Anodes transfer

The quantity a is the anodic transfer coefficient-, the factor l/F was introduced, because Fcf> is the electrostatic contribution to the molar Gibbs energy, and the sign was chosen such that a is positive - obviously an increase in the electrode potential makes the anodic reaction go faster, and decreases the corresponding energy of activation. Note that a is dimensionless. For the cathodic reaction ... 

Both contributions to the current obey the Butler-Volmer law. The current flowing through the conduction band has a vanishing anodic transfer coefficient, ac = 0, and a cathodic coefficient of unity, /3C — 1. Conversely, the current through the valence band has av — 1 and j3v = 0. Real systems do not always show this perfect behavior. There can be various reasons for this we list a few of the more common ones ... 

The notation of the transfer coefficients differs in many sources. Some texts use p or (1-P) in place of a. Others use a for the anodic transfer coefficient and p for the cathodic transfer coefficient. Transfer coefficients are typically close to... 

From the flow of electric charge it follows that the cathodic transfer of metal ions requires the electrode to accept electrons from an external cell circuit, and that the anodic transfer of metal ions requires the electrode to donate electrons to an external cell circuit. No electron transfer, however, takes place across the electrode interface this is the reason why no electrons are involves in the metal ion transfer reactions in Eqns. 7-3 and 7-4. 

Next, we consider the anodic reaction current of redox electron transfer via the conduction band, of which the exchange reaction current has been shown in Fig. 8-16. Application of a slight anodic polarization to the electrode lowers the Fermi level of electrode fix>m the equilibrium level (Ep(sc)( n = 0) = eiiOTSDca)) to a polarized level (ep(8C)( n) = ep(REDox)- n)withoutchanging at the electrode interface the electron level relative to the redox electron level (the band edge level pinning) as shown in Fig. 8-20. As a result of anodic polarization, the concentration of interfacial electrons, n, in the conduction band decreases, and the concentration of interfadal holes, Pm, in the valence band increases. Thus, the cathodic transfer current of redox electrons, in, via the conduction band decreases (with the anodic electron im ection current, ii, being constant), and the anodic transfer current of redox holes, (p, via the valence band increases (with the cathodic hole injection... 

Under the condition of band edge level pinning, where the interfacial electron level of electrode relative to the redox electron level of redox particles is imchanged, the level differences of ej - ered and ej. - eqx remain constant irrespective of any change of the electrode potential. Consequently, the anodic transfer current of redox electrons, in(T ), in Eqn. 8—60 is independent of the overvoltage and remains equal to the exchange current ia.o as expressed in Eqn. 8-62 ... 

As shown in Fig. 8-34, when the most probable electron level of the reductant particle is higher in the ligand-coordinated state cred(chydrated state ereix i). ibe transfer of anodic electrons occurs at higher energy levels (at less anodic potentials) with the ligand-coordinated reductant particle than with the simply hydrated reductant particle. In such a case the complexation of redox particles will accelerate the anodic transfer of redox electrons. 

Fig. 8-34. Anodic transfer of redox electrons of simply hydrated reduc-tants and of ligand-oooidinated complex reductants at a metal electrode (1) anodic reaction of complex reductants takes place at less anodic potentials, (2) anodic reaction of hydrated reductants can not occur unless at more anodic potentials where CRsnaq) is dose to Cp(M).

The effects of complexation of redox particles on the redox reaction kinetics are frequently more evident with semiconductor electrodes than with metal electrodes, since the transfer of electrons takes place at the band edge levels rather than at the Fermi level of electrodes. For example, the anodic transfer of... 

Using Eqn. 9-4 for the activation energy, we obtain the anodic transfer current, r, of metallic ions as given by Eqn. 9-6 ... 

Figure 9—4 shows the polarization curves observed for the transfer reaction of cadmium ions (Cd Cd ) at a metallic cadmium electrode in a sulfuric acid solution. It has been proposed in the literature that the transfer of cadmium ions is a single elemental step involving divalent cadmium ions [Conway-Bockris, 1968]. The Tafel constant, a, obtained from the observed polarization curves in Fig. 9-4 agrees well with that derived for a single transfer step of divalent ions the Tafel constant is = (1- P) 1 in the anodic transfer and is a = z p = 1 in the cathodic transfer. 

