Vacuum scale of electrode potential

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 

Albery W. J. and Archer M. D. (1977), Optimum efficiency of photogalvanic cells for solar energy conversion , Nature 270, 399-402. 

and Sammells A. F. (1980), Faraday Discussions of the Chemical Society, GeneralDiscussionsNo. 70, Photoelecnochemistry, St. Catherine s College, Oxford, 8-10 September 1980. 

Connolly J. S. (ed.). Photochemical Conversion and Storage of Solar Energy, Academic Press, New York. 

Ashokkumar M., Kudo A., Saito N. and Sakata T. (1994), Semiconductor sensitization by RuSi colloids on TiOi electrodes , Chem. Phys. Lett. 229, 383-388. 

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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. 

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. 

The SHE and SCE scales do not allow electrode potentials to be directly compared with the electronic energy levels (such as the band-edge energies of a semiconductor) in the electrode. To do this, we need a scale of electrode potential based, not on a reference electrode, but on a reference electronic energy level. A good choice, which allows different electrodes to be compared in the same solvent, is the local vacuum level of the... 

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

Equation (22) shows that since electrode potentials measure electronic energies, their zero level is the same as that for electronic energy. Equation (22) expresses the possibility of a comparison between electrochemical and UHV quantities. Since the definition of 0 is6 the minimum work to extract an electron from the Fermi level of a metal in a vacuum, the definition of electrode potential in the UHV scale is the minimum work to extract an electron from the Fermi level of a metal covered by a (macroscopic) layer of solvent. ... 

In this chapter we introduce and discuss a number of concepts that are commonly used in the electrochemical literature and in the remainder of this book. In particular we will illuminate the relation of electrochemical concepts to those used in related disciplines. Electrochemistry has much in common with surface science, which is the study of solid surfaces in contact with a gas phase or, more commonly, with ultra-high vacuum (uhv). A number of surface science techniques has been applied to electrochemical interfaces with great success. Conversely, surface scientists have become attracted to electrochemistry because the electrode charge (or equivalently the potential) is a useful variable which cannot be well controlled for surfaces in uhv. This has led to a laudable attempt to use similar terminologies for these two related sciences, and to introduce the concepts of the absolute scale of electrochemical potentials and the Fermi level of a redox reaction into electrochemistry. Unfortunately, there is some confusion of these terms in the literature, even though they are quite simple. 

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. 

Electron transfer is a fast reaction ( 10-12s) and obeys the Franck-Condon Principle of energy conservation. To describe the transfer of electron between an electrolyte in solution and a semiconductor electrode, the energy levels of both the systems at electrode-electrolyte interface must be described in terms of a common energy scale. The absolute scale of redox potential is defined with reference to free electron in vacuum where E=0. The energy levels of an electron donor and an electron acceptor are directly related to the gas phase electronic work function of the donor and to the electron affinity of the acceptor respectively. In solution, the energetics of donor-acceptor property can be described as in Figure 9.6. 

In electrochemistry, it is usual to measure potentials with respect to a stable and reproducible system, known as - reference electrode. For the vast majority of practical electrochemical problems there is no need to determine - absolute potentials. However, this is necessary in cases where one wants to connect the relative electrode potential with the absolute physical quantities of the system, like electronic energies, as is the case of the work function. It is possible to convert all relative values of electrode potential to absolute-scale values and to electronic energies. For aqueous systems the - standard hydrogen electrode potential corresponds to -4.44 V in the physical scale taking electrons at rest in vacuum as reference and the absolute potential is given by the relation T(abs) = T(SHE) + 4.44 [vii]. 

The connection between this "absolute scale of redox potentials and the conventional scale is given by a linear shift of the zero points (shifted by the energy level of the electrons in the standard hydrogen electrode versus the vacuum level) and by an inversion of the sign of this scale. For photoelectrochemical reactions it is convenient to use the absolute scale even if one measures the redox potentials as usual in the conventional scale versus an arbitrarily chosen reference electrode. 

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 the last section it was shown that instead of representing an electrode potential on a relative scale (arbitrarily setting the standard hydrogen electrode potential equal to zero), it is possible to numerically calculate the actual value of the latter, with a reference state of zero energy for the stationary electron at infinity in a vacuum. 

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

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)]...

Absolute potential (also called single electrode potential) — is a hypothetic p. of an isolated - electrode without referring it to any reference electrode. Although it has long been known that only relative - electrode p. can be measured experimentally, numerous attempts were undertaken to determine such a value (see in [i-x]). The problem was also formulated as a search for the hypothetical reference state determined as reckoned from the ground state of - electron in vacuum (a physical scale of energy with the opposite sign). In... 

The redox potential is generally referred to the standard hydrogen potential (SHE), which has an exactly defined energy, E y, relative to the energy of the free electron in vacuum or at infinity. Thus, electrode potentials of redox couples can be expressed on the absolute energy scale according 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... 

For most purposes in electrochemistry, it is sufficient to reference the potentials of electrodes (and half-cell emfs) arbitrarily to the NHE, but it is sometimes of interest to have an estimate of the absolute or single electrode potential (i.e., the potential of a free electron in vacuum). This interest arises, for example, if one would like to estimate relative potentials of metals or semiconductors based on their work functions. The absolute potential of the NHE can be estimated as 4.5 0.1 V, based on certain extrather-modynamic assumptions, such as about the energy involved in moving a proton from the gas phase into an aqueous solution (10, 29). Thus, the amount of energy needed to remove an electron from Pt/H2/H ( = 1) to vacuum is about 4.5 eV or 434 kJ. With this value, the standard potentials of other couples and reference electrodes can be expressed on the absolute scale (Figure 2.1.1). 

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