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RAYLEIGH AND BRILLOUIN SCATTERING IN LIQUID AND GASESBRILLOUIN SCATTERING IN
ORDINARY LIQUIDS
W. Low
To cite this version:
W. Low. RAYLEIGH AND BRILLOUIN SCATTERING IN LIQUID AND GASESBRILLOUIN
SCATTERING IN ORDINARY LIQUIDS. Journal de Physique Colloques, 1972, 33 (C1), pp.C1-1-
C1-5. �10.1051/jphyscol:1972101�. �jpa-00214891�
IN LIQUID AND GASES
BRILLOUIN SCATTERING IN ORDINARY LIQUIDS
W. LOW
Microwave Division, The Racah Institute of Physics, The Hebrew University, Jerusalem, Israel
R6sum6.
-On presente les resultats de la diffusion Brillouin dans trois systkmes liquides.
1) Vitesse de phase
vet attknuation
ades hypersons dans de l'eau de diverses constitutions iso- topiques. On montre qu'on ne peut pas rendre compte du rapport
v/apour H20, DzO et Hz018 dans la plupart des theories de la structure de I'eau.
2)
Mesures de
uet
apour le benzkne dans la region de dispersion. On a mesure la forme de raie pour le benzene. On a trouve qu'on ne peut pas rendre compte
8la fois de
vet de
apour les basses et hautes frequences en se servant d'un ou de deux temps de relaxation. On prksente des expli- cations possibles de ces deviations.
3)
On prksente la diffusion Brillouin dans ZnS04 et dans MnS04. On compare les resultats obtenus ainsi a ceux que Yon dkduit de la diffusion Rayleigh.
On decrit le montage experimental de la technique des phonons injectts.
Abstract. - Results of Brillouin Scattering on three liquid systems are reported.
1) Phase velocity
vand attenuation
aof hypersound in water of different isotopic constitution.
It is shown that the ratio of
vand
afor H20, D2O and Hz018 cannot be accounted for by most theories of the structure of water.
2)
Measurements of
vand
aon benzene in the dispersion region. The line shape of benzene has been measured. It was found that one cannot fit
vand
asimultaneously from low to high frequency data using one or two relaxation times. Possible explanations for these deviations are reported.
3)
Brillouin scattering on ZnS04 and on MnS04 are reported. Results are compared with those on Rayleigh scattering.
The experimental arrangement of the injected phonon technique is described.
I. Introduction.
-The development of new tech- niques in Brillouin scattering has increased the activity in the study of hypersound propagation in liquids. Attempts were made to connect the experi- mental results in the measurements of the sound velocity v and the sound attenuation a with current theories of the liquid state. In a number of liquids relaxation phenomena were found. It is not always easy, however, to establish a simple relationship between relaxation phenomena and the structural phenomena underlying theories of the liquid state.
There have been, in general, two approaches to the theory of liquids. In one theory the liquid is treated as an extension of gas. This thermodynamic treatment involves macroscopic quantities such as the viscosity, specific heats and collision frequencies. This yields simple expressions for the real and imaginary quantities that are proportional to the sound velocity and atte- nuation. Another theory increases the knowledge of the solid state, by introducing disorder through break- ing of bonds and jumping through potenitial barriers.
This results in frequency dependent bulk and shear viscosities, as well as other mechanical macroscopic quantities.
The study here reported, deals with different liquids. In nearly all cases it is found that the theories are too crude and that the approximations are either invalid or unsatisfactory. It is likely that most liquids do not conform to either of the two models, i. e. are not a simple perturbation of the gaseous or solid state.
Brillouin scattering, the study of the propagation of hypersound in liquids, is only one of the tools in the study of liquids. Its importance lies mainly in that it extends our knowledge into the gigahertz region, a region in which some of the microscopic properties of matter are beginning to be felt.
This study will deal with Brillouin scattering in water, in benzene, in chemical reacting liquids and binary liquids.
11. Phase velocity and attenuation of water.
-Water is an associated liquid. Its relaxation lies on the region of lo-'' to 10-l2 S, much higher than the usual operating frequencies. The acoustic attenuation a at ultrasound is much larger than that predicted from classical considerations (a,,,,,). Hall [I] developed a theory based on a model of Bernal and Fowler [2]
in which he assumes that water consists of two struc-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972101
Cl-2 W. LOW
TABLE I
Phase velocity v for H
20 , D
20 and H
20
1 8T Frequency n
2(index of Density p
bvp
YlSubstance (°C) (GHz) i>(m/s) refraction) (10
3kg/m
3) 10
4(kg/m-s
2)
I/2H
20 23 4.41 1 485 ± 10 1.331 5 0.9971 4.69
D
20 23 4.09 1375 + 8 1.327 0 1.107 37 4.57
H
20
1 823 4.14 1390 ± 8 1.332 0 1.113 4 4.64
tural forms, with a potential barrier of AE between the two minima. The resulting relaxation time is then a function of the height AE. This, in turn, will determine the temperature and frequency dependence of macro- scopic quantities, such as the viscosity. The theory has been criticized by Litowitz and E. H. Carne- vale [3].