If the anodic anion transfer (anionic adsorption, Eqn. 9-13a) to form an adsorbed metallic ion complex is the rate-determining step, the Tafel constant, a = 1 - p, win be obtained from Eqn. 9-14. If the anodic transfer of the adsorbed metallic ion complex (desorption of complexes, Eqn. 9-13b) is the rate-determining step, the Tafel constant, a = 2 - p, will be obtained from Eqns. 9-16 and 9-17. Similarly, if the cathodic anion transfer (anionic desorption, Eqn. 9-13a) is determining the rate, the Tafel constant in the cathodic reaction, a = 1 p, will be obtained from Eqns. 9-15 and 9-16 and if the cathodic transfer of a metallic ion complex (adsorption of complexes, Eqn. 9-13b) is determining the rate, the Tafel constant, a-sp, will be obtained from Eqn. 9-18. In this discussion we have assumed Pi = Ps P then, Eqns. 9-19 and 9-20 follow ... 

Equation 9—49 is the anodic transfer of surface cation into aqueous solution (cation dissolution) and Eqn. 9-60 is the anodic oxidation (hole capture) of surface anion producing molecules ofX2, i (e.g. gaseous oxygen molecules irom oxide ions). Electric neutrality requires that the rate of cation dissolution equals the rate of anion oxidation hence, the rate of the oxidative dissolution of semiconductor electrode can be represented by the anodic hole current for the oxidation of surface anions. 

Fig. 10-13. Anodic transfer of pho-toexdted boles (minority charge carrier) at an n>type semiconductor electrode E( -e 9o/e) = electrode potential E% (= — c /e) = potential of the valence band edge B02 (= - = equilibrium...

Fig. 10-14. Energy levels and polarization curves (current vs. potential) for anodic transfer ofphotoexdted holes in oxygen reaction (2 HgO. -t- 4h O24 4 H. ) on a metal electrode and on an n-type semiconductor electrode j = anodic reaction current ep(02 20)- Fermi level of oxygen electrode reaction dCpi, = gain of photoenergy q = potential for the onset of anodic photoexdted ox en reacti . 4 pi, (=-Ae.. le) = shift of potential for the onset of anodic oxygen reaction from equilibrium oxygen potential in the negative direction due to gain of photoenergy in an n-type electrode Eib = flat band potential of an n-type electrode.

A shift of the flat band potential due to photoexcitation of the type shown in Fig. 10-18 results from the capture of holes in the surface state level, e , on the electrode as shown in Fig. 10-19. We now consider a dissolution reaction involving the anodic transfer of ions of a simple elemental semiconductor electrode according to Eqns. 10-24 and 10-25 ... 

Fig. 10-23. Energy levels and polarization curves for a redox reaction of anodic redox holes at a photoexdted n-type electrode and at a dark p-type electrode of the same semiconductor curve (1) = polarization curve of anodic transfer of photoexdted holes at an n-type electrode curve (2)= polarization curve of anodic transfer of holes at a p-type electrode in the dark (equivalent to a curve representing anodic current as a function of quasi-Fermi level of interfadal holes in a photoexdted n-type electrode) i = anodic transfer current of holes Eredox = equilibriiun potential of redox hole transfer N = anodic polarization at potential n (t) of a photoexdted n-type electrode P = anodic polarization at potential pE(i) of a dark p-type electrode.

Figure 10-30(c) applies to the photoexcited cell, where oxj en evolution proceeds via the anodic transfer of holes at the n-type anode and hydrogen evolution proceeds via the cathodic transfer of electrons at the p-type cathode. In order for the photoelectrolytic decomposition of water to proceed in such a cell, the edge level of the valence band sCy of n-type anode needs to be lower than the Fermi level tr(02ai20) of oxygen redox reaction and the edge level of the conduction band p c of p-type cathode needs to be higher than the Fermi level of... 

On the mixed electrode of metallic iron immersed in acidic solutions, the anodic and cathodic charge transfer reactions (the anodic transfer of iron ions and the cathodic transfer of electrons) proceed across the electrode interface, at which the anodic ciurent (the positive charge current) is exactly balanced with the cathodic current (the negative charge current) producing thereby zero net current. 

The potential of a mixed electrode at which a coupled reaction of charge transfer proceeds is called the mixed electrode potential , this mixed electrode potential is obviously different from the single electrode potential at which a single reaction of charge transfer is at equilibrium. For corroding metal electrodes, as shown in Fig. 11—2, the mixed potential is often called the corrosion potential, E . At this corrosion potential Eemt the anodic transfer current of metallic ions i, which corresponds to the corrosion rate (the corrosion current ), is exactly balanced with the cathodic transfer current of electrons for reduction of oxidants (e.g. hydrogen ions) i as shown in Eqn. 11-4 ... 

