Analytical Solution to the Flory–Huggins Model

A self-consistent analytical solution for binodal concentrations of the two-component Flory–Huggins phase separation model is derived. We show that this form extends the validity of the Ginzburg–Landau expansion away from the critical point to cover the whole phase space. Furthermore, this analytical solution reveals an exponential scaling law of the dilute phase binodal concentration as a function of the interaction strength and chain length. We demonstrate explicitly the power of this approach by fitting experimental protein liquid–liquid phase separation boundaries to determine the effective chain length and solute–solvent interaction energies. Moreover, we demonstrate that this strategy allows us to resolve differences in interaction energy contributions of individual amino acids. This analytical framework can serve as a new way to decode the protein sequence grammar for liquid–liquid phase separation.