Activity coefficients and free energies of nonionic mixed surfactant solutions from vapor-pressure and freezing-point...

The thermodynamic properties of mixed surfactant solutions are widely investigated, prompted by numerous practical applications of these systems and by interest in molecular association and self-organization. General techniques for measuring thermodynamic activities, such as isopiestic equilibration, are well-established for multicomponent solutions. Surprisingly, these techniques have not yet been applied to mixed surfactant solutions, despite the importance of the free energy for micelle stability. In this study, equations are developed for the osmotic coefficients of solutions of nonionic surfactant A + nonionic surfactant B. A mass-action model is used, with virial equations for the activity coefficients of the micelles and free surfactant monomer species. The equations are fitted to osmotic coefficients of aqueous decylsulfobetaine + dodecylsulfobetaine solutions measured by vapor-pressure and freezing-point osmometry. Equilibrium constants for mixed-micelle formation are calculated from the free monomer concentrations at the critical micelle concentrations. The derived activity coefficients of the micelles and free monomers indicate large departures from ideal solution behavior, even for dilute solutions of the surfactants. Stoichiometric activity coefficients of the total surfactant components are evaluated by Gibbs-Duhem integration of the osmotic coefficients. Relatively simple colligative property measurements hold considerable promise for free energy studies of multicomponent surfactant solutions.