Heterogeneous electron-transfer rate constant

Fig. 5. Plot of apparent electron self exchange rate constants kf P, derived from polymer De values for films containing the indicated metals, mixed valent states, and ligands, all in acetonitrile, using Equation 2, vs. literature heterogeneous electron transfer rate constants k° for the corresponding monomers in nitrile solvents. See Ref. 6 for details. (Reproduced from Ref. 6. Copyright 1987 American Chemical Society.)...

Fig. 2. Influence of value of the heterogeneous electron-transfer rate constant kh on the shape...

There has been keen interest in determination of activation parameters for electrode reactions. The enthalpy of activation for a heterogeneous electron transfer reaction, AH X, is the quantity usually sought [3,4]. It is determined by measuring the temperature dependence of the rate constant for electron transfer at the formal potential, that is, the standard heterogeneous electron transfer rate constant, ks. The activation enthalpy is then computed by Equation 16.7 ... 

It is much more popular to use nonaqueous solvents for low-temperature studies. There are two motivations, the more common of which is the desire to make measurements down to the lowest temperature possible using a solvent/ electrolyte system compatible with the chemical properties of the substances to be studied. In other instances, the purpose of the experiments is to study the effect of solvent on a temperature-sensitive parameter (e.g., a heterogeneous electron-transfer rate constant [5]), so a variety of solvents is sought in which low-temperature measurements can be made. 

Heterogeneous electron transfer rate constant, see equation (8) in text, for i oxidation determined as in ref. 16. dData from ref. 16. 

The kinetics of an electron transfer reaction are described by the heterogeneous electron transfer rate constants, kj ed and k°x, where the subscript s indicates that the process takes place at an electrode surface. The values of Zcsred and kfx depend exponentially on E as seen in Equations 6.10 and 6.11 ... 

Here, k° is the standard heterogeneous electron transfer rate constant and a is the electrochemical transfer coefficient [33], which corresponds in electrochemistry to the Bronsted coefficient in organic chemistry. It is seen from Equations 6.10 and 6.11 that kTsei and k°x are both equal to k° at E = E°. 

Forster and Keyes prepared the tetrazine containing [Os(II)(BL)Os(III)] dimer (see below) and examined light induced intramolecular electron transfer in the system. They also measured heterogeneous electron transfer rate constants for oxidation of the complex at a Pt electrode [38]. The work is... 

The first exponential term in both equations is independent of the applied potential and is designated as k and A(L for the forward and backward processes, respectively. These represent the rate constants for the reaction at equilibrium, e.g. for a monolayer containing equal concentrations of both oxidized and reduced forms. However, the system is at equilibrium at E0/ and the products of the rate constant and the bulk concentration are equal for the forward and backward reactions, i.e. k must equal Therefore, the standard heterogeneous electron transfer rate constant is designated simply as k°. Substitution into Equations (2.19) and (2.20) then yields the Butler-Volmer equations as follows ... 

Therefore, unlike the empirical Butler-Volmer theory, in the Marcus formulation the heterogeneous electron transfer rate constant is sensitive to both the structure of the redox center and the solvent. 

The sensitivity of the heterogeneous electron transfer rate constant to the overpotential depends on the extent of electronic coupling between the reactant and the electrode [19]. For strongly coupled reactants, electron transfer occurs predominantly through states near the Fermi level of the electrode and the adiabatic potential-dependent rate constant is given by the product of the frequency factor, vn, and the density of acceptor states in the molecule, Dox, according to the following ... 

Figure 5.1 Semi-log plots of the standard heterogeneous electron transfer rate constant, fc°, versus the number of methylene units in the alkane thiol bridge for various materials electrostatically adsorbed on HS(CH2) COOH , [HS(CH2) CONHCH2py-Ru(NH3)5]2+ A, HS(CH2) NHCO-ferrocene , HS(CH2) OOC-ferrocene 0, cytochrome C...

Figure 5.2 Tafel plots of In k versus overpotential for a mixed self-assembled monolayer containing HS(CH2)i600C-ferrocene and HS(CH2)isCH3 in 1.0 M HCIO4 at three different temperatures V, 1 °C O/ 25 °C , 47°C. The solid lines are the predictions of the Marcus theory for a standard heterogeneous electron transfer rate constant of 1.25 s-1 at 25 °C, and a reorganization energy of 0.85 eV (= 54.8 kj moh1). Reprinted with permission from C. E. D Chidsey, Free energy and temperature dependence of electron transfer at the metal-electrolyte interface, Science, 251, 919-922 (1991). Copyright (1991) American Association for the Advancement of Science...

The electron transfer dynamics of monolayers based on osmium polypyridyl complexes linked to an electrode surface through conjugated and non-conjugated bridges, e.g. frans-l,2-bis(4-pyridyl)ethylene (bpe) and 1,2-bis(4-pyridyl)ethane (p2p), respectively, have been explored [18]. The standard heterogeneous electron transfer rate constant, k°, depends on both a frequency factor and a Franck-Condon barrier, as follows [19-21] ... 

The sensitizer molecules adsorbed on Ti02 surface have a significantly shorter fluorescence lifetime than in the homogeneous solution and this decrease in lifetime has been attributed to the charge injection process [83,181-183,186-188, 197,218,225,236-239]. Heterogeneous electron transfer rate constants in the range of 107—1011 have been reported in these studies. 

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