Ring polymers on percolation clusters

TL;DR

This study investigates the conformational properties of ring polymers on three-dimensional percolation clusters, revealing increased elongation and anisotropy in disordered environments through numerical simulations.

Contribution

It introduces a model of cyclic polymers on percolation clusters and provides quantitative analysis of their size and shape characteristics in disordered media.

Findings

Ring polymers become more elongated in disordered environments.

Anisotropy of ring conformations increases on percolation clusters.

Universal size ratios and shape parameters are estimated.

Abstract

In the present work, the cyclic polymer chains (rings) in structurally disordered environment (e.g. in the cross-linked polymer gel) are studied exploiting the model of closed self-avoiding walks (SAWs) trajectories on $d=3$-dimensional percolation clusters. Numerical simulations with an application of pivot algorithm are performed. The estimates for the universal size and shape characteristics such as size ratios, averaged asphericity and prolateness of typical polymer conformation are obtained. Our results quantitatively describe an elongation and increase of anisotropy of ring polymers in disordered environment comparing with the pure solvent.