Long-time dynamics of de Gennes' model for reptation

TL;DR

This paper investigates the long-time behavior of polymer diffusion in gels using de Gennes' reptation model, confirming key scaling laws and providing insights into finite-size effects.

Contribution

It presents new results on the scaling of diffusion and relaxation times that align with de Gennes' theoretical predictions, contrasting recent findings.

Findings

Diffusion coefficient D scales as 1/N^2

Relaxation time tau scales as N^3

Finite-size correction exponent is -2/3

Abstract

Diffusion of a polymer in a gel is studied within the framework of de Gennes' model for reptation. Our results for the scaling of the diffusion coefficient D and the longest relaxation time tau are markedly different from the most recently reported results, and are in agreement with de Gennes' reptation arguments: D ~ 1/N^2 and tau ~ N^3. The leading exponent of the finite-size corrections to the diffusion coefficient is consistent with the value of -2/3 that was reported for the Rubinstein model. This agreement suggests that its origin might be physical rather than an artifact of these models.