Quasielastic scattering by dilute polymer solutions

Abstract

Abstract The scattering law S ( k , w ) for dilute polymer solutions is obtained from Kirkwood's diffusion equation via the projection operator technique. The width Ω( k ) of S ( k ,w) is obtained for all k without replacing the Oseen tensor by its average (as is done in the Rouse–Zimm model) using the “spring‐bead” model ignoring memory effects. For small ( ka \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt N $ \end{document} ≪ 1) and large ( ka ≫ 1) values of k we find Ω = 0.195 k 2 /β α η 0 \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt N $ \end{document} and Ω = k 2 /βξ, respectively, indicating that the width is governed mainly by the viscosity η 0 for small k values and by the friction coefficient ξ for large k values. For intermediate k values which are of importance in neutron scattering we find that in the Rouse limit Ω = k 4 a 2 /12βξ. When the hydrodynamic effects are included, Ω( k ) becomes 0.055 k 3 /βη 0 . Using the Rouse–Zimm model, it is seen that the effect of pre‐averaging the Oseen tensor is to underestimate the half‐width Ω( k ). The implications of the theoretical predictions for scattering experiments are discussed.