Mapping the landscape of polymer network topologies with graph-generative modeling*

A polymer network is an irregular mesh composed of chains connected via covalent bonds or supramolecular interactions. This network topology is a key driver of physical properties and represents a rich, complex design space to exploit for materials discovery. Recent synthetic strategies allow for increasingly sophisticated control of topology, with the goal of tailoring properties such as bulk modulus and fracture toughness. However, these efforts have been undertaken without a clear understanding of the feasible space of polymer network designs, primarily due to the vastness and complexity associated with large network topologies. To address this challenge, we leverage recent advances in graph-generative machine learning to populate the feasible polymer topology design space. In so doing, the topological structure of polymer networks is represented as a spatial graph with periodic boundaries, where nodes correspond to cross-link sites and edges correspond to chains. Such networks are computationally synthesized by molecular dynamics or Monte Carlo simulations. These networks are used to train a machine learning model, thereby allowing large sets of realistic topologies to be efficiently generated and explored. Graph metrics related to network mechanics -- node degree, edge length, loop order, etc. -- are measured to provide insight into the types of topologies that could be realistic targets for polymer design.