Kinetics of electron transfer

We consider a simple electron transfer reaction (an outer-sphere electron transfer) between h3 rated redox particles OX /RED and a metal electrode M as shown in Eqn. 8-1  

The plane of closest approach of hydrated ions, the outer Helmholtz plane (OHP), is located 0.3 to 0.5 run away from the electrode interface hence, the thickness of the interfacial compact layer across which electrons transfer is in the range of 0.3 to 0.5 nm. Electron transfer across the interfacial energy barrier occurs through a quantum tunneling mechanism at the identical electron energy level between the metal electrode and the hydrated redox particles as shown in Fig. 8-1. 

The rate of cathodic electron transfer by tunneling, at an electron level c, from the electrode to the oxidant particles is proportional to the product of the state density occupied by electrons Ai(.)(c) in the electrode and the state density 

The state density of electrons ZXe) in the reductant and oxidant particles is given in Eqn. 8-2 by the product of the probability density W(e) and the particle concentration c as has been shown in Eqns. 2-48 and 2-49  

The total state density of redox electrons is then expressed in Eqn. 8-3  

---

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

Heterogeneous electron reactions at liquid liquid interfaces occur in many chemical and biological systems. The interfaces between two immiscible solutions in water-nitrobenzene and water 1,2-dichloroethane are broadly used for modeling studies of kinetics of electron transfer between redox couples present in both media. The basic scheme of such a reaction is... 

A question arises as to what happens if the Nernstian approximation breaks down. Under these circumstances, we must use the proper equations for the kinetics of electron transfer discussed in chapter 1. The simplest case is that of a completely irreversible system, where only oxidation (or reduction) is possible and a single electron is transferred, i.e. consider the process ... 

Jin, Q. and C. M. Bethke, 2002, Kinetics of electron transfer through the respiratory chain. Biophysical Journal 83, 1797-1808. 

The structure of HRP-I has been identified as an Fe(IV) porphyrin -ir-cation radical by a variety of spectroscopic methods (71-74). The oxidized forms of HRP present differences in their visible absorption spectra (75-77). These distinct spectral characteristics of HRP have made this a very useful redox protein for studying one-electron transfers in alkaloid reactions. An example is illustrated in Fig. 2 where the one-electron oxidation of vindoline is followed by observing the oxidation of native HRP (curve A) with equimolar H202 to HRP-compound I (curve B). Addition of vindoline to the reaction mixture yields the absorption spectrum of HRP-compound II (curve C) (78). This methodology can yield useful information on the stoichiometry and kinetics of electron transfer from an alkaloid substrate to HRP. Several excellent reviews on the properties, mechanism, and oxidation states of peroxidases have been published (79-81). 

If the kinetics of electron transfer does not obey the Butler-Volmer law, as when it follows a quadratic or quasi-quadratic law of the MHL type, convolution (Sections 1.3.2 and 1.4.3) offers the most convenient treatment of the kinetic data. A potential-dependent apparent rate constant, kap(E), may indeed be obtained derived from a dimensioned version of equation (2.10) ... 

As with the other reaction schemes involving the coupling of electron transfer with a follow-up homogeneous reaction, the kinetics of electron transfer may interfere in the rate control of the overall process, similar to what was described earlier for the EC mechanism. Under these conditions a convenient way of obtaining the rate constant for the follow-up reaction with no interference from the electron transfer kinetics is to use double potential chronoamperometry in place of cyclic voltammetry. The variations of normalized anodic-to-cathodic current ratio with the dimensionless rate parameter are summarized in Figure 2.15 for all four electrodimerization mechanisms. 

The information thus obtained on the redox properties of the radicals is a global reduction potential in which the thermodynamic and kinetic parameters are intermingled [equation (2.39)]. It is possible to separate these parameters if it is assumed that the kinetics of electron transfer to the radical obeys the MHL law in its approximate quadratic version (see Section 1.4.2) ... 

Effect of surface chelation on the kinetics of electron transfer from the conduction band of Ti02 to methylviologen (MV2+). Oscillograms showing the time-dependent growth of the MV+ absorption at 630 nm after laser excitation (at 355 nm) of aqueous solutions (pH 4.85) containing colloidal Ti02 (1 g/e) and 10 3 M MV2+ ... 

In order to probe these effects, a number of studies on the kinetics of electron transfer between small molecule redox reagents and proteins, as well as protein-protein electron transfer reactions, have been carried out (38-41). The studies on reactions of small molecules with electron transfer proteins have pointed to some specificity in the electron transfer process as a function of the nature of the ligands around the small molecule redox reagents, especially the hydrophobicity of these... 

We consider a simple redox electron transfer of hydrated redox particles (an outer-sphere electron transfer) of Eqn. -1 at semiconductor electrodes. The kinetics of electron transfer reactions is the same in principal at both metal and semiconductor electrodes but the rate of electron transfer at semiconductor electrodes differs considerably from that at metal electrodes because the electron occupation in the electron energy bands differs distinctly with metals and semiconductors. 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

Flash photolysis has been used to investigate the kinetics of electron transfer from tyrosine to Ru in [Ru(bpy)2(4-Me-4 -CONH-L-tyrosine ethyl ester-2,2 -bpy)] " as a function of pH and temperature. " Model systems for PSII have moved to di- and trimanganese systems containing... 

In the last two decades, studies on the kinetics of electron transfer (ET) processes have made considerable progress in many chemical and biological fields. Of special interest to us is that the dynamical properties of solvents have remarkable influences on the ET processes that occur either heterogeneously at the electrode or homogeneously in the solution. The theoretical and experimental details of the dynamical solvent effects on ET processes have been reviewed in the literature [6], The following is an outline of the important role of dynamical solvent properties in ET processes. 

The dynamical solvent effects on the kinetics of electron-transfer processes have been reviewed in detail in Refs [24a] and [32] and concisely in Section 3.6 of Ref. [8]. 

The kinetics of electron transfer reactions at electrodes can be explained either by surmounting an activation barrier due to the chemical reorganization of the reactants or by tunnelling through the potential barrier across the electrode—solution interface. 

Both the thermodynamics and kinetics of electron transfer reactions (redox potentials and electron transfer rates) have steric contributions, and molecular mechanics calculations have been used to identity them. A large amount of data have been assembled on Co3+/Co2+ couples, and the majority of the molecular mechanics calculations reported so far have dealt with hexaaminecobalt (III/II) complexes. 

---