Staircase, cyclic and differential voltammetries of the nine-member square scheme at microelectrodes of any geometry with arbitrary chemical stabilization of the three redox states

Abstract

Simple analytical expressions are deduced for the cyclic (staircase) and differential cyclic (staircase) voltammetric responses of the 9-member square scheme at the most widely-used microelectrode geometries: disc, (hemi)spheres, cylinders and bands. The generality of the reaction scheme considered enables us to tackle many different and common electrochemical situations where the oxidized, intermediate and/or reduced species of a two-electron transfer also take part in homogeneous chemical equilibria such as protonations, complexations or ion pairings. The effect of the coupled chemical processes on the voltammograms is analyzed at electrodes of different size and shape under a variety of conditions depending on which redox state is chemically stabilized most significantly. Also, working curves for the determination of the formal potentials and the chemical equilibrium constants are given for macro-, micro-and ultramicro-electrodes in cyclic voltammetry and differential cyclic voltammetry.

Size Effects in Nanoparticle Catalysis at Nanoparticle Modified Electrodes: The Interplay of Diffusion and Chemical Reactions

“…Moreover, similar to a double electron transfer reaction (so-called 'EE' reaction), 34 a split in the current-potential curve can be observed for large values of K cat in Figure 6, indicating the two separate electron-transfer processes, with that at lower overpotentials reflects the full amount of reactant R in solution with the second wave reflects the concentration of A.…”

A Theoretical Framework for the Electrochemical Characterization of Anisotropic Micro‐Emulsions**

“…Since any electron transfer reaction in a ME may thus occur from either phase, a successive two‐step two‐electron reaction might be regarded as a kinetically controlled version of the well‐known extended six‐member square scheme which is depicted in Figure 1. Though the theoretical model of such square scheme(s) is well established for reversible electron transfers [10–15] the implementation of Butler–Volmer electrode kinetics is performed rarely [15] . Usually – i. e. for the purpose of electrochemical trace analysis and sensing applications – this somewhat simplified treatment is fairly sufficient, since the settings of the electroanalytical experiment can be tuned in a way such that the electrochemical kinetics can be neglected [8] .…”

A Theoretical Framework for the Electrochemical Characterization of Anisotropic Micro-Emulsions

“…Since any electron transfer reaction in a ME may thus occur from either phase, a successive two-step two-electron reaction might be regarded as a kinetically controlled version of the well-known extended six-member square scheme which is depicted in figure 1. Though the theoretical model of such square scheme(s) is well established for reversible electron transfers [10][11][12][13][14][15] the implementation of Butler-Volmer electrode kinetics is performed rarely [15] . Usually -i.e.…”