A thermodynamic analysis of charged mixed micelles in water

A thermodynamic analysis is presented for electrically charged mixed micelles in water on the basis of the Gibbs-Duhem relation proposed by Hall in combination with the information on the degree of counterion binding. The proposed analyses are shown to work well for both ionic/nonionic mixed micelles and those consisting of ionic surfactants of like charges. Conclusions for ionic/nonionic mixed micelles are as follows. (1) The contribution from counterions is significant. (2) In media of low ionic strengths, the counterion concentration varies with the micellar mole fraction of the ionic species x. The dependency of the activity coefficients and the excess free energy on x is significantly influenced by this effect, but it can be corrected to a large extent in terms of the Corrin-Harkins relation. (3) The regular solution theory (RST) is not always valid even when the excess free energy is described well with the RST expression unless the observed range of the micelle composition is wide enough. (4) The RST overestimates x and underestimates the activity coefficient of the ionic species when applied to the mixed micelles to which it is inapplicable. For the ionic mixed micelles consisting of surfactants of like charges, the Lange-Shinoda approach is shown to be consistent with the present analysis in terms of the Gibbs-Duhem relation, but Motomura's approach is found to be not exact but approximate.