Theory of partial diffusion-limited interfacial transfer/reaction on realistic fractals

Generalization of Randles-Ershler admittance for an arbitrary topography electrode: application to random finite fractal roughness

“…Theoretically, there are three approaches: equivalent circuit approach [58], scaling approach [58,57] and ab initio approach [59,60,62,61] that aid to the understanding of the role of roughness on the transport and kinetic phenomena at the interface. Kant and coworkers have solved the problem of charge transfer taking under quasireversible and pseudo-quasireversible (partial diffusion limited) processes on rough electrode [59][60][61]63,65]. An elegant formalism based on the diffusion adopting ab initio methodology has been successfully developed to understand the influence of roughness on the electrochemical response.…”

“…An elegant formalism based on the diffusion adopting ab initio methodology has been successfully developed to understand the influence of roughness on the electrochemical response. Recently, theories for diffusion limited charge transfer process on rough electrode are developed to generalize various fundamental equations for smooth electrodes: Warburg [22], Gerischer [25], Anson [62,66], quasi-reversible charge transfer admittance has been developed for finite fractal electrodes [63,65]. Similarly, theories for the anomalous Cottrell [64,68,67] and anomalous Warburg admittance [61,22] with ohmic effects [23,69] in rough electrode modeled as finite fractals have also been developed.…”

Theory of Anomalous Dynamics of Electric Double Layer at Heterogeneous and Rough Electrodes

“…The influence of electrode morphology and heterogeneity on the electrochemical response is ubiquitous, and these are considered theoretically difficult problems − in electrochemistry. One important problem still unsolved is the anomalous capacitive behavior and constant phase element (CPE) associated with the electric double layer formed at the electrode–electrolyte interface. − The problem of CPE remains controversial as there is no universal theory describing varieties of causes which are responsible for this phenomenon …”

“…The effect of roughness and the physical origin of CPE or capacitance dispersion in the electrochemical interface are addressed by equivalent circuit, − scaling, ,,− fractional diffusion, , and the ab initio approach. − ,− The equivalent circuit and scaling methods treat the CPE exponent as a measure of roughness (or heterogeneity) ,,, and use it to explain impedance data of heterogeneous, ,, rough, porous electrodes and the corroding system . But the CPE exponent is found to be a model-dependent quantity with no specific relation to the fractal dimension of the surface. , The analyses using equivalent circuits or scaling are misleading as they neglect the influence of physical length scales of roughness and heterogeneity seen in experiments. ,, …”

Theory of Absorbance Transients of an Optically Transparent Rough Electrode

“…The recent interest in realistic fractal geometry and methodology used for its characterization has opened a new window to understand the influence of surface disorder. This includes potential sweep methods on an arbitrary topography, Cottrellian current at a rough electrode with the solution resistance effect, partial diffusion-limited interfacial transfer/reaction, , Gerischer admittance at a rough electrode, anomalous Warburg impedance at a rough electrode, – and anomalous diffusion reaction rates or diffusion controlled potentiostatic current transients. – In this paper also, we wish to use same approach to characterize the rough OTE in relation to the diffusion-limited reversible redox reactions taking place at the electrode/electrolyte interface through absorbance transients. Figure depicts the rough OTE with emphasis on morphological and phenomenological scales that control the spectroelectrochemical response of such electrode/electrolyte interface.…”