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CPP: Fachverband Chemische Physik und Polymerphysik

CPP 58: Gels, Polymer Networks and Elastomers III

CPP 58.3: Vortrag

Freitag, 13. März 2026, 12:00–12:15, ZEU/0255

From real polymers to random graphs: percolation thresholds in associative polymer solutions — •Xinxiang Chen, Lennart Hebestreit, and Friederike Schmid — Johannes Gutenberg-University Mainz, Mainz, Germany

Multivalent reversible crosslinking is ubiquitous in soft matter and biomolecular condensates, yet their sol-gel transitions often deviate from the classical Flory-Stockmayer picture due to chain conformations, intrachain binding, and loop formation. Here, we develop a unified framework combining molecular dynamics simulations with random-graph and random-geometric-graph approaches to quantitatively link real polymer architectures to abstract network models. For single- and two-component reversible polymers with one-to-one specific binding, we determine gel points from topological connectivity and find percolation thresholds substantially higher than Flory-Stockmayer predictions. By comparing spatially unconstrained random graphs with spatially correlated random geometric graphs, we show that intrachain binding and loops markedly reduce the effective interchain bonding needed to form an infinite cluster. Meanwhile, the theoretical results of the generating function and the Lagrange inversion further yield cluster size distributions and giant cluster fractions. Our work demonstrates how spatial correlations and polymer conformations fundamentally reshape reversible network formation, offering a unified topological and physical perspective on reversible gels and biomolecular condensates.

Keywords: Sol-gel transition; Percolation threshold; Random graph; Flory-Stockmayer theory; Associative polymer