On the Localization of CMC and Maximum Concentration of Surface-Active Ions According to the Theory of Micellar Solutions
The micellization theory that I previously developed on the basis of the definition of critical micelle concentration (CMC) using the constant of the law of mass action as applied to ionic surfactants (Colloid. J., 2016, vol. 78, p. 669) has been supplemented and refined. The problem concerning the relative positions of the maximum in the surface-active ion concentration and CMC as functions of aggregation number has been solved in the general form. It has been shown that the curves of these functions may intersect. On the side of smaller aggregation numbers relative to the intersection point, the maximum lies above the CMC, while, at larger aggregation numbers, it is, on the contrary, located below the CMC in the concentration axis. The influence of the type of an electrolyte on this effect has been studied by the example of an ionic surfactant. If the charge of a counterion is higher than the charge of a surface-active ion, the maximum is located above the CMC; otherwise, it is below the CMC. At the same time, the question of the formulation of the law of mass action for ionic surfactants with multivalent ions has been answered. It has been shown that the definition of CMC via the constant of the law of mass action must, in this case, comprise stoichiometric coefficients. The theory has been formulated under the condition of a constant aggregation number in the vicinity of CMC. In addition, an ideal behavior of a mixture of monomers and micelles is assumed, which is inherent in ionic surfactants with rather low CMCs.
This work was supported by the Russian Science Foundation, project no. 14-13-00112.
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