Faradic reaction rates

Analysis of experimental data that yield a full semicircular arc in the complex plane, such as that in Figure 3. b, can provide estimates of the parameters R and Ci and hence lead to quantitative estimates of conductivity, faradic reaction rates, relaxation times, and interfacial capacitance (see detailed discussion in Section 2.2.3.3). In practice, however, experimental data are only rarely found to yield a full semicircle with its center on the real axis of the complex plane. There are three common perturbations which may still lead to at least part of a semicircular arc in the complex plane ... 

W.H. Miller, Spiers Memorial Lecture. Quantum and semiclassical theory of reaction rates. Farad. Discuss. 110 (1998) 1-21. 

Cell or stack aging is indicated by a loss in overall performance due to diminishing capacitance, slower charging and discharging rates, and increased series resistance. In addition, these signs can also be associated with macroscopic phenomena, for example, localized detachment of electrode materials from the metallic collector through electrode swelling, gas evolution, and loss of elements involved in faradic reactions. 

In theory, the transient state is assumed to take place at times short enough to keep the concentration of (FeOH)j, frozen at its initial value. Therefore the initial transition is due only to the change of the reaction rate of step (26) or (27) under the effect of potential at constant (FeOH) concentration. The same discrimination between instantaneous and delayed contributions is at the origin of the frequency dependence of the faradic impedance. Table 1 shows the theoretical and experimental values of the steady-state and transient kinetic parameters for both mechanisms, according to Ref. 12. 

When the rate determining step of the electrode reaction is the charge transfer process (kinetic control), the faradic impedance ZF in Figure 1.18 can be described as RCJ, the charge transfer resistance [7,8], The impedance plot in the Nyquist plane describes a semicircle, as shown in Figure 1.19. 

Faradic impedance (//) is directly related to the rates of charge transfer reactions at and near the electrode/electrode interface. As shown in Figure 3.1, the Faradaic impedance acts in parallel with the double-layer capacitance Cd, and this combination is in series with the electrolyte resistance Rei The parameters Rei and Cd in the equivalent circuit are similar to the idea of electrical elements. However, X/ is different from those normal electrical elements because Faradaic impedance is not purely resistive. It contains a capacitive contribution, and changes with frequency. Faradaic impedance includes both the finite rate of electron transfer and the transport rate of the electroactive reagent to the electrode surface. It is helpful to subdivide Zj into Rs and Cs, and then seek their frequency dependencies in order to obtain useful information on the electrochemical reaction. 

Variations in cathodic peak current with the square of the sweep rate [/p,.. = /(v -)] for. selected PACE/electrolyte systems are shown in Figs. 13a and 13b [194]. In all ca.ses the relation is linear and the correlation coefficient tends to unity, especially in the lower ranges of the potential sweep rates. In agreement with numerous researchers [7,9,14,16,24,26,132], we also suggest that the cathodic peak is due to the reduction of quinonelike groups, whereas the anodic wave is due to the oxidation of hydroquinonelike groups in different environments on the active carbon surface of the electrode. These reactions are faradic... 

The faradic part of the current is a direct measure of the reaction extent rate in the case of a single reaction. Namely, this corresponds to how the system has evolved compared to the initial system, meaning that it characterises the amount of substance that has been transformed. The amount of electric charge is a measure of the reaction extent rate. This is what Faraday s law represents in quantitative terms. 

There are various metrics utilized to quantify the efficiency of different aspects of an electrochemical reaction. One type of efficiency for a purely electrochemical reaction is based on species consumption. For a galvanic process, there will be a minimum amount of reactant required for a given reaction, as calculated by Faraday s law, Eq. [2.33]. In practice, we are not constrained to provide exactly the minimum amount of reactant. For a given current, there is a calculated minimum amount of reactant, but there is no maximum. The actual flow rate of reactants is a function of the pumps and blowers that are used for reactant dehvery. Obviously, the more flow delivered, the higher the parasitic power required, so we generally seek to dehver something close to the minimum requirement. The Faradic efficiency is a measure of the percent utilization of reactant in a galvanic process ... 

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