Effects of oil on the curvature elastic properties of nonionic surfactant films: Thermodynamics of balanced microemulsions

The free energy of nonionic balanced microemulsions based on nonionic surfactants are analyzed using experimental data from (i) phase behavior, (ii) osmotic compressibility of the balanced microemulsion structure, which is obtained from small angle neutron scattering (SANS) experiments, and (iii) data on interfacial tensions obtained by T. Sottmann and R. Strey [J. Chem. Phys. 106 8606 (1997)]. The balanced microemulsion, where the spontaneous curvature vanishes at equal volumes of water and oil, has a finite swelling with the solvent with a minimum surfactant volume fraction, ΦS*. At higher surfactant concentrations the balanced microemulsion phase having the surfactant volume fraction ΦS1 coexists with a lamellar phase of volume fraction ΦS2. Under the constraint of ΦW=ΦO, where ΦW and ΦO are the water and oil volume fractions, respectively, the free energy density can be written as an expansion in the surfactant concentration. While the phase equilibria only depend on relative values of the expansion coefficients, absolute values can be obtained from compressibility and interfacial tension data. The osmotic compressibility of the surfactant film was measured by SANS through contrast matching water and oil. The phase behavior of nonionic surfactant-water-oil systems depends strongly on the chain length of the oil, when comparing a homologous series from octane to hexadecane using the same surfactant, here being pentaethylene oxide dodecyl ether (C₁₂E₅). The three concentrations ΦS*, ΦS1, and ΦS2 increase markedly as the chain length of the oil is increased. However, from the analysis of the surface tension data it is concluded that there are no major changes in the bending rigidities as the oil is changed. The data are analyzed within the model free energy densities G∕V=a₃ΦS³+a₅ΦS⁵ and G∕V=aΦS³(1+b0.2em0exln0.2em0exΦS). We find that within experimental accuracy, the first of these models provides a quantitatively consistent description of the data. For the second model there is a larger discrepancy between observed and calculated values.