Role of Non-Equilibrium Conformations on Driven Polymer Translocation

TL;DR

This study investigates how non-equilibrium initial conformations of polyelectrolyte chains affect their translocation through nanopores, revealing conditions where quasi-equilibrium assumptions fail and confirming the $1/V$ scaling law.

Contribution

It demonstrates that artificially stretched initial conformations violate quasi-equilibrium conditions and confirms the $1/V$ scaling law in translocation dynamics.

Findings

Stretched initial conformations have translocation times shorter than relaxation times.

The $\langle \tau \rangle \sim 1/V$ scaling law holds even for out-of-equilibrium states.

Quasi-equilibrium approximation is invalid for certain initial conformations.

Abstract

One of the major theoretical methods in understanding polymer translocation through a nanopore is the Fokker-Planck formalism based on the assumption of quasi-equilibrium of polymer conformations. The criterion for applicability of the quasi-equilibrium approximation for polymer translocation is that the average translocation time per Kuhn segment, $\langle \tau \rangle/N_K$ is longer than the relaxation time $\tau_0$ of the polymer. Towards an understanding of conditions that would satisfy this criterion, we have performed coarse-grained three dimensional Langevin dynamics and multi-particle collision dynamics simulations. We have studied the role of initial conformations of a polyelectrolyte chain (which were artificially generated with a flow field) on the kinetics of its translocation across a nanopore under the action of an externally applied transmembrane voltage $V$ (in the absence of the initial flow field). Stretched (out-of-equilibrium) polyelectrolyte chain conformations are deliberately and systematically generated and used as initial conformations in translocation simulations. Independent simulations are performed to study the relaxation behavior of these stretched chains and a comparison is made between the relaxation timescale and the mean translocation time ($\langle \tau \rangle$). For such artificially stretched initial states, $\langle \tau \rangle/N_K < \tau_0$, demonstrating the inapplicability of the quasi-equilibrium approximation. Nevertheless, we observe a scaling of $\langle \tau \rangle \sim 1/V$ over the entire range of chain stretching studied, in agreement with the predictions of the Fokker-Planck model. On the other hand, for realistic situations where initial artificially imposed flow field is absent, a comparison of experimental data reported in the literature with the theory