Phenomenological approaches in the thermodynamics of mixed micelles with electric charges

The stability of mixed micelles in general has been extensively studied by the molecular thermodynamic approaches as well as by the phenomenological or thermodynamic approaches. In this article, phenomenological approaches in the thermodynamics of charged mixed micelles, mostly on ionic/nonionic mixed micelles, are reviewed. The electrostatic interaction constitutes a main contribution to the excess free energy per monomer (in kT unit) g(ex) in the case of ionic/nonionic mixed micelles and the corresponding contribution is generally negative, known as the electric synergism. The origin of the electric synergism is shown to reside in positive curvatures of g(ex,el) (the electric part of g(ex)) when plotted against the mole fraction of the ionic species x. Two types of the micellar Gibbs-Duhem (MGD) relations with (type 1) or without (type 2) the contribution from counterions are discussed to clarify various confusions found in the literature. Effects of varying ionic strengths with the micelle composition in the case of charged mixed micelles without any supporting electrolyte are discussed and a relevant way to correct for the effects is proposed. For ionic/nonionic mixed micelles, the regular solution model (RSM) and some two-parameter models to overcome the limitations inherent to the RSM are discussed. For mixed micelles subject to type 2 MGD relation, hydrogen ion titrations could provide g(el) experimentally just as in the case of linear polyelectrolytes and for those micelles subject to RSM, the titration curve becomes a straight line. Useful information is presented originating from the thermodynamic analysis on the difference of the intrinsic proton dissociation constants between the micelle and the monomer. An analytical expression of the dependence of the degree of counterion binding on x is discussed in comparison with the molecular thermodynamic results. The Corrin-Harkins relation is compared with the degree of counterion binding for ionic/nonionic mixed micelles. Mixed micelles in the concentration range higher than the critical micelle concentration (cmc) are discussed for three cases, the general method of Funasaki-Hada, the ideal mixing case, and the RSM.