Electron Gerischer theory

Figure 42. Scheme comparing expected potential-independent charge-transfer rates from Marcus-Gerischer theory of interfacia) electron transfer (left) with possible mechanisms for explaining the experimental observation of potential-dependent electron-transfer rates (right) a potential-dependent concentration of surface states, or a charge-transfer rate that depends on the thermodynamic force (electric potential difference) in the interface. 

If the graphical description of the Gerischer theory is used (Figure 25), it follows that cathodic electron transfer will predominantly occur by tunneling in the energy range close to Asq)]. It follows that the rate of cathodic transfer will increase less than exponentially with If becomes equal to or higher than the cathodic... 

Semiconductor-Liquid Junction From Fundamentals to Solar Fuel Generating Structures, Fig. 7 Overview of selected output power characteristics of photoelectrochemical solar cells operating in the photovoltaic mode note that here, also 2-electron transfCT redox couples have been used, for which the Marcus-Gerischer theory does not apply the output power characteristics have been normalized and the respective efficiencies are given at each characteristic the conditions (illumination intensity and source) are as follows n-GaAs 95mWcm (sunlight) [15, 17] p-InP ... 

Attempts were made to quantitatively treat the elementary process in electrode reactions since the 1920s by J. A. V. Butler (the transfer of a metal ion from the solution into a metal lattice) and by J. Horiuti and M. Polanyi (the reduction of the oxonium ion with formation of a hydrogen atom adsorbed on the electrode). In its initial form, the theory of the elementary process of electron transfer was presented by R. Gurney, J. B. E. Randles, and H. Gerischer. Fundamental work on electron transfer in polar media, namely, in a homogeneous redox reaction as well as in the elementary step in the electrode reaction was made by R. A. Marcus (Nobel Prize for Chemistry, 1992), R. R. Dogonadze, and V. G. Levich. 

Gerischer developed a complete theory for redox systems at metal and semiconductor electrodes on the basis of Gurney s treatment [69], The difference between the metal and a semiconductor is the integration over the electronic states in the electrode [17]. 

Three landmark papers on the application of time-dependent perturbation theory to electrochemical problems were published in rapid succession by - Levich and - Dogonadze in 1959 [iii], - Gerischer in 1960 [iv], and McConnell in 1961 [v]. A very large literature has subsequently sprung from these works, driven by developments in scanning tunneling microscopy, molecular electronics, and biological electron transfer. 

Information about further energy levels in a redox system can be derived from the theory of electron transfer between a redox system and an electrode, which has been derived by various authors [2-5]. In all these theories it is assumed that the vibration of redox molecules and their surrounding solvation shell is slow, compared to the actual electron transfer, i.e. it is assumed that the Frank-Condon principle is valid. As shown by Gerischer [44], this assumption leads to the consequence that the energy levels involved in the charge transfer differ from the thermodynamic value Ep, jox- This model leads to a distribution of empty and occupied states versus electron energy, as illustrated in Fig. 6. These electron states are not discrete energy levels, but are distributed over... 

During the last 30 years, a number of theories on electron transfer processes have been published by Gerischer [1, 5], Marcus [2], Levich [4] and Dogonadze [3,82]. Especially the models and theories developed by Marcus and Gerischer are applied for electrochemical reactions at metal and semiconductor electrodes by many other scientists. On the basis of these theories, the electron flux or interfacial currents can be derived as follows ... 

A review of electrochemical models of development has been given by Sahyun [109] in which selectivity is treated in terms of the Marcus and Gerischer [110] theories of electron transfer. 

Theory Gerischer has described a theory for excited-state electron transfer to semiconductors.90-92 The rate constant for interfacial electron transfer is proportional to the overlap of occupied donor levels of the excited state, fTdon( ), with unoccupied acceptor states in the semiconductor IXE) (Equation 12.6) ... 

A second technique that has been used is the measurement of photovoltage. The basis of this technique is that, on illumination under open-circuit conditions, the potential distribution will be modified so as to eliminate the potential drop within the depletion layer. In fact, as has been demonstrated by Kautek and Gerischer [7], the theory of the photovoltage effect is far from straightforward, especially in the presence of surface states. The effect is a steady-state rather than equilbrium phenomenon the potential distribution will change until the flux of holes to the surface is equal to the flux of electrons and the potential at which this occurs will depend on the recombination kinetics at the surface. Only when these kinetics are slow, i.e. when the surface states are slow and the main surface state equilbrium is with the redox couple in solution, is the technique likely to give results that can be interpreted within a consistent framework. 

How does the electron transfer occur in a redox process One description of this process was developed by Gerischer, based on the former work of Gurney and Essin. Another description goes back to the work of Marcus.Other contributions during the development of the basic theory came from Dogonadze, Levich, Chizmadzhev, Kuznetsov, and others. The model will be described for a simple redox reaction, the oxidation of a two-valent iron ion into a three-valent iron ion and vice versa. 

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