A SANS study of the interfacial curvatures and the phase behavior in bicontinuous microemulsions

Abstract

A microemulsion is a three-component system in which oil and water are solubilized via an interfacial surfactant monolayer. Depending on the composition and various external conditions, it exhibits a wide variety of phases with corresponding mesoscopic scale interfacial structures. For scientific as well as industrial purposes, knowledge of the relation between the interfacial structure and the phase behavior is crucial but its quantitative measure is lacking. To identify the relation in a quantitative way, the natural parameters to be measured are the interfacial curvatures : Gaussian, mean, and square mean curvatures. A new small-angle neutron scattering (SANS) data analysis method to extract the interfacial curvatures was developed and applied to various microemulsions. The method involves the use of a clipped random wave model with an inverse 8th order polynomial spectral function. The spectral density function contains three basic length scales : the inter-domain distance, the coherence length, and the surface roughness parameter. These three length scales are essential to describe mesoscopic scale interfaces. A series of SANS experiments were performed at various phase points of isometric and non-isometric microemulsions. Using the developed model, the three interfacial curvatures at each phase point were determined for the first time in a practical way. In isometric bicontinuous microemulsions, the Gaussian curvature is negative and has a parabolic dependence on the surfactant volume fraction. In non-isometric systems, based on the measured interfacial curvatures, a characteristic structural transformation was identified. As the water and oil volume ratio moves away from unity, the bicontinuous structure transforms to a spherical structure through an intermediate cylindrical structure.