Quantification of Cyclic Topology in Polymer Networks Using 3D Nets

Polymer networks invariably possess topological inhomogeneities in the form of loops and dangling ends. The macroscopic properties of such materials are directly dependent on the local cyclic topology around nodes and chains. Here, a new formalism to model polymer network topology is presented based on the concept of 3D nets that enables computation of these local cyclic topologies. A cycle counting algorithm is developed which characterizes the relevant local topological cycles around every node, enabling comparison of networks to ideal nets based on local cycle distributions. Comparison of networks formed by different simulation algorithms, using a topology-based distance metric, reveals that polymer networks possess a fundamental cycle size which depends on the topological proximity of crosslinkers during bond formation. This parameter identifies distinct topological classes of networks and provides an effective method to simulate a wide array of networks starting from suitable 3D nets. This approach can be readily generalized beyond polymer networks, enabling quantification of the cyclic topology and facilitating study of topology-property correlations.