Effect of Anomalous Dynamics on Unbiased Polymer Translocation

Abstract

In this paper, we investigate the microscopic dynamics of a polymer of length $N$ translocating through a narrow pore. Characterization of its purportedly anomalous dynamics has so far remained incomplete. We show that the polymer dynamics is anomalous until the Rouse time $τ_{R}\sim N^{1+2ν}$, with a mean square displacement through the pore consistent with $t^{(1+ν)/(1+2ν)}$, with $ν\approx0.588$ the Flory exponent. This is shown to be directly related to a decay in time of the excess monomer density near the pore as $t^{-(1+ν)/(1+2ν)}\exp(-t/τ_{R})$. Beyond the Rouse time translocation becomes diffusive. In consequence of this, the dwell-time $τ_{d}$, the time a translocating polymer typically spends within the pore, scales as $N^{2+ν}$, in contrast to previous claims.