Cyclization in random graph modeling of acrylate copolymerization

Despite its many applications, three-dimensional radical polymerization remains poorly understood. A major challenge is the considerable kinetic slowdown caused by gelation-a liquid-to-solid phase transition that produces a network permeating the entire volume. This rapidly developing structure greatly obscures direct experimental observations of kinetic mechanisms during network formation. Although molecular dynamics (MD) simulations can qualitatively reproduce the gelation process, they are restricted to unrealistically short time scales. To address this limitation, particularly with respect to cycle formation, we propose coarse-grained modeling techniques based on random graphs (RG) and Monte Carlo (MC) simulations, and apply them to the polymerization of (multi)functional acrylates: N-butyl acrylate (NBA), 1,6-hexanediol diacrylate (HDDA), and trimethylolpropane triacrylate (TMPTA). This approach emphasizes the network of monomer units in the polymer rather than representing individual molecules in atomistic detail. In our models, cycles are represented as special types of vertices, depending on their size. The model demonstrates the impact of cycles, such as a delay in the gel point, which varies with cycle size. The number and size of cycles predicted by the coarse-grained models agree well with MD simulations, but they still fail to capture certain structural features, such as overlapping cycles. Typically, in the gel regime, RG and MC models predict structures with many connected cycles essentially in a tree-like pattern.