Electrode kinetics redox reaction

S. U. M. Khan, P. Wright, and J. O M. Bockris, Elektrokhimya 13 914 (1977). The first application of time-dependent perturbation theory to quantum electrode kinetics redox reactions. 

By the method of introducing Pt into the DLC, the platinum metal is assumed to be distributed over the carbonaceous material bulk as discrete atoms or clusters [154], Essentially, Pt is not a dopant in the DLC, in the sense that the term is used in semiconductor physics. Nor is the percolation threshold surpassed, since the admixture of Pt (not exceeding 15 at. %) did not affect the a-C H resistivity, as was shown by impedance spectroscopy tests p 105 Q, cm, like that of the undoped DLC (see Table 3). It was thus proposed that the Pt effect is purely catalytic one Pt atoms on the DLC surface are the active sites on which adsorption and/or charge transfer is enhanced [75], (And the contact of the carbon matrix to the Pt clusters is entirely ohmic.) This conclusion was corroborated by the studies of Co tetramethylphenyl-porphyrin reaction kinetics at the DLC Pt electrodes [155] redox reactions involving the Co central ion proceed partly under the adsorption of the porphyrin ring on the electrode. 

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. 

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... 

When the area A of the eleetrode/solution interface with a redox system in the solution varies (e.g. when using a streaming mercury electrode), the double layer capacity which is proportional to A, varies too. The corresponding double layer eharging current has to be supplied at open eireuit eonditions by the Faradaic current of the redox reaction. The associated overpotential can be measured with respect to a reference electrode. By measuring the overpotential at different capaeitive eurrent densities (i.e. Faradaic current densities) the current density vs. eleetrode potential relationship can be determined, subsequently kinetic data can be obtained [65Del3]. (Data obtained with this method are labelled OC.)... 

The field of modified electrodes spans a wide area of novel and promising research. The work dted in this article covers fundamental experimental aspects of electrochemistry such as the rate of electron transfer reactions and charge propagation within threedimensional arrays of redox centers and the distances over which electrons can be transferred in outer sphere redox reactions. Questions of polymer chemistry such as the study of permeability of membranes and the diffusion of ions and neutrals in solvent swollen polymers are accessible by new experimental techniques. There is hope of new solutions of macroscopic as well as microscopic electrochemical phenomena the selective and kinetically facile production of substances at square meters of modified electrodes and the detection of trace levels of substances in wastes or in biological material. Technical applications of electronic devices based on molecular chemistry, even those that mimic biological systems of impulse transmission appear feasible and the construction of organic polymer batteries and color displays is close to industrial use. 

If a system is not at equilibrium, which is common for natural systems, each reaction has its own Eh value and the observed electrode potential is a mixed potential depending on the kinetics of several reactions. A redox pair with relatively high ion activity and whose electron exchange process is fast tends to dominate the registered Eh. Thus, measurements in a natural environment may not reveal information about all redox reactions but only from those reactions that are active enough to create a measurable potential difference on the electrode surface. 

In the present chapter we want to look at certain electrochemical redox reactions occurring at inert electrodes not involved in the reactions stoichiometrically. The reactions to be considered are the change of charge of ions in an electrolyte solution, the evolution and ionization of hydrogen, oxygen, and chlorine, the oxidation and reduction of organic compounds, and the like. The rates of these reactions, often also their direction, depend on the catalytic properties of the electrode employed (discussed in greater detail in Chapter 28). It is for this reason that these reactions are sometimes called electrocatalytic. For each of the examples, we point out its practical value at present and in the future and provide certain kinetic and mechanistic details. Some catalytic features are also discussed. 

Charge transfer reactions represent an important category of electrochemical behavior. As already pointed out above, an appropriate investigation of kinetic parameters of electrochemical reactions in aqueous electrolytes suffers from the small temperature range experimentally accessible. In the following, some preliminary results using the FREECE technique are presented for the Fe2+/Fe3+ redox reaction and for hydrogen evolution at various metal electrodes. 

Consider the fast redox reaction on the electrode surface (i.e., fast heterogeneous charge transfer kinetics) ... 

Electrode reactions can be classified into two groups one in which an electron transfer takes place across the electrode interface, such as ferric-ferrous redox reaction (Fet, + e = Fe ) and the other in which an ion transfer takes place across the electrode interface, such as iron dissolution-deposition reaction (Fe M = FeVq). Since electrons are Fermi particles in contrast to ions that obey the Boltzmann statistics as described in Chap. 1, the reaction kinetics of the two groups differ in their electrode reactions. 

For the electron transfer of hydrated redox particles (the outer-sphere electron transfer), the electrode acts merely as a source or sink of electrons transferring across the compact double layer so that the nature of the electrode hardly affects the reaction kinetics this lack of influence by the electrode has been observed for the ferric-ferrous redox reaction. On the other hand, the electron transfer of adsorbed redox particles (the inner-sphere electron transfer) is affected by the state of adsorption so that the nature of the electrode exerts a definite influence on the reaction kinetics, as has been observed with the hydrogen electrode reaction where the reaction rate depends on the property of electrode. 

As discussed in Sec. 8.3.5, a redox reaction current due to electron or hole transfer depends not only on the concentration of interfadal electrons or holes at the electrode but also on the state density of the redox electrons or redox holes in the range of energy where the electron transfer takes place. Hence, it is important in the kinetics of electron or hole transfer to realize the level of the band edge Cc or Ev of the electrode relative to the most probable level cred or cox of redox electrons or redox holes in the hydrated redox particles. 

The effects of complexation of redox particles on the redox reaction kinetics are frequently more evident with semiconductor electrodes than with metal electrodes, since the transfer of electrons takes place at the band edge levels rather than at the Fermi level of electrodes. For example, the anodic transfer of... 

