Electrode kinetics,

Electrode Electrolyte species Electrode Electrolyte species 

Fermi level in electrode for different applied potential. 

Consider an electrochemical reaction occurring at an electrode between reduction (Red) and oxidation (Ox) forms of a chemical species 

An activation energy barrier for conversion of reactant to products. 

the rates of reactions (mol/s) for forward and backward reactions are dependent on the reaction rate constants ( /s) and /c / respectively. 

Turning to the electrode kinetics current voltage curves for the reduction of thionine and of Fe (III) on clean and on coated electrodes are shown in figure 8. 

It can be seen that the coating process hardly affects the electrode kinetics of the thionine reduction, while the current voltage curve for the Fe (III) reduction is shifted and much reduced. This is exactly the type of electrode that we need for an efficient photogalvanic cell. 

The selective electrode kinetics of the thionine coated electrode extends to other systems. For instance, the coat hardly affects the kinetics of organic systems such as quinone / hydroquinone, but other inorganic systems such as the reduction of Ru (bpy) 3 and Ce (IV) are blocked.26 por inorganic systems it appears that the ions are reduced by direct reaction with the leucothionine present in the coat rather than with the metal itself. This explains why the current voltage curves are shifted close to for thionine / leucothionine in the coat. Because of its more rapid kinetics Ru (bpy)3 requires much less L than Fe(lII) hence the former is reduced efficiently a hundred mV or so more positive than E oat hile Fe (III) is reduced inefficiently at a potential that is several hundred millivolts more negative than E oat- presume that 

Concentration variations in the vicinity of an electrode. When Ox undergoes reduction, its concentration at A-A becomes depleted and a concentration gradient is set up between A-A and the bulk B-B. Across the transport layer thus formed, mass transfer takes place. 

The forward and backward rates may be expressed in terms of the forward (cathodic) and backward (anodic) current densities, /j and / i, thus 

Consider the case that /- i, i.e. if Ox refers to a metal ion and Red to the metal itself, discharge occurs more rapidly than dissolution. The process is irreversible and the potential departs from the reversible value by 17 = 

Effect of overvoltage, (E - E ). upon free energy profUe of an electrode reaction. 

if O is the fraction of the overpotential assisting discharge, the activation energy, AG, which would be required if the process were to occur reversibly is reduced to (AG - xnF(E - E )). Similarly, the activation energy, AGli, is increased to (AGti + (1 - a)nF(E - E )). We may therefore express the forward and backward rates in the form 

Now let us consider briefly electrode kinetics, i.e., k or—since we have not involved any chemical capacitance effects—the exchange rate 

Let us follow the work by Wang and Nowick256 on electrode kinetics of Pt, 02/Ce02 (doped) which was indeed invoking the model mechanism given by Eqs. (163) and (164). If the transfer step is assumed to be rate determining and the symmetry factors are set to 1/2, 

The Po2 - and T-dependencies of the exchange current density are then given by 

As a in the bulk case, the exchange rate includes reaction and activation energies. The results shown in Fig. 68 as a function of Pq2 

As seen above, just as insonated electrodes may be used to determine quite fast heterogeneous kinetics, so they may be used to probe coupled 

The Born equation is not expected to give very accurate results (often calculated solvation energies are too high). However, it is useful for estimates and qualitative predictions. Dielectric constants for some common electrochemical solvents are given in the next chapter (Table 2-1). 

In estimating chemical properties, it is sometimes very useful to combine reduction potentials with other physical quantities. For instance, solution bond dissociation energies for organo acids have been estimated by combining reduction potentials with pK values.  

The entropy of reduction can be obtained by measuring the reduction potential as a function of temperature. 

In such experiments the temperature dependence of the reference cell potential must be taken into account. The most convenient method of doing this entails the use of a nonisothermal cell, in which the reference is kept at a constant temperature while the temperature of the remaining half-cell reaction is changed. 

7 Influence of Coupled Chemical Reactions on the Reduction Potential 

Assuming the rate constants, k ed and kox behave in an Arrhenius form  

This shows that the electrochemical rate constants for the one electron oxidation of Fe kox) and for the reduction of Fe kred) depend exponentially on the electrode potential k increases as the electrode is made more positive relative to the solution whilst kred increases as the electrode is made more negative relative to the solution. It is clear that changing the voltage affects the rate constants. However, the kinetics of the electron transfer is not the sole process which can control the electrochemical reaction in many circumstances it is the rate of mass transport to the electrode which controls the overall reaction, which we dUigently explore later. 

