Formal potential, electrochemical reactions

Equation (4.2) predicts a linear dependence of Efvs. A with a slope 1, and a linear dependence between Ef vs. log(o ) with a slope 2.303. These two dependencies can serve as diagnostic criteria to identify the electrochemical mechanism (4.1). Figure 4.4a shows the effect of different anions on the position of the net peak recorded at the three-phase electrode with a droplet configuration, where DMFC is the redox probe and nitrobenzene is the organic solvent. Figure 4.4b shows the linear variation of the net peak potential with A, with a slope close to 1. Recalling that the net peak potential of a reversible reaction is equivalent to the formal potential of the electrochemical reaction (Sect. 2.1.1), the results in Fig. 4.4 confirm the validity and applicability of Eq. (4.2). 

Chemical reaction steps Even if the overall electrochemical reaction involves a molecular species (O2). it must first be converted to some electroactive intermediate form via one or more processes. Although these processes are ultimately driven by depletion or surplus of intermediates relative to equilibrium, the rate at which these processes occur is independent of the current except in the limit of steady state. We therefore label these processes as chemical processes in the sense that they are driven by chemical potential driving forces. In the case of Pt, these steps include dissociative adsorption of O2 onto the gas-exposed Pt surface and surface diffusion of the resulting adsorbates to the Pt/YSZ interface (where formal reduction occurs via electrochemical-kinetic processes occurring at a rate proportional to the current). 

The mixed phase is reduced at a potential that depends on the molar ratio of the two salts formally forming the mixed crystal, as can be seen in Fig. 4.2, where peak potentials of different mixed crystals of CuSei xSx are plotted against the molar ratio xs/(xse + xs) [224], Since the peak potentials vary slightly with the total amount of charge (Q) consumed in the electrochemical reaction, standardized peak potentials extrapolated to values for Q = 0 were taken. 

In order to express explicitly the dependence of the reaction rate on potential, it is necessary to re-introduce this dependence for every electrochemical reaction-speed constant. These constants concern reactions where one electron is transferred and to which Equation 4.20 applies. In this relation, the potential of the redox system involved is referred to as the formal potential, so that the anodic and cathodic subcurrent can be expressed as a function of the same rate constant, k0. This is not possible in Equation 4.26 because there are rate constants of different redox systems, or because formal potentials of intermediary redox systems are not known. 

Multi-electron (multistep) electrode processes will be studied in Sect. 3.3, underlining the key role of the difference of the formal potentials between each two consecutive electrochemical steps on the current-potential curves and also the comproportionation/disproportionation reactions that take place in the vicinity of the electrode surface. In the case of two-step reactions, interesting aspects of the current-potential curves will be discussed and related to the surface concentrations of the participating species. 

Equation (3.140) shows that the electrochemical response of an EE mechanism depends on the difference between the formal potentials t Ef and is not influenced by the homogeneous reaction. This behavior is shown in Fig. 3.16 where the current... 

The voltammetric response for the reaction scheme (3. XI) depends on the difference between the formal potentials of both electrochemical steps, ACt°, and on the equilibrium and kinetic constants of the intermediate chemical reaction. If AE = Ef.2 — Ef j [Pg.217]

In Sect. 6.2, multi-electron (multistep) electrochemical reactions are surveyed, especially two-electron reactions. It is shown that, when all the electron transfer reactions behave as reversible and the diffusion coefficients of all species are equal, the CSCV and CV curves of these processes are expressed by explicit analytical equations applicable to any electrode geometry and size. The influence of the difference between the formal potentials of the different electrochemical reactions on these... 

The effect of the reversibility of electrochemical reaction on the theoretical Qp —t curves calculated from Eq. (6.131) is shown in Fig. 6.22. For reversible processes (k°t > 10), the charge-time curves present a stepped sigmoid feature and are located around the formal potential of the electro-active couple. Under these conditions, the charge becomes time independent (see Eq. (6.132)). As the process becomes less reversible, both the shape and location of the Qp — t curves change in such a way that the successive plateaus tend to disappear and a practically continuous quasi-sigmoid, located at more negative potentials as k°r decreases, is obtained. For k°r < 0.1, general Eq. (6.131) simplifies to Eq. (6.134), valid for irreversible processes and leads to a practically continuous Qp — t curve. 

The electrochemical characterization of multi-electron electrochemical reactions involves the determination of the formal potentials of the different steps, as these indicate the thermodynamic stability of the different oxidation states. For this purpose, subtractive multipulse techniques are very valuable since they combine the advantages of differential pulse techniques and scanning voltammetric ones [6, 19, 45-52]. All these techniques lead to peak-shaped voltammograms, even under steady-state conditions. 

