Charge Transfer Processes at Metal Electrodes

Kinetics of Eiectron Transfer at the Metai-Liquid Interface 

In this section, we only consider electron transfer processes between a redox couple dissolved in the electrolyte and an inert metal electrode such as platinum. Here an inert electrode means that we work in a potential range where essentially no other electrochemical reactions take place. Considering a single electron transfer step as given by 

Semiconductor Electrochemistry, Zweite Auflage. Rudiger Memming. 

As already mentioned in the introduction to this chapter, kinetic models describing electron transfer processes at metal electrodes had been used for a long time before Marcus developed his theory. At a fairly early stage, a transition state model was applied the rate constants were described in terms of activation energy so that we have 

Considering now the equilibrium case, the two partial currents given in Eq. (7.2) must be equal ( = ). Substituting Eq. (7.3) into Eq. (7.2), one obtains after rearranging the equation 

---

A theoretical current-potential curve (/7/q vs. fj) is given in Fig. 7.3 for r] = 0.5. It should be emphasized here that Eq. (7.11) is only valid in this simple form if the current is really kinetically controlled, i.e. if diffusion of the redox species toward the electrode surface is sufficiently fast. According to the Butler-Volmer equation (Eq. 7.11) the current increases exponentially with potential in both directions. In this aspect charge transfer processes at metal electrodes differ completely from those at semiconductors. When the overpotential is sufficiently large, erj/kT 1. one of the exponential terms in Eq. (7.11) can be neglected compared to the other. In this case we have either... 

Eqs. (7.18a) and (7.18b), but now using boundary conditions which are specific for semiconductors. Since the integral in Eq. (7.18) cannot be solved analytically, we assumed in the case of metal electrodes that the electron transfer occurs mainly around the Fermi level. As proved in Section 7.1, this is a satisfactory approximation. Using an equivalent approach for charge transfer processes at semiconductor electrodes, the anodic current corresponding to an electron transfer from the occupied states of the redox system to empty states of the conduction band, is given by [22]... 

Solid state materials that can conduct electricity, are electrochemically of interest with a view to (a) the conduction mechanism, (b) the properties of the electrical double layer inside a solid electrolyte or semiconductor, adjacent to an interface with a metallic conductor or a liquid electrolyte, (c) charge-transfer processes at such interfaces, (d) their possible application in systems of practical interest, e.g. batteries, fuel cells, electrolysis cells, and (e) improvement of their operation in these applications by modifications of the electrode surface, etc. 

Figure 6 An energy diagram of the charge-transfer process at an n-type semiconductor/metal interface when an external potential (F) is applied across the semiconductor electrode. The applied potential changes the electric potential difference between the semiconductor surface and the bulk region. This perturbs the concentration of electrons at the surface of the semiconductor (ns), and a net current flows through the semiconductor/metal interface. The forward reaction represents the transfer of electrons from the semiconductor to the metal and the reverse reaction represents the injection of electrons into the semiconductor from the metal. The width of the arrows indicates schematically the relative magnitude of the current, (a) The reverse bias condition for an n-type semiconductor (V > 0). The forward reaction rate is reduced relative to its equilibrium value, while the reverse reaction rate remains constant. A net positive current exists at the electrode surface, (b) The forward bias condition (V < 0), the forward reaction rate increases compared to its equilibrium value, while the reverse reaction rate remains unaffected. A net negative current exists at the electrode surface...

It is a point peculiar to electrochemical reaction kinetics (77), however, that the rates of charge-transfer processes at electrodes measured, as they have to be, at some well-defined potential relative to that of a reference electrode, are independent of the work function of the electrocatalyst metal surface. This is due to cancellation of electron-transfer energies, O, at interfaces around the measuring circuit. In electrochemistry, this is a well-understood matter, and its detailed origin and a description of the effect may be found, among other places, in the monograph by Conway (77). 

Surface-modified electrodes — In order to alter the properties of an electron-conducting substrate, i.e., a metal or graphite or semiconductor used as a part of an electrode, different chemical compounds are produced/deposited/attached/immobilized on the surface. These electrodes are most frequently called surface-modified, chemically-modified, or polymer-modified electrodes, depending on the methods and materials used for the modification. The obvious purpose of these efforts is the production of electrodes with novel and useful properties for special applications, but also to help gain a better understanding of the fundamental charge transfer processes at the interfaces. Usually the enhancement of the rate of the electrode reaction... 

Electroactive materials are often used as thin films coating a metallic electrode. Charge transport in these films and charge transfer reactions at metal/film and film/electrol5de interfaces play key roles in the reduction and oxidation of these electroactive films. As an example, it is commonly accepted that the oxidation process of such a film requires either cation expulsion or anion entry to compensate for the positive charges formed inside the film. However, it has been shown that the redox processes in electroactive films are accompanied not only by the exchange of ions with the electrolyte solution but also by solvent exchanges. ... 

The essential features of the electrochemical mechanism of corrosion were outlined at the beginning of the section, and it is now necessary to consider the factors that control the rate of corrosion of a single metal in more detail. However, before doing so it is helpful to examine the charge transfer processes that occur at the two separable electrodes of a well-defined electrochemical cell in order to show that since the two half reactions constituting the overall reaction are interdependent, their rates and extents will be equal. 

Consider now the transfer of electrons from electrode II to electrode I by means of an external source of e.m.f. and a variable resistance (Fig.. 20b). Prior to this transfer the electrodes are both at equilibrium, and the equilibrium potentials of the metal/solution interfaces will therefore be the same, i.e. Ey — Ell = E, where E, is the reversible or equilibrium potential. When transfer of electrons at a slow rate is made to take place by means of the external e.m.f., the equilibrium is disturbed and Uie rat of the charge transfer processes become unequal. At electrode I, /ai.i > - ai.i. 3nd there is... 

Semiconductor electrodes can be used in galvanic cells like metal electrodes and a controlled electrode potential can be applied by means of a potentiostat, if the electrode can be contacted with a suitable metal without formation of a barrier layer (ohmic contact). Suitable techniques for ohmic contacts have been worked out in connection with semiconductor electronics. Surface treatment is important for the properties of semiconductor electrodes in all kind of charge transfer processes and especially in the photoresponse. Mechanical polishing generates a great number of new electronic states underneath the surface 29> which can act as quenchers for excited molecules at the interface. Therefore, sufficient etching is imperative for studying photocurrents caused by excited dyes. 

---