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Simple inversion formula for the small-angle X-ray scattering intensity from polydisperse systems of spheres

Botet, Robert and Cabane, Bernard LU (2012) In Journal of Applied Crystallography 45. p.406-416
Abstract
A practical inversion method to calculate the size distribution of colloidal homogeneous particles from small-angle scattering experiments is presented. It is based on the analysis of the deviations of the scattering signal from the Porod law. The resulting inversion formula provides a reliable way to assess complex size distributions such as power-law, multimodal or very broad distributions. It is particularly suitable for colloidal dispersions that have a substantial fraction of very small particles. These cases correspond to large deviations from the Porod law over a broad range of scattering vector values, q. Shannon's theorem gives a way to obtain the maximum amount of information concerning the size distribution, without requiring an... (More)
A practical inversion method to calculate the size distribution of colloidal homogeneous particles from small-angle scattering experiments is presented. It is based on the analysis of the deviations of the scattering signal from the Porod law. The resulting inversion formula provides a reliable way to assess complex size distributions such as power-law, multimodal or very broad distributions. It is particularly suitable for colloidal dispersions that have a substantial fraction of very small particles. These cases correspond to large deviations from the Porod law over a broad range of scattering vector values, q. Shannon's theorem gives a way to obtain the maximum amount of information concerning the size distribution, without requiring an arbitrary extrapolation of the data beyond the available q range. It is demonstrated that this protocol yields a calculated distribution of particle sizes that is stable. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Applied Crystallography
volume
45
pages
406 - 416
publisher
Wiley-Blackwell
external identifiers
  • wos:000304402500005
  • scopus:84861494911
ISSN
1600-5767
DOI
10.1107/S0021889812012812
language
English
LU publication?
yes
id
40df176b-32bb-4ad0-92d2-07cbbbd87707 (old id 2906548)
date added to LUP
2012-07-23 16:10:42
date last changed
2017-06-11 03:11:33
@article{40df176b-32bb-4ad0-92d2-07cbbbd87707,
  abstract     = {A practical inversion method to calculate the size distribution of colloidal homogeneous particles from small-angle scattering experiments is presented. It is based on the analysis of the deviations of the scattering signal from the Porod law. The resulting inversion formula provides a reliable way to assess complex size distributions such as power-law, multimodal or very broad distributions. It is particularly suitable for colloidal dispersions that have a substantial fraction of very small particles. These cases correspond to large deviations from the Porod law over a broad range of scattering vector values, q. Shannon's theorem gives a way to obtain the maximum amount of information concerning the size distribution, without requiring an arbitrary extrapolation of the data beyond the available q range. It is demonstrated that this protocol yields a calculated distribution of particle sizes that is stable.},
  author       = {Botet, Robert and Cabane, Bernard},
  issn         = {1600-5767},
  language     = {eng},
  pages        = {406--416},
  publisher    = {Wiley-Blackwell},
  series       = {Journal of Applied Crystallography},
  title        = {Simple inversion formula for the small-angle X-ray scattering intensity from polydisperse systems of spheres},
  url          = {http://dx.doi.org/10.1107/S0021889812012812},
  volume       = {45},
  year         = {2012},
}