Fracture Behavior of Monodisperse and Polydisperse Polymer Networks: Effects of Topology and Strand-Length Dispersity

Polymer network fracture reflects a complex interplay between molecular-scale topology and large-scale mechanical response. While classical frameworks such as the affine network theory and Lake–Thomas model successfully describe the modulus and toughness of monodisperse, end-linked networks, their applicability to polydisperse systems remains less known. In this work, we employ coarse-grained molecular dynamics simulations to systematically compare the mechanical and fracture properties of monodisperse end-linked and polydisperse polymerized networks. Detailed graph-theoretic analyses reveal distinct topological differences between the classes of networks, including strand-length distributions, loop-order populations, and effective cross-link functionalities. Despite these differences, both network types exhibit fracture evolution governed by geodesic edge betweenness centrality (GEBC), highlighting the universal role of topology and stress localization in controlling rupture. Fracture consistently initiates at strands with high GEBC scores, independent of strand length, and spatial correlations in scission events emerge when the networks approach their peak stress. The affine network model accurately predicts elastic moduli in monodisperse networks when network topology is explicitly resolved, but fails for polydisperse systems. Similarly, the real elastic network theory (RENT)-modified Lake–Thomas model quantitatively describes fracture energies in monodisperse networks when both defect and connectivity corrections are applied, but fails in predicting the fracture energies in polydisperse networks due to their evolving heterogeneity. These results underscore the limitations of current elasticity and fracture models for chemically heterogeneous networks and motivate the development of new theoretical frameworks incorporating both strand-length dispersity and topological complexity.