Measurement and Interpretation of Curvatures of the Oil-Water Interface in Isometric Bicontinuous Microemulsions

A small-angle neutron scattering (SANS) study was carried out on a three-component isometric (equal volume fractions of water and oil) ionic microemulsion system, composed of AOT/brine/decane [AOT= surfactant sodium bis(ethylhexylsufo)succinate]. SANS measurements were made as a function of volume fraction of surfactant within the one-phase channel at the hydrophile-lipophile balance (HLB) salinity and at a constant temperature. We analyzed SANS data taken with oil-water contrast in terms of a modified Berk random wave model. The good agreement of the model with SANS intensity requires a proper form of spectral function. We chose a spectral function which is an inverse eighth-order polynomial in wave number k, containing three length scales 1/a, 1/b and 1/c. The spectral function has finite second and fourth moments. The model shows good agreement with the intensity data in an absolute scale. The three parameters so obtained were then used to calculate the average square mean curvature and the average Gaussian curvature of the interface. The variation of these curvatures and the underlying spectral functions as a function of the surfactant volume fraction were determined and their implications for the degree of local order of the bicontinuous structure are discussed.