Broadening of molecular-weight distribution in solid-state polymerization resulting from condensate diffusion

A kinetic model for the solid-state polymerization of poly(bisphenol A carbonate) in a single particle has been developed and used to investigate the broadening of molecular-weight distribution as a result of slow condensate diffusion. The model is based on melt-phase transesterification kinetics and Fickian diffusion of phenol, the condensate, in the amorphous regions of the semicrystalline particle. Model predictions compare favorably to experimental data. When diffusion is slow compared to reaction, a condensate concentration gradient is established. This gradient induces a molecular-weight gradient, which results in a broadened overall molecular-weight distribution with an overall polydispersity above the theoretical limit for homogenous step-growth polymerization. As the mass transfer resistance inside the particle is decreased, the average molecular weight increases faster with time, and the overall polydispersity decreases. A stoichiometric imbalance of end groups decreases the obtainable molecular weight but mitigates the deleterious effects of slow condensate diffusion.