We have measured the sound velocity, using spon- taneous Brillouin scattering techniques, and the attenuation, with an injected phonon scattering tech- nique, for different isotopic constitutions of water.
The main reason for measuring on water with diffe- rent isotopes is that a priori calculations of a are difficult but it may not be so difficult to calculate the ratio of attenuation for water with two isotopic constituents. Some of the microscopic quantities are only slightly dependent on the different isotopic constitution.
Assuming that water can be regarded as an extension of ice, a solid, the acoustic attenuation can be written as
\2p
0vl' L\ 3 / C
pJ
where co is the applied frequency p
0the density at zero frequency v
0the velocity of sound
t]
cthe shear viscosity n
sthe dilatational viscosity
K
tcoefficient of thermal conductivity C
pspecific heat at constant pressure.
For water (y - 1) KJC
Pis small and hence
" - ( V ^ T ) " (2)
\2 p
0vp
where the relaxation effects are contained in n.
F o r two isotopes 1 and 2
Similarly the phase velocities can be obtained.
Figure 1 shows a typical Brillouin triplet from which the phase velocity is determined. In Tables I and II, the experimental results of v and a for H
20 , H
20
1 8, and D
20 are listed.
FIG. 1. — Brillouin doubled in D20. The central line is the Rayleigh line.
TABLE II
Attenuation coefficient afar H
20 , D
20 , and H
20
1 8Frequency
T (GHz) a 10
17a//
2Substance (°C) / (cm"
1) (cm"
1s
2)
H
20 25 0.90 178 ± 3 22.0 ± 0.4
D
20 25 0.90 222 + 4 27.4 + 0.5
H
20
1 825 0.90 201 + 4 25.0 + 0.5
These data have to be compared with a model. The ratio of the macroscopic viscosities H20, D 2 0 is 0.83 + 0.02 which is very different from 0.70, the computed value. Hence, a classical theory cannot account for this. Similarly, from classical considera- tion, one would expect the v2 a yK,/p. Hence, v2 p is expected to be a constant, since K, differs only slightly for H 2 0 and D 2 0 . The values seen in table I indicate again that classical theories are invalid.
This is seen even more drastically if one considers the ratio of
a in our frequency range is proportional to
yor to the product of z and Ks, the adiabatic compressibility.
Such large changes must be attributed to changes in z. i. e.
zD 2 0 >
zH,OL8 > z H 2 0 .
In the potential well model this means that the well is deeper for D 2 0 than for H20. This is consistent with a number of theories of water, such as that of Fors- lind
[4].The results on H2018 are somewhat surprising since they suggest a deeper potential well and stronger hydrogen bonding. Further work for different isotopic constituents and for different temperatures is being planned.
III. Measurements of the phase velocity and atte- nuation in benzene.
-The unusually large attenua- tion which Benzene has, is not completely understood.
There is a relaxation in the neighbourhood of 600 Mc/s.
Nichols et al. [5] have reviewed all the experimental evidence and have concluded that a two relaxation theory with additional relaxation above 1 GHz can account for the experimental data. The low frequency relaxation is attributed to the vibrational specific heats, except for the lowest vibrational mode which is presumably the cause for the high frequency rela- xation.
We have performed precision measurements in the 600-1 000 Mc/s range [6]. In the method described below we measure, by means of the injected phonon Brillouin scattering technique, the spatial decay of the phonons. The Fourier transform is then expected to be Lorentzian. In figure 2 we show the line shape. The Lorentzian shape is clearly established even down to the wings.
ANGLE
FIG. 2. -Line shape of Brillouin line of benzene. The line is pure Lorentzian.
The linewidth gives directly the attenuation to an accuracy better than 5 %. Figure 3 and figure 4 show the calculated group and phase velocities, the calcu- lated a/f2 with the experimental results.
/-- 1
FIG. 3. - Calculated phase and group velocities as a function of the frequency. The experimental points are indicated.
000 I I 1 1 , 1 1 1 1
0 01
FREQUENCY (GHZ) 10
FIG. 4.
-
Calculated attenuation a/f as a function of the frequency with experimental points. The experimental points are taken from many authors and are listed in reference 6 .We have attempted to find the dispersion of the velocity and the attenuation by simulating computer fitted curves with one, two or three relaxation fre- quencies. It was not possible to fit simultaneously both curves over the whole frequency region.
A number of possible conclusions can be drawn from this
:a) The theory is not complete.
b) The low frequency data do not present the whole story. There may be some low frequency relaxation effects. These may give an additional contribution to the specific heat. A possible mechanism may be intermolecular ordering, such as stacking of benzene molecules.
c) The high frequency data, in particular in the
2-5 GHz region, may be in need of re-evaluation.
C1-4 W. LOW
It is clear from the above that a simple system, such as benzene, which should be accounted for by a thermal relaxation theory, still awaits a solution.
