Volume 79, Number 1, July 2007
Article Number 18002
Number of page(s) 6
Section Interdisciplinary Physics and Related Areas of Science and Technology
Published online 07 June 2007
EPL, 79 (2007) 18002
DOI: 10.1209/0295-5075/79/18002

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

J. L. A. Dubbeldam1, 2, A. Milchev1, 3, V. G. Rostiashvili1 and T. A. Vilgis1

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 in final form 18 May 2007; published July 2007
published online 7 June 2007

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 $\alpha =2/(2\nu +2-\gamma _{1})$, where $\nu $ is the Flory exponent and $\gamma _{1}$ 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 $\tau \propto f^{-1}N^{\frac{2}{\alpha} -1} $. Also the corresponding time-dependent statistical moments, $\left\langle s(t) \right\rangle \propto t^{\alpha} $ and $\left\langle s(t)^2 \right\rangle \propto t^{2\alpha} $ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $\alpha $ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.

82.35.Lr - Physical properties of polymers.
87.15.Vv - Diffusion.
87.15.Aa - Theory and modeling; computer simulation.

© Europhysics Letters Association 2007