Irreversible electrode reaction impedance

Cao CN (1990) On the impedance plane displays for irreversible electrode reactions based on the stability conditions of the steady-state—II. Two state variables besides electrode potential, Electrochim Acta 35 (5) 837-44... 

Fig. 10. The complex impedance plot for several simple electrode processes at the electrode and their equivalent circuits (A) Ideally polarizable electrode. (B) Diffusion-controlled fast redox reaction. (C) Irreversible electrode reaction. (D) Quasi-reversible electrode reaction. Arrows indicate the increasing frequency.

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 effect of adsorption of electroactive species in ac methods is taken into account by modification of the equivalent circuit representing the electrode reaction (44, 64-68). This is usually accomplished by adding an adsorption impedance in parallel with the Warburg impedance and double-layer capacitance. Expressions for this impedance have been suggested for reversible (65, 66) and irreversible (67, 68) systems, but the complexity of the resulting analysis has limited the application of these techniques. 

Figure 10. Kleitz s reaction pathway model for solid-state gas-diffusion electrodes. Traditionally, losses in reversible work at an electrochemical interface can be described as a series of contiguous drops in electrical state along a current pathway, for example. A—E—B. However, if charge transfer at point E is limited by the availability of a neutral electroactive intermediate (in this case ad (b) sorbed oxygen at the interface), a thermodynamic (Nernstian) step in electrical state [d/j) develops, related to the displacement in concentration of that intermediate from equilibrium. In this way it is possible for irreversibilities along a current-independent pathway (in this case formation and transport of electroactive oxygen) to manifest themselves as electrical resistance. This type of chemical valve , as Kleitz calls it, may also involve a significant reservoir of intermediates that appears as a capacitance in transient measurements such as impedance. Portions of this image are adapted from ref 46. (Adapted with permission from ref 46. Copyright 1993 Rise National Laboratory, Denmark.)...

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