Redox electron transfer

As described in the introduction, certain cosurfactants appear able to drive percolation transitions. Variations in the cosurfactant chemical potential, RT n (where is cosurfactant concentration or activity), holding other compositional features constant, provide the driving force for these percolation transitions. A water, toluene, and AOT microemulsion system using acrylamide as cosurfactant exhibited percolation type behavior for a variety of redox electron-transfer processes. The corresponding low-frequency electrical conductivity data for such a system is illustrated in Fig. 8, where the water, toluene, and AOT mole ratio (11.2 19.2 1.00) is held approximately constant, and the acrylamide concentration, is varied from 0 to 6% (w/w). At about = 1.2%, the arrow labeled in Fig. 8 indicates the onset of percolation in electrical conductivity. 

Metal oxides possess multiple functional properties, such as acid-base, redox, electron transfer and transport, chemisorption by a and 71-bonding of hydrocarbons, O-insertion and H-abstract, etc. which make them very suitable in heterogeneous catalysis, particularly in allowing multistep transformations of hydrocarbons1-8 and other catalytic applications (NO, conversion, for example9,10). They are also widely used as supports for other active components (metal particles or other metal oxides), but it is known that they do not act often as a simple supports. Rather, they participate as co-catalysts in the reaction mechanism (in bifunctional catalysts, for example).11,12... 

Fig. 4-18. Electron levels of an electronic electrode in equilibrium of redox electron transfer eojenox s> = redox electron at equilibrium e ) = electrons in metal electrode .q = electrode potential in equilibrium of electron transfer.

The electrode potential in the equilibrium of redox electron transfer may also be defined by the free enthalpy change in the reaction of the hydrated redox particles with the standard gaseous electron eisro) as shown in Eqn. 4—20 ... 

Figure 5-64 shows the band edge potential for compound semiconductor electrodes in aqueous solutions, in which the standard redox potentials (the Fermi levels) of some hydrated redox particles are also shown on the right hand side. In studying reaction kinetics of redox electron transfer at semiconductor electrodes, it is important to find the relationship between the band edge level (the band edge potential) and the Fermi level of redox electrons (the redox potential) as is described in Chap. 8. 

To illustrate this relationship to the normal hydrogen electrode, we consider an electrode reaction of redox electron transfer as shown in Eqn. 6-12 ... 

Fig. 6-6. Electrochemical cell composed of an elecirode of redox electron transfer on the right hand side and a normal hydrogen electrode on the left hand side.

For redox electron transfer reactions, the transfer of electrons from an electrode to an oxidfmt particle to form a reductant particle is the cathodic reaction (the electron-accepting reduction of oxidants) and the transfer of electrons from a reductant particle to an electrode to form an oxidant particle is the anodic reaction... 

As the adsorption affinity of redox particles on the electrode interface increases, the hydrated redox particles is adsorbed in the dehydrated state (chemical adsorption, contact adsorption) rather than in the hydrated state (ph3 ical adsorption) as shown in Fig. 7-2 (b). Typical reactions of redox electron transfer of dehydrated and adsorbed redox particles on electrodes are the hydrogen and the oxygen electrode reactions in Eqns. 7-6 and 7-7 ... 

Figure 8-2 illustrates the distribution of the state density of electrons in the metal electrode and in the redox particles on both sides of the electrode interface in equilibrium with redox electron transfer. 

Figures 8-5 and 8-6 are energy diagrams, as functions of electron energy e imder anodic and cathodic polarization, respectively, for the electron state density Dyf.t) in the metal electrode the electron state density AtEDox(c) in the redox particles and the differential reaction current ((e). From these figures it is revealed that most of the reaction current of redox electron transfer occurs in a narrow range of energy centered at the Fermi level of metal electrode even in the state of polarization. Further, polarization of the electrode potential causes the ratio to change between the occupied electron state density Dazc/itnu md the imoccupied...

