Dynamics of coarse-grained helical wormlike chains. I. Diffusion equation

Abstract

An alternative representation of the diffusion equation is derived for the discrete helical wormlike (HW) chain model by treating the constraints in a manner different from that previously adopted. In contrast to the previous diffusion equation for the same HW model, which can describe local motions but not global to quasi-global motions of flexible polymers in dilute solution because of the defect arising from the preaveraging of the constraining matrix, the present equation may be considered to be suitable for the description of the latter since it can give explicitly the Rouse–Zimm eigenvalues in the ground (global) state. It is shown that the present and previous equations are exactly the same before the constraining matrix common to them is preaveraged, as is natural, and that the above difference between their characteristics arises from the difference in the effect of the preaveraging approximation. A comparison is also made of the present model (or diffusion equation) with other models for polymer chain dynamics. In particular, the present theory is shown to be rather similar to the Fixman–Kovac theory for the conventional bond chain in the physical meaning as well as the formulation.