Monte Carlo simulations of polymer translocation through a nanopore

We investigate the problem of polymer translocation through a nanopore using the fluctuating bond model with single-segment Monte Carlo moves. For non-driven case we study the escape time $\tau_e$ required for a polymer, which is initially placed in the middle of the pore, to completely exit the pore on either end. We find $\tau _e \sim N^{1 + 2\nu }$, where $N$ is the chain length and $\nu $ is the Flory exponent. We also examine the interplay between the pore length $L$ and the radius of gyration $R_{g}$. For driven case we find a crossover scaling for the translocation time $\tau$ with $N$ from $\tau \sim N^{2\nu } $ for relatively short polymers to $\tau \sim N^{1 + \nu }$ for longer chains. This crossover is due to the change of the translocation velocity v from $v \sim N^{ - \nu }$ for relatively short chains to $v \sim N^{ - 1}$ for long polymers. The reason is that a high density of segments near the exit of the pore for long polymer slows down the translocation process due to slow relaxation of the chain.