Fig. 8-5. Electron state density in a metal electrode and in hydrated redox particles, and anodic and cathodic currents of redox electron transfer under cathodic polarization n s cathodic overvoltage (negative) i = anodic current i = cathodic current. [From (lerischer, I960.]...

It is characteristic of metal electrodes that the reaction current of redox electron transfer, under the anodic and cathodic polarization conditions, occurs mostly at the Fermi level of metal electrodes rather than at the Fermi level of redox particles. In contrast to metal electrodes, as is discussed in Sec. 8.2, semiconductor electrodes exhibit no electron transfer current at the Fermi level of the electrodes. 

Fig. 8-8. Energy levels for redox electron transfer reaction at a metal electrode (a) in equilibrium, (b) in anodic polarization with reao tion rate determined by interfadal electron transfer, (c) anodic polarization with reaction rate determined by both interfadal electron transfer and diffusion of hydrated partides. EF0)Eooxj.a= Fenni level of redox electrons at an interface.

Fig. 8-10. Anodic reaction current vs. potential curve for a redox electron transfer of hydrated redox particles at a metal electrode iibi = limiting diffusion current of redox particles 1/3 = potential at which reaction current is half the limiting diffusion current ( = 0.6iiin). [From Bard-Paulkner, 1980.]...

We consider a simple redox electron transfer of hydrated redox particles (an outer-sphere electron transfer) of Eqn. -1 at semiconductor electrodes. The kinetics of electron transfer reactions is the same in principal at both metal and semiconductor electrodes but the rate of electron transfer at semiconductor electrodes differs considerably from that at metal electrodes because the electron occupation in the electron energy bands differs distinctly with metals and semiconductors. 

Fig. 8-11. Electron state density in a metal electrode, semiconductor electrode, and redox particles in equilibrium with a redox electron transfer reaction. [From Glerischer, 1961.]...

Fig. 8-14. Electron state density for a redox electron transfer reaction and profile of electrostatic inner potential, across an electrode interface = potential...

Fig. 8-16. Electron state density for a redox electron transfer reaction of h3rdrated redox particles at semiconductor electrodes (a) in the state of band edge level pinning and (b) in the state of Fermi level pinning dashed curve = band edge levels in reaction equilibrium solid curve = band edge levels in anodic polarization e p,sq = Fermi level of electrode in anodic polarization e v and c c = band edge levels in anodic polarization.

Fig. 8-16. Electron state density in a semiconductor electrode and in hjrdrated redox partides, rate constant of electron tunneling, and exchange redox current in equilibrium with a redox electron transfer reaction for which the Fermi level is close to the conduction band edge eF(sc) = Fermi level of intrinsic semiconductor at the flat band potential 1. 0 (tp.o) = exchange reaction current of electrons (holes) (hvp)) - tunneling rate constant of electrons (holes).

Fig. S-19. Surface states participating in reaction equilibrium of redox electron transfer at a semiconductor electrode with a wide band gap t = smiace state level i c = exchange current via surface states.

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... 

Fig. 8-21. State density of redox electrons and reaction current ibr a redox electron transfer at a semiconductor electrode further polarized beyond that in Fig. 8-20 in anodic direction T =T gc.

Fig. 8-23. Energy diagram for a redox electron transfer via the conduction band of semiconductor electrode (a) anodic redox electron transfer, (b) cathodic redox electron transfer.

Fig. 8-29. Energy diagram for the most probable electron level, eck, of oxidant particles and the conduction band edge level, Bq, in a cathodic redox electron transfer via the conduction band cathodic current is maximum when cqx equals e. ...

On account of these effects, the contact adsorption of redox particles frequently accelerates the redox electron transfer, as compared with the direct electron transfer between the hydrated redox particle and the electrode. In other words, the reaction current due to redox electron transfer will be greater with adsorbed redox particles than with simply hydrated redox particles if the contact adsorption shifts the energy level of redox electrons in the favorable direction. 

