Standard heterogeneous electron transfer rate constant

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 ... 

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°. 

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 ... 

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] ... 

Research into this area is dominated by microelectrodes. At short times, the diffusion layer thickness is much smaller than the microelectrode radius and the dominant mass transport mechanism is planar diffusion. Under these conditions, the classical theories, e.g., that of Nicholson and Shain, can be used to extract kinetic parameters from the scan rate dependence of the separation between the anodic and cathodic peak potentials. Using this approach, the standard heterogeneous electron transfer rate constant, k°, may be determined from the published working curves relating AEp to a kinetic parameter The variation of AEp with o is determined and, from this, T is calculated. k° is then determined by the following equation ... 

The relationship between the standard heterogeneous electron transfer rate constant, k, h> and structural factors is expressed in terms of the Marcus-Hush theory applied to electrode reactions [2] ... 

At macroelectrodes the Nicholson method is routinely used to estimate the observed standard heterogeneous electron transfer rate constant (k°, cm s ) for quasi-reversible systems using the following equation [3] ... 

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