Electronic structure of the electrode

To be specific, let us consider electron transfer from the reduced form of the reactant to the metal electrode. The electron may be transferred to any empty state on the metal denoting by e the difference in energy between the final state of the electron and the Fermi level, the energy of activation for the transfer is  

To obtain the total rate kox and hence the total anodic current density ja = Fkox, we integrate over all allowed values of e  

The integrals are to be performed over the conduction band of the metal in practice the limits can be extended to oo, since the integrands are negligible far from the Fermi level. 

A good approximation to the current-potential curve is obtained by 

The complete current-potential relation is shown in Fig. 6.3. For small overpotentials we observe Butler-Volmer behavior, for large overpotentials a limiting current. 

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Many naturally occurring substances, in particular the oxide films that form spontaneously on some metals, are semiconductors. Also, electrochemical reactions are used in the production of semiconductor chips, and recently semiconductors have been used in the construction of electrochemical photocells. So there are good technological reasons to study the interface between a semiconductor and an electrolyte. Our main interest, however, lies in more fundamental questions How does the electronic structure of the electrode influence the properties of the electrochemical interface, and how does it affect electrochemical reactions What new processes can occur at semiconductors that are not known from metals ... 

Also, as would be expected, the type of metal (i.e., the electronic structure of the electrode) influences the adsorbility of the organic molecules. For example, Fig. 6.116 shows the free energy of adsorption of amyl alcohol and acetonitrile on different metals. This figure indicates how the adsorption energy of the organic molecule decreases as the strength of metal-water interaction increases (the AX parameter in Fig. 6.116) (Trasatti, 1995). 

In fact these calculations did not treat the time scales correctly because they generally fixed most features of the atomic structure of solvent and then calculated the resulting electronic structure, for fixed potential drop across the interface. (A recent calculation [34] that takes more detailed account of the electronic structure of the electrode than these early calculations also suffers from this defect.) In fact, of course, in the Bom-Oppenheimer approximation, the electronic structure should be recalculated for each atomic configuration in an ensemble of atomic configurations that follow the Bom-Oppenheimer surface. This became possible with Car-Parrinello... 

With (3.6.29) and (3.6.30), it is apparently possible to account for kinetic effects of the electronic structure of the electrode by using an appropriate density of states, p(E), for... 

A complex and radically new situation evolves in the case of a direct, mediatorless, transport between the enzyme active center and the electrode. Apart from the problems mentioned above, some new fundamental questions arise, which have not been encountered either in electrochemistry or enzy-mology. In the case of preservation of the molecular integrity of the immobilized enzyme, electrochemical transformations of the substrate in this system take place at large (some 10-A) distances from the conductive phase. Therefore, it is necessary to investigate the mechanism of electron transfer and of the distribution of the potential jump (the structure of the electric double layer) in the electrode-enzyme-electrolyte system. The electrode becomes the donor or acceptor of electrons when the reaction proceeds at the enzyme active center. This implies a change in the functioning mechanism of the enzyme as compared to the native conditions. The chemical and electronic structure of the electrode surface must play an extremely important role in... 

At noble metals, the growth of submonolayer and monolayer oxides can be studied in detail by application of electrochemical techniques such as cyclic-voltammetry, CV 11-20) and such measurements allow precise determination of the oxide reduction charge densities. Complementary X-Ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), infra-red (IR) or elUpsommetry experiments lead to elucidation of the oxidation state of the metal cation within the oxide and estimation of the thickness of one oxide monolayer 12,21-23), Coupling of electrochemical and surface-science techniques results in meaningful characterization of the electrified solid/liquid interface and in assessment of the relation between the mechanism and kinetics of the anodic process under scrutiny and the chemical and electronic structure of the electrode s surface 21-23). 

The older versions of the theory considered the electrode as a reservoir of electrons and hence could not explain catalysis. Substantial progress was achieved when two of us [6,7] connected electron transfer with ideas from the Anderson-Newns theory [8,9] and applied Green s function techniques. This made it possible to consider the electronic structure of the electrode, distinguish between d bands and sp bands, and treat the case of strong electronic interactions, which give rise to catalysis. Since it does not contain many-body effects, it requires input from DFT for quantitative calculations—this will be treated later (see Section 1.2.3). However, the theory by itself already does offer a nice way to understand qualitatively how a catalyst worics, which we proceed to present. 

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