Premium
An iterative method to extract the size distribution of non‐interacting polydisperse spherical particles from small‐angle scattering data
Author(s) -
Sen D.,
Das Avik,
Mazumder S.
Publication year - 2014
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576714003835
Subject(s) - scattering , iterative method , lagrange multiplier , robustness (evolution) , particle size distribution , distribution (mathematics) , distribution function , particle size , small angle scattering , physics , computational physics , mathematical analysis , materials science , optics , mathematics , algorithm , chemistry , thermodynamics , quantum mechanics , biochemistry , gene
In this article, an iterative method for estimating the size distribution of non‐interacting polydisperse spherical particles from small‐angle scattering data is presented. It utilizes the iterative addition of relevant contributions to an instantaneous size distribution, as obtained from the fractional difference between the experimental data and the simulated profile. An inverse relation between scattering vector and real space is assumed. This method does not demand the consideration of any basis function set together with an imposed constraint such as a Lagrange multiplier, nor does it depend on the Titchmarsh transform. It is demonstrated that the method works quite well in extracting several forms of distribution. The robustness of the present method is examined through the successful retrieval of several forms of distribution, namely monomodal, bimodal, trimodal, triangular and bitriangular distributions. Finally, the method has also been employed to extract the particle size distribution from experimental small‐angle X‐ray scattering data obtained from colloidal dispersions of silica.