Abstract
In order to obtain useful information from a perturbation expansion of hydrodynamic-interaction effects for long Rouse chains the basic equations of polymer kinetic theory are generalized to d-dimensional space. After solving the Kirkwood diffusion equation to first order in the strength of the hydrodynamic interactions, the Kramers expression for the stress tensor is used to calculate the corresponding first-order expansions of the zero-shear-rate viscometric functions for arbitrary d. Singularities occurring in these expansions near four dimensions indicate that local hydrodynamic interactions are not described in a proper way and, therefore, a renormalization of one of the model parameters, the bead friction coefficient, is necessary. With the renomalized perturbation expansions, various ratios of experimentally accessible quantities are calculated; in particular, ratios involving normal-stress coefficients are calculated for the first time by renormalization-group methods.
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