Further information on this subject can be obtained by frequency response analysis and this technique has proved to be very valuable for studying the kinetics of polymer electrodes. Initially, it has been shown that the overall impedance response of polymer electrodes generally resembles that of intercalation electrodes, such as TiS2 and WO3 (Ho, Raistrick and Huggins, 1980 Naoi, Ueyama, Osaka and Smyrl, 1990). On the other hand this was to be expected since polymer and intercalation electrodes both undergo somewhat similar electrochemical redox reactions, which include the diffusion of ions in the bulk of the host structures. One aspect of this conclusion is that the impedance response of polymer electrodes may be interpreted on the basis of electrical circuits which are representative of the intercalation electrodes, such as the Randles circuit illustrated in Fig. 9.13. The figure also illustrates the idealised response of this circuit in the complex impedance jZ"-Z ) plane. 

The theory for the reaction of an adsorbed redox couple (2.146) has been exemplified by experiments with methylene blue [92], and azobenzene [79], Both redox couples, methylene blue/leucomethylene, and azobenzene/hydrazobenzene adsorb strongly on the mercury electrode surface. The reduction of methlylene blue involves a very fast two-step redox reaction with a standard rate constants of 3000 s and 6000 s for the first and second step, respectively. Thus, for / < 50 Hz, the kinetic parameter for the first electron transfer is log(m) > 1.8, implying that the reaction appears reversible. Therefore, regardless of the adsorptive accumulation, the net response of methylene blue is a small peak, the peak current of which depends linearly on /J. Increasing the frequency above 50 Hz, the electrochemical... 

It must be emphasized again that the mid-peak potential is equal to E° for a simple, reversible redox reaction when neither any experimental artifact nor kinetic effect (ohmic drop effect, capacitive current, adsorption side reactions, etc.) occurs, and macroscopic inlaid disc electrodes are used, that is, the thickness of the diffusion layer is much higher than that of the diameter of the electrode. 

Tafel s law is the primary law of electrode kinetics, in the sense that Arrhenius law is the basic law of thermal reaction. It applies universally to all processes that are controlled in rate by the interfacial transfer of electrons or by a rate-determining surface reaction that may be coupled to the interfacial electron [Fig. 9.25(a)]. Redox reactions without surface intermediates demonstrate Tafel s law well [Fig. 9.25(b)]. 

This chapter deals with the fundamental aspects of redox reactions in non-aque-ous solutions. In Section 4.1, we discuss solvent effects on the potentials of various types of redox couples and on reaction mechanisms. Solvent effects on redox potentials are important in connection with the electrochemical studies of such basic problems as ion solvation and electronic properties of chemical species. We then consider solvent effects on reaction kinetics, paying attention to the role of dynamical solvent properties in electron transfer processes. In Section 4.2, we deal with the potential windows in various solvents, in order to show the advantages of non-aqueous solvents as media for redox reactions. In Section 4.3, we describe some examples of practical redox titrations in non-aqueous solvents. Because many of the redox reactions are realized as electrode reactions, the subjects covered in this chapter will also appear in Part II in connection with electrochemical measurements. 

Many redox reactions at electrodes involve transfer of more than one electron. It is agreed that such processes usually involve several consecutive one-electron steps rather than a simultaneous multi-electron transfer. The kinetics of the overall reaction (and hence the current flowing) are complicated by such factors as the lifetimes of the transient intermediate species. 

It is important to notice that the rate of a given outer sphere electrode redox reaction should be independent of the nature of the metal electrode if allowance is made for electrostatic work terms or double layer effects which will, of course, be dependent on the nature of the electrode material. Inner sphere reactions, on the other hand, are expected to be catalytic with kinetics strongly dependent on the electrode surface due to specific adsorption interactions. 

The mass transport rate coefficient, kd, for a RDE at the maximum practical rotation speed of 10000 per min"1 is approximately 2 x 10-2 cms-1 [28], which sets a limit of about 10 3 cms 1 for the electrode reaction kinetics. For the study of very fast electrode processes, such as some outer sphere redox reactions on noble metal electrodes under stationary conditions, higher mass transport rates in the solution adjacent to the electrode must be employed. 

Underpotential deposition of metal adatoms at foreign metal electrodes shows a strong effect on the kinetics of inner sphere redox reactions such as the reduction of Cr(OH2)sCl2+ [130] due to electrostatic and specific interactions. 

In Fig. 13(a), the occurrence of two simultaneous redox reactions at an electrode surface has been considered. However, in most corrosion problems, more than two reactions may take place and both forward and backward individual electrode reactions may not take place at significant rates in the potential range where the mixed potential is observed, due to the slow kinetics of the participating reactions under those conditions. Figure 13(b) illustrates the corrosion of two metals, M and M, in aqueous aerated (oxygenated) solutions. 

Gerischer(16), Bard and Wrighton(17) have recently discussed a simple model for the thermodynamic stability of a range of photoelectrodes. As has been discussed previously, except for the rare case where the anodic and cathodic decomposition potentials lie outside the band gap, the electrode will be intrinsically unstable anodically, cathodically, or both.(16) It is the relative overpotential of the redox reaction of interest compared to that of the appropriate decomposition potential which determines the relative kinetics and thus stability of the electrode as illustrated in Figure 4. The cathodic and anodic decomposition potentials may be roughly estimated by thermodynamic free-energy calculations but these numbers may not be truly representative due to the mediation of surface effects. 

McCreery and co-workers have investigated the redox reactions for several redox analytes at glassy carbon electrodes, and have summarized the categorization of redox systems according to the effects of surface modification on electrode kinetics [1-3]. These redox analytes in the present study are known to be sensitive or insensitive to the electronic properties, surface microstructure, and surface termination of the carbon electrodes. 

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