Rate potential-dependent electrochemical

Given that electrochemical rate constants are usually extremely sensitive to the electrode potential, there has been longstanding interest in examining the nature of the rate-potential dependence. Broadly speaking, these examinations are of two types. Firstly, for multistep (especially multielectron) processes, the slope of the log kob-E plots (so-called "Tafel slopes ) can yield information on the reaction mechanism. Such treatments, although beyond the scope of the present discussion, are detailed elsewhere [13, 72]. Secondly, for single-electron processes, the functional form of log k-E plots has come under detailed scrutiny in connection with the prediction of electron-transfer models that the activation free energy should depend non-linearly upon the overpotential (Sect. 3.2). 

The dimensionless, potential-dependent electrochemical rate constants of the adsorbed species i d/ox given by... 

Neufeld, P. and Queenan, E. D., Frequency Dependence of Polarisation Resistance Measured with Square Wave Alternating Potential , Br. Corros. J., 5, 72-75, March (1970) Fontana, M. G., Corrosion Engineering, 3rd edn., McGraw-Hill, pp 194-8 (1986) Dawson, J. L., Callow, L. M., Hlady, K. and Richardson, J. A., Corrosion Rate Determination By Electrochemical Impedance Measurement , Conf. On-Line Surveillance and Monitoring of Process Plant, London, Society of Chemical Industry (1977)... 

Conway, B. E. The Temperature and Potential Dependence of Electrochemical Reaction Rates, and the Real Form of the Tafel Equation 16... 

The current is recorded as a function of time. Since the potential also varies with time, the results are usually reported as the potential dependence of current, or plots of i vs. E (Fig.12.7), hence the name voltammetry. Curve 1 in Fig. 12.7 shows schematically the polarization curve recorded for an electrochemical reaction under steady-state conditions, and curve 2 shows the corresponding kinetic current 4 (the current in the absence of concentration changes). Unless the potential scan rate v is very low, there is no time for attainment of the steady state, and the reactant surface concentration will be higher than it would be in the steady state. For this reason the... 

Alexander N. Frumkin pointed out in 1932 that an electrochemical reaction occnrring at different potentials can be regarded as an ideal set of chemical reactions of the same type, and suggested that the Brpnsted relation be nsed to explain the potential dependence of electrochemical reaction rates. On the basis of Eqs. (14.6) and (14.11), the relation for the activation energy becomes... 

A basic defect of these ideas is their failure to provide an explanation of the substantial effects of sofution composition, in particular the pH value, on the rate of the electrochemical reaction. Since hydrogen ions are not involved in the recombination step, the rate of this step according to Eq. (15.12) should not depend on solution pH. Yet in many cases the rate of hydrogen evolution at constant potential is proportional to the hydrogen ion concentration in solution. 

In 1930, Max Volmer and Tibor Erdey-Griiz used the concept of a slow discharge step for cathodic hydrogen evolntion (slow discharge theory). According to these ideas, the potential dependence of electrochemical reaction rate constants is described by Eq. (6.5). Since hydrogen ions are involved in the slow step A, the reaction rate will be proportional to their concentration. Thus, the overall kinetic equation can be written as... 

The rate of an electrochemical reaction depends, not only on given system parameters (composition of the catalyst and electrolyte, temperature, state of the catalytic electrode surface) but also on electrode potential. The latter parameter has no analog in heterogeneous catalytic gas-phase reactions. Thus, in a given system, the potential can be varied by a few tenths of a volt, while as a result, the reaction rate will change by several orders of magnitude. 

Figure 4 illustrates that our present knowledge about the dependence of the standard potential of very small silver microelectrodes on the agglomeration number is rather fragmentary. Even less is known about this dependence for other metals. The experiments of Fig. 5 prove that the rate of an electrochemical reaction in which a small microelectrode is involved, may strongly depend on the size of the microelectrode. 

The overall rate of an electrochemical reaction is measured by the current flow through the cell. In order to make valid comparisons between different electrode systems, this current is expressed as cunent density,/, the current per unit area of electrode surface. Tire current density that can be achieved in an electrochemical cell is dependent on many factors. The rate constant of the initial electron transfer step depends on the working electrode potential, Tlie concentration of the substrate maintained at the electrode surface depends on the diffusion coefficient, which is temperature dependent, and the thickness of the diffusion layer, which depends on the stirring rate. Under experimental conditions, current density is dependent on substrate concentration, stirring rate, temperature and electrode potential. 

One other effect that deals with the structure of the interface and how it affects electrochemical reaction rates can be mentioned. As explained in Cliapter 6, some ions (usually anions) chemisorb on the electrode, bending back their solvation sheaths so that the ion itself comes into contact with the electrode surface and forms valence bonds with it. Such effects are potential dependent, and since the adsorption will tend to block the electrode surface, it will change the dependence of log i on Aty assumed earlier [Eq. (7.7)]. Such effects are particularly important in organoelectrochemistiy (see Cliapter 11) where the reactants themselves may adsorb in contact with the electrode as a function of potential and complicate the theory of the dependence of the rate of reaction (or current density, i) on potential... 

Of course, clectrocalalytic reactions are potential dependent in rate, as are all other electrode reactions,87 and one of the subjects to which attention will be given in the following discussion is the reference potential at which a comparison of electrocatalysts should be made. Table 7.17 contains a comparison of chemical (thermal) and electrochemical (electrical) catalysis. 

In electrochemical kinetics, the same view is frequently adopted and the same reasonings are applied [121]. A great advantage, compared with non-electrochemical reactions, is that the possibility of external potential control allows us to find out which step is rate-determining by virtue of the different potential dependencies of the rate constants. This is most clearly seen in Fig. 30(a). If the first electron transfer step is ratedetermining, the forward rate constant of the overall reduction is equal to the forward rate constant of the first step, which can be written as... 

As in the case of differential double potential pulse techniques like DDPV, slow electrochemical reactions lead to a decrease in the peak height and a broadening of the response of differential multipulse and square wave voltammetries as compared with the response obtained for a Nemstian process. Moreover, the peak potential depends on the rate constant and is typically shifted toward more negative potentials (when a reduction is considered) as the rate constant or the pulse length decreases. SWV is the most interesting technique for the analysis of non-reversible electrochemical reactions since it presents unique features which allow us to characterize the process (see below). Hereinafter, unless expressly stated, a Butler-Volmer potential dependence is assumed for the rate constants (see Sect. 1.7.1). 

By the beginning of the 20th century an independent field of physical chemistry, namely chemical kinetics, had been developed. Temkin treats chemical kinetics as a science dealing with chemical reaction rates and specifies the reaction kinetics as "the dependence of the rate of a given reaction on the substance concentration, temperature and some other parameters, e.g. the electrode potential in electrochemical reactions . Semenov interprets chemical kinetics as a science "not only about the rates but also about the mechanism of chemical reactions [5, p. 9]. 

Fig. 2.2S. A comparison of the potential dependence for the electrochemical oxidation of NADH at a poly(aniline)/poly(vinylsulfonate)-coated electrode. (fccu,[site]Ds /AwM). and the second-order rate constant for the homogeneous oxidation of NADH by a range of two-electron mediators, k2- The open symbols correspond to homogeneous oxidation by ortho. , and para, O, substituted quinones and diaminobenzenes. the filled triangles. , are the...

Costentin, C., Robert, M. and Savcant, J.-M. (2006b) Electrochemical concerted proton and electron transfers. Potential-dependent rate constant, reorganization factors, proton tunneling and isotope effects. J. Electroanal. Chem. 588, 197-206. 

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