Dynamic light scattering, mutual diffusion, and linear viscoelasticity of polymer solutions

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Abstract
A theoretical study of the dynamic light scattering spectrum from a binary solution consisting of a polymer and a small molecular weight solvent is carried out. The study is based upon a modified hydrodynamic equation previously derived from statistical mechanics by Bearman and Kirkwood for a multicomponent solution. The result shows that mutual diffusion arising from the osmotic pressure fluctuation and the viscoelasticity affecting mechanical properties of the polymer solution are, in general, mixed. The extent of mixing depends on the frequency and a coupling parameter β, which is proportional to the difference between the partial specific volume of the polymer and that of the small molecular solvent. At low frequency the coupling is negligible, and one obtains a diffusion equation with the mutual diffusion coefficient dependent only on the osmotic modulus. At the frequency in the plateau stress modulus region, the result predicts a cooperative diffusion coefficient which consists of both the osmotic modulus and the longitudinal elastic modulus of the polymer solution, provided that β=1. The result is equivalent to that previously obtained by de Gennes, assuming a transient gel network model for the semidilute polymer solution. The present calculation also provides new results for the polymer solution in which the transient gel network model is not applicable. The overall light scattering spectral density is calculated in terms of the autocorrelation functions of the local pressure and the local concentration, as well as cross correlation functions between them. The result shows that as the polymer concentration is gradually increased toward the bulk state, the concentration fluctuation spectrum losses its importance, and the pressure (or density) fluctuation spectrum dominates the overall light scattering spectral density.