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Small-Angle Scattering from Nanoscale Fat Fractals

Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and s...

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Autores principales: Anitas, E. M., Slyamov, A., Todoran, R., Szakacs, Z.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5459787/
https://www.ncbi.nlm.nih.gov/pubmed/28587439
http://dx.doi.org/10.1186/s11671-017-2147-0
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author Anitas, E. M.
Slyamov, A.
Todoran, R.
Szakacs, Z.
author_facet Anitas, E. M.
Slyamov, A.
Todoran, R.
Szakacs, Z.
author_sort Anitas, E. M.
collection PubMed
description Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and scaling factors at each structural level. This is in agreement with general results deduced in the context of small-angle scattering analysis of a system of randomly oriented, non-interacting, nano-/micro-fractals. We apply our results to a two-dimensional fat Cantor-like fractal, calculating analytic expressions for the scattering intensities and structure factors. We explain how the structural properties can be computed from experimental data and show their correlation to the variation of the scaling factor with the iteration number. The model can be used to interpret recorded experimental SAS data in the framework of fat fractals and can reveal structural properties of materials characterized by a regular law of changing of the fractal dimensions. It can describe successions of power-law decays, with arbitrary decreasing values of the scattering exponents, and interleaved by regions of constant intensity.
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spelling pubmed-54597872017-06-22 Small-Angle Scattering from Nanoscale Fat Fractals Anitas, E. M. Slyamov, A. Todoran, R. Szakacs, Z. Nanoscale Res Lett Nano Express Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and scaling factors at each structural level. This is in agreement with general results deduced in the context of small-angle scattering analysis of a system of randomly oriented, non-interacting, nano-/micro-fractals. We apply our results to a two-dimensional fat Cantor-like fractal, calculating analytic expressions for the scattering intensities and structure factors. We explain how the structural properties can be computed from experimental data and show their correlation to the variation of the scaling factor with the iteration number. The model can be used to interpret recorded experimental SAS data in the framework of fat fractals and can reveal structural properties of materials characterized by a regular law of changing of the fractal dimensions. It can describe successions of power-law decays, with arbitrary decreasing values of the scattering exponents, and interleaved by regions of constant intensity. Springer US 2017-06-05 /pmc/articles/PMC5459787/ /pubmed/28587439 http://dx.doi.org/10.1186/s11671-017-2147-0 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Nano Express
Anitas, E. M.
Slyamov, A.
Todoran, R.
Szakacs, Z.
Small-Angle Scattering from Nanoscale Fat Fractals
title Small-Angle Scattering from Nanoscale Fat Fractals
title_full Small-Angle Scattering from Nanoscale Fat Fractals
title_fullStr Small-Angle Scattering from Nanoscale Fat Fractals
title_full_unstemmed Small-Angle Scattering from Nanoscale Fat Fractals
title_short Small-Angle Scattering from Nanoscale Fat Fractals
title_sort small-angle scattering from nanoscale fat fractals
topic Nano Express
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5459787/
https://www.ncbi.nlm.nih.gov/pubmed/28587439
http://dx.doi.org/10.1186/s11671-017-2147-0
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