Formal electrode systems

The theory for cyclic voltammetry was developed by Nicholson and Shain [80]. The mid-peak potential of the anodic and cathodic peak potentials obtained under our experimental conditions defines an electrolyte-dependent formal electrode potential for the [Fe(CN)g] /[Fe(CN)g]" couple E°, whose meaning is close to the genuine thermodynamic, electrolyte-independent, electrode potential E° [79, 80]. For electrochemically reversible systems, the value of7i° (= ( pc- - pa)/2) remains constant upon varying the potential scan rate, while the peak potential separation provides information on the number of electrons involved in the electrochemical process (Epa - pc) = 59/n mV at 298 K [79, 80]. Another interesting relationship is provided by the variation of peak current on the potential scan rate for diffusion-controlled processes, tp becomes proportional to the square root of the potential scan rate, while in the case of reactants confined to the electrode surface, ip is proportional to V [79]. 

Fig. 3.23 Simulated cyclic voltammograms (1st and 2nd cycle) of an electrochemically reversible system with the depolarizer in the bulk of the solution in its reduced and oxidized forms, respectively taking Estart = E%,c = —500mV, Dox = Drd lO cm /s, scan rate 0.1 V/s. The potential scan is initiated at the formal electrode potential of that couple in the anodic direction. Adapted from [203]...

The electrostatic aspects of electrochemical systems will be introduced first and the electrochemical potential as a key concept is presented (Sects. 1.2-1.4). The electrochemical equilibrium is discussed and Nemst s equation and standard and formal electrode potentials are introduced (Sect. 1.5). The study of electrochemical interfaces under equilibrium ends with the phenomenological and theoretical treatment of the electrical double layer (Sect. 1.6). 

Electrode processes are conveniently classified according to the nature of the final product1 and its formal mode of formation, since then the interplay between nucleophile(s) or electrophile(s), substrate, and loss or addition of electron(s) is best expressed. It is upon our ingenuity to choose the correct combination of electrolyte components that the practical success of an electrochemical reaction rests, and therefore the rather formalized classification system to be outlined and exemplified below is the logical point of departure into the maze of mechanistic intricacies of electrode processes. 

Depending upon the nature of the /3-diketonato ligand, they may exhibit a single two-electron reduction or two separate one-electron reductions. In any case, the electron transfer processes are coupled to more or less fast release of the diketonato ligand, which means that copper(II) is the only stable oxidation state in the system. Table 17 summarizes the formal electrode potentials for the Cu(II) —Cu(I) — Cu(0) reductions of selected copper(II) )3-diketonates. 

If the electrode reaction proceeds with the participation of anions in the electrode system A/A" , A" /A, or A" /A "", the interaction of these anions with the solvent can now be understood as the reaction between the base (anion) and the acid (solvent). Now the formal potential should be dependent on the acceptor number of the solvent,... 

The measurement of a formal pe or formal electrode potential consists of measurement of the emf of an electrochemical cell in which, under the specified conditions, the analytical concentration of the two oxidation states is varied. For example, in a 0.1 M H2SO4 solution, the formal electrode potential for Fe(III)-Fe(II) is 0.68 V in comparison to 0.77 V for the Fe /Fe (/ = 0) system ... 

It is important to obtain experimental information on the thermodynamics of electrode processes to ascertain the tendency of a particular reaction to occur under a given set of experimental conditions namely temperature, pressure, system com H)sition and electrode potential. Such information is provided by the standard- or formal-electrode potentials for the redox couple under consideration. Appropriate combinations of these potentials enable the thermodynamics of homogeneous redox processes to be determined accurately. However, such quantities often are subject to confusion and misinterpretation. It is, therefore, worthwhile to outline their significance for simple electrochemical reactions. This discussion provides background to the sections on electrochemical kinetics which follow. The evaluation of formal potentials for various types of electrode-reaction mechanisms is dealt with in 12.3.2.2. 

Fig. la-c. Schematic representation of the cyclic voltammetric response exhibited by the system Ox + e - Red, having a formal electrode potential E° = 0.00 V, which ideally proceeds through a) a reversible electron transfer b) a quasireversible electron transfer, c) an irreversible electron transfer... 

The measurement of formal potentials allows the determination of the Gibbs free energy of amalgamation (cf Eq. 1.2.27), acidity constants (pATa values) (cf. Eq. 1.2.32), stability constants of complexes (cf. Eq. 1.2.34), solubility constants, and all other equilibrium constants, provided that there is a definite relationship between the activity of the reactants and the activity of the electrochemical active species, and provided that the electrochemical system is reversible. Today, the most frequently applied technique is cyclic voltammetry. The equations derived for the half-wave potentials in dc polarography can also be used when the mid-peak potentials derived from cyclic voltammograms are used instead. Provided that the mechanism of the electrode system is clear and the same as used for the derivation of the equations in dc polarography, and provided that the electfode kinetics is not fully different in differential pulse or square-wave voltammetry, the latter methods can also be used to measure the formal potentials. However, extreme care is advisable to first establish these prerequisites, as otherwise erroneous results will be obtained. 