Equation (6.15) is now applied to SWV in order to characterize a two-electron electrochemical reaction. The effects of the difference between the formal potentials, the frequency, the square wave potential, and the staircase potential of the SWV are discussed and procedures for the determination of the formal potentials of both electrochemical reactions are proposed. 

When the formal potential of the first step is much more positive than that of the second, AE f < — 200mV (Fig. 7.31c), the intermediate species 02 is stable and two well-separated peaks are obtained, centered on the formal potential of each process and with the features of the voltammograms of one-electron electrochemical reaction. When the A7 ° value increases, the stability of the intermediate decreases and the two peaks are closer, and the transition from two peaks to a single peak is observed (AE —71.2 mV). Eventually, when the formal potential of the second electron transfer is much more positive than that of the first one, AE > 200 mV, the characteristics of the voltammograms are those of an apparently simultaneous two-electron electrochemical reaction (Fig. 7.31a). Note that the... 

As in the case of a reversible one-electron electrochemical reaction, the halfpeak width of the SWV does not depend on the electrode geometry. For a two-electron electrochemical reaction, Wy2 is only a function of the difference between formal potentials AE f and of the square wave amplitude sw. The evolution of the half-peak width Wy2 with AEcspherical electrodes has been plotted in Fig. 7.32. These curves give a very general criterion for the characterization of the EE process through Wy2. 

In order to analyze the influence of the chemical kinetics on the SWV response of this mechanism when the chemical reaction behaves as irreversible (Keq —> oo), it can be compared with that obtained for a reversible two-electron electrochemical reaction (EE mechanism) at the same values of the difference between the formal potentials of the electrochemical steps, A= E 2 — E (which is always centered atE-mA 1L = (E +E 2)/2). 

The influence of the reversibility of the electrochemical reaction on the SW net charge-potential curves ( (Gsw/Gf) - (Eindex is plotted in Fig. 7.48 for different values of the square wave amplitude ( sw = 25,50,100, and 150mV) and three values of the dimensionless surface rate constant (1° ( k°t) = 10,0.25, and 0.01), which correspond to reversible, quasi-reversible, and fully irreversible behaviors. Thus, it can be seen that for a reversible process (Fig. 7.48a), the (Gsw/Gf) — (Eindex EL°) curves present a well-defined peak centered at the formal potential (dotted line), whose height and half-peak width increase with Esw (in line with Eqs. (7.118) and (7.119)), until, for sw > lOOmV, the peak becomes a broad plateau whose height coincides with Q s. This behavior can also be observed for the quasi-reversible case shown in Fig. 7.48b, although in this case, there is a smaller increase of the net charge curves with sw, and the plateau is not obtained for the values of sw used, with a higher square wave amplitude needed to obtain it. Nevertheless, even for this low value of the dimensionless rate constant, the peak potential of the SWVC curves coincides with the formal potential. This coincidence can be observed for values of sw > 10 mV. 

The dimensionless SWV curve is identical to the stationary SWV curve obtained for a fast electrochemical reaction with solution soluble molecules given by Eqs. (7.35) or (7.36) for spherical or disc electrodes, respectively, and also to that obtained for a reversible surface electrode process (Eq. (7.116)). Therefore, the peak potential coincides with the formal potential and the half-peak width is given by Eq. (7.32). The peak height is amplified by kc ... 

We have also recently examined the electrooxidation of iodide at gold using the combined SERS-RDV approach.(22)The system was chosen as a simple example of a multistep process where the reaction products (iodine and/or triodide) as well as the reactant and any intermediates should be strongly adsorbed. This reaction has been studied extensively using conventional electrochemical techniques, yet the reaction mechanism remains in doubt.(23) At potentials well negative of the I /I2 formal potential, iodide yields a pair of SERS bands at gold at 124 and 158 cm-1, associated with adsorbed I -surface vibrations. 

The formal potential of the NAD+/NADH redox couple is -0.56 V vs. SCE at pH 7 [15, 17]. However, at platinum and glassy carbon electrodes NADH, oxidation occurs at 0.7 V and 0.6 V vs. SCE, respectively [18]. From these oxidation potentials, it is clear that the direct electrochemical oxidation of NADH requires a substantial overpotential. In nature, NADH oxidation is thought to occur by a one-step hydride transfer. However, on bare electrodes the reaction has been shown to occur via a different and higher energy pathway which produces NAD radicals as intermediates. 

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