Approaches for improving the quality of particle size distribution reconstructions from small-angle scattering data

Abstract

Using a series of two- and three-component model data of small-angle scattering from systems of polydisperse spherical particles, the possibility of determination of the particle size distribution function by regularization methods, a direct histogram search, and as a superposition of smooth analytical functions has been investigated. The advantages and disadvantages of these approaches are considered. It is shown that their combined use allows one to improve the quality particle size distribution and find acceptable solutions even in the case of significant data noise. The choice of the appropriate minimization algorithms is also an important factor for efficient data analysis. A number of iterative algorithms based on the gradient minimization method, the simulated annealing method, their combination, and the Nelder-Mead method is tested and their efficiency is compared for the small-angle scattering data of a silicasol solution.