Theoretical study of light-scattering spectrum of a pure relaxing fluid

Abstract

Starting from a phenomenological description of fluctuations in relaxing fluids, we calculate the spectrum of the light scattered by density fluctuations, studying in particular the case where the Mountain and Rayleigh line widths are of the same order of magnitude. We first describe the relaxation phenomenon by an internal variable, whose equilibrium value may depend on the density (structural relaxation), on the temperature (thermal relaxation) or both (mixed case). This allows one to relate the parameters of the scattered-light spectrum to the dispersion in the velocity of sound and in the specific heat at constant pressure. We show in particular that, depending upon the values of the thermodynamic parameters and the type of relaxation, one can obtain qualitatively different predictions for the low frequency part of the spectrum. We then discuss an extension of the pure structural case to a many-relaxation-times phenomenon and show that this problem may be treated in the frame-work of generalized hydrodynamics, introducing a frequency-dependent longitudinal viscosity. We then establish relations, allowing a meaningful comparison between the distributions of relaxation times used to fit ultrasonic and light-scattering data. This discussion is then applied to glycerol for which both kinds of data are available.