Cyclic voltammetry formal potential

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. 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

By varying the scan rate, this equation allows then the evaluation of the diffusion coefficient of the transferring ion. With the determination of the formal transfer potential of an ion and thus of its Gibbs energy of transfer by application of Eq. (10), this is the most important application of cyclic voltammetry. 

Thin films of a composite nickel-iron (9 1 Ni/Fe ratio) and iron-free oxyhydroxides were deposited from metal nitrate solutions onto Ni foils by electroprecipitation at constant current density. A comparison of the cyclic voltammetry of such films in 1M KOH at room temperature (see Fig. 6) shows that the incorporation of iron in the lattice shifts the potentials associated formally with the Ni00H/Ni(0H)2 redox processes towards negative potentials, and decreases considerably the onset potential for oxygen evolution. The oxidation peak, as shown in the voltammo-gram, is much larger than the reduction counterpart, providing evidence that within the time scale of the cyclic voltammetry, a fraction of the nickel sites remains in the oxidized state at potentials more negative than the reduction peak. 

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. 

Standard potential of the second electron transfer more cathodic than that of the first electron transfer (AE0 negative). One can consider the case where the formal electrode potential of the second couple is more cathodic, by at least 180 mV, with respect to the first couple (which has, for example, E01 = 0.00 V). If kf is low (compared to the intervention times of cyclic voltammetry i.e. if k[< n F- v/R T), the response will be due to the first electron transfer process, without complications caused by the following chemical reaction. As increases, the second process will have increasing effect up to the limiting case in which kt >n-F-v/R-T. In this limiting case the voltammogram will display two forward peaks, but only the second electron transfer will exhibit a return peak. 

In polarography, we obtained the half-wave potential E// by analysing the shapes of the polarographic wave. E1/2 is a useful characteristic of the analyte in the same way as E . In cyclic voltammetry, the position o/both peaks (both forward and back in Figure 6.13 cathodic and anodic, respectively, in this example) gives us thermodynamic information. Provided that the couple is fully reversible, in the thermodynamic sense defined in Table 6.3, the two peaks are positioned on either side of the formal electrode potential E of the analyte redox couple, as follows ... 

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 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]. 

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. 

Reduction potentials for a variety of the 11-atom ligand complexes have been measured either by cyclic voltammetry or by polarographic methods (see Table IV). In certain cases the most stable formal oxidation state for... 

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