Translational Diffusion Coefficients of Plane-Polygonal Polymers: Application of the Modified Oseen Tensor

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Abstract
The translational diffusion coefficient of a plane‐polygonal polymer is investigated in the Kirkwood‐Riseman scheme following the procedure of Paul and Mazo with the use of the modified Oseen tensor for the finite bead model. Required summations over indices are exactly carried out with the aid of a digital computer. It is pointed out that the mathematical singularities or zeroes can occur in both cases of the Oseen tensor and the modified Oseen tensor, but never appear within the physically possible range of the strength of the hydrodynamic interaction if the beads are assumed to obey Stokes' law. The correct asymptotic solution is also obtained and the results are compared with those for a continuous rigid ring.