Dynamics of weakly bending rods: A trumbbell model

Abstract

Some dynamic properties of weakly bending rod-like polymers are studied on the basis of a trumbbell model which consists of two frictionless bonds and three beads with constraints on bondlengths and with a bending potential between the bonds. The diffusion equation is formulated by imposing the constraints in the diffusion limit (Smoluchowski level), considering fluctuating hydrodynamic interaction. All evaluation is carried out analytically, though only near the rod limit, i.e., to terms of O(α−1) with α the bending force constant. The mean translational diffusion coefficient Dt (at long times) and the dynamic intrinsic viscosity [η] are evaluated by the projection operator method and by the time-correlation function formalism, respectively. The former and the steady-state intrinsic viscosity are evaluated also in the rigid-body ensemble approximation, and it is found that this approximation is very good near the rod limit. Some other features of Dt, including its dependence on time, are also discussed. The results for [η] are equivalent to those of Roitman and Zimm, who have solved the problem numerically for the trumbbell as the Kramers-type chain in the free-draining case; [η] relaxes by end-over-end rotation and bending near the rod limit. However, a comparison of theory with experiment for storage and loss moduli for light meromyosin leads to an estimate of the persistence length too large compared to its known reasonable value.