Modeling polymer blend demixing: complications and simplifications in the Gibbs energy of mixing function*

The Cahn-Hilliard equation, which can be used to model polymer blend morphology at a continuum scale, tracks the decrease of the Gibbs energy of the system through changes in the homogenous free energy, which is given the Gibbs energy of mixing, and the interfacial energy. In most problems, the Gibbs energy of mixing function is typically set as a simple quartic polynomial or in the case of polymer blends, the Flory-Huggins equation. In certain cases, such as for mineral solutions or alloys, more suitable free energy functions have been employed. However, more accurate and complex equations of state (EoS) applicable to polymer blends such as Statistical Associating Fluid Theory (SAFT) based EoS have yet to be explored within a phase-field setting. In this work, we explore how these advanced EoS can be integrated to model binary polymer blends, looking at both thermophysical properties and blend morphology. At the other end of the complexity spectrum, we also investigate the impact of various simplifications to the free energy function and the Cahn-Hilliard equation on the numerical solution.