Fig. 8-38. Redox electron transfer at film-covered metal electrodes (a) transfer of redox electionB across a thin semiconductor film (direct tunneling transfer of electrons), (b) transfer of redox elections throu a thidc semiconductor film (indirect transfer of elections through electron levels in a thick film).

For the transfer of redox electrons (inner-sphere electron transfer) in which redox particles are adsorbed on a thin superficial film that covers a metal electrode, the transfer current of redox electrons is not always decreased but rather increased by the presence of the thin film. Such an increase in the reaction ciurent will occur, if the film acts as a reaction catalyst providing the adsorbed state of redox particles favorable for the redox electron transfer. For example, the anodic oxidation of carbon monoxide is catalyzed by the presence of an anodic oxide film on... 

Figure 8-42 illustrates the anodic and cathodic polarization curves observed for an outer-sphere electron transfer reaction with a typical thick film on a metallic niobium electrode. The thick film is anodically formed n-type Nb206 with a band gap of 5.3 eV and the redox particles are hydrated ferric/ferrous cyano-complexes. The Tafel constant obtained from the observed polarization curve is a- 0 for the anodic reaction and a" = 1 for the cathodic reaction these values agree with the Tafel constants for redox electron transfers via the conduction band of n-lype semiconductor electrodes already described in Sec. 8.3.2 and shown in Fig. 8-27. 

Figure S-4S shows the polarization curves observed, as a function of the film thickness, for the anodic and cathodic transfer reactions of redox electrons of hydrated ferric/ferrous cyano-complex particles on metallic tin electrodes that are covered with an anodic tin oxide film of various thicknesses. The anodic oxide film of Sn02 is an n-type semiconductor with a band gap of 3.7 eV this film usually contains a donor concentration of 1x10" ° to lxl0 °cm °. For the film thicknesses less than 2.5 nm, the redox electron transfer occurs directly between the redox particles and the electrode metal the Tafel constant, a, is close to 0.5 both in the anodic and in the cathodic curves, indicating that the film-covered tin electrode behaves as a metallic tin electrode with the electron transfer current decreasing with increasing film thickness.

Fig. 8-43. Anodic and cathodic polarization curves observed for a redox electron transfer at metallic tin electrodes covered with an anodic oxide Sn02 film of various thicknesses d in a basic solution reaction is a redox electron transfer of 0.25 M Fe(CN)6 A).25 M Fe(CN)6 in 0.2 M borate buffer solution of pH 9.1 at 25°C. d = film thickness dj = 2 nm ...

Figure 8-44 shows the exchange currents of the redox electron transfer illustrated in Fig. 8-43 as a function of film thickness. It is obvious in this figure that the exchange current decreases steeply in the range of thin films, but much less in the range of thick films. The results in Fig. 8—44 indicates that the direct electron tunneling occurs only when the film is sufficiently thin. 

Fig. 8-44. Exchange current of a redox electron transfer observed in Fig. 8-43 as a function of thidmess of an oxide-film on metallic tin electrodes the scale of film thickness differs for thin films and for thick films. [From Kapusta-Hackerman, 1981.1...

Charge transfer reactions on semiconductor electrodes proceed under the condition of anodic and cathodic polarization in which the Fermi level epfsc) is different either from the Fermi level Eputicox) of redox electron transfer reactions or from the equivalent Fermi level ep,ioN) of ion transfer reactions. For redox electron transfer reactions, thermodynamic requirement for the anodic and cathodic reactions to proceed is given by the following inequalities ... 

Under the condition of photoexcitation, the quasi-Fermi level, instead of the original Fermi level, determines the possibility of redox electron transfer reactions. The thermodynamic requirement is then given, for the transfer of cathodic electrons to proceed from the conduction band to oxidant particles, by the inequality of Eqn. 10-7 ... 

The catalyst constitutes an electron shuttle between the electrode and the solution, where it is engaged in a direct redox electron transfer with the substrate. This type of catalysis is termed redox catalysis. 

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