Flory–Huggins solution theory is a lattice model of the thermodynamics of polymer solutions which 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 for mixing a polymer with a solvent. Although it makes simplifying assumptions, it generates useful results for interpreting experiments. Theory The thermodynamic equation for the Gibbs energy change accompanying mixing at constant temperature and (external) pressure is A change, denoted by , is the value of a variable for a solution or mixture minus the values for the pure components considered separately. The objective is to find explicit formulas for and , the enthalpy and entropy increments associated with the mixing process. The result obtained by Flory and Huggins is The right-hand side is a function of the number of moles and volume fraction of solvent (component ), the number of moles and volume fraction of polymer (component ), with the introduction of a parameter to take account of the energy of interdispersing polymer and solvent molecules. is the gas constant and is the absolute temperature. The volume fraction is analogous to the mole fraction, but is weighted to take account of the relative sizes of the molecules. For a small solute, the mole fractions would appear instead, and this modification is the innovation due to Flory and Huggins. In the most general case the mixing parameter, , is a free energy parameter, thus including an entropic component. Derivation We first calculate the entropy of mixing, the increase in the uncertainty about the locations of the molecules when they are interspersed. In the pure condensed phases — solvent and polymer — everywhere we look we find a molecule. Of course, any notion of "finding" a molecule in a given location is a thought experiment since we can't actually examine spatial locations the size of molecules. The expression for the entropy of mixing of small molecules in terms of mole fractions is no longer reasonable when the solute is a macromolecular chain. We take account of this dissymmetry in molecular sizes by assuming that individual polymer segments and individual solvent molecules occupy sites on a lattice. Each site is occupied by exactly one molecule of the solvent or by one monomer of the polymer chain, so the total number of sites is is the number of solvent