Liquid-liquid equilibria of polydisperse polymer systems showing both UCST and LCST phase behaviors

To describe liquid-liquid equilibria of polydisperse polymer/solvent systems in the framework of continuous thermodynamics, a continuous distribution function for describing the composition of polydisperse polymers must be considered. In this study, we introduce the log-normal distribution function and then calculate the molar mass distributions of both principal phases and conjugate phases. We apply these different molar mass distributions to the extended Flory-Huggins model. Experimentally, we investigate both the upper critical solution temperature (UCST) and the lower critical solution temperature (LCST) phase behavior of various polydisperse polystyrene/cyclohexane systems and compare the proposed model with experimental data. Although the proposed model does not theoretically consider the free volume and the specific interaction effects related to LCST, it is suitable for the representation of liquid-liquid equilbria of polydisperse polymer solutions, using a few semiempirical adjustable parameters.