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 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.

Automated summary

Recent advances in nanotechnology have allowed the fabrication of advanced materials with fractal-like geometries, where Fractional Brownian surfaces are often used to model and characterize these complex geometries. A method based on small-angle scattering technique is proposed to extract main structural parameters of surfaces/interfaces from experimental data, showing good agreement with theoretical values for various classes of Fractional Brownian surfaces.