Structural heterogeneity in tetra-armed gels revealed by computer simulation: Evidence from a graph theory assisted characterization

Designing homogeneous networks is considered one typical strategy for solving the problem of strength and toughness conflict of polymer network materials. Experimentalists have proposed the hypothesis of obtaining a structurally homogeneous hydrogel by crosslinking tetra-armed polymers, whose homogeneity was claimed to be verified by scattering characterization and other methods. Nevertheless, it is highly desirable to further evaluate this issue from other perspectives. In this study, a coarse-grained molecular dynamics simulation coupled with a stochastic reaction model is applied to reveal the topological structure of a polymer network synthesized by tetra-armed monomers as precursors. Two different scenarios, distinguished by whether internal cross-linking is allowed, are considered. We introduce the Dijkstra algorithm from graph theory to precisely characterize the network structure. The microscopic features of the network structure, e.g., loop size, dispersity, and size distribution, are obtained via the Dijkstra algorithm. By comparing the two reaction scenarios, Scenario II exhibits an overall more idealized structure. Our results demonstrate the feasibility of the Dijkstra algorithm for precisely characterizing the polymer network structure. We expect this work will provide a new insight for the evaluation and description of gel networks and further help to reveal the dynamic process of network formation.