Polymer translocation through a nanopore under a pulling force

We investigate polymer translocation through a nanopore under a pulling force using Langevin dynamics simulations. We concentrate on the influence of the chain length N and the pulling force F on the translocation time τ. The distribution of τ is symmetric and narrow for strong F. We find that τ~N² and translocation velocity v~N^-1 for both moderate and strong F. For infinitely wide pores, three regimes are observed for τ as a function of F. With increasing F, τ is independent of F for weak F, and then τ~F^-2+ν^-1 for moderate F, where ν is the Flory exponent, which finally crosses over to τ~F^-1 for strong force. For narrow pores, even for moderate force τ~F^-1. Finally, the waiting time, for monomer s and monomer $s+1$ to exit the pore, has a maximum for s close to the end of the chain, in contrast to the case where the polymer is driven by an external force within the pore.