Phase field model for reactive blending of a symmetric binary polymer blend

Reactive blending is a process for forming polymer alloys where mutually reactive homopolymers are mixed together to form compatibilizers in-situ. The dynamics of the problem is replete with rich nonequilibrium physics stemming from reactions between the polymers, spatiotemporal transport, thermodynamics of mixing, and externally imposed processing conditions, and has hence been poorly understood. To study this process, we develop a coarse-grained phase-field model designed to capture all of the above physical effects. We then implement the model using pseudospectral collocation and semi-implicit time stepping to solve for temporal evolution of concentration distributions. In the case of reaction-diffusion dynamics, we find that the reaction typically progresses with the formation of an interfacial, diblock-rich layer. Eventually, the diblock diffuses out of the interface and the homopolymers diffuse in, as the reaction proceeds toward completion. The reaction rates in each stage depend on the incompatibility of the species, the Damkohler number and the initial distribution.