STATISTICAL APPROACH TO NON-FICKIAN DIFFUSION

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 statistical approach, which is applied to the study of the "anomalous" (non-Fickian) diffusion that is involved in experiments of cyclic voltammetry in electro-physical chemistry. In these experiments, one is dealing with the fractal-like structure of the thin film morphology present in electrodes in microbatteries. Fractional-power laws are evidenced in the voltammetry measurements and in the analysis of the interphase width obtained using atomic force microscopy. The resulting fractional-powers are related to each other and to the statistical fractal dimension, and can be expressed in terms of the index on which Renyi's statistical approach depends. The important fact that this index, which is restricted to a given interval, provides a measure of the micro-roughness of the electrode surface, and is related to the dynamics involved, the nonequilibrium thermodynamic state of the system, and to the experimental protocol is clarified.