Anomalous Dynamics of Unbiased Polymer Translocation through a Narrow Pore

TL;DR

This paper investigates the anomalous dynamics of an unbiased polymer translocating through a narrow pore, revealing a crossover from anomalous to diffusive behavior at the Rouse time and providing a new scaling for dwell-time.

Contribution

It demonstrates that polymer translocation dynamics are anomalous until the Rouse time and introduces a revised scaling law for dwell-time, contrasting previous claims.

Findings

Polymer dynamics are anomalous until the Rouse time, scaling as N^{1+2 u}.

Mean square displacement scales as t^{(1+ u)/(1+2 u)}.

Dwell-time scales as N^{2+ u}, differing from earlier results.

Abstract

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