How local factors affect the exponents of forced polymer translocation through a nano-pore

Abstract

We study polymer translocation through a narrow pore driven by a bias present inside the pore with an aim to compare predictions of the existing theoretical results with those that we obtain using Langevin dynamics simulation in three dimensions(3D). We find that the translocation exponent α(〈τ〉∼Nα) decreases from 1.35 to 1.2 as the width of the pore is decreased from 1.5σ to 1.1σ. The exponent ℵ=1.2 (extracted from chain lengths up to N=256) not only violates the lower limit 1+ν proposed by Kantor and Kardar (Y. Kantor and M. Kardar, Phys. Rev. E, 69, 021806 (2004)) earlier but also lower than the more recently proposed lower limit (1+2ν)/(1+ν) by Vocks et al. (H. Vocks, D. Panja, G. T. Barkema, and R. C. Ball, J. Phys.: Condens. Matter 20, 095224 (2008)). We find that the average 〈R̄g〉 calculated during the entire translocation process is dominated by the equilibrium configurations at the cis side and therefore, relatively insensitive to the pore width and approximately described by the equilibrium Flory exponent ν. The velocity of the center of mass of the translocating chain on the contrary exhibits a systematic variation. Therefore, if we assume (〈τ〉∼〈R̄g〉/〈vCM〉), the dependence of 〈vCM〉 on the pore width appears to be the primary factor that affects the translocation exponent.