Reactant diffusion process electrode electron-transfer

The current density measured from the rotating electrode is contributed by both the current densities of electrode electron-transfer reaction and the reactant diffusion. In order to obtain the kinetic parameters of these two processes and their associated reaction mechanisms based on the experiment data, both the theories of electrode electron-transfer reaction and reactant diffusion should be studied and understood. In this chapter, the general theories for electrode kinetics of electron-transfer reaction and reactant diffusion will be given in a detailed level, and we hope these theories will form a solid knowledge for a continuing study in the following chapters of this book. 

Figure 2.1 Schematic of the electrode electron-transfer and reactant diffusion process in an electrochemical system. Cb(0,t) is the surface concentration of oxidant species, ChlO.t) is the surface concentration of reductant species, Co(x,f) is the bulk solution concentration of oxidant, and Cr(x, ) is the bulk solution concentration of reductant species. In these four expressions of concentration, tis the reaction time. (For color version of this figure, the reader is referred to the online version of this book.)...

Electrogenerated chemiluminescence (ECL) is the process whereby a chemiluminescence emission is produced directly, or indirectly, as a result of electrochemical reactions. It is also commonly known as electrochemiluminescence and electroluminescence. In general, electrically generated reactants diffuse from one or more electrodes, and undergo high-energy electron transfer reactions either with one another or with chemicals in the bulk solution. This process yields excited-state molecules, which produce a chemiluminescent emission in the vicinity of the electrode surface. 

As the field of electrochemical kinetics may be relatively unfamiliar to some readers, it is important to realize that the rate of an electrochemical process is the current. In transient techniques such as cyclic and pulse voltammetry, the current typically consists of a nonfaradaic component derived from capacitive charging of the ionic medium near the electrode and a faradaic component that corresponds to electron transfer between the electrode and the reactant. In a steady-state technique such as rotating-disk voltammetry the current is purely faradaic. The faradaic current is often limited by the rate of diffusion of the reactant to the electrode, but it is also possible that electron transfer between the electrode and the molecules at the surface is the slow step. In this latter case one can define the rate constant as ... 

As a result, a stationary voltammogram cannot be expected under these conditions since it shows a behavior similar to that of a macrointerface with respect to the egress of the ion, and features of radial diffusion for the ingress process, reaching a time-independent response [73, 74]. Both are consequences of the markedly different diffusion fields inside and outside the capillaries which give rise to very different concentration profiles (see Fig. 5.21). A similar voltammetric behavior has been reported for electron transfer processes at electrode I solution interfaces where the diffusion fields of the reactant and product species differ greatly. 

Electron, energy and proton transfer or molecular rearrangements are the most important events that occur in interfacial supramolecular assemblies. In this chapter, the general theories of electron transfer, both within ISAs and across the film/electrode interface, are described. Moreover, photoinduced electron, energy and proton transfer processes are discussed. As this book focuses on supramolecular species, the treatment is restricted to intramolecular or interfacial processes without the requirement for prior diffusion of reactants. 

Such an energy transfer is taken into account in the encounter pre-equilibrium model [131, 133], which considers the outer-sphere electrode reaction to be a two-step process. In the first step the reactant diffuses to the reaction zone with a thickness dr at the electrode surface, where the probability of the charge transfer process between reactant and electrode is significant [133]. Here the electrode and reactant in the reaction zone are similar to a pair of reactants which exchange the electrons in a homogeneous reaction. 

For disk-type electrodes, usually with a radius of O.l-l.O cm the thickness of the diffusion layer that is depleted of reactant is much smaller than the electrode size so that mass transport can be described in terms of planar diffusion of the electroactive species from the bulk solution to the electrode surface as schematized in Figure 1.2a, where semi-infinite diffusion conditions apply. The thickness of the diffusion layer can be estimated as for a time electrolysis t and usually ranges between 0.01 and 0.1 mm (Bard et al., 2008). For an electrochemically reversible -electron transfer process in the absence of parallel chemical reactions, the variation of the faradaic current with time is then given by the Cottrell equation ... 

An important point on the curve is that at which the diflfiision current is equal to one-half of the total diffusion current the voltage at which this current is reached is the half-wave potential Ei. The half-wave potential is used to characterize the current waveforms of particular reactants. Whether a process is termed reversible or not depends on whether equilibrium is reached at the surface of the electrode in the time frame of the measurements. In other words, a process is reversible when the electron transfer reactions are sufficiently fast so that the equilibrium... 

This first chapter to Volume 2 Interfadal Kinetics and Mass Transport introduces the following sections, with particular focus on the distinctive feature of electrode reactions, namely, the exponential current-potential relationship, which reflects the strong effect of the interfacial electric field on the kinetics of chemical reactions at electrode surfaces. We then analyze the consequence of this accelerating effect on the reaction kinetics upon the surface concentration of reactants and products and the role played by mass transport on the current-potential curves. The theory of electron-transfer reactions, migration, and diffusion processes and digital simulation of convective-diffusion are analyzed in the first four chapters. New experimental evidence of mechanistic aspects in electrode kinetics from different in-situ spectroscopies and structural studies are discussed in the second section. The last... 

In most electrochemical reactions, except very fast diffusion-controlled processes, the adsorption of reactants is a relatively fast step compared with succeeding electron transfer steps and can be considered in quasi-equilibrium. A knowledge of reactant adsorption behavior is necessary for interpretation of the mechanism of the reaction. Equilibrium adsorption studies are directed toward the evaluation of the surface concentration of reactants in relation to the electrode potential, the temperature, the activity of reactants, and other species in the bulk and the energy of adsorption as a function of the partial coverage 0. Study of the surface coverage by adsorbed intermediates can in some cases give additional information to the kinetic approach. Determination of adsorbed intermediates would indicate the path which the reaction follows. 

Electrode potentials measure only the relative thermodynamic likelihood for various halfreactions. In practice, kinetic factors can comphcate matters. For instance, sometimes the electrode process is limited by the rate of diffusion of dissolved species to or from the electrode surface. At some cathodes, the rate of electron transfer from the electrode to a reactant is the rate-limiting step, and a higher voltage (called overvoltage) must be apphed to accom-... 

This chapter is concerned with measurements of kinetic parameters of heterogeneous electron transfer (ET) processes (i.e., standard heterogeneous rate constant k° and transfer coefficient a) and homogeneous rate constants of coupled chemical reactions. A typical electrochemical process comprises at least three consecutive steps diffusion of the reactant to the electrode surface, heterogeneous ET, and diffusion of the product into the bulk solution. The overall kinetics of such a multi-step process is determined by its slow step whose rate can be measured experimentally. The principles of such measurements can be seen from the simplified equivalence circuit of an electrochemical cell (Figure 15.1). 

Two main contributions to the overpotential will be discussed in this book in some details. The first one is the charge (electron) transfer overpotential, which is due to a particular rate of the electrochemical reaction and takes place just at the electrodesolution interface. The second one is the mass transfer overpotential, which is due to delivering reactants to the electrochemical reaction interface or due to transporting products to the bulk solution. Other physicochemical processes taking place in the Nernst diffusion layer (e.g., chemical reactions and adsorption/desorption) can also contribute to the electrode overpotential, but they will not be discussed in this book. Note that chemical reactions occurring in the bulk solution should be taken into account to correctly estimate the concentration of the reduced, / buik nd oxidized, Obuik. species. 

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