Short Time Behavior in De Gennes' Reptation Model

TL;DR

This paper analyzes the early-time behavior of polymer chain diffusion in an obstacle array, showing that the characteristic t^{1/4} reptation signature appears only after long transient periods for long chains, supported by theory and simulations.

Contribution

It provides an analytical and numerical study clarifying the transient dynamics of reptation, emphasizing the long transient needed for the t^{1/4} signature to emerge.

Findings

Reptation signature (t^{1/4}) appears after long transient for chains with N > 100.

Short transient observed for the fourth moment of displacement.

Theory and simulations agree quantitatively on the transient behavior.

Abstract

To establish a standard for the distinction of reptation from other modes of polymer diffusion, we analytically and numerically study the displacement of the central bead of a chain diffusing through an ordered obstacle array for times $t < O(N^2)$. Our theory and simulations agree quantitatively and show that the second moment approaches the $t^{1/4}$ often viewed as signature of reptation only after a very long transient and only for long chains (N > 100). Our analytically solvable model furthermore predicts a very short transient for the fourth moment. This is verified by computer experiment.