Electrochemical reaction impedance Resistance

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 electrochemical impedance gradually decreases but does not vary very much with the DDTC concentration increasing. It indicates that DDTC takes part in the electrochemical reaction and the reaction rate increases as the DDTC concentration enhances. As contrasted with it, the passivation of the collector-salts of reaction production on the mineral electrode further inhibits the anodic reaction so that the electrochemical resistance is wholly much bigger than that of self-corrosive reaction in the absence of DDTC. 

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... 

Data from electrochemical impedance diagrams yield a simplified quantitative analysis for an appropriate interpretation of the linear sweep voltammetry (LSV) experiments. In fact, the Si electrode potential measured with respect to the reference electrode represents the value within the bulk of the material. The direct current flow for the electrochemical reaction has to overcome the resistance of the space charge layer, which can reach extremely high values when a depletion layer is formed. For p-type Si in the potential range for the HER onset, this excess surface resistance is over 10 f2 cm. Thus, even with a bias of —1 V, the DC... 

The same consideration applies to the impedance measurement according to Fig. 8.1b. It is a normal electrochemical interface to which the Warburg element (Zw) has been added. This element corresponds to resistance due to translational motion (i.e., diffusion) of mobile oxidized and reduced species in the depletion layer due to the periodically changing excitation signal. This refinement of the charge-transfer resistance (see (5.23), Chapter 5) is linked to the electrochemical reaction which adds a characteristic line at 45° to the Nyquist plot at low frequencies (Fig. 8.2)... 

Impedance spectroscopy is an effective technique for probing the features of chemically-modified electrodes and for understanding electrochemical reaction rates (87,88). Impedance is the totally complex resistance encountered... 

In a simple case, the electrochemical reaction at the electrode-electrolyte interface of one of the electrodes of the battery can be represented by the so-called Randles circuit (Figure 8.19), which is composed of [129] a double layer capacitor formed by the charge separation at the electrodeelectrolyte interface, in parallel to a polarization resistor and the Warburg impedance connected in series with a resistor, which represents the resistance of the electrolyte. 

A typical impedance spectrum obtained on LSM microelectrodes is shown in Fig. 42a. The arc represents the impedance due to the electrochemical reaction at the LSM microelectrode. A small ohmic drop caused by the YSZ electrolyte (and partly by the sheet resistance due to the finite electronic conductivity of the LSM electrode) is more than three orders of magnitude smaller than the electrode resistance and not visible in the figure. The impedance spectra for nominally identical microelectrodes turned out to be reproducible with a standard deviation <15%. The data of Fig. 42b display the relation between the electrode resistance Rei and the microelectrode diameter dme several series of experiments with different electrode thicknesses consistently revealed that the resistance Rei is approximately proportional to dmc 2. and hence to the inverse electrode area. 

Fig. 43. Double-logarithmic plot of the electrode polarization resistance versus the microelectrode diameter measured with impedance spectroscopy (ca. 800 °C) at (a) a cathodic dc bias of -300 mV, and (b) at an anodic dc bias of +300 mV. In (b) the first data point of the 20-pm microelectrode is not included in the fit. (c) Sketch illustrating the path of the oxygen reduction reaction for cathodic bias, (d) Path of the electrochemical reaction under anodic bias the rate-determining step occurs close to the three-phase boundary.

AC impedance spectra provide a large amount of information about the electrochemical system being investigated. However, the analysis of AC impedance spectra and the correlation of AC impedance spectra with a specific parameter are still not fully understood. For example, for electrochemical reactions under load (or with a certain reaction rate), how the charge-transfer resistance relates to the reaction rate is not clear. More work is needed to deduce electrochemical reaction parameters from these spectra. In a later part of this book, impedance derived from reaction mechanisms and its correlation with electric circuit components will be discussed. 

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. 

If a resistor is added in series with the parallel RC circuit, the overall circuit becomes the well-known Randles cell, as shown in Figure 4.11a. This is a model representing a polarizable electrode (or an irreversible electrode process), based on the assumptions that a diffusion limitation does not exist, and that a simple single-step electrochemical reaction takes place on the electrode surface. Thus, the Faradaic impedance can be simplified to a resistance, called the charge-transfer resistance. The single-step electrochemical reaction is described as... 

The electrolyte resistance Re is added in series with the previous impedance. If the electrochemical reaction is mass-trai3sport limited, the previous equivalent circuit is still valid, but the Faradaic impedance includes a diffusion impedance as described in Chapter 11. 

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 homogeneous corrosion systems (active dissolution, passive state) where the same electrochemical reactions occur over the whole surface, the interrupter and ac technique can be successfully applied and the same value for the ohmic resistance is measured by both techniques. Problems arise in localized corrosion systems, where small active areas coexist with a large passive surface and the impedance of the active areas (pits) is short circuited by the surrounding passive surface. 

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 ... 

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