Thermodynamic consideration of mixtures of surfactants in adsorbed films and micelles

The thermodynamic relations describing the equilibrium between the bulk solution and the adsorbed film were derived for two-component surfactant mixtures that do not share common ions. The mean activity coefficients in the adsorbed film, which can be estimated experimentally, were introduced and proven to comprise a factor attributable to the preferential adsorption of ions. The excess Gibbs energy of adsorption was defined by using the mean activity coefficients and the composition of adsorbed film. The equation of ideal mixing of two components in the adsorbed film was also derived. The analogous equations were developed with respect to the equilibrium between the bulk solution and the micelles. The equations derived were shown to be easily converted to those for ionic-ionic surfactant mixtures with common ions, and ionic-nonionic and nonionic-nonionic surfactant mixtures. Furthermore, the equations were utilized for examining the miscibility of surfactants in the decylammonium bromide (DeAB)-dodecylammonium chloride (DAC), decylammonium chloride (DeAC)-DAC, and DeAB-DeAC mixtures.