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

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 two-dimensional 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 nonaffine contribution to the shear modulus is negligible, i.e., the Born approximation is satisfactory, and (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.