Electrode Potential in Charge Transfer Equilibrium

For electrodes which have no electron energy levels in the energy range of general interest, such as ionic crystalline sohd electrodes and membrane electrodes, only the concept of ionic electrode potential can be of practical significance. 

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Next, we consider the interface M/S of a nonpolarizable electrode where electron or ion transfer is in equilibrium between a solid metal M and an aqueous solution S. Here, the interfadal potential is determined by the charge transfer equilibrium. As shown in Fig. 4-9, the electron transfer equilibrium equates the Fermi level, Enn) (= P (M)), of electrons in the metal with the Fermi level, erredox) (= P s)), of redox electrons in hydrated redox particles in the solution this gives rise to the inner and the outer potential differences, and respectively, as shown in Eqn. 4-10 ... 

The electrode potential defined in Sec. 4.3 applies to both nonpolarizable electrodes at which charge transfer reactions may take place and polarizable electrodes at which no charge transfer takes place. For nonpolarizable electrodes at which the charge transfer is in equilibrium, the interfacial potential is determined by the equilibrium of the charge transfer reaction. 

Since the electron transfer of the interfacial redox reaction, + cm = H.a> on electrodes takes place between the iimer Helmholtz plane (adsorption plane at distance d ) and the electrode metal, the ratio of adsorption coverages 0h,j/ in electron transfer equilibrium (hence, the charge transfer coefficient, 6z) is given in Eqn. 5-58 as a function of the potential vid /diOMn across the inner Helmholtz layer ... 

Although the kinetic variable in electrode reactions in the current density, extensive use of the overpotential concept has been made in the electrochemical literature to indicate the departure from equilibrium [7]. Depending on the particular rate-determining process, in the overall electrode kinetics ohmic, charge transfer, reaction, concentration or mass transport, and crystallization overpotentials are described in the literature. Vetter [7] distinguished the concept of overpotential from that of polarization in the case of mixed potentials when the zero current condition does not correspond to an equilibrium potential as will be discussed in Sect. 8. 

In order to characterize the equilibrium state of the electrochemical cells, the electronic conductor connecting the electrodes of Figure 3.1.5 is removed. Now, both electrodes may establish their individual charge-transfer equilibrium state. A stable equilibrium potential difference, E, is established between the two electrodes. 

Once faradaic current flows, the equilibrium between oxidized and reduced species is disturbed, and can be continually reestablished only if all the steps involved in the electrode process are rapid enough. (These steps include charge transfer, movement of depolarizer to the electrode and of product away from it (mass transport), and possibly adsorption or chemical reactions.) If there is a lag, then the electrode potential changes from its equilibrium value, the magnitude of the change being the overpotential or overvoltage. 

Fig. 1.20 Cell consisting of two reversible Ag /Ag electrodes (Ag in AgN03 solution). The rate and direction of charge transfer is indicated by the length and arrow-head as follows gain of electrons by Ag -he- Ag—> loss of electrons by Ag - Ag + e- —. (o) Both electrodes at equilibrium and (f>) electrodes polarised by an external source of e.m.f. the position of the electrodes in the vertical direction indicates the potential change. (K, high-impedance voltmeter A, ammeter R, variable resistance)...

In the case of electrode reactions, the activation energy depends on the electrode potential. We now consider an elementary step in which a charged particle (charge number, zi) transfers across the compact double layer on the electrode interface as shown in Fig. 7-7. In the reaction equilibrium, where the electrochemical potentials of reacting particles are equilibrated between the initial state and the final state (Pk o = Pf( i)), the forward activation energy equals the backward activation energy (P , - Pi = P, i- Pr) P , is the electrochemical potential of the reacting particle at the activated state in equilibrium. 

The potential, E, for the onset of the photoexdted reaction relative to the equilibrium electrode potential E of the same reaction can also be derived in a kinetics-based approach [Memming, 1987]. Here, we consider the transfer of anodic holes (minority charge carriers) at an n-type semiconductor electrode at which the hole transfer is in quasi-equilibrium then, the anodic reaction rate is controlled by the photogeneration and transport of holes in the n-type semiconductor electrode. The current of hole transport, has been given by Eqn. 8-71 as a function of polarization ( - ,) as shown in Eqn. 10-20 ... 

The potential of a mixed electrode at which a coupled reaction of charge transfer proceeds is called the mixed electrode potential , this mixed electrode potential is obviously different from the single electrode potential at which a single reaction of charge transfer is at equilibrium. For corroding metal electrodes, as shown in Fig. 11—2, the mixed potential is often called the corrosion potential, E . At this corrosion potential Eemt the anodic transfer current of metallic ions i, which corresponds to the corrosion rate (the corrosion current ), is exactly balanced with the cathodic transfer current of electrons for reduction of oxidants (e.g. hydrogen ions) i as shown in Eqn. 11-4 ... 

Consider a system in which a potential difference AV, in general different from the equilibrium potential between the two phases A 0, is applied from an external source to the phase boundary between two immiscible electrolyte solutions. Then an electric current is passed, which in the simplest case corresponds to the transfer of a single kind of ion across the phase boundary. Assume that the Butler-Volmer equation for the rate of an electrode reaction (see p. 255 of [18]) can also be used for charge transfer across the phase boundary between two electrolytes (cf. [16, 19]). It is mostly assumed (in the framework of the Frumkin correction) that only the potential difference in the compact part of the double layer affects the actual charge transfer, so that it follows for the current density in our system that... 

Galvanostatic Transient Technique. In the galvanostatic method a constant-current pulse is applied to the cell at equilibrium state and the resulting variation of the potential with time is recorded. The total galvanostatic current ig is accounted for (1) by the double-layer charging, /ji, and (2) by the electrode reaction (charge transfer), i. ... 

Ve - Vo) is the overpotential, the potential required to initiate reactions at the electrode surface, the difference between the equilibrium potential Vo (no current flowing) and operating potential Ve (current flowing). The above kinetics indicate that the rate of electron transfer from the n-type semiconductor to the redox system depends on the surface electron concentration, while electron injection from the redox system into the conduction band is constant independent of applied potential [11,76,77]. If the Helmholtz layer potential (pn varies across the interface the description of electron transfer becomes considerably more complicated requiring a charge transfer coefficient in equation (3.4.34). 

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