Extended hildebrand approach: Solubility of caffeine in dioxane–water mixtures

The solubility of caffeine in various dioxane–water mixtures was analyzed in terms of solute–solvent interactions using a modified version of the Hildebrand treatment for regular solutions. The solubility equation employs a term (W) to replace the geometric mean (c₁c₂)^1/2, where c₁ and c₂ are the cohesive energy densities for the solvent and solute, respectively. The new equation provides an accurate prediction of solubility once the interaction energy, W, is obtained. In this case, the energy term is regressed against a polynomial in δ₁ of the binary mixture. A quartic expression of W in terms of the solvent solubility parameter was found for predicting the solubility of caffeine in dioxane–water mixtures. The expression yields an error in mole fraction solubility of <3%, a value approximating that of the experimentally determined solubility. The one exception to a good fit is near the maximum solubility, where a depression or valley occurs between the two peaks in solubility data; at this point, the theoretical equation predicts the solubility within ∼9%. The new model also may be used to estimate the solubility of drug molecules employing the volume fraction of water in the solvent mixture instead of the composite solubility parameter, δ₁. The method has potential usefulness in preformulation and formulation studies during which solubility determination is important for drug design.