Effects from bead size and hydrodynamic interactions on the translational and rotational coefficients of macromolecular bead models

In this work, we analyze a deficiency of the currently used form of the Kirkwood–Riseman (KR) theory for macromolecular bead models in regard to the finite size of the beads and illustrate the importance of a more complete description of hydrodynamic interactions. We consider several exact or very accurate theories for two-bead models and compare their results with different KR-based methods. One of them is the substitution technique in which the beads are substituted by a cubic array of smaller spheres. Its disadvantage is an increase in computer requirements. A novel result of our work is a very simple correction for the KR rotational coefficients intended to correct, in part, the failure originated by size effects. The comparison of the various approaches has been made for two specific cases, the rigid dumbbell and prolate ellipsoids, for which rigorous results are available. We show that the performance of the substitution technique is excellent, and that our correction improves in many cases the KR results for rotation.