Phantom Chain Simulations for Fracture of End-linking Networks

Despite numerous studies, the relationship between network structure and fracture remains unclear. In this study, the fracture properties of end-linking networks were compared with those of loop-free analogs made from star prepolymers by performing phantom chain simulations. The networks were created from equilibrated sols of stoichiometric mixtures of linear prepolymers and f-functional linkers through end-linking reactions using Brownian dynamics schemes. The examined networks, with various f values (between 3 and 8) and strand-connection rates ({\phi}_s), were evaluated in terms of the primary loop fraction and the cycle rank {\xi}. These structural characteristics were consistent with mean-field theories that assume independent reactions. Energy minimization and uniaxial stretch were applied to the networks until they broke without Brownian motion. The fracture characteristics, including strain ({\epsilon}_b), stress ({\sigma}_b), and work for fracture (W_b), were obtained from stress-strain curves. The end-linking networks exhibited larger {\epsilon}_b and smaller {\sigma}_b and W_b than those for star networks due to primary loops, at the same set of f and {\phi}_s. However, {\epsilon}_b, {\sigma}_b/{\nu}_br and W_b/{\nu}_br (with {\nu}_br being the branch point density) lie on the same master curves as those for star networks if they are plotted against {\xi}. This result implies that the fracture of end-linking networks is essentially the same as that for star analogs, and the effects of primary loops are embedded in {\xi}.