A robust expectation‐maximization method for the interpretation of small‐angle scattering data from dense nanoparticle samples

• Published in: Journal of applied crystallography Vol. 52; no. 5; pp. 926 - 936
• Main Authors: Bakry, M., Haddar, H., Bunău, O.
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.10.2019; Blackwell Publishing Ltd
• Subjects: Computer Science; Data acquisition; expectation maximization; interacting nanoparticles; Inverse scattering; Iterative algorithms; Iterative methods; local monodisperse approximation; Mathematical models; Maximization; Nanoparticles; nanopowders; Numerical Analysis; Optimization; Parameters; small‐angle scattering
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576719009373

The local monodisperse approximation (LMA) is a two‐parameter model commonly employed for the retrieval of size distributions from the small‐angle scattering (SAS) patterns obtained from dense nanoparticle samples (e.g. dry powders and concentrated solutions). This work features a novel implementation of the LMA model resolution for the inverse scattering problem. The method is based on the expectation‐maximization iterative algorithm and is free of any fine‐tuning of model parameters. The application of this method to SAS data acquired under laboratory conditions from dense nanoparticle samples is shown to provide good results. A robust method is presented for the resolution of small‐angle scattering problems featuring a structure factor. It is based on the local monodisperse approximation and the expectation‐maximization algorithm.