Heterogeneous electron transfer electronic coupling

Cyclic voltammetry is the most widely used technique for acquiring qualitative information about electrochemical reactions. The power of cyclic voltammetry results from its ability to rapidly provide considerable information on the thermodynamics of redox processes, on the kinetics of heterogeneous electron-transfer reactions, and on coupled chemical reactions or adsorption processes. Cyclic voltammetry is often the first experiment performed in an electroanalytical study. In particular, it offers a rapid location of redox potentials of the electroactive species, and convenient evaluation of the effect of media upon the redox process. 

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... 

Unlike solid state -stacks, however, double helical DNA is a molecular structure. Here CT processes are considered in terms of electron or hole transfer and transport, rather than in terms of material conductivity. Moreover, the 7r-stack of DNA is constructed of four distinct bases and is therefore heterogeneous and generally non-periodic. This establishes differences in redox energetics and electronic coupling along the w-stack. The intimate association of DNA with the water and counterions of its environment further defines its structure and contributes to inhomogeneity along the mole-... 

The EC mechanism (Scheme 2.1) associates an electrode electron transfer with a first-order (or pseudo-first-order) follow-up homogeneous reaction. It is one of the simplest reaction schemes where a heterogeneous electron transfer is coupled with a reaction that takes place in the adjacent solution. This is the reason that it is worth discussing in some detail as a prelude to more complicated mechanisms involving more steps and/or reactions with higher reaction orders. As before, the cyclic voltammetric response to this reaction scheme will be taken as an example of the way it can be characterized qualitatively and quantitatively. 

The preceding approach applies to all linear systems that is, those involving mechanisms in which only first-order or pseudo-first-order homogeneous reactions are coupled with the heterogeneous electron transfer steps. As seen, for example, in Section 2.2.5, it also applies to higher-order systems, involving second-order reactions, when they obey pure kinetic conditions (i.e., when the kinetic dimensionless parameters are large). If this is not the case, nonlinear partial derivative equations of the type... 

Commonly, in the description of chemical reactions coupled to electron transfer, the homogeneous chemical reaction is indicated by C and the heterogeneous electron transfer by E. The order of C with respect to E then follows the chronological order in which the two events occur. Furthermore, while Ox and Red indicate the electro active species, other non-electro active species which result from the coupled chemical complications are indicated by Y, Z, W, etc. 

From Eq. (9.6), mo D/d if L<1. This suggests the usefulness of SECM for the study of rapid heterogeneous electron transfer kinetics, the largest ks values that can be determined being of the order of D/d. The largest ks values measurable by voltammetry at UMEs are of the order of D/a. It is easier to get a small L value with SECM than to prepare a UME of very small a value. For example, ks for the Fc+/Fc couple in AN has been determined by SECM to be 3.7 cm s-1 [29]. 

The distance dependence of electron transfer has been studied extensively for the homogeneous case. An approximately exponential decay of the electronic coupling has been found with the number of saturated bonds in the spacer unit (see for example [6,7]). The results presented here suggest that an exponential dependence fits also our data for heterogeneous electron transfer in ultra-high vacuum. A different result has been reported for electron transfer from Re complexes to anatase where a local triplet state can play a role [8]. 

Quantitative studies using LSV and CV can be carried out for both heterogeneous charge transfer kinetics and the kinetics of homogeneous chemical reactions coupled to charge transfer at electrodes. These methods should continue to play a major role in the study of electron transfer reactions. 

Thus for large amplitudes, the current is logarithmically related to overpotential as shown in Figure 2.17. Tafel plots (Fig. 2.17) are frequently employed by physical electrochemists to determine exchange currents and transfer coefficients. There are many other ways to obtain these parameters experimentally, but such numbers are rarely of interest to the analytical chemist. As we will see later, the rate of the heterogeneous electron transfer relative to other controlling factors (e.g., diffusion and coupled chemical reactions) is of critical importance to most experiments. 

SEV is an effective means of probing homogeneous chemical reactions that are coupled to electrode reactions, especially when it is extended to cyclic voltammetry as described in the next section. Considerable information can be obtained from the dependence of ip and Ep on the rate of potential scan. Figure 3.20 illustrates the behavior of ip and Ep with variation in scan rate for a reversible heterogeneous electron transfer reaction that is coupled to various types of homogeneous chemical reactions. The current function j/p is proportional to ip according to the equation... 

Achieving resonance is a necessary but not sufficient condition for successful heterogeneous electron transfer. Once isoenergetic reactants have been created, the donor or acceptor orbitals and the electrode manifold states must couple electronically. The extent to which the redox centers and the electrode are electronically coupled typically increases exponentially with decreasing separation between the reactant and the electrode. 

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 ... 

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