Interfaces equivalent circuit representation

FIGURE 4.3.19. Equivalent circuit representation of an electrode-solution interface for a simple charge-transfer process. (A) Without adsorbed intermediates, and (B) with adsorbed intermediates. 

Figure 6.3 (a) Schematic representation of equivalent circuit for an ion conductor put between a pair of blocking electrode, and (b) the corresponding Nyquist plot. Ideally the sample-electrode interface is composed only of the double-layer capacitance. However, the practical Nyquist plot that corresponds to this frequency region is not vertical to the real axis. The rate-limiting process of this plot is that the ion diffuses to form a double layer. 

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. 

Figure 5.25 The equivalent circuit models proposed for the interpretation of EIS results measured in corroding systems (a) simplest representation of an electrochemical interface, (b) one relaxation time constant with extended diffusion.

Of the numerous equivalent circuits that have been proposed to describe electrochemical interfaces, only a few really apply in the context of a freely corroding interface at or close to kinetic equilibrium. The first circuit (Fig. 7.25a) corresponds to Eq. (7.2) and to the simplest equivalent circuit that can describe a metal/electrolyte interface. Following Boukamp,25 the term Q has been adopted here to describe the leaky capacitor behavior corresponding to the presence of a constant phase element explained by a fundamental dispersion effect. The admittance representation Y of the CPE behavior with frequency w can be described by Eq. (7.5). For n = (1 - p), Eq. (7.5) describes the behavior of a resistor with R = Yq" and for n = P, that of a capacitor with C = Yo- For n = 0.5, Eq. (7.5) becomes the expression of a Warburg (W) component, and when n = -p, it emulates an inductance with L = Yq-1.25... 

Modeling an electrochemical interface by the equivalent circuit (EC) representation approach has been exceptionally popular in studies of electrodes modified with polymer membranes, although an analytical approach based on transport equations derived from irreversible thermodynamics was also attempted [6,7]. ECs are typically composed of numerous ideal electrical components, which attempt to represent the redox electrochemistry of the polymer itself, its highly developed morphology, the interpenetration of the electrolyte solution and the polymer matrix, and the extended electrochemical double layer established between the solution and the polymer with variable localized properties (degree of oxidation, porosity, conductivity, etc.). 

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