Reaction rates, heterogeneous electron

Section 3 deals with reactions in which at least one of the reactants is an inorganic compound. Many of the processes considered also involve organic compounds, but autocatalytic oxidations and flames, polymerisation and reactions of metals themselves and of certain unstable ionic species, e.g. the solvated electron, are discussed in later sections. Where appropriate, the effects of low and high energy radiation are considered, as are gas and condensed phase systems but not fully heterogeneous processes or solid reactions. Rate parameters of individual elementary steps, as well as of overall reactions, are given if available. 

Interfacial electron transfer is the critical process occurring in all electrochemical cells in which molecular species are oxidized or reduced. While transfer of an electron between an electrode and a solvated molecule or ion is conceptually a simple reaction, rates of heterogeneous electron transfer processes depend on a multitude of factors and can vary over many orders of magnitude. Since control of interfacial electron transfer rates is usually essential for successful operation of electrochemical devices, understanding the kinetics of these reactions has been and remains a challenging and technologically important goal. 

Definition of symbols AEp = peak potential difference, Epa = peak potential at cathodic peak current, Epc = peak potential at anodic peak current, tpa = anodic peak current, ipc = cathodic peak current, s = scan rate, t = time after peak (the Cottrell region), n = number of electrons involved in redox reaction. Rate parameters (acn ) and heterogeneous rate constant can be found from irreversible wave. 

In photosynthetic systems, some electron transfer processes exhibit nonexponential kinetics at low temperature, which are generally attributed to the existence of different conformations of the system. While the differences between the reaction rates corresponding to these conformations do not exceed a factor of four in some cases [157,158,159], they are sufficient to lead to different quantum yields in others [160, 161]. Sometimes, the heterogeneous character of the kinetics disappears at room temperature, which probably reflects a fast exchange between the conformations that are frozen at low temperature [157, 158]. A systematic study of all these effects, similar to that performed in Ref [159], could give useful information about the nature of the conformational differences. 

If the first e step, i.e., heterogeneous electron transfer, is slow (non-Nernstian) or if the cyclization reaction is faster than the electron transfer itself, the electron transfer becomes rate-determining and nothing can be done about the mechanism of cyclization. 

Electron movement across the electrode solution interface. The rate of electron transfer across the electrode solution interface is sometimes called k. This parameter can be thought of as a rate constant, although here it represents the rate of a heterogeneous reaction. Like a rate constant, its value is constant until variables are altered. The rate constants of chemical reactions, for example, increase exponentially with an increasing temperature T according to the Arrhenius equation. While the rate constant of electron transfer, ka, is also temperature-dependent, we usually perform the electrode reactions with the cell immersed in a thermostatted water bath. It is more important to appreciate that kei depends on the potential of the electrode, as follows ... 

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 combined use of the modem tools of surface science should allow one to understand many fundamental questions in catalysis, at least for metals. These tools afford the experimentalist with an abundance of information on surface structure, surface composition, surface electronic structure, reaction mechanism, and reaction rate parameters for elementary steps. In combination they yield direct information on the effects of surface structure and composition on heterogeneous reactivity or, more accurately, surface reactivity. Consequently, the origin of well-known effects in catalysis such as structure sensitivity, selective poisoning, ligand and ensemble effects in alloy catalysis, catalytic promotion, chemical specificity, volcano effects, to name just a few, should be subject to study via surface science. In addition, mechanistic and kinetic studies can yield information helpful in unraveling results obtained in flow reactors under greatly different operating conditions. 

As shown by the cyclic voltammetric response in Fig. 10, the peak potential separation of the initial Mn(II,II) — Mn(II,III) electrode reaction is much larger than that of the other steps. This suggests significant inner-shell reorganization and a small rate of heterogenous electron transfer for oxidation of the fully reduced Mn(II,II) state. Similar kinetic sluggishness is observed for Mn(III)/Mn(II) electron-transfer reactions of some mononuclear complexes (see Sects 16.1.2 and 16.1.3). 

We are currently carrying out further investigations with neutral ferrocene derivatives in an attempt to resolve the apparent disconnection between the effects of CB7 encapsulation on homogenous and heterogeneous electron transfer reactions rates. 

In a direct electrolysis, the electron is exchanged between the electrode and the substrate, and the rate of the reaction depends on the electrode potential and the rate constant of the heterogeneous electron-transfer reaction. In an indirect electrolysis, the electron is primarily exchanged with a substance (a mediator) that exchanges the electron with the substrate in a chemical reaction, and the rate does not depend on the ability of the substrate to exchange an electron with the electrode. 

Electrode reactions may include elementary steps involving electron transfer, ion transfer, potential-independent or chemical steps, etc. Since electrochemical reactions are heterogeneous processes, the reaction rate coefficients have units of m s 1... 

The rate coefficient for a heterogeneous electron transfer reaction at an electrode can be written, according to the absolute rate theory [54], as... 

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. 

One of the simplest electrode reactions is the EC mechanism (also called a following chemical reaction) in which the electrogenerated species (R) rearranges or reacts with some other solution component (Z) at a rate characterized by the rate constant k. The EC mechanism is summarized by the following reaction sequence, in which the labels E and C identify the heterogeneous electron-transfer reaction (electrode reaction) and the subsequent homogeneous solution reaction (chemical reaction), respectively ... 

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... 

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