Electrodes energy levels

The use of interpenetrating donor-acceptor heterojunctions, such as PPVs/C60 composites, polymer/CdS composites, and interpenetrating polymer networks, substantially improves photoconductivity, and thus the quantum efficiency, of polymer-based photo-voltaics. In these devices, an exciton is photogenerated in the active material, diffuses toward the donor-acceptor interface, and dissociates via charge transfer across the interface. The internal electric field set up by the difference between the electrode energy levels, along with the donor-acceptor morphology, controls the quantum efficiency of the PV cell (Fig. 51). 

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 equiUbrate. When an electrode, ie, electronic conductor, is immersed in an electrolyte, ie, 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 equiUbrium. 

A value close to 4.8 V has been obtained in four different laboratories using quite different approaches (solid metal/solution Ay, 44 emersed electrodes,40,47 work function changes48), and is apparently supported by indirect estimates of electronic energy levels. The consistency of results around 4.8 V suggests that the value of 4.44 V is probably due to the value of 0 not reflecting the actual state of an Hg jet or pool. According to some authors,44 the actual value of 0 for Hg in the stream should be 4.8 V in that the metal surface would be oxidized. 

Figure 7.1. Definition of absolute electron potential in aqueous electrochemistry according to Trasatti16 in a classical (a) and liquid covered (b) electrode geometry. Point C corresponds to the zero energy level. O0 is the work function of the bare electrode surface and AC>(=eA P) is the work function modification induced by the presence of the electrolyte layer (b). Reprinted with permission from Elsevier Science.

It is worth noting in Figures 7. lb and 7.2b that the zero energy level choice (point C) is not only, by definition, a point in vacuum close to the surface of the solution (Fig. 7.1a, 7.2a), but also, as clearly shown by Trasatti,16 a point in vacuum close to the surface of the emersed (liquid or adsorption covered) electrode. 

Fig. 5.6 (Left) Comparison of band energy levels for different II-VI compounds. Note the high-energy levels of ZnSe. Representation is made here for electrodes in contact with 1 M HQO4. The reference is a saturated mercury-mercurous sulfate electrode, denoted as esm (0 V/esm = +0.65 V vs. SHE). (Right) Anodic and cathodic decomposition reactions for ZnSe at their respective potentials (fidp, Fdn) and water redox levels in the electrolytic medium of pH 0. (Adapted from [121])...

The physical concept of a single electrode potential has been also discussed in terms of the energy levels of ions in electrode systems. This concept may be usefirl in the cases where the system has no electronic energy levels in a range of practical interest, such as in ionic solid crystalline and electronically nonconductive membrane electrodes. "... 

In view of very small spacing of the energy levels, one may not restrict oneself by consideration of the electron transfer from only one electron state in the metal, and all energy spectra shonld be taken into account. However, the entire process is composed of transitions with the participation of individnal energy levels 8. Therefore, the electron transfer from an energy level s to the reactant located a distance X from the electrode snrface in the solntion is considered first (Fig. 34.3). 

The physical picture of the transition is the same as for electron transfer in the bulk solution. At the initial eqnilibrinm polarization Pg, the positions of the energy levels 8 and 8 do not coincide and flnctnation of the polarization is required to bring them into the resonance position where electron transfer from the electrode to the acceptor is possible. The following points should be taken into account, which are specific for electrode processes ... 

Only if one takes into account the solvent dynamics, the situation changes. The electron transfer from the metal to the acceptor results in the transition from the initial free energy surface to the final surface and subsequent relaxation of the solvent polarization to the final equilibrium value Pqj,. This brings the energy level (now occupied) to its equilibrium position e red far below the Fermi level, where it remains occupied independent of the position of the acceptor with respect to the electrode surface. 

Oxidation-reduction electrodes. An inert metal (usually Pt, Au, or Hg) is immersed in a solution of two soluble oxidation forms of a substance. Equilibrium is established through electrons, whose concentration in solution is only hypothetical and whose electrochemical potential in solution is expressed in terms of the appropriate combination of the electrochemical potentials of the reduced and oxidized forms, which then correspond to a given energy level of the electrons in solution (cf. page 151). This type of electrode differs from electrodes of the first kind only in that both oxidation states can be present in variable concentrations, while, in electrodes of the first kind, one of the oxidation states is the electrode material (cf. Eqs 3.1.19 and 3.1.21). 

The basic condition for electron transfer in cathodic processes (reduction) to an electroactive substance is that this substance (Ox) be an electron acceptor. It must thus have an unoccupied energy level that can accept an electron from the electrode. The corresponding donor energy level in the electrode must have approximately the same energy as the unoccupied level in the substance Ox. 

Fig. 5.4 Electron transfer in vacuo and in solution. (A) When the electron donor and the proton acceptor have very different corresponding energy levels the electron transfer is impossible. (B) When the reaction partners are present in a solution, then a change in their configuration can bring their corresponding energy levels close together (dashed line) so that electron transfer is possible. (C) An analogous situation is in the system of an electrode and an electroactive particle in solution...

The development of the theory of the rate of electrode reactions (i.e. formulation of a dependence between the rate constants A a and kc and the physical parameters of the system) for the general case is a difficult quantum-mechanical problem, even when adsorption does not occur. It would be necessary to consider the vibrational spectrum of the solvation shell and its vicinity and quantum-mechanical interactions between the reacting particles and the electron at various energy levels in the electrode. 

Let us choose, as an arbitrary reference level, the energy of an electron at rest in vacuum, e ) (cf. Section 3.1.2). This reference energy is obvious in studies of the solid phase, but for the liquid phase, the Trasatti s conception of absolute electrode potentials (Section 3.1.5) has to be adopted. The formal energy levels of the electrolyte redox systems, REDox, referred to o, are given by the relationship ... 

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 ... 

In many problems for which no direct solution can be obtained, there is a wave equation which differs but slightly from one that can be solved analytically. As an example, consider die hydrogen atom, a problem that was resolved in Section 6.6. Suppose now that an electric field is applied to the atom. The energy levels of the atom are affected by the field, an example of the Stark effect. If die field (due to the potential difference between two electrodes, for example) is gradually reduced, the system approaches that of the unperturbed hydrogen atom. 

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