Structural Properties of Molecular Sierpiński Triangle Fractals.

The structure of fractals at nano and micro scales is decisive for their physical properties. Generally, statistically self-similar (random) fractals occur in natural systems, and exactly self-similar (deterministic) fractals are artificially created. However, the existing fabrication methods of deterministic fractals are seldom defect-free. Here, are investigated the effects of deviations from an ideal deterministic structure, including small random displacements and different shapes and sizes of the basic units composing the fractal, on the structural properties of a common molecular fractal-the Sierpiński triangle (ST). To this aim, analytic expressions of small-angle scattering (SAS) intensities are derived, and it is shown that each type of deviation has its own unique imprint on the scattering curve. This allows the extraction of specific structural parameters, and thus the design and fabrication of artificial structures with pre-defined properties and functions. Moreover, the influence on the SAS intensity of various configurations induced in ST, can readily be extended to other 2D or 3D structures, allowing for exploration of structure-property relationships in various well-defined fractal geometries.