Do Cycles Matter? A Comprehensive Study of Intra- and Intermolecular Reactions in Uncontrolled Branched Polymerization

Abstract Branched polymer formation is governed by a competition between intermolecular crosslinking, which promotes the molecular growth and gelation, and intramolecular cyclization, which consumes reactive groups without increasing intermolecular connectivity. Using three-dimensional coarse-grained molecular dynamics, we study this competition for A2 + B3 step-growth polymerization and free-radical polymerization with a divinyl crosslinker and a chain-transfer agent. In both systems, cyclization delays gelation but reduces molecular weight at a fixed conversion. We introduce a phenomenological crossover concentration c∗∗ at which intra- and intermolecular reactions occur at comparable rates, with αinterαintra≈cc∗∗, where αintra and αinter denote the instantaneous rates of intra- and intermolecular reactions, respectively. Three regimes emerge: intermolecular-crosslinking-dominated at c ≫ c∗∗, cyclization-dominated at c ≪ c∗∗, and an intermediate regime near c ∼ c∗∗ that balances delayed gelation with substantial branching. These results identify the monomer concentration as a practical control parameter for tuning cyclization, branching, and gelation in branched-polymer synthesis.