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Statistical Approach to Fractal-Structured Physico-Chemical Systems: Analysis of non-Fickian diffusion

Aurea R. Vasconcellos·J. Galvão Ramos·A. Gorenstein·M. U. Kleinke·T. G. Souza Cruz·Roberto Luzzi
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Abstract

Competing styles in Statistical Mechanics have been introduced to investigate physico-chemical systems displaying complex structures, when one faces difficulties to handle the standard formalism in the well established Boltzmann-Gibbs statistics. After a brief description of the question, we consider the particular case of Renyi statistics whose use is illustrated in a study of the question of the ''anomalous'' (non-Fickian) diffusion that it is involved in experiments of cyclic voltammetry in electro-physical chemistry. In them one is dealing with the fractal-like structure of the thin film morphology present in eletrodes in microbatteries which leads to fractional-power laws for describing voltammetry measurements and in the determination of the interphase width derived using atomic force microscopy. The fractional-powers associated to these quantities are related to each other and to the statistical fractal dimension, and can be expressed in terms of a power index, on which depends Renyi's statistical mechanics. It is clarified the important fact that this index, which is limited to a given interval, provides a measure of the microroughness of the electrode surface, and is related to the dynamics involved, the non-equilibrium thermodynamic state of the system, and to the experimental protocol. \\

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Aurea R. Vasconcellos, J. Galvão Ramos, A. Gorenstein, M. U. Kleinke, T. G. Souza Cruz, Roberto Luzzi. 2004-12-06. Statistical Approach to Fractal-Structured Physico-Chemical Systems: Analysis of non-Fickian diffusion. https://arxiv.org/abs/cond-mat/0412131

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