If we consider the case of a dynamic equilibrium at the working electrode such that the oxidation and reduction currents exactly balance each other then, since no net current flows, 7 = 0 and the fact that a = 0.5, we see that  

From the discussion earlier it is clear that when no net current flows the potential is given by  

Equations (2.23) and (2.24) are the most convenient forms of the Butler-Volmer expression for the electrochemical rate constants and The quantity k, with units of cm s is the standard electrochemical rate constant 

The reaction rate at the interface between the active material and the electrolyte can be expressed using the generahzed Butler-Vohner equation  

Sequence of Reaction Steps for Complex Electrochemical Reactions 

Chemical reaction (homogeneous, heterogeneous) Reaction overvoltage, tir 

Adsorption on electrode surface Charge transfer Charge transfer overvoltage, T ct 

1 Charge Transfer Overvoltage tier and Butler-Volmer Equation 

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The first law of electrode kinetics, observed by Tafel in 1905 [197], is that overvoltage i) varies with current density i according to the equation... 

P. Delahay, Double Layer and Electrode Kinetics, Interscience, New York, 1965. 

Electrode kinetics lend themselves to treatment usiag the absolute reaction rate theory or the transition state theory (36,37). In these treatments, the path followed by the reaction proceeds by a route involving an activated complex where the element determining the reaction rate, ie, the rate limiting step, is the dissociation of the activated complex. The general electrode reaction may be described as ... 

The rate of an electrochemical process can be limited by kinetics and mass transfer. Before considering electrode kinetics, however, an examination of the nature of the iaterface between the electrode and the electrolyte, where electron-transfer reactions occur, is ia order. 

In electrode kinetics a relationship is sought between the current density and the composition of the electrolyte, surface overpotential, and the electrode material. This microscopic description of the double layer indicates how stmcture and chemistry affect the rate of charge-transfer reactions. Generally in electrode kinetics the double layer is regarded as part of the interface, and a macroscopic relationship is sought. For the general reaction... 

In addition to electrode kinetics, the rate of an electrochemical reaction can be limited by the rate of mass transfer of reactants to and from the electrode surface. In dilute solutions, four principal equations are used. The flux of species i is... 

These four equations, using the appropriate boundary conditions, can be solved to give current and potential distributions, and concentration profiles. Electrode kinetics would enter as part of the boundary conditions. The solution of these equations is not easy and often involves detailed numerical work. Electroneutrahty (eq. 28) is not strictly correct. More properly, equation 28 should be replaced with Poisson s equation... 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

Reaction Engineering. Electrochemical reaction engineering considers the performance of the overall cell design ia carrying out a reaction. The joining of electrode kinetics with the physical environment of the reaction provides a description of the reaction system. Both the electrode configuration and the reactant flow patterns are taken iato account. More ia-depth treatments of this topic are available (8,9,10,12). 

In this section the interaction of a metal with its aqueous environment will be considered from the viewpoint Of thermodynamics and electrode kinetics, and in order to simplify the discussion it will be assumed that the metal is a homogeneous continuum, and no account will be taken of submicroscopic, microscopic and macroscopic heterogeneities, which are dealt with elsewhere see Sections 1.3 and 20.4). Furthermore, emphasis will be placed on uniform corrosion since localised attack is considered in Section 1.6. 

Over the years the original Evans diagrams have been modified by various workers who have replaced the linear E-I curves by curves that provide a more fundamental representation of the electrode kinetics of the anodic and cathodic processes constituting a corrosion reaction (see Fig. 1.26). This has been possible partly by the application of electrochemical theory and partly by the development of newer experimental techniques. Thus the cathodic curve is plotted so that it shows whether activation-controlled charge transfer (equation 1.70) or mass transfer (equation 1.74) is rate determining. In addition, the potentiostat (see Section 20.2) has provided... 

Haynie, F. H. and Ketcham, S. J., Electrochemical Behaviour of A1 Alloys Susceptible to Intergranular Corrosion. Electrode Kinetics of Oxide-covered Al , Corrosion, 19,403t (1963) Ketcham, S. J. and Haynie, F. H., Electrochemical Behaviour of Al Alloys Susceptible to Intergranular Corrosion. Effect of Cooling Rate on Structure and Electrochemical Behaviour in 202A Al Alloy , Corrosion, 19, 242t (1963)... 

The solution of the Laplace equation is not trivial even for relatively simple geometries and analytical solutions are usually not possible. Series solutions have been obtained for simple geometries assuming linear polarisation kinetics "" . More complex electrode kinetics and/or geometries have been dealt with by various numerical methods of solution such as finite differencefinite elementand boundary element. ... 

The thermodynamic and electrode-kinetic principles of cathodic protection have been discussed at some length in Section 10.1. It has been shown that, if electrons are supplied to the metal/electrolyte solution interface, the rate of the cathodic reaction is increased whilst the rate of the anodic reaction is decreased. Thus, corrosion is reduced. Concomitantly, the electrode potential of the metal becomes more negative. Corrosion may be prevented entirely if the rate of electron supply is such that the potential of the metal is lowered to the value where it is found that anodic dissolution does not occur. This may not necessarily be the potential at which dissolution is thermodynamically impossible. 

