# Extending the Flory–Huggins Theory for Crystalline Multicomponent Mixtures

## TL;DR

This paper extends the Flory–Huggins theory to account for crystallization in mixtures, enabling the study of phase separation in both amorphous and crystalline systems.

## Contribution

A new free energy model is derived to capture the interplay between crystallization and demixing in multicomponent mixtures.

## Key findings

- The extended model incorporates both crystallization and amorphous demixing mechanisms.
- Examples of binary and ternary phase diagrams demonstrate the model's versatility.
- Chemical potential calculations are adapted to the new framework.

## Abstract

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.