Theoretical View: Thermodynamics of the Saturation Dissolution of a Molecular (Solid) Dispersion of a Hydrophobic Molecule and Polymeric Surfactant in an Aqueous Solution

Hot-melt extrusion produces a solid dispersion (SD) containing a poorly water-soluble drug (<b><i>k</i></b>) and matrix polymer surfactant (PS), thereby enhancing <b><i>k</i></b>'s solubility. When dissolving the SD, the PS is first dissolved, forming micelles. The amorphous form of the solid phase <b><i>k</i></b> remains and is further dissolved by micellar solubilization. The goal here is to rigorously derive, on the basis of thermodynamics, a new expression for the change in the standard Gibbs free energy (∆GΣ 0). This change serves as a measure for increasing the degree of spontaneity in the dissolution of amorphous <b><i>k</i></b> from an SD with a polymeric surfactant relative to the dissolution of the crystalline-form <b><i>k</i></b> in an aqueous solution without surfactants (reference state). In the micelle-pseudophase model, it was found that ∆GΣ 0 depends on the natural logarithm of the ratio of mole fraction <b><i>k</i></b> in the aqueous phase to mole fraction <b><i>k</i></b> in the micellar pseudophase. In a simpler model, ∆GΣ 0 can be expressed as ln of the solubility ratio of the crystalline and SD forms, assuming that the activity coefficient depends on the process of incorporating <b><i>k</i></b> into the micellar particles and that the total amount of surfactants is many times smaller than the water amount, which is acceptable for polymeric surfactants with low values of the critical micellar concentration.