Mesoscopic modelling of frustration in microemulsions

The swelling behaviour of water–oil microemulsions – considering a surfactant layer between oil and water – has been studied using a two level-cuts Gaussian random field approach based on the Helfrich formalism. Microstructures and scattering properties of microemulsions have been calculated for different amounts of oil (and water) for flexible and rigid microemulsions. When the stiffness, the spontaneous curvature of the interfacial film, and the surface to volume ratio of the immiscible fluids are varied, the microemulsion topology and morphology change in order to minimize the microemulsion free energy. Our simulations point out a change in the microemulsion morphology as a function of the surfactant film rigidity and the composition of oil, water and the surfactant. Locally lamellar structures are found for rigid microemulsions, whereas for more flexible ones, the connected-droplet and/or bicontinuous structures are preferred. Furthermore, we show that the microemulsion swelling versus the volume fraction gives a specific signature of the microemulsion microstructure. This allows for discriminating between different types of microemulsions: flexible, frustrated and unfrustrated (close to bi-liquid foams), and connected structures as molten hexagonal and cubic phases. The universal swelling behaviour is compared to different analytic expressions of Disordered Open Connected (DOC) models for the microemulsion swelling versus the volume fraction.