Diffusion of small particles in a solid polymeric medium

TL;DR

This paper investigates how small particles diffuse through a solid polymer medium, considering particle-polymer interactions, and finds complex temperature-dependent behaviors influenced by interaction sign and percolation properties.

Contribution

It introduces a lattice model incorporating particle-polymer interactions and analyzes diffusion behavior using analytical and simulation methods, revealing non-trivial temperature dependence.

Findings

Diffusion coefficient weakly depends on polymer chain length without interactions.

Interactions cause non-trivial temperature dependence, including Arrhenius and non-Arrhenius behaviors.

Analytical results agree qualitatively with Monte Carlo simulations.

Abstract

We analyze diffusion of small particles in a solid polymeric medium taking into account a short range particle-polymer interaction. The system is modeled by a particle diffusion on a ternary lattice where the sites occupied by polymer segments are blocked, the ones forming the hull of the chains correspond to the places at which the interaction takes place, and the rest are voids, in which the diffusion is free. In the absence of interaction the diffusion coefficient shows only a weak dependence on the polymer chain length and its behavior strongly resembles usual site percolation. In presence of interactions the diffusion coefficient (and especially its temperature dependence) shows a non-trivial behavior depending on the sign of interaction and on whether the voids and the hulls of the chains percolate or not. The temperature dependence may be Arrhenius-like or strongly non-Arrhenius, depending on parameters. The analytical results obtained within the effective medium approximation are in qualitative agreement with those of Monte Carlo simulations.