Long-time dynamics of Rouse-Zimm polymers in dilute solutions with hydrodynamic memory

TL;DR

This paper investigates the long-time dynamics of Rouse-Zimm polymers in dilute solutions considering hydrodynamic memory, revealing significant deviations from classical models and predicting observable effects in scattering experiments.

Contribution

It introduces a generalized Rouse-Zimm model incorporating hydrodynamic memory and fluid inertia, providing new insights into polymer dynamics and correlation functions.

Findings

MSD scales as t^2 at short times

Long-time MSD includes a t^(1/2) contribution

Normal mode relaxation exhibits long-time tails with t^(-3/2) and t^(-5/2) decay

Abstract

The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polymer coil is at short times \~ t^2 (instead of ~ t). At long times the MSD contains additional (to the Einstein term) contributions, the leading of which is ~ t^(1/2). The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. It is displayed in the long-time tails of their correlation functions, the longest-lived being ~ t^(-3/2) in the Rouse limit and t^(-5/2) in the Zimm case, when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular an effectively slower diffusion of the polymer coil, should be observable in dynamic scattering experiments.