Schmickler transfer

Schmickler,W. Electron Transfer Reactions on Oxide-Covered Metal Electrodes 17... 

These ideas can be applied to electrochemical reactions, treating the electrode as one of the reacting partners. There is, however, an important difference electrodes are electronic conductors and do not posses discrete electronic levels but electronic bands. In particular, metal electrodes, to which we restrict our subsequent treatment, have a wide band of states near the Fermi level. Thus, a model Hamiltonian for electron transfer must contains terms for an electronic level on the reactant, a band of states on the metal, and interaction terms. It can be conveniently written in second quantized form, as was first proposed by one of the authors [Schmickler, 1986] ... 

Figure 2.5 Electron transfer rate as a function of the electronic interaction A. The full line is the prediction of first-order perturbation theory. The upper points correspond to a solvent with a low friction the lower points to a high friction. The data have been taken from Schmickler and Mohr [2002].

In a simple electron transfer reaction, the reactant is situated in front of the electrode, and the electron is transferred when there is a favorable solvent fluctuation. In contrast, during ion transfer, the reactant itself moves from the bulk of the solution to the double layer, and then becomes adsorbed on, or incorporated into, the electrode. Despite these differences, ion transfer can be described by essentially the same formalism [Schmickler, 1995], but the interactions both with the solvent and with the metal depend on the position of the ion. In addition, the electronic level on the reactant depends on the local electric potential in the double layer, which also varies with the distance. These complications make it difficult to perform quantitative calculations. 

Besides these generalities, little is known about proton transfer towards an electrode surface. Based on classical molecular dynamics, it has been suggested that the ratedetermining step is the orientation of the HsO with one proton towards the surface [Pecina and Schmickler, 1998] this would be in line with proton transport in bulk water, where the proton transfer itself occurs without a barrier, once the participating molecules have a suitable orientation. This is also supported by a recent quantum chemical study of hydrogen evolution on a Pt(lll) surface [Skulason et al., 2007], in which the barrier for proton transfer to the surface was found to be lower than 0.15 eV. This extensive study used a highly idealized model for the solution—a bilayer of water with a few protons added—and it is not clear how this simplification affects the result. However, a fully quantum chemical model must necessarily limit the number of particles, and this study is probably among the best that one can do at present. 

In the electron transfer theories discussed so far, the metal has been treated as a structureless donor or acceptor of electrons—its electronic structure has not been considered. Mathematically, this view is expressed in the wide band approximation, in which A is considered as independent of the electronic energy e. For the. sp-metals, which near the Fermi level have just a wide, stmctureless band composed of. s- and p-states, this approximation is justified. However, these metals are generally bad catalysts for example, the hydrogen oxidation reaction proceeds very slowly on all. sp-metals, but rapidly on transition metals such as platinum and palladium [Trasatti, 1977]. Therefore, a theory of electrocatalysis must abandon the wide band approximation, and take account of the details of the electronic structure of the metal near the Fermi level [Santos and Schmickler, 2007a, b, c Santos and Schmickler, 2006]. 

Grimminger J, Bartenschlager S, Schmickler W. 2005. A model for combined electron and proton transfer in electrochemical systems. Chem Phys Lett 416 316-320. 

Pecina O, Schmickler W, Spohr E. 1995. On the mechanism of electrochemical ion transfer... 

Santos E, Koper MTM, Schmickler W. 2006. A model for bond-breaking electron transfer at metal electrodes. Chem Phys Lett 419 421-425. 

Santos E, Schmickler W. 2007a. Catalyzed bond-breaking electron transfer Effect of the separation of the reactant from the electrode. J Electroanal Chem 607 101-106. 

Schmickler W. 1986. A theory of adiabatic electron transfer reactions. J Electroanal Chem 204 31-43. 

Schmickler W. 1995. A unified model for electrochemical electron and ion transfer reactions. Chem Phys Lett 152-160. 

Schmickler W. 1996. Interfacial Electrochemistry. New York Oxford University Press. Schmickler W, Koper MTM. 1999. Adiabahc electrochemical electron-transfer reactions involving frequency changes of iimer-sphete modes. Electrochem Comm 1 402-405. Schmickler W, Mohr J. 2002. The rate of electrochemical electron-transfer reachons. J Chem Phys 117 2867-2872. 

