Driven polymer translocation through a nanopore: A manifestation of anomalous diffusion

We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments s(t), displays an anomalous diffusive behavior even in the presence of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent α=2/(2ν+2−γ₁), where ν is the Flory exponent and γ₁ the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function W(s, t), which follows from the relevant fractional Fokker-Planck equation, is derived in terms of the polymer chain length N and the applied drag force f. It is found that the average translocation time scales as . Also the corresponding time-dependent statistical moments, and reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of α in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.