In Section 1.4 it was assumed that the rate equation for the h.e.r. involved a parameter, namely the transfer coefficient a, which was taken as approximately 0-5. However, in the previous consideration of the rate of a simple one-step electron-transfer process the concept of the symmetry factor /3 was introduced, and was used in place of a, and it was assumed that the energy barrier was almost symmetrical and that /3 0-5. Since this may lead to some confusion, an attempt will be made to clarify the situation, although an adequate treatment of this complex aspect of electrode kinetics is clearly impossible in a book of this nature and the reader is recommended to study the comprehensive work by Bockris and Reddy. ... 

W.J. Albery, Electrode Kinetics, Clarendon Press, Oxford, 1975. 

For a metal/solution interface, the pcz is as informative as the electron work function is for a metal/vacuum interface.6,15 It is a property of the nature of the metal and of its surface structure (see later discussion) it is sensitive to the presence of impurities. Its value can be used to check the cleanliness and perfection of a metal surface. Its position determines the potential ranges of ionic and nonionic adsorption, and the region where double-layer effects are possible in electrode kinetics.8,10,16... 

Kahn, S. U. M. Quantum Mechanical Treatments in Electrode Kinetics 31... 

E. Gileadi, Electrode kinetics for chemists, chemical engineers, and materials scientists, Wiley-VCH, Weinheim (1993). 

W. Gopel, and H.-D. Wiemhofer, Electrode kinetics and interface analysis of solid electrolytes for fuel cells and sensors, Ber. Buns. Phys. Chem. 94, 981-987 (1990). 

The principle of electrochemical noise experiments is to monitor, without perturbation, the spontaneous fluctuations of potential or current which occur at the electrode surface. The stochastic processes which give rise to the noise signals are related to the electrode kinetics which govern the corrosion rate of the system. Much can be learned about the corrosion of the coated substrate from these experiments. The technique of these measurements is discussed elsewhere (A). 

A quantitative analysis of the kinetics of CdSe deposition from selenosulfate, Cd(II)-EDTA baths in terms of a mechanism involving nucleation and electrode kinetics has been given by Kutzmutz et al. [65], Note also that selenosulfate-containing baths have been used for the anodic selenization of vacuum-deposited metal films in order to synthesize CdSe and other binary selenide semiconductor thin films such as CuSe and InSe [66],... 

Fhosphoric acid does not have all the properties of an ideal fuel cell electrolyte. Because it is chemically stable, relatively nonvolatile at temperatures above 200 C, and rejects carbon dioxide, it is useful in electric utility fuel cell power plants that use fuel cell waste heat to raise steam for reforming natural gas and liquid fuels. Although phosphoric acid is the only common acid combining the above properties, it does exhibit a deleterious effect on air electrode kinetics when compared with other electrolytes ( ) including such materials as sulfuric and perchloric acids, whose chemical instability at T > 120 C render them unsuitable for utility fuel cell use. In the second part of this paper, we will review progress towards the development of new acid electrolytes for fuel cells. 

Table 1. The reasons for the apparent breakdown of the original principle have included chemical interaction between one couple and an intermediate species of the other, changes produced in the structure of the electrode surface and, most common of all, adsorption on the surface of a component of one couple that affected the electrode kinetics of the other. The underlying problem in these cases has been the untenable premise that each couple acts quite independently of the other and is not affected by the other s presence. However, as many of these studies have shown, the premise of additivity still applies whenever the interactions have been allowed for by carrying out the electrochemical experiments in an appropriate fashion. The validity of adding or superimposing electrochemical curves can therefore be considerably extended by restating the principle as follows ...

III. ELECTRODE KINETICS AND ELECTROCATALY SIS OF METHANOL OXIDATION—ELECTROCHEMICAL AND SPECTROSCOPIC INVESTIGATIONS... 

Thus, worldwide efforts have focused on the elucidation of the reaction mechanism. For this purpose, knowledge about the following items is vital (1) identification of reaction products and the electrode kinetics of the reactions involved, (2) identification of adsorbed intermediate species and their distribution on the electrode surface, and (3) dependence of the electrode kinetics of the intermediate steps in the overall and parasitic reactions on the structure and composition of the electrocatalyst. It is only after a better knowledge of the reaction mechanisms is obtained that it will be possible to propose modifications of the composition and/or structure of the electrocatalyst in order to significantly increase the rate of the reaction. 

The electrocatalytic oxidation of methanol has been thoroughly investigated during the past three decades (see reviews in Refs. 21-27), particularly in regard to the possible development of DMFCs. The oxidation of methanol, the electrocatalytic reaction, consists of several steps, which also include adsorbed species. The determination of the mechanism of this reaction needs two kinds of information (1) the electrode kinetics of the formation of partially oxidized and completely oxidized products (main and side products) and (2) the nature and the distribution of intermediates adsorbed at the electrode surface. 

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