Nernstian Charge Transfer

In order to make the comparison between Ep and Ep/2 measurements summarized in Table 9, the two quantities were measured in separate experiments. A recent study by Eliason and Parker has shown that this is not necessary [57]. Analysis of theoretical LSV waves by second-order linear regression showed that data in the region of Ep are very nearly parabolic. The data in Fig. 9 are for the LSV wave for Nernstian charge transfer. The circles are theoretical data and the solid line is that described by a second-order polynomial equation. It was concluded that no detectable error will be invoked in the measurement of LSV Ep and Ip by the assumption that the data fit the equation for a parabola as long as the data is restricted to about 10 mV on either side of the maximum. This was verified by experimental measurements on both a Nernstian and a kinetic system. 

A significant feature of NPSV analysis is that linear relationships were observed when theoretical data for Nernstian charge transfer were taken as the X axis and theoretical data for various electrode mechanisms were taken as the Y axis. The slopes of the resulting straight lines are indications of the mechanisms of the electrode processes. Some of the slopes are included in Table 25. 

Reaction (77) was also studied using only the forward LSV scan by NPSV analysis [46]. The data are shown in Table 28. The value of fe° determined over a wide range of conditions was 0.29 0.02, which is somewhat lower than that resulting from the DCV study but close to that reported by BarAnski and Fawcett [83] from a.c. measurements, i.e. 0.30 cm s 1. The term mT — 1 is the NPSV slope, i.e. experimental data vs. that for Nernstian charge transfer, with /N ranging from 0.20 to 0.80. 

Figure 10. Kleitz s reaction pathway model for solid-state gas-diffusion electrodes. Traditionally, losses in reversible work at an electrochemical interface can be described as a series of contiguous drops in electrical state along a current pathway, for example. A—E—B. However, if charge transfer at point E is limited by the availability of a neutral electroactive intermediate (in this case ad (b) sorbed oxygen at the interface), a thermodynamic (Nernstian) step in electrical state [d/j) develops, related to the displacement in concentration of that intermediate from equilibrium. In this way it is possible for irreversibilities along a current-independent pathway (in this case formation and transport of electroactive oxygen) to manifest themselves as electrical resistance. This type of chemical valve , as Kleitz calls it, may also involve a significant reservoir of intermediates that appears as a capacitance in transient measurements such as impedance. Portions of this image are adapted from ref 46. (Adapted with permission from ref 46. Copyright 1993 Rise National Laboratory, Denmark.)...

Quasi-reversible charge transfer differs from the Nernstian case in that Co (0, f)/CR (0, t) is not dictated by the Nernst equation and depends both on the rates of the forward and reverse charge transfer reactions. The flux of O at the surface, where f = F/RT, is given by [15]... 

The rate laws and hence the mechanisms of chemical reactions coupled to charge transfer can be deduced from LSV measurements. The measurements are most applicable under conditions where the charge transfer can be considered to be Nernstian and the homogeneous reactions are sufficiently rapid that dEv/d log v is a linear function, i.e. the process falls into the KP or purely kinetic zone. In the 1960s and 1970s, extensive... 

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 ... 

We have observed that p-GaP seems to be an effective hydrogen electrode because of the adsorbed aqueous species on the surface as reflected by the Nernstian dependence of on pH in Figure 3. Thus, it appears in many cases the chemisorption of ions at the interface is a necessary step for rapid charge transfer to occur. This clearly has a strong bearing on recent observations of Fermi level pinning in various PEC devices where strong chemisorption does not occur.(14,15)... 

This is the case for CdS in acidic or basic aqueous solution where photocurrents are nonlinear at low-light intensities and the dependence of on pH is non-Nernstian. (20) Recent observations by Bard and Wrighton(14,15) indicate that Fermi level pinning and therefore supra-band edge charge transfer can occur in Si and GaAs in those systems (i.e., CH CN/t n-Bu NjClO ) with various redox couples where little electrolyte interaction is anticipated. 

In the preceding chapter, the charge transfer was assumed to be so fast that it was Nernstian. However, this condition cannot always be fulfilled, either because the charge transfer is intrinsically slow (i.e., k° is small), or because the follow-up reaction causes the voltammetric wave to shift, thereby lowering the apparent heterogeneous rate constant kapp by the potential factor (Eq. 59). Let us consider once more the DIM 1 (EC2) mechanism, but now open for the possibility that the heterogeneous step is not necessarily reversible. It is then convenient to define two dimensionless parameters related to k° and /cdimi... 

In Fig. 9.6, the four redox couples all have roughly equivalent nernstian solution potentials, but their X values span a range of 1 eV. The differences in X result in measured charge-transfer rates that differ by almost a factor of 1000 even though the... 

We have already seen that a system that is always at equilibrium is termed a reversible system thus it is logical that an electrochemical system in which the charge-transfer interface is always at equilibrium be called a reversible (or, alternatively, a nernstian) system. These terms simply refer to cases in which the interfacial redox kinetics are so fast that activation effects cannot be seen. Many such systems exist in electrochemistry, and we will consider this case frequently under different sets of experimental circumstances. We will also see that any given system may appear reversible, quasire-versible, or totally irreversible, depending on the demands we make on the charge-transfer kinetics. 

We now use an equivalent circuit representing an electrode/solution interface where the electrode surface is covered by an electroactive monolayer. The simplest circuit is shown in Fig. 2.18. We assume that the molecules in a Langmuir monolayer undergo an n-electron transfer reaction in response to ac and that the ER signal is exclusively due to this faradaic process [69]. The faradaic process of the surface-confined species at the formal potential is represented by a series connection of a constant capacitance associated with the redox reaction of the adsorbed species Q and a charge transfer resistance Ret. where Q is written for a Nernstian process as... 

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... 

Despite the dependence of ip on charge-transfer kinetics (eqns [5] and [6]), the sensitivity of LSV is almost independent of the reversibility degree (only a decrease of 25% is found on passing from a Nernstian to a totally irreversible process with a = 0.5). This fact makes LSV the most sensitive voltammetric technique for analytes involved in irreversible processes because pulsed voltammetric methods or alternating current voltammetry provide for these processes very low signals. 

However, if the kinetics of charge transfer at the electrode/ electrolyte interface are so rapid that the electrochemical reactants and products stay in equilibrium at the electrode surface even though a current passes, the Nernst equation still applies to the surface concentrations. Such a process is said to be electrochemically reversible or Nernstian - sometimes written with a lower case n, a mark of distinction also accorded to the adjectives coulombic, ohmic and faradaic. 

This study is also a good example of how EIS provides additional data to what can be obtained from chronoamperometry or CV. As the data can be fit to a circuit, parameters such as charge transfer resistance and diffusion lengths can be obtained from the fitting. In this case, charge transfer resistance was used to validate the Nernstian-based model used to fit the j-V relationship. Also, Dominguez-Benetton and Sevda [37]... 

In the presence of kinetic complications, the waves become drawn out. Figure 20.10 shows three simulated cyclic voltammograms for the reversible (Nernstian), quasi-reversible, and irreversible charge transfer cases. Obviously, kinetic information is contained in the CV wave shapes, and quantitative estimates of A, A, and Ao are possible if account is taken of the effects due to [61]. 

A representative thin-layer cyclic voltamogram for the Nernstian ideal case is illustrated in Fig. 20.11. Note that ip is now proportional to v (instead of i -), but the total charge under the i-E curve is independent of v. In fact, this provides a direct route to assay of the electroactive species (Fig. 20.11). Again, extension to irreversible charge transfer cases has been made, and reference is made to the original literature [53-55] for a discussion of these aspects. 

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