MANDEL'STAM-BRILLOUIN LIGHT SCATTERING AND SOUND VELOCITY DISPERSION IN CRITICAL MIXTURES

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MANDEL’STAM-BRILLOUIN LIGHT SCATTERING AND SOUND VELOCITY DISPERSION IN

CRITICAL MIXTURES

I. Aref’Ev, I. Fabelinskii

To cite this version:

I. Aref’Ev, I. Fabelinskii. MANDEL’STAM-BRILLOUIN LIGHT SCATTERING AND SOUND VE- LOCITY DISPERSION IN CRITICAL MIXTURES. Journal de Physique Colloques, 1972, 33 (C1), pp.C1-131-C1-134. �10.1051/jphyscol:1972123�. �jpa-00214913�

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JOURNAL DE PHYSIQUE Colloque Cl, supplément au no 2-3, Tome 33, Février-Mars 1972, page Cl-131

MANDEL' STAIM-BRILLOUIN LIGHT SCATTERING AND SOUND VELOCITY DISPERSION IN CRITICAL MIXTURES

1. M. AREF'EV and S. L. FABELINSKII

P. N. Lebedev Physical Institute, U. S. S. R. Academy of Sciences, Moscow

Résumé. - Dans des composés liquides binaires, la diffusion Mandel'stam-Brillouin de la lumière a été étudiée dans le domaine critique de stratification. La vitesse des hypersons est déter- minée par mesure des positions des composantes Mandel'stam-Brillouin, cette vitesse est comparée avec celle des ultrasons. La dispersion de la vitesse du son est décelée. Les différentes causes de la dispersion de la vitesse du son sont indiquées ; parmi elles : l'augmentation de la viscosité de volume, un écart à la propagation adiabatique, l'apparition du régime non hydrodynamique de la propagation et d'autres causes.

Abstract. - The Mandel'stam-Brillouin light scattering was studied in binary liquid mixtures near the critical stratification point. The hypersound velocity was obtained from Mandel'stam- Brillouin component shifts and compared with the ultrasound velocity. The sound velocity dispersion was observed. The different mechanisms of sound velocity dispersion including volume viscosity growth, deflexion from adiabatic propagation, existence of non-hydrodynamic propagation regime are pointed out.

It is well known [l] that Mandel'stam-Brillouin (MB) light scattering spectra give an opportunity t o determine a hypersound velocity and attenuation in liquids at frequencies about 5 GHz, which are for the present inaccessible for direct acoustical measurements.

The investigations of high frequency sound propagation features near the critical stratification point of binary mixtures are carried out lately in Our labora- tory. The different factors can lead to the difference of the hypersound velocity from the low frequency sound velocity, in other words, to the sound velocity dispersion near the mixture critical point. For sound waves with wave vectors q such as gr,

>

1, (r,) - the radius of concentration fluctuation correlation) comes the nonhydrodynamic regime of sound propagation.

In this region one can expect the appreciable spatial sound velocity dispersion. In the region qr, < 1 the hypersound propagation may be described in terms of hydrodynamics. In this region the difference of the hypersound velocity from the low frequency sound velocity can be connected with the growth of volume viscosity, which always leads to the positive sound velocity dispersion.

The investigations of the sound velocity dispersion in mixtures under usual conditions showed that in mixtures, with the maximum of ultrasound absorption in dependence of concentration, the maximum of the sound velocity dispersion was observed [2], and in mixtures, with the minimum in the concentration dependence of ultrasound absorption, the minimum

of the sound velocity dispersion was observed [3].

Thus, it was found that the sound velocity dispersion followed the ultrasound absorption. This result may be easily understood from the point of view of a simple relaxation theory of sound propagation if one assumes that the time of volume viscosity relaxation does not change essentially.

Near the mixture critical point the sound absorption increases owing to the volume viscosity growth. As a result one can expect an increase of the positive sound velocity dispersion. Indeed, one of the authors in triethylamine-water mixture observed the hypersound velocity dispersion relative to the sound velocity at the frequency 0.6 MHz which was equal to

-

¹⁵

^%

^[4].

Apparently this dispersion was mainly due to the volume viscosity growth.

