Modeling the competition between phase separation and polymerization under explicit polydispersity

The dynamics of phase separation for polymer blends is important in determining the final morphology and properties of polymer materials; in practical applications, this phase separation can be controlled by coupling to polymerization reaction kinetics via a process called 'polymerization-induced phase separation'. We develop a phase-field model for a polymer melt blend using a polymerizing Cahn-Hilliard (pCH) formalism to understand the fundamental processes underlying phase separation behavior of a mixture of two species independently undergoing linear step-growth polymerization. In our method, we explicitly model polydispersity in these systems to consider different molecular-weight components that will diffuse at different rates. We first show that this pCH model predicts results consistent with the Carothers predictions for step-growth polymerization kinetics, the Flory-Huggins theory of polymer mixing, and the classical predictions of spinodal decomposition in symmetric polymer blends. The model is then used to characterize (i) the competition between phase separation dynamics and polymerization kinetics, and (ii) the effect of unequal reaction rates between species. For large incompatibility between the species (i.e. high χ), our pCH model demonstrates that the strength for phase separation directly corresponds to the kinetics of phase separation. We find that increasing the reaction rate k̃, first induces faster phase separation but this trend reverses as we further increase k̃ due to the competition between molecular diffusion and polymerization. In this case, phase separation is delayed for faster polymerization rates due to the rapid accumulation of slow-moving, high molecular weight components.