Adsorption equivalent circuit representation

In another study of DMFC anodes, shovm in Figure 16.10, the complex-plane impedance plots were studied as a function of the current density applied. The diameters of the semicircles were found to decrease with increasing current density, as expected, but the new feature observed is an inductive branch of the curves. This can be modeled, of course, by adding an inductive element to the equivalent circuit representation, in series with the Faradaic resistance, but the physical origin of this added circuit element is still open for debate. There is a tendency to associate it with sluggish adsorption of CO, formed as an intermediate in the oxidation of methanol. However, unlike the adsorption pseudocapacitance, which is well understood (cf Section 11.2), there is no theory for the dependence of the pseudoinductance on potential, coverage or any other measured parameter. 

The above analysis shows that in the simple case of one adsorbed intermediate (according to Langmuirian adsorption), various complex plane plots may be obtained, depending on the relative values of the system parameters. These plots are described by various equivalent circuits, which are only the electrical representations of the interfacial phenomena. In fact, there are no real capacitances, inductances, or resistances in the circuit (faradaic process). These parameters originate from the behavior of the kinetic equations and are functions of the rate constants, transfer coefficients, potential, diffusion coefficients, concentrations, etc. In addition, all these parameters are highly nonlinear, that is, they depend on the electrode potential. It seems that the electrical representation of the faradaic impedance, however useful it may sound, is not necessary in the description of the system. The systen may be described in a simpler way directly by the equations describing impedances or admittances (see also Section IV). In... 

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. 

When an Mg alloy does not fulfill the chemical composition specified for a sacrificial magnesium anode, features as inductive loops at lower frequencies appear in the Nyquist representation of the measured impedance. As the magnesium alloy is polarized further away from its E, in the anodic direction, the Nyquist representation of the impedance exhibits inductive loop behavior (Fig. 2.18). This fact leads to the consideration of an inductor component in the corresponding electrical equivalent circuit. This inductive loop can be associated with the adsorption and desorption phenomena occurring on the surface of the sample and leading to the process of formation of the corrosion product layer on the surface of the electrode (Guadarrama-Mu-oz et al., 2006). 

III.l [see also Eq. (17) and Fig. 2], and that in the presence of a faradaic reaction [Section III. 2, Fig. 4(a)] are found experimentally on liquid electrodes (e.g., mercury, amalgams, and indium-gallium). On solid electrodes, deviations from the ideal behavior are often observed. On ideally polarizable solid electrodes, the electrically equivalent model usually cannot be represented (with the exception of monocrystalline electrodes in the absence of adsorption) as a smies connection of the solution resistance and double-layer capacitance. However, on solid electrodes a frequency dispersion is observed that is, the observed impedances cannot be represented by the connection of simple R-C-L elements. The impedance of such systems may be approximated by an infinite series of parallel R-C circuits, that is, a transmission line [see Section VI, Fig. 41(b), ladder circuit]. The impedances may often be represented by an equation without simple electrical representation, through distributed elements. The Warburg impedance is an example of a distributed element. 

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