Solubility Parameter

The solubility parameterδ is a thermodynamic quantity introduced by Hildebrand and Scatchard (HS) to describe the behavior of the so-called regular solutions. Such solutions have a negligible mixing volume and excess entropy of mixing, so that the excess Gibbs free energy coincides with the mixing enthalpy. The HS model uses the idea of cohesive energy density (CED), that is, the difference between the internal energy of the system and that of the corresponding system in the ideal gas state, per volume of liquid substance, estimated as follows: (Sandler 2006)

(1)

And the solubility parameter δ is defined as:

$$ \delta \equiv \sqrt{CED} $$

(2)

The solubility parameter is related to the molar excess Gibbs free energy, ${\tilde{G}}^{EX}$, and to the mixing enthalpy, $\Delta {\tilde{H}}_{MIX}$, by the following expression valid for a binary mixture:

(3)

where:

(4)

And for the activity coefficient of species i:

(5)

The model is predictive for the solubility as far as the δvalues...