Kinetic parameters heterogeneous electron-transfer

Morris studied the aqueous solution voltammetric behavior of some uranyl coordination complexes to learn how changes in the ligand environment influence the redox potentials and heterogeneous electron-transfer kinetic parameters for the single-electron transfer... 

When the electrolysis process is irreversible (in a thermodynamic sense) but still limited by linear diffusion, the potential-time relationship takes a form that includes the heterogeneous electron-transfer kinetic parameters. For a cathodic process the relation is... 

Heterogeneous Electron Transfer Kinetic Parameters of Redox Proteins by Single Potential Step Chronoabsorptometry... 

E. E. Bancroft, H. N. Blount, and F. M. Hawkridge, in Spectroelectrochemical Determination of Heterogeneous Electron Transfer Kinetic Parameters (K. M. Kadish, ed.). Advances in Chemistry Series No. 201, Chap. 2, American Chemical Society, Washington,... 

References in italics cite heterogeneous electron transfer kinetic parameters. 

The single potential step chronoabsorptometry technique has been employed to determine the heterogeneous electron transfer kinetic parameters of myoglobin [36], horse heart cytochrome c [37] and soluble spinach ferredoxin [38]. In every case, the chronoabsorptometric data were analysed according to the irreversible model (the reverse reaction is ignored). The error associated with the use of this model for the kinetic analysis of these systems is most pronounced at low overpotentials, long transient times, and large reaction rates. 

Edmund E. Bowden conducted potential step chronoabsorptometry experiments on the reaction of myoglobin at modified gold minigrid electrodes [40]. Although these experiments were very reproducible, the heterogeneous electron transfer kinetic parameters raised concerns, namely, the rate constant was very low (k° = 3.9 X 10-11 cm/s) and alpha was high (a = 0.88). These issues became muted as the work progressed, as will be discussed below. 

The previous sections dealt with a generalized theory of heterogeneous electron-transfer kinetics based on macroscopic concepts, in which the rate of the reaction was expressed in terms of the phenomenological parameters, and a. While useful in helping to organize the results of experimental studies and in providing information about reaction mechanisms, such an approach cannot be employed to predict how the kinetics are affected by such factors as the nature and structure of the reacting species, the solvent, the electrode material, and adsorbed layers on the electrode. To obtain such information, one needs a microscopic theory that describes how molecular structure and environment affect the electron-transfer process. 

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... 

The validity of an electroanalytical measurement is enhanced if it can be simulated mathematically within a reasonable model , that is, one comprising all of the necessary elements, both kinetic and thermodynamic, needed to describe the system studied. Within the chosen model, the simulation is performed by first deciding which of the possible parameters are indeed variables. Then, a series of mathematical equations are formulated in terms of time, current and potential, thereby allowing the other implicit variables (rate constants of heterogeneous electron-transfer or homogeneous reactions in solution) to be obtained. 

The application of CA for monitoring the progress of a chemical reaction following the heterogeneous electron transfer is limited by the nature of the process. It is clear from the Cottrell equation, Equation 6.33, that the only parameter that may be affected by a follow-up reaction is the number of electrons, n. Thus, important mechanisms such as eC and eC(dim) cannot be distinguished by CA. This limits the application of CA for kinetic studies. In contrast, DPSCA is a most useful method. 

Electrochemical studies on SAMs have proven invaluable in elucidating the impact of various molecular parameters such as bridge structure, molecular orientation or the distance between the electroactive species and electrode surface. As described above in Section 5.2.1, the kinetics of heterogeneous electron transfer have been studied as a function of bond length for many systems. Similarly, the impact of bridge structure and inter-site distances have been studied for various supramolecu-lar donor-acceptor systems undergoing photoinduced electron transfer in solution. In both types of study, electron transfer is observed to increase as the distance between the donor and acceptor decreases. As discussed earlier in Chapter 2, the functional relationship between the donor-acceptor distance and the electron transfer rate depends on the mechanism of electron transfer, which in turn depends on the electronic nature of the bridge. 

The above analysis also shows that for almost all applications of fast CV employing V > 1 kV s , the quasi-reversible or irreversible nature of heterogeneous electron transfer reactions must be considered. In particular, this becomes important when fast CV is used in a kinetic analysis of fast homogeneous follow-up reactions. The extraction of the relevant rate constants is complicated by the mixed kinetic control of the electrode process and the chemical reaction. As a result, the number of parameters involved in the fitting procedures is increased considerably and with it the possibility of introducing errors. 

Chronoabsorptometry has been applied to the determination of heterogeneous electron-transfer parameters in single-step irreversible [55] and quasi-irreversible kinetics [56] and in double potential step modes [57]. In the case of a single potential step for the reaction... 

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 ... 

This section concerns heterogeneous electron transfer reactions coupled with homogeneous chemical reactions in which either the electroactive species A or the product of the electron transfer B participate as reactants. Perturbations of electrochemical responses of different techniques evoked by these reactions enable the elucidation of the mechaism and the evaluation of the kinetic parameters of the chemical steps. Chemical reactions that are indicated in the electrochemical way occur in the thin layer reaction layer) adjacent to the electrode surface only. This is illustrated in Fig. 1 where the concentration dependence of the product B on the distance from the electrode plane (with and without follow-up chemical reaction) is plotted. It must be stressed that the kinetics and the electrode mechanism are affected not only by the nature of the electroactive as well as electroinactive species including the type of the solvent, but also by the electrode material and substances adsorbed on the electrode surface. 

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