Flory–Huggins solution theory

Lore & Background

The thermodynamic equation for the Gibbs energy change accompanying mixing at constant temperature and (external) pressure is ΔG_mix = ΔH_mix − TΔS_mix. The objective is to find explicit formulas for ΔH_mix and ΔS_mix, the enthalpy and entropy increments associated with the mixing process.

Reader's Guide

Flory–Huggins solution theory provides a foundational framework for understanding polymer solutions by introducing a lattice model that accounts for the size disparity between polymer chains and solvent molecules. The key innovation is the use of volume fractions instead of mole fractions, reflecting the relative sizes of the molecules. The theory yields an expression for the Gibbs free energy of mixing that includes a parameter χ, which takes account of the energy of interdispersing polymer and solvent molecules. While the model makes simplifying assumptions, such as treating polymer segments and solvent molecules as occupying sites on a lattice, it remains widely used for interpreting experimental data on polymer solutions. The entropy of mixing is derived from a random walk on a lattice, leading to an expression involving the Boltzmann constant and the number of solvent molecules and polymer segments. The theory's significance lies in its ability to predict phase behavior and miscibility in polymer systems, despite its approximations.

Did You Know?

• The theory is a lattice model of the thermodynamics of polymer solutions.
• It takes account of the great dissimilarity in molecular sizes in adapting the usual expression for the entropy of mixing.
• The result is an equation for the Gibbs free energy change ΔG_mix for mixing a polymer with a solvent.
• The mixing parameter χ is a free energy parameter, thus including an entropic component.