Brillouin linewidth

Brillouin scattering of laser light in liquids has been studied by several authors. Shapiro etal. 233) measured hypersonic velocities in various liquids and obtained a Brillouin linewidth of 0.011 cm" in methylene chloride but of less than 0.002 cm in benzene, carbon disulfide and chloroform. The broadening of the Brillouin components arises from damping of thermal phonons and is closely connected with the viscosity coefficient of the medium. From the measured linewidths, the lifetimes of the phonons responsible for Brillouin scattering at 89 45 were calculated to be 4.8 x 10 sec for methylene chloride and 7.6 x 10 sec for toluene. 

Typical Brillouin splittings are in the range 108-1010 Hz. Brillouin linewidths are in the range 166-109 Hz. Thus, a very high resolution instrument is required. Brillouin scattering is a weak effect so that an intense source of light is needed and a sensitive means of detection. All of these criteria have been met, and Brillouin scattering is now a routine tool of experimental physics (13). 

The Brillouin linewidth Td) depends on the dynamic shear and volume viscosities r s(w) and t v(w). If the hypersonic shear viscosity r s(Aa)(i)) is equal to the zero frequency shear viscosity and the small term caused by thermal conductivity is neglected, then measurements of Td) can be used to obtain the volume viscosity. Champion and Jackson (8) noticed that the volume viscosities determined in the above manner for the n-alkanes were essentially independent of temperature. The values of r(i) measured in the authors laboratory for n-hexadecane are plotted... 

Figure 5. Longitudinal Brillouin linewidth for n-hexadecane vs temperature. Also plotted are the part of the linewidth owing to shear viscosity Tg = [2q rfJo)]/3p and the part caused by volume viscosity calculated as...

As a liquid is cooled, the values of Mo, Mj, and tj increase. If the longitudinal Brillouin linewidth were given by Equation 16, F(d would broaden and eventually exceed Awd). If we consider only a single struc-... 

PMMA by weight at its T(g) = 20°C is shown in Figure 16. The sharp peaks confirm that the sample is a homogeneous amorphous mixture. Measurements of the Brillouin linewidth are a sensitive measure of the homogeneity of the sample. 

Brillouin scattering from the nematic (racemic) lyotropic polymer poly-y-benzyl glutamate (PBG) shows a significant anisotropy in both the sound velocity (22%) and the Brillouin linewidth (40%) in the solutions [22], when measurements are made at different angles with respect to the nematic director. Figure 4 shows typical Brillouin spectra of PBG as a function of scattering angle. This work indicates the importance of elastic relaxations due to concentration fluctuations in these nematic polymeric materials. 

Experimental data of Gibson and Sibener appears to confirm qualitatively these predictions at least for monolayers. The phonon linewidths were broadened around T up to half of the Brillouin zone. The hybridization splitting could not be resolved, but an increase of the inelastic transition probability centered around the crossing with the Rayleigh wave and extending up to 3/4 of the zone has been observed and attributed to a resonance between the adatom and substrate modes. 

In interpreting the hypersonic data of this kind one should keep in mind the connection of sound velocity to the elastic moduli of the medium. At the high frequency involved in Brillouin scattering, the frequency dependence of these moduli is important. The Brillouin shift and linewidth depend on the real and the imaginary parts of the complex longitudinal modulus M( w ) repec-tively (11). The longitudinal modulus is connected to the compres-sional modulus K(w) and to the transversal modulus G( w ) by the equation ... 

The quantity K is the static modulus of compression, S and T are the correspSnding relaxation amplitudes. These equations describe the frequency dependence of the moduli in a liquid in nfhich a single relaxation process is effective, characterized by the shear and the bulk relaxation times X 3f,and x and the corresponding amplitudes T and S. If there are more relaxation pro -cesses, we sum over their respective contributions. The connection between the elastic moduli and the Brillouin shift and linewidth is given by the two equations for the real and the imaginary part of the longitudinal modulus as a function of the frequency ... 

Fig.5 Dispersion of the Brillouin shift f and linewidth To i or the two pentanediols as a function or temperature...

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