Parallel (competitive) reactions of micelle formation and cyclodextrin–surfactant inclusion complex formation in aqueous solution: A consequence of the Gibbs–Duhem equation—invariance of the mass action law and the possibility of determining the equilibrium constant of the inclusion complex

The Gibbs–Duhem equation results in the independence between the standard Gibbs free energy of micelle formation and the standard Gibbs free energy of monocomponent surfactant’s and cyclodextrin’s (CD’s) inclusion complex formation in aqueous solution. The experimental data show that the surfactant’s critical micellar concentration increases in the presence of CD. At a constant temperature, the standard Gibbs free energy of micelle formation remains constant, irrespective of the presence of parallel competitive processes such as inclusion complex formation. This indicates that the critical micellar concentration remains unchanged at the corresponding concentration scale. As a result, the equilibrium constant for surfactant–CD inclusion complex formation can be determined by changing the critical micellar concentration in the presence and absence of CD. A graphical method for determining the equilibrium constant of the inclusion complex is also presented. An analytical approach for analyzing the influence of the formation of the inclusion complex with CD on the formation of the binary mixed micellar pseudophase is presented. Suppose that different values exist for the equilibrium constants of the formation of the inclusion complex for two surfactants from their binary mixture. In this case, there is a change in the initial mole fraction from the initial mixture of surfactants, which should be considered when applying the regular solution theory protocol when determining the parameters of a binary mixed micelle in the presence of CD.