Thermodynamics of mixed micelles: Determination of the aggregate composition

In most studies concerning surfactant mixtures, the determination of the composition of mixed micelles is often tricky. This composition can be obtained by different ways. One of them, undoubtedly the most used, supposes, a priori, that the surfactant in the micelle follows the regular solution model. This poses a problem on the thermodynamic point of view because in these studies, a model of behavior is first admitted for deducing a composition. In a correct thermodynamic approach, a composition should first be determined and then, a model of behavior which accounts for the observed physicochemical properties can be found. This approach is all the more questionable since the application of the Gibbs-Duhem relationship to the pseudo-phase allows aggregate composition to be determined simply, without using a solution model, because the composition of the bulk at the threshold of aggregation is known. In this article, we describe and validate a simple procedure, which supplements that proposed by Rodenas et al. [E. Rodenas, M. Valiente, M.D. Villafruela, J. Phys. Chem. B 103 (1999) 4549], and which allows determination of the activities of the components of the micellar aggregate and its composition. The results are compared to those obtained with other approaches such as molecular-thermodynamic model.