EV. Chemical reactions by means of BriIIonin scatte- ring. - Tamm and Kurtzt: [7] have measured sound absorption in the frequency region from 10, to lo9 Hz for MnSO, and ZnSO,. Recently Yeh and Keeler [8] measured the polarized Rayleigh linewidth using light scattering techniques. From their measu- rements they inferred the time constant of the reaction
Their data are consistent with Tamm's ultrasonic relaxation spectroscopy.
We have measured the attenuation at about 900 Mc/s for 0.1 M ZnSO, and MnSO,. This fre- quency is outside the main relaxation region. The attenuation is small and the difference between the attenuation of water and the electrolytic solution is small as well. No definite conclusions can be drawn except that our data are consistent with those obtained by Tamm et
a!.However, our measurements indicate their usefulness for chemical reactions with time constants of lo-" s, in which the theories of Berne and Frisch [9] as well as Blum and Salsburg [lo]
can be tested.
Finally we would like to report preliminary measu- rements by D. Sarid on binary mixtures of Kneser liquids in the relaxation region. The theory of unasso- diated liquid mixtures has been tested outside the dispersion region [l 11. Sarid measured the attenua- tion of mixtures of benzene and cyclohexane. Assum- ing one dominant relaxation frequency of benzene and assuming an effective vibrational contribution to the specific heats at 500-1 000 MHz range, he could extend the ordinary theory and show that the data can be fitted, as seen in the following Table 111.
af for binary benzene-cyclohexane mixtures
V. Experimental techniques. -- Two experimental techniques were employed. The velocity of sound and the attenuation at frequencies higher than 2 GHz were measured with a piezoe1ec:tric scanned Fabry- Perot interferometer of a very great finesse. The detection system was a simple photon counting system.
The other technique used the injected phonon technique developed by Gordon and Cohen [13].
In this technique, sound at high frequency is injected through a ZnO transducer into the liquid. The phonon decay is equivalent to a spread in AO, the change in angle of the scattered light. The center angle
8,the angle of the Brillouin scattered light, determines the velocity of the sound. The spread A9 gives a direct measure of the decay distance and, therefore, of the attenuation constant a.
The detection system uses a superheterodyne technique with a square law detector. On this detector fall both the light scattered and the transmitted beam, properly attenuated as the local oscillator. The microwave frequency angle is homodyned in turn with the CW microwave oscillator used to drive the transducer. The output is detected by means of a phase sensitive detector synchronous with the fre- quency of the chopped laser light beam. The angular width
A8is determined by rotating the turntable and measuring the line shape and linewidth of the output as a function of 8.
The advantages of this method are as follows
:1) Increased signal to noise ratio, which is achieved because a la~gt: number of coherent phonons are injected into the sample.
2) The resolution is mainly limited by the diffrac- tion pattern of the acoustic beam. This can be reduced to about 1 MHz. Hence, in most cases, there is no large instrumental linewidth, and no convolution calculations have to be made.
3) Attenuation and velocity are determined as a function off, the frequency, rather than 1, the wave- length. The disadvantage is that for large f the atte- nuation may become very large and the angular spread correspondingly large. Therefore:, the signal to noise ratio may not be sufficiently big to obtain good line shapes and hence the accuracy in a may be small.
Acknowledgement. - A large fraction of this work was carried out by Dr J. Shaha:m, Mr. D. Sarid and Dr. S. Sussman, some of it as part of their research theses.
References
[I] HALL (L.), Phys.
Rev., 1948,73,775. [31LITOVITZ (T.
A.)and CARNEVALE (E. H.), J. Appl.
[2]
BERNAL
(J.)and FOWLER (R.), J. Chem. Phys.,
1933,Phys.,
1955,26,816.1,515. 141
FORSLIND (E.), Acta Polytech.,
1952, 115,9 .
See also KAVANU
(J.L.), Structure and Function in Biological Membranes, Holden Day Inc., San Francisco, Cal.
171, 1965.151
NICHOLS (W. H.), KUNSITIS-SWYT (C. R.) and SINGAL (S. P.),
J.Chem. Phys.,
1969, 51, 5659.161
Low (W.), SARID (D.), SUSSMAN (S.),
J.Chem. Phys.
(in press). This paper summarizes the experimental data from other sources as well.
171
TAMM (K.), KURTZE (G.), Acustica,
1954, 4, 380.KURTZE
(G.) and TAMM(K.),
Ibid., 1953, 3, 33.[8]
YEH
(Y.)and KEELER (R.
N.), J.Chem. Phys.,
1969, 51,1120.[9]
BERNE (B.
J.) and FRISCH(H. L.),
J.Chem. Phys.,
1967, 47, 3675.[lo] BLUM
(L.) and SALSBURG(Z. W.),
J.Chem. Phys.,
1968,48,2292and
1969,50,1654.[ l l ]
SETTE
(D.),Acoustics
I,Handbook der Physik (S.
Flugge, Ed.),
X111, Springer Berlin, 1961.[12]
ILGMAS
(V.), PAULANSKAS(K.), TAMASHAUSKAZ (A.), Soviet Physics Acoustics,
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