Searching for an Efficient Solution Reconstruction Algorithm in the Analysis of Small-Angle Scattering Data from Silicasol Solution

The stabilities of reconstructing the solution to the problem of determining the volume particle size distributions are compared by the example of small-angle scattering data on a silicasol solution consisting of TM-50 and SM monodisperse solutions. Several iterative algorithms are investigated: the quasi-Newtonian gradient minimization method in the Broyden–Fletcher–Goldfarb–Shanno scheme with simple constraints on parameters, the simulated annealing method, their combination, and the Nelder–Mead simplex method. As a result of the comparison of the stability ranges for three pairs of silicasol solution parameters (particle radii and polydispersities), the methods have been arranged in the order of increasing efficiency. It is found that the most suitable approach is a combination of the gradient minimization method and simulated annealing algorithm for a two-component polydisperse system of silicasol solution with a slightly overlapping volume particle size distribution. The approach can be used to study various systems, including solutions of protein complexes.