CHOICE OF STARTING VALUES OF PARTICLE-SIZE DISTRIBUTION PARAMETERS FOR THEIR CALCULATION FROM SMALL-ANGLE X-RAY SCATTERING DATA

S. V. Amarantov; Амарантов С. В.; G. S. Peters; Петерс Г. С.

doi:10.31857/S0023476122600549

CHOICE OF STARTING VALUES OF PARTICLE-SIZE DISTRIBUTION PARAMETERS FOR THEIR CALCULATION FROM SMALL-ANGLE X-RAY SCATTERING DATA

Authors: Amarantov S.V.¹, Peters G.S.²
Affiliations:
1. Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” Russian Academy of Sciences, Moscow, 119333 Russia
2. National Research Centre “Kurchatov Institute,” Moscow, 123182 Russia
Issue: Vol 68, No 4 (2023)
Pages: 514-530
Section: ДИФРАКЦИЯ И РАССЕЯНИЕ ИОНИЗИРУЮЩИХ ИЗЛУЧЕНИЙ
URL: https://rjmseer.com/0023-4761/article/view/673377
DOI: https://doi.org/10.31857/S0023476122600549
EDN: https://elibrary.ru/JOJQKJ
ID: 673377

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Abstract

Simple methods are proposed for determining the starting values of the parameters of particle-size distribution models (mean radius and its standard deviation), calculated from small-angle X-ray scattering curves. Estimates of these parameters from above based on the obtained analytical expression for the Guinier region of the scattering curve from a polydisperse system obeying the Schultz distribution are proposed for systems with narrow distributions. It is proposed to estimate the parameters and range of sizes from below based on the obtained expression of the Porod asymptotics for a polydisperse system. A method for calculating the generalized Guinier–Porod approximation in Kratky coordinates, from which independent estimates of the average size and variance can also be obtained, is proposed. The efficiency of the developed approach is demonstrated by an example of analyzing the scattering intensity from aqueous solutions of silicasol nanoparticles.

Keywords

PARTICLE-SIZE DISTRIBUTION, SMALL-ANGLE X-RAY SCATTERING

About the authors

S. V. Amarantov

Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” Russian Academy of Sciences, Moscow, 119333 Russia

Email: amarantov_s@mail.ru
Россия, Москва

G. S. Peters

National Research Centre “Kurchatov Institute,” Moscow, 123182 Russia

Author for correspondence.
Email: amarantov_s@mail.ru
Россия, Москва

References

Svergun D.I., Konarev P.V., Volkov V.V. et al. // J. Chem. Phys. 2000. V. 113. P. 1651. https://doi.org/10.1063/1.481954
Peters G.S., Zakharchenko O.A., Konarev P.V. et al. // Nucl. Instrum. Methods Phys. Res. A. 2019. V. 945. P. 162616. https://doi.org/10.1016/j.nima.2019.162616
Peters G.S., Gaponov Yu.A., Konarev P.V. et al. // Nucl. Instrum. Methods Phys. Res. A. 2022. V. 1025. P. 166170. https://doi.org/10.1016/j.nima.2021.166170
Hammertsley A.P. // J. Appl. Cryst. 2016. V. 49. P. 646. https://doi.org/10.1107/S1600576716000455
Schulz G.V. // J. Phys. Chem. B. 1935. V. 30. P. 379.
Svergun D.I. // J. Appl. Cryst. 1992. V. 25. P. 495.
Васильева А.Б., Тихонов Н.А. Интегральные уравнения. Изд. 2-е. М.: ФИЗМАТЛИТ, 2004. 160.
Тихонов А.Н., Арсенин В.Я. Методы решения некорректных задач. Учебное пособие для вузов. Изд. 3-е, исправленное. М.: Гл. ред. физ.-мат. лит., 1986. 288 с.
Верлань А.Ф., Сизиков В.С. Методы решения интегральных уравнений с программами для ЭВМ. Киев: Наук. думка, 1978. 292 с.
Тихонов А.Н., Гончарский А.В., Степанов В.В., Ягола А.Г. Численные методы решения некорректных задач. М.: Наука. Гл. ред. физ.-мат. лит., 1990. 232 с.
Гилл Ф., Мюррей У., Райт М. Практическая оптимизация. М.: Мир, 1985. 509 с.
Dennis J.E., Gay D.M., Welsch R.E. // ACM Trans. Math. Softw. 1981. V. 7. № 3. P. 369.
Porod G. // Kolloid-Zeitschrift. 1952. V. 125. P. 108.
Jerri Abdul J. // A Tutorial Review. Proc. IEEE. 1977. V. 65. P. 1565. /https://doi.org/10.1109/proc.1977.10771
Шеннон К.Э. Работы по теории информации и кибернетике. Сб. статей. М.: Изд-во. иностр. лит. 1963. 807 с.
http://www.OriginLab.com
Svergun D.I., Koch M.H.J., Timmins P.A., May R.P. // Small Angle X-Ray and Neutron Scattering from Solution of Biological Macromolecules. Oxford University Press, 2013.
Guinier A., Fournet G. // Small-Angle Scattering of X-Rays. John Wiley & Sons, Inc., 1955.
Свергун Д.И., Фейгин Л.А. Рентгеновское и нейтронное малоугловое рассеяние. М.: Наука. Гл. ред. физ.-мат. лит., 1986. 280 с.
Бейкер Дж. мл., Грейвс-Моррис П. Аппроксимация Паде. Пер. с анг. М.: Мир, 1986. 502 с.