Modeling of branching and gelation in living copolymerization of monomer and divinyl cross-linker using dynamic lattice liquid model (DLL) and Flory–Stockmayer model

The random living copolymerization of vinyl and divinyl monomers with fast initiation and slow propagation was simulated using two Monte Carlo methods: one, purely statistical, corresponding to the mean-field Flory–Stockmayer (FS) theory and the dynamic lattice liquid model (DLL). The results were compared with experiments in which atom transfer radical polymerization (ATRP) method was used. Molecular weights, polydispersities and the cross-linking/cyclization of macromolecules were modeled as a function of conversion for various cross-linker concentrations. The results obtained by the DLL and FS methods and experiments are presented and the sources of discrepancies are discussed. The DLL method yields gel points, molecular weight distributions and critical exponents closer to experimental values and gives an insight into cross-linking processes near the gel point (leading to gelation). More realistic gel structure is obtained due to an appropriate modeling of intra-chain cyclization and diffusion effects, especially close to and above the gel point.