FloryHugginsChiParameter

The Flory–Huggins theory is a foundational framework in polymer science for describing the thermodynamics of mixing polymers with solvents and for polymer blends. Developed independently by Paul Flory and Maurice Huggins in the 1940s, it uses a lattice model to capture the balance between the entropy of mixing and the enthalpic interactions between components. The theory provides a simple, general way to predict when a polymer solution will be homogeneous or undergo phase separation, and it has become a standard tool in understanding solvent quality and miscibility.

The central result is a lattice-based expression for the dimensionless free energy of mixing per lattice site. If φp is the polymer volume fraction, φs is the solvent volume fraction, Np is the polymer degree of polymerization, and χ is the Flory–Huggins interaction parameter, the free energy change upon mixing is written as ΔGm/(kT) = (φp/Np) ln φp + φs ln φs + χ φp φs. The first two terms represent the entropy of mixing (with a reduced contribution from long polymer chains), while the last term accounts for enthalpic interactions. Phase behavior is inferred from this expression by locating binodal and spinodal curves, with demixing favored at high χ or for sufficiently large Np.

Limitations of the model include its mean-field nature and the assumptions of incompressibility and a regular lattice; it neglects concentration fluctuations, specific chemical details, and some molecular architectures. Extensions and refinements address polymers with more complex architectures, multiple solvents, and nonidealities.

Applications include predicting solubility, solvent quality, and phase diagrams of polymer solutions and blends, as well as guiding solvent selection and the interpretation of experimental cloud points.