Electronic equilibrium electrolytic phase

In redox electrodes an inert metal conductor acts as a source or sink for electrons. The components of the half-reaction are the two oxidation states of a constituent of the electrolytic phase. Examples of this type of system include the ferric/ferrous electrode where the active components are cations, the ferricyanide/ferrocyanide electrode where they are anionic complexes, the hydrogen electrode, the chlorine electrode, etc. In the gaseous electrodes equilibrium exists between electrons in the metal, ions in solution and dissolved gas molecules. For the half-reaction... 

Figure 31 contains a schematic representation of the nanocrystalline semiconductor film-electrolyte interface at equilibrium (Figure 31a) and the corresponding situation under bandgap irradiation of the semiconductor (Figure 31b) [9]. Since the difiFusion length of the photogenerated carriers is usually larger than the physical dimensions of the structural units, holes and electrons can reach the impregnated electrolyte phase before they are lost via bulk recombination. This contrasts the situation with the single-crystal cases discussed earlier.

If a semiconductor is brought into contact with an electrolyte containing one or more redox couples, charge transfer between the two phases occurs until electrostatic equilibrium (equality of the free energies of the electron in both phases) is attained. 

Relationships such as those expressed in equation (5.6) cannot be employed for species that are in chemical equilibrium but do not exist in the adjoining phases. Electrons, for example, are present in the metal of the electrode (phase LE) and in chemical equilibrium with ionic species in the electrolyte (phase E), but are not present in the electrolyte. An equilibrium relationship between the electrons and ionic species can be expressed, however, in terms of electrochemical reactions, and... 

From a physicist s point of view, the condition for electronic equilibrium is equal values of the Fermi energy E. Electronic equilibrium concerns all charged particles and might also be formulated for the metal ions. The equilibrium contact between a metal phase and an electrolyte phase is shown in Figure 3.1. 

Figure 3.1 Electronic equilibrium between a metallic phase and an electrolyte phase. The electronic energy states in the metal are described by the energy band (Section 2.9). The occupied states are and The density of states of electrons in the electrolyte are the energy distribution functions of the reduced and oxidized components of a redox system, e.g., Fe and Fe ions (Section 2.9.10). The equilibrium condition is equal values of the electrochemical potentials /x of the electrons in both phases. An alternative condition is equal values of the Fermi energy Ep in both phases.

In electrochemistry the semiconductor (phase I) is connected to an electrolyte (phase II). In equilibrium the electrochemical potential for the electrons in both phases must be equal. The electrochemical potential of the electrons in the semiconductor is equal to the Fermi energy. 

Fig. 1 A scheme of the energetics at an n-type semiconductor electrode in contact with a redox system in an electrolyte solution, (a) The situation under conditions of electronic equilibrium. The electrochemical potential of the electrons is the same in both phases, i.e. the electron Fermi-level in the semiconductor Ep.n has the same value as the Fermi-level of the electrons in the redox system fRed/Ox- (t>) Case in which the energy bands in the semiconductor are flat this situation, corresponding to maximum photovoltage, is reached under strong illumination at open circuit. Wsc is the width of the depletion layer and e(j>sc is the band-bending.

In Fig. 17(a), the energetics of a typical interfacial region between an n-type semiconductor and an electrolyte solution is shown (see also Sect. 2.1.2.2). Electronic equilibrium exists between the semiconductor and a redox system present in the solution the electrochemical potential of electrons /Xg in the solid is equal to that in the liquid phase, and does not change with the spatial coordinate x, perpendicular to the solid/liquid interface. The electrochemical potential of the electrons is also equal to the electron Fermi level, denoted as and can be written as... 

Note the peculiarities of the work functions in a nonconducting medium (vacuum, pure solvent) and a conducting medium (electrolyte solution) when two metals contact each other, an electron equilibrium is always established between them, i.e., the condition te(l) = is met. The work function W is defined as the work of electron transfer from a metal to a point in the nonmetallic phase which is in the proximity to the interface at such a distance that the potential variation with distance can be ignored, i.e., beyond the superficial electric double layer, including the region in which the image forces are active ... 

In one-dimensional electrode modeling, (x) denotes the metal phase potential and (x) the electrolyte phase potential. The gradient of the metal (carbon) phase potential drives the electron flux, while protons move along the potential gradient of the electrolyte (ionomer) phase. At equilibrium, these gradients are zero and the potentials in the distinct phases are constant, (p (x) = and O (x) = 4) . The potential distribution of a working PEFC with porous electrodes of finite thickness is shown in Figure 1.9. For illustrative purposes, a simple assembly of anode catalyst layer, PEM and cathode catalyst layer is displayed. 

The main function of a fuel cell electrode is to convert a chemical flux of reactants into fluxes of charged particles, or vice versa, at the electrochemical interface. Electrochemical kinetics relates the local interfacial current density j to the local interfacial potential drop between metal and electrolyte phases, illustrated in Figure 1.8. A deviation of the potential drop from equilibrium corresponds to a local overpotential q at the interface, which is the driving force for the interfacial reaction. The reaction rate depends on overpotential, concentrations of active species, and temperature. For the remainder of this section, it is assumed that the metal electrode material is an ideal catalyst, that is, it does not undergo chemical transformation and serves as a sink or source of electrons. The basic question of electrochemical kinetics is how does the rate of interfacial electron transfer depend on the metal phase potential ... 

