The existence of three length scales and their relation to the interfacial curvatures in bicontinuous microemulsions

A clipped random wave model (CRW) with an inverse 8th-order polynomial spectral density function (SDF) is proposed for the analysis of small-angle neutron scattering intensities from isometric bicontinuous microemulsions. The spectral density function contains three basic length scales which are essential in describing mesoscopic scale structures of porous materials. The scattering intensities from ionic and non-ionic bicontinuous microemulsions were analyzed using the model to obtain the average Gaussian and square mean curvatures, the specific interfacial area and the bending rigidity constant.