A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E , we observe a change in the scaling law for the translocation time τ as function of the polymer length N : In the general expression τ ∼ N β ∕ E , the exponent changes from β = 1 for moderately long chains to β = 1 + ν or β = 2 ν for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains.