Scaling exponents of forced polymer translocation through a nanopore

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 , the average velocity of the center of mass , and the effective radius of gyration < R-g > during the translocation process defined as similar to N-alpha, similar to N-delta, and R-g similar to N-(nu) over bar. respectively, and the exponent of the translocation coordinate (s-coordinate) as a function of the translocation time < s(2)(t)> similar to t(beta). We find alpha = 1.36 +/- 0.01, beta = 1.60 +/- 0.01 for < s(2)(t)> similar to tau(beta) and (beta) over bar = 1.44 +/- 0.02 for similar to tau((beta) over bar), delta = 0.81 +/- 0.04, and (nu) over bar similar or equal to nu = 0.59 +/- 0.01, where nu is the equilibrium Flory exponent in 3D. Therefore, we find that similar to N-1.36 is consistent with the estimate of similar to < R-g >/. 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.