Modeling Competition between Phase Separation and Polymerization under the Effect of Polydispersity*

The dynamics of phase separation for polymer blends is important in determining the final morphology and properties of polymer materials; in practical applications such as surface coatings, 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 blend using a polymerizing Cahn-Hilliard (pCH) formalism to understand the fundamental processes underlying the 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 the competition between phase separation dynamics and polymerization kinetics. Our pCH model shows that the strength of phase separation directly corresponds to the incompatibility, χ, between the species. We show that the dominant driving forces for inducing phase separation vary from smaller to larger molecules depending on χ. At a fixed χ, phase separation occurs more rapidly with the initial increase in the reaction rate, k, due to the faster growth of molecular weight. However, further increases in k lead to the accumulation of slow-moving, high molecular weight components too quickly, which in turn slows down the phase separation. We then study how this phase separation process is affected by the presence of surfaces.