Graph-Theoretical Analysis of Structural Evolution in Conducting Polymer Networks

Understanding the structural evolution of conducting polymer systems is essential for advancing next-generation organic electronic materials. While atomistic molecular dynamics (MD) simulations have provided microscopic insights into their structural dynamics and phase transitions during electrochemical switching, how these dynamics influence network connectivity and overall morphology remains largely unexplored. In this work, we integrate MD simulations with graph-theoretical (GT) analysis to investigate the structural evolution of poly(benzimidazobenzophenanthroline) (BBL) across different reduction levels. By mapping MD trajectories onto graph representations at multiple coarse-graining scales, we apply network science metrics to uncover structure–property relationships from a topological perspective. This framework extends conventional MD analyses such as X-ray diffraction and radial distribution functions by quantifying changes in network topology, connectivity, and clustering. GT enables the identification of emergent structural correlations in seemingly disordered macromolecular networks, revealing how short- and long-range order evolve with reduction and allowing one to decouple structural reorganization from conductivity changes upon doping.