Statistical theory for self-condensing vinyl polymerization system with any initial distribution

Abstract

A generation function method is used to obtain some average polymer physical quantities in the self-condensing vinyl polymerization (SCVP) system with any initial distribution. For the system under study, the generation function is explicitly derived in terms of the corresponding differential kinetic equations. As an application, two SCVP systems with uniform and dispersed prepolymers were discussed, respectively. As a result, the number-, weight- and Z-average degrees of polymerization and polydispersity index were presented. It is shown that, on the one hand, the initial distribution plays an important role in these physical quantities, and on the other hand, the generation function method is found to be very convenient in the calculations of average polymer quantities. It is expected that the present method can be applied in more complex SCVP systems with such as semi-batch process, multi-components and unequal reactivity.