Diffusion in a generalized Rubinstein-Duke model of electrophoresis with kinematic disorder

TL;DR

This paper rigorously proves that kinematic disorder does not alter the long-chain scaling law of diffusion in a generalized Rubinstein-Duke model, but it affects the diffusion constant similarly to a random barrier model.

Contribution

It introduces a generalized Rubinstein-Duke model with kinematic disorder and analytically and numerically shows its impact on polymer diffusion.

Findings

Kinematic disorder does not change the $D o L^{-2}$ scaling law.

Kinematic disorder reduces the diffusion constant by a factor similar to a random barrier model.

Theoretical and Monte Carlo methods confirm the effects of disorder on polymer diffusion.

Abstract

Using a generalized Rubinstein-Duke model we prove rigorously that kinematic disorder leaves the prediction of standard reptation theory for the scaling of the diffusion constant in the limit for long polymer chains $D \propto L^{-2}$ unaffected. Based on an analytical calculation as well as Monte Carlo simulations we predict kinematic disorder to affect the center of mass diffusion constant of an entangled polymer in the limit for long chains by the same factor as single particle diffusion in a random barrier model.