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

¹  Max Planck Institute for Polymer Research - 10 Ackermannweg 55128 Mainz, Germany
²  Delft University of Technology - 2628CD Delft, The Netherlands
³  Institute for Physical Chemistry Bulgarian Academy of Science - 1113 Sofia, Bulgaria

Received: 20 February 2007
Accepted: 18 May 2007

Abstract

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 , 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 , where ν is the Flory exponent and 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 , 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.