been recently measured experimentally for formamide by depolarized Rayleigh ~ c a t t e r i n g . ~ To derive the effect of the molecular anisotropy on the Brillouin line width, one must also include orientational variables in the set of conserved variables. The extended hydrodynamic equations of Lipeles and Kivelson couple the Fourier transformed densities (7) Lipeles, R.; Kivelson, D. J . Chem. Phys. 1977, 67, 4564. (8) Wang, C. H. Mol. Phys. 1986, 58,497. (9) Whittenburg, S. L.; Jain, V. K.; McKinnon, S. J. J. Phys. Chem. 1986, 90, 1004.
1635
of orientation with the reduced momentum divergence and the number density. In these equations the shear modes are coupled to the orientational modes and give the frequency dependence of the shear viscosity due to translation-rotation coupling. The expression for the Brillouin line width given by Lipeles and Kivelson is
rl = (q2/2P)[?Y + (4/3)%(1 - R) + ror2vsR/(ro,Z
+ w2)1 (5)
where Foris the depolarized line width and R is the translational-rotational coupling constant. Both of these parameters have been experimentally determined by using the depolarized Rayleigh scattering t e c h n i q ~ e . ~ A theoretical expression for the depolarized Rayleigh light scattering spectrum has been derived by Andersen and Pecora.l o The coupling of orientation to the shear wave arises because the symmetry of the certain elements of the polarizability and the linear velocity are identical. The two-variable theory of Andersen and Pecora predicts that the depolarized Rayleigh spectrum is
+
+
+
IVH(q,w) = k~xa/x{ror/(r,,;w 2 ) sin2 (8/2) ror[u2 (q211s/P>2(1- R)1 cos2 (6/2)/([w2 - q211sror/Pl2 + w2[ror + (q211s/p)(l - WI21 ( 6 )
The theory predicts that the translation-rotation coupling in this limit will consist of a broad Lorentzian due to orientational relaxation plus a dip at zero-frequency shift due to the coupling to the shear wave. The amplitude of the dip is the coupling constant, R, and the width is related to q2vs/p. The dip will be wide enough to be experimentally observable if the value of q2vS/proris around the critical value 0.7." Experimental Section Formamide (Aldrich, spectroscopic grade) and acetamide (Baker) were used after vacuum distillation over molecular sieve to remove trace water. The following volume percent solutions of formamide were made: 80% in water, 80% and 60% in ethanol, and 60% in methanol. A solution of acetamide in 60% water was also prepared. In order to remove dust, the solutions were filtered through a 4-5" fritted glass filter into a fluorescence cell. Rayleigh-Brillouin spectra were obtained as described previously.6 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 fO.l "C. Spectra were taken in the temperature range from 5 to 100 "C. The free spectral range was optimized to avoid overlap of adjacent orders and was 19.34 GHz for the aqueous and neat formamide, 19.52 GHz for the aqueous acetamide, and 19.77 GHz for the ethanol and methanol solutions. The finesse, which is a measure of the line width of the instrumental peak, was typically 60-70. The scattered light was collimated through a Fabry-Perot interferometer, and the 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 Zenith ZlOO microcomputer for analysis. One thousand data points were collected over two orders of Brillouin spectra. All spectra were deconvoluted by using a modified Van Cittert method,l2~l3 which has the advantage in that the deconvolution can be done with the actual experimental instrumental spectrum and does not assume any functional form for the line shape. The deconvoluted spectra were fit by using a nonlinear least-squares fit to a series of Lorentzian peaks and a base line. (10) Andersen, H. C.; Pecora, R. J . Chem. Phys. 1971, 54, 2584. (11) Patterson, G. D.; Carroll, P. J. J . Phys. Chem. 1985, 89, 1344. (12) Burger, C. H.; Van Cittert, P. H. Z . Phys. 1932, 79, 722; 1933, 81,
428. (13) Jones, R. N.; Venkataraghavan, R.; Hopkins, J. W. Spectrochim. Acta 1967, 23, 925.
1636 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Goodman et al.
