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

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 $\mathrm{\Delta }$. The first one from normal to anomalous diffusion regime is found at short time ${\tau }_1$ and observed to vanish rapidly as $\tau_1 \propto \Delta^{- 11}$withgrowingdisorder\mathrm{.}Thesecondcrossoverbacktonormaldiffusion,$\tau_2$,scalesas$\tau_2 \propto N^{2\nu + 1} f(N^{2-3\nu}\Delta)$with$f$beingsomescalingfunction\mathrm{.}Thediffusioncoefficient$D_N$ depends strongly on disorder and drops dramatically at a {\em critical dispersion} $\Delta_{c} \propto N^{-2 + 3\nu}$ofthedisorderpotentialsothatfor$\Delta > \Delta_c$ the chain center of mass is practically frozen.The time-dependent Rouse modes correlation function $C_p(t)$ reveals a characteristic plateau at $\mathrm{\Delta }>{\mathrm{\Delta }}_c$ which is the hallmark of a non - ergodic regime. These findings agree well with our recent theoretical predictions.