Scaling in the Rubinstein-Duke Model for Reptation

TL;DR

This paper analyzes the scaling behavior of charged polymers in the Rubinstein-Duke model under weak driving fields, providing a unified framework for understanding drift, diffusion, and orientation through a random walk analogy.

Contribution

It introduces a unified scaling expression for local orientation and clarifies the role of corrections to scaling in the Rubinstein-Duke model.

Findings

Derived expressions for drift velocity, diffusion constant, and orientation.

Mapped the problem to a one-dimensional random walk for analytical insights.

Provided a unified scaling framework for charged polymer behavior.

Abstract

We consider an arbitrarily charged polymer driven by a weak field through a gel according to the rules of the Rubinstein-Duke model. The probability distribution in the stationary state is related to that of the model in which only the head is charged. Thereby drift velocity, diffusion constant and orientation of any charged polymers are expressed in terms of those of the central model. Mapping the problem on a random walk of a tagged particle along a one-dimenional chain, leads to a unified scaling expression for the local orientation. It provides also an elucidation of the role of corrections to scaling.