Phase boundaries, electron transfer

At low currents, the rate of change of die electrode potential with current is associated with the limiting rate of electron transfer across the phase boundary between the electronically conducting electrode and the ionically conducting solution, and is temied the electron transfer overpotential. The electron transfer rate at a given overpotential has been found to depend on the nature of the species participating in the reaction, and the properties of the electrolyte and the electrode itself (such as, for example, the chemical nature of the metal). 

The explicit mathematical treatment for such stationary-state situations at certain ion-selective membranes was performed by Iljuschenko and Mirkin 106). As the publication is in Russian and in a not widely distributed journal, their work will be cited in the appendix. The authors obtain an equation (s. (34) on page 28) similar to the one developed by Eisenman et al. 6) for glass membranes using the three-segment potential approach. However, the mobilities used in the stationary-state treatment are those which describe the ion migration in an electric field through a diffusion layer at the phase boundary. A diffusion process through the entire membrane with constant ion mobilities does not have to be assumed. The non-Nernstian behavior of extremely thin layers (i.e., ISFET) can therefore also be described, as well as the role of an electron transfer at solid-state membranes. 

The presupposition is that parallel electrochemical reactions (i.e., ion or electron transfer) occur across the phase boundary, if the measured ions and interfering ions are both present in the solution. A redox process in which electrons pass the phase boundary is also considered an interfering electrochemical reaction. 

Three kinds of equilibrium potentials are distinguishable. A metal-ion potential exists if a metal and its ions are present in balanced phases, e.g., zinc and zinc ions at the anode of the Daniell element. A redox potential can be found if both phases exchange electrons and the electron exchange is in equilibrium for example, the normal hydrogen half-cell with an electron transfer between hydrogen and protons at the platinum electrode. In the case where a couple of different ions are present, of which only one can cross the phase boundary — a situation which may exist at a semiperme-able membrane — one obtains a so called membrane potential. Well-known examples are the sodium/potassium ion pumps in human cells. 

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 ... 

Before a heterogeneous electron-transfer reaction can take place, be it oxidation or reduction, we must appreciate that the redox reaction occurs at the interface that separates the electrode and the solution containing the electroanalyte. Some electrochemists call this interface a phase boundary since either side of the interface is a different phase (i.e. solid, liquid or gas). An electrochemist would usually indicate such a phase boundary with a vertical line, . Accordingly, the interface could have been written as solution electrode . 

Because the reaction in a CL requires three-phase boundaries (or interfaces) among Nafion (for proton transfer), platinum (for catalysis), and carbon (for electron transfer), as well as reacfanf, an optimized CL structure should balance electrochemical activity, gas transport capability, and effective wafer management. These goals are achieved through modeling simulations and experimental investigations, as well as the interplay between modeling and experimental validation. 

It will be shown further on that the phases on either side of the boundary become charged to an equal and opposite extent and this gives rise to a potential difference across the boundary. There are several ways in which this potential difference can arise. If one of the phases is an electronic conductor and the other is an ionic conductor, electron-transfer reactions can occur at the boundary and lead to the development of a potential difference. A discussion of this type of mechanism will be reserved for Section 7.5. Or, the electronic conductor can be deliberately charged by a flow of electrons from an external source of electricity. The electrolyte side of the boundary then responds with an equal and opposite charge, and a potential difference develops across the boundary. However, even without an external connection or the occurrence... 

In the case of electrochemical cells capable of passing significant direct currents, the principal mechanism for the formation of such potential differences at phase boundaries within the cell is charge transfer, e.g. electron transfer between two metals or semiconductors, ion transfer... 

In Chapter 3 we described the structure of interfaces and in the previous section we described their thermodynamic properties. In the following, we will discuss the kinetics of interfaces. However, kinetic effects due to interface energies (eg., Ostwald ripening) are treated in Chapter 12 on phase transformations, whereas Chapter 14 is devoted to the influence of elasticity on the kinetics. As such, we will concentrate here on the basic kinetics of interface reactions. Stationary, immobile phase boundaries in solids (e.g., A/B, A/AX, AX/AY, etc.) may be compared to two-phase heterogeneous systems of which one phase is a liquid. Their kinetics have been extensively studied in electrochemistry and we shall make use of the concepts developed in that subject. For electrodes in dynamic equilibrium, we know that charged atomic particles are continuously crossing the boundary in both directions. This transfer is thermally activated. At the stationary equilibrium boundary, the opposite fluxes of both electrons and ions are necessarily equal. Figure 10-7 shows this situation schematically for two different crystals bounded by the (b) interface. This was already presented in Section 4.5 and we continue that preliminary discussion now in more detail. 

Charge will spontaneously develop at the interface between two phases when there is a difference in the ease with which particles with charge of opposite sign can be transferred across the phase boundary. One example of this is at the interface between a metal and a solution, where metallic ions, but not electrons, can dissolve in the solution.10 Another example is at the interface between two metals, where electrons, but not ions, undergo rapid transfer. In the latter case, the electron transfer depends on temperature and forms the basis for measuring temperature differences by means of thermocouples. 

Charge-transfer overpotential — The essential step of an - electrode reaction is the charge (- electron or - ion) transfer across the phase boundary (- interface). In order to overcome the activation barrier related to this process and thus enhance the desirable reaction, an - overpotential is needed. It is called charge-transfer (or transfer or electron transfer) overpotential (f/ct). This overpotential is identical with the - activation overpotential. Both expressions are used in the literature [i-iv]. Refs. [i] Bard A], Faulkner LR (2001) Electrochemical methods. Wiley, New York, pp 87-124 [ii] Erdey-Gruz T (1972) Kinetics of electrode processes. Akademiai Kiadd, Budapest, pp 19-56 [Hi] Inzelt G (2002) Kinetics of electrochemical reactions. In Scholz F (ed) Electroanalytical methods. Springer, Berlin, pp 29-33 [iv] Hamann CH, Hamnett A, Viel-stich W (1998) Electrochemistry. Wiley VCH, Weinheim, p 145... 

Polymer-modified electrodes — A polymer-modified electrode or polymer film electrode can be defined as an - electrode in which at least three phases are contacted successively in such a way that between a first-order - conductor (usually a metal) and a second-order conductor (usually an -> electrolyte solution) is an elec-trochemically active polymer layer this polymer is, in general, a mixed (electronic and ionic) conductor [i], A transfer of electrons to solution species may occur at the two - interfaces (phase boundaries) and as a mediated reaction inside the film. The essential characteristic of polymer-modified electrodes is the mechanism of the... 

Figure. For a modeling of the coupled ion and electron transfer at a three-phase boundary see [v-vii]. Three-phase boundaries play a crucial rule in fuel cells, and many electrochemical sensors.

---