Fractal geometry, applications

Many of the adsorbents used have rough surfaces they may consist of clusters of very small particles, for example. It appears that the concept of self-similarity or fractal geometry (see Section VII-4C) may be applicable [210,211]. In the case of quenching of emission by a coadsorbed species, Q, some fraction of Q may be hidden from the emitter if Q is a small molecule that can fit into surface regions not accessible to the emitter [211]. 

K. Falconer, Fractal Geometry Mathematical Foundations and Application, Wiley, New York, 1990. 

In Section IV, from the studies on diffusion towards self-affine fractal interface, the surface fractal dimension as determined by the electrochemical method is characterized as being self-similar, even though the rough surfaces and interfaces show the self-affine scaling property. Finally, in Section V, we exemplified the application of fractal geometry in electrochemical systems in view of the characterization of rough surfaces and interfaces by the surface fractal dimension. 

Baveye, P., Boast, C. W., Gaspard, S., and Tarquis, A. M. (2008). Introduction to fractal geometry, fragmentation processes and multifractal measures Theory and operational aspects of their application to natural systems In Bio-Physical Chemistry of Fractal Structures and Process in Environmental Systems, Senesi, N., and Wilkinson, K., eds. IUPAC Series on Analytical and Physical Chemistry of Environmental Systems. Vol. 11, John Wiley Sons, Chichester, pp. 11-67. 

Fractal Approach to Rough Surfaces and Interfaces in Electrochemistry, from a review of Fractal Geometry to the application of Fractal Geometry to the classification of surfaces and Electrochemistry... 

Tromelin, A., Hautbout, G., and Pourcelot, Y., Application of fractal geometry to dissolution kinetic study of a sweetener excipient, International Journal of Pharmaceutics, Vol. 224, No. 1-2, 2001, pp. 131-140. 

Since Mandelbrot s original description (1977,1983), fractal geometry has found relevance in a number of scientific disciplines including aerosol technology and science [e.g., see Lovejoy (1982), Meakin (1983), Kaye (1984), Sheaffer (1987), Reist et al. (1989)]. Many applications are covered in some detail by Kaye (1989), so only a brief description of fractals is given here. 

Le Mehaute A (1991) Fractal geometries. Theory and applications. CRC Press, Boca Raton Ann Arbor London Le Mehaute A, Crepy G (1983) Solid State Ionics 9/10 17... 

The emerging concept of fractal geometry has opened a wide area of research. The review will begin with a brief description on the methods for obtaining fractal dimension, followed by the use of fractal concept on pharmaceutical and biological applications with specific examples. 

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