Predicting Colloidal Interaction Parameters from Small-Angle X-ray Scattering Curves Using Artificial Neural Networks and Markov Chain Monte Carlo Sampling

Abstract

Small-angle X-ray scattering (SAXS) is a characterization technique that allows for the study of colloidal interactions by fitting the structure factor of the SAXS profile with a selected model and closure relation. However, the applicability of this approach is constrained by the limited number of existing models that can be fitted analytically, as well as the narrow operating range for which the models are valid. In this work, we demonstrate a proof of concept for using an artificial neural network (ANN) trained on SAXS curves obtained from Monte Carlo (MC) simulations to predict values of the effective macroion valency (Z_eff) and the Debye length (κ^–1) for a given SAXS profile. This ANN, which was trained on 200,000 simulated SAXS curves, was able to predict values of Z_eff and κ^–1 for a test set containing 25,000 simulated SAXS curves, where most predicted values had errors smaller than 20%. Subsequently, an ANN was used as a surrogate model in a Markov chain Monte Carlo sampling algorithm to obtain maximum a posteriori estimates of Z_eff and κ^–1, as well as the associated confidence intervals and correlations between Z_eff and κ^–1 for an experimentally obtained SAXS profile.