(32g) Fracture in Polymer Networks with Topological Defects

The fracture of polymer networks is one of their most important properties, governing both their toughness and their ultimate extension. The venerable Lake-Thomas theory is the classical foundation for our understanding of network fracture; however, while this theory makes many important and accurate scaling predictions, it often requires quantitative adjustment to predict fracture energy. A limit of the Lake-Thomas approach is that it considers only perfect networks; the presence of defects, shown to influence linear elastic properties, may play an even larger role in governing fracture behavior. Here, we explore the effect of topological defects on fracture using two separate approaches: a single chain approach adapted from the Lake-Thomas formalism and coarse-grained simulations.

In the single chain approach, we consider a network composed of individually stretched elastic strands; the presence of defects in this network leads to a bimodal distribution of strand lengths. As the network is deformed, shorter chains stretch to a greater degree at a given strain, resulting in early fracture of shorter chains. To quantify fracture, we propose a new criterion, micronetwork fracture theory (MFT) that identifies the fracture point as the strain at which chain rupture pushes the network across the inverse gel point. In this framework, when the number of defect chains becomes large, there is a transition from relatively brittle gels to highly extensible networks, consistent with experimental results from the literature, from our group on both PEG and PDMS systems, and with simulation results on idealized bimodal networks.

In order to capture correlations between chains that are beyond the single chain approach, we have also developed a coarse-grained simulation methodology capable of modeling deformation at realistically slow deformation rates by using energy minimization to relax out high frequency degrees of freedom within the system. Using Gusev’s method for network generation in 3D, networks may be initialized and stretched, modeling the rupture of each individual chain using a Bell’s Law formalism. This simulation allows monitoring of stresses on each chain as a function of local network topology, providing deep insight into the molecular-level physics underlying fracture.