Electrochemical Potential of Electrons

At open-circuit, the current in the cell is 2ero, and species in adjoining phases are in equilibrium. Eor example, the electrochemical potential of electrons in phases d and P are identical. Furthermore, the two electrochemical reactions are equilibrated. Thus,... 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

As already noted the electrochemical potential of electrons in a metal, jl, is related to the Galvani potential q> via ... 

Figure 5.17. Schematic representation of a metal crystallite deposited on YSZ and of the changes induced in its electronic properties upon polarizing the catalyst-solid electrolyte interface and changing the Fermi level (or electrochemical potential of electrons) from an initial value p to a new value p -eri30 31 Reprinted with permission from Elsevier Science.

Figure 5.20. Left Schematic of an O2 conducting solid electrolyte cell with fixed P02 and PO2 values at the porous working (W) and reference (R ) electrodes without (top) and with (bottom) ion backspillover on the gas exposed electrodes surfaces, showing also the range of spatial constancy of the electrochemical potential, PQ2-, of O2. Right Corresponding spatial variation in the electrochemical potential of electrons, ]Ie(= Ef) UWR is fixed in both cases to the value (RT/4F)ln( P02 /pc>2 ) also shown in the relative position of the valence band, Ev, and of the bottom of the conduction band, Ec, in the solid electrolyte (SE) numerical values correspond to 8 mol% Y203-stabilized-Zr02, pc>2=10 6 bar, po2=l bar and T=673 K.32 Reproduced by permission of The Electrochemical Society.

One might righteously ask why this close and preferential connection exists between the r vs and the r vs po dependencies. The answer is straightforward and has simply to do with the definitions of O and Fermi level EF (or electrochemical potential of electrons j (=EF))7 which are connected via ... 

The common underlying principle was shown in Figure 11.2. The electrochemical potential of electrons jl e(=Ep, the Fermi level) in the metal catalyst is fixed at that of the Fermi level of the support.37 This is valid both for electrochemically promoted model catalysts (left) and for seminconducting or ion-conducting-supported metal nanoparticles (right). 

On the other hand, the electrochemical potentials of electrons, pe, oxygen ions, jIo2, and gaseous oxygen, po2 are related via the charge transfer equilibrium at the three-phase-boundaries (tpb) metal-support-gas38"40 ... 

Is work function (O), Fermi level EF or electrochemical potential of electrons jJ more relevant for describing NEMCA ... 

Fw electrochemical potential of electrons in the working catalyst-electrode... 

In electron emission from a metal into vacuum, primarily electrons from the highest occupied level are extracted. Therefore, the work function involved in this act, under the assumptions made, is equal to the Fermi level or electrochemical potential of electrons in the metal, but with an inverted sign [compare with Eq. (9.2)] ... 

Fig. 3.4 A metal in contact with a solution of an oxidation-reduction system. (A) Situation before the contact when the electrochemical potential of electrons in the electronic conductor (fiXa) = f(< )) has a different value from the electrochemical potential of electrons in the oxidation-reduction system. (B) When the phases are in contact the electrochemical potential of electrons becomes identical in both a and by charge transfer between them...

Basic properties of semiconductors and phenomena occurring at the semiconductor/electrolyte interface in the dark have already been discussed in Sections 2.4.1 and 4.5.1. The crucial effect after immersing the semiconductor electrode into an electrolyte solution is the equilibration of electrochemical potentials of electrons in both phases. In order to quantify the dark- and photoeffects at the semiconductor/electrolyte interface, a common reference level of electron energies in both phases has to be defined. 

Since electrons are charged particles, the electrochemical potential of electrons (Fermi level, Ep) depends on the inner potential, of the electron ensemble as in... 

As mentioned in Sec. 1.3, the electrochemical potential of electrons in condensed phases corresponds to the Fermi level of electrons in the phases. There are two possible cases of electron ensembles in condensed phases one to which the band model is applicable (in the state of degenera< where the wave functions of electrons overlap), and the other to which the band model cannot apply (in the state of nondegeneracy where no overlap of electron wave functions occurs). In the former case electrons or holes are allowed to move in the bands, while in the latter case electrons are assumed to be individual particles rather than waves and move in accord with a thermal hopping mechanism between the a4jacent sites of localized electron levels. 

We now consider the relationship which connects the electrochemical potential of electrons in the hopping model with that in the band model. The total concentration, N, of electron sites for the hopping model may be replaced by the effective state density, JVc, for the band model. For the two models thereby we obtain from Eqn. 2-27 the following equation ... 

Since the electrochemical potential of electrons in metals is a function of the inner potential of the metal (P ca) = p. - inner potential difference, Mmb, across the interface where electron transfer is in equilibrium is represented by the difference in the chemical potential of electrons between the two metal phases A and B is shown in Eqn. 4-8 ... 

Fig. 4-17. Electronic electrode in equilibrium of electron transfer OX = hydrated oxidant particles RED = hydrated reductant partides FWEDQx, s) = Fermi level of redox electrons in hydrated redox partides in solution S p. = electrochemical potential of electrons.

The Electrochemical Potential of Electrons in Solution and Their Quantal Energy States... 

If a redox couple is present in a solution and the equilibrium is attained in accordance with reaction (1), the concept of electrochemical potential of electrons in an electrolyte solution, Fredox, can be introduced. Let us stress the fact that from the point of view of thermodynamics a detailed mechanism of attaining the equilibriun is of no importance, so one may assume, in particular,... 

Since the quantities fiTCd and depend only on the properties of Ox and Red components in the solution bulk, the quantity Fredox defined by Eq. (6) is in no way related to the electrode nature and does not depend on the interface structure. Moreover, under thermodynamic equilibrium between the electrode and solution it is Fredox that determines the electrochemical potential of electrons in the electrode. This implies, in particular, that the value of F is the same for any electrode that is in equilibrium with a given redox system. Thus, the position of the Fredox level in a solution is determined by the redox system contained in it. The more positive the equilibrium potential of this system [Pg.262]

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