Vacuum scale potentials

A Preliminary Discussion Absolute or Vacuum-Scale Potentials... 

In calculating this "absolute or "vacuum scale potential of the standard hydrogen electrode, the expression quoted as an electrode potential was... 

The Vacuum Reference The first reference in the double-reference method enables the surface potential of the metal slab to be related to the vacuum scale. This relationship is determined by calculating the workfunction of the model metal/water/adsorbate interface, including a few layers of water molecules. The workfunction, — < ermi. is then used to calibrate the system Fermi level to an electrochemical reference electrode. It is convenient to choose the normal hydrogen electrode (NHE), as it has been experimentally and theoretically determined that the NHE potential is —4.8 V with respect to the free electron in a vacuum [Wagner, 1993]. We therefore apply the relationship... 

Consider the interface between a semiconductor and an aqueous electrolyte containing a redox system. Let the flat-band potential of the electrode be fb = 0.2 V and the equilibrium potential of the redox system o = 0.5 V, both versus SHE. Sketch the band bending when the interface is at equilibrium. Estimate the Fermi level of the semiconductor on the vacuum scale, ignoring the effect of dipole potentials at the interface. 

In a real experiment one uses at least four electrodes (see Fig. 12.2), one counter and one reference electrode on each side, and measures the difference in potential between the two reference electrodes. In principle each reference electrode could be referred to the vacuum scale using the same procedure that was outlined in Chapter 2. However, in practice the required data are not available with sufficient accuracy. Of course, the voltage between the two reference electrodes characterizes the potential difference between the two phases uniquely. It can be converted to an (estimated) scale of inner potential differences by using the energies of transfer of the ions involved. 

However, some electrochemists prefer to call potentials calculated from Eq. (9.2) potentials on the "vacuum scale, rather than an absolute, potential. Thus, "absolute is a loaded word and requires detailed explanation. Some chemists are surprised when one identifies the word electrode potential with (9.1), for they tend, intuitively, to... 

Therefore, by measuring the flatband potential at pzc, one can determine the energy level of the semiconductor band in an electrolyte relative to the absolute scale or the vacuum scale. The pzc of a silicon electrode in aqueous electrolyte is similar to that of SiOi, at about pH 2.2, since the silicon surface is generally covered with a thin layer... 

THE VACUUM SCALE OF ELECTRODE POTENTIAL AND THE CONCEPT OF THE SOLUTION FERMI LEVEL... 

It is often helpful in photoelectrochemistry to locate electronic energy levels in the electrode and solution on a common scale. This appendix explains how this can be achieved by defining the so-called vacuum scale of electrode potential, which is referenced to the energy of an electron in a vacuum. 

Figure 1A3 Relation between the vacuum scale of electron energy E and the standard hydrogen electrode (SHE) scale of electrode potential U.

Since EF = ji , the redox potential on the vacuum scale, Vredox(vac. scale), should give the Fermi level of the electrolyte with respect to vacuum. It is obvious that... 

Although Vredox(vac. scale) is determined as a measure for the Fermi level of a metal which is in equilibrium with a redox couple, it has a unique value for the redox couple, and, therefore, it can be considered as a measure of the electronic energy level of the redox couple on a vacuum scale. Thus, as at a metal/metal or a metal/semiconductor interface, Al p can be determined at the solid phase/electrolyte interface as a difference between M and eVredox(vac. scale), which can be considered as a reverse of the real potential or the effective work function of the redox couple. At equilibrium, the Fermi level of the solid phase and the electronic energy level of the redox couple is the same (/ij1 = /I ) and sometimes the energy level of the redox couple is called the Fermi level of the redox couple in analogy to that of the solid phase.5,23 26 32 54 55 As already mentioned, Fermi statistics is not applicable to the redox couple and, therefore, there is no Fermi level in an electrolyte, but one may accept this terminology with the understanding that the Fermi level of the redox couple actually means the Fermi level of the solid phase in equilibrium with the redox couple. 

The potential of the couple on the vacuum scale is related to that of the NHE by the amount of work required to transfer an electron from the NHE to vacuum ... 

The potential on an electrode can also be expressed in a different scale, used by some theoretical electrochemists. This is the so-called vacuum scale of electrode potentials (cf. Bockris and Argade). Thus, it has been shown by Trassatti and others that if one adds 4.5 V to the potential on the hydrogen scale already described, then one would obtain the value of the potential for the transfer of electrons from a vacuum level to the oxidized ion in solution to form the reduced ion of the overall reaction. 

Thus, from Eq. (106), the chemical potential of an electron in solution is equal to the negative of the vacuum scale redox potential. 

Thus, /xT is not equal to the Fermi energy in a semiconductor, which reduces the validity of equating -Co Vredox(vacuum scale) with the Fermi energy at the solution (for it is a chemical, not an electrochemical, potential). 

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