Monte Carlo Simulations of Atom Transfer Radical (Homo)polymerization of Divinyl Monomers: Applicability of Flory–Stockmayer Theory

It is well known that free radical (co)polymerization of multivinyl monomers (MVMs) leads to insoluble gels even at a low monomer conversion, and the gelation point can be predicted by Flory–Stockmayer theory (F–S theory) based on two assumptions: (1) equal reactivity of all vinyl groups and (2) the absence of intramolecular cyclization. This theory has been experimentally studied and verified with conventional free radical (co)polymerization (FRP) of several MVMs (e.g., divinylbenzene, DVB). However, it is still debatable whether this theory is applicable for the polymerization of MVMs using reversible deactivation radical polymerization (RDRP) approaches, such as atom transfer radical polymerization (ATRP). Herein, Monte Carlo simulations using two statistical models—with cyclization (w.c.) and without cyclization (wo.c., corresponding to F–S theory)—and dynamic lattice liquid (DLL) models were conducted to study ATRP of divinyl monomers. The simulated gel points using w.c. and wo.c. models were compared with those obtained from ATRP experiments, from calculation using F–S theory, and from simulations using DLL models. The molecular weights, dispersity, and extent of intermolecular/intramolecular cross-linking were calculated as a function of double bond and cross-linker conversion. The results demonstrated that the gel points obtained from both w.c. and wo.c. models were lower than the values from DLL models and experiments. This indicates that F–S theory cannot be used to accurately predict the polymerization of divinyl monomers via ATRP. Our study shows that the limitation of F–S theory in predicting ATRP reaction of divinyl monomers is not only due to neglecting intramolecular cyclization but also due to spatial restrictions which can cause the reactivity and accessibility of vinyl groups becoming nonequivalent in ATRP of divinyl monomers.