In this work, we propose a mathematical model to reproduce the solubilization, equivalent droplet radius, interfacial tension, and phase transitions of anionic surfactant microemulsions by scaling the curvature of the surfactant membranes to the electrolyte concentration required to obtain an optimum microemulsion formulation. At optimum formulation, equal amounts of oil and water are cosolubilized in a bicontinuous media that has a zero net curvature. Our first modeling approach is to use a single curvature term (inverse of an equivalent spherical droplet ratio) which proves to be inadequate as the system transitions to a bicontinuous microemulsion (supersolubilization), where the micelles become swollen and are no longer spherical. Later we introduce two curvature terms (net and average curvature) to interpret bicontinuous microemulsion behavior. The scaling constant (L), which has a length scale, was obtained for sodium dihexyl sulfosuccinate microemulsions with styrene, trichloroethylene, and limonene. This scaling constant (L) is shown to be independent of the oil type, temperature, surfactant, or additive concentration. We use this net-average curvature model to reproduce selected published data. We also compare the scaling constants (L values) for the different microemulsion systems studied, finding that this parameter is proportional to the length of the extended tail of the surfactant and reflects the surfactant solubilization potential. Additionally, the model was modified to account for palisade micellar solubilization. Finally, we introduce the interfacial rigidity concept to reproduce the interfacial tension of these systems.
Microemulsion (mE) literature presents numerous scattering studies (neutron, X-ray, light) of ionic and nonionic surfactants that have elucidated the morphological transitions that mEs experience upon changes in formulation conditions such as electrolyte concentration and temperature. Unfortunately, up to now, there is no way to predict the morphology of these mEs, and only after the mE is prepared can the morphology be determined using scattering techniques. In this work we compare the average curvature and drop size predicted by the net-average curvature (NAC) model to the Porod radii and characteristic length obtained from neutron scattering of toluene mEs prepared with sodium dihexyl sulfosuccinate (SDHS) and electrolyte. While the drop sizes predicted by the NAC model do not exactly correspond to the aggregate size obtained after applying a Porod analysis of the SANS profiles, the inverse of the average curvature does match the characteristic size obtained from SANS. This observation is consistent with previous comparisons made for nonionic mEs. The difference between the drop size predicted by the NAC model (that matches the solubilization curves) and SANS morphology suggests that the area per molecule of the surfactant (in contact with the internal phase) changes with the curvature of the system. The area per molecule obtained from Porod plots of Type I and II mEs and from the analysis of the scattering profiles of film-contrast Type III mEs show that as the system approaches net zero curvature the area per molecule increases to a maximum value. The data presented in this work suggests that the NAC model can be used to predict essential elements of the morphology of mEs, which may help in the design of mE-based templated structures (nanoparticles, nanoporous materials, etc.).
When surfactants are used to solubilize oil, the oil to be solubilized is often a mixture of components with differing properties, for example, solubilization of drug molecules in microemulsion formulations, remediation of organic polluted aquifers using surfactants, and so forth. Previous research has demonstrated that selective solubilization of one organic component over the other may occur if the organic components are dissimilar. In this research, we investigated selective solubilization from benzene-limonene mixtures in Winsor type I and III microemulsion systems containing water, sodium di-n-hexyl sulfosuccinate, and NaCl. The effect of the oil phase composition and the electrolyte concentration on the selectivity was studied. It was found that the selectivity toward benzene was highest at low electrolyte and benzene concentrations, decreasing as the electrolyte or benzene concentration increased. The results are discussed on the basis of the two-state solubilization theory and by correlating the curvature of the surfactant film in the microemulsion with changes of the electrolyte concentration and the oil phase composition. A simple mathematical model is developed for the selectivity, which combines the two-state solubilization theory and the net-average curvature model of microemulsion solubilization to yield close agreement with the experimental data.
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