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

J. L. A. Dubbeldam; A. Milchev; V. G. Rostiashvili; T. A. Vilgis

doi:10.1209/0295-5075/79/18002

paper

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

arXiv:cond-mat/0702463 · doi:10.1209/0295-5075/79/18002

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 $s (t)$ , displays an {\em anomalous} diffusive behavior even in the {\em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $α = 2/ (2 ν + 2 - γ_{1})$ , where $ν$ is the Flory exponent and $γ_{1}$ - 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 {\em 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 $τ \propto f^{- 1} N^{\frac{2}{α} - 1}$ . Also the corresponding time dependent statistical moments, $< s (t) >\propto t^{α}$ and $< s (t)^{2} >\propto t^{2 α}$ 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.

arXiv comment6 pages, 4 figures, accepted to Europhys. Lett; some references were supplemented; typos were corrected

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

Abstract

References in corpus (11)

Cited by in corpus (43)