Faradaic parameters

Based on these transform results, it is possible to extract the Faradaic parameters from resistance (RB) and capacitance (CB) measured using EIS. The solutions are depicted in Figure 3.5. 

Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or nonfaradaic) at a given applied potential.268,269 EIS has been used to study polycrystalline Au, Cd, Ag, Bi, Sb, and other electrodes.152249 270-273... 

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

A certain potential is applied to the electrode with the potentiostatic equipment, and the variation of current is recorded as a function of time. At the very beginning a large current flows, which is due largely to charging of the electrode s EDL as required by the potential change. The maximum current and the time of EDL charging depend not only on the electrode system and size but also on the parameters of the potentiostat used. When this process has ended, mainly the faradaic component of current remains, which in particular will cause the changes in surface concentrations described in Section 11.2. 

A quantitative correlation between the charges under the current and mass intensity signals can be carried out as suggested by Heitbaum and Wolter [11]. The magnitude of the mass intensity response depends not only on the electrochemical properties of the system under study but also on the permeability of the electrode to the volatile products in addition to mass spectrometer parameters. A calibration of the actual experimental setup is therefore necessary. The proportionality between mass intensity (MI), and faradaic current (/) can be formulated as follows ... 

The present chapter will cover detailed studies of kinetic parameters of several reversible, quasi-reversible, and irreversible reactions accompanied by either single-electron charge transfer or multiple-electrons charge transfer. To evaluate the kinetic parameters for each step of electron charge transfer in any multistep reaction, the suitably developed and modified theory of faradaic rectification will be discussed. The results reported relate to the reactions at redox couple/metal, metal ion/metal, and metal ion/mercury interfaces in the audio and higher frequency ranges. The zero-point method has also been applied to some multiple-electron charge transfer reactions and, wheresoever possible, these results have been incorporated. Other related methods and applications will also be treated. 

From the derivations in Appendix B, it is evident that the present faradaic rectification formulations for multiple-electron charge transfer not only enable the determination of kinetic parameters for each step of three-electron charge transfer processes but may also be extended to charge transfer processes involving a higher number of electrons. However, the calculations become highly involved and complicated. 

Recently, the kinetic parameters for each step of this reaction in different supporting electrolytes have been obtained39,42 by applying the faradaic rectification theory as extended to multiple-electron charge transfer reactions. The kinetic parameters are listed in Table 1. 

By applying the recently developed theory of faradaic rectification as applied to multiple-electron charge transfer reactions under the condition that k° and C°R = 1. Kinetic parameters are obtained for each step of the electron charge transfer. The value of /c° reported is of the order of 10 6 to 10-9 cm/s whereas that of fc is of the order of 10 3 cm/s in different supporting electrolytes.51... 

Faradaic rectification polarographic studies have been carried out for a mixture containing several metal ions together and also for individual inorganic depolarizers so as to explore the applicability and limitations of the method and to determine kinetic parameters for some of them. For comparison, some of the dc and ac polarograms have also been recorded simultaneously. In the following, the details of the experimental technique used will be described and the potentiality of the technique in qualitative and quantitative analysis will be examined. The applicability of the method in the... 

The reduction of zinc ions at d.m.e. has widely been studied and the reaction has been reported to be quasi-reversible.94 Van Der Pol and co-workers54 studied this reaction by the faradaic rectification polarographic technique using high-frequency modulated signals. The kinetic parameters have been evaluated by the... 

Earlier studies generally involved the evaluation of kinetic parameters of reactions which are accompanied by single-electron charge transfer.116 Some reactions involving two-electron charge transfer were also studied, assuming either that both electrons are transferred in a single step or that the slower step in the two-step reaction is in overall control of the rate process. As described in this chapter for the first time, the faradaic rectification theory for... 

Mehdizadeh et al. exploited the separability of current distribution on different scales to model the macroscopic current distribution on patterns made up of lines or points distributed over a large workpeice [136], They solved the secondary distribution of the superficial current density sup using a boundary condition which captures the density of small features but not their geometry. The boundary condition is based on a smoothly varying parameter representing the Faradaically active fraction of surface area. 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

The electrode was then swept further negative to -1.1 V, a potential more negative than the onset of the faradaic current in the voltammogram, yielding after about two hours of measurement, a strong, clearly defined doublet (Curve b, Fig. 4), with parameters in excellent agreement with those of Fe(OH)2 ( see Tables II and III). The potential was then stepped to -0.3 V. In contrast to the... 

The Faradaic and capacitive components of the current both increase with the scan rate. The latter increases faster (proportionally to v) than the former (proportionally to y/v), making the extraction of the Faradaic component from the total current less and less precise as the scan rate increases, particularly if the concentration of the molecules under investigation is small. The variations of the capacitive and Faradaic responses are illustrated in Figure 1.7 with typical values of the various parameters. The analysis above assumed implicitly that the double-layer capacitance is independent of the electrode potential. In fact, this is not strictly true. It may, however, be regarded as a good approximation in most cases, especially when care is taken to limit the overall potential variation to values on the order of half-a-volt.10 13... 

Amounts of are being monitored at a wall-jet electrode. When a sample of concentration 3.23 pg cm" is squirted over the electrode, the limiting current is 152 pA. Keeping the flow rate and all other parameters constant, what is the concentration of a sample of Co when the limiting current is 214 pA Assume complete faradaic efficiency in both cases. 

Obviously, the faradaic impedance equals the sum of the two contributions f ct, the charge transfer resistance, and Zw = aco-1/2 (1 — i), the Warburg impedance. Again, the meaning of the parameters Rct and a is still implicit at this stage of the treatment and explicit expressions have to be deduced from an explicit rate equation, e.g. the expressions given in eqns. (51). 

It is quite easy to derive the faradaic admittance from eqns. (63) using eqn. (57). For the sake of simplicity, we introduce the parameter p defined by... 

---