Effect of Spatial Heterogeneity on the Elasticity and Fracture of Polymer Networks

Mechanical properties of elastomers and gels depend intricately on the underlying polymer network, which is often topologically inhomogeneous comprising several defects such as primary loops and dangling ends. Depending upon the curing conditions, the polymer network may also possess spatial heterogeneity, comprising localized regions of significantly high and low cross-linker densities. In this work, coarse-grained simulations are used to investigate the coupled effect of topological and spatial heterogeneity on the elasticity and fracture of polymer networks. Spatially heterogeneous networks are generated by forming concentrated domains of cross-linkers at random positions in the simulation box, while homogeneous networks are produced by randomly distributing the cross-linkers throughout the simulation box. For the homogeneous networks, it is observed that the shear modulus decreases almost linearly with the increase in primary-loop fraction, in accordance with the predictions from the real-elastic network theory. Increasing the spatial heterogeneity in the network decreases both the shear modulus and the ultimate stress before failure. This is attributed to the significant change in the distribution of chain end-to-end distance, resulting in an increased population of chains with short end-to-end distances due to the formation of local clusters of cross-linkers. It is observed that the chains with short end-to-end distances do not stretch significantly throughout the entire deformation, while only a small fraction of chains that interconnect the local heterogeneous regions break to produce fracture. In contrast to the homogeneous networks, the shear modulus of heterogeneous networks varies nonmonotonically with the primary-loop fraction; the decrease in modulus with increasing spatial heterogeneity is much more pronounced for the networks with fewer primary loops compared to those with relatively large primary-loop fraction. This nonmonotonic variation occurs due to a competing effect of increasing chain end-to-end distance and decreasing effective cross-linking density with the increase in primary-loop fraction. Overall, this work sheds light on the complex interplay of spatial and topological heterogeneity in polymer networks and provides insights into designing elastomers with tailored mechanical properties.