Role of Polyradicals in Predicting Chain Length Distribution and Gelation for Radical Polymerization with Transfer to Polymer

A Galerkin finite element method (GF) model using pseudo-distributions was developed to predict the full two-dimensional chain length number of radical sites per chain distribution (CLD/RSD) for radical polymerization in a CSTR with transfer to polymer, without and with termination by recombination. A special variant deals with gelation using recently developed ideas involving the sol and gel moments of all chains present. The overall chain length distributions were compared to those obtained from Monte Carlo (MC) simulations, yielding almost perfect agreement in cases without and with termination by recombination, even when gelation occurs. GF models and MC simulations predict identical gel points and weight fractions gel. With increasing transfer to polymer rate coefficient k tp the CLDs become broader until the gel point, while at further increase they become narrower again. It turns out that the monoradical assumption is not valid in the case of termination by disproportionation, when transfer to polymer rate to propagation rate is high and extremely long chains (>10 8 ) are formed (but no gel), even for a relatively low propagation-to-termination ratio. On the contrary, in the case of recombination−termination under circumstances leading to gelation, the assumption is valid for the sol molecules up to a ratio of 0.025 because of their relatively small size. The study reveals a deeper understanding of the polyradical issue in radical polymerization and in addition shows that two completely different computation methods Galerkin FEM population balance equations and Monte Carlo simulations yield perfectly matching results.