Extended Hansen solubility approach: naphthalene in individual solvents

A multiple regression method using Hansen partial solubility parameters, delta D, delta p, and delta H, was used to reproduce the solubilities of naphthalene in pure polar and nonpolar solvents and to predict its solubility in untested solvents. The method, called the extended Hansen approach, was compared with the extended Hildebrand solubility approach and the universal-functional-group-activity-coefficient (UNIFAC) method. The Hildebrand regular solution theory was also used to calculate naphthalene solubility. Naphthalene, an aromatic molecule having no side chains or functional groups, is "well-behaved', i.e., its solubility in active solvents known to interact with drug molecules is fairly regular. Because of its simplicity, naphthalene is a suitable solute with which to initiate the difficult study of solubility phenomena. The three methods tested (Hildebrand regular solution theory was introduced only for comparison of solubilities in regular solution) yielded similar results, reproducing naphthalene solubilities within approximately 30% of literature values. In some cases, however, the error was considerably greater. The UNIFAC calculation is superior in that it requires only the solute's heat of fusion, the melting point, and a knowledge of chemical structures of solute and solvent. The extended Hansen and extended Hildebrand methods need experimental solubility data on which to carry out regression analysis. The extended Hansen approach was the method of second choice because of its adaptability to solutes and solvents from various classes. Sample calculations are included to illustrate methods of predicting solubilities in untested solvents at various temperatures. The UNIFAC method was successful in this regard.

Extended Hildebrand Solubility Approach: methylxanthines in mixed solvents

The solubility profiles of theobromine, theophylline, and caffeine at 25 degrees were examined in binary solvent systems including dioxane-formamide, water-polyethylene glycol 400, and glycerin-propylene glycol. Theobromine solubility was studied in dioxane-water mixtures, a solvent system that was investigated earlier for the solubility of theophylline and caffeine. Solubilities were calculated in these polar systems by a regression method, based on an extension of the Hildebrand-Scatchard equation of regular solution theory. A linear relationship between the mixed solvent solubility parameter, and dielectric constant, epsilon, was introduced earlier and was confirmed in the present study. In addition, it was observed that a regression of log (activity coefficient) on epsilon in a second or higher degree polynomial provides reasonable solubility values for the methylxanthines in mixed solvents. A direct regression of molal or mole fraction (but not molar) solubility against delta 1, epsilon, or against volume percent of one or the other solvent in a binary solvent mixture provided a suitable measure of solubility for these crystalline drugs in mixed polar solvents. The drug's solubility parameter as determined from peak solubility in mixed polar solvents varied somewhat, depending on the specific solvent system employed. It is suggested that a drug may exhibit one (or more) solubility parameters in nonpolar solutions and multiple solubility parameters in polar systems. The extended solubility approach serves for the back-calculation of solubilities in mixed solvent systems, even though the solubility parameter of the solute may vary from one solvent system to the next.

A simplified method to estimate total area under the blood plasma concentration-versus-time curve

A simplified method is presented to determine the total area under the blood plasma concentration-versus-time curve whose results compare favorably with those obtained using the classical method. The advantage of this method is that no additional parameters are needed to evaluate the area under the curve.

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 delta 1 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 less than 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 approximately 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, delta 1. The method has potential usefulness in preformulation and formulation studies during which solubility determination is important for drug design.

Extended Hildebrand solubility approach: solubility of theophylline in polar binary solvents

A quantitative approach is presented for predicting solubilities of crystalline compounds in binary solvent systems. The solubility of theophylline in mixed solvents consisting of dioxane and water was determined at 25 +/- 0.1 degrees. The solubilities across this range of polar solvents were back-calculated using a technique involving an interaction energy term, W. This parameter is regressed against a polynomial expression in delta 1, the solubility parameter for the mixed solvents. Except for the end-points, solubilities were predicted within less than 12% and with considerably better accuracy in most cases. The new approach modifies the well-known Hildebrand solubility equation to make it applicable to polar systems. Although the method may be used with solutes in pure solvents, its greatest application appears to be the prediction of drug solubility in binary solvent mixtures.