Analysis of Sans Data from Dense Microemulsions

Abstract

Measurements of AOT/D2O/n-decane microemulsions containing comparable volumes of water, oil, and surfactant have been obtained with the small-angle scattering (SANS) technique. Each intensity spectrum exhibits a clear diffraction maximum. As the surfactant volume fraction Ψs increases, the peak position moves to higher values of Q, while the peak height diminishes. Attempts were made to interpret the intensity spectra using the following models: simple bicontinuous phase, lamellar structure, a dispersion of hard spheres, and spherical droplets interacting through a square--well attraction. These models proved to be unsatisfactory for understanding the SANS data. However, by assuming a phase consisting of spherical droplets with a very well-defined nearest-neighbor ordering, it is possible to successfully describe the shift in peak position Qmax. In particular, for microemulsions with equal volumes of water and oil, such a model predicts that $$ {{\rm{Q}}_{\max }} = {{2.25} \over }{{{\phi _{\rm{s}}}} \over {{{(1 - {{\rm{\varphi }}_{\rm{s}}})}^{2/3}}}} $$ where Δ is the length of the surfactant molecule.