Voltammetry formal potentials

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-... 

If the film is nonconductive, the ion must diffuse to the electrode surface before it can be oxidized or reduced, or electrons must diffuse (hop) through the film by self-exchange, as in regular ionomer-modified electrodes.9 Cyclic voltammograms have the characteristic shape for diffusion control, and peak currents are proportional to the square root of the scan speed, as seen for species in solution. This is illustrated in Fig. 21 (A) for [Fe(CN)6]3 /4 in polypyrrole with a pyridinium substituent at the 1-position.243 This N-substituted polypyrrole does not become conductive until potentials significantly above the formal potential of the [Fe(CN)6]3"/4 couple. In contrast, a similar polymer with a pyridinium substituent at the 3-position is conductive at this potential. The polymer can therefore mediate electron transport to and from the immobilized ions, and their voltammetry becomes characteristic of thin-layer electrochemistry [Fig. 21(B)], with sharp symmetrical peaks that increase linearly with increasing scan speed. 

Electrochemistry. The redox processes for porphyrazines 21, 25, 28, 29, the heteroleptic Zr (pz/porphyrin) 30 and 31 have been measured by cyclic voltammetry and the formal potentials are given in Table VII. The potentials are compared to the available data for the analogous porphyrin and pc complexes. In general, the electrochemical behavior of the pz sandwiches more closely mirror that observed for the phthalocyanines than the porphyrins. In particular, all of the porphyrazines have at least one ring-based oxidation, attributable to the formation of the bis Jt-radical cation for Lu(III) sandwiches and the formation of the 7T-radical cation for the Zr(IV) and Ce(IV) sandwiches. Additionally, all of the porphyrazines exhibit at least one ring-based reduction. 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

C. P. Andrieux, P. Hapiot, J. Pinson, J.-M. Saveant. Determination of Formal Potentials of Chemically Unstable Redox Couples by Second-Harmonic Alternating Current Voltammetry and Cyclic Voltammetry. Application to the Oxidation of Thiophenoxide Ions. J.Am. Chem. Soc. 1993,115, 7783-7788. 

If kfchemical reaction is very slow compared to the intervention times of cyclic voltammetry) the response is very similar to that of a simple reversible electron transfer and occurs at the formal potential, E°, of the couple Ox/Red. 

Cyclic voltammetry has perhaps become the most popular electroanalytical, electrochemical technique [23, 27], and many reports have appeared in which E° values were determined in this way. However, reliable formal potentials can be determined only for electrochemically reversible systems [28]. For any reversible redox system - provided that the electrode applied is perfectly inert, that is, there are... 

The experimental data verifying the dependencies of the formal potentials on ion parameters, as shown in Figs 4, 5, and 6 have been accessible only by application of voltammetry of immobilized particles [59], since that method is the only one that allows the study of different compounds that have been chemically synthesized and completely characterized to be measured under the very same conditions. This is not, or only to some extent possible with electrochemically prepared thin films on electrodes. 

A more broadly applicable approach to evaluating the formal potential of an adsorbed dye is cyclic voltammetry (CV). Under dark conditions, nanocrystalline Sn02, 2, and ZrC2 electrodes behave as insulators at the potentials needed to oxidize the dyes discussed here. If the dye loading is high, however, the percola-... 

In fact, the potentiometric or voltammetric measurement is carried out using a conventional reference electrode (e.g. Ag+/Ag electrode).3 After measurement in the test solution, Fc or BCr+ (BPhJ salt) is added to the solution and the half-wave potential of the reference system is measured by polarography or voltammetry. Here, the half-wave potential for the reference system is almost equal to its formal potential. Thus, the potential for the test system is converted to the value versus the formal potential of the reference system. The example in Fig. 6.2 is for a situation where both the test and the reference systems are measured by cyclic voltammetry, where E1/2=(Epc+Epi)/2. Curve 1 was obtained before the addition of Fc and curve 2 was obtained after the addition of Fc. It is essential that the half-wave potential of the test system is not affected by the addition of the reference system. 

Cyclic voltammetry can (i) determine the electrochemical reversibility of the primary oxidation (or reduction) step (ii) allow the formal potential, E°, of the reversible process to be estimated (iii) provide information on the number of electrons, n, involved in the primary process and (iv) allow the rate constant for the decomposition of the M"+ species to be measured. Additional information can often be obtained if intermediates or products derived from M"+ are themselves electroactive, since peaks associated with their formation may be apparent in the cyclic voltam-mogram. The idealized behaviour illustrated by Scheme 1 is a relatively simple process more complicated processes such as those which involve further electron transfer following the chemical step, pre-equilibria, adsorption of reactants or products on the electrode surface, or the attack of an electrogenerated product on the starting material, are also amenable to analysis. 

This is an appropriate point at which to comment on the common practice of evaluating the formal potential from voltammetric measurements. When a reversible response is obtained in voltammetry, what is actually measured is the reversible half-wave potential, E1/2, which (except for hydrodynamic voltammetry) is related to the formal potential by a term involving the diffusion coefficients of the oxidized and reduced forms of the half-reaction, D0 and DR, respectively. 

It is also common to measure by voltammetry the thermodynamic properties of purely chemical reactions that are in some way coupled to the electron transfer step. Examples include the determination of solubility products, acid dissociation constants, and metal-ligand complex formation constants for cases in which precipitation, proton transfer, and complexation reactions affect the measured formal potential. Also in these instances, studies at variable temperature will afford the thermodynamic parameters of these coupled chemical reactions. 

From the voltammograms of Fig. 5.12, the evolution of the response from a reversible behavior for values of K hme > 10 to a totally irreversible one (for Kplane < 0.05) can be observed. The limits of the different reversibility zones of the charge transfer process depend on the electrochemical technique considered. For Normal or Single Pulse Voltammetry, this question was analyzed in Sect. 3.2.1.4, and the relation between the heterogeneous rate constant and the mass transport coefficient, m°, defined as the ratio between the surface flux and the difference of bulk and surface concentrations evaluated at the formal potential of the charge transfer process was considered [36, 37]. The expression of m° depends on the electrochemical technique considered (see for example Sect. 1.8.4). For CV or SCV it takes the form... 

---