In other mixtures being investigated the sound absorption is by two orders smaller than that in the triethylamine-water system. Therefore the contribution of volume viscosity relaxation to the sound velocity dispersion in these systems is not so large and one can expect a display of other dispersion mechanisms.

Chen and Polonsky [5], Shilin and one of the authors 161 in nitrobenzene-normal hexane mixture and Anisimov, Voronel', Voronov, Kiyachenko and the authors 171 in nitroethane-isooctan mixture near the critical stratification temperature t, observed a decrease of the hypersound velocity. The comparison with ultrasound data in this temperature interval have led to negative sound velocity dispersion.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972123

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Cl-132 1. M. AREF'EV AND I. L. FABELINSKII The decrease of the hypersound velocity may be

connected with its nonadiabatic propagation. It is known [SI, that in pure liquids at frequencies

where (dP/Bp), is the adiabatic compressibility, ^J;is the thermal conductivity, p is the density and C, is the specific heat at the constant volume, the sound becomes isothermal. The estimates give

w

*

-

1012 H z . 2 n

Near the critical point X increases and o* decreases.

The similar situation may occur in mixtures owing to a divergence of heat and mass transport coefficients.

At the nonadiabatic propagation the sound velocity always decreases.

Although the characteristic frequencies for total transition in nonadiabatic sound propagation are not achieved in experiments, the deflexion from the adiabatic propagation can lead to a decrease of the sound velocity dispersion by a value of

-

¹

^%

^{171. The}

decrease of the measured hypersound velocity and the appearance of the seeming negative sound velocity dispersion, connected with this fact, may be caused by reasons, which rnay be named methodical ones, - these are an influence of the hypersound absorption on the MB component position and an effect of gravity [6].

The account given above will be now illustrated by experimental results which we have recently obtained in the teamwork with Professor Voronel, Doctor Anisimov and coworkers [7]. The MB scattering in the critical region of nitroethane-isooctan mixture with nitroethane concentration 0,4 mole fraction (m. f.) was studied. This mixture has an upper critical strati- fication point with t, = 30.95 f 0.05 OC. In this system the refractive indices of the components differ at the fourth sign after the point. This means, that in this mixture the concentration scattering is very small ; there is practically no opalescence in the critical point, which leads to an increase of an error in the ME component position measurements, there is no multiple light scattering which leads to a boardening of the spectrum. 1. e. in this system the ME component position is defined in the critical region with the same accuracy as out of the critical region (Fig. 1).

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FIG. 1. - Rayleigh line fine structure spectra in nitroethane- isooctan mixture at temperatures : (a) t = tc & 0.05O and (6) t = tc f 6.1°. Interferorneter spectral range is 0.5 cm-*.

In this experiment, except tlie Ne-He laser, we used also Cd114-He laser, radiating the light with the wave length Â. = 4 416

A.

It gave us an opportunity to fulfil measurements of the hypersound velocity at frequencies more than 7 GHz. The temperature of the mixture was measured anil kept up constant with the accuracy better than 0.001 OC. The scattering volume was in an immediate proximity to the stratification boundary (in the lower phase) to except the appreciable deflexion of the concentration from its critical value due to the effect of gravity 161.

Figure 2 (a and b) shows the temperature behaviour of the MB component shift Liv for two values of q :

~2 x IO5 cm- l (the scattering angle 8 = 900, exciting by the Ne-He laser, Â = 6 328 A) and

-

⁴^x^{IO5 cm-'}

(0 = 1 5 3 O , = 4 416

A).

Tlie hypersound velocity

FIG. 2. - MB component shift Av near the critical point of nitroethane-isooctan mixture at wave vectors of scattering fluctua- tions (a)

-

²^x^10s^{cm-1 and}^(/!)

-

⁴^x¹⁰⁵cm-1. Points,

circles and crosses show different series of measurements.

values V,, calculated from these data, are given in figure 3. The temperature dependence of ultrasound velocity Vu at frequency 10 MHz is given in this figure as well.

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MANDEL'STAM-BRILLOUIN LIGHT SCATTERING Cl-133

FIG. 3.

