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 Δ. 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 DN depends strongly on disorder and drops dramatically at a critical dispersion $\Delta_{\ab{c}}\propto N^{-2+3\nu}$ of the disorder potential so that for $\Delta>\Delta_{\ab{c}}$ the chain center of mass is practically frozen. These findings agree well with our recent theoretical predictions.