Chemical potential of electrons

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

No. Because that would imply we know how to split, at least conceptually, the electrochemical potential, jl, of electrons (which is the same in the metal and in the electrolyte at their contact) into the chemical potential of electrons, p, and the electrical potential of electrons, (p, in the metal and in the electrolyte. 

It is typical that in Eq. (3.23) for the EMF, all terms containing the chemical potential of electrons in the electrodes cancel in pairs, since they are contained in the expressions for the Galvani potentials, both at the interface with the electrolyte and at the interface with the other electrode. This is due to the fact that the overall current-producing reaction comprises the transfer of electrons across the interface between two metals in addition to the electrode reactions. 

At the contact of two electronic conductors (metals or semiconductors— see Fig. 3.3), equilibrium is attained when the Fermi levels (and thus the electrochemical potentials of the electrons) are identical in both phases. The chemical potentials of electrons in metals and semiconductors are constant, as the number of electrons is practically constant (the charge of the phase is the result of a negligible excess of electrons or holes, which is incomparably smaller than the total number of electrons present in the phase). The values of chemical potentials of electrons in various substances are of course different and thus the Galvani potential differences between various metals and semiconductors in contact are non-zero, which follows from Eq. (3.1.6). According to Eq. (3.1.2) the electrochemical potential of an electron in... 

Here

work function, is the chemical potential of electrons in the metal, and Sxois the change of the metal surface potential upon contact with the solution. Hence, the modification of electronic distribution in the metal is due to the adsorbed solvent molecules, which change the surface potential of the metal, dxo- A similar concept was developed in numerous works of Trasatti (e.g.. Ref. 30). The value of Sxo at [Pg.7]

In general, the chemical potential of electrons, t., is characteristic of individual electron ensembles, but the electrostatic energy of-e< > varies with the choice of zero electrostatic potential. In electrochemistry, as is described in Sec. 1.5, the reference level of electrostatic potential is set at the outer potential of the electron ensemble. 

Fig. 2-8. Ihe electrochemical potential, p., the real potential, a, and the chemical potential, , of electrons in metals 4 = inner potential X = surface potential = outer potential MS= metal surface VL = vacuum infinity level.

The real potential and the chemical potential of electrons in metals... 

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 ... 

It follows from Eqn. 4—13 that the electron level o u/av) in the electrode is a function of the chemical potential p.(M) of electrons in the electrode, the interfacial potential (the inner potential difference) between the electrode and the electrolyte solution, and the surface potential Xs/v of the electrolyte solution. It appears that the electron level cx (ii/a/v) in the electrode depends on the interfacial potential of the electrode and the chemical potential of electron in the electrode but does not depend upon the chemical potential of electron in the electrolyte solution. Equation 4-13 is valid when no electrostatic potential gradient exists in the electrolyte solution. In the presence of a potential gradient, an additional electrostatic energy has to be included in Eqn. 4-13. 

According to this concept of asymmetric trapping — which is also discussed for inorganic photoconductors by Rose 3.89) the chemical potential of electrons (i.e. the Fermi potential) should be situated close to the conduction band (in -type photoconductors) and valence band (in p-type photoconductors), respectively, as illustrated in Fig. 9. 

Why does the energy of electrons inside a metal depend upon the electrical potential difference across its interface with the solution The reason is that the energy of electrons at the Fermi level is equated to and this quantity is then equal to pj, the chemical potential of electrons within the metal, which is independent of the electrode potential-together with the inner potential of the metal, which is a function... 

DsoIvd A+so1va+ -I- EpJedox A G = 0 where Eredo is the Fermi level or filled level of the metal. The chemical potential of electrons in the metal, Epredox we have from Figure 9.6. 

Here jtt is the chemical potential of electrons in the semiconductor (the electron-lattice interaction energy) and /if is the electrochemical potential of an electron in phase 5, normally known as the Fermi level (see Appendix A for explanation of the difference). Similarly, the inner potential of the membrane (3) is... 

This equation gives the relation between the electrical potential difference between the copper wires attached to the electrodes when the cell is at equilibrium and the change of the Gibbs energy for the change of state that would take place in the cell if the cell were short-circuited. We point out here that the chemical potentials of electrons refer to 1 mole of electrons or 1 faraday of electricity. Therefore, A G refers to the change of state per faraday. If the change of state requires n faradays,... 

What is wrong with the following argument If the terminals of an electrochemical cell are constructed from the same metal, the chemical potential of electrons [species i in Eq. (36)] at the terminals, which depends only on T, P and concentrations, are the same. From Eq. (36), the electromotive force of the cell is therefore zero ... 

The difference between the Fermi energies /xeh == f2 — fi is the free energy per electron-hole pair of the ensemble, also called the chemical potential of electron-hole pairs. It is free of entropy and we may therefore hope to transfer it into electrical energy without losses. If electron-hole pairs are not allowed to leave the 2-level system, i.e., under open-circuit conditions, they have to recombine and emit one photon per pair annihilation. These photons carry the free energy of the electron-hole pairs, and /n7 = /ieh = f2 — fi is recognised as their chemical potential. 

Fermi level ( p) The chemical potential of electrons in a solid (metals, semiconductors or insulators) or in an electrolyte solution. 

Many organic compounds involved in photosynthesis accept or donate electrons (see Table 5-3). The negatively charged electrons spontaneously flow toward more positive electrical potentials (A > 0), which are termed redox potentials for the components involved with electron flow in chlo-roplast lamellae (Fig. 1-10) or the inner membranes of mitochondria (Fig. 1-9). Redox potentials are a measure of the relative chemical potential of electrons accepted or donated by a particular type of molecule. The oxidized form plus the reduced form of each electron transfer component can be regarded as an electrode, or half-cell. Such a half-cell can interact with other electron-accepting and electron-donating molecules in the membrane, in which case the electrons spontaneously move toward the component with the higher redox potential. 

Fig. 1. Four possible states of an n-type semiconductor as the sign of the charge in the surface region changes from positive to negative (a) an n-type accumulation layer, (b) the flat band condition, (c) a depletion layer, (d) an inversion layer. Ec and Ev represent the edge of the conduction band and valence band respectively. Bp represents the Fermi energy or chemical potential of electrons in the solid. + represents ionized donor atoms, mobile electrons and mobile holes.

Now, the metal used as the electrode does not appear explicitly in any of the last three equations, but it is implicit in the half-cell reactions, since the electrons are either taken from or returned to the metal, and we might expect the metal-solution potential difference to include a term for the chemical potential of electrons in platinum. To show this, consider Eq. 27B at equilibrium. We can write... 

For metal electrodes, the Fermi level is embedded within a broad distribution of closely spaced electronic levels. The Fermi level describes the occupancy of energy levels of a system at equilibrium and can simply be thought of as the chemical potential of electrons in the solid [10]. When employed in the Fermi-Dirac distribution function, Eq. 3 results ... 

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