Polarized half-cell reaction

It should be noted that Eq 3.41 and 3.42 have the relatively simple form of an exponential term involving the overpotential, r CT, multiplying the exchange current density to give the current densities of the oxidation and reduction components of the polarized half-cell reaction. When an overpotential exists, the oxidation and reduction current densities are no longer equal When r CT > 0, then iox M > ired M, and when r CT < 0, then ired M > i0X M-... 

Fig. 3.1 Polarization curves illustrating charge-transfer polarization (Tafel ° behavior) for a single half-cell reaction, (a) Anodic polarization,...

These equations are frequently called the Tafel equations for the oxidation and reduction components of the half-cell reaction (Ref 3). Thus, the polarized potentials should plot as linear functions of the logarithm of current density as shown in Fig. 3.9(a). Note that the lines cross when iox m = hed,M = i0,M at the equilibrium half-cell potential, E M. 

Complete Polarization Curves for a Single Half-Cell Reaction... 

By combining the Nernst equation with the expressions for charge-transfer overpotential (r CT) and diffusion overpotential (r D), equations can be written for the total experimental polarization behavior, E(iex ox) and E(iex red), of a single half-cell reaction ... 

The following problem is designed to provide understanding of Tafel plots for individual half-cell reactions and the form of experimental polarization curves to be expected based on the theory. Assume that for a given metal, M,... 

The earlier sections of this chapter discuss the mixed electrode as the interaction of anodic and cathodic reactions at respective anodic and cathodic sites on a metal surface. The mixed electrode is described in terms of the effects of the sizes and distributions of the anodic and cathodic sites on the potential measured as a function of the position of a reference electrode in the adjacent electrolyte and on the distribution of corrosion rates over the surface. For a metal with fine dispersions of anodic and cathodic reactions occurring under Tafel polarization behavior, it is shown (Fig. 4.8) that a single mixed electrode potential, Ecorr, would be measured by a reference electrode at any position in the electrolyte. The counterpart of this mixed electrode potential is the equilibrium potential, E M (or E x), associated with a single half-cell reaction such as Cu in contact with Cu2+ ions under deaerated conditions. The forms of the anodic and cathodic branches of the experimental polarization curves for a single half-cell reaction under charge-transfer control are shown in Fig. 3.11. It is emphasized that the observed experimental curves are curved near i0 and become asymptotic to E M at very low values of the external current. In this section, the experimental polarization of mixed electrodes is interpreted in terms of the polarization parameters of the individual anodic and cathodic reactions establishing the mixed electrode. The interpretation then leads to determination of the corrosion potential, Ecorr, and to determination of the corrosion current density, icorr, from which the corrosion rate can be calculated. 

Knowledge of the parameters of the individual electrode reactions permits writing expressions for the individual oxidation or reduction curves (see the section Complete Polarization Curves for a Single Half-Cell Reaction in Chapter 3). Thus, the expression for the cathodic-reactant reduction reaction ... 

In Chapter 4, analysis of the kinetics of coupled half-cell reactions shows how the corrosion potential and corrosion current density depend on the positions of the anodic and cathodic polarization curves. The anodic polarization curves are generally represented as showing linear or Tafel behavior, and the cathodic curves are shown with both Tafel and... 

Interpretation of an experimentally determined polarization curve, including an understanding of the information derivable therefrom, is based on the form of the polarization curve, which results from the polarization curves for the individual anodic and cathodic half-cell reactions occurring on the metal surface. These individual polarization curves, assuming Tafel behavior in all cases, are shown in Fig. 6.2 (dashed curves) with Ecorr and the corrosion current, Icorr, identified. It is assumed that over the potential range of concern, the Iox x and Ired M contributions to the sum-anodic and sum-cathodic curves are negligible consequently, Uox = Iox M and Ured = Ired x. At any potential of the... 

It is shown in Chapter 3 that a simple kinetic model of half-cell reactions leads to Tafel equations in which the overpotentials (r ) or polarizations of the oxidation and reduction components of a half-cell reaction are linearly dependent on the logarithm of the oxidation and reduction currents (Iox and Ired), respectively, or... 

To begin our discussion, it is useful to consider current-voltage curves for an ideal polarized and an ideal nonpolarized elearode. Polarization at a single electrode can be studied by coupling it with an electrode that is not easily polarized. Such electrodes have large surface areas and have half-cell reactions that are rapid and reversible. Design details of nonpolarized electrodes are described in subsequent chapters. 

Sharp current minimums in Figure 2 for magnetite (400 mV) and ilmenite (-40 mV) correspond to conditions in which no current is applied and the rates for the anodic and cathodic half cell reactions are equivalent and equal to equation 1. Polarization of the magnetite electrode to potentials less than 400 mV results in the dominance of the reductive dissolution of magnetite as described by equation 6. This reaction consumes electrons by reducing ferric atoms in the magnetite structure and releasing Fe(II) to solution. 

