Particle‐size polydispersity analysis based on the unified exponential/power‐law approach to small‐angle scattering

• Published in: Journal of applied crystallography 2023-08, Vol.56 (4), p.1099-1107
• Main Authors: Tomchuk, Oleksandr V., Kryshtal, Oleksandr P., Juszyńska-Gałązka, Ewa, Zając, Wojciech M.
• Format: Article
• Language: English
• Subjects: correlation lengths; Distribution functions; hydrosols; Nanoparticles; Nanotechnology; Neutrons; Polydispersity; Porod integral; Regularization; Scattering; Size distribution; small‐angle scattering; Technology assessment; unified exponential/power‐law approach
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576723004752

Controlling particle dispersity is of huge importance for practical applications in nanoscience and technology. The analysis of small‐angle scattering of X‐rays and neutrons for strongly polydisperse particulate systems is considered from the point of view of describing the type of size distribution function without applying classical regularization approaches. This article presents the development of a method for determining the polydispersity parameters of nanoobjects, based on the analysis of the ratio of various moments of the size distribution function, which are proportional to different invariants of the scattering curve. The use of the unified exponential/power‐law approximation to describe small‐angle scattering data makes it possible to determine the type of distribution, the average size and the spread. The possibilities of the method were tested for several hydrosols of metallic nanoparticles. This article introduces a generalized approach to determine polydispersity characteristics from small‐angle scattering analysis based on the Beaucage model without numerical integration of experimental data.