Shortest Paths Govern Bond Rupture in Thermoset Networks

Understanding bond rupture in polymer networks remains a fundamental challenge due to the interplay of network topology and condensed phase effects. In this work, we introduce a predictive approach for determining bond rupture in thermosets based on shortest paths (SPs) analysis of the network topology. This method enumerates SP sets in networks with periodic boundary conditions, with applications to both all-atom and coarse-grained simulations. We find that bond rupture is most likely to initiate on the first (shortest) SP in the thermoset network and the strain at which the first bond ruptures is linearly correlated with the topological path length. As a result, one can predict the first bond rupture by computing the first SP directly from the initial thermoset topology without resorting to MD simulations. Furthermore, the specific bond rupture location along the first SP follows a probability distribution associated with the SP-based betweenness centrality. Subsequent bond rupture events are dictated by the instantaneous SP of partially broken networks. Moreover, we quantify the length scale dependence of SP distributions, introducing a means of partially bridging the observed ductile rupture in molecular simulations and brittle rupture in experiments.