Can one electrochemically measure the statistical morphology of a rough electrode?

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].…”

“…The response of a rough interface depends on the electrochemical regime. Two regimes in the electrochemical context have drawn particular attention: (i) the diffusion controlled charge transfer of rough/porous electrodes [11][12][13][16][17][18][19][22][23][24][25][26][27][28], (ii) the diffusion-kinetic controlled charge transfer on the rough/porous interface [9,27,29,42].…”

Self-affine roughness influence on redox reaction charge admittance

“…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].…”

“…[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].…”

“…In the more general case, the power-law flux transient on a fractal interface with Euclidean dimension D E of the embedding space has the form c = ( [8,12,13]. Other general results were obtained in understanding the effect of roughness on the interfacial reaction current in terms of an arbitrary weak roughness profile and an arbitrary roughness power spectrum [18][19][20][21]23] without however addressing the questions related to finite scale-invariant interfaces.…”