Polarization electrode

Since the energy required to strip the electrons from plutonium metal at the anode is exactly matched by the energy returned at the cathode, the potential required by the process is only that required to overcome time invariant (i2r) losses in the cell circuit, and time dependent resistance (electrode polarization). 

Figure 10.7. Turnover frequency of S02 catalytic oxidation [mol S02 (conv.)/mol V2Os/s] vs working electrode polarization for the molten 10 mol % V20s - 90 mol% K2S207 catalyst at (1) 440°C and (2) 460°C.12 Reproduced by permission of the Electrochemical Society.

Two cases where equihbrium is lacking must be distinguished that which is unrelated to current flow and can be observed even for a nonworking electrode, and that which is related exclusively to the passage of current through the electrode. The former is the case of nonequilibrium open-circuit potentials (nonequihbrium OCP), and the latter is that of electrode polarization. 

In the electrochemical literature, the concept of electrode polarization has three meanings ... 

The specific rate of an electrode reaction depends not only on electrode polarization but also on tfie reactant concentrations. Changes in reactant concentrations affect not only reaction rates but also the values of equilibrium potentials. To differentiate both these influences, kinetic equations are generally used (especially at high values of polarization), relating the current density not with the value of polarization AE but with the potential of the electrode E ... 

The trends of behavior described above are found in solutions containing an excess of foreign electrolyte, which by definition is not involved in the electrode reaction. Without this excess of foreign electrolyte, additional effects arise that are most distinct in binary solutions. An appreciable diffusion potential q) arises in the diffusion layer because of the gradient of overall electrolyte concentration that is present there. Moreover, the conductivity of the solution will decrease and an additional ohmic potential drop will arise when an electrolyte ion is the reactant and the overall concentration decreases. Both of these potential differences are associated with the diffusion layer in the solution, and strictly speaking, are not a part of electrode polarization. But in polarization measurements, the potential of the electrode usually is defined relative to a point in the solution which, although not far from the electrode, is outside the diffusion layer. Hence, in addition to the true polarization AE, the overall potential drop across the diffusion layer, 9 = 9 + 9ohm is included in the measured value of polarization, AE. ... 

Electrode polarization is associated with a change in EDL charge density at the electrode surface. Other changes in surface state of the electrode are possible, too (e.g., the adsorption or desorption of different components, which also involve a consumption of electric charge). By convention, we describe this set of nonfaradaic processes as charging of the electrode surface. 

As an example, consider a simple reaction of the type (6.2) taking place under pure diffusion control. At all times the electrode potential, according to the Nemst equation, is determined by the reactant concentrations at the electrode surface. It was shown in Section 11.2.3 that periodic changes in the surface concentrations which can be described by Eq. (11.19) are produced by ac flow. We shall assume that the amplitude of these changes is small (i.e., that Ac electrode polarization. With this substitution and using Eq. (11.19), we obtain... 

Each of the intermediate electrochemical or chemical steps is a reaction of its own (i.e., it has its own kinetic pecnliarities and rules. Despite the fact that all steps occur with the same rate in the steady state, it is true that some steps occur readily, without kinetic limitations, and others, to the contrary, occur with limitations. Kinetic limitations that are present in electrochemical steps show up in the form of appreciable electrode polarization. It is a very important task of electrochemical kinetics to establish the nature and kinetic parameters of the intermediate steps as well as the way in which the kinetic parameters of the individual steps correlate with those of the overall reaction. 

Another example are the sometimes rather complex relations existing between the potential and the reaction rate. The electrode potential influences not only the parameter h [see, e.g., Eq. (14.15)] but also the degree of surface coverage by reactant particles [i.e., the coefficients in Eq. (14.18) or (14.20)]. When a sharp drop in adsorption occurs with increasing electrode polarization (rising values of hj, the monotonic relation between reaction rate and potential may break down and the current actually may decrease within a certain region while polarization increases. 

In an electrochemical system, gas supersaturation of the solution layer next to the electrode will produce a shift of equilibrium potential (as in diffusional concentration polarization). In the cathodic evolution of hydrogen, the shift is in the negative direction, in the anodic evolution of chlorine it is in the positive direction. When this step is rate determining and other causes of polarization do not exist, the value of electrode polarization will be related to solution supersaturation by... 

After complete formation of each successive monolayer of atoms, the next layer should start to form. This requires two-dimensional nucleation by the union of several adatoms in a position 1. Like three-dimensional nucleation, two-dimensional nucleation requires some excess energy (i.e., elevated electrode polarization). Introducing the concept of excess linear energy p of the one-dimensional face (of length L) of the nucleus, we can derive an expression for the work of formation of such a nucleus (analogous to that used in Section 14.2.2). When the step of two-dimensional nucleation is rate determining, the polarization equation becomes, instead of (14.39),... 

