Quasielastic scattering by dilute polymer solutions A summary of this work was presented at the IUPAP International Conference on Statistical Physics, August 25–29, 1975.

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.