Interplay of Coil-Globule Transitions and Aggregation in Homopolymer Aqueous Solutions: Simulation and Topological Insights

Abstract: We investigate the structural and topological behavior of interacting hydrophobic polymer chains in aqueous solutions by combining molecular dynamics simulations with circuit topology (CT) analysis. Combining geometric observables such as the radius of gyration and degree of aggregation with CT data we are able to capture the relationship between the coil-globule and aggregation transitions, resolving the underlying organizational changes of the system. Our results uncover a clear temperature-driven collective transition from isolated coiled polymers to aggregated globular clusters. This transition is reflected not only in conventional geometric descriptors but also in a striking reorganization of CT motifs: from dominant intrachain motifs at low temperatures to a rich ensemble of multichain motifs as temperature increases. We demonstrate that CT motif enumeration reproduces standard contact statistics via combinatorics while simultaneously providing a higher-order, topologically informed view of polymer organization. These findings highlight the power of CT as a structural descriptor for complex soft-matter systems and suggest broad applicability to biologically relevant phenomena.