Theory of Absorbance Transients of an Optically Transparent Rough Electrode

Abstract

Theory for the potentiostatic absorbance transient for a species generated at the rough electrode/electrolyte interface is developed. Absorbance transients are strongly affected by electrode geometries, particularly the effect of electrode roughness which is the least understood area, is dealt here. A general operator structure between concentration, surface absorbance density, absorbance transients and arbitrary roughness profile of electrode is emphasized. The statistically averaged absorbance transients is obtained by ensemble averaging over all possible surface roughness configurations. An elegant mathematical formula between the average spectroelectrochemical absorbance transient and surface structure factor or power spectrum of roughness is obtained. This formula is used to obtain an explicit equation for the absorbance on an approximately self-affine (or realistic) fractal and nonfractal electrode. Our results are also applicable to chronocoulometric response as its directly related to chronoabsorptometric response. Limiting behavior in short time, is attributed to the electrode roughness factor and surface curvatures. Limiting behavior in long time is like a smooth electrode response but the transition region is attributed to the mean square width of roughness. In the intermediate time, the absorbance has anomalous power law behavior which is attributed to the diffusion length weighted spatial frequency features of roughness and becomes almost time independent for large roughness electrodes. Finally, this theory provides a quantitative description of the role of roughness on potential step transmission chronoabsorptometry and chronocoulometric measurements, therefore opening up the way to explore and understand various anomalies in their response.

Theory for Anomalous Response in Cyclic Staircase Voltammetry: Electrode Roughness and Unequal Diffusivities

“…Out of these four, only D H , , and τ are found to dominantly control the electrochemical response of diffusion limited charge transfer systems. 22,28,29,34 Before starting the elaborate discussion of the influence of electrode morphology on cyclic voltammetry, we want to analyze the influence of starting potential and initial composition on the current in multiple cycling.…”

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

“…Macdonald and coworkers also have addressed the problem of charge transfer [34,56,55] on planar electrode in finite electrochemical cells. 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. 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.…”

Simultaneous Detection of Catechol and Hydroquinone Using Acetylene Black and Gold Nanoparticle Composite Modified Electrodes

“…Though these results were obtained from potassium ferrocyanide solution, it would also reflect the electron transfer properties of the analytes on our modified electrodes with improved sensing capability. [19] Electrochemistry behaviors on modified electrodes…”