The unusual importance of activity coefficients for micelle solutions illustrated by an osmometry study of aqueous sodium decanoate and aqueous sodium decanoate + sodium chloride solutions.

Freezing-point and vapor-pressure osmometry data are reported for aqueous sodium decanoate (NaD) solutions and aqueous NaD + NaCl solutions. The derived osmotic coefficients are analyzed with a mass-action model based on the micelle formation reaction qNa(+) + nD(-) = (Na(q)D(n))(q-n) and Guggenheim equations for the micelle and ionic activity coefficients. Stoichiometric activity coefficients of the NaD and NaCl components and the equilibrium constant for micelle formation are evaluated. Illustrating the remarkable but not widely appreciated nonideal behavior of ionic surfactant solutions, the micelle activity coefficient drops to astonishingly low values, below 10(-7) (relative to unity for ideal solutions). The activity coefficients of the Na(+) and D(-) ions, raised to large powers of q and n, reduce calculated extents of micelle formation by up to 15 orders of magnitude. Activity coefficients, frequently omitted from the Gibbs equation, are found to increase the calculated surface excess concentration of NaD by up to an order of magnitude. Inflection points in the extent of micelle formation, used to calculate critical micelle concentration (cmc) lowering caused by added salt, provide unexpected thermodynamic evidence for the elusive second cmc.

Simulations of a lattice model of two-headed linear amphiphiles: influence of amphiphile asymmetry.

Using a 2D lattice model, we conduct Monte Carlo simulations of micellar aggregation of linear-chain amphiphiles having two solvophilic head groups. In the context of this simple model, we quantify how the amphiphile architecture influences the critical micelle concentration (CMC), with a particular focus on the role of the asymmetry of the amphiphile structure. Accordingly, we study all possible arrangements of the head groups along amphiphile chains of fixed length N = 12 and 16 molecular units. This set of idealized amphiphile architectures approximates many cases of symmetric and asymmetric gemini surfactants, double-headed surfactants, and boloform surfactants. Consistent with earlier results, we find that the number of spacer units s separating the heads has a significant influence on the CMC, with the CMC increasing with s for s < N/2. In comparison, the influence of the asymmetry of the chain architecture on the CMC is much weaker, as is also found experimentally.

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

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.

Coupled mutual diffusion in solutions of micelles and solubilizates.

The coupled diffusion of micelles and solubilizates has been studied by measuring ternary mutual diffusion coefficients (D(ik)) for aqueous solutions of dodecylsulfobetaine (SB12) with added butanol, pentanol, or hexanol. SB12 micelles solubilize alcohols, so diffusing SB12(1) might be expected to co-transport alcohol(2). Negative values of cross-coefficient D(21) indicate, however, that the diffusion of SB12 drives substantial counterflows of alcohol. To help interpret the results, measured decreases in critical micelle concentrations with added alcohol (ROH) are used to evaluate equilibrium constants for the formation of (SB12)(m)(ROH)(n) mixed micelles. Increasing the concentration of SB12 along a diffusion path raises the concentrations of micelles and solubilized alcohol while lowering the concentration of free alcohol. The resulting flux of relatively mobile free alcohol molecules up SB12 concentration gradients is larger than the flux of solubilized alcohol down SB12 gradients, producing net countercurrent coupled fluxes of alcohol. The measured D(ik) coefficients are in close agreement (+/- 0.05 x 10(-5) cm(2) s(-1)) with predictions using self-diffusion coefficients (D(i)*) for SB12 and alcohol in solutions at thermodynamic equilibrium and the relations D(ik) = partial differential(C(i)D(i)*)/ partial differentialC(k) proposed recently for mutual diffusion in non-equilibrium solutions of associating solutes. Mutual diffusion coefficients for coupled surfactant-solubilizate diffusion are used to evaluate equilibrium constants for the formation of surfactant-solubilizate mixed micelles.