VOLDIS: A Direct Search for the Size Distribution of Nanoparticles from Small-Angle Scattering Data and Stability of the Solution

Abstract

The paper considers an algorithm for the direct search for a nonparametric smooth histogram of the particle size distribution from small-angle X-ray and neutron scattering data. The features and details of the implementation of the method, which consists in the sequential search for several solutions with different degrees of smoothness of the distribution contour, are considered. Methods for evaluating the stability of both the whole distribution contour and its individual parts are discussed. The work of the program is illustrated by examples of the analysis of polydisperse spherical particles in silicasol solutions.

Keywords

• small-angle scattering
• particle size distribution
• non-linear least squares
• numerical methods