A theoretical investigation of the influence of the second critical micelle concentration on the solubilization capacity of surfactant micelles

Abstract

The solubilization of hydrophobic components by surfactants that form microemulsion droplets has been investigated from a theoretical point of view. By means of combining thermodynamics of self-assembly to form small systems with bending elasticity theory, we have been able to demonstrate a strong correlation between the second critical micelle concentration (CMC2) of surfactant micelles and their solubilization capacity (σ). The correlation may be rationalized as a consequence of all three bending elasticity constants spontaneous curvature (H0), bending rigidity (kc) and saddle-splay constant (k¯c) showing similar trends with respect to the two quantities, i.e. σ increases and CMC2 decreases with decreasing values of kcH0 and increasing values of kc and k¯c, respectively. As a result, we demonstrate that the solubilization capacity is predicted to always be higher for a gemini surfactant with CMC2 = 11 mM as compared with a gemini surfactant with CMC2 = 18 mM. The predicted correlation between solubilization capacity and CMC2 agrees with experimental observations showing that surfactants forming larger micelles in general have better solubilization capacity than surfactants forming smaller micelles. The theory also demonstrates, in agreement with experiments, that σ is raised in the entire range of surfactant concentrations, below as well as above CMC2, regardless of micelle size. Consequently, our theory predicts that small micelles formed below CMC2 increase in size, whereas large rodlike or wormlike micelles formed above CMC2 decrease in size, as a hydrophobic solubilizate is added to a micellar solution.