Accelerated small angle neutron scattering algorithms for polymeric materials

Abstract

Small-angle neutron scattering (SANS) is an extremely powerful technique for characterizing a wide variety of soft, biological, magnetic, and quantum materials, but it is often throughput-limited. This work proposes an algorithm to accelerate small angle neutron scattering (SANS) experiments by estimating the minimum number of counts to perform parameter estimation and model differentiation tasks to a specified level of certainty. Three classes of model polymer materials were examined and analyzed, and time slices of SANS data were used to model a reduced number of counts. The scattering data with reduced numbers of counts were fitted to SANS model functions to perform parameter estimation and model differentiation tasks. For parameter estimation, estimators accurate to within 5–10% of the full count estimator can be produced with only 1–50% of the full counts depending upon the sample and parameter of interest. In order to project parameter uncertainties at lower number of counts prior to the completion of experiments, it is crucial to have a robust error quantification method that reflects the true uncertainty associated with each parameter. Uncertainties from Monte Carlo (MC) bootstrapping are shown to in general overestimate the error from fitting many experimental replicates. For most parameter estimation techniques, the weighted least squares estimator is unbiased; however, certain models yield biased estimators. To differentiate between models, both the Akaike information criterion (AIC) and Bayesian information criterion (BIC) can be used, and with either criterion, reduced numbers of counts can still identify the best model for our samples from a group of related candidate models for each material. The proposed algorithm can help SANS users optimize valuable beamtime and accelerate the use of SANS for structural characterization of libraries of materials while obtaining reasonable parameter estimation and model differentiation when scattering models are available.