TABLE I: Frequency Shifts and Line Widths of Formamide Solutions"
r,
"I
7.13 6.93 6.76 6.60
1.09 0.78 0.60 0.54
6.53
0.44
6.46 6.43 6.38
0.42 0.42 0.42
6.35 6.28 6.26 6.25 6.18 6.17 6.14 6.13 6.10 6.07 5.99 5.98 5.96 5.92 5.89 5.85 5.83
0.38 0.36 0.37 0.3 1 0.28 0.28 0.26 0.26 0.26 0.24 0.24 0.25 0.23 0.22 0.22 0.21 0.20
"I
0.33 0.34 0.30 0.30 0.35 0.25 0.27 0.22 0.22 0.22 0.21 0.16 0.18 0.21 0.20 0.18 0.19 0.19 0.16 0.13 0.17 0.16 0.18
E
r,
"I
rl
6.27 6.24 6.23 6.18 6.17 6.1 1 6.10 6.06 6.04 6.01 5.99 5.94 5.93 5.90
0.43 0.40 0.41 0.34 0.34 0.34 0.32 0.3 1 0.30 0.27 0.26 0.25 0.27 0.26
6.47 6.43 6.44 6.40 6.38 6.34 6.3 1 6.30 6.29 6.27 6.26 6.23 6.16 6.13
0.36 0.47 0.38 0.35 0.33 0.31 0.31 0.31 0.29 0.29 0.32 0.27 0.22 0.19
5.81
0.15
6.10
0.21
5.78
0.22
6.06
0.20
5.69
0.19
5.98
0.17
5.62
0.19
5.92
0.18
5.59
0.18
"I
rl
6.46 6.43 6.39 6.37 6.35 6.31 6.29 6.26 6.24 6.21 6.18 6.13 6.09 6.09 6.07 6.05 6.02 5.98 5.94 5.93 5.89 5.88 5.84
D
C
B
A
T, O C 5.0 10.0 15.0 20.0 24.3 27.2 30.6 33.8 36.8 40.0 43.7 46.4 49.6 53.8 56.3 59.0 63.0 66.0 69.1 72.0 75.4 80.0 83.0 86.2 89.8 92.8 95.6 98.9
"I
PI
6.22 6.21 6.20 6.15 6.12 6.10 6.07
0.39 0.30 0.32 0.31 0.29 0.28 0.27
6.01 5.98 5.95 5.93
0.25 0.23 0.22 0.23
" A = neat formamide, B = 80% (v/v) formamide in water. C = 80% (v/v) formamide in ethanol, D = 80% (v/v) formamide in methanol, and E = 60% (v/v) formamide in ethanol.
!1
TABLE 11: Frequency Shifts and Line Widths (in GHz) of 80% Acetamide in Water T, OC 23.0 24.6 27.2 30.6 33.8 36.8 40.0 43.7 46.4
"I
6.72 6.71 6.68 6.66 6.65 6.61 6.57 6.52 6.51
ri 0.38 0.41 0.40 0.37 0.37 0.36 0.36 0.31 0.31
T, O C 49.6 53.8 59.0 66.0 72.0 80.0 86.2 92.8 98.9
WI
r,
6.46 6.40 6.39 6.20 6.26 6.19 6.12 6.04 5.97
0.27 0.25 0.24 0.21 0.19 0.19 0.17 0.15 0.17
Results and Discussion The experimentally measured values for the frequency shift and line width of the formamide and acetamide solutions obtained from the fits to a series of Lorentzians are listed in Tables I and 11, respectively. The experimental spectrum at several temperatures is shown in Figure 1. A plot of the Brillouin line width and frequency shift for the neat formamide is given in Figure 2. 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 strutural and a reorientational term. The frequency-dependent shear viscosity can be written as
293K
Figure 1. Experimental Rayleigh-Brillouin spectra of neat formamide at 278, 283, and 293 K.
(7)
where T~~ is the reorientation relaxation time and is related to orientational line width via T~~ = ( ~ T F ~ ~ ) - ~ . Orientational contributions to the shear viscosity may be subtracted from the measured shear viscosity, and therefore the Brillouin line width, if the reorientation time, T ~ and ~ , the translation-rotation coupling constant, R,are known. The orientational relaxation time for formamide has been measured as a function of t e m p e r a t ~ r e .The ~ temperature dependence of the Rayleigh reorientational time can be described by Tor = (g2/J2)(Ctls/T + TO) (8) where g , is the static orientation pair correlation factor, J 2 is the
5.0 273
temperature (K)
383
Figure 2. Brillouin line width and frequency shift of neat formamide plotted as a function of temperature.
