Translational Diffusion of Polymer Chains with Excluded Volume and Hydrodynamic Interactions by Brownian Dynamics Simulation

TL;DR

This study uses Brownian Dynamics simulations to accurately analyze the small correction to the polymer chain's diffusion coefficient predicted by Kirkwood theory, resolving previous discrepancies and exploring hydrodynamic effects.

Contribution

The paper provides highly accurate simulation data confirming the correction to Kirkwood's diffusion coefficient and clarifies the behavior of the Green--Kubo integrand under different hydrodynamic models.

Findings

Simulation confirms D < D^{(K)} as predicted.

Green--Kubo integrand varies significantly between models.

Older data lacked sufficient accuracy to resolve the correction.

Abstract

Within Kirkwood theory, we study the translational diffusion coefficient of a single polymer chain in dilute solution, and focus on the small difference between the short--time Kirkwood value $D^{(K)}$ and the asymptotic long--time value $D$. We calculate this correction term by highly accurate large--scale Brownian Dynamics simulations, and show that it is in perfect agreement with the rigorous variational result $D < D^{(K)}$, and with Fixman's Green--Kubo formula, which is re--derived. This resolves the puzzle posed by earlier numerical results (Rey {\em et al.}, Macromolecules 24, 4666 (1991)), which rather seemed to indicate $D > D^{(K)}$; the older data are shown to have insufficient statistical accuracy to resolve this question. We then discuss the Green--Kubo integrand in some detail. This function behaves very differently for pre--averaged vs. fluctuating hydrodynamics, as shown for the initial value by analytical considerations corroborated by numerical results. We also present further numerical data on the chain's statics and dynamics.