MODELING FREE-RADICAL COPOLYMERIZATION KINETICS - EVALUATION OF THE PSEUDO-KINETIC RATE-CONSTANT METHOD .2. MOLECULAR-WEIGHT CALCULATIONS FOR COPOLYMERS WITH LONG-CHAIN BRANCHING

The full moment equations and equations using pseudo-kinetic rate cons tants for binary copolymerization with chain transfer to polymer in th e context of the terminal model have been developed and solved numeric ally for a batch reactor operating over a wide range of conditions. Ca lculated number- and weight-average molecular weights (M(n)BAR and M(w )BAR) were compared with those found using the pseudo-kinetic rate con stant method (PKRCM). The results show that the weight-average molecul ar weights calculated using PKRCM are in agreement with those found us ing the method of full moments for binary copolymerization when polyme ric radical fractions PHI1. and PHI2. of type 1 and 2 (radical centers are on monomer types 1 and 2 for a binary copolymerization) are calcu lated accounting for chain transfer to small molecules and polymer rea ctions in addition to propagation reactions. Errors in calculating M(w )BAR using PKRCM are not always negligible when polymer radical fracti ons are calculated neglecting chain transfer to small molecules and po lymer. In this case, the relative error in M(w)BAR by PKRCM increases with increase in monomer conversion, extent of copolymer compositional drift and chain transfer to polymer rates. The erros in calculating M (w)BAR, however, vanish over the entire monomer conversion range for a ll polymerization conditions when chain transfer reactions are properl y taken into account. It is theoretically proven that the pseudo-kinet ic rate constant for chain transfer to polymer is valid for copolymeri zations. One can therefore conclude that the pseudo-kinetic rate const ant method is a valid method for molecular weight modelling for binary and multicomponent polymerizations.