corresponding dynamic quantity, and T~ is the zero-viscosity intercept. A plot of T , vs. q , / T has an experimental slope of (1.36 f 0.12) X lo-' s K / P and an intercept of 0.5 f 0.2 ps. The experimental orientation pair correlation is 1.9. A comparison of the experimental slope with theoretical slopes for both the slip
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987 1637
Hypersonic Attenuation in the Simple Amides TABLE III: Contributions to Brillouin Line Width (in CHz) for Neat Formamide"
T,OC
rl
r,,
5.0 10.0 15.0 20.0 27.2 33.8 36.8 40.0 46.4 49.6 53.8 56.3 59.0 63.0 66.0 69.1 72.0 75.4 80.0 83.0 86.2 89.8 92.8 95.6 98.9
1.09 0.78 0.60 0.54 0.44 0.42 0.42 0.42 0.38 0.36 0.37 0.31 0.28 0.28 0.26 0.26 0.26 0.24 0.24 0.25 0.23 0.22 0.22 0.21 0.20
0.04 0.04 0.04 0.04 0.04 0.03 0.03 0.03 0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01
e
r.,
p.
0.14 0.13 0.1 1 0.10 0.09 0.07 0.06 0.05 0.05 0.05 0.04 0.04 0.04 0.04 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.02 0.02 0.02
r, 0.90 0.61 0.45 0.40 0.32 0.32 0.32 0.33 0.30 0.29 0.30 0.25 0.22 0.22 0.20 0.21 0.21 0.21 0.19 0.20 0.19 0.18 0.18 0.16 0.17
n.
nv
T. OC
n.
n,
5.0 10.0 15.0 20.0 27.2 33.8 36.8 40.0 46.4 49.6 53.8 56.3 59.0
3.66 3.21 2.82 2.49 2.16 1.81 1.71 1.58 1.38 1.29 1.18 1.12 1.07
20.71 14.02 10.27 9.23 7.28 7.24 7.35 7.51 6.83 6.46 6.82 5.56 4.9 1
63.0 66.0 69.1 72.0 75.4 80.0 83.0 86.2 89.8 92.8 95.6 98.9
0.99 0.95 0.87 0.85 0.80 0.74 0.71 0.67 0.64 0.61 0.58 0.56
5.02 4.61 4.72 4.74 4.68 4.34 4.67 4.27 4.08 4.12 3.99 3.72
I kinematic VlSCOSlty (cS)
4
Figure 3. Brillouin line width as a function of the kinematic viscosity for
is the structural shear line width, and rvis the total bulk width, line width.
and stick model of rotation diffusion indicates that the slip conditions are a better assumption. The shear wave dip was not observed in the experimental spectra for formamide over this temperature range since q2qs/proris less than the critical value. Although the shear wave dip was not observed in formamide, the translational-rotational coupling constant R is often observed to be near 0.33.5,9J4 That is, 33% of the shear viscosity (at zero frequency) is due to reorientation. Although it would be preferable to experimentally measure R , we must assume some value, since it cannot be measured by depolarized Rayleigh light scattering. Note from Table I11 that the contribution from orientation, to the total line width is negligible. Even if a large value for R is assumed, the contribution of orientation is at the limit of error in the measured line width. The structural and reorientational contributions of the shear viscosity to the Brillouin line width, assuming R for the amides to be 0.33 and using the measured depolarized Rayleigh relaxation times, are presented in Table 111. The calculated orientational shear line width, and the structural shear line width, rst,s, contributions to longitudinal line width are given in Table 111. These were calculated from the equations
= vv(q2/2P)
T,OC
0.0
"r,is the Brillouin line width, ror,s is the orientational shear line
rv
TABLE I V Shear and Bulk Viscosities (in cP) for Formamide
(11)
It has been shown previously that the orientational contribution to the line width is very small for p-anisaldehyde, aniline,I5and benzonitrile.16 Since in these highly anisotropic molecules the orientational contribution to the line width is small, it should be negligible in the simple amides. Thus, this study on the simple amides supports the conclusion that orientational relaxation in the hypersonic frequency region does not contribute significantly to the line width. The zero-frequency viscosities, densities, and (14) Stegeman, G. I. A,; Stoicheff, B. P. Phys. Reu. Lett. 1968, 21, 202. Patterson, G. D.; Griffiths, J. E. J . Chem. Phys. 1975, 63, 2406. Patterson, G. D.; Lindsey, C. P. J . Appl. Phys. 1978, 49, 5039. (15) O'Steen, B. L.; Wang, C. H.; Fytas, G. J . Chem. Phys. 1984, 80, 3774. (16) Goodman, M. A.; Whittenburg, S . L. J. Phys. Chem. 1984,88, 5653.
