Generalized Zimm model for dilute polymer solutions under theta conditions

Abstract

The consistent averaging approximation for the hydrodynamic interaction is applied to linear chains with Gaussian chain statistics in order to improve the well-known Zimm model, which is based on the preaveraged hydrodynamic interaction. For the resulting generalized Zimm model a rheological equation of state is derived which is then used as a starting point for the derivation of a codeformational memory integral expansion and a retarded motion expansion as well as for numerical investigations. The material functions predicted by the generalized Zimm model for steady shear flow and for small amplitude oscillatory shear flow are discussed in great detail. Finally, the limit of infinitely long chains is thoroughly studied by analytical and numerical techniques.