Exact curvilinear diffusion coefficients in the repton model

TL;DR

This paper derives exact curvilinear diffusion coefficients for the repton model and its variant with hardcore interactions, for all chain lengths and boundary conditions, advancing understanding of polymer reptation dynamics.

Contribution

It provides the first exact analytical expressions for curvilinear diffusion coefficients in both the standard and modified repton models across all chain lengths.

Findings

Exact diffusion coefficients for all chain lengths

Inclusion of hardcore interactions in the model

Analysis of periodic boundary conditions

Abstract

The Rubinstein-Duke or repton model is one of the simplest lattice model of reptation for the diffusion of a polymer in a gel or a melt. Recently, a slightly modified model with hardcore interactions between the reptons has been introduced. The curvilinear diffusion coefficients of both models are exactly determined for all chain lengths. The case of periodic boundary conditions is also considered.