Effects of disorder and chain stiffening on the elasticity of flexible polymer networks

TL;DR

This study investigates how disorder and chain stiffening influence the elasticity of flexible polymer networks, revealing that chain tension dominates the shear modulus and that node equilibration induces specific correlations.

Contribution

It demonstrates that in flexible polymer gels, the shear modulus is primarily governed by chain tensions and highlights the importance of node-induced correlations for accurate modeling.

Findings

Non-affine contributions are negligible in the studied range.

Shear modulus is dominated by chain tension contributions.

Node equilibration induces specific correlations between chain properties.

Abstract

We examine how the distribution of contour lengths and the high-stretch stiffening of individual chain segments affect the macroscopic shear modulus of flexible polymer gels, using a 2D numerical model, in which polymer segments form a triangular network and disorder is introduced by varying their contour lengths. We show that in the relevant parameter range: (i) the non-affine contribution to the shear modulus is negligible, i.e. the Born approximation is satisfactory; (ii) the shear modulus is dominated by the contribution originating from equilibrium chain tensions. Moreover, mechanical equilibration at the nodes induces specific correlations between the end-to-end distances and contour lengths of chain segments, which must be properly accounted for to construct reasonable estimates of chain pressure and shear modulus.