Dynamics of a polymer in a quenched random medium: A Monte Carlo investigation

TL;DR

This study uses Monte Carlo simulations to explore how a polymer's dynamics in a quenched random medium depend on disorder and chain length, revealing two diffusion crossovers and a transition to a non-ergodic, frozen state.

Contribution

It provides a detailed numerical investigation of polymer dynamics in disordered media, confirming theoretical predictions about diffusion crossovers and ergodicity breaking.

Findings

Two diffusion crossovers depend on disorder and chain length.

Diffusion coefficient drops sharply at a critical disorder level.

Non-ergodic regime characterized by a plateau in Rouse mode correlations.

Abstract

We use an off - lattice bead - spring model of a self - avoiding polymer chain immersed in a 3-dimensional quenched random medium to study chain dynamics by means of a Monte - Carlo (MC) simulation. The chain center of mass mean-squared displacement as a function of time reveals two crossovers which depend both on chain length $N$ and on the degree of Gaussian disorder $\Delta$. The first one from normal to anomalous diffusion regime is found at short time $\tau_1$ and observed to vanish rapidly as $\tau_1 \propto \Delta^{- 11}$ with growing disorder. The second crossover back to normal diffusion, $\tau_2$, scales as $\tau_2 \propto N^{2\nu + 1} f(N^{2-3\nu}\Delta)$ with $f$ being some scaling function. The diffusion coefficient $D_N$ depends strongly on disorder and drops dramatically at a {\em critical dispersion} $\Delta_{c} \propto N^{-2 + 3\nu}$ of the disorder potential so that for $\Delta > \Delta_c$ the chain center of mass is practically frozen.The time-dependent Rouse modes correlation function $C_{p}(t)$ reveals a characteristic plateau at $\Delta > \Delta_c$ which is the hallmark of a non - ergodic regime. These findings agree well with our recent theoretical predictions.