The above model can be extended to assisted ion transfer, in which the ion forms a complex with a suitable ionophore. The various mechanisms for such reactions have been classified by Shao et al. [21] and reviewed by Girault [22]. Schmickler [23] has examined the case of transfer by interfacial complexation, which is marked by the following reaction sequence (see Fig. 14) The transferring ion moves from the bulk of solution 1 towards the interface with solution 2, in which it is poorly soluble. At the interface it reacts with an ionophore from solution 2, and then the complexed ion is transferred towards the bulk of solution 2. 

Although the correlation between ket and the driving force determined by Eq. (14) has been confirmed by various experimental approaches, the effect of the Galvani potential difference remains to be fully understood. The elegant theoretical description by Schmickler seems to be in conflict with a great deal of experimental results. Even clearer evidence of the k t dependence on A 0 has been presented by Fermin et al. for photo-induced electron-transfer processes involving water-soluble porphyrins [50,83]. As discussed in the next section, the rationalization of the potential dependence of ket iti these systems is complicated by perturbations of the interfacial potential associated with the specific adsorption of the ionic dye. 

Schmickler W, Tao N (1997) Measuring the inverted region of an electron transfer reaction with a scanning tunneling microscope. Electrochim Acta 42 2809-2815... 

In the early 1990s a few classical semimoleculai and molecular models of electron transfer reactions involving bond breaking appeared in the literature. A quantum mechanical treatment of a unified mr el of electrochemical electron and ion transfer reactions involving bond breaking was put forward by Schmickler using Anderson-Newns Hamiltonian formalism (see Section V.2). 

Miller RDJ, Mclendon G, Nojik AJ, Schmickler W, Willing F (1995) Surface electron transfer Processes, VCH Publishers, New York... 

RJ.D. Miller, G.L. McLendon, A.J. Noszik, W. Schmickler, F. Willig Surface Electron Transfer Processes, VCH, New York, 1995. 

R. J. Dewayne Miller, G. McLendon, A. J. Nozik, W. Schmickler, and Frank Willig, Surface Electron Transfer, VCH Publishers, New York (1995). Advanced discussions. 

A lively subsection in applications of quantum theory to transitions at electrodes concerns the tunneling of electrons through oxide films. This work has been led by Schmickler (1980, 1996), who has used a quantum mechanical approach known as resonance tunneling to explain the unexpected curvature of Tafel lines for electron transfer through oxide-covered electrodes (Fig. 9.21). 

Fig. 9.22. Electron-transfer reaction curves. The potential energy of the system is drawn as a function of the nuclear coordinate surface. The parabolic surface that signifies that the nuclear displacements are within harmonic limits of their respective in-ternuclear potentials is the key feature. (Reprinted from R. J. D. Miller, G. McLendon, A. J. Nozik, W. Schmickler, and F. Willig, Surface Electron Transfer Processes, p. 9, copyright 1995 VCH-Wiley. Reprinted by permission of John Wiley Sons, Inc.)...

Fig. 9.25. (c) Tafel plots for the exchange of the acetylchoiine ion between an aqueous solution and one containing organic molecules the branch on the right-hand side corresponds to transfer from the aqueous to the organic solution. (Reprinted from Wolfgang Schmickler, Interfacial Electrochemistry. Copyright 1996 by Oxford University Press, Inc. Used by permission of Oxford University Press.)... 

Tafel s law applies also in current density ranges well below that of the limiting current at semiconductor/solution interfaces and to photoelectrochemical reactions. Its application to liquid-liquid interfacial electron transfer is also good [see Fig. 9.25(d)] (Schmickler 1995). In hydrogen evolution, it has been followed down to the picoam-pere region and up to 100 A cm-2. 

A thoroughgoing restudy of Tafel s law, involving the use of fast-flow techniques to avoid the introduction of diffusion control at high rates (Iwasita, Schmickler, and Schultze, 1985) shows excellent verification.19 Tafel s law is one of the most tested and verified laws in nature. It Ls also one with the broadest applicability (e.g., in interfacial charge-transfer control, e.g., corrosion metabolism and photosynthesis). In... 

W. Schmickler, J. Electroanal. Chem. 204 31 (1986). A discussion of the influence of the choice of Hamiltonian on electron-transfer theory. 

W. Schmickler, Chem. Phys. Lett. 237 152 (1995). Electron-transfer and ion-transfer reactions at electrodes distinguished. 

Theoretical treatments of electron transfer via adsorbed intermediates have been presented by Dogonazde et al. [127] and Schmickler [128]. 

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