Stability of spherical and rod-like micelles of ionic surfactants, in relation to their counterion binding and modes of hydration

Aqueous salt solutions of ionic surfactants in both spherical and rod-like micelles have been treated on the basis of a statistical thermodynamic theory, and the double logarithmic relationship between micelle molecular weight and ionic strength is derived for each micelle. Counterion binding on both micelles are assumed to occur specifically, and their degrees of dissociation are related to the slopes of the linear double logarithmic relations. It is found from the relationship observed for typical surfactants that the effective charge of spherical micelles is 29±4. The degree of dissociation of rod-like micelles of these surfactants is primarily determined by the counterion species, yielding values 0.8 for Na+, 0.4–0.6 for Cl− and 0.2–0.3 for Br−. Hydrophilic hydration of both micelles can be evaluated from the intercepts of the linear relations. Hydrophilic hydration acts repulsively in spherical micelles, while it is attractive or much less repulsive in rod-like micelles.