Rayleigh-Brillouin Spectra Research Articles

Rayleigh–Brillouin scattering of transverse and longitudinal acoustic waves in a supercooled viscoelastic liquid

Rayleigh–Brillouin spectra of 3-phenyl propanol are studied over the temperature range from −119.5° to 98.1 °C. The orientation relaxation time is obtained as a function of temperature. The depolarized spectra exhibit clear shear wave sidebands at temperatures below −29.5 °C. The polarized spectra give peaks due to the longitudinal acoustic wave whose frequency displays kinks at the glass transition temperature and at 37 °C (Tk). Tk is 55 °C above the melting temperature (−18 °C). The shear wave frequency decreases linearly with increasing temperature. The experimental results on the VH scattering spectra are analyzed according to viscoelastic theories based upon the Voigt and Maxwell models. Comparison of the theory with observed spectra shows that the Voigt model gives a better fit to the experimental data. Microscopic theory has also been developed to derive the Voigt and Maxwell models. Angular dependent studies are proposed to differentiate the various theories which give different predictions about the physical nature of the parameters.

Rayleigh–Brillouin spectroscopy of n-tetracosane. Are there transitions in the melt?

It has recently been suggested that a mesomorphic transition in the melt of n-tetracosane can be detected using Brillouin scattering. In the present paper we report measurements of both the longitudinal Rayleigh–Brillouin spectrum and the depolarized Rayleigh spectrum as a function of temperature from the melting point to 240 °C. The spectra are discussed in detail and it is shown conclusively that the light-scattering results are inconsistent with the existence of a mesomorphic transition above the melting point of n-tetracosane.

The effect of the membrane compression wave on the light scattering spectrum from a protein monomer-dimer equilibrium

The membrane compression wave on the Rayleigh-Brillouin spectrum of a solution of protein in a monomer-timer equilibrium has been calculated. When the frequency of the longitudinal wave is slow compared to the monomer-dimer exchange frequency the compaction wave produces an asymmetry in the spectrum. The asymmetry is small and may be undetectable in the experimental spectra. If the frequency of the compression wave is high compared to the exchange rate then new bands will appear in the experimental spectra. The amplitude and shift of these peaks are related to the amplitude and frequency of the longitudinal wave, respectively. The bands due to the compression wave in this limit should be detectable in the experimental spectrum. Fitting of the experimental spectrum to the form calculated below will yield valuable information about the membrane compression wave.

LOW FREQUENCY LIGHT SCATTERING SPECTRA OF AgI

The Rayleigh-Brillouin spectra of α- and β-AgI have been measured with a Fabry-Perot interferometer in a back scattering geometry. The longitudinal acoustic phonon frequency in the β-phase gradually decreases with increasing temperature from 17.4 GHz at room temperature to 16 GHz just below the transition. At the transition temperature (145°C) the frequency of the LA-mode shifts suddenly to 13.5 GHz, and thereafter it remains independent of temperature. No peak corresponding to the TA phonon was observed. A broad peak was observed in the frequency region near 27 GHz where a conductivity anomaly was found by earlier infrared reflectivity measurements.

Light-scattering studies of moderately dense gas mixtures: Hydrodynamic regime

Measurements of the Rayleigh-Brillouin spectra of light scattered by two classes of gaseous mixture; helium-xenon, and helium-hydrogen and helium-deuterium, have been performed over a range of density, concentration, and wave vectors. For He-Xe mixtures, under certain experimental conditions the data are accurately accounted for by a complete two-component hydrodynamic theory and light scattering has been shown to be a good method to deduce the thermal diffusion coefficient. We have thus determined in a quantitative way the range of applicability of the hydrodynamic theory. On the other hand, when the partial desnity of helium is not too small, systematic deviations between experimental and the calculated spectra are observed. These deviations can be understood in terms of kinetic effects to be discussed in a subsequent paper. For He-${\mathrm{H}}_{2}$ and He-${\mathrm{D}}_{2}$ mixtures, the hydrodynamic theory is in good agreement with our experimental data in the full range of densities and concentrations. We discuss the reason for this different behavior for the two classes of mixtures.

Comment on "Comparison of the Rayleigh-Brillouin spectrum of He, Ne, and Ar with a generalized Enskog theory"

A discrepancy between the hydrodynamic limit for the Brillouin spectrum in a low to moderately dense gas and that calculated from a kinetic model of the generalized Enskog equation is removed.Received 26 February 1981DOI:https://doi.org/10.1103/PhysRevA.24.1132©1981 American Physical Society

Rayleigh–Brillouin spectra of polymer fluids: Polyphenylmethyl siloxane and polydimethylphenylmethyl siloxane

Measurements of Rayleigh–Brillouin spectra of polyphenylmethyl siloxane (A) and of polydimethylphenylmethyl siloxane (B) over a wide range of temperatures (270 to 520 K for A; 280 to 390 K for B) are reported. By using the generalized hydrodynamic theory for Rayleigh–Brillouin spectra as developed by Lin and Wang, we have determined the relaxation strength R, the relaxation rate t, the activation energy Ea, and the adiabatic sound frequency ws (T), which are the characteristic physical quantities describing the dynamics of a viscoelastic polymer fluid in the GHz region. Based on those parameters, we were able to obtain excellent agreement between the theoretical and the measured spectra.

