Energy Levels of Redox Couples

Usually it is thought that electron transfer can take place only between electronic energy states of equal energies, one being occupied and the other vacant. Gumey applied this concept for the electrode kinetics at a metal electrode and obtained the following rate expression  

In Sections II and III we correlated the electronic energy level of the solid phase, Ep, and that of electrolyte, This com- 

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The Gaussian distribution is most often used in photoelectrochemistry to describe the energy levels of redox couples and to discuss qualitatively the possibility of the reaction. The major difficulty of this model is that it cannot explain the Tafel behavior... 

Fig. 5.8 The energy levels of n-type M0S2 at the flat band potential relative to the positions of various redox couples in CH3CN/[n-Bu4N]C104 solution. The valence band edge of the semiconductor as revealed by accurate flat band potential measurement is at ca. +1.9 V vs. SCE implying that photooxrdations workable at Ti02 are thermodynamically possible at illuminated M0S2 as well. (Reproduced with permission from [137], Copyright 2010, American Chemical Society)...

The energy levels of several redox couples as well as the positions of the band edges of typical semiconductors in equilibrium with aqueous electrolyte (pH 7) are compared in Fig. 5.59. 

Figure 3.6 shows the various relationships between the energy levels of solids and liquids. In electrolytes three energy levels exist, Ep, redox, Eox and Ered- The energy levels of a redox couple in an electrolyte is controlled by the ionization energy of the reduced species Ered, and the electron affinity of the oxidized species Eox in solution in their most probable state of solvation due to varying interaction with the surrounding electrolyte, a considerable... 

Figure 30(a) concerns the EE mechanism for the reaction O + 2 e = R. The solid curve represents the standard free energy profile pertaining to the standard potential E° of the redox couple O/R. In this case, the energy levels of the initial and the final state are equal by definition. Well... 

Hetero junctions, forming a Schottky barrier like a metal-semiconductor junction, normally change the energy levels of conduction and valence bands. When the Fermi level of the semiconductor equilibrates with the energy level of the redox couple in the solution, the electric energy level at the surface is pinned and a depletion layer is formed. This is postulated since the rectified current can be observed at semiconductor plate electrodes. The bending of the band in the semiconductor at the surface can be described as a solution of the one-dimensional Poisson-Boltzmann equation... 

Fig. 16.9 CB and VB energy levels of several semiconductors. (The semiconductors are in contact with aqueous electrolyte at pH 1. The energy scale is indicated in electron volts using either the normal hydrogen electrode (NHE) or vacuum level as reference. On the right the standard potentials of several redox couples are presented against the standard hydrogen electrode potential.) [Reprinted by permission from Macmillan Publishers Ltd [Nature] (Gratzel 2001), copyright (2001)]...

Fig. 42. Distribution functions Sox (E) and SIei(E) for electronic energy levels of a redox couple in the electrolyte.

Jsc, and (2) the open-circuit photovoltage, which is denoted as Vbc- Jsc is generally related to the mobility of the redox couple in an electrolyte. Vqc is basically the energy difference between the energy level of the semiconductor electrode and the redox potential using a redox couple, as shown in Figure 15.2. A fill factor, which is denoted as FF, is reflected in the overall performance of a PEC cell. The conversion efficiency is the most important parameter in terms of the practicality of the PEC cells. This review focuses on Jsc in order to clarify the relationship between Jsc and the viscosity of the RTELs. 

FIGURE 1.4. Electron energy levels of a redox couple with respect to the standard hydrogen electrode and the vacuum level. 

The measured potential Vm, and thus jEf and K. can be varied through external polarization. Vm is the applied potential when the electrode is externally polarized and is the open-circuit potential without external polarization. When the semiconductor has no excess charge, there is no space charge region and the bands are not bent. The electrode potential under this condition is called the flatband potential Vn,. The flatband potential is an important quantity for a semiconductor electrode because it connects the energy levels of the carriers in the semiconductor to those of the redox couple in the electrolyte and it connects the paramete s that can be experimentally determined to those derived from solid-state physics and electrochemistry. It can generally be expressed as... 

FIGURE 2.34. Examples of the energetic positions of the band edges determined for a number of silicon/electrolyte interfaces. The energy levels of the redox couples related to Si and H2O are also plotted. 

Deposition of a small amount of noble metals such as Cu, Pt, and Au increases the kinetics of redox reactions on silicon electrodes as shown in Fig. 6.3. Deposition of equivalent of 1 to 10 monolayers of Pt on silicon surface results in a shift of about 0.2V of the onset potential for hydrogen evolution to the positive direction. Because the flatband potential does not change with the Pt deposition, the enhanced hydrogen reaction kinetics is due to the catalytic effect of the deposited metal. The energy levels of the deposited metal grains are considered to lie in the middle of the band gap and communicate favorably to the surface states both energetically and spatially. The photovoltage of n-Si coated with sparsely scattered Pt islands has been found to increase proportionally to the inaease in the potential of the redox couple. Noble metal islands effectively collect photoelectrons and thus prevent the oxidation of the silicon surface by the photoelectrons. 

We are now in a position to relate the electronic energy levels of the solution and the electrode on the same scale. It follows from the definition of absolute electrode potential and its value for the SHE, given in eq. 1A.14, that the solution Fermi level qr of a redox couple 0,R is related to its electrode potential Uq r (SHE) on the SHE scale by... 

For all types of cells, the position of the valence and conduction bands of the semiconductor relative to the redox energy levels of the redox couple is an important parameter with regard to estimate the efficiency of the cell in energetic terms. 

Figure 1. Determination of the position of energy levels of an electron in the solution containing a redox couple. E is the internal energy and G is the free energy.

Now let us turn to the semiconductor/electrolyte interface, which is our main concern. In the electrolyte, there are no electrons nor holes but oxidized and/or reduced forms of a redox couple. Thus, the Fermi statistics developed for the solid state phase are not applicable and rather careful consideration of the electronic energy level of the electrolyte is required. 

In electrochemistry the energy level of a solution is represented by the redox potential. The measurement of the redox potential is carried out in an arrangement schematically shown in Fig. 3.21 The electrode M is in electrochemical equilibrium with a redox couple... 

Thus, is a measure of the energy level of an electron in metal M with respect to that in M,. In other words, E represents the energy level of the redox couple with respect to a reference electrode since ji = jjfi, where /le is the electrochemical potential of electron in a solution S, and is called a redox potential. For the convention, E with respect to the hydrogen electrode is most often used. Once a value with respect to the hydrogen electrode or any other reference electrode is known, a value with respect to some other reference electrode is easily calculated by using... 

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