There are also other electrode systems of the type Hg Hg2X2, Hg2Y X , or HgaY I Y which may be potentially used for the construction of a reference electrode. In theory such electrodes of the second kind should maintain a constant potential at a constant activity of X or Y . In Table 5.3.3 some of such systems were listed with their standard or formal potentials [101]. 

Conventional batteries consist of a liquid electrolyte separating two solid electrodes. In the Na/S battery this is inverted a solid electrolyte separates two liquid electrodes a ceramic tube made from the solid electrolyte sodium /5-alumina (p. 249) separates an inner pool of molten. sodium (mp 98°) from an outer bath of molten sulfur (mp 119°) and allows Na" " ions to pass through. The whole system is sealed and is encased in a stainless steel canister which also serves as the sulfur-electrode current collector. Within the battery, the current is passed by Na+ ions which pass through the solid electrolyte and react with the sulfur. The cell reaction can be written formally as... 

Rotating-disk voltammetry is the most appropriate and most commonly employed method for studying mediation. In most systems that have been studied, there has been little penetration of the substrate in solution into the polymer film. This can be demonstrated most easily if the polymer film is nonconductive at the formal potential of the substrate. Then the absence of a redox wave close to this potential for an electrode coated with a very thin film provides excellent evidence that the substrate does not penetrate the film significantly.143 For cases where the film is conductive at the formal potential of the substrate, more subtle argu-... 

Although the extended ab initio atomistic thermodynamics approach provides an exact expression for the interfacial stability, the formalism requires self-consistent modeling of the entire electrochemical system, or electrode/electrolyte interface, exceeding presently available computational capabilities. Therefore, certain assumptions had to be made that reduce the effort to the calculation of the electrode surface only. Even with this simplified approach, which has been applied to the two examples discussed in this chapter, the qualitative behavior can be reproduced. 

It is very often necessary to characterize the redox properties of a given system with unknown activity coefficients in a state far from standard conditions. For this purpose, formal (solution with unit concentrations of all the species appearing in the Nernst equation its value depends on the overall composition of the solution. If the solution also contains additional species that do not appear in the Nernst equation (indifferent electrolyte, buffer components, etc.), their concentrations must be precisely specified in the formal potential data. The formal potential, denoted as E0, is best characterized by an expression in parentheses, giving both the half-cell reaction and the composition of the medium, for example E0,(Zn2+ + 2e = Zn, 10-3M H2S04). 

The formal potential of a reduction-oxidation electrode is defined as the equilibrium potential at the unit concentration ratio of the oxidized and reduced forms of the given redox system (the actual concentrations of these two forms should not be too low). If, in addition to the concentrations of the reduced and oxidized forms, the Nernst equation also contains the concentration of some other species, then this concentration must equal unity. This is mostly the concentration of hydrogen ions. If the concentration of some species appearing in the Nernst equation is not equal to unity, then it must be precisely specified and the term apparent formal potential is then employed to designate the potential of this electrode. 

Let us choose, as an arbitrary reference level, the energy of an electron at rest in vacuum, e ) (cf. Section 3.1.2). This reference energy is obvious in studies of the solid phase, but for the liquid phase, the Trasatti s conception of absolute electrode potentials (Section 3.1.5) has to be adopted. The formal energy levels of the electrolyte redox systems, REDox, referred to o, are given by the relationship ... 

Due to the presence of interactions, the apparent redox potential of a redox couple inside a polyelectrolyte film can differ from that of the isolated redox couple in solution (i.e. the standard formal redox potential) [121]. In other words, the free energy required to oxidize a mole of redox sites in the film differs from that needed in solution. One particular case is when these interations have an origin in the presence of immobile electrostatically charged groups in the polymer phase. Under such conditions, there is a potential difference between this phase and the solution (reference electrode in the electrolyte), knovm as the Donnan or membrane potential that contributes to the apparent potential of the redox couple. The presence of the Donnan potential in redox polyelectrolyte systems was demonstrated for the first time by Anson [24, 122]. Considering only this contribution to peak position, we can vwite ... 

To summarize, one can say that the electrochemical performance of CNT electrodes is correlated to the DOS of the CNT electrode with energies close to the redox formal potential of the solution species. The electron transfer and adsorption reactivity of CNT electrodes is remarkably dependent on the density of edge sites/defects that are the more reactive sites for that process, increasing considerably the electron-transfer rate. Additionally, surface oxygen functionalities can exert a big influence on the electrode kinetics. However, not all redox systems respond in the same way to the surface characteristics or can have electrocatalytical activity. This is very dependent on their own redox mechanism. Moreover, the high surface area and the nanometer size are the key factors in the electrochemical performance of the carbon nanotubes. 

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