Similarly, the emf, polarity, and spontaneous reaction can be determined for any cell for which half-cell reactions and standard potentials are known. 

The saturated copper-copper sulfate reference electrode consists of metallic copper immersed in saturated copper sulfate, as shown in Fig. 3.6. It is used primarily in field measurements where the electrode must be resistant to shock and where its usual large size minimizes polarization errors. The accuracy of this electrode is adequate for most corrosion investigations, even though it falls somewhat below the precision obtainable with the calomel or silver chloride electrodes. The half-cell reaction is... 

Here AS is the entropy change in the half-cell reaction, rj is the half-cell polarization voltage, j is the mean current density in the cell, I is the thickness of the respective catalyst layer, at is the proton conductivity of the catalyst layer, am is the proton conductivity of the bulk membrane, and A and Am are the thermal conductivities of the catalyst layers and membrane, respectively. Note that the thermal conductivities of the ACL and CCL are assumed to be the same. 

When a conductive particle is exposed to an electric field, it causes the particle to polarize. As a consequence an overpotential r varying according to a cosine law is induced at the surface of the particle (Eq. 1, Fig. l) Thus, a maximum potential difference will occur at opposite poles of the particle. In order to carry out electrochemistry at the surface of the particle a critical voltage difference corresponding to the sum of two half-cell reactions must be reached. Thus, for a given particle of radius r and an applied electric field E there will exist two polar regions defined by a critical angle 0 within which electrochemistry will occur. (Eq. 2, Fig. 2). This forms the theoretical basis of toposelective electrodeposition. 

This chapter is coniined to analyze the complex aqueous corrosion phenomaion using the principles of mixed-potential, which in turn is related to the mixed electrode electrochemical corrosion process. This theory has been introduced in Chapter 3 and 4 as oxidation and reduction electrochemical reactions. Basically, this Chapter is an extension of the principles of electrochemistry, in which partial reactions were introduced as half-cell reactions, and their related kinetics were related to activation and concentration polarization processes. The principles and concepts introduced in this chapter represent a unique and yet, simplified approach for understanding the electrochemical behavior of corrosion (oxidation) and reduction reactions in simple electrochemical systems. 

Activation polarization can be a slow step in the electrical reaction for which an activation energy in the form of potential is reqnired for the reaction to proceed. When a certain step in a half cell reaction controls the rate of electron flow, the reaction is said to be under activation charge transfer control and activation polarization occurs. For example, consider the reduction of hydrogen ions ... 

Given that the rates of oxidation and reduction of the half-reactions are controlled by activation polarization only, that = 4-0.07 and = —0.08, and that the exchange current densities for both the oxidation of Fe and reduction of hydrogen in acidic solution are identical, use the data in Tables 3.3 and 3.4 to determine the following quantities. Recall that the potential for each half-cell is the sum of the equilibrium potential and the corresponding overpotential, in this case, r]a-... 

Reactive electrodes refer mostly to metals from the alkaline (e.g., lithium, sodium) and the alkaline earth (e.g., calcium, magnesium) groups. These metals may react spontaneously with most of the nonaqueous polar solvents, salt anions containing elements in a high oxidation state (e.g., C104 , AsF6 , PF6 , SO CF ) and atmospheric components (02, C02, H20, N2). Note that ah the polar solvents have groups that may contain C—O, C—S, C—N, C—Cl, C—F, S—O, S—Cl, etc. These bonds can be attacked by active metals to form ionic species, and thus the electrode-solution reactions may produce reduction products that are more stable thermodynamically than the mother solution components. Consequently, active metals in nonaqueous systems are always covered by surface films [46], When introduced to the solutions, active metals are usually already covered by native films (formed by reactions with atmospheric species), and then these initial layers are substituted by surface species formed by the reduction of solution components [47], In most of these cases, the open circuit potentials of these metals reflect the potential of the M/MX/MZ+ half-cell, where MX refers to the metal salts/oxide/hydroxide/carbonates which comprise the surface films. The potential of this half-cell may be close to that of the M/Mz+ couple [48],... 

Electrochemical cells employed to carry out voltammet-ric or amperometric measurements can involve either a two or three electrode configuration. In the two electrode mode, the external voltage is applied between the working and a reference electrode, and the current monitored. Since the current must also pass through the reference electrode, such current flow can potentially alter the surface concentration of electroactive species that poises the actual half-cell potential of the reference electrode, changing its value by a concentration polarization process. For example, if an Ag/AgCl reference electrode were used in a cell in which a reduction reaction for the analyte occurs at the working electrode, then an oxidation reaction would take place at the surface of the reference electrode ... 

Regardless of the cause of the electron flow at the interface, deviations of the half-cell potentials along the interface from their equilibrium values are functions of the current density. These deviations reflect the polarization behavior of the reaction, a phenomenon of... 

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