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

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 $Δ$. The first one from normal to anomalous diffusion regime is found at short time $τ_1$ and observed to vanish rapidly as $τ_1 \propto Δ^{- 11}$ with growing disorder. The second crossover back to normal diffusion, $τ_2$, scales as $τ_2 \propto N^{2ν+ 1} f(N^{2-3ν}Δ)$ with $f$ being some scaling function. The diffusion coefficient $D_N$ depends strongly on disorder and drops dramatically at a {\em critical dispersion} $Δ_{c} \propto N^{-2 + 3ν}$ of the disorder potential so that for $Δ> Δ_c$ the chain center of mass is practically frozen.The time-dependent Rouse modes correlation function $C_{p}(t)$ reveals a characteristic plateau at $Δ> Δ_c$ which is the hallmark of a non - ergodic regime. These findings agree well with our recent theoretical predictions.