Dynamics of helical worm-like chains. XI. Translational diffusion with fluctuating hydrodynamic interaction

Abstract

The translational diffusion coefficient D of long enough polymer chains without excluded volume is studied on the basis of the discrete helical worm-like (HW) chain with partially fluctuating (orientation-dependent) hydrodynamic interaction (HI). In order to evaluate D(∞) in the long time limit, which corresponds to diffusion experiments usually done on the long time scales, the time-dependent part of D is explicitly treated by an application of the projection operator method. The result may be written as D(∞)=D(Z)(1−δ0−δ1), where D(Z) is the Zimm value with preaveraged HI, δ0 is the relative decrease at time t=0 due to constraints, and δ1 is the additional relative decrease at t=∞ due to coupling between the translational motion and the Rouse vector (dielectric) modes for the HW chain, especially the long wavelength ones. It is found that D(∞) is decreased as the local conformation of the chain becomes rather compact, and that D(∞)=D(Z) (i.e., δ0=δ1=0) in the stiff-chain limit. Thus the ratio ρ of the root-mean-square radius of gyration to the hydrodynamic radius defined from D is not a universal constant but depends on the chain conformation and stiffness. A comparison of theory with experiment is made with respect to ρ, and it is found that the theory may well explain experimental results. For comparison, also for the Gaussian chain (spring–bead model), which is an unconstrained chain, D(∞) is evaluated, and it is found that δ0=0 but δ1≠0.