Concentration dependence of friction coefficients for polymer chains in solution

The multiple scattering formalism is used to provide a theory of the concentration dependence of the cooperative and self-translational friction coefficients for polymer chains in solution. The specific case of Gaussian chains is analyzed, but extensions to good solutions can be made using previously described models. We stress the importance of dynamical contributions to the effective screened concentration dependent hydrodynamic interactions, which have been omitted in previous algebraically tractable static approximations. The theory is represented explicitly as an expansion in concentration and as an expansion in the effective medium representation. Explicit calculation of the leading concentration dependence is given in the following paper, fully including the dynamical effective hydrodynamic interactions.