Transport Properties of Polymer Chains in Dilute Solution: Hydrodynamic Interaction

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Abstract
Several problems related to hydrodynamic interaction in flexible chain polymers without excluded volume are investigated. First, a correction to the Oseen hydrodynamic interaction tensor for a system of many spheres is derived, taking into account the finite volume of the spheres. The new hydrodynamic interaction tensor gives the positive definite diffusion tensor identical with that of Rotne and Prager. Second, the possible effects of the correction term in the hydrodynamic interaction tensor on the translational diffusion coefficient and intrinsic viscosity are examined when preaveraging the hydrodynamic interaction tensor is avoided following the procedure of Pyun and Fixman. If the Rouse free-draining normal coordinates together with the diagonal approximation are used, the effects are shown to be negligibly small in the case of flexible chains. Third, however, the intrinsic viscosity and diffusion coefficient are re-evaluated, taking the lower limit of | i − j | as unity in the evaluation of sums over the segment indices i and j. The results are similar to those derived by Hearst and Stockmayer for wormlike chains. That is, the present theory also predicts that the draining effect vanishes under certain conditions. It is emphasized that the Oseen tensor has still some practical value in the case of flexible chains when it is used carefully.

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