Measurement of the Gaussian curvature of the surfactant film in an isometric bicontinuous one-phase microemulsion

Small-angle x-ray and neutron-scattering (SAXS and SANS) measurements are mode of a three-component isometric microemulsion, C(10)E(4)-D2O-octane, in the one-phase channel around the hydrophile-lipophile balance temperature of the system. A previous SANS contrast variation experiment indicated that the microstructure of this isometric microemulsion is bicontinuous in water and oil, with the surfactant film having a zero mean curvature. We analyze the SAXS and SANS data taken with a bulk 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 for the microemulsion. The analysis gives an excellent agreement with the intensity data in an absolute scale. We then use the three parameters so obtained to calculate the mean Gaussian curvature of the surfactant film. We also show a three-dimensional-reconstructed morphology of the microemulsion.