Faradaic component

Nonfaradaic Currents Faradaic currents result from a redox reaction at the electrode surface. Other currents may also exist in an electrochemical cell that are unrelated to any redox reaction. These currents are called nonfaradaic currents and must be accounted for if the faradaic component of the measured current is to be determined. 

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. 

When an electrode reaction takes place, the applied current is divided between the nonfaradaic components and a faradaic component. Because of the latter, there is a gradual decrease in surface concentration of the reactant [according to Eq. (11.6)]. When the time, required for diffusion to change from transient to steady is large compared to the transition time [Eq. (11.9)], the reactant s surface concentration will fall to zero within the time (see Fig. 11.3). 

The conducting polymers show a significant non-faradaic component of the electrochemical mechanism. The essential differences of faradaic and non-faradaic systems in equilibrium behavior, trends of galvanostatic charge - discharge curves and cyclic voltammograms have been shown, and criteria for the identification of these mechanisms are proposed [8],... 

The conducting polymers show a significant non-faradaic component of the electrochemical mechanism inside the main range of potentials AEn. Nevertheless, the possibilities of redox processes at the limits and beyond this range of potentials should be taken into account. At the same time, these processes can lead to rapid formation of thin insulating... 

As the field of electrochemical kinetics may be relatively unfamiliar to some readers, it is important to realize that the rate of an electrochemical process is the current. In transient techniques such as cyclic and pulse voltammetry, the current typically consists of a nonfaradaic component derived from capacitive charging of the ionic medium near the electrode and a faradaic component that corresponds to electron transfer between the electrode and the reactant. In a steady-state technique such as rotating-disk voltammetry the current is purely faradaic. The faradaic current is often limited by the rate of diffusion of the reactant to the electrode, but it is also possible that electron transfer between the electrode and the molecules at the surface is the slow step. In this latter case one can define the rate constant as ... 

The current-potential curves that we have considered so far dealt exclusively with the Faradaic component of the current and concerned a reaction that takes place at one electrode, the potential of which is defined against a fixed reference. It was also assumed that the reactants were transported between the electrode and the bulk of the solution exclusively by diffusion. How the experiments should be carried out to approach this ideal situation is the object of this section. 

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... 

With real cells, the resistance Ru is measured by augmenting positive feedback until sustained oscillations are observed. Then R = Re and the value of Ru is obtained by a simple reading of Re. The amount of positive feedback is then decreased back to a new value of Re so as to obtain damped oscillations compatible with the measure of the Faradaic component of the current, as in Figure 1.8 for ARu =412. The remaining resistance is thus obtained as ARu = R — Re. In a number of cases, the residual ohmic drop is negligible. If not, it may be taken into account in a simulation of the voltammograms, as depicted below. 

The preceding derivation has assumed implicitly that the double-layer charging current is negligible in front of the Faradaic current or that it can be eliminated by a simple subtraction procedure. In cases where these conditions are not fulfilled, the following treatment will take care of the problem under the assumption that the double-layer capacitance is not affected appreciably by the Faradaic reaction but may nevertheless vary in the potential range explored. The first step of the treatment then consists of extracting the Faradaic component from the total current according to (see Section 1.3)... 

Double-layer charging current and ohmic drop are likely to interfere at high scan rates. The procedures for extracting the Faradaic component of the current and correcting the potential axis from the effect of ohmic drop described earlier (see Sections 1.3.2 and 1.4.3) should then be applied. The same is true for the double-layer effect on the electron transfer kinetics (Section 1.4.2). 

The existence of a non-faradaic component to the overall current explains why the amount of material formed by electrochemical formation will generally be less than the theoretical amount, since the theoretical amount relates only to ffaradaic- Clearly, the coulometric efficiency should be maximized, i.e. /non-faradaic should be minimized by careful ehoice of experimental design, reagents and apparatus. Note that coulometric efficiency is also called faradaic efficiency. 

A fast rate of mass transport is useful to the electroanalyst because the faradaic component of the charge is made greater, while the non-faradaic current is not affected. In addition, note that /non-faradaic will be small anyway since it is in proportion to electrode area. 

In the previous chapter, it was emphasized that the non-faradaic component of current should be minimized. Is non-faradaic current a problem in polarography ... 

Figure 6.15 Plot of peak current (/p) in a voltammogram (either linear-sweep or cyclic) against analyte concentration. The linear portion obeys the Randles-SevCik equation, while the horizontal plateau at low Ca aiyie values is usually caused by non-faradaic components of Ip, such as double-layer charging.

The difference between the faradaic components of the two current samples is usually negligible so, in practice, the current difference A/puise is only significant... 

Figure 23.4 CV scans of 0.7 mAf Cp2Cr2(CO)6 in CH2C12/0.1 M Bu4NPF6 at T = 243 K, v = 100 V/s (A) raw data (B) faradaic component after background subtraction. Adapted from study in Ref. 18.

Fig. 5.11 Current-potential response of CV and SCV (for A = 5mV) for a Nemstian charge transfer process taking place at a planar electrode for different values of the scan rate (shown in the figure). Dashed-dotted lines Pure faradaic component (SCV and CV) calculated by using the numerical procedure proposed in [21, 22]. Dashed lines Charging current calculated from Eqs. (5.77) (SCV) and (5.76) (CV). Solid lines total current calculated as indicated in Eq. (5.75). /JU = 0.1K 2, C,u 20pFcm 2, Area = 0.05 cm2, cj, = ImM, = 0, Do = Dr = 10 5cm2s 1...

For the evaluation of the non-faradaic component of the response in a more realistic way, different proposals have been made. A useful idea is that corresponding to the interfacial potential distribution proposed in [59] which assumes that the redox center of the molecules can be considered as being distributed homogeneously in a plane, referred to as the plane of electron transfer (PET), located at a finite distance d from the electrode surface. The diffuse capacitance of the solution is modeled by the Gouy-Chapman theory and the dielectric permittivity of the adsorbed layer is considered as constant. Under these conditions, the CV current corresponding to reversible electron transfer reactions can be written as... 

This technique is of special interest in the case of charge transfer processes at surface-bound molecules since it allows a simple and more effective correction of the non-faradaic components of the response than Cyclic Voltammetry. Moreover, this technique presents an intense peak-shaped signal for fast charge transfer, whereas other multipulse techniques give rise to nonmeasurable currents under these conditions and it is necessary to use short potential pulses to transform the response to quasi-reversible, which is much more difficult to analyze [4, 6, 10]. 

As stated in Sect. 6.4.1, in the theoretical treatment of the electrochemical responses of surface-bound molecules, it has been assumed that the measured experimental currents and converted charges when a potential Ep is applied can be considered as the sum of a pure faradaic contribution, given by Eqs. (6.130) and (6.131), and a non-faradaic one, Qp nf and fpnt (given by Eqs. (6.150) and (6.157)). The correction of this non-faradaic component of the response can be done simply when subtractive electrochemical techniques are used). We assume the parallel capacitors model introduced by Damaskin [78], for which CAnf can be written as... 

The analysis of the influence of the non-faradaic component corresponding to the converted charge-potential (Q-E) and current-potential (I-E) curves, is very different. A short discussion of this influence in some of the subtractive techniques analyzed follows. 

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