Nernstian electron transfer

Considering the Nernstian electron-transfer rate for the reversible redox reactions of the free and bound forms of compounds and the corresponding equilibrium constants for binding of each oxidation state to DNA yields, for a l-e redox process. 

The explicit mathematical treatment for such stationary-state situations at certain ion-selective membranes was performed by Iljuschenko and Mirkin 106). As the publication is in Russian and in a not widely distributed journal, their work will be cited in the appendix. The authors obtain an equation (s. (34) on page 28) similar to the one developed by Eisenman et al. 6) for glass membranes using the three-segment potential approach. However, the mobilities used in the stationary-state treatment are those which describe the ion migration in an electric field through a diffusion layer at the phase boundary. A diffusion process through the entire membrane with constant ion mobilities does not have to be assumed. The non-Nernstian behavior of extremely thin layers (i.e., ISFET) can therefore also be described, as well as the role of an electron transfer at solid-state membranes. 

A question arises as to what happens if the Nernstian approximation breaks down. Under these circumstances, we must use the proper equations for the kinetics of electron transfer discussed in chapter 1. The simplest case is that of a completely irreversible system, where only oxidation (or reduction) is possible and a single electron is transferred, i.e. consider the process ... 

CYCLIC VOLTAMMETRY OF FAST ELECTRON TRANSFERS. NERNSTIAN WAVES... 

When Afh -a oo, a Nernstian response is obtained. The half-wave potential is equal to the standard potential. Conversely, when Afh —> 0, the electrode electron transfer is irreversible. In the case of a Butler-Volmer kinetic law, the half-wave potential is expressed as... 

In addition to this, and in contrast with the homogeneous case discussed in Section 5.2.2, the diffusion of P and Q is therefore not perturbed by any homogeneous reaction. If, furthermore, the P/Q electron transfer at the electrode is fast and thus obeys Nernst s law, the diffusive contribution to the current in equations (5.11) and (5.12) is simply equal to the reversible diffusion-controlled Nernstian response, idif, discussed in Section 1.2. The mutual independence of the diffusive and catalytic contributions to the current, expressed as... 

If the first e step, i.e., heterogeneous electron transfer, is slow (non-Nernstian) or if the cyclization reaction is faster than the electron transfer itself, the electron transfer becomes rate-determining and nothing can be done about the mechanism of cyclization. 

CH3CN V = 0.2 V s ) indicated that the electrode process was not a Nernstian two-electron transfer but involved two successive one-electron steps, with the second thermodynamically more favorable than the first one [32]. Therefore, the reversible, overall two-electron process in Sch. 11 is better represented by two successive, reversible, one-electron steps involving a thermodynamically unstable and undetected cation intermediate (see Sch. 13 EE process, or ECE process, where the chemical step C is a fast, reversible deformation of the M2S2 core). In agreement with this, it should be noted that the oxidation of ds-[Mo2(cp )2(/x-SMe)2(CO)4] ds-13 also... 

The voltammogram shown in Figure 13.2 is for the reversible or Nern-stian case. As discussed in Chapters 2 and 3, this means that at the scan rate employed, the rate of electron transfer is sufficiently high that the surface concentrations of -Fc and -Fc+ are always at equilibrium with the applied electrode potential. For a surface-bound redox couple, the Nernstian case is characterized by a difference in potentials between the anodic and cathodic peaks (AEpk) of zero volts that is, the cathodic wave sits right on top of the anodic wave (Fig. 13.2). It is worth mentioning that the formal potential (see Chaps. 2 and 3) for the Nernstian case is simply the potential of the anodic and cathodic peak. 

When M = Rh, AE° -0.20 V, and two separate waves are observed (Fig. 23.10, left). When M = Ir, AE° +0.30 V, and a single wave is seen that has properties approaching those of a two-electron Nernstian process. These systems deviate slightly from ideality owing to quasireversibility of the second electron transfer, as evidenced by the somewhat larger peak separation in the second wave of the rhodium complex [15]. 

Thus, the peak separation can be used to determine the number of electrons transferred, and as a criterion for a Nernstian behavior. Accordingly, a fast one-electron process exhibits a AEp of about 59 mV. Both the cathodic and... 

Recall that a Nernstian behavior of diffusing species yields a vm dependence. In practice, the ideal behavior is approached for relatively slow scan rates, and for an adsorbed layer that shows no intermolecular interactions and fast electron transfers. 

In fact, at equilibrium, not only are electrons transferred across the interface, but ions also cross the <3 1% interface. Taking into account this additional transfer yields non-Nernstian behavior. In the simple case of polarons being the predominant species, one obtains [8]. 

As noted in Section 2, when the electron-transfer kinetics are slow relative to mass transport (rate determining), the process is no longer in equilibrium and does not therefore obey the Nernst equation. As a result of the departure from equilibrium, the kinetics of electron transfer at the electrode surface have to be considered when discussing the voltammetry of non-reversible systems. This is achieved by replacement of the Nernstian thermodynamic condition by a kinetic boundary condition (36). 

Obviously, therefore there must be an intermediate case in which the kinetics of both the forward and reverse electron-transfer processes have to be taken account of. Such systems are described as being quasi-reversible and as would be expected, the scan rate can have a considerable effect on the nature of the cyclic voltammetry. At sufficiently slow scan rates, quasi-reversible processes appear to be fully reversible. However, as the scan rate is increased, the kinetics of the electron transfer are not fast enough to maintain (Nernstian) equilibrium. In the scan-rate region when the process is quasi-reversible, the following observations are made. 

The electrochemical redox reaction of a substrate resulting from the heterogeneous electron transfer from the electrode to this substrate (cathodic reduction) or the opposite (anodic oxidation) is said to be electrochemically reversible if it occurs at the Nernstian redox potential without surtension (overpotential). This is the case if the heterogeneous electron transfer is fast, i.e. there must not be a significant structural change in the substrate upon electron transfer. Any structural change slows down the electron transfer. When the rate of heterogeneous electron transfer is within the time scale of the electrochemical experiment, the electrochemical process is fast (reversible). In the opposite case, it appears to be slow (electrochemically irreversible). Structural transformations are accompanied by a slow electron transfer (slow E), except if this transformation occms after electron transfer (EC mechanism). 

---