Fractals characterization

However, the relationship between dF and CPE is dependent on the model used in the fractal characterization of the electrode.144,145... 

The present article summarized the fractal characterization of the rough surfaces and interfaces by using the physical and the electrochemical methods in electrochemistry. In much research, both the physical and the electrochemical methods were used to evaluate the fractal dimension and they are complementary to each other. It should be stressed that the surface fractal dimension must be determined by using the adequate method, according to the inherent scaling properties of the rough surfaces and interfaces. 

For a perfectly smooth surface with c/F ss = 2 at all scales, Eq. (33) predicts a = 1, i.e., purely capacitive behavior. In other limit as c/F ss = 3, a = 0.5 which is de Levie s well-known result for the electrode with cylindrical pore. Eq. (33) also implies that the surfaces with different morphologies but with same surface fractal dimension are equivalent as far as the impedance is concerned. The relationship between dFss and a is dependent upon the model used in the fractal characterization of the electrode. 

Solid surfaces have been found to exhibit fractal morphology. A study of the quality and accuracy of the methods based on frequency analysis for the fractal characterization of solid surfaces was carried out by STM. The study was based on computer simulation of images of fractal surfaces. Measurement of the fractal character of a surface in the microscope range has specific problems. The most important is that the images of a given solid surface arise from the projections of the surface topography in which the vertical dimension is unknown, whereas from both STM and AFM we can obtain the vertical dimensions. 

Filter, A.H., andT.R. Strickland. 1992. Fractal characterization of root system architecture. Funct. Ecol. 6 632-635. 

Carr. J. R. 1989. Fractal characterization of joint surface roughness in welded tuff at Yucca Mountain, Nevada. 30th U. S. Symp. On rock mech, Rotterdam Balkema Publisher. 

Han, J.H., Ping, S. and Shengsun, H. (2005) Fractal characterization and simulation of surface profiles of copper electrodes and aluminum sheets. Materials Science and Engineering A, 403 174-81. 

Majumdar, A. and Tien, C.L. (1990) Fractal characterization and simulation of rough surfaces. Wear, 136 313-27. 

The development of the fractal characterization of irregular lines and surfaces was initiated by Mandelbrot, who introduced in two books in 1977 and 1983 the fractal concept to many fields of science. 

Pirard, R., Pirard, J.-P., 2000. Fractal characterization of wide pore range catalysts application to Pd-Ag/Si02 xerogels. 

Richards L.E., Dempsey B.D. Fractal Characterization of Fractured Surfaces. Scripta Metal., 1988,22(5), 687-689. 

Fractal characterization of the porosity of organic tissue by interferometry. ... 

Se88] M. Semetz, H.R. Bittner, C. Baumhoer, S. Schwarz, H. Willems Interferometric determination and fractal characterization of gel porosity Irn Characterization of Porous Solids. K.K. Unger, J. Rouquerol, K.S.W. Sing and H. Krai (eds.), Elsevier Amsterdam (1988) 461-472. 

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