Abstract
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.
Highlights
Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries
The pddfs are different within each class, they, have a common feature that allows distinguishing fractional Brownian surfaces (fBss) belonging to different classes
For class Class III fBss (CIII) (Figure 4c), the right side of the bell becomes completely linear, which is specific to elongated structures [30]
Summary
Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. 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. The third dimension has been proved to be important for the interpretation of experimental data on singlet-triplet transitions in the ground states of the two-electron quantum dots under a perpendicular magnetic field [11,12] For both artificial and natural surfaces and interfaces, a frequently employed realistic model that aims to relate the observed physical/chemical/biological properties with the roughness is based on the concept of fractional Brownian surface (fBs) [13]. This has been successfully used in describing various rough structures, including the contact zone between two distinct materials in layered composites [14], substrates subjected to plasma-chemical etching [15] or soil structures [16,17]
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