MODELING FREE-RADICAL COPOLYMERIZATION KINETICS .3. MOLECULAR-WEIGHT CALCULATIONS FOR COPOLYMERS WITH CROSS-LINKING

A comprehensive model for molecular weight calculations of free-radica l crosslinking copolymerizations was developed using the pseudo-kineti c rate constants and the method of moments. The moments of copolymer c hain distributions are defined in such a way so that the molecular wei ght averages of crosslinking copolymers can be calculated using the mo ments. The present model is based on a general crosslinking copolymeri zation scheme, accounting for chain transfer to small molecules and po lymer, bimolecular termination, and crosslinking reactions. The influe nce of crosslinking reactions on molecular weight development is discu ssed. The effects of the reactivity of pendant double bonds on the mom ents development were further demonstrated using model simulations. Th e simulation results suggest that the higher-order molecular weight av erages are very sensitive to the reactivity of pendant double bonds. I t was found that chain transfer to polymer affects the gelation point significantly. The radical fractions must be calculated accounting for chain transfer reactions in addition to propagations in order to prop erly evaluate pseudo-kinetic rate constants. The present model was use d to predict kinetic behavior and molecular weight development of styr ene/m-divinylbenzene and styrene/ethylene dimethacrylate free-radical crosslinking copolymerizations in benzene solution at 60-degrees-C. It was found that the present model is in excellent agreement with the e xperimental data published in the literature. Model predictions and ex perimental data show that the reactivity of pendant double bonds is mu ch lower than that of vinyl and divinyl monomers. The simulation resul ts suggest that the assumption of the same reactivity of functionl gro ups is likely not valid for many free-radical crosslinking copolymeriz ations. The present model based on a kinetics approach can be used to predict molecular weight development for vinyl/divinyl free-radical cr osslinking copolymerizations and to estimate kinetic parameters in the pre-gelation period.