Electrode electron-transfer kinetics

In the case where the electrode electron transfer kinetics interferes, equation (4.9) replaces Nemst s law, and therefore... 

Carbon7 exists in various conducting forms. Electrochemical reactions are normally slower at carbon than at metallic electrodes, electron transfer kinetics being dependent on structure and surface preparation8. 

Electron-transfer coefficient (a). As discussed previously, this a is called the electron-transfer coefficient, which is one of the important parameters for the electrode electron-transfer kinetics. For majority of electrochemical reaction systems, the value of this a is in the range of 0.2—0.8, depending on the nature of the studied system. However, in the electrochemical research, if this value is not measured, people normally assume its value to be 0.5. 

Ramesh, P. Sampafh, S. Electrochemical characterization of binderless, recompressed exfoUated graphite electrodes Electron-transfer kinetics and diffusion characteristics. Anal. Chem. IS (2003), pp. 6949-6957. 

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. 

This chapter attempts to give an overview of electrode processes, together with discussion of electron transfer kinetics, mass transport, and the electrode-solution interface. 

S.3.3 Electrocatalytic Modified Electrodes Often the desired redox reaction at the bare electrode involves slow electron-transfer kinetics and therefore occurs at an appreciable rate only at potentials substantially higher than its thermodynamic redox potential. Such reactions can be catalyzed by attaching to the surface a suitable electron transfer mediator (45,46). Knowledge of homogeneous solution kinetics is often used to select the surface-bound catalyst. The function of the mediator is to facilitate the charge transfer between the analyte and the electrode. In most cases the mediated reaction sequence (e.g., for a reduction process) can be described by... 

R.L. McCreery, Carbon Electrodes Structural Effects on Electron Transfer Kinetics, in A.J. Bard, Ed., Electroanalytical Chemistry, Vol 18, Marcel Dekker, New York, 1991. 

The oxidation or reduction of a substrate suffering from sluggish electron transfer kinetics at the electrode surface is mediated by a redox system that can exchange electrons rapidly with the electrode and the substrate. The situation is clear when the half-wave potential of the mediator is equal to or more positive than that of the substrate (for oxidations, and vice versa for reductions). The mediated reaction path is favored over direct electrochemistry of the substrate at the electrode because, by the diffusion/reaction layer of the redox mediator, the electron transfer step takes place in a three-dimensional reaction zone rather than at the surface Mediation can also occur when the half-wave potential of the mediator is on the thermodynamically less favorable side, in cases where the redox equilibrium between mediator and substrate is disturbed by an irreversible follow-up reaction of the latter. The requirement of sufficiently fast electron transfer reactions of the mediator is usually fulfilled by such revemible redox couples PjQ in which bond and solvate... 

As the immunocomplex structure is generally electroinactive, its coverage on the electrode surface will decrease the double layer capacitance and retard the interfacial electron transfer kinetics of a redox probe present in the electrolyte solution. In this case, Ra can be expressed as the sum of the electron transfer resistance of the bare electrode CRbare) and that of the electrode immobilized with an immunocomplex (R immun) ... 

Prior to the 1970 s, electrochemical kinetic studies were largely directed towards faradaic reactions occurring at metal electrodes. While certain questions remain unanswered, a combination of theoretical and experimental studies has produced a relatively mature picture of electron transfer at the metal-solution interface f1-41. Recent interest in photoelectrochemical processes has extended the interest in electrochemical kinetics to semiconductor electrodes f5-151. Despite the pioneering work of Gerischer (11-141 and Memming (15), many aspects of electron transfer kinetics at the semiconductor-solution interface remain controversial or unexplained. 

An interesting approach to measuring rates of electron transfer reactions at electrodes is through the study of surface bound molecules (43-451. Molecules can be attached to electrode surfaces by irreversible adsorption or the formation of chemical bonds (461. Electron transfer kinetics to and from surface bound species is simplified because there is no mass transport and because the electron transfer distance is controlled to some degree. 

With the introduction of modern electronics, inexpensive computers, and new materials there is a resurgence of voltammetric techniques in various branches of science as evident in hundreds of new publications. Now, voltammetry can be performed with a nano-electrode for the detection of single molecular events [1], similar electrodes can be used to monitor the activity of neurotransmitter in a single living cell in subnanoliter volume electrochemical cell [2], measurement of fast electron transfer kinetics, trace metal analysis, etc. Voltammetric sensors are now commonplace in gas sensors (home CO sensor), biomedical sensors (blood glucose meter), and detectors for liquid chromatography. Voltammetric sensors appear to be an ideal candidate for miniaturization and mass production. This is evident in the development of lab-on-chip... 

In Section 1.4.4 we describe some typical examples of outer-sphere electron transfer kinetics, with particular emphasis on the variation of the transfer coefficient (symmetry factor) with the electrode potential (driving force). 

