Electron energy levels of adsorbed particles

The frontier electron level of adsorbed particles splits itself into an occupied level (donor level) in a reduced state (reductant, RED) and a vacant level (acceptor level) in an oxidized state (oxidant, OX), because the reduced and oxidized particles differ from each other both in their respective adsorption energies on the interface of metal electrodes and in their respective interaction energies with molecules of adsorbed water. The most probable electron levels, gred and eqx, of the adsorbed reductant and oxidant particles are separated from each other by a magnitude equivalent to the reorganization energy 2 . ki in the same way as occurs with hydrated redox particles described in Sec. 2.10. 

We consider, as an example, adsorbed redox particles comprising protons and hydrogen atoms as shown in Eqn. 5-53 , 

In adsorption equUibrimn, the Fermi level c m) of electrons in the metal electrode equals the Fermi level ep(HyH ) oi redox electrons in the adsorbed redox particles the state density of the occupied electron level equals the state density of the vacant electron level at the Fermi level ( b = Da). Assuming the Langmuir adsorption isotherm at low adsorption coverages and the Gaussian distribution for the state density, we obtain Eqn. 5-55 for the Fermi level  

Since the electron transfer of the interfacial redox reaction, + cm = H.a on electrodes takes place between the iimer Helmholtz plane (adsorption plane at distance d ) and the electrode metal, the ratio of adsorption coverages 0h,j/ in electron transfer equilibrium (hence, the charge transfer coefficient, 6z) is given in Eqn. 5-58 as a function of the potential vid /diOMn across the inner Helmholtz layer  

The same approach may also apply to the adsorption of redox particles other than the adsorption of proton-hydrogen atom on metal electrodes. To understand electrosorption phenomena, various concepts have been proposed such as the charge transfer coefficient and the adsorption valence [Vetter-Schultze, 1972]. The concept of the redox electron level in adsorbed particles introduced in this textbook is usefiil in dealing with the adsorption of partially ionized particles at electrodes. 

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Further, the electron level of adsorbed particles differs from that of isolated adsorbate i>articles in vacuum as shown in Fig. 5-5, this electron level of the adsorbate particle shifts in the course of adsorption by a magnitude equivalent to the adsorption energy of the particles [Gomer-Swanson, 1963]. In the illustration of Fig. 5-5, the electron level of adsorbate particles is reduced in accordance with the potential energy curve of adsorption towards its lowest level at the plane of adsorption where the level width is broadened. In the case in which the allowed electron energy level of adsorbed particles, such as elumo and ehcmio, approaches the Fermi level, ep, of the adsorbent metal, an electron transfer occurs between... 

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