J. Phys. Chem. 1903, 87,5197-5201
Conclusions Our data indicate that orientational motion of the anions NO3- and C032-does not involve breakage of hydrogen bonds of the surrounding water molecules. The orientational motion of the anions does not carry along tightly bonded water molecules. The carbonate anion, even in as low as 1 M aqueous solution, seems to be associated with its Na+ counterion forming a species of one net negative electronic charge. (27) Patterson, G. D.; Griffiths, J. E. J. Chem. Phys. 1975, 63, 2406.
5197
This associate should be considered a dynamic species, of a lifetime longer than orientational correlation times (order of,picoseconds) but shorter than typical lifetimes of configurations of water layers (cage) around the anions (of the order of s).~*
Acknowledgment. This work benefitted from the financial support of NATO Research Grant No. 1977. (28) Hertz, H. G.; Zeidler, M. D. In "The Hydrogen Bond. Recent Developments in Theory and Experiment"; Schuster, P.; Zundel, C.; Sandorfy, C., Ed.; North-Holland: Amsterdam, 1976; p 1041.
Density and Temperature Effects on Vibrational Relaxation in Liquid Tetramethylsilane Paul Theodore Sharko, Marcel Besnard, and Jlrl Jonas" Department of Ch8miStty, School of Chemical Sciences, University of Illinois, Urbana, Illinois 6 180 1 (Received: June 6, 1983)
The isotropic Raman band associated with the totally symmetric vg Si-CH3 stretching mode of liquid tetramethylsilane has been measured in the temperature range 298 to 373 K and pressure range 1 bar to 4 kbar. Under isothermal conditions, we found a progressive broadening and a shift of the center of the line toward high frequencies with increasing pressure. The line shape was close to a Lorentzian profile at all the pressures and temperatures investigated. Under isothermal conditions the relative change in line width fwhh(p)/fwhh(po) as a function of the reduced density p/po, where po is the density at 4 kbar, was evaluated and compared to the predictions of different models of vibrational dephasing. The best agreement was obtained by using the isolated binary collision model of Fischer-Laubereau. In the density range investigated, the dephasing of the Si-CH, stretching mode of Me4Si is governed by the harsh repulsive forces which dominate the slowly varying attractive forces.
Introduction The study of vibrational relaxation in the liquid state via isotropic Raman line-shape analysis is a subject of considerable interest from both the theoretical and experimental points of Furthermore, it is now well established, as illustrated by a number of studies performed in our laboratory, that it is essential to use both temperature and pressure as experimental variables. Indeed, the isothermal density studies represent a powerful tool to compare experimental observation to existing theoretical models. For a. given molecule, it is also known that vibrational relaxation contributes differently to the Raman bands associated with different normal modes. These findings were clearly illustrated in the study of Schindler and Jonas on i s o b ~ t y l e n e . ~Let ? ~ us recall that two strongly polarized Raman profiles associated respectively with the v4 C=CH2 and the symmetric vg C-CH3 stretching modes were studied over a large temperature and pressure range. The striking result found in this study was the different behavior under isothermal density condition of the isotropic Raman profile associated with these two modes. At constant temperature and increasing density the Raman profile associated with the ug mode exhibits an increasing line width together with an important blue shift of the peak frequency while the opposite trend was found for the Raman profile associated with the (1) D. W. Oxtoby, Adu. Chem. Phys., 40, 1 (1979). (2) D. W. Oxtoby, Annu. Reu. Phys. Chem., 32, 77 (1981). (3) S. Bratos in "Vibrational Spectroscopy of Molecular Liquids and Solids", S. Bratos and R. M. Pick, Ed., Plenum, New York, 1980, pp 43-60. (4) W. Schindler and J. Jonas, J. Chem. Phys., 72, 5019 (1980). (5) W. Schindler and J. Jonas, J. Chem. Phys., 73, 3547 (1980).
u4 mode.
