Impedance ideally polarizable electrode

Total electrode impedance consists of the contributions of the electrolyte, the electrode solution interface, and the electrochemical reactions taking place on the electrode. First, we consider the case of an ideally polarizable electrode, followed by semi-infinite diffusion in linear, spherical, and cylindrical geometry and, finally a finite-length diffusion. 

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. 

An ideally polarizable electrode also called blocking electrode, is an electrode at which there is no charge transfer between electrode and solutimi [17], Such an electrode immersed in a solution containing supporting electrolyte can be represented as a connection of the solution resistance and electrode capacitance in series (Fig. 4.1 a), and its impedance is described as... 

In the industrial applications of electrochemistiy, the use of smooth surfaces is impractical and the electrodes must possess a large real surface area in order to increase the total current per unit of geometric surface area. For that reason porous electrodes are usually used, for example, in industrial electrolysis, fuel cells, batteries, and supercapacitors [400]. Porous siufaces are different from rough surfaces in the depth, /, and diameter, r, of pores for porous electrodes the ratio Hr is very important. Characterization of porous electrodes can supply information about their real surface area and electrochemical utilization. These factors are important in their design, and it makes no sense to design pores that are too long and that are impenetrable by a current. Impedance studies provide simple tools to characterize such materials. Initially, an electrode model was developed by several authors for dc response of porous electrodes [401-406]. Such solutions must be known first to be able to develop the ac response. In what follows, porous electrode response for ideally polarizable electrodes will be presented, followed by a response in the presence of redox processes. Finally, more elaborate models involving pore size distribution and continuous porous models will be presented. 

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.

Some inferred data, regarding the role of Sn ions in the absorption processes, can be taken from the comparison of the impedance spectra obtained in the presence and in the absence of Sn(II). Impedance characteristics in Sn(II)-free solutions (Figure 8.41) are far from those typical of ideally polarizable electrodes and large frequency dispersion is observed. Similar behavior was also observed in tin systems involving specific adsorption of polyethers and other surfactants [100,... 

Consider a metal electrode consisting of a silver wire placed inside the body, with a solution of silver ions between the wire and ECF, supporting the reaction Ag" + e <— Ag. This is an example of an electrode of the first kind, which is defined as a metal electrode directly immersed into an electrolyte of ions of the metal s salt. As the concentration of silver ions [Ag" ] decreases, the resistance of the interface increases. At very low silver ion concentrations, the Faradaic impedance Zfaradaic becomes very large, and the interface model shown in Fig. 3(a) reduces to a solution resistance in series with the capacitance C. Such an electrode is an ideally polarizable electrode. At very high silver concentrations, the Faradaic impedance approaches zero and the interface model of Fig. 3(a) reduces to a solution resistance in series with the Faradaic impedance Zfaradaic. which is approximated by the solution resistance only. Such an electrode is an ideally nonpolarizable electrode. 

First attempts to study the electrical double layer at A1 electrodes in aqueous and nonaqueous solutions were made in 1962-1965,182,747,748 but the results were not successful.190 The electrical double-layer structure at a renewed Al/nonaqueous solution of surface-inactive electrolytes such as (CH3)4NBF4) (CH3)4NC104, (CH3>4NPF6, and (C4H9)4NBF4, has been investigated by impedance.749-751 y-butyrolactone (y-BL), DMSO, and DMF have been used as solvents. In a wide region of E [-2.5 [Pg.128]

Here is more impedance study the simplest cell. In a real-life experiment, one can only work with a complete circuit, which consists of at least two electrodes. Now, to test our newly acquired impedance knowledge on a real-life problem, let s consider a circuit consisting of two identical electrodes. Draw its equivalent circuit and make a try at its impedance expression. Try harder to imagine its Cole-C ole plot You may also use a computer to simulate the situation by using reasonable parameters. To make the situation less complicated, we assume the interface is ideally polarizable. (Kang)... 

Impedance spectroscopy a single interface. Draw the equivalent circuits for the following electrode/electrolyte interfaces, then derive their impedance expression and explain what their Cole-Cole plot will look like (a) An ideally polarizable interface between electrode and electrolyte, (b) An ideally nonpolarizable interface between electrode and electrolyte, (c) A real-life electrode/... 

If one studies an (almost) ideally polarizable interphase, such as the mercury electrode in pure acids, there is no need to measure at high frequency. In this case the equivalent circuit is a resistor and a capacitor in series. The accuracy of measurement is actually enhanced by making measurements at lower frequencies, since the impedance of the capacitor is higher. The high accuracy and resolution offered by modem instmmentation allows measurement in such cases in very dilute solutions or in poorly conducting nonaqueous media, which could not have been performed until about a decade ago. 

The double-layer structure at the electrochemically polished and chemically treated Cd(OOOl), Cd(lOiO), Cd(1120), Cd(lOil). and Cd(1121) surface electrodes was studied using cyclic voltammetry, impedance spectroscopy, and chronocoulometry [9, 10]. The limits of ideal polarizability, pzc, and capacity of the inner layer were established in the aqueous surface inactive solutions. The values of Ep c decrease, and the capacity of the inner layer increases, if the superficial density of atoms decreases. The capacity of metal was established using various theoretical approximations. The effective thickness of the thin metal layer increases in the sequence of planes Cd(1120) < Cd(lOiO) < Cd(OOOl). It was also found that the surface activity of C1O4 was higher than that of F anions [10]. 

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. 

Problems similar to those observed on ideally polarizable solid electrodes also arise in the presence of faradaic reactions at these electrodes. In the next section, various models used to explain solid electrode impedance behavior are presented. 

E.C. Dutoit, RLv Melrhaeghe, F. Cardon, W.P. Gomes, Investigation on the frequency-dependence of the impedance of the nearly ideally polarizable semiconductor electrodes CdSe, CdS and Ti02. Berichte der Bunsengellschaft fur physikalische Chemie 79, 1206-1213... 

Figure 27.11. (a) Equivalent electric circuit and (b) impedance complex plane plot for an ideally polarizable porous electrode. 

According to the theory of de Levie, the impedance complex plane plots of an ideally polarizable porous electrode take the form shown in Figure 27.1 la. 

The impedance of ideally polarizable liquid electrodes (e.g., mercury, amalgams, indium-gallium) may be modeled by an R-C circuit (Fig. 4.1a). However, most impedance studies are now carried out at solid electrodes. At these electrodes the double-layer capacitance is not purely capacitive and often displays a certain frequency dispersion. Such behavior cannot be modeled by a simple circuit consisting of R, L, and C elements. To explain such behavior, a constant phase element (CPE) is usually used. 

---