The Ideally Polarizable Electrode

An ideally polarizable electrode behaves as an ideal capacitor because there is no charge transfer across the solution/electrode boundary. In this case, the equivalent electrical model consists of the solution resistance, R, in series with the double-layer capacitance, Cdi. An analysis of such a circuit was presented in Section I.2(i). 

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Another progress in our understanding of the ideally polarizable electrode came from theoretical works showing that the metal side of the interface cannot be considered just as an ideal charged plane. A simple quantum-mechanical approach shows that the distribution of the electron gas depends both on the charge of the electrode and on the metal-solution coupling [12,13]. 

There is no thermodynamic equilibrium between the ideally polarizable electrode (more exactly the metal phase) and the solution phase because there is no common component capable of changing its charge and being transferred between the phases, conditions necessary for equilibrium. The state of an ideally polarizable electrode is well defined only if an external source is used to maintain a constant polarization potential, i.e., the double-layer capacitor charged with a definite charge. The polarization potential is an independent parameter of the system. 

For ideally polarizable electrodes - since as a whole, the double layer is electrically neutral - the absolute value of the -> surface charge on the metal (opposite charge accumulated at the solution phase near the metal (surface charge density and for the ideally polarizable electrode it is equal to the surface charge density (Q), i.e., electrocapillary measurements. When oM = os = 0, i.e., at the -> potential of zero charge (pzc, Ea = Eq = 0) the - Galvani potential difference between the two phases is due to the orientation of dipoles (e.g., water molecules) [i.v]. 

A typical example of the ideal polarizable electrode is Hg, which shows a double-layer capacitance of 10 20 pF cm in aqueous electrolyte solutions. Since the double-layer capacitance is dependent on electrode potential V, minimum values of differential double-layer capacitance Ca were adopted, as defined below, where Q is the charge ... 

Badiali, J.P. (1986) Contribution of the metal to the differential capacitance of the ideally polarizable electrode. Electrochimica Acta, 31,149-154. 

The general model of the ideally polarizable electrode presented in Section... 

The models clearly have not assigned any atomic structure to the metal side. With a metallic substrate Rice, in 1928,- showed the electric field penetration was indeed slight. Consequently, this model was adequate for the ideal polarizable electrode without Faradaic charge transfer. 

One type of electrode has no defined DC voltage at all, the ideally polarizable electrode. 

Experimental confirmation of the theory of electron transfer with polymer films, and the ramifications of this new knowledge demonstrate that there is a tremendous opportunity to control interfa-cial electron transfer via surface and thin-film chemistry. The ideal, polarizable electrode, once an icon for electroanalytical chemists, now serves as a hypothetical support for molecular-scale organized assemblies that carry out the business of controlled electron transfer. Examples of early prototype assemblies are given below. 

In order to describe the effects of resistance and electrode capacitance in electrochemical cells, it is useful to introduce the concept of the ideal polarizable electrode (IPE). The IPE (Figure 1.6) is one that will not pass any charge across the solution/metal interface when the potential across it is changed. The behavior of the IPE then mimics that of a capacitor in an electrical circuit, with the one difference being that the capacitance of an... 

Figure 1.6 The ideal polarizable electrode in theory (dashed line) and in practice (solid line).

Two limiting cases for the description of an electrode are the ideally polarizable electrode and the ideally nonpolarizable electrode [8, 9, 14], The ideally polarizable electrode corresponds to an electrode for which the Zfaiadaic element has infinite resistance (i.e., this element is absent). Such an electrode is modeled as a pure capacitor, with Cdi = Aq 6V (equation 26), in series with the solution resistance. In an ideally polarizable electrode, no electron transfer occurs across the electrode/electrolyte interface at any potential when current is passed rather all current is through capacitive action. No sustained current flow is required to support a large voltage change across the electrode interface. An ideally polarizable electrode is not used as a reference electrode, since the electrode potential is easily perturbed... 

At the other extreme one finds the ideally polarizable electrode . This electrode does not transfer current, no matter what potential is applied to it. Its current-potential curve is a horizontal line and its resistance is infinity. 

In addition, the potential of the electrode can be varied, resulting in a change in the stmcture of the interface. If no current is passed when the potential of the electrode changes, the electrode is called an ideally polarizable electrode, and can be described using thermodynamics. 

Even in the absence of Faradaic current, ie, in the case of an ideally polarizable electrode, changing the potential of the electrode causes a transient current to flow, charging the double layer. The metal may have an excess charge near its surface to balance the charge of the specifically adsorbed ions. These two planes of charge separated by a small distance are analogous to a capacitor. Thus the electrode is analogous to a double-layer capacitance in parallel with a kinetic resistance. 

The structure and composition of the lithium surface layers in carbonate-based electrolytes have been studied extensively by many investigators [19-37], High reactivity of propylene carbonate (PC) to the bare lithium metal is expected, since its reduction on an ideal polarizable electrode takes place at much more positive potentials compared with THF and 2Me-THF [18]. Thevenin and Muller [29] found that the surface layer in LiC104/PC electrolyte is a mixture of solid Li2C03 and a... 

For an ideally polarizable electrode, q has a unique value for a given set of conditions.1 For a nonpolarizable electrode, q does not have a unique value. It depends on the choice of the set of chemical potentials as independent variables1 and does not coincide with the physical charge residing at the interface. This can be easily understood if one considers that q measures the electric charge that must be supplied to the electrode as its surface area is increased by a unit at a constant potential." Clearly, with a nonpolarizable interface, only part of the charge exchanged between the phases remains localized at the interface to form the electrical double layer. 

Data from many experiments64,71,72,74,287-289 indicate that the differential capacitance of an ideally polarizable electrode at ff jin nonideal... 

Another type of supercapacitor has been developed in whieh instead of ideally polarizable electrodes, electrodes consisting of disperse platinum metals are used at which thin oxide films are formed by anodic polarization. Film formation is a faradaic process which in certain cases, such as the further partial oxidation and reduction of these layers, occurs under conditions close to reversibility. 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

The interfacial tension always depends on the potential of the ideal polarized electrode. In order to derive this dependence, consider a cell consisting of an ideal polarized electrode of metal M and a reference non-polarizable electrode of the second kind of the same metal covered with a sparingly soluble salt MA. Anion A is a component of the electrolyte in the cell. The quantities related to the first electrode will be denoted as m, the quantities related to the reference electrode as m and to the solution as 1. For equilibrium between the electrons and ions M+ in the metal phase, Eq. (4.2.17) can be written in the form (s = n — 2)... 

Double-layer properties in aqueous, propylene carbonate and formamide solutions have been studied at room temperature for liquid Ga-Pb alloy (0.06 atom % of Pb) [15], as a model of Pb electrode with renewable surface. The electrode behaves as an ideally polarizable electrode in a wide potential range, and its capacitance is intermediate between that of Ga and Hg electrodes and is independent of the solvent. This electrode is much less lipophilic than Ga. Adsorption of anions on this electrode increases in the sequence -BP4 = S042 < Gl < Br < r. 

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