2024 AIChE Annual Meeting
(32c) Exact Analytical Solution of the Flory-Huggins Model and Extensions to Multicomponent Systems
Authors
de Souza, P. - Presenter, Massachusetts Institute of Technology
Stone, H. A., Princeton University
The Flory-Huggins theory captures the basic features of phase separation in polymeric solutions, and it therefore finds widespread application in polymer physics, materials science, and biology. Even so, thus far, the theory predictions for the composition of coexisting phases have been computed by numerically solving systems of nonlinear equations, which hinders the use of the theory. In this work, we derive an implicit analytical solution for the composition of coexisting phases in the Flory-Huggins theory of a single polymer-solvent mixture. The solutions are expressed in terms of composite composition variables, which are explicitly mapped to phase diagrams in composition space. Extending the same methods to multicomponent solutions, we also derive analytical solutions for a polydisperse polymer of one type in solvent. While complete analytical solutions are not available for general mixtures, we simplify the systems of equations down to one nonlinear equation in one unknown, the solvent partitioning between phases. Finally, we propose computationally efficient strategies to map out the coexistence curves for systems with many components.