Electrode kinetics elementary equations

This is a one-valent electrode reaction. The stoichiometric number of the electron is one, which is usually assumed for the elementary charge transfer step. Reduced and oxidized components have different solvation numbers. The general kinetic equations vsdll be developed for this reaction. 

The following description is confined to systems that follow an E mechanism at a metallic electrode. As is usual in most documents dealing with this aspect of electrochemistry, we have taken a redox reaction involving only two species. Ox and Red, with vox = vRed = 1/ but possibly v = n. Flowever, according to kinetic theory and mechanism, an elementary step can only involve few species and in particular the exchange of several electrons is unlikely in such a step. When a redox couple involves two or more exchanged electrons, then the overall number n is often involved in the final equation of the current-potential curve. However, all the kinetic equations must be written for each elementary step involved. This generally complex task will not be tackled in this document. 

The values of the Tafel coefficients and j8c depend on the mechanism of the electrode reactions, which often consist of several elementary steps (Section 5.1). It is however not necessary to know the mechanism in order to apply the Butler-Volmer equation. Indeed, equation (4.36) describes the charge-transfer kinetics in a global, mechanism-independent fashion, making reference to three easily measured quantities t o, nd The formulae (4.37) and (4.38) then define the anodic and cathodic Tafel coefficients ... 

Eor very high exchange current densities (i.e., rapid reactions), a linearized form of Eq. 27 can often be used. For very slow reaction kinetics, either the anodic or cathodic term dominates the kinetics, and so the other term is often ignored, yielded what is known as a Tafel equation for the kinetics. Often, more complicated expressions than that of Eq. 27 are used. For example, if the elementary reaction steps are known, one can write down the individual steps and derive the concentration dependence of the exchange current density and the kinetic equation. Other examples include accounting for surface species adsorption or additional internal or external mass transfer to the reaction site [9]. All of these additional issues are beyond the scope of this chapter, and often an empirically based Butler-Volmer equation is used for modeling the charge transfer in porous electrodes. 

More recently, Wang et al. [28] derived an intrinsic kinetic equation for the four-electron (4e ) oxygen reduction reaction (ORR) in acidic media, by using free energies of activation and adsorption as the kinetic parameters, which were obtained through fitting experimental ORR data from a Pt(lll) rotating disk electrode (RDE). Their kinetic model consists of four essential elementary reactions (1) a dissociative adsorption (DA) (2) a reductive adsorption (RA), which yields two reaction intermediates, O and OH (3) a reductive transition (RT) from O to OH and (4) a reductive desorption (RD) of OH, as shown below [28] (Reproduced with permission from [28]). 

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