Elasticity of entangled polymer loops: Olympic gels

TL;DR

This paper develops a scaling theory for the elasticity of olympic gels, where elasticity arises solely from topology, revealing two deformation regimes with distinct free energy scaling behaviors.

Contribution

It introduces a novel scaling theory distinguishing non affine and affine deformation regimes in olympic gels, predicting a non-Hookian stress-strain relation.

Findings

Two deformation regimes identified: non affine and affine.

In the affine regime, free energy scales as λ^{5/2}.

Predicts highly non Hookian stress-strain behavior.

Abstract

In this note we present a scaling theory for the elasticity of olympic gels, i.e., gels where the elasticity is a consequence of topology only. It is shown that two deformation regimes exist. The first is the non affine deformation regime where the free energy scales linear with the deformation. In the large (affine) deformation regime the free energy is shown to scale as $F \propto \lambda^{5/2}$ where $\lambda$ is the deformation ratio. Thus a highly non Hookian stress - strain relation is predicted.