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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/11/2042 |
| _version_ | 1797508356137549824 |
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| author | Eugen Mircea Anitas |
| author_facet | Eugen Mircea Anitas |
| author_sort | Eugen Mircea Anitas |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T05:00:58Z |
| format | Article |
| id | doaj.art-3b5fbe1ad2634a248878cf10c49775ac |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T05:00:58Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3b5fbe1ad2634a248878cf10c49775ac2023-11-23T01:43:55ZengMDPI AGSymmetry2073-89942021-10-011311204210.3390/sym13112042Small-Angle Scattering from Fractional Brownian SurfacesEugen Mircea Anitas0Joint Institute for Nuclear Research, 141980 Dubna, RussiaRecent 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.https://www.mdpi.com/2073-8994/13/11/2042small-angle scatteringfractional Brownian surfacesfractal dimensionHurst exponentspectral exponent |
| spellingShingle | Eugen Mircea Anitas Small-Angle Scattering from Fractional Brownian Surfaces Symmetry small-angle scattering fractional Brownian surfaces fractal dimension Hurst exponent spectral exponent |
| title | 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_short | Small-Angle Scattering from Fractional Brownian Surfaces |
| title_sort | small angle scattering from fractional brownian surfaces |
| topic | small-angle scattering fractional Brownian surfaces fractal dimension Hurst exponent spectral exponent |
| url | https://www.mdpi.com/2073-8994/13/11/2042 |
| work_keys_str_mv | AT eugenmirceaanitas smallanglescatteringfromfractionalbrowniansurfaces |