Standard Fermi level of redox electron

Fig. 2-39. Gaussian normal distri bution of the probabili density of redox electron levels due to thermal fluctuation of hydrate structures epd)Bx>X) = standard Fermi level of redox electrons.

In transfer equilibrium of redox electrons, the Fermi level of the electrode crm) equals the Fermi level of the redox particles crredox). at the electrode interface. Hence, with the standard Fermi level, of redox electrons, we obtain the... 

Complexation therefore raises the standard Fermi level of redox electrons ep(KEDcs)> provided that the affinity of ligand coordination is greater with the oxidant particle than with the reductant particle (- dGox > - dG c) whereas, the complexation lowers the standard Fermi level of redox electrons Ef(redox)> provided that the affinity of ligand coordination is smaller with the oxidant particle than with the reductant particle (- dGox < - dG o)- With a shift of the standard Fermi level of redox electrons due to complexation, the most probable electron levels esED and cox of the redox particles are also shifted in the same direction. 

The kinetic treatment for the electron transfer of ligand-coordinated redox particles described in Sec. 8.4.1 may, in principal, apply also to the electron transfer of adsorbed redox particles (inner-sphere electron transfer). The contact adsorption of redox particles on metal electrodes requires the dehydration of hydrated redox particles and hence inevitably shifts the standard Fermi level of redox electrons from in the hydrated state to in the adsorbed state. This shift of the Fermi level of redox electrons due to the contact adsorption of redox particles is expressed in Eqn. 8-83 similarly to Eqn. 8-79 for the complexation of redox particles (ligand coordination) ... 

FIGURE 22.2 Electron energy levels for a standard pair of hydrated redox particles and for an intrinsic semiconductor ered = the most probable electron level of oxidant, eox = the most probable electron level of reductant, 8p(redox) = standard Fermi level of redox electrons, 8p = Fermi level of an intrinsic semiconductor, v = valence band edge level, and c = conduction band edge level. 

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. 

The most probable donor level, ered, the most probable acceptor level, eox, and the standard Fermi level, e redox) of redox electrons are characteristic of individual redox particles but the Fermi level, e m dox), of redox electrons depends on the concentration ratio of the reductant to the oxidant, which fact is similar to the Fermi level of extrinsic semiconductors depending on the concentration ratio of the donor to the acceptor. 

It follows from Eqn. 8-53 that the ratio of participation of the conduction band to the valence band in the exchange reaction current depends on the standard Fermi level of the redox electrons relative to the middle level in the band gap at the interface of semiconductor electrode. 

Fig. 8-33. Energy diagram showing a shift of redox electron level due to complexation of reductant and oxidant particles (1) afSnity for complexation is greater with oxidants than with reductants, (2) affinity for complexation is greater with reductants than with oxidants. COMPLEX z ligand-coordinated complex redox particles HYDRATE = simply hydrated redox particles W = probability density of electron states e., ) - standard Fermi level of hydrated redox particles - standard Fermi level of ligand-coordinated...

Fig. 9-19. Electron state density of adsorbed proton/lpndrogen redox particles on metal electrodes (a) the relative concentration of adsorbed reductant hydrogen atoms (Had) will be hitler if the Fermi level ef(h, of electrode is higher than the standard Fermi level of adsorbed redox particles, (b) the relative concentration of adsorbed oxidant...

Fermi level of standard redox electrons in hydrated redox particles... 

Fermi level of standard redox electrons in complexed redox particles Fermi level of standard redox electrons in adsorbed redox particles Fermi level of n-type or p-type semiconductor electrodes quasi-Fermi level of electrons in semiconductor electrodes quasi-Fermi level of holes in semiconductor electrodes energy of a particle i... 

Choi et al. reported the spontaneous reduction of metal ions to metallic form on the sidewalls of the CNTs in aqueous solutions of noble metal ions. They reported that Au and Pt could be deposited spontaneously on the sidewall of the CNTs by a direct redox reaction between the CNTs and metal ions via the immersion of the CNTs in HAuCU (Au +3 and Na2PtCU (Pt +) solutions, respectively. They explained that the principle for the spontaneous reduction of the metal ions on the sidewalls of the CNTs is the difference in the reduction potential between the CNTs and the metal ions. Similarly, the spontaneous formation of Mn02 from MnOJ ions on the CNT sidewall may also be explained by the difference in the reduction potential between the CNT and MnOJ ions. The work function of the CNTs was determined to be nearly 5 eV. The Fermi level of the CNTs is approximately +0.5 V above the potential of the standard hydrogen electrode (SHE), which is well above the reduction potential of Mn04 ions, which is +1.692 V (vs. SHE). The relative potential levels may explain the spontaneous electron transfer from the CNTs to the Mn04 ions. 

