Fraktale in der physikalischen Chemie
Fraktale in der physikalischen Chemie
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物理化学中的碎片
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
G. Vojta
中科院分区：
文献类型：
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作者：
H. Spindler;G. Vojta
分形概念是曼德布洛特创造的，对物理化学的发展有着重要的影响。从非整数Hausdorff维的思想出发，分形数学是描述物理和化学中不规则结构和过程的有力工具。分形维数D仅在自相似范围内严格定义，通常不低于嵌入维数超过1。但是，如果处理分形对象的子集（子分形维数），D的值也可能更小。此外，提出了多孔固体的分形模型，并证明了分形物体的表面积值是测量方法的函数。固体和表面上的原子和分子的动力学可以用分形维数Ds < d来描述。分形系统中的扩散通常比普通系统中的扩散进行得慢。指出渗流受分形几何的支配。许多聚集体的形成可以用分形几何来描述。分形反应维数Dr有助于理解反应动力学中的问题。对于耗散结构和混沌反应的讨论，分形的概念也很重要。
The fractal concept, created by Mandelbrot, has important consequences for the development of physical chemistry. Starting from the idea of the non-integer Hausdorff dimension fractal mathematics is a powerful tool for the description of irregular structures and processes in physics and chemistry. The fractal dimension D is strictly only defined in the ranges of self-similarity and normally does not fall below the embedding dimension by more than one. But smaller values of D are possible, too, if subsets of the fractal object are treated (subfractal dimension). Furthermore, a fractal model for porous solids is presented, and it is shown that the value of surface area for fractal objects is a function of measuring approach. The dynamics of atoms and molecules in solids and at surfaces can be described using the fracton dimension Ds < D. Diffusion in a fractal system generally proceeds more slowly than in a normal one. It is stated that percolation is governed by fractal geometry. The formation of many aggregates can be described in terms of fractal geometry. The fractal reaction dimension Dr may help to understand problems in reaction kinetics. For the discussion of dissipative structures and chaotic reactions, too, the fractal concept gains importance.