Reversible Nernstian Processes

In order to look at the multiple shapes that the cyclic voltammograms can assume as a function of the nature of the different electrode processes, let us begin by examining the case of a reversible reduction process, not complicated by homogeneous reactions  

As previously stated, an electrode process is defined as electrochemi-cally reversible when the rate of the electron transfer is higher than the rate of the mass transport. 

When the scan of the potential reaches a value appropriate for the reduction of Ox, the concentration of Ox at the electrode surface begins to decrease with respect to that present in the bulk of the solution, Cqx. This implies that a concentration gradient (8C0x(x,t)/8x) becomes established (recalling that 8CQx(x,r) = C0x(x,t)-C 0x), and thus, from 

CRedOM), still present close to the electrode surface. Obviously, as a consequence of the variation of the potential towards more positive values, this new species will be reoxidized. 

The above qualitative discussion is quantitatively described by solving Fick s second law for both Ox and Red. 

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Thus, for a reversible (Nernstian) process, ip is proportional to Ep is independent of 0,... 

Resulting cyclic voltammogram for a Nernstian reversible redox process. 

We found that for the hypoxic selective atsm and ptsm complexes the reduction process is reversible (Nernstian) and addition of small amounts of acid has little effect. By contrast [Cu(gts)] shows a very much less reversible reduction process which becomes completely irreversible on the addition of even traces of acid. This suggests strongly that the stability of the Cu state is crucial in determining the selectivity and that irreversibility is caused by protic attack on the anion. But the question of why backbone methylation should increase the stability of the Cu state has remained unanswered. 

The procedure employed assumes that the heterogeneous charge transfer process is quasi-reversible on the a.c. time scale and reversible (nernstian) on the d.c. time scale (quasi-reversible systems on the d.c. time scale normally are not selected for assay work). Under these conditions, the faradaic rate law may be written as... 

Interface (Junction) in an electrochemical cell, it represents the location where two distinct phases come in contact with each other solid-liquid (electrode-solution), two liquids of different concentrations and/or compositions (reference electrode-solution), etc. Nernstian a reversible redox process that follows equilibria equations. 

Thus, in the Nernstian regime, a plot of / vs. / - will be linear, and useful information about the parameters n and Dr can be obtained from its slope for the electrode process of interest. (Double potential step experiments similarly afford information about the reverse process, reduction.) Likewise a plot of it vs, (Fig. 20.7c) yields kinetics information for a non-Nernstian process. The horizontal region at large values of it - corresponds to the Cottrell regime, whereas the short-time data are... 

Spectroelectrochemical studies refer to the measurement of variables which are related individually to the concentrations of the oxidized and reduced species and then relating these measured variables to electrochemical relationships like the Nernst equation. Because of the large number of bands in vibrational spectra, it should be relatively easy to find SERS bands which are proportional to oxidized and reduced species surface concentrations. If the surface concentrations are related to bulk concentrations by a Langmuir isotherm, it can be shown for a reversible (Nernstian) redox process involving adsorbed species that... 

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 voltammetric data and other relevant kinetic and thermodynamic information are summarized in Table 2. While for X = H the initial ET controls the electrode rate, as indicated by the rather large p shift and peak width, the electrode process is, at low scan rates, under mixed ET-bond cleavage kinetic control (see Section 2) for X = Ph, and CN. Although the voltammetric reduction of these ethers is irreversible, in the case of the COMe derivative, some reversibility starts to show up at 500 Vs in fact, this reduction features a classical case of Nernstian ET followed by a first-order reaction. The reduction of the nitro derivative is reversible even at very low scan rate although, on a much longer timescale, this radical anion also decays. 

These expressions can be simplified to the so-called d.c.-reversible , or Nernstian , expressions if kf is sufficiently large to omit the terms in aQjkt. In that case, the charge transfer process is no longer co-determining the reaction rate and it is easily seen that, in fact, the rate equation is replaced by Nernst s law holding for c 0 and Cr ... 

The foregoing has been concerned with the application of SERS to gain information on surface electronic coupling effects for simple adsorbed redox couples that are reversible in the electrochemical as well as chemical sense, that is, exhibit Nernstian potential-dependent responses on the electrochemical time scale. As noted in the Introduction, a major hoped-for application of SERS to electrochemical processes is to gain surface molecular information regarding the kinetics and mechanisms of multiple-step electrode reactions, including the identification of reactive surface intermediates. 

Chronopotentiometry — is a controlled-current technique (- dynamic technique) in which the - potential variation with time is measured following a current step (also cyclic, or current reversals, or linearly increasing currents are used). For a - nernstian electrode process,... 

Reversibility — This concept is used in several ways. We may speak of chemical reversibility when the same reaction (e.g., -> cell reaction) can take place in both directions. Thermodynamic reversibility means that an infinitesimal reversal of a driving force causes the process to reverse its direction. The reaction proceeds through a series of equilibrium states, however, such a path would require an infinite length of time. The electrochemical reversibility is a practical concept. In short, it means that the -> Nernst equation can be applied also when the actual electrode potential (E) is higher (anodic reaction) or lower (cathodic reaction) than the - equilibrium potential (Ee), E > Ee. Therefore, such a process is called a reversible or nernstian reaction (reversible or nerns-tian system, behavior). It is the case when the - activation energy is small, consequently the -> standard rate constants (ks) and the -> exchange current density (jo) are high. 

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). 

It can be seen that cyclic voltammograms at low scan rate have peak-to-peak separations close to the value theoretically expected for a reversible process of A p = 2.218 X 7 r/ = 57 mV at 298 K [47] and the peak current increases with the square root of the scan rate. Under these conditions, the process is diffusion controlled and termed electrochemically reversible or Nernstian within the timescale applicable to the experiment under consideration. Hence, as with all reversible systems operating under thermodynamic rather than kinetic control, no information concerning the rate of electron transfer at the electrode surface or the mechanism of the process can be obtained from data obtained at slow scan rate. The increase of A p at faster scan rate may be indicative of the introduction of kinetic control on the shorter timescale now being applied (hence the rate constant could be calculated) or it may arise because of a small amount of uncompensated resistance. Considerable care is required to distinguish between these two possible origins of enhancement of A p. For example, repetition of the experiments in Table II.l.l at... 

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. 

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