Quasielastic scattering by dilute polymer solutions

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}$ \sqrt N $ ≪ 1) and large (ka ≫ 1) values of k we find Ω = 0.195 k²/β α η₀ \documentclass{article}\pagestyle{empty}$ \sqrt N $ and Ω = k²/βξ, respectively, indicating that the width is governed mainly by the viscosity η₀ 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 = k⁴a²/12βξ. When the hydrodynamic effects are included, Ω(k) becomes 0.055 k³/βη₀. 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.