In a following theoretical paper Schweizer and Chandler6showed that these findings can be interpreted on the basis of the competition of the rapidly varying repulsive forces with the slowly varying attractive forces. In order to investigate systematically vibrational relaxation of the X-CH3 oscilator in the liquid phase and compare the result with the C-CH3 mode of isobutylene we choose to study the totally symmetric vibration associated with the u3 Si-CH, stretching mode in neat liquid tetramethylsilane (Me,Si). This choice is convenient for a number of reasons. MelSi is a spherical molecule and the u3 mode is not infrared inactive. As a consequence neither dipolar nor inductive interactions are present. Furthermore as the dipolar effects which generally give rise to the most important contribution in the resonant energy transfer mechanism are nonexistent, we suspect that this last contribution in Me,Si is negligible. From a purely experimental point of view, the Raman profile associated with the u3 mode can be easily studied as it is well isolated from other Raman peaks and as this mode is completely polarized, the isotropic Raman profile is readily obtained without correction for the anisotropic one. Finally, extensive measurements of density, viscosity, self-diffusion coefficients, and hard-sphere diameters were reported in a previous study by Parkhurst and J o n a ~ . ~These , ~ data are essential for a detailed comparison of experimental results with the theoretical models available. General models which lead to dephasing of molecular vibrations in the liquid state have been extensively re(6) K. S. Schweizer and D. Chandler, J. Chem. Phys., 76, 2296 (1982). (7) H. J. Parkhurst and J. Jonas, J. Chem. Phys., 63, 2698 (1975). (8) H. J. Parkhurst and J. Jonas, J. Chem. Phys., 63, 2705 (1975).
0022-3654/83/2087-5 197$01.50/0 0 1983 American Chemical Society
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The Journal of Physical Chemistry, Vol. 87, No. 25, 1983
viewed.lW3We present here only briefly the theoretical material needed in our study. We have focused our interest on four different models selected for their success in describing vibrational dephasing in the liquid state and which can be compared to experimental results on a quite simple basis. The first one is the isolated binary collision (IBC) model of Fischer and L a ~ b e r e a u . ~This model extended by OxtobylJOgives the dephasing time as
Sharko et al.
I .5
,/ \
L L
298K-4Kbor
rl
I
i\ 298K- I bar
where B represents the correction for anharmonicity, L is the range of interaction of the intermolecular potential, w is the frequency of the oscillator, T, is the elastic collision time, and p', ?A, yB, and I.L are mass factors. The vibrational correlation time T, which can be obtained from the experimental full width a t half-height (fwhh) Av of the isotropic Raman profile is related to the dephasing time Tph by T, = 2rph= (?rcAv)-l. Oxtobyll has developed a hydrodynamic model for vibrational dephasing of an anharmonic diatomic oscillator A-B which is nonlinearly coupled to the thermal bath. He found that the vibrational correlation time is given by
0
547.4
567.4
5874
601,4
6274
641,4
FREQUENCY
Flgure 1. Experimental isotropic Raman band of the v3 mode of Me,Si at 298 K at pressures of 1 bar and 4 kbar. The best-fit Lorentzian line shapes are also given. The intensities are arbitrary.
I .5
where q is the viscosity, f the anharmonic force constant,
Ri the radius of the atom i, and the other parameters have the same meaning as in the IBC model. Wertheimer12J3has developed a model for vibrational relaxation which combines both dephasing and resonance contributions into a single expression. The fluid is modeled as a collection of breathing spheres which interact through an exponential potential. The resultant calculation yields an expression
where D is the coefficient of self-diffusion, ylois a constant which couples the oscillator coordinate to the exponential potential, and is dependent on the anharmonicity of the oscillator. It should be noted that suppression of the factor 2 in this equation leads to an expression which gives only the pure dephasing contribution. Finally, Lynden-Bell14 has proposed a theory for vibrational line widths in which dephasing is due to very rapidly varying fluctuations in intermolecular forces resulting from relative translational motion. The expected vibrational correlation time is T,-~
= A'(p/D)
(4)
where A ' is a constant, p the density, and D the self-diffusion coefficient.
Experimental Section 'I'etramethylsilane was supplied by Aldrich Chemical Co. Inc., a t a stated purity of 99.9%. The Raman spectrometer and the high-pressure, hightemperature cell of our laboratory have been described a t
5474
567,4
581,4
6074
6224
6424
FREQUENCY (cm-l)
Figure 2. Experimental isotropic Raman band of the u3 mode of Me,Si at 373 K at pressures of 50 bar and 4 kbar. The best-fit Lorentzian line shapes are also given. The intensities are arbitrary.
length elsewhere.15J6 We mention here only the main features of this equipment. The excitation source used was a Spectra Physics argon ion laser operating at 4880 8,with 1.2-W pow- output. The spectrometer was a Spex Industries model 14018 double monochromator containing holographically ruled gratings (1800 lines/mm). The scattered light observed at 90° from the beam direction goes through a quartz 1/4-wave plate used as a polarization scrambler. As the vg band is totally polarized the spectrum could be recorded without a polarization analyzer which improves the signal-to-noise ratio because the use of an analyzer introduces inevitable losses. The slit width was 0.18 cm-'. The spectra were taken a t pressures ranging from 1.00 to 4000 bars and a t temperatures between 25 and 100 "C with the high-pressure, high-temperature cell built in our laboratory. We use float glass windows to keep pressure-induced birefringence to a minimum. The temperature of the sample was monitored with a copper constantan thermocouple mounted so that the measuring junction is located within 0.5 cm of the scattering volume. All the data were collected with an LSI 11 computer and stored on flexible magnetic disks for further processing with a VAX computer connected to the LSI 11 computer. (15) J. Schroeder, V. E. Schiemann, P. T. Sharko, and J. Jonas, J. Chem. Phys., 66, 3215 (1977). (16) J. Schroeder, V. E. Schiemann, and J. Jonas, Mol. Phys., 34,1501 (1977).