Depolarized Rayleigh-Brillouin scattering of shear waves and molecular reorientation in a viscoelastic liquid

A microscopic theory of depolarized Rayleigh-Brillouin spectra for viscoelastic liquids is developed. The theory takes into account the oscillation as well as relaxation of shear modes which couple to the polarizability density in a rotationally isotropic system. The experimental results of liquid and supercooled liquid salol have been analysed using the present theoretical result. Not only the detailed lineshape of the spectra at all temperatures can be interpreted consistently using one equation, the temperature dependence of the intensity ratio of the central component to the shifted shear mode side bands can also be accounted for. It is expected that this theory is applicable to the interpretation of depolarized Rayleigh spectra of supercooled liquids or glasses consisting of optically anisotropic molecules.

Comparison of the Rayleigh-Brillouin spectrum of He, Ne, and Ar with a generalized Enskog theory

The generalized Enskog model solution of Furtado et al. for the Brillouin spectrum $S(q,\ensuremath{\omega})$ is compared with the experimental results for compressed He, Ne, and Ar. A discrepancy between the two which localizes around the Brillouin component at high densities is found. It is also noted that the calculated spectrum disagrees with the equivalent curve for pure hydrodynamics at high densities and with an equivalent-model solution of the Boltzmann equation at low densities.

Rayleigh-Brillouin spectrum of compressed He, Ne, and Ar. II. The hydrodynamic region

The Rayleigh-Brillouin spectra of He, Ne, and Ar are reported for the hydrodynamic region. The experiments show that light scattering may be used to determine thermodynamic and transport properties of gases as a function of density and thus provide another method of probing intermolecular potentials. In addition, the transition from the hydrodynamic to the kinetic regime is examined in terms of generalized hydrodynamics.

Rayleigh-Brillouin spectrum of compressed He, Ne, and Ar. I. Scaling

The Rayleigh-Brillouin spectrum of He, Ne, and Ar is reported for 90\ifmmode^\circ\else\textdegree\fi{} scattering at a number of densities spanning the kinetic and hydrodynamic regime. A purely experimental test of scaling is made and it is found that deviations from scaling at high density can be attributed to mean-field effects. At low densities there is evidence that deviations from scaling, which arise from the detailed dependence of the spectrum on the intermolecular potential, are detectable at the few percent level. Some insight into scaling is obtained by comparing the results at low densities with curves predicted from a $3E$ kinetic model and from hydrodynamic theory.

Theory of depolarized Rayleigh–Brillouin spectra and rotation–translation coupling in molecular liquids and solids

The dynamics of translations and rotations of molecular solids and liquids has been studied by using a microscopic theory. The effects of translation–rotation coupling on the depolarized Rayleigh–Brillouin spectrum are investigated in detail. The theory takes into account anharmonicity and thus includes both the static and the dynamic couplings. In the limit of the harmonic approximation, the present theory reduces to the earlier published result for solids. The earlier published result for ideal liquids can also be derived from the present theory. This calculation is based on linear response theory and thus provides a statistical mechanical deviation of the phenomenological theory of the depolarized Rayleigh scattering spectrum of condensed matter. The relations between the transport coefficients as well as the potential and coupling constants in the macroscopic theory and the kinetic coefficients in the microscopic theory are established. The correlation function for the lattice displacement derived from solving the macroscopic equation is shown to be in agreement with the microscopic theory. It is shown, however, that the phenomenological theory does not provide the same polarizability correlation function for solids as that obtained from microscopic theory, despite the fact that the two theories agree in the case of liquids. The effects of relaxation and resonance behavior of the depolarized Rayleigh–Brillouin spectral density are also discussed in detail.

Rayleigh–Brillouin scattering and structural relaxation of a viscoelastic liquid

The linear response theory using a complete set of dynamic variables involving density, velocity, and energy fluctuations is used to analyze the Rayleigh–Brillouin spectrum of a viscoelastic liquid. The result is discussed in the fast and slow relaxation limits. In the former case, the Rayleigh–Brillouin spectrum is identical to that predicted by the classical hydrodynamic equations; whereas in the latter case a new structural central peak is found, in addition to the anomalous dispersion and relaxation effects present in the frequency and linewidth data associated with the Brillouin peak. The evolution of structural relaxation and its effect on the entire Rayleigh–Brillouin spectrum is described. The structural central peak is most pronounced when the frequency dispersion and the linewidth maximum are present. The theoretical result has been used to calculate the Rayleigh–Brillouin spectra of polypropylene glycol at various temperatures. The results of the frequency shift, the spectral linewidth, and the Landau–Placzek ratio are in good agreement with the experiment.

