Extending the Flory-Huggins Theory for Crystalline Multicomponent Mixtures

The Flory-Huggins theory is a well-established lattice model that is commonly used to study the mixing of distinct chemical species. It can successfully predict phase separation phenomena in blends of incompatible materials. However, it is limited to amorphous mixtures, excluding systems where the phase segregation is shaped by the concurrent crystallization of one or several blend components. A generalization of the Flory-Huggins formalism is thus necessary to capture the coupling and the interplay of crystallization with amorphous demixing mechanisms, such as spinodal decomposition. This work, therefore, revolves around the derivation of a free energy model for multicomponent mixtures that encompasses the physics of both processes. It is detailed which concepts from the original Flory-Huggins theory are required to apprehend the presented developments and how the current framework is built upon them. Furthermore, additional discussion points address chemical potential calculations and selected examples of binary and ternary phase diagrams, thereby highlighting the variety of blend behaviors that can be represented.