Vibrational Relaxation in Me,Si
The Journal of Physical Chemistry, Vol. 87, No. 25, 1983
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TABLE I: Density, Viscosity, Diffusion Constant, Hard-Sphere Diameter for Liquid Me, Si,' the Enskog Collision Time, and the Experimental Vibrational Relaxation Time T, K 298
P, bar 1.0
323
348
373
a
P, g
'1,
CP
105D,cm2 s-l
1000 2000 3000 4000
0.640 0.731 0.778 0.812 0.839
0.21 4 0.584 1.101 1.868 2.989
3.92 1.62 0.877 0.507 0.329
50 1000 2000 3000 4000
0.621 0.714 0.764 0.800 0.829
0.160 0.451 0.826 1.350 2.067
5.87 2.22 1.153 0.752 0.503
50 1000 2000 3000 4000
0.594 0.701 0.753 0.789 0.818
0.138 0.367 0.651 1.025 1.532
6.99 2.97 1.72 1.07 0.737
50 1000 2000 3000 4000
0.564 0.689 0.743 0.780 0.809
0.106 0.308 0.534 0.835 1.221
9.24 3.65 2.05 1.39 0.972
Ps
u, A
73,
5.68
0.222 0.145 0.116 0.0983 0.0857
4.42 2.63 2.23 1.84 1.65
5.66
0.239 0.156 0.124 0.104 0.0902
3.85 2.65 2.08 1.75 1.60
5.64
0.266 0.165 0.130 0.110 0.096
3.56 2.41 1.99 1.81 1.56
5.63
0.296 0.170 0.133 0.112 0.098
3.63 2.27 1.91 1.65 1.47
TV,
PS
From ref 7 and 8.
1) ;JL; , I
I
29SK- I bar
0,5
0 547,4
!
5624
!
5824
607.4
590 0.5
,
627.4
647,4
FREQUENCY (cm' I
o f t h e center of line. These two findings are aiways"ob1 served a t all the temperatures investigated. In these figures, one can note also that the low-frequency side of the line shapes shows a very weak shoulder which is clearly apparent in the low-pressure spectra. In Figures 1and 2 we compare the experimental Raman spectra with the fitted line shape resulting from the addition of a simple Lorentzian line shape plus a constant background. It appears that the experimental line shapes are close to Lorentzian ones under all conditions investigated. The only small deviation is observed on the lowfrequency side of the low-pressure spectra and results from the very weak shoulder mentioned previously. We estimate its contribution by adjusting a second Lorentzian centered on this shoulder with the same fwhh as the fun-
0.6
I
I
0.7
0.8
p (g.
-1 0.9
Cm-3)
Figure 4. Isothermal density dependence of the peak frequency uo of the isotropic Raman band of the v3 mode of Me,Si in the temperature range 298-373 K.
Figure 3. Comparison of the experimental isotropic Raman band of the vg mode of Me,Si at 298 K, 1 bar and 373 K, 50 bar with the calculated profile including the hot band contribution (see the text for explanation).
Results We present in Figures 1 and 2 the isotropic Raman spectra associated with the u3 mode of MelSi a t the two extreme temperatures investigated, 298 and 313 K. The spectra recorded under two extreme values of the pressure are reported. One sees that a t constant temperature the increase of pressure leads to a broadening of the spectra
I
,
"I
'5 4
6
t
I
298K 0 323K o 34SK A 373K
0
4
2
p ( g , cm-' I
Figure 5. Isothermal density dependence of the experimental fwhh for the v3 mode of Me,Si in the temperature range 298-373 K.
damental. The result is given on Figure 3. We see that the comparison between the experimental and calculated profile is clearly improved. The fractional relative intensity of the shoulder to the u3 profile varies slightly with increasing temperature from 5% a t 298 K to 8% a t 373 K indicating that this shoulder might be attributed to a hot band. Nevertheless, one can conclude that this contribution is very small and the change of fwhh of the v3 profile at low pressure is less than 5%. At higher pressure (=lo00 bar) this correction does not lead to an appreciable change of the fwhh of the fundamental. One can also notice that
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The Journal of Physical Chemistry, Vol. 87,
No. 25, 1983
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I
O1
017
I
I
0.8
1
0
