Fractals physical properties

Physically, the wetting abdity increases (the contact angle decreases) as the values of the fractal dimension of the electrode increases if the electrode material is same. However, in this study, we could not obtain a good correlation between the fractal dimensions and the wetting abilities as shown in Table 1. It means that not only the physical properties such as the surface irregularity and roughness but also the chemical interaction between electrolyte and electrode were important in wetting ability. 

With the experimental results about the wetting ability and the fractal dimension of four kinds of anode electrodes, we could conclude the following. The addition of NisAl could make the electrolyte wet the electrode very well. The pore structures of all the electrodes prepared in this study were highly irregular and rough. Finally, the chemical properties of the surfaces were as important as the physical properties in determining the wetting ability of the electrodes in this study. 

Power-law expressions are found at all hierarchical levels of organization from the molecular level of elementary chemical reactions to the organismal level of growth and allometric morphogenesis. This recurrence of the power law at different levels of organization is reminiscent of fractal phenomena. In the case of fractal phenomena, it has been shown that this self-similar property is intimately associated with the power-law expression [28]. The reverse is also true if a power function of time describes the observed kinetic data or a reaction rate higher than 2 is revealed, the reaction takes place in fractal physical support. 

Daoud M, Stanley HE and Stauffer D, "Scaling, Exponents and Fractal Dimensions", In Mark JE (Ed), "Physical Properties of Polymers Handbook", 2nd Ed, Springer-Verlag, Berlin, 2007, Chap. 6. 

Fractal-Like Dimensions of Graphs 3-2 Correlation with Physical Properties 3-3 Ordering of Structures ... 

Table 17.7 summarizes the effects of the microstructural factors on the microscopy fractal dimensions, Dj, y, and Zlpr- Different fractal dimensions reflect different aspects of the microstructure of the fat crystal networks and thus have different meanings. It is necessary to define which structural characteristic is most closely related to the macroscopic physical property of interest (mechanical strength, permeability, diffusion) and then use the fractal dimension that is most closely related to the particular structural characteristic in the modeling of that physical property. 

Use of the concept of the fractal set allows one to examine the dependence of physical properties on the behavior of hierarchical structures. Such structures appear in stochastic inhomogeneous medium. 

The idea that every fractal set needs its own ruler in order to be measured will be used when analyzing the physical properties of heterogeneous media. 

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