Ideal polarizable electrodes

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. 

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]. 

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. 

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. 

A similar effect of band unbending under illumination also takes plat at an ideally polarizable electrode when ip = i° = 0 (Garrett and Brattain, 1955). 

Let us consider in more detail, using the above concepts, how a photocorrosion process occurs under the illumination of a semiconductor. Suppose that electron transitions at the interface between the semiconductor and solution do not take place in darkness in a certain potential range (the semiconductor behaves like an ideally polarizable electrode). This range is confined to the potentials of decomposition of the semiconductor and/or solution. The steady state potential of a semiconductor is usually determined in this case by chemisorption processes (e.g., of oxygen) or, which is the same in the language of the physics of semiconductor surface, by charging of slow surface states. It is these processes that determine the steady state band bending. 

Ideally polarizable electrode — Upon transferring electric charge to -> electrodes (to the -> interfaces between the electronically and ionically conducting phases, respectively) by means of - charge-carrier ions, various changes occur. The charge carriers (ions,... 

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]. 

The attainment of equilibrium between the semiconductor and solution, however, is somewhat hindered. Many semiconductor electrodes behave over a broad range of potentials as ideally polarizable electrodes. 

The simplest model is the connection of resistor and capacitor in either series or parallel. Figure 4.2a shows the connection of a resistor and a capacitor in series. This equivalent circuit is the simplest model for an ideal polarizable electrode, with the assumption that neither the charge transfer on the electrode surface nor the diffusion limitations are present. 

---