Refining the ionic surfactant micellization theory based on the law of mass action

The micellization theory previously elaborated based on the determination of critical micelle concentration using the constant of the law of mass action is refined for ionic surfactants. The degree of micellization is used as a parameter to obtain implicit dependences of monomer and micelle concentrations on overall surfactant concentration in an ideal micellar solution. As expected, the counterion concentration increases monotonically, while the surface-active ion concentration passes through a maximum immediately after the critical micelle concentration. Repeated calculations performed at different degrees of counterion binding show that, as this parameter is decreased, the maximum becomes sharper, disappearing when the parameter becomes equal to unity. The complex character of the exact analytical description of the concentration functions for monomers and micelles is in contrast to their simple graphical representations. This fact makes it possible to derive simple analytical approximations for them in the form of explicit functions useful for calculations.