Phenomenological models compatible with acoustical and thermal properties of viscous liquids

Abstract

After a very brief review on the dispersion of acoustical and thermal properties of viscous liquids at the liquid-glass transition, some information is given about the standard models : viscoelastic theory and irreversible thermodynamics as used by Mountain. Part 1 of the paper is devoted to the theory of forced Rayleigh scattering experiments using the model due to Mountain with one relaxing variable. Part 2 extends this work to several relaxing variables both in spontaneous and forced Rayleigh scattering. Here time correlation functions are calculated explicitly given the results of acoustical and thermal experiments. It is then indicated that the predictions of these models are not consistent with experimental data. Part 3 is devoted to a generalized hydrodynamics model in which both the viscosity and the thermal diffusivity can be frequency dependent. This model, called generalized viscoelasticity, is then applied to a variety of experimental situations first for a single relaxation process and then for a Cole-Davidson distribution of relaxation times. It is shown that in glycerol the acoustical properties depend mainly on the viscosity while the thermal properties depend essentially upon the thermal diffusivity