The standard redox Fermi energies of the two-one electron transfer step processes are connected with the Fermi level of the overall redox reaction by the relation... 

Fig. 7 Energetic scheme of the components of a DSC. The position of the conduction band of Ti02 and the density of states (DOS) in the bandgap is indicated. Also shown is the photovoltage by difference of the Fermi level of electrons and the redox potential in the electrolyte. At the right are shown the redox potential of conventional hole conductors. In the center is shown ground and excited state of standard dyes. More accurately, the excited and ground states are spread over an energy interval. Energy differences are expressed in eV...

The photoelectrolysis of H2O can be performed in cells being very similar to those applied for the production of electricity. They differ only insofar as no additional redox couple is used in a photoelectrolysis cell. The energy scheme of corresponding systems, semiconductor/liquid/Pt, is illustrated in Fig. 9, the upper scheme for an n-type, the lower for a p-type electrode. In the case of an n-type electrode the hole created by light excitation must react with H2O resulting in 02-formation whereas at the counter electrode H2 is produced. The electrolyte can be described by two redox potentials, E°(H20/H2) and E (H20/02) which differ by 1.23 eV. At equilibrium (left side of Fig. 9) the electrochemical potential (Fermi level) is constant in the whole system and it occurs in the electrolyte somewhere between the two standard energies E°(H20/H2) and E°(H20/02). The exact position depends on the relative concentrations of H2 and O2. Illuminating the n-type electrode the electrons are driven toward the bulk of the semiconductor and reach the counter electrode via the external circuit at which they are consumed for Hj-evolution whereas the holes are dir tly... 

ECb. Evb. Ef. ancl Eg are, respectively, the energies of the conduction band, of the valence band, of the Fermi level, and of the band gap. R and O stand for the reduced and oxidized species, respectively, of a redox couple in the electrolyte. Note, that the redox system is characterized by its standard potential referred to the normal hydrogen electrode (NHE) as a reference point, E°(nhe) (V) (right scale in Fig. 10.6a), while for solids the vacuum level is commonly used as a reference point, E(vac) (eV) (left scale in Fig. 10.6a). Note, that the energy and the potential-scale differ by the Faraday constant, F, E(vac) = F x E°(nhe). where F = 96 484.56 C/mol = 1.60219 10"19 C per electron, which is by definition 1e. The values of the two scales differ by about 4.5 eV, i.e., E(vac) = eE°(NHE) -4-5 eV, which corresponds to the energy required to bring an electron from the hydrogen electrode to the vacuum level. 

Figure 2-41 compares the electron level diagram of intrinsic semiconductors with that of hydrated redox particles at the standard concentration. The two diagrams resemble each other in that the Fermi level is located midway between the occupied level and the vacant level. It is, however, obvious that the occupied and vacant bands for semiconductors are the bands of delocalized electron states, whereas they are the fluctuation bands of localized electron states for hydrated redox particles. 

While the two-state approximation (TSA) introduced in Section 1.3.1 accounts well for many classes of electron-transfer kinetics, there are, of course, situations in which a high density of electronic states in the initial- and final-state manifolds makes it necessary to generalize the TSA expressions given, for example, by Eqs. 31-37. A paramount example is the case of metal or semiconductor electrodes, where one must deal essentially with an electronic continuum [25, 31, 32, 106]. In spite of this complication, one may still obtain expressions with similar form to those shown above when reaction exothermicity is small (i.e., the difference between the electrode Fermi level and the standard potential of the redox species is small compared to /) [25b]. Nevertheless, in the inverted region , at electrodes is generally observed to approach a constant maximum value with increasing driving force (for an exception, see [107]), in contrast to the fall-off predicted in the case of the TSA (see Eq. 27). 

Figure 1.8 Cell schematics for a regenerative solar cell based on (a) an n-type photoelectrode (b) ap-type photoelectrode. The top diagrams show the cell reactions under illumination, the middle diagrams the electronic energy levels and band bending, and the bottom diagrams the cell current-voltage (I-U) characteristics with the photoelectrode and counter electrode (CE) currents shown in the same quadrant. The maximum power point is located at the point on the current-voltage curve at which the rectangle of maximum area may be inscribed in this quadrant. The photovoltage V, the electron and hole quasi-Fermi levels E and fip and the solution Fermi level f o.R, the open-circuit potential Ugc of the photoelectrode and the standard redox potential 17 ° of the 0,R redox couple are also shown.

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