Diffusion to fractal surfaces—V. quasi-random interfaces

A Review of Non-Cottrellian Diffusion Towards Micro- and Nano-Structured Electrodes

“…Pajkossy and co-workers have published an interesting series of papers devoted to the electrochemistry on fractal surfaces (Nyikos & Pajkossy, 1986;Pajkossy & Nyikos, 1989a;Pajkossy & Nyikos, 1989b;Nyikos et al, 1990;Borosy et al, 1991). Diffusion to rough surfaces plays an important role in diverse fields, e.g., in catalysis, enzyme kinetics, fluorescence quenching and spin relaxation.…”

“…Its experimental verification on an electrode with a well defined fractal geometry D f = 1.585 was presented for a rotating disc electrode of fractal surface (Nyikos et al, 1990). The fractal approximation has been shown to be useful for describing the geometrical aspects of diffusion processes at realistic rough or irregular-interfaces (Borosy et al, 1991). The authors have concluded that diffusion towards a self-affine fractal surface with much smaller vertical irregularity than horizontal irregularity leads to the conventional Cottrell relation between current and time of the Euclidean object, not the generalised Cottrell relation including fractal dimension.…”

Self-affine roughness influence on redox reaction charge admittance

“…Scaling arguments in combination with numerical and experimental studies [2,[12][13][14][15][16][17][24][25][26] have shown that the reaction admittance follows approximately a power-law of the frequency of the form Y(x) $ x c . Indeed, c = (D H À 1)/2 for the problem of diffusion-controlled nuclear magnetic relaxation in porous media with fractal dimension D H [1].…”

“…[8,9]. The frequency response of rough interface depends on the regime under consideration such as for example (i) the capacitive behavior of rough electrodes [24][25][26][27][28][29][30][31][32][33][34][35][36], and (ii) diffusion controlled charge transfer on rough interfaces [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

“…Studies related to transport to and across a rough interface are of general interest in a wide variety of research fields as for example spin relaxation [1], fluorescence quenching [1,2], heterogeneous catalysis [3], enzyme kinetics [4], heat diffusion [5], membrane transport [6,7], and electrochemistry [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In the latter case, the exploration of the mechanism of interfacial processes and the evaluation of parameters such as double-layer capacitance and charge rate constants can be performed by impedance spectroscopy [8,9].…”