Corrosion Butler-Volmer equation

The introduction of 0 in the equations for current density need by no means refer only to the adsorbed intermediates in the electrode reaction. What of other entities that may he adsorbed on the surface For example, suppose one adds to the solution an oiganic substance (e.g., aniline) and this becomes adsorbed on the electrode surface. Then, the 0 for the adsorbed organic substance must also be allowed for in the electrode kinetic equations. So, in Eq. (7.149), the value of 0 would really have to become a 0, where the summation is over all the entities that remain upon the surface and block off sites for the discharging entities. Many practical aspects of electrodics arise from this aspect of the Butler-Volmer equation. For example, the action of organic corrosion inhibitors partly arises in this way (adsorption and blocking of the surface of the electrode and hence reduction of the rate of the corrosion reaction per apparent unit area).67... 

The expression (12.27) for the corrosion potential can be introduced into Eq. (12.22) and thus, an explicit result for the corrosion current can be obtained. But the resulting equation is quite cumbersome and therefore a simpler equation will be derived by assuming that overpotentials are sufficiently large that the high-field approximation of the Butler-Volmer equation can be used for the electronation- and deelectronation-current densities. Thus, Eqs. (12.22) and (12.23) become... 

Corrosion current density — Anodic metal dissolution is compensated electronically by a cathodic process, like cathodic hydrogen evolution or oxygen reduction. These processes follow the exponential current density-potential relationship of the - Butler-Volmer equation in case of their charge transfer control or they may be transport controlled (- diffusion or - migration). At the -> rest potential Er both - current densities have the same value with opposite sign and compensate each other with a zero current density in the outer electronic circuit. In this case the rest potential is a -> mixed potential. This metal dissolution is related to the corro-... 

The concept of the corrosion potential can also be illustrated in a Knear i -E plot. Figure 7 shows two curves representing the Butler-Volmer equation for the metal and hydrogen reactions. The pointat which the rate of metal dissolution equals the rate of hydrogen evolution is the potential at which the metal curve is as high above the potential axis as the hydrogen curve is below the axis. That distance is the corrosion rate. 

In the electrochemical mechanism of corrosion, the metal dissolution—which involves the loss of electrons vis- -vis oxidation—must be accompanied by a cathodic reaction that consumes electrons, which is typically oxygen or proton or water reduction. According to the Butler-Volmer equation, the current density for the anodic reaction varies according to... 

The theory of mixed electrodes was developed by Wagner and Traud [1] and first applied to corrosion by Stern and Geary [2]. In the following we develop the Butler-Volmer equation for a mixed electrode by taking a specific example the uniform corrosion of iron in hydrochloric acid in the absence of concentration gradients (Cj s = Ci b). Two electrode reactions take place simultaneously ... 

Equations (4.91) to (4.93) can be applied to any cathodic partial reaction for which the charge-transfer step obeys the Butler-Volmer equation. In corrosion, oxygen reduction is often under mixed control. Figure 4.25 shows the cathodic polarization curve for oxygen reduction, measured on a platinum electrode [6]. The shape of the curve suggests a relatively low value for the ratio I o/ltil-... 

Figure 3.2 Schematic Evans diagrams illustrating an example of mixed potential reactions associated with the chemical component of copper-CMP in an acidic medium. These diagrams only show the high overpotential (Tafel) trends of the Butler Volmer equation, and extrapolate the resulting lines through the low-overpotential regions, (a) shows how the cathodic step of reaction (3.9) couples to the anodic step of reaction (3.10). The solid lines in (b) indicate the resulting plot of the mixed reactions, while the dashed lines show the contributions of the individual reactions. The effects of a cathodic inhibitor (lowering of the values of both Ecotr and /corr) are displayed in (c).The mixed potential situation for bimetalhc corrosion is considered in (d).

Hu et al. also report the modeling of MEA and carbon corrosion based on four electrochemical and one chemical reactions taking place within the MEA (Hu et al, 2009). The two-dimensional model considers coupled transport of charged and noncharged species. The model was set up to solve for the local fuel starvation case and the start-up and shut-down case with the Butler-Volmer equation governing the kinetics of each half-cell reaction ... 

Assuming that the applied current density is i = io — c and substituting eqs. (3.36) and (3.37) into this expression yields the Butler-Volmer equation that quantifies the kinetics of the electrochemical corrosion... 

Here again, the concentration of the species might enter additionally into the rate equation which catalyze the cation transfer. This situation is often encountered for metal corrosion as, e.g., in the OH catalysis of active iron dissolution. In the following part, the Butler-Volmer equation will be developed for a simple redox process. For metal dissolution and deposition the rate equation is similar. The concentrations [Red] and... 

Assuming the Butler-Volmer equation for most electrode processes yields a similar discussion as in Sec. 1.3.1 Eqs. (1-20) to (1-31). Simplifying the Butler-Volmer equation with the constants A and B, and assuming hydrogen evolution as a possible counter reaction, gives Eq. (1-63). For the rest potential, E= r follows an expression for the corrosion current density Iq. For... 

However, as during corrosion no net current will pass the interface, the theory of electrochemical reaction kinetics will have to be applied in order to calculate the current density under free corrosion conditions. This current density is called the corrosion current density. For a corroding surface under simple electrochemical conditions (no mass transfer effect), the relation between the current density and its driving force, the potential drop across the interface (electrode potential), is given by the Butler-Volmer equation... 

The Butler-Volmer equation written in the form (44) is frequently used in corrosion. It describes the relationship between current density and potential of an electrode reaction under charge transfer control in terms of three easily measurable quantities P, and P, . For large anodic overvoltages (tl/p 1) Eq. (44)... 

With these expressions one can easily derive the Butler-Volmer equation of a mixed electrode corresponding to the corrosion reaction (49) ... 

Equation (1) has a form analogous to the Butler-Volmer equation of electrode kinetics therefore, it is not surprising that the techniques of determinations are analogous in many ways to those for the determination of exchange current density in electrode kinetics (see, for example. Ref. 15 and 16). The corrosion rate measurement techniques can be classified in two ways. First, one can consider the different ways that Eq. (1), or its equivalent, is used to calculate the corrosion current density from measured current-density-polarization data. Second, one can consider the different ways that the current-density-polarization data are measured experimentally. The first classification is used in this chapter. The second classification is discussed briefly in Section II.7. 

For many reactions, the charge transfer is only one elementary step in a sequence of many others. Some substances break chemical bonds and form new ones. Oxygen reduction is a relatively complicated process with several intermediate species corresponding to a sequence of reaction steps. Nevertheless, a corrosion reaction is often ruled by the Butler-Volmer equation, although reaction steps other than the charge transfer may be rate determining as well. 

Friedrich and Filers [113] have proposed a corrosion model of development and derived electron transfer equations based on the Butler-Volmer expression which can be simplified into three cases. Case 1 is when both the forward and reverse processes of developer oxidation are important. Case 2 is when the net rate is limited by the forward rate of developer oxidation. Case 3 corresponds to a rate which is limited by the kinetics of both developer oxidation and silver halide reduction. 

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