Thermodynamics of ionic surfactant adsorption with account for the counterion binding: Effect of salts of various valency

The effect of counterion binding on the surface tension and surface potential of ionic surfactant solutions is accounted for theoretically. It turns out that no every couple of surfactant and counterion adsorption isotherms are thermodynamically compatible. To solve the problem, we develop a formalism which enables one to obtain the counterion adsorption isotherm corresponding to a given surfactant adsorption isotherm. Further, these adsorption isotherms are integrated to obtain the respective expression for the surface tension. The results are extended to the case when the solution contains ionic-nonionic surfactant mixtures and electrolytes of various valency. The integral, which takes into account the electrostatic interactions, is solved analytically for aqueous solutions containing 1:1, 2:1, 1:2, and 2:2 electrolytes. It is demonstrated that the derived equations can be applied to process experimental data for the surface tension as a function of the surfactant and salt concentrations. As a result one determines the adsorptions of surfactant and counterions and the surface electric potential. The derived equations can also be applied to calculate the surface elasticity of ionic surfactant adsorption monolayers and the diffusion relaxation time in the kinetics of adsorption.