Rates standard heterogeneous

Second-order rate constant of forward reaction, mol i Standard heterogeneous rate constant, ms ... 

At the standard potential, kfh = kb h = ks h, for all reactants in the standard state, where ks h is the standard heterogeneous rate constant, defined according to the Arrhenius equation as... 

If the rate of electron transfer is low (or the scan rate is too high), electron transfer will not be able to adjust the surface concentrations of -Fc and -Fc+ to values that are at equilibrium with the applied potential (quasireversible or totally irreversible case, see Chap. 3). In this case, the anodic peak and the cathodic peaks will not be at the same potential that is, AEpk will be greater than zero volts. Kinetic information about the surface-bound redox couple can be obtained from such quasireversible or irreversible voltammograms. For example, methods for obtaining the standard heterogeneous rate constant (see Chap. 2) for the surface-confined redox couple have been developed [41,42]. 

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 ... 

When the heterogeneous electron transfer (ET) between the electrode and the molecule in solution is slow, dramatic changes may be exhibited in the CV diagnostic criteria. Modest decreases in kf and kb (a quasireversible system) cause a modest increase in AEp, the change of which with v may be used to calculate ks, the standard heterogeneous ET rate (ks = kf = kb at E = E° ). As the ET rates become smaller, the waves are more likely to reflect the influence of the transfer coefficient, a, on the wave shape. The forward and reverse branches are shaped as mirror images only if a = 0.5. If a < 0.5, the cathodic branch is broader the converse is true if a > 0.5 (Fig. 23.7). 

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°. 

As in BV, the MHC model describes the electrode kinetics as a function of three parameters the formal potential, the standard heterogeneous rate constant, and the reorganization energy. Nevertheless, important differences can be observed between the two kinetic models with respect to the variation of the rate constants with the applied potential. Whereas in BV rate constants vary exponentially and... 

Fig. 1.18 Variation of the standard heterogeneous rate constant, k°, with the electronic coupling element for different vn and X values. The effect of the electronic interaction on the activation energy has been ignored [2, 49]. / r = 108cm I, pM = 0.3 eV4, T = 298 K...

It is interesting to analyze the transition between the non-adiabatic and adiabatic regimes in terms of the standard heterogeneous rate constant, k°, given that this is the parameter commonly referred to in kinetic studies. Considering that k° is defined as the value of the reduction and oxidation rate constants at the formal... 

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] ... 

Electron transfer properties of polyhalogenated biphenyls were investigated by cyclic voltammetry. The primary reduction peak of 4,4 -dichlorobiphenyl, involving replacement of halide with hydrogen in an irreversible ECE- type reaction, are under kinetic control of the initial ET step. Electrochemical transfer coefficients, standard potentials and standard heterogeneous rate constants were also estimated from the voltammetric data230. 

The standard heterogeneous rate constant, seen in (2.21) and (2.22), with dimensions ms-1, is normalised by... 

Blaedel and Engstrom [48] noted that for a quasi-reversible process the current could be simply expressed in terms of the rate constant and mass-transport coefficient. Application of a square wave step in the rotation rate of a RDE (i.e., PRV, see Section 10.4.1.3) resulted in modulation of the diffusion-limited current and hence modulation of the mass-transfer coefficient. By solving the appropriate quadratic equation it was possible to derive a value for the heterogeneous rate constant for the electrochemical cathodic, kf, or anodic, kb, process of interest. Values for the standard heterogeneous rate constant and transfer coefficient were subsequently... 

Activation volume — As in case of homogeneous chemical reactions, also the rate of heterogeneous electron transfer reactions at electrode interfaces can depend on pressure. The activation volume AVZ involved in electrochemical reactions can be determined by studying the pressure dependence of the heterogeneous -> standard rate constant ks AVa = -RT j (p is the molar - gas constant, T absolute temperature, and P the pressure inside the electrochemical cell). If AI4 is smaller than zero, i.e., when the volume of the activated complex is smaller than the volume of the reactant molecule, an increase of pressure will enhance the reaction rate and the opposite holds true when A14 is larger than zero. Refs. [i] Swaddle TW, Tregloan PA (1999) Coord Chem Rev 187 255 [ii] Dolidze TD, Khoshtariya DE, Waldeck DH, Macyk J, van Eldik R (2003) JPhys Chem B 107 7172... 

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