An iterative method to extract the size distribution of non-interacting polydisperse spherical particles from small-angle scattering data

2014 ◽  
Vol 47 (2) ◽  
pp. 712-718 ◽  
Author(s):  
D. Sen ◽  
Avik Das ◽  
S. Mazumder

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.

2021 ◽  
Vol 54 (5) ◽  
Author(s):  
Debasis Sen ◽  
Ashwani Kumar ◽  
Avik Das ◽  
Jitendra Bahadur

A new method to estimate the size distribution of non-interacting colloidal particles from small-angle scattering data is presented. The method demonstrates that the distribution can be efficiently retrieved through features of the scattering data when plotted in the Porod representation, thus avoiding the standard fitting procedure of nonlinear least squares. The present approach is elaborated using log-normal and Weibull distributions. The method can differentiate whether the distribution actually follows the functionality of either of these two distributions, unlike the standard fitting procedure which requires a prior assumption of the functionality of the distribution. After validation with various simulated scattering profiles, the formalism is used to estimate the size distribution from experimental small-angle X-ray scattering data from two different dilute dispersions of silica. At present the method is limited to monomodal distributions of dilute spherical particles only.


2017 ◽  
Vol 50 (3) ◽  
pp. 951-958 ◽  
Author(s):  
Sen Chen ◽  
Juncheng E ◽  
Sheng-Nian Luo

SLADS(http://www.pims.ac.cn/Resources.html), a parallel code for direct simulations of X-ray scattering of large anisotropic dense nanoparticle systems of arbitrary species and atomic configurations, is presented. Particles can be of arbitrary shapes and dispersities, and interactions between particles are considered. Parallelization is achieved in real space for the sake of memory limitation. The system sizes attempted are up to one billion atoms, and particle concentrations in dense systems up to 0.36. Anisotropy is explored in terms of superlattices. One- and two-dimensional small-angle scattering or diffraction patterns are obtained.SLADSis validated self-consistently or against cases with analytical solutions.


2020 ◽  
Vol 22 (22) ◽  
pp. 12713-12723 ◽  
Author(s):  
Lukas Ludescher ◽  
Roland Morak ◽  
Stephan Braxmeier ◽  
Florian Putz ◽  
Nicola Hüsing ◽  
...  

Apparent strain artifacts resulting from the evaluation of small-angle X-ray scattering data superimpose the actual adsorption induced deformation in silica with hierarchical porosity. These artifacts can be corrected for by detailed modelling.


2014 ◽  
Vol 47 (2) ◽  
pp. 810-815 ◽  
Author(s):  
Andreas Hofmann ◽  
Andrew E. Whitten

Small-angle X-ray scattering has established itself as a common technique in structural biology research. Here, two novel Java applications to aid modelling of three-dimensional macromolecular structures based on small-angle scattering data are described.MolScatis an application that computes small-angle scattering intensities from user-provided three-dimensional models. The program can fit the theoretical scattering intensities to experimental X-ray scattering data.SAFIRis a program for interactive rigid-body modelling into low-resolution shapes restored from small-angle scattering data. The program has been designed with an emphasis on ease of use and intuitive handling. An embedded version ofMolScatis used to enable quick evaluation of the fit between the model and experimental scattering data.SAFIRalso provides options to refine macromolecular complexes with optional user-specified restraints against scattering data by means of a Monte Carlo approach.


2011 ◽  
Vol 13 (13) ◽  
pp. 5872 ◽  
Author(s):  
Gerhard Fritz-Popovski ◽  
Alexander Bergmann ◽  
Otto Glatter

1994 ◽  
Vol 27 (5) ◽  
pp. 693-702 ◽  
Author(s):  
P. R. Jemian ◽  
A. J. Allen

Analysis of small-angle scattering data to obtain a particle-size distribution is dependent upon the shape function used to model the scattering. From a maximum-entropy analysis of small-angle scattering data, the effect of shape-function selection on the obtained size distribution is demonstrated using three different shape functions to describe the same scattering data from each of two alloys. The alloys have been revealed by electron microscopy to contain a distribution of randomly oriented and mainly noninteracting irregular ellipsoidal precipitates. A comparison is made between the different forms of the shape function. The effect of an incident-wavelength distribution is also shown. The importance of testing appropriate shape functions and validating these against other microstructural studies is discussed.


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