A small angle x-ray scattering study of the droplet-cylinder transition in oil-rich sodium bis(2-ethylhexyl) sulfosuccinate microemulsions

A method for nonlinear fitting of x-ray scattering data from polydisperse mixtures was developed. It was applied to the analysis of the structural changes in the droplet phase of oil-rich water-in-oil (w/o) sodium bis(2-ethylhexyl) sulfosuccinate (AOT) microemulsions with increasing temperature or upon addition of salt. Data were collected at different temperatures (15 to 60 °C) and salt concentrations (up to 0.6% NaCl) within the one-phase region of the L₂ phase (w/o microemulsion) for different droplet sizes (water/AOT molar ratio w_o=25 to 56) and concentrations (droplet weight fraction c_w =2% to 20%). This allowed us to distinguish between contributions from individual scattering particles, e.g., droplets and cylinders to the total scattering intensity. The complete data set containing over 500 scattering curves could be interpreted by fitting the scattering of weighted sums of AOT covered water droplets, long cylinders, and inverse AOT micelles containing bound water only, to the experimental scattering curves. The polydispersity of the droplets and cylinders is described by Schulz distributions and the interactions between the droplets are calculated using a sticky hard-sphere potential in the Percus–Yevick approximation. The volume fractions of the components, their average sizes and polydispersity, and the stickiness of the water/AOT droplets are determined by a nonlinear fit to the experimental data.