Gas permeation through a polymer network

TL;DR

This study uses Monte Carlo simulations to explore how gas molecules diffuse through a 2D polymer network, revealing complex dependencies of gas current on polymer density, length, and hopping probability.

Contribution

It introduces a detailed simulation model of gas permeation through a polymer network, analyzing the effects of polymer length, density, and energy barriers on gas flow.

Findings

Gas current decreases with polymer density for fixed length.

For small non-zero hopping probability, current increases with polymer length.

At zero hopping probability, behavior is governed by percolation phenomena.

Abstract

We study the diffusion of gas molecules through a two-dimensional network of polymers with the help of Monte Carlo simulations. The polymers are modeled as non-interacting random walks on the bonds of a two-dimensional square lattice, while the gas particles occupy the lattice cells. When a particle attempts to jump to a nearest-neighbor empty cell, it has to overcome an energy barrier which is determined by the number of polymer segments on the bond separating the two cells. We investigate the gas current $J$ as a function of the mean segment density $\rho$, the polymer length $\ell$ and the probability $q^{m}$ for hopping across $m$ segments. Whereas $J$ decreases monotonically with $\rho$ for fixed $\ell$, its behavior for fixed $\rho$ and increasing $\ell$ depends strongly on $q$. For small, non-zero $q$, $J$ appears to increase slowly with $\ell$. In contrast, for $q=0$, it is dominated by the underlying percolation problem and can be non-monotonic. We provide heuristic arguments to put these interesting phenomena into context.