neat formamide. refractive indexes used in calculating the line width contributions were obtained from previously published va1ues.l' The bulk line width, rV, is obtained by subtracting the shear contributions from the total Brillouin line width and is also given in Table 111. From the bulk line width, the bulk viscosity can be calculated from eq 11. The calculated bulk viscosities are given in Table IV. The shear viscosity in the hypersonic frequency region is approximately vs(l - R). This assumes that the structural contribution to the shear viscosity at hypersonic frequencies is equal to its unrelaxed or zero-frequency value. For comparison to the bulk viscosities the hypersonic shear viscosities are also given in Table IV. Note that the bulk viscosity is roughly triple the shear viscosity which accounts for the large bulk contribution to the Brillouin line width in formamide. This result supports the prediction of the continuum mechanics theory. As we mentioned before, the bulk viscosity is dependent on two terms; structural relaxation and translation-vibration relaxation. Little is known about the temperature dependence of the structural contribution to the bulk viscosity. It is expected that the vibrational relaxation should be very fast in an associated liquid and that it would depend only weakly on temperature; therefore, the vibrational contribution to the bulk viscosity should be small. Calculating the vibrational relaxation time by the method outlined by Dorfmuller,I8 we found the vibrational relaxation frequency to be 2 orders of magnitude higher than the longitudinal frequency. Therefore, vibrational relaxation in our frequency region would not be expected. In addition, the value of kBT at 25 "C is -200 cm-' while the lowest vibrational mode in formamideI9 is at -600 cm-'; this energy difference is too large to expect T-V transfer. Thus, we expect structural relaxation to be the dominant mechanism in the bulk viscosity in the simple amides. This is in agreement with the assignment in acetic a ~ i d . Structural ~.~ relaxation due to the bulk viscosity is accompanied by volume changes. Therefore, this attenuation in formamide results in changing the molecular arrangement of the molecules along with the molecular volume. In this analysis we have taken the thermal contribution to the Brillouin line width to be negligible. The (17) International Critical Tables of Numerical Data, Physics, Chemistry and Technology; McGraw-Hill: New York, 1933. Bolt, H. G. Beilsteins Handbuch der Organischen Chemie; Springer-Verlag: West Berlin, 1920; Vol. 2. (18) Dorfmuller, Th.; Fytas, G.; Mersch, W.; Samios, D. Symp. Faraday Sot. 1977, 11, 106. (19) Evans, J. C. J . Chem. Phys. 1954,22,1228. Smith, C . H.; Thompson, R. H . J . Mol. Spectrosc. 1972, 42, 221.
1638 The Journal of Physical Chemistry, Vol. 91, No. 6,1987
Goodman et al.
TABLE V Refractive Indexes, Density, Hypersonic Velocity, and Isentropic Compressibility of Formamide Solutions at 25 OC“ A B C D E
refractive index density, g/cm velocity, m/s compressibility, GPa
1.445 1.12gb 1644 0.328
1.423 1.102b 1651 0.333
1.426 1.066 1640 0.348
1.432 1.064 1585 0.373
1.417 0.983 1594 0.400
“ A = neat formamide, B = 80% formamide in water, C = 80% formamide in methanol, D = 80% formamide in ethanol, and E = 60% formamide in ethanol. *Reference 19
thermal contribution is independent of the kinematic viscosity, while the other contributions are proportional to the viscosity. Thus, the magnitude of the thermal contributions can be obtained by plotting the measured line width vs. the kinematic viscosity as is done in Figure 3 and observing the zero-viscosity intercept. Within our experimental error the zero-viscosity intercept is zero, and therefore the thermal contribution to the Brillouin in formamide is negligible. The concentration dependence of formamide was also studied in this work. The hypersonic velocity is related to the frequency of our measurement by and is a function of the density of the liquid via eq 3. The density of the 80% formamide-water solution a t 25 OC was obtained from the literature.