Anitas Eugen Mircea
Joint Institute for Nuclear Research, Dubna 141980, Russian.
Horia Hulubei, National Institute of Physics and Nuclear Engineering, 077125 Bucharest-Magurele, Romania.
Nanomaterials (Basel). 2020 May 11;10(5):925. doi: 10.3390/nano10050925.
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.
纳米和微米尺度下分形的结构对其物理性质起着决定性作用。一般来说，统计自相似（随机）分形出现在自然系统中，而精确自相似（确定性）分形是人工制造的。然而，现有的确定性分形制造方法很少是无缺陷的。在此，研究了偏离理想确定性结构的影响，包括小的随机位移以及构成分形的基本单元的不同形状和尺寸，对一种常见分子分形——谢尔宾斯基三角形（ST）结构性质的影响。为此，推导了小角散射（SAS）强度的解析表达式，结果表明每种类型的偏差在散射曲线上都有其独特的印记。这使得能够提取特定的结构参数，从而设计和制造具有预定义性质和功能的人工结构。此外，ST中诱导的各种构型对SAS强度的影响可以很容易地扩展到其他二维或三维结构，从而有助于探索各种明确分形几何中的结构 - 性质关系。
