Reversible electron transfer cyclic voltammogram

FIGURE 2-6 Cyclic voltammograms for a reversible electron transfer followed by an irreversible step for various ratios of chemical rate constant to scan rate, k/a, where a = nFv/RT. (Reproduced with permission from reference 1.)... 

Figure 21 Typical cyclic voltammograms recorded at increasing scan rates (a < b < c) for a reversible electron transfer (having E° = 0.0 V) coupled to catalytic regeneration of the reagent...

The simplest electrochemical reaction which a compound can undergo at an electrode in an electrolyte is single, reversible electron transfer there are innumerable examples of coordination compounds which show this type of behaviour. Figure 1 shows a cyclic voltammogram of one such example, the reversible one-electron oxidation of frans-[MoIICl2(Ph2PCH2CH2PPh2)2] (equation 1). 

When the formal potentials of the adsorbed and non-adsorbed redox couples are similar, a single wave is obtained where the contribution of the electron transfer involving the adsorbed species increases with the scan rate. Thus, there is a transition from diffusional-shaped voltammograms at slow scan rates to adsorptive-shaped at fast scan rates. To understand this behaviour and illustrate the characteristics of adsorptive voltammograms let us consider the response in cyclic voltammetry of a monolayer of species A that undergoes a one-electron, fully reversible electron transfer ... 

FIGURE 6.16. Simulation of a cyclic voltammogram for finite diffusion in a polymeric film. Ten reversible electron transfer processes at a microscopic redox potential of 0.0 V build up the peak. Further redox steps with equal standard potential differences (50 mV) between each other form the plateau. [Reprinted with permission from J. Heinze, M. Storzbach, and J. Mortensen, Ber Bunsenges. Physikal. Chemie. 91,960(1987).]... 

Fig. 3 Current-potential curves for a reversible electron transfer (a) shape and important features of a linear sweep voltammogram (b) linear sweep voltammograms as a function of the scan rate v = 0.1, 0.2, 0.5, 1., 2., 5. V s with increasing ip (c) cyclic voltammograms and their...

Fig. 8 Cyclic voltammograms of a reversible electron transfer without (a) and with a homogeneous follow-up reaction (c) and their derivatives (b, d).

Fig. 1 shows typical cyclic voltammogr ams with and without large excess of CD. The shape of the voltammogr am is sensitive to the heterogeneous electron transfer rate[8] between the substrate and electrode, and also to the dissociation and formation rates. If the electron transfer is reversible, i.e., the concentrations of the electroactive species at the electrode surface are determined by the Nernst equation, and if the relative contribution of the latter factor is small, the cyclic voltammogram shows a typical shape[8] with reversible electron transfer and no chemical reaction. In this case, the electrochemical response is purely controlled by the diffusion process of the substrate, CD and the complex. The peak separation in this case is 57 mV at 25°C, which is not affected by addition of CD to the electrolyte solution. This situation is usually attained by the use of slow scan rates[9] in CV. Since complexation reaction can be assumed to remain at equilibrium everywhere in the diffusion layer in the present circumstance, the apparent diffusion coefficient, D from the voltammogram in the presence of CD is written as... 

Fig. 7.17 The cyclic voltammogram of an ideally adsorbed surface species, showing reversible electron transfer kinetics.

The simple use of a chemically irreversible chemical reaction step representing a chemical process is physically unrealistic, because the law of microscopic reversibility or detailed balance [94] is violated. More realistic is the use of an reaction scheme (Eq. 11.1.22, Fig. 11.1.21b). Even for the relatively simple reaction scheme, interesting additional consequences arise when the possibility of reversibility of the chemical step is considered. In Fig. II. 1.2lb, cyclic voltammograms for the case of a reversible electron transfer process coupled to a chemical process with kf = 10 s and fcb = 10 s" are shown. At a scan rate of 10 mV s a well-defined electrochemically and chemically reversible voltammetric wave is found with a shift in the reversible half-wave potential E1/2 from Ef being evident due to the presence of the fast equilibrium step. The shift is AEi/2 = RT/F ln(X) = -177 mV at 298 K in the example considered. At faster scan rates the voltammetric response departs from chemical reversibility since equilibrium can no longer be maintained. The reason for this is associated with the back reaction rate of ky, = 10 s or, correspondingly, the reaction layer, Reaction = = 32 pm. At Sufficiently fast scan rates, the product B is irre-... 

Cyclic and square wave voltammograms showed that an ECjrrev mechanism appears as the most probable to describe the surface electrochemical reaction, where E represent a reversible electron transfer reaction, and Cinev an irreversible homogeneous chemical reaction (Laviron, 1972). The dependence between /pn and Epn on the logarithm of acid bulk concentration would indicate that a deprotonation reaction should be the fast follow-up chemical reaction coupled to the initial electron transfer reaction (Laviron, 1972 Mirceski Lovric, 2000). 

Cyclic voltammetry (CV) can provide information about the thermodynamics of the redox process, kinetics of heterogeneous electron transfer reactions and coupled chemical reactions [32]. The reversible electron transfer steps inform us about the compound s ability to accept electrons however, experimental conditions, such as solvent and temperature also influence the voltammogram. The structure of the lowest unoccupied molecular orbital (LUMO) levels of the compound can be determined from the number of CV waves and reduction potentials ( 1/2)- Moreover, the CV can serve as a spectroscopy as demonstrated by Heinze [32], since the characteristic shapes of the waves and their unequivocal positions on the potential scale are effectively a fingerprint of the individual electrochemical properties of the redox system. 

In theory, D, c, or n can be calculated from the peak current (Ip) of a dc linear-sweep or cyclic voltammogram by employing the relationships described by the Randles-Sevcik equation for a reversible electron-transfer process of the kind Ox+ne" Red, when the effect of is negligible [6]. When woiking in a viscous RTIL, however, very few of the electrochemical systems of interest fulfill these criteria, which severely limits the direct application of dc voltammetry for this purpose. Assuming the Randles-Sevcik equation is not applicable, a best-fit approach with numerical simulation may be a viable alternative, although even this method has its limitations, as mechanistic complexities or other uncertainties can make the modeling process difficult [10]. 

Example 2-2 The following cyclic voltammogram was recorded for a reversible couple Calculate the number of electrons transferred and the formal potential for the couple. 

As mentioned above, the distribution of the various species in the two adjacent phases changes during a potential sweep which induces the transfer of an ion I across the interface when the potential approaches its standard transfer potential. This flux of charges across the interface leads to a measurable current which is recorded as a function of the applied potential. Such curves are called voltammograms and a typical example for the transfer of pilocarpine [229] is shown in Fig. 6, illustrating that cyclic voltammograms produced by reversible ion transfer reactions are similar to those obtained for electron transfer reactions at a metal-electrolyte solution interface. 

Cyclic voltammograms of DTT-TTF, 86a and 86b, exhibited two reversible one-electron transfer processes corresponding to the successive formation for the stable cation radical and dication <2003JMC1324>. 

Concerted Reduction of O and Cu+ or Acr+. Figure 5 illustrates the cyclic voltammograms for O2 in MeCN(0.1M TEAP) at glassy carbon, Cu, Ag, and Au electrodes (each polished immediately prior to exposure to O2). The drawn out reduction waves and the absence of significant anodic peaks upon scan reversal for the three metal electrodes indicate that 02 reacts with the surface prior to electron transfer. 

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