Electrochemical reaction impedance Capacitance

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. 

Figure 5.10 is EIS of marmatite electrode in O.lmol/L KNO3 solution with different pH modifiers at open circuit potential. This EIS is very complicated. Simple equivalent circuit can be treated as the series of electrochemical reaction resistance R with the capacitance impedance Q == (nFr )/(icR ) resulting fi-om adsorbing action, and then parallel with the capacitance Ca of double electric... 

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. 

Understanding the oxidation mechanism is important. Impedance spectroscopy was recently used to study methanol electrooxidation, and kinetic parameters can be deduced from impedance spectra. Figure 6.58 shows an equivalent circuit that was developed for methanol oxidation on a Pt electrode, but which is common for all electrochemical reactions. In this circuit, a constant phase element was used rather than a double-layer capacitance, since a CPE is more realistic than a simple capacitor in representing the capacitive behaviour. 

After analyzing the Nyquist and Bode plots (Figure 8a and b), the equivalent circuit model used to fit the impedance spectra is shown in Figure 8c, where the elements Re/ Rr/ and C are assumed to correspond to the electrolyte resistance, the electrochemical reaction resistance, and the total capacitance, respectively. While... 

The effect of DC bias on a contaminated sample at 100% RH is shown in Figure 5. At bias levels corresponding to threshold and super-threshold levels for electrochemical reactions, the impedance spectrum shows the capacitive loop that intersects the real axis at low frequency (.1 Hz). Zero-DC-bias data, which are not shown, form a similar arc that is large compared to the scale of this plot. This behavior is modelled by a parallel RC circuit, whose resistance decreases from 1 x 10 to 1.6 x 10 and whose capacitance remains constant at approximately 30000 pF, as DC bias is raised from 0 to 3.0 V. The resistances agree with those measured in DC leakage current experiments. The capacitances are 100 times larger than those measured on the clean sample at 100 % RH. 

AC Impedance of Contaminated Specimens. The ACIS of the contaminated sample under DC bias at 100% RH is consistent with a corroding system (15) in which a fixed number of aqueous pathways have formed, resulting in a constant area of metallization exposed to the electrolyte. In this case, the parallel capacitance corresponds to an electrical double layer of ions on the metallization. The capacitance of the contaminated sample is > 100 times larger than that of the clean sample at 100% RH due to the relatively larger concentrations of ions and water at the IC surface, which overwhelms the oxide capacitance described earlier. The reduction in the parallel resistance with increasing bias arises from the voltage dependent charge transfer process (i.e. electrochemical reaction). 

In Chap. 2 we saw the responses of electrical circuits containing the elements R, C, and L. Because these are linear elements, their impedance is independent of the ac amplitude used. However, in electrochemical systems, we do not have such elements we have solution-electrode interfaces, redox species, adsorption, etc. In this and the following chapters, we will learn how to express the electrochemical interfaces and reactions in terms of equations that, in particular cases, can be represented by the electrical equivalent circuits. Of comse, such circuits are only the electrical representations of physicochemical phenomena, and electrical elements such as resistance, capacitance, or inductance do not exist physically in cells. However, such a presentation is useful and helps in our understanding of the physicochemical phenomena taking place in electrochemical cells. Before presenting the case of electrochemical reactions, the case of an ideally polarizable electrode will be presented. 

Formulating the problem in a discretized way allows us to extend it effortlessly to more complicated cases. Let s assume, for example, that in addition to double-layer capacitance we will have an electrochemical reaction on the pore surface, as would be the case in a battery or fuel-cell electrode. The equivalent circuit for the pore surface now will involve a capacitor in parallel with a charge transfer resistance, Ra, and the surface impedance Z oss will be given as follows ... 

Mogensen et al. [24] investigated Ni/YSZ cermet electrodes at 1273 K and found the electrode impedance to be formed by a low-fiequency contribution, with resistance decreased by increasing both the partial pressure of hydrogen and water, and a high-frequency contribution with resistance and capacitance almost independent of the partial pressures of hydrogen and water. The proposed model does not respect the stoichiometry of the electrochemical reaction ... 

The equivalent circuit corresponding to an uncomplicated electrochemical reaction (i.e., a one-step CT process) is shown in Figure 15.1. An important advantage of ac voltammetry is that it allows relatively easy evaluation of the solution resistance ( J and double layer capacitance (C4). These elements can be separated from the and components, which together make faradaic impedance. Without simplifying assumptions, the analysis of faradaic impedance even for a simple ET reaction is rather complicated (9). The commonly used assumptions are that the dc and ac components of the total current can be uncoupled, and the dc response is Nemstian because of the long dc time scale. The latter assumption is reasonable because ac voltammetry is typically used to measure fast electrode kinetics. The ac response of the same electrochemical process may be quasi-reversible on the much shorter ac time scale. Quasi-reversible ac voltammograms are bell-shaped. 

Figure 11.13 illustrates a basic equivalent circuit to represent a general electrochemical reaction. Rs represents the electric resistance, which consists of the ionic, electronic, and contact resistances. Since the electronic resistance is typically much lower than the ionic resistances for a typical fuel cell MEA, the contribution of the electronic resistance to Rs is often negligible. Cj is the double-layer capacitance associated with the electrode-electrolyte interfaees. Since a fuel cell electrode is three-dimensional, the interfaces include not only Arose between Are surfaces of the electrodes and the membrane but also those between the catalysts and the ionomer within the electrodes. Ret is the resistanee associated with the charge transfer process and is called charge transfer resistanee. Z is called the Warburg impedance it deseribes the resistance arising from the mass transport processes. 

Figure 11.13. Illustration of a basic equivalent circuit for an electrochemical reaction. -Ohmic resistance R., - charge transfer resistance Cd - double-layer capacitance Z -Warburg impedance.

The impedance at the electrochemical reaction interface where reaction occurs can be represented as a parallel combination of charge transfer resistance and a double-layer capacitance. The Nyquist plot for the parallel RC circuit is a characteristic semicircle where the high-frequency intercept of the impedance semicircle is zero and the low-frequency intercept of the semicircle is resistance Rqj. The diameter of the semicircle Rct provides information on the reaction kinetics of the electrochemical reaction interface. A large-diameter semicircle (large Rct) indicates sluggish reaction kinetics while a small-diameter semicircle indicates facile reaction kinetics. 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

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