Self-affine roughness influence on redox reaction charge admittance

Abstract

In this work we investigate the influence of self-affine electrode roughness on the admittance of redox reactions during facile charge transfer kinetics. The self-affine roughness is characterized by the rms roughness amplitude w, the correlation length n, and the roughness exponent H (0 < H < 1). Our calculations allow analytic expressions to be derived for the admittance as a function of the characteristic self-affine roughness parameters. Furthermore, it is shown that the magnitude of the reaction admittance is strongly influenced by the local roughness exponent H or the fine roughness details at short roughness wavelengths, while the influence of the lateral correlation length n or the long wavelength roughness ratio w/n is of secondary importance. In addition, the dynamic roughness evolution can strongly influence the reaction admittance and it should taken carefully into consideration.

Generalized Warburg impedance on realistic self-affine fractals: Comparative study of statistically corrugated and isotropic roughness

“…Diffusion-limited processes on such interfaces show anomalous diffusive behaviour and realized in various physical phenomena such as: spin relaxation, 13 fluorescence quenching, 13,14 heterogeneous catalysis, 15 enzyme kinetics, 16 heat diffusion, 17 membrane transport, 18,19 electrochemistry, and impedance response. [24][25][26][40][41][42][43][44][45][46] Most of the real interfacial system can exhibit complex shapes with varying degree of irregularity or disorder. Such complex unconventional geometrical presence influences the electrode response.…”

“…Such complex unconventional geometrical presence influences the electrode response. The recent interest in realistic fractal geometry 26,28,29,40,44 has helped to understand the influence of surface disorder over the electrode response. The surface irregularities over realistic objects are characterized as two class of random fractals: (i) statistically isotropic fractals and (ii) statistically corrugated fractals.…”

Theory of Anomalous Diffusion Impedance of Realistic Fractal Electrode

“…De Gennes analyzed it for the diffusion- controlled nuclear magnetic relaxation in porous media with fractal dimension D H . Later similar results discussed for other diffusion controlled situations such as impedance of rough electrode. , There are some other general results which emphasize the concept of current/impedance for the diffusion-limited transfer at corrugated surface. ,,− Palasantzas also used the formalism discussed in ref to study the admittance of self-affine rough electrode but their analysis is limited to high-frequency region. They completely missed the essential intermediate anomalous frequency behavior of this problem.…”

Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

“…Some of the examples of diffusive transport are of general interest and studied in very different fields like: spin relaxation [1], fluorescence quenching [1,2], heterogeneous catalysis [3,4], enzyme kinetics [5,6], heat diffusion [7], membrane transport [8,9] and electrochemistry . Moreover, there are several studies in electrochemistry to understand the effect of electrode roughness on various transient techniques in electrochemistry like potentiostatic current transient technique [16][17][18][19][20][21][22][23][24][25][26] and impedance [19,[28][29][30]. In order to capture the complexity arising from the irregular interfaces (i.e., rough, porous, and partially active interfaces) one often uses the concept of fractals [31,32].…”