Dynamical Scaling Exponents for Polymer Translocation through a Nanopore

TL;DR

This study uses extensive computer simulations to determine the scaling exponents of polymer translocation through a nanopore, revealing different behaviors in 2D and 3D and establishing relations between key exponents.

Contribution

The paper provides the first comprehensive numerical determination of the scaling exponents for polymer translocation in 2D and 3D, including the effects of driving forces and chain length crossover behaviors.

Findings

lpha=1+2 u for unbiased PT in 2D and 3D

eta=2/lpha for unbiased PT

lpha eta  2 in driven PT in 2D

Abstract

We determine the scaling exponents of polymer translocation (PT) through a nanopore by extensive computer simulations of various microscopic models for chain lengths extending up to N=800 in some cases. We focus on the scaling of the average PT time $\tau \sim N^{\alpha}$ and the mean-square change of the PT coordinate $<s^2(t)> \sim t^\beta$. We find $\alpha=1+2\nu$ and $\beta=2/\alpha$ for unbiased PT in 2D and 3D. The relation $\alpha \beta=2$ holds for driven PT in 2D, with crossover from $\alpha \approx 2\nu$ for short chains to $\alpha \approx 1+\nu$ for long chains. This crossover is, however, absent in 3D where $\alpha = 1.42 \pm 0.01$ and $\alpha \beta \approx 2.2$ for $N \approx 40-800$.