Microelectrode voltammetry of multi-electron transfers complicated by coupled chemical equilibria: a general theory for the extended square scheme

Abstract

A very general and simple theoretical solution is presented for the current-potential-time response of reversible multi-electron transfer processes complicated by homogeneous chemical equilibria (the so-called extended square scheme). The expressions presented here are applicable regardless of the number of electrons transferred and coupled chemical processes, and they are particularized for a wide variety of microelectrode geometries. The voltammetric response of very different systems presenting multi-electron transfers is considered for the most widely-used techniques (namely, cyclic voltammetry, square wave voltammetry, differential pulse voltammetry and steady state voltammetry), studying the influence of the microelectrode geometry and the number and thermodynamics of the (electro)chemical steps. Most appropriate techniques and procedures for the determination of the 'interaction' between successive transfers are discussed. Special attention is paid to those situations where homogeneous chemical processes, such as protonation, complexation or ion association, affect the electrochemical behaviour of the system by different stabilization of the oxidation states.

Electrochemical and Computational Study of Ion Association in the Electroreduction of PW12O403–

“…E -Eº' Fc/Fc + (mV) As can be seen in Figure 1, when the concentration of TMA + is increased, the positions of the two peaks shift towards less negative values, which reveals the occurrence of ion associations between the polyoxometalate anions and TMA + . The shift is more obvious in the second peak such that it can be concluded that the strength of the association follows the order Next, as indicated previously (Section 3.1) and as detailed in 39 , the elucidation of the ion pairing mechanism and the determination of the association constants and stoichiometries of the different PW12 species were performed by the analysis of the variation of the apparent formal potentials with the concentration of TMA + (Eq. ( 9)), with the corresponding equilibrium constants as adjustable parameters.…”

“…being the apparent formal potentials that depend on the values of the ion association constants as follows 39,50,69,70 :…”

“…(9). By determining their values from the SW signal as detailed in 50,71 for different values of * X c , the association constants and stoichiometries can be investigated as discussed in the following sections 39 .…”

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.…”