Scaling Behaviors of a Polymer Ejected from a Cavity through a Small Pore

TL;DR

This study uses Langevin dynamics simulations to analyze how flexible polymers are ejected from a cavity through a small pore, revealing distinct scaling behaviors influenced by chain length and initial monomer concentration.

Contribution

The paper develops a robust scaling theory for polymer ejection dynamics, dividing the process into stages and deriving equations based on energy dissipation, which advances understanding of polymer translocation.

Findings

Ejection velocity scales differently for large and small monomer numbers.

Ejection time follows two distinct scaling laws depending on initial conditions.

Theoretical predictions match simulation results across different regimes.

Abstract

Langevin dynamics simulations are performed to investigate ejection dynamics of spherically confined flexible polymers through a pore. By varying the chain length $N$ and the initial volume fraction $\phi_0$ of the monomers, two scaling behaviors for the ejection velocity $v$ on the monomer number $m$ in the cavity are obtained: $v \sim m^{1.25}\phi_0^{1.25}/N^{1.6}$ for large $m$ and $v \sim m^{-1.4}$ as $m$ is small. A robust scaling theory is developed by dividing the process into the confined and the non-confined stages, and the dynamical equation is derived via the study of energy dissipation. After trimming the prior stage related to the escape of the head monomer across the pore, the evolution of $m$ is shown to be well described by the scaling theory. The ejection time exhibits two proper scaling behaviors: $N^{2/(3\nu)+y_1}\phi_0^{-2/(3\nu)}$ and $N^{2+y_2}$ under the large and small $\phi_0$- or $N$-conditions, respectively, where $y_1=1/3$, $y_2=1-\nu$, and $\nu$ is the Flory exponent.