-

Velocity of hypersound with q Z 2 x 10s cm-1 (points) and q ^E4 X 105 cm-1 (circles) and velocity of ultrasound (solid curves) near the critical point of nitroethane-

isooctan mixture.

Figure 4 shows the temperature dependence of the hypersound velocity change relative to ultrasound data

FIG. 4. -Dispersion of hypersound velocity relative to ultrasound velocity in the region of the critical point of nitroethane-

isooctan mixture.

For q

=

2 x IO5 cm-' the dispersion A V / V , first slightly increases at approaching t, from homogeneous phase. This increase may be attributed to the volume viscosity growth. At (t - t,)

-

10 AV/Vu begins to decrease. This decrease may be explained by a decrease of the characteristic frequency of volume viscosity relaxation, by an influence of hypersound damping on the MB component shift and by a deflexion from the adiabatic propagation. The combination of the two last factors causes, from Our point of view, the negative sound velocity dispersion near t,.

The data for q

=

4 x IO5 cm-' are significantly more scattered but as a whole they repeat the previous picture with the exception of the region

1

t - t,

1 <

^0.2O,

where the increase of the sound velocity dispersion is observed. In this region r,

2

200

k

and qr, >, 1. 1. e.

this is a region of the nonhydrodynamic sound propagation.

For q

=

2 x IO5 cm-' the region gr, 2 1 lies in the interval

1

t - t,

1 <

0.050, which is inside of the temperature step in the experiment figure 4. The small-scale temperature measurements proved to be unexpedient because of heating of the scattering volume by the laser beam [7].

The quantitative interpretation of the experimental data meets difficulties because of the lower accuracy of the measurements relative to the effect values. The accuracy of hypersound velocity measurements is especially low in the mixtures with strong opalescence.

Biryukov and one of the authors [9] showed that in this case may be the stimulated MB scattering (SMBS) would be useful. It is obvious that with SMBS the MB component position near t, is measured with the same accuracy as far from t,.

Figure 5 shows the MB component shifts in the spectra of the thermal and stimulated scattering near the critical point of nitrobenzene-normal hexane mixture. The increase of SMBS component shift relative to the thermal MB scattering (TMBS) data,

FIG. 5. - Shift of SMBS components in mixture of 0.4 m. f.

nitrobenzene in normal hexane near t e (points). The dotted curve-shift of TMBS components in the same mixture fitted to

0 = 180° and ruby laser frequency.

being observed near t,, may be partially explained by the absence of the systematic error in the SMBS component shift measurements appearing in the TMBS spectra as a result of strong scattering on the unshifted frequency.

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1. M. AREF'EV AND 1. L. FABELINSKII

[ l ] FABELINSKII (1. L.), Molecular Scattering of Light, Plenum Press, New York, 1968.

[2] AREF'EV (1. M.), STARUNOV (V. S.), FABELINSKII (1. L.), Sov. Phys. JETP Letters, 1967, 6,677.

[3] AREF'EV (1. M.), ZAITSEV (G. I.), KRIVOKHIZHA (S. V.), OZHOGIN (Ya. P.), SCHREINER (V. Ya.), Sov.

Phys. Short Physical Commuizications, 1970,7, 37.

[4] AREF'EV (1. M.), SOV. Phys. JETP Letters, 1969,7, 361.

[5] CHEN (S. H.), POLONSKY (N.), Phys. Rev. Letfers, 1968, 20, 909.

[6] AREF'EV (1. M.), SHILIN (N. V.), SOV. Phys. JETP Letters, 1969, 10, 138.

[7] ANISIMOV (M. A.), AREF'EV (1. M.) VORONEL' (A. V.), VORONOV (V. P.), KIYACHENKO (Yu. F.), FABE-

LINSKII (1. L.), SOV. Phys. JETP, 1971, 61, 1526.

[8] LANDAU (L. D.), LIFSCHITZ (E. M.), Fluid Mechanics, Addison-Wesley Publishing Company Reading Mass., 1959.

[9] AREF'EV (1. M.), BIRWKOV O/. N.), SOV. Phys. JETP Letters, 1970, 12, 352.