In the following, the equilibrium state of an electroactive polymer in an electroinactive electrolyte is considered (Fig. 20. la). Using an inert electrolyte reduces the complexity of the system it is of interest also because the oxidation/reduction of the polymer in inert electrolytes is a subject of great technical potential (batteries, etc.). For characterizing these systems, one has to consider both the ion-partitioning (ion-exchange) equilibrium across the polymer/solution interface fEqs. (23)-(27)] and the electronic equilibrium between the electrode and the polymer phase [Eqs. (19)-(22)]. 

The Nemst equation above for the dependence of the equilibrium potential of redox electrodes on the activity of solution species is also valid for uncharged species in the gas phase that take part in electron exchange reactions at the electrode-electrolyte interface. For the specific equilibrium process involved in the reduction of chlorine ... 

Figure 1. Sketch of an electrochemical cell whose equilibrium (open circuit) potential difference is AE. (a) Conventional configuration and (b) short-circuited configuration with an air gap. M and R are the electrodes, S is the solvent (electrolyte solution). Cu indicates the cables connecting the two electrodes to a measuring instrument (or to each other).

Experimental studies in electrochemistry deal with the bulk properties of electrolytes (conductivity, etc.) equilibrium and nonequilibrium electrode potentials the structure, properties, and condition of interfaces between different phases (electrolytes and electronic conductors, other electrolytes, or insulators) and the namre, kinetics, and mechanism of electrochemical reactions. 

Figure 29.4 shows an example, the energy diagram of a cell where n-type cadmium sulfide CdS is used as a photoanode, a metal that is corrosion resistant and catalytically active is used as the (dark) cathode, and an alkaline solution with S and S2 ions between which the redox equilibrium S + 2e 2S exists is used as the electrolyte. In this system, equilibrium is practically established, not only at the metal-solution interface but also at the semiconductor-solution interface. Hence, in the dark, the electrochemical potentials of the electrons in all three phases are identical. 

The interface separating two immiscible electrolyte solutions, e.g., one aqueous and the other based on a polar organic solvent, may be reversible with respect to one or many ions simultaneously, and also to electrons. Works by Nernst constitute a fundamental contribution to the electrochemical analysis of the phase equilibrium between two immiscible electrolyte solutions [1-3]. According to these works, in the above system electrical potentials originate from the difference of distribution coefficients of ions of the electrolyte present in the both phases. 

The interfacial tension always depends on the potential of the ideal polarized electrode. In order to derive this dependence, consider a cell consisting of an ideal polarized electrode of metal M and a reference non-polarizable electrode of the second kind of the same metal covered with a sparingly soluble salt MA. Anion A is a component of the electrolyte in the cell. The quantities related to the first electrode will be denoted as m, the quantities related to the reference electrode as m and to the solution as 1. For equilibrium between the electrons and ions M+ in the metal phase, Eq. (4.2.17) can be written in the form (s = n — 2)... 

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 ... 

The cell potential is simply the work that can be accomplished by the electrons produced in the SOFC, and this potential decreases from the equilibrium value due to losses in the electrodes and the electrolyte. For YSZ electrolytes, the losses are purely ohmic and are equal to the product of the current and the electrolyte resistance. Within the electrodes, the losses are more complex. While there can be an ohmic component, most of the losses are associated with diffusion (both of gas-phase molecules to the TPB and of ions within the electrode) and slow surface kinetics. For example, concentration gradients for either O2 (in the cathode) or H2 (in the anode) can change the concentrations at the electrolyte interface,which in turn establish the cell potential. Similarly, slow surface kinetics could result in the surface at the electrolyte interface not being in equilibrium with the gas phase. 

We now come to internal metal contacts in ISEs without an internal solution. As discussed above, systems without internal electrolytes are used very often, with both solid and liquid membranes. Obviously, the condition of thermodynamic equilibrium requires that common electrically-charged particles (ions or electrons) be present in electrically-charged phases that are in contact (see chapter 2). ISEs with a silver halide membrane to which a silver contact is attached are relatively simple. In the system... 

It is possible to find a range in which the electrode potential is changed and no steady state net current flows. An electrode is called ideally polarized when no charge flows accross the interface, regardless of the interfacial potential gradient. In real systems, this situation is observed only in a restricted potential range, either because electronic aceptors or donors in the electrolyte (redox systems) are absent or, even in their presence, when the electrode kinetics are far too slow in that potential range. This represents a non-equilibrium situation since the electrochemical potential of electrons is different in both phases. 

When two conducting phases come into contact with each other, a redistribution of charge occurs as a result of any electron energy level difference between the phases. If the two phases are metals, electrons flow from one metal to the other until the electron levels equilibrate. When an electrode, i.e., electronic conductor, is immersed in an electrolyte, i.e., ionic conductor, an electrical double layer forms at the electrode-solution interface resulting from the unequal tendency for distribution of electrical charges in the two phases. Because overall electrical neutrality must be maintained, this separation of charge between the electrode and solution gives rise to a potential difference between the two phases, equal to that needed to ensure equilibrium. 

We will see that in the steady state of the blocking cells, we can extract partial conductivities, and from the transients chemical diffusion coefficients (and/or interfacial rate constants). Cell 7 combines electronic with ionic electrodes here a steady state does not occur but the cell can be used to titrate the sample, i.e., to precisely tune stoichiometry. Cell 1 is an equilibrium cell which allows the determination of total conductivity, dielectric constant or boundary parameters as a function of state parameters. In contrast to cell 1, cell 2 exhibits a chemical gradient, and can be used to e.g., derive partial conductivities. If these oxygen potentials are made of phase mixtures212 (e.g., AO, A or AB03, B203, A) and if MO is a solid electrolyte, thermodynamic formation data can be extracted for the electrode phases. 

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