Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures
Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures
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DOI：
10.3390/sym12010065
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发表时间：
2020-01-01
期刊：
影响因子：
2.7
通讯作者：
Anitas, Eugen Mircea
中科院分区：
文献类型：
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作者：
Anitas, Eugen Mircea
小角散射（SAS; X射线，中子，光）正越来越多地用于更好地理解基于分形的材料的结构，并描述它们在纳米和微米尺度上的相互作用。为了这个目的，已经开发了几种利用分形对称性的最低限度但具体的理论模型，以从SAS数据中提取额外的信息。尽管对于许多特定的分形结构可以精确地解决这个问题，但是由于SAS方法的固有限制，逆散射问题，即，从强度曲线确定分形结构，是不适定的。然而，分形可以分为各种类别，不一定是脱节的，最常见的是随机的、确定性的、质量的、表面的、孔隙的、脂肪的和多重分形的。每个类别都有自己的散射强度的印记，虽然不能唯一地识别一个分形的结构，仅基于SAS数据，人们可以区分它们所属的各种类别。这在将它们的结构性质与物理性质相关联方面具有重要的实际应用。本文回顾了SAS从几个分形模型，重点描述哪些信息可以从每个类中提取，以及如何进行实验。为了说明这一过程，并验证理论模型，基于蒙特卡罗方法进行数值模拟。
Small-angle scattering (SAS; X-rays, neutrons, light) is being increasingly used to better understand the structure of fractal-based materials and to describe their interaction at nano- and micro-scales. To this aim, several minimalist yet specific theoretical models which exploit the fractal symmetry have been developed to extract additional information from SAS data. Although this problem can be solved exactly for many particular fractal structures, due to the intrinsic limitations of the SAS method, the inverse scattering problem, i.e., determination of the fractal structure from the intensity curve, is ill-posed. However, fractals can be divided into various classes, not necessarily disjointed, with the most common being random, deterministic, mass, surface, pore, fat and multifractals. Each class has its own imprint on the scattering intensity, and although one cannot uniquely identify the structure of a fractal based solely on SAS data, one can differentiate between various classes to which they belong. This has important practical applications in correlating their structural properties with physical ones. The article reviews SAS from several fractal models with an emphasis on describing which information can be extracted from each class, and how this can be performed experimentally. To illustrate this procedure and to validate the theoretical models, numerical simulations based on Monte Carlo methods are performed.