Equation 11-6 corresponds to the affinity for the reaction of metallic corrosion. As described in Chaps. 8 and 9, the anodic transfer current i of metal ions and the cathodic transfer current i of electrons across the interface of corroding metallic electrodes are, respectively, given in Eqns. 11-7 and 11-8 ... 

Figure 11-7 shows the polarization curve of an iron electrode in an acidic solution in which the anodic reaction is the anodic transfer of iron ions for metal dissolution (Tafel slope 40 mV/decade) the cathodic reaction is the cathodic transfer of electrons for reduction of hydrogen ions (Tafel slope 120 mV /decade) across the interface of iron electrode. 

In the active state, the dissolution of metals proceeds through the anodic transfer of metal ions across the compact electric double layer at the interface between the bare metal and the aqueous solution. In the passive state, the formation of a thin passive oxide film causes the interfadal structure to change from a simple metal/solution interface to a three-phase structure composed of the metal/fUm interface, a thin film layer, and the film/solution interface [Sato, 1976, 1990]. The rate of metal dissolution in the passive state, then, is controlled by the transfer rate of metal ions across the film/solution interface (the dissolution rate of a passive semiconductor oxide film) this rate is a function of the potential across the film/solution interface. Since the potential across the film/solution interface is constant in the stationary state of the passive oxide film (in the state of band edge level pinning), the rate of the film dissolution is independent of the electrode potential in the range of potential of the passive state. In the transpassive state, however, the potential across the film/solution interface becomes dependent on the electrode potential (in the state of Fermi level pinning), and the dissolution of the thin transpassive film depends on the electrode potential as described in Sec. 11.4.2. 

In the stationary state of anodic dissolution of metals in the passive and transpassive states, the anodic transfer of metallic ions metal ion dissolution) takes place across the film/solution interface, but the anodic transfer of o Q en ions across the Qm/solution interface is in the equilibrium state. In other words, the rate of film formation (the anodic transfer oS metal ions across the metal lm interface combined with anodic transfer of osygen ions across the film/solution interface) equals the rate of film dissolution (the anodic transfer of metal ions across the film/solution interface combined with cathodic transfer of oitygen ions across the film/solution interface). 

Thus, in the stationary state, the rate of anodic transfer of metal ions across the metal/film interface equals the rate of anodic transfer of metal ions across the film/solution interface this rate of metal ion transfer represents the dissolution rate of the passive film. The thickness of the passive film at constant potential remains generally constant with time in the stationary state of dissolution, although the thickness of the film depends on the electrode potential and also on the dissolution current of the passive film. 

For metallic iron and nickel electrodes, the transpassive dissolution causes no change in the valence of metal ions during anodic transfer of metal ions across the film/solution interface (non-oxidative dissolution). However, there are some metals in which transpassive dissolution proceeds by an oxidative mode of film dissolution (Sefer to Sec. 9.2.). For example, in the case of chromium electrodes, on whidi the passive film is trivalent chromium oxide (CrgOj), the transpassive dissolution proceeds via soluble hexavalent chromate ions. This process can be... 

The equilibrium potential value was 0.683 V vs. SHE. Assuming that the reaction is first order with respect to hydroquinone, determine the anodic transfer coefficient and exchange current density. (Gokjovic)... 

Although the anodic term is dependent both on the hydrogen peroxide concentration and on the hydroxide ions concentration, the theoretically predicted value of the anodic transfer coefficient, i.e. 1, is twice that at the experimentally observed value. Moreover, Equation 4.36 predicts that the anodic current depends on the concentration of dissolved oxygen, which is not observed experimentally. When k 2 k3 is assumed, this mechanism also should consequently be rejected. 

Here subscripts a and c denote anode and cathode respectively, iref is the reference exchange current density, y is the concentration dependence exponent, [ ] and [ ]ref represent the local species concentration and its reference concentration, respectively. Anode transfer current, Ra, is the source in the electric potential equations at the anode/electrolyte interface with positive sign on membrane (electrolyte) side and negative sign on solid (anode) side. Similarly, near the cathode interface, the source on membrane (electrolyte) side is negative of the cathode transfer current, Rc and that on solid (cathode) side is positive of Rc. The activation over-potentials, in Equations (5.35) and (5.36) are given by... 

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