Quasielastic Scattering by Semidilute Polymer Solutions

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Abstract
We compute the coherent dynamic form factor for the scattering of neutrons by a “semidilute” solution of polymers, in which the radius of gyration R G of each coil is assumed much larger than the average distance between neighboring coils. In this case, in the presence of a strong excluded volume, the coils are nearly ideal, and correlations between monomers can be obtained accurately by a random phase approximation. Backflow effects (which complicated seriously the one‐coil problem) are not important here for the longitudinal motion of interest, and a simple Rouse equation can be applied to describe the motion. The most interesting region corresponds to spatial wavelengths q −1 which are large compared to the screening length K −1 (although smaller than R G ). In this domain, the frequency halfwidth Δω q at a fixed wave vector q becomes roughly proportional to q 2 . The effects of entanglement between chains are taken into account only in terms of a phenomenological effective viscosity of the solution.