Rayleigh-Brillouin spectra of the solid electrolyte RbAg4I5

The low-frequency Raman spectra and the Rayleigh-Brillouin spectra of the crystalline electrolyte, rubidium silver iodide have been measured. At 90\ifmmode^\circ\else\textdegree\fi{}C the longitudinal-acoustical phonon was observed by Brillouin scattering with a triply-passed Fabry-Perot interferometer to have a frequency consistent with known and measured physical properties of the crystal. The absolute intensity was compared with that of fused silica, yielding a value for the Rayleigh ratio of 2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and for the Pockels' coefficient of 0.15. The Brillouin linewidth was instrumental and less than 0.3 GHz. The Rayleigh-Brillouin spectra were dominated by an intense Rayleigh peak of width less than 10 MHz and Rayleigh ratio of 0.14 ${\mathrm{cm}}^{\ensuremath{-}1}$. Removal of this feature with an iodine filter revealed a dynamic central peak wider than the 350-MHz half-width of the filter. Analysis and comparison between data from an interferometer and a double monochromator lead to the conclusion that the central peak may be described as a sum of two Lorentzians. The narrower peak has a half-width of roughly 9\ifmmode\pm\else\textpm\fi{}3 GHz and a Rayleigh ratio of 4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. Its width is consistent with a relaxation rate estimated from the diffusivity. The broader peak has a half-width of 40\ifmmode\pm\else\textpm\fi{}6 GHz and a Rayleigh ratio of about 9 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. Its origin is less certain, but it may be a measure of the time of flight of mobile silver ions.

The Rayleigh–Brillouin spectrum of hydrogen at high densities

The Rayleigh–Brillouin spectrum of light scattered from hydrogen at high densities is reported. The observations are compared with translational hydrodynamic theory and ultrasonic experiments. The range of densities includes the relaxation region and we find evidence for multiple relaxation. A mean relaxation time for normal hydrogen at 24 °C of (1.41 ± 0.06) × 10−8 s is found, in agreement with theoretical calculations.

The Rayleigh–Brillouin spectrum of compressed H2; a test of translational hydrodynamics

This paper reports on a comparison between the observed Rayleigh–Brillouin spectra of compressed hydrogen and those computed according to the translational hydrodynamic theory of Desai and Kapral. Reasonable agreement is found in the range of densities from 19 to 61 amagat units. It is suggested that small residual discrepancies may be due to the neglect of part of the coupling between the energy and momentum fluctuations arising from relaxation of the rotational states, i.e. due to the neglect of the 1ν1 terms.

Rayleigh–Brillouin scattering in gaseous mixtures He–Kr and Ar–Kr

Measurements of Rayleigh–Brillouin spectra of gaseous mixtures helium–krypton and argon–krypton have been performed over a range of concentrations and temperatures. The data have been compared successfully with the theoretical spectra using the approximate equation of Cohen, Sutherland, and Deutch. We have considered, for the first time, the effects of temperature changes upon the spectra and have also successfully employed the analytical expressions of Kestin et al. to determine the thermodynamic constants of our mixtures.

Rayleigh-Brillouin spectra in molecular nitrogen

Rayleigh-Brillouin spectra of gaseous ${\mathrm{N}}_{2}$ is measured for light scattered at 15\ifmmode^\circ\else\textdegree\fi{} over a pressure range from 1 to 661 Torr. Spectral profiles are analyzed by means of an appropriate kinetic model. A least-${\ensuremath{\chi}}^{2}$ method determines the optimum values of the theory parameters: total collision frequency and rotational relaxation number. These parameters are compared with values obtained by other methods. Information provided by light-scattering measurements concerning rotational relaxation in dilute systems is discussed.

A study of the polymerization of styrene by Rayleigh-Brillouin spectroscopy

The Rayleigh-Brillouin spectrum has been used to probe the kinetics of the thermal polymerization of styrene. The behaviour of the velocity and attenuation of hypersound in the medium is consistent with frequency-dependent bulk and shear viscosities. The characteristic relaxation times are dependent on the degree of polymerization. The relaxation times continuously increase as the polymerization proceeds. In the initial stages of the experiment the measured sound velocity and absorption coefficients correspond to the zero frequency values, and as the polymerization proceeds these quantities go over to the infinite frequency values.

The Rayleigh – Brillouin Spectrum of Normal and Parahydrogen: A Test of Model Solutions of the Wang–Chang Uhlenbeck Equation

This paper reports the observation at high resolution of the Rayleigh–Brillouin spectrum of normal and parahydrogen at room temperature. The spectra are compared with a number of kinetic model calculations based on the Wang–Chang Uhlenbeck equation. It is concluded that n-H2 behaves effectively as a system characterized by a single relaxation time for the internal degrees of freedom and that the S6 model of Tenti et al. gives a very good description of the Rayleigh–Brillouin spectrum of a molecular gas at low and medium densities. At higher densities the models fail because the Wang–Chang Uhlenbeck equation is no longer valid.