Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the 2D fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength $E$, length of the chain $N$, and length of the pore $L$ on forced translocation. As our main result, we find a crossover scaling for the translocation time $\tau $ with the chain length from $\tau \sim N^{2\nu}$ for relatively short polymers to $\tau \sim N^{1 + \nu}$ for longer chains, where $\nu $ is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains $v \sim N^{- \nu}$, which crosses over to $v \sim N^{- 1}$ for long polymers. The reason for this is that with increasing $N$ there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which $R_\parallel $, the radius of gyration $R_{g}$ along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large $N$, however, the asymptotic scaling $\tau \sim N^{1 + \nu}$ is recovered. In this regime, $\tau $ is almost independent of $L$. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for $R_\parallel \approx L$. We show here that this minimum persists for a weak fields $E$ such that $EL$ is less than some critical value, but vanishes for large values of $EL$.