(494a) Modeling Multiradicals in Crosslinking MMA/Egdma Bulk Copolymerization
One of the most common assumptions underlying the kinetic modeling of free radical polymerization is that the maximum number of active sites per chain is one (monoradical assumption). The mathematical and numerical simplifications resulting from this assumption are indeed of great benefit to limit the computational effort. While in linear copolymerization the latter assumption holds, things might change when crosslinking, or transfer to polymer and termination by combination occur. In these cases, a gel phase arises, changing the reaction environment to such an extent that radicals can accumulate in the reactive mixture and coexist on the same chain.
The first authors to raise this problem were Kuchanov and Pis’men, who discussed the role of multiradicals (MRs) in the gel formation and concluded that further investigation was required. Later on, Zhu and Hamielec addressed this problem and solved the non-stationary, multiradical population balance equations already introduced by Kuchanov and Pis’men, up to the gel point by means of the method of moments. They established a criterion for deciding whether or not taking into account MRs: the critical parameter identified was the ratio of the propagation constant over the termination one, kp/kt: if the ratio is larger than 10-3, MRs should be accounted for. The aforementioned criterion is indeed of practical utility but it was justified only by a set of parametric calculations.
To further validate the existing criterion, a kinetic model of crosslinking free-radical copolymerization based on multidimensional population balances and accounting for multiradicals is developed. It gives access to average properties of interest, such as average degree of polymerization of the sol polymer, weight fractions of sol and gel and crosslinking densities. Model validation is carried out by comparison with experimental data for the bulk copolymerization of methyl methacrylate (MMA)/ethylene glycol-dimethacrylate (EGDMA). Then, the model is used to deepen the relevance of multiradicals in the specific system under examination. In particular, the aforementioned literature criterion of model discrimination (mono or multiradicals) is revisited and improved: first, the applicability of this criterion is extended to the case of systems suffering diffusion limitations, a situation of great importance for industrially relevant polymers. Then, the impact of the amount of crosslinking agent is explored, a parameter not accounted for in all previous analyses. Even though the reported results apply to the specific system under examination, this analysis offers better understanding of the complex interplay between reactions producing chain nonlinearity and diffusion limitations.