Efficient algorithms for calculating small-angle scattering from large model structures

This paper compares Monte Carlo approaches and fast Fourier transform (FFT) methods to efficiently calculate small-angle scattering (SAS) profiles from large morphological models. These methods enable calculation of SAS from complex nanoscale morphologies commonly encountered in modern polymeric and nanoparticle-based systems which have no exact analytical representation and are instead represented digitally using many millions of subunits, so that algorithms with linear or near-linear scaling are essential. The Monte Carlo method, referred to as the Monte Carlo distribution function method (MC-DFM), is presented and its accuracy validated using a number of simple morphologies, while the FFT calculations are based on the fastest implementations available. The efficiency, usefulness and inherent limits of DFM and FFT approaches are explored using a series of complex morphological models, including Gaussian chain ensembles and two-phase three-dimensional interpenetrating nanostructures.