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

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.