Diffusion at Ultramicro Disk Electrodes: Chronoamperometric Current for Steady-State Ec‘ Reaction Using Scattering Analogue Techniques

Abstract

An accurate polynomial expression for the steady-state current in the case of first-order EC′ reaction is reported using scattering analogue techniques for ultramicro disk electrodes. When the reaction rate is small, seven terms of diffusion-limited current are reported, and when it is large, five terms of the same are reported. A two-point Pade ´approximant is derived for all values of reaction rates. By a proper transcription of variables, the methodology is extended to derive chronoamperometric current for diffusion-controlled processes, and excellent agreement with digital simulation data is noticed.

Singularities of the catalytic mechanism in its route to the steady state

“…It is interesting to note that this important and fundamental difference between the catalytic mechanism and the CE and/or EC processes under steady-state conditions has not been highlighted before, although a great number of papers exists which study the behaviour of these mechanisms at ultramicroelectrodes [1][2][3][4]8,18].…”

“…However, as far as we know to date, it has been only considered as a particular case of an EC process. This fact is probably because in most cases Scheme (III) has been treated when K = 0 [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

A comparison of diffusion-limited currents at microelectrodes of various geometries for EC′ reactions

“…Much work has been carried out to study the EC mechanism at ultramicroelectrodes using analytical approximations [3][4][5][6][7][8][9][10][11][12][13][14] and numerical methods [15][16][17][18][19][20][21][22]. Space permits us to mention only a few of them below.…”

“…Most recently, Galceran et al [13] obtained the current of inlaid and recessed microdisc electrodes using the finite element method. Rajendran and Sangaranarayanan [14] have derived an exact analytical expression for steady-state current for all K using the two-point Pade approximation. Most recently Galceran et al [13] presented three new formulas for steady-state current, among which they highlighted one equation with an accuracy better than 0.27%.…”

Computation of currents at microelectrodes using hp-DGFEM

“…Analytical and finite difference solutions to the EC 0 reaction mechanism at the microdisc electrode can be found in [20,47,45]. Previous mathematical studies of reaction mechanisms at channel microband electrodes have involved the use of finite difference methods [6,10,[12][13][14], finite element methods [49,50] and analytical techniques [2,8,12,15,38,42,46].…”