Free Enthalpy Functions and Fractionation Equation

Phase relationships in equilibrium are determined by the free enthalpy (Gibbs free energy) of the system. The thermodynamic bdiaviour of polymer solutions can be very well described with the free enthalpy of mixing function derived, independently, by Florv (6,7) and Huggins (8—10) on the basis of the lattice theory of the liquid state. For the simplest case conceivable — a solution of a polydisperse polymer in a single solvent quasi-binary system) — we have 

The other symbols have the usual nrcaning. In the fnmnlation of Eq. (1), the solvent molecules are taken to occupy one lattice ate each. 

(1) supplies at least a qualitative description of the oteorved liquid-liquid phase behaviour (6—10). Quantitative agreement is not found very often, but can in many cases be readily achieved if g is not taken to depend on temperature alone but also on the polymer concentration (6—10, 12—18)  

It might be of interest not to restrict considerations to solvent molecules of small size. If they are chain-like in shape and occupy lattice sites each, Eq. (1) changes into  

In practice, most fractionations are not carried out in quasi-binary, but in quasi-temary mixtures. The latter consist of a polydisperse polymer, a non-solvent (precipitant) and a solvent. The relevant AG function reads (7. 79-27)  

---