Scaling exponents of forced polymer translocation through a nanopore

Abstract

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (N) of the average translocation time <tau>, the average velocity of the center of mass <vCM>, and the effective radius of gyration <Rg> during the translocation process defined as <tau> approximately Nalpha, <vCM> approximately N(-delta), and Rg approximately Nnu respectively, and the exponent of the translocation coordinate (s-coordinate) as a function of the translocation time <s2(t)> approximately tbeta. We find alpha = 1.36 +/- 0.01, beta = 1.60+/- 0.01 for <s2(t)> approximately taubeta and beta = 1.44 +/- 0.02 for <Deltas2(t)> approximately taubeta, delta = 0.81 +/- 0.04, and nu congruent with nu = 0.59 +/- 0.01, where nu is the equilibrium Flory exponent in 3D. Therefore, we find that <tau> approximately N1.36 is consistent with the estimate of <tau> approximately <Rg>/<vCM>. However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent alpha = 1.36 +/- 0.01 < 1 + nu. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the "cis" and "trans" parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here.