Prediction of nabumetone solubility in propylene glycol-water mixtures using extended hildebrand solubility approach

Extended Hildebrand solubility approach is used to estimate the solubility of nabumetone in binary solvent systems. The solubility of nabumetone in various propylene glycol-water mixtures was analyzed in terms of solute-solvent interactions using a modified version of Hildebrand-Scatchard treatment for regular solutions. The solubility of nabumetone in the binary solvent, propylene glycol-water, shows a bell-shaped profile with solubility maxima well below the ideal solubility of the drug. The discrepancy between the results using the original Hildebrand-Scatchard equation and experimental points demonstrates that regular solution theory cannot be used to predict drug solubility in propylene glycol-water binary solvent systems. This behavior has been dealt with the theoretical replacement of mean geometric solubility parameters (δ1δ2) term with the interaction energy term (W), where δ1 and δ2 are the cohesive energy densities for the solvent and solute, respectively. The new approach 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 solvent mixture. Quadratic, cubic, and quartic expressions of ‘W’ in terms of solvent solubility parameter were utilized for predicting the solubility of nabumetone in propylene glycol-water mixtures. But from these three polynomial expressions, a quartic expression of ‘W’ in terms of solvent solubility parameter was found suitable for predicting the mole fraction solubility and yields an error in mole fraction solubility of ~7.72%, a value approximating that of the experimentally determined solubility. The method has potential usefulness in preformulation and formulation studies during which solubility prediction is important for drug design.