Characterization of Surfactant Spheroidal Micelle Structure for Pharmaceutical Applications: A Novel Analytical Framework.

We introduce an innovative theoretical framework tailored for the analysis of Pair Distribution Function (PDF) data derived from Small-Angle X-ray Scattering (SAXS) measurements of core-shell micelles. The new approach involves the exploitation of the first derivative of the PDF and the derivation of analytical equations to solve the core-shell micelle structure under the hypothesis of a spheroidal shape. These analytical equations enable us to determine the micelle's aggregation number, degree of ellipticity, and contrast in electron density between the core-shell and shell-buffer regions after having determined the whole micelle size and its shell size from the analysis of the first derivative of the PDF. We have formulated an overdetermined system of analytical equations based on the unknowns that characterize the micelle structure. This allows us to establish a Figure of Merit, which is utilized to identify the most reliable solution within the system of equations.