Phase Solubility Diagrams of Cocrystals Are Explained by Solubility Product and Solution Complexation

The purpose of this work was to develop a mathematical model that describes the solubility of cocrystals by taking into consideration the equilibria between cocrystal, cocrystal components, and solution complexes. These models are applied to the phase diagrams of carbamazepine/nicotinamide (CBZ/NCT) cocrystal in organic solvents. The CBZ/NCT (1:1) cocrystal solubility was measured by suspending cocrystal in solutions of varying nicotinamide concentrations in ethanol, 2-propanol, or ethyl acetate. Results show that the solubility of the cocrystal decreases with increasing nicotinamide concentration. Mathematical models demonstrate that (1) the solubility of a cocrystal AB is described by the solubility product of cocrystal components and by solution complexation constants, (2) these equilibrium constants can be determined from solubility methods, and (3) graphical representation of the cocrystal solubility dependence on ligand concentration will serve as a diagnostic tool for the stoichiometry of solution complexes. CBZ/NCT cocrystal Ksp values increase as the cocrystal solubility increases, while K11 values decrease. The dependence of cocrystal solubility on solubility product and complexation constants provides a powerful approach to design cocrystal screening methods and to formulate solutions with cocrystal components where crystallization does not occur.