Theory of rate of solubilization into surfactant solutions

Abstract

Solubilization of sparingly soluble solutes into aqueous surfactant solutions has attracted considerable attention in view of its application in many areas. Earlier studies differ, both qualitatively and quantitatively, in their conclusions about the beneficial role played by micelles on the rate of solubilization. In the present work, a general model is developed to explain the solubilization kinetics in the presence of micelles. The model considers molecular solubilization and exchange of solute between the micelles and the continuous phase to be the basic steps in the dissolution of solutes. Additionally, in the case of ionic surfactants, contact between the micelles and the solute surface is prohibited to account for ionic repulsion. It is shown that when the partition coefficient of the solute between the micellar phase and the continuous phase is small and the diffusion coefficient of the micelles is comparable to that of the solute in the continuous phase, the micelles and the continuous phase exist in equilibrium. This occurs even if direct contact between the micelles and the solute surface is prevented. Under these circumstances, the solubilization occurs by diffusion, in parallel, through the continuous and the micellar phases. Due to the latter, the solubilization rate can be enhanced in proportion to the magnitude of the partition coefficient and the amount of surfactant added. If the partition coefficient is large and the diffusion coefficient of the micelles is small, the enhancement factor is considerably smaller than that when the two phases are in equilibrium. The enhancement factor in this limit is proportional to the square root of the amount of surfactant added. Under such circumstances, the exclusion of direct contact between the micelles and the solute surface, and surface resistance if present, lower the enhancement factors further. The model quantitatively predicts the observations on the dissolution rates of decane and benzene drops into SDS solutions reported by Todorov et al. (J. Colloid Interface Sci. 2002, 245, 371). For benzene drops, the surface resistance is negligible, the micelles are in equilibrium with the continuous phase, and the enhancement factor is proportional to the surfactant concentration. On the other hand, for decane drops, the micelles are not in equilibrium with the continuous phase, and the enhancement is proportional to the square root of the surfactant concentration. The enhancements in Ostwald ripening rates in the presence of surfactants are also predicted from the model, and these are in good agreement with observations for decane emulsions in sodium dodecyl sulfate. The model is also applied to dissolution of fatty acids into SDS solutions in the rotating disk setup. It is observed that surface resistance plays an important role and that the diffusivities of micelles obtained here are different from the ones obtained in dissolution of benzene drops.