An Exact Algorithm to Detect the Percolation Transition in Molecular Dynamics Simulations of Cross-Linking Polymer Networks

Periodic molecular dynamics simulations are developing to a routine tool for the investigation of complex, polymeric materials. A typical application is the simulation of the curing reaction of covalently cross-linked polymers, which provides detailed understanding of network formation at the molecular scale, with examples including gelation and glass transitions. In this article, we delineate the connection between percolation theory and gel-point detection in periodic polymeric networks. Specifically, we present an algorithm that can detect the onset of percolation during cross-linking of polymers in periodic molecular dynamic simulations. A sample implementation is provided at https://github.com/puls-group/percolation-analyzer. As an example, we apply the algorithm to simulations of an epoxy resin undergoing curing with an amine hardener. We also compare results with indirect gel point measurements obtained from monitoring the growth of the largest mass and the onset of secondary cycles.