Small-Angle Scattering from Fractional Brownian Surfaces

Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. Fractional Brownian surfaces (fBs) are often used as models to simulate and characterize these complex geometries, such as the surface of particles in di...

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Autor principal:	Eugen Mircea Anitas
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	small-angle scattering fractional Brownian surfaces fractal dimension Hurst exponent spectral exponent Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/3b5fbe1ad2634a248878cf10c49775ac
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id	oai:doaj.org-article:3b5fbe1ad2634a248878cf10c49775ac
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spelling	oai:doaj.org-article:3b5fbe1ad2634a248878cf10c49775ac2021-11-25T19:06:16ZSmall-Angle Scattering from Fractional Brownian Surfaces10.3390/sym131120422073-8994https://doaj.org/article/3b5fbe1ad2634a248878cf10c49775ac2021-10-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2042https://doaj.org/toc/2073-8994Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. Fractional Brownian surfaces (fBs) are often used as models to simulate and characterize these complex geometries, such as the surface of particles in dilute particulate systems (e.g., colloids) or the interfaces in non-particulate two-phase systems (e.g., semicrystalline polymers with crystalline and amorphous phases). However, for such systems, a realistic simulation involves parameters averaged over a macroscopic volume. Here, a method based on small-angle scattering technique is proposed to extract the main structural parameters of surfaces/interfaces from experimental data. It involves the analysis of scattering intensities and the corresponding pair distance distribution functions. This allows the extraction of information with respect to the overall size, fractal dimension, Hurst and spectral exponents. The method is applied to several classes of fBs, and it is shown that the obtained numerical values of the structural parameters are in very good agreement with theoretical ones.Eugen Mircea AnitasMDPI AGarticlesmall-angle scatteringfractional Brownian surfacesfractal dimensionHurst exponentspectral exponentMathematicsQA1-939ENSymmetry, Vol 13, Iss 2042, p 2042 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	small-angle scattering fractional Brownian surfaces fractal dimension Hurst exponent spectral exponent Mathematics QA1-939
spellingShingle	small-angle scattering fractional Brownian surfaces fractal dimension Hurst exponent spectral exponent Mathematics QA1-939 Eugen Mircea Anitas Small-Angle Scattering from Fractional Brownian Surfaces
description	Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. Fractional Brownian surfaces (fBs) are often used as models to simulate and characterize these complex geometries, such as the surface of particles in dilute particulate systems (e.g., colloids) or the interfaces in non-particulate two-phase systems (e.g., semicrystalline polymers with crystalline and amorphous phases). However, for such systems, a realistic simulation involves parameters averaged over a macroscopic volume. Here, a method based on small-angle scattering technique is proposed to extract the main structural parameters of surfaces/interfaces from experimental data. It involves the analysis of scattering intensities and the corresponding pair distance distribution functions. This allows the extraction of information with respect to the overall size, fractal dimension, Hurst and spectral exponents. The method is applied to several classes of fBs, and it is shown that the obtained numerical values of the structural parameters are in very good agreement with theoretical ones.
format	article
author	Eugen Mircea Anitas
author_facet	Eugen Mircea Anitas
author_sort	Eugen Mircea Anitas
title	Small-Angle Scattering from Fractional Brownian Surfaces
title_short	Small-Angle Scattering from Fractional Brownian Surfaces
title_full	Small-Angle Scattering from Fractional Brownian Surfaces
title_fullStr	Small-Angle Scattering from Fractional Brownian Surfaces
title_full_unstemmed	Small-Angle Scattering from Fractional Brownian Surfaces
title_sort	small-angle scattering from fractional brownian surfaces
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3b5fbe1ad2634a248878cf10c49775ac
work_keys_str_mv	AT eugenmirceaanitas smallanglescatteringfromfractionalbrowniansurfaces
_version_	1718410271216631808

Small-Angle Scattering from Fractional Brownian Surfaces

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