*O All the refractive indexes and other densities at 25 OC were measured in our laboratory and are given in Table V, along with the calculated hypersonic velocity and isentropic compressibility. Within our limit of error the compressibility of the neat formula and the formamide-water solution are nearly the same, being 0.328 and 0.333 GPa, respectively, while the formamide-methanol compressibility is 0.348 GPa. The compressibility for the formamide-ethanol solution is even larger, 0.373 GPa. As the interaction between molecules becomes stronger, the molecules become more compact and therefore have lower compressibilities. From this we can conclude that the formamide-formamide interaction is about the same as that of formamide-water. The formamide-methanol interaction is weaker since its compressibility is larger than that of formamide-water, and the formamide-ethanol interaction is expected to be the weakest. It is clear from Figure 1 that a relaxation mechanism with a characteristic frequency exists in formamide and which occurs at Brillouin frequencies below the melting temperature ( TM = 2.55 “C). Although many attempts were tried at obtaining good Rayleigh-Brillouin spectra below the melting points of formamide by supercooling the sample, these attempts failed. As the melting point is approached, small crystallites begin to form and the experimental spectrum is dominated by the Rayleigh component. Apparently, formamide is difficult to supercool. The low-temperature spectra shown in Figure 1 begin to display many of the features associated with glasses near the glass transition temperature.21 As the transition temperature is approached from above, the Brillouin peaks lose intensity and broaden and the Brillouin shift increases dramatically. The total Rayleigh-Brillouin intensity for simple and viscoelastic fluids is proportional to kBT/Ko. The total scattering intensity is conserved. The ratio of the Rayleigh or central peak to the total Brillouin intensity is y-1.22Since the total Rayleigh-Brillouin intensity is constant, the decrease in the Brillouin intensity must be compensated by the appearance of a new spectral feature. This new peak is the Mountain component and is observed in the low-temperature (20) Egan, E. P.; Luff, B. B. J . Chem. Eng. Data 1966, 11, 194. (21) Carroll, P. J.: Patterson, G . D. J . Chem. Phys. 1984, 81, 1666-1675. (22) Landau, L.; Placzek, G. Phys. 2. Sowjetunion 1934, 5 , 172.
formamide spectra. Both the Brillouin intensity, I,, and Mountain intensity, IM,are related to the real part of the adiabatic longitudinal modulus at the experimental frequency, M’( Awl), via IB
Ot
PkBT/M’(AWI)
(12)
and IM0~ P(kBT/yKo)[(M’(Aul)- yKo)/M’(Awl)l
(13)
The decrease in the Brillouin intensity as the transition temperature is approached is due to the increase in M’(Au,) at the transition temperature. Since G(Awl) is decreasing, the increase in the longitudinal modulus must be due to an increase in the modulus of compression, K(Aw,). As the temperature is lowered further, the Mountain peak grows in intensity but also sharpens. At this point the Mountain peak is difficult to resolve from the Rayleigh component. As the temperature is lowered below the transition temperature, the Brillouin peaks sharpen while the frequency shift continues to increase.*’ It should be noted that fluctuations in the anisotropic scattering also contribute to the polarized spectrum. The anisotropic scattering gives rise to an unshifted component and may hide the Mountain component. Formamide has a moderately weak depolarized component and is negligible at the intensity level measured in the polarized s p e ~ t r u m . ~
Conclusions A dispersion in the Brillouin line width for formamide and an acetamide-water solution is observed when the Brillouin line width is studied as a function of temperature. Varying the temperature of the sample changes both the frequency of our measurement by changing the density of the liquid and the characteristic relaxation time. The extended hydrodynamics theory allows the various contributions to the line width to be subtracted from the measured line width. For formamide the dispersion in the line width is due to dispersion in the bulk viscosity. Around the melting point of formamide the bulk viscosity increases dramatically and becomes the dominant contribution to the fluid viscosity. Several relaxation mechanisms may contribute to the dispersion in the bulk viscosity, and separation of these contributions is more difficult since a general procedure for inclusion of vibrational relaxation into the hydrodynamic equations is not currently available. We present several arguments as to why the dispersion is probably not vibrational relaxation. These arguments are probably correct, and the dispersion is most likely due to structural relaxation as described above. Until a general theory is available, however, no specific mechanism may be ruled out. Acknowledgment. We 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 UNO Research Council, and the U N O Computer Research Center. Registry No. Acetamide, 60-35-5, formamide, 75-12-7
