The Gaussian curvature of the oil-water interface in an isometric bicontinuous microemulsion

Small-angle neutron scattering (SANS) measurements are made on a three-component isometric (equal volume fractions of water and oil) microemulsion system, composed of AOT/water (0.4% NaCl)/D-octane, in the one-phase channel near the three-phase region at and around the hydrophile-lipophile balance temperature. A previous SANS contrast variation experiment indicated that the microstructure of this type of isometric microemulsion is bicontinuous in water and oil with the surfactant film at the interface having a zero mean curvature. We analyze SANS data taken with an oil-water contrast in terms of a modified Berk's random wave model. We choose a spectral function which is an inverse sixth-order polynomial, with three parameters a, b and c, as introduced by Lee and Chen earlier. This three-parameter spectral function is then used in conjunction with Cahn's clipping scheme to obtain the Debye correlation function appropriate for the microemulsion system. The model analysis results in good agreement with the intensity data in an absolute scale. We then use the three parameters so obtained to calculate the average Gaussian curvature of the interface. We discuss the variation of the average Gaussian curvature as a function of the surfactant volume fraction and its implication on the degree of local order of the bicontinuous structure. We also show a 3-D reconstructed morphology of the most disordered microemulsion.