Mathematical Modelling and Phase Separation Kinetics of Polystyrene/Polyvinylmethylether Blend

A mathematical model based on the Cahn-Hilliard non-linear theory of phase separation has been developed. The model equation has been solved using a discrete cosine transform spectrum method to provide dynamic spatial concentration field of a polymer blend and predicting the morphology evolution during the course of a temperature-induced phase separation process. The model shows an accurate qualitative agreement with experimental observation using parameters of the polystyrene/polyvinylmethylether blend and different initial concentrations of the blend have been tested in relation to the microstructure, transient and later stages of blend morphologies. It has been observed that kinetics and morphology of the phase separated blend are affected by the initial concentration of the blend. In this study, different types of microstructures, e.g., droplet-like and rod-like morphologies have been identified. It is concluded that the initial concentration of each component of the blend and temperature are the most important variables which control the kinetics of phase separation and blend morphology. The mathematical model provides a suitable tool for better understanding of the kinetics and phase separation process as well as the microstructure of the polymer blends. The discrete cosine transform method for solving a high non-linear partial differential equation is considered as a suitable numerical approach where the other conventional mathematical numerical methods such as finite element and finite volume methods require many computational facilities. The model is very useful for studies of the early and later stages of phase separation process and provides information on concentration profile of the separated phases which would be useful in the determination of the interfacial properties