Translational Diffusion Coefficients of Rodlike Polymers: Application of the Modified Oseen Tensor

Abstract

The translational diffusion coefficient of a rodlike polymer is investigated in the Kirkwood‐Riseman scheme with the use of the modified Oseen tensor derived previously by Yamakawa for the finite bead model. If it is assumed that the friction coefficient of the beads may be described by Stokes' law, this tensor can remove the Zwanzig singularities from the possible range of the strength of the hydrodynamic interaction. It is pointed out that the preaveraging of the Oseen tensor may remove the singularities apparently in some cases. The correct asymptotic solution is also obtained without transforming a set of simultaneous equations determining the frictional forces to an integral equation. The results show that the finite bead model of a rodlike polymer is intermediate between the ellipsoid and cylinder models in transport behavior.