Effect of composition dependence in Flory-Huggins parameters on solid dispersion stability prediction

Flory-Huggins models underpin phase diagram construction and stability analysis in a wide range of polymer-solute systems, including pharmaceutical solid dispersions, where phase diagrams are routinely used to guide formulation design and stability risk assessment during product development. In practice, the interaction parameter is commonly represented as a temperature-dependent function, χ=χ(T), fitted to experimental data. However, multiple studies and experimental observations suggest that χ may depend on both temperature and composition (ϕ), that is, χ=χ(ϕ,T). Focusing on solid dispersions, here we develop and interrogate a novel composition-dependent Flory-Huggins mathematical framework and quantify the consequences of using χ(ϕ,T) in place of χ(T) when predicting and interpreting phase behaviour. We derive the appropriate chemical potentials and stability conditions required for binodal and spinodal calculations when χ depends on both composition and temperature, and we present generalized criteria for the existence of both upper critical solution temperature (UCST) and lower critical solution temperature (LCST) behaviour. We construct phase diagrams for three solid dispersion systems based on independent experimental data taken from the literature and directly compare predictions obtained using χ=χ(T) and χ=χ(ϕ,T) for each system. We demonstrate that allowing χ to depend on composition can lead not only to substantial quantitative differences, but also to qualitatively different phase behaviour. Finally, we illustrate the implications of these differing phase diagrams by developing a partial differential equation model that enables simulation of microstructural spatiotemporal evolution. The resulting simulations validate the predicted stability landscapes and reveal rich demixing morphologies, including bicontinuous networks and droplet formation.