A theory of quasielastic laser light scattering by polymer gels

Abstract

New theory is developed for interpreting periodic time correlations of coherent light scattered from soft polymer gels. Scattering is assumed to be caused by time-varying refractive-index changes which occur when a polymer lattice is distorted by macroscopic displacement waves. The frequencies of these waves are found to depend on the elastic moduli, material density, and dimensions of a sample, and are identical with central frequencies of resonances which would be noted in self-beat light-scattering spectra. The effects of friction between polymer strands and surrounding solvent, and of internal energy dissipation by the polymer lattice, also are investigated. Expressions are obtained for the widths of spectral resonances which are induced when a gel is excited by a sound field deriving from a sweep generator. Comparison with experimental results (reported elsewhere) leads to the conclusion that our previously proposed light-scattering scheme—involving mechanical excitation of a sample—measures the shear modulus of bulk gel rather than the rigidity of the polymer lattice alone.