Gibbs energy of electrons

Gibbs energy of electron transfer (AGe ) and the work terms for precursor formation (Wp) and successor dissociation (ws),... 

Fig. 23. Logarithm of the true backward rate constant lc vs. the corrected standard Gibbs energy of electron transfer (corrected Thfel plot) between ferrocene in nitrobenzene and hexacyano-ferrate(III) in water. Composition of the aqueous phase 1 mM K3(Fe(CN)g]+LiCl. Nitrobenzene phase 0.01 M ferrocene and Bu4NPh4B. Concentration of both base electroiytes 0.01 M (O), 0.05 M ( ) or 0.1 M (V). (After [193]).

FIGURE 1.26 Water-soluble porphyrin (CHL) (Jensen, H D. J. Fermin, and H. H. Girault, 2001, Phys Chem Chem Phys, Vol. 3, p. 2503) and photocurrent dependence on the formal Gibbs energy of electron transfer. (Eugster, N., D. J. Fermin, and H. H. Girault, 2002, J Phys Chem B, Vol. 106, p. 3428. Used with permission.)... 

Under the conditions of electrochemical experiment, the charge transfer occurs near the equilibrium state when the Gibbs energy of electron transfer (AGj.) can be thought of as zero. As a result, the Marcus general formula (Equation 3.6.1) can be simplified [12] ... 

Furthermore, equilibria hold for ions and electrons. In every case, the Gibbs energy of the defect reaction has to provide a minimum for the equilibrium concentrations ... 

On application of an overpotential rj, the Gibbs energy of the electron-transfer step changes by eo[r) — Afa rj), where Afa(rj) is the corresponding change in the potential fa at the reaction site. Consequently, rj must be replaced by [rj — Afa r )] in the Butler-Volmer equation (5.13). 

There is a fundamental difference between electron-transfer reactions on metals and on semiconductors. On metals the variation of the electrode potential causes a corresponding change in the molar Gibbs energy of the reaction. Due to the comparatively low conductivity of semiconductors, the positions of the band edges at the semiconductor surface do not change with respect to the solution as the potential is varied. However, the relative position of the Fermi level in the semiconductor is changed, and so are the densities of electrons and holes on the metal surface. 

Polynomial expressions are conveniently used to represent a condensed phase which is stable in the whole temperature range of interest and which does not undergo any structural, electronic or magnetic transformations. The Gibbs energy of a compound is in the CALPHAD approach represented relative to the elements in their defined standard state at 298.15 K as a power series in terms of temperature in the form of [16] ... 

Table 2.1. Values o f standard Gibbs energies of ion transfer from water to nitrobenzene in electron volts. From P. Vanysek, Thesis, J. Heyrovsky Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, Prague (1982).

The development of a consistent theory for a dissociative electron transfer is a recent challenge in the field of theoretical electrocatalysis. Progress in this field of electrochemistry has involved the use of an harmonic Morse curves [25] instead of harmonic approximations. Applying the principles of the theory of the activated complex to adiabatic dissociative electron transfer reactions, the work of Saveant resulted in the following expressions [24] for the Gibbs energy of activation... 

As discussed below, any proper description of the system needs to consider the continuum of electronic levels in the metal (see Sect. 1.7.2.1). Therefore, one can act on the activation barriers, and hence, on the electrode kinetics, by varying the applied potential difference, E. For example, when the electrode potential is set to a value smaller than the formal potential (see Fig. 1.13), the Gibbs energy of the electrons (and therefore that of the reactants O I e ) is increased by... 

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