This situation is rather easy to explain. If the primary step of metal ion discharge is hindered, the appreciable electrode polarization associated with it will compensate for the energetic difficulties of formation of new metal nuclei and lead to the formation of more nuclei. Here, the overall charge is distributed over a large number of nuclei, and any individual nucleus will not undergo much further growth. 

Constant A in Eqs. (29.5) and (29.6) is about 4.4 eV when the standard hydrogen electrode is used as the reference electrode. This value has been determined from experimental values for the electron work function of mercury in vacuum, which is 4.48 eV, and for the Volta potential, between the solution and a mercury electrode polarized to = 0 V (SHE), which is -0.07 V (the work of electron transfer is 0.07 eV). The sum of these two values, according to Eq. (9.8), corresponds to the solution s electron work function at this potential (i.e., to the value of constant A with an inverted sign). 

Equation (6.13), in fact, reflects the physical nature of the electrode process, consisting of the anode (the first term) and cathode (the second term) reactions. At equilibrium potential, E = Eq, the rates of both reactions are equal and the net current is zero, although both anode and cathode currents are nonzero and are equal to the exchange current f. With the variation of the electrode potential, the rate of one of these reactions increases, whereas that of the other decreases. At sufficiently large electrode polarization (i.e., deviation of the electrode potential from Eg), one of these processes dominates (depending on the sign of E - Eg) and the dependence of the net current on the potential is approximately exponential (Tafel equation). 

I In this chapter we use notations generally accepted in theoretical physics instead of those used in other chapters of this book the Boltzmann constant instead of the gas constant R, the elementary electrical charge e (in Chapter 1 denoted Q ) instead of the Faraday constant F (obviously, k T/e = RTIF). Electrode polarization (overvoltage) AE is denoted T. For all reactions we assume that n = 1. 

During measurement, the conductivity cell is filled with an electrolyte solution this cell is usually made of glass with sealed platinum electrodes. Various shapes are used, depending on the purpose that it is to serve. Figure 2.9 depicts examples of suitable cell arrangements. The electrodes are covered with platinum black, to avoid electrode polarization. The electrodes are placed close to one another in poorly conductive solutions and further apart in more conductive solutions. 

If current passes through an electrolytic cell, then the potential of each of the electrodes attains a value different from the equilibrium value that the electrode should have in the same system in the absence of current flow. This phenomenon is termed electrode polarization. When a single electrode reaction occurs at a given current density at the electrode, then the degree of polarization can be defined in terms of the over potential. The overpotential r) is equal to the electrode potential E under the given conditions minus the equilibrium electrode potential corresponding to the considered electrode reaction Ec ... 

We and others have been involved in the study of such systems including Cu/Au(lll),85 86 Ag/Au(lll),87 Pb/Ag(lll),88 and Cu/Pt(lll).89 The first three systems involved the use of epitaxially deposited metal films on mica as electrodes.90 92 Such deposition gives rise to electrodes with well-defined single-crystalline structures. In the last case a bulk platinum single crystal was employed. Because of the single-crystalline nature of the electrodes, polarization dependence studies could be used to ascertain surface structure. 

According to a Macherey-Nagel application note [35], a mixture of 20 ng each of (i)-cysteine, (L)-glutathione, and (L)-penicillamine was resolved in less than 12 min by HPLC. The method used a Nucleosil 100-5SA column (15 cm x 4.6 mm i.d.) with aqueous 4.5 g/L ammonium citrate-6 g/L phosphoric acid at pH 2.2 as the mobile phase (eluted at 1 mL/min) and electrochemical detection at a gold electrode polarized at +800 mV. 

When the electrolyte solutions are not too reactive, as in the case of ethereal solutions, there is no massive formation of protective surface films at potentials above Li intercalation potential, and most of the solvent reduction processes may occur at potentials lower than 0.3 V vs. Li/Li+. Hence, the passivation of the electrodes is not sufficient to prevent cointercalation of solvent molecules. This leads to an exfoliation of the graphite particles into amorphous dust (expholiated graphene planes). This scenario is demonstrated in Figure 2a as the reduction of the 002 diffraction peak21 of the graphite electrode, polarized cathodically in an ethereal solution. 

The surface reactions of graphite electrodes in many nonaqueous solutions have been investigated intensively,29 30 and the major reaction paths in a variety of alkyl carbonate solutions seem to be quite clear. Both EC and PC decompose on graphite electrodes, polarized cathodically, to form solid surface films with R0C02Li species as major components,31 and ethylene or propylene gases, respectively, as co-products. 

Figure 3. Current density versus electrode polarization (Ag/AgCl ref. electrode) for oxygen reduction in 1MKOH at20°C on Co-Ni modified AG-3 carbon.

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