Particle Size Distribution of Nanospheres by Monte Carlo Fitting of Small Angle X-Ray Scattering Curves

Abstract

A method for recovering the size distribution of spherical particles from small angle scattering data by using a Monte Carlo interference function fitting algorithm is presented. The method is based on the direct simulation of the small angle scattering data upon the assumption of non-interacting hard sphere ensembles (“dilute” solution approximation). The algorithm for retrieving the particle size distribution does not require any additional parameters apart from the input of the scattering data. The fitting strategy necessarily implies positive particle size distributions, while preserving the advantage of the indirect transformation method for data desmearing. Furthermore, the present approach does not use any regularisation procedures of the best fit solution and favours smooth particle size distributions. The Monte Carlo procedure has been tested against several simulated cases with various types of mono- and bi-modal size distributions and different noise levels. In the special case of non-interacting spheres, the Monte Carlo fitting algorithm had the same retrieving ability as the well assessed indirect transformation, structure interference and maximum entropy methods. Finally, the algorithm was applied to retrieve the distribution of spherical nanopowders produced by gas-to-particle conversion both as free powder and as reinforcing second-phase agent in polymer nanocomposites.