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-o ctane, in the one-phase channel around the hydrophile-lipophile balanc e temperature of the system. A previous SANS contrast variation experi ment indicated that the microstructure of this isometric microemulsion is bicontinuous in water and oil, with the surfactant film having a z ero mean curvature. We analyze the SAXS and SANS data taken with a bul k contrast in terms of a modified Berk's random wave model. We choose a spectral function which is an inverse sixth-order polynomial, with t hree parameters a, b, and c, as introduced by Lee and Chen earlier. Th is three-parameter spectral function is then used in conjunction with Cahn's clipping scheme to obtain the Debye correlation function for th e microemulsion. The analysis gives an excellent agreement with the in tensity data in an absolute scale. We then use the three parameters so obtained to calculate the mean Gaussian curvature of the surfactant f ilm. We also show a three-dimensional-reconstructed morphology of the microemulsion.