RETRIEVING THE SIZE DISTRIBUTION OF CORE-SHELL PARTICLES FROM SMALL-ANGLE X-RAY SCATTERING DATA: A MONTE CARLO APPROACH

Core-shell particles in solution, such as micelles and coated nanoparticles, are in general polydisperse and, for many applications, the determination of their size distribution, described by the function D(R), is fundamental. To this end, scattering techniques, particularly dynamic and static light scattering (DLS and SLS), are probably the most used because the measurements are fast and simple. However, due to the features of the radiation used (visible light), it is impossible to analyze the inner structure of the particles. Moreover, in the case of DLS, spherical shape is often assumed in the modeling, which limits its application to systems formed by globular objects. To overcome these issues, small-angle X-ray scattering (SAXS) can be used instead, allowing the simultaneous determination of both size distribution and inner structure (if necessary, particles larger than ~50 nm could still be probed by ultra small-angle X-ray scattering – USAXS). For this evaluation, data modeling must also be performed, which in general assumes a mathematical profile for the size distribution, for instance Gaussian, Lognormal, Schulz-Zimm, etc. The major concern in this approach is related to the fact that D(R) could be none of those, e.g., a bimodal distribution, common for many systems in solution. In this work, by using Monte Carlo method, we propose a model that can be easily used for spherical and cylindrical core-shell particles and, assuming no a priori information, can retrieve D(R) along all remaining structural features. As will be shown, the model was successfully applied to analyze experimental SAXS data of micelles in solution.