Solubility prediction fluctuation solution theory

The main difficulty in predicting the solid solubility in a mixed solvent consists in calculating the activity coefficient of a solute in a ternary mixture In this paper, the Kirkwood-Buff (KB) theory of solutions (or fluctuation theory) (Kirkwood and Buff, 1951) is employed to analyze the solid (particularly drug) solubility in mixed (mainly aqueous) solvents. The analysis is based on results obtained previously regarding the composition derivatives of the activity coefficients in ternary solutions (Ruckenstein and Shulgin, 2001). These equations were successfully applied to gas solubilities in mixed solvents (Ruckenstein and Shulgin, 2002 Shulgin and Ruckenstein, 2002). 

In this paper, the fluctuation theory of solutions was applied to the solubility of drugs in aqueous mixed solvents. A rigorous expression for the composition derivative of the activity coefficient of a solute in a ternary solution (Ruckenstein and Shulgin, 2001) was used to derive an equation for the activity coefficient of a solute at infinite dilution in an ideal mixed solvent and an expression for the solubility of a poorly soluble solid in an ideal mixed solvent (Eq. (23)). This simple equation can predict the solubility in terms of those in the individual constituents of the mixed solvent and... 

First, a rigorous expression for the activity coefficient of a solid solute at infinite dilution in an ideal multicomponent solvent was derived using the fluctuation theory of solution. Second, the obtained expression was used to express the solubility of a poorly soluble solid in an ideal multicomponent solvent in terms of the solubilities of this solid in two subsystems of the multicomponent solvent and their molar volumes. Finally, the developed procedure was used to predict the drug solubilities in ternary and quaternary aqueous mixed solvents using the drug solubilities in the constituent binary aqueous mixed solvents. The predicted solubilities were compared with the experimental ones and good agreement was found. 

In our previous papers regarding the solubility of poorly soluble drugs in aqueous mixed solvents (Ruckenstein and Shulgin, 2003a-c), the fluctuation theory of solutions (Kirkwood and Buff, 1951) was used for their correlation and prediction. Such infor-... 

As for infinite dilution, the main difficulty in predicting the solid solute solubility in a mixed solvent for a dilute solution is provided by the calculation of the activity coefficient of the solute in a ternary mixture. To obtain an expression for the activity coefficient of a low concentration solute in a ternary mixture, the fluctuation theory of solution will be combined with the assumption that the system is dilute with respect to the solute. 

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