Clipped random wave analysis of isometric lamellar microemulsions

We have made small angle neutron scattering studies of C10E4-D2O-octane isometric microemulsions in the lamellar phase at the hydrophile-lipophile balance temperature. The scattering intensity distributions were then analyzed with a particular choice of a spectral density function (SDF) derived by maximization of generalized entropy. The model agrees well with the measured intensities on an absolute scale, and allowed us to derive various length scales associated with the microemulsion mesoscopic structure as well as the average interfacial curvatures. We also used the experimentally determined SDF to generate a three-dimensional snapshot of the fluctuating microemulsion microstructure. Unlike conventional pictures of extended lamellar planes, we observed small domains which were internally lamellar but randomly oriented with respect to each other. Finally, we computed the probability distributions of the mean curvature H and the Gaussian curvature K on the oil-water interface. The former showed a symmetric distribution centered around H = 0, while the latter showed a skewed distribution peaked at a negative value of K, but with a wing extending to positive values.