Electrochemical potentials solids

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

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.

It must be emphasized that Equations (5.24) and (5.25) stem from the definitions of Fermi level, work function and Volta potential and are generally valid for any electrochemical cell, solid state or aqueous. We can now compare these equations with the corresponding experimental equations (5.18) and (5.19) found to hold, under rather broad temperature, gaseous composition and overpotential conditions (Figs. 5.8 to 5.16), in solid state electrochemistry ... 

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.

Very simply these equations are valid as long as ion backspillover from the solid electrolyte onto the gas-exposed electrode surfaces is fast relative to other processes involving these ionic species (desorption, reaction) and thus spillover-backspillover is at equilibrium, so that the electrochemical potential of these ionic species is the same in the solid electrolyte and on the gas exposed electrode surface. As long as this is the case, equation (5.29) and its consequent Eqs. (5.18) and (5.19) simply reflect the fact that an overall neutral double layer is established at the metal/gas interface. 

Now eUWR is still fixed by the Nemst Eq. 7.16 but w are variables. They can change due to the spillover of ions which can now establish a constant electrochemical potential not only in the solid electrolyte but on the gas exposed electrode surfaces as well. They will change in such a way as to minimize the excess electrostatic energy of the system... 

In solid-state physics, the electrochemical potential of the electron pe(a) is mostly replaced by the equivalent energy of the Fermi level eF. While the electrochemical potential is usually related to one mole of particles, the Fermi energy is related to a single electron, so that... 

The electrochemical potential of an electron in a solid defines the Fermi energy (cf. Eq. 3.1.9). The Fermi energy of a semiconductor electrode (e ) and the electrolyte energy level (credox) are generally different before contact of both phases (Fig. 5.60a). After immersing the semiconductor electrode into the electrolyte, an equilibrium is attained ... 

We managed to obtain dense and solid thin films of 3d-metal oxides using the techniques of electrochemical deposition from aqueous fluorine-containing electrolytes. The films have been studied as a possible cathode material for secondary cells. The best samples show good cycle retention and acceptable specific capacity in the range of 180 mAh/g. They also feature a plateau of electrochemical potential at approximately 3,5 V, which is acceptable for present industrially produced electrochemical devices. 

Redox potentials in the solid state are expected to differ from those in solution [97]. Moreover, there will be shifts in the potentials of a thin film, relative to that of a solid, due to interactions with the metal support and counter electrode, including image-charge effects. There may be an opposite signed shift due to the absence of a covering layer of adsorbed molecules [99]. Another complication is the fact that electrochemical potentials are equilibrium values, and therefore reflect the energy associated with the formation of an ion in its equilibrium geometry. OMTS transitions, as discussed above, may occur so rapidly that the ion is formed in an excited... 

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. 

At zero temperature the electrons in a solid occupy the lowest energy levels compatible with the Pauli exclusion principle. The highest energy level occupied at T = 0 is the Fermi level, Ep. For metals the Fermi level and the electrochemical potential are identical at T = 0, since any electron that is added to the system must occupy the Fermi level. At finite temperatures Ep and the electrochemical potential p of the electrons differ by terms of the order of (kT)2, which are typically... 

For electrons in a metal the work function is defined as the minimum work required to take an electron from inside the metal to a place just outside (c.f. the preceding definition of the outer potential). In taking the electron across the metal surface, work is done against the surface dipole potential x So the work function contains a surface term, and it may hence be different for different surfaces of a single crystal. The work function is the negative of the Fermi level, provided the reference point for the latter is chosen just outside the metal surface. If the reference point for the Fermi level is taken to be the vacuum level instead, then Ep = —, since an extra work —eoV> is required to take the electron from the vacuum level to the surface of the metal. The relations of the electrochemical potential to the work function and the Fermi level are important because one may want to relate electrochemical and solid-state properties. 

Wagner pioneered the use of solid electrolytes for thermochemical studies of solids [62], Electrochemical methods for the determination of the Gibbs energy of solids utilize the measurement of the electromotive force set up across an electrolyte in a chemical potential gradient. The electrochemical potential of an electrochemical cell is given by ... 

Figure4. Comparison of UHV and in situ electrochemical data. Solid and dotted lines correspond to the potential drop across the inner layer for the Br/H20 and Cl / H2O systems at a Ag 110 electrode. Full circles correspond to the change in work function of a Ag l 10 surface with Br and water to complete the inner layer (taken from figure 3 c). Open triangles correspond to similar work function data for the Cl / H2O system on Ag l 10. ...

Semiconductor - Electrolyte Interlace The electric field in the space charge region that may develop at the semiconductor electrolyte interface can help to separate photogenerated e /h 1 couples, effectively suppressing recombination. When a semiconductor is brought into contact with an electrolyte, the electrochemical potential of the semiconductor (corresponding to the Fermi level, Ey of the solid [50]) and of the redox couple (A/A ) in solution equilibrate. When an n-type semiconductor is considered, before contact the Ey of the solid is in the band gap, near the conduction band edge. After contact and equilibration the Ey will... 

For high density electron ensembles such as free valence electrons in solid metals where electrons are in the state of degeneracy, the distribution of electron energy follows the Fermi function of Eqn. 1-1. According to quantum statistical dynamics [Davidson, 1962], the electrochemical potential, P., of electrons is represented by the Fermi level, ep, as shown in Eqn. 1-10 ... 

Fig. 7-7. Potential energy curves for an elementary step of reaction in equilibrium (solid curve) and in nonequilibrium (dashed curve) 4glq = activation energy in equilibrium 4gj s forward activation energy in nonequilibrium p>. , -electrochemical potential of activated partide in equilibrium p = symmetry factor Zi = charge number of reacting partide.

Fig. 6.3 Schematic picture of the electrochemical potential ( > as a function of distance x in an oxide semiconductor electrolyte system a) bulk semiconductor potential b) solid/solution interface potential c) space charge potential d) flat band potential e) potential in the double layer (White, 1990, with permission.

Equilibrium between the two phases at a semiconductor-electrolyte interface, solid and liquid, can only be achieved if their electrochemical potential is the same, that is ... 

The state of a gaseous or solid phase containing electrons may be described thermodynamically by the electrochemical potential of the electrons. Thus, in an isolated body of volume V containing n electrons, the electrochemical potential jS is defined as... 

Solid state reactions occur mainly by diffusional transport. This transport and other kinetic processes in crystals are always regulated by crystal imperfections. Reaction partners in the crystal are its structure elements (SE) as defined in the list of symbols (see also [W. Schottky (1958)]). Structure elements do not exist outside the crystal lattice and are therefore not independent components of the crystal in a thermodynamic sense. In the framework of linear irreversible thermodynamics, the chemical (electrochemical) potential gradients of the independent components of a non-equilibrium (reacting) system are the driving forces for fluxes and reactions. However, the flux of one independent chemical component always consists of the fluxes of more than one SE in the crystal. In addition, local reactions between SE s may occur. 

In heterogeneous solid state reactions, the phase boundaries move under the action of chemical (electrochemical) potential gradients. If the Gibbs energy of reaction is dissipated mainly at the interface, the reaction is named an interface controlled chemical reaction. Sometimes a thermodynamic pressure (AG/AK) is invoked to formalize the movement of the phase boundaries during heterogeneous reactions. This force, however, is a virtual thermodynamic force and must not be confused with mechanical (electrical) forces. 

The electrochemical potential of an electron in a (solid) phase p is equal to the Fermi potential of that phase. Because at equilibrium, dG = 0,... 

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