Topological Interaction between Loop Structures in Polymer Networks and the Nonlinear Rubber Elasticity

TL;DR

This paper introduces a new topological model for nonlinear rubber elasticity in polymer networks, accounting for nonequilibrium effects and entanglement, successfully matching experimental data across different deformation regimes.

Contribution

It proposes a novel model incorporating a parameter for entanglement effects, improving understanding of topological influences on rubber elasticity.

Findings

Model reproduces Mooney-Rivlin behavior in small extensions

Captures stress divergence in elongation limit

Qualitatively aligns with biaxial experimental results

Abstract

We numerically examine the nonlinear rubber elasticity of topologically constrained polymer networks. We propose a simple and effective model based on Graessley and Pearson's topological model (GP model) for describing the topological effect. The main point is to take account of a nonequilibrium effect in the synthesis process of the polymer network. We introduce a new parameter $\gamma$ to describe entropic contributions from the entanglement of polymer loops, which may be determined from the structural characteristics of the sample. The model is evaluated in the light of experimental data under uniaxial and biaxial deformations. As a result, our model exhibits uniaxial behaviors which are common to many elastomers in various deformation regimes such as Mooney-Rivlin's relation in small extension, stress divergence in the elongation limit and the declined stress in compression. Furthermore, it is also qualitatively consistent with biaxial experiments, which can be explained by few theoretical models.