Electrode kinetics transfer coefficient

Thus bubbles on an electrode introduce an additional current-dependent term in the kinetic equation. In addition, Ah must be a function of the exchange current density, temperature, kinetic transfer coefficients, the average bubble diameter, and the void fraction, all of which determine the secondary current distribution on the electrode. 

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. ... 

From a kinetic point of view a describes the influence of a change of the electrode potential on the energy of activation for the charge transfer reaction which in turn influences the partial current density. The transfer coefficients % for the anodic charge transfer reaction and for the cathodic reaction add up according to... 

The usual Tafel evaluation yielded a transfer coefficient a = 0.52 and a rate constant k of 4x 10 cm s at the standard potential of the MV /MV couple. This k value corresponds to a moderately fast electrochemical reaction. In this electrode-kinetic treatment the changes in the rate of electron transfer with pH were attributed only to the changes in the overpotential. A more exact treatment should also take into account the electrostatic effect on the rate of reaction which also changes with pH. 

Hence the picture of the cathodic and anodic waves obtainable for a completely reversible redox couple by means of the RDE corresponds fully with that in Fig. 3.9 the value of i, i.e., the height of the sigmoidal waves, is linearly proportional to to1/2 and to C (see eqn. 3.89 and the Levich constant). If for a well chosen combination of C and E a plot of i against co1/2 deviates from a straight line passing through the origin, then in the kinetics of the electrode reaction we have to deal only with a rapid electron transfer (cf., Fig. 3.10) or even with a slow electron transfer (cf., Fig. 3.11), in which latter instance the transfer coefficient a plays an appreciable role (cf., eqns. 3.17 and 3.18). 

In addition to the thermodynamic quantity E°, the electrode reaction is characterized by two kinetic quantities the charge transfer coefficient a and the conditional rate constant k°. These quantities are often sufficient for a complete description of an electrode reaction, assuming that they are constant over the given potential range. Table 5.1 lists some examples of the constant k. If the constant k° is small, then the electrode reaction occurs only at potentials considerably removed from the standard potential. At these potential values practically only one of the pair of electrode reactions proceeds which is the case of an irreversible or one-way electrode reaction. 

Here ia is the exchange current density of the electrode reaction based on the bulk concentration aa and ac are the anodic and cathodic charge transfer coefficients, respectively and y is a dimensionless kinetic parameter. 

The RHSE has the same limitation as the rotating disk that it cannot be used to study very fast electrochemical reactions. Since the evaluation of kinetic data with a RHSE requires a potential sweep to gradually change the reaction rate from the state of charge-transfer control to the state of mass transport control, the reaction rate constant thus determined can never exceed the rate of mass transfer to the electrode surface. An upper limit can be estimated by using Eq. (44). If one uses a typical Schmidt number of Sc 1000, a diffusivity D 10 5 cm/s, a nominal hemisphere radius a 0.3 cm, and a practically achievable rotational speed of 10000 rpm (Re 104), the mass transfer coefficient in laminar flow may be estimated to be ... 

The kinetic parameters (Table 9) obtained for the reaction110 are a = 0.04 and k°a = 2.6 x 10 2 cm/s. The rate constant is of the same order as reported by ac polarography.109 The low value of the transfer coefficient indicates that the compound is excessively adsorbed at the electrode surface. 

In order to investigate the dependence of a fast reaction on the nature of the metal, Iwasita et al. [3] measured the kinetics of the [Ru(NH,3)6]2+/3+ couple on six different metals. Since this reaction is very fast, with rate constants of the order of 1 cm s-1, a turbulent pipe flow method (see Chapter 14) was used to achieve rapid mass transport. The results are summarized in Table 8.1 within the experimental accuracy both the rate constants and the transfer coefficients are independent of the nature of the metal. This remains true if the electrode surfaces axe modified by metal atoms deposited at underpotential [4]. It should be noted that the metals investigated have quite different chemical characteristics Pt, and Pd are transition metals Au, Ag, Cu are sd metals Hg and the adsorbates T1 and Pb are sp metals. The rate constant on mercury involved a greater error than the others... 

Hydrogen evolution, the other reaction studied, is a classical reaction for electrochemical kinetic studies. It was this reaction that led Tafel (24) to formulate his semi-logarithmic relation between potential and current which is named for him and that later resulted in the derivation of the equation that today is called "Butler-Volmer-equation" (25,26). The influence of the electrode potential is considered to modify the activation barrier for the charge transfer step of the reaction at the interface. This results in an exponential dependence of the reaction rate on the electrode potential, the extent of which is given by the transfer coefficient, a. 

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). 

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. 

D0 and DR are the respective diffusion coefficients k° and a are known as the standard (electron transfer) rate constant and electron transfer coefficient respectively, and both are kinetic parameters characterizing the feasibility of the