Phantom chain simulations for fracture of end-linking networks

Abstract

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 (φs), were evaluated in terms of the primary loop fraction and the cycle rank ξ. 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 at break (εb), stress at break (σb), and work for fracture (Wb), were obtained from stress-strain curves. The end-linking networks exhibited larger εb and smaller σb and Wb than those for star networks due to primary loops, at the same set of f and φs. However, εb, σb/νbr and Wb/νbr (with νbr being the branch point density) lie on the same master curves as those for star networks if they are plotted against ξ. 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 ξ.