How electron transfer kinetics may be investigated by means of an electrochemical method such as cyclic voltammetry is the question we address now, starting with the case where the reactants are immobilized on the electrode surface, as in the beginning of Section 1.2. The key equations are those that relate the surface concentrations rA and rB to the current. The first of these expresses the Faradaic consumption of A and production of B as the current flows ... 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

We now remove the assumption that electron transfer is fast and discuss the influence of the follow-up reaction on the electron transfer kinetics. The simplest case is when the follow-up reaction is fast so as to stay unconditionally at equilibrium. The concentrations at the electrode surface may thus be expressed as... 

The opposite situation (y/D/k -C <5), where the reaction layer is much thinner than the diffusion layer (as represented in the lower diagram of Figure 2.31) is more specific of electrochemistry, in the sense that the homogeneous follow-up reactions are more intimately connected with the electrode electron transfer step. The same pure kinetic conditions discussed earlier for cyclic voltammetry (Section 2.2.1) apply. In the case of a simple EC reaction scheme, as shown in the figure, the production of C in the bulk solution obeys exactly the same equations (2.32) to (2.34) as for B in the preceding case, as established in Section 6.2.8. 

Depending on the catalyst, electron transfer at the electrode is not necessarily fast. The Nemst law used as electrode surface boundary condition may thus have to be replaced by an equation depicting the electron transfer kinetic law (Section 1.4.2) ... 

As compared to the Nemstian case, the plateau is the same but the wave is shifted toward more negative potentials, the more so the slower the electrode electron transfer. An illustration is given in Figure 4.13 for a value of the kinetic parameter where the catalytic plateau is under mixed kinetic control, in between catalytic reaction and substrate diffusion control. For the kjet(E) function, rather than the classical Butler-Volmer law [equation (1.26)], we have chosen the nonlinear MHL law [equation (1.37)]. 

Application of these curves may have as other objective to uncover the kinetic characteristics of the electrode electron transfer. This cannot be done in the absence of catalysis since the RDEV response is nil insofar as the steady-state response of an attached species is nil. Cyclic voltammetry could be used instead. The response is not nil, but the signal is in general small, often hardly emerging from the baseline current. Determining the standard potential under these conditions is generally feasible, but an accurate... 

FIGURE 4.1 3. a RDEV response of a monolayer catalytic coating for the reaction scheme in Figure 4.10 with a slow P/Q electron transfer. Kinetic parameter [equation (4.5)] kr°8/DA = 5. The same electrode transfer MHL law as in Figure 1.18. Dotted line Nemstian limiting case. Solid lines from left to right, e (5r0DAC = 1, 0.1, 0.01. h Derivation of the catalytic rate constant, c Derivation of the kinetic law. 

In the case of cyclic voltammetry, too, amplification of the current upon addition of the substrate may be exploited to determine the kinetic characteristics of the electrode electron transfer. Replacing Nemst s law by a kinetic law and assuming, as already discussed, that dr /dt is negligible, the dimensionless current-potential curves are given by... 

Curves in Figure 4.15a and similar curves corresponding to other values of the two parameters k,r° / DAFv/1ZT and r()kf / CA a/DaFv/TIT give an idea of the changes expected in the current-potential curves as the kinetics of the electrode electron transfer starts interfering. 

Convolution may again be used to analyze the current response so as to determine both the kinetics of the catalytic reaction and the kinetics of the electrode electron transfer, as illustrated in Figure 4.15. Starting with the current... 

The catalytic kinetic constant may thus be derived from the asymptotic behavior observed for this first combination of current and convoluted current when the electrode potential becomes more and more negative. Once this first parameter is known, the second combination, shown in Figure 4.15d, provides the rate law characterizing the electrode electron transfer. Meaningful potential ranges, from the foot of the wave to just after the peak, are represented in Figure 4.15d by open symbols. 

When Afh -a oo, a Nernstian response is obtained. The half-wave potential is equal to the standard potential. Conversely, when Afh —> 0, the electrode electron transfer is irreversible. In the case of a Butler-Volmer kinetic law, the half-wave potential is expressed as... 

Analysis of the cyclic voltammetric responses is also possible if a kinetic law different from Butler-Volmers governs the electrode electron transfer. Derivation of the kinetic law from the cyclic voltammetric responses may benefit from a convolution approach similar to that described in the preceding section. 

We consider now the case where the kinetics of the electrode electron transfer may interfere. Equations (6.213) and (6.214) are still valid and Nernst s law is replaced by equation (4.9). Combination of these three equations leads to equation (4.10), and from it, to equation (4.11). 

In a recent upsurge of studies on electron transfer kinetics, importance was placed on the outer shell solvent continuum, and the solvent was replaced by an effective model potential or a continuum medium with an effective dielectric constant. Studies in which the electronic and molecular structure of the solvent molecules are explicitly considered are still very rare. No further modem quantum mechanical studies were made to advance the original molecular and quantum mechanical approach of Gurney on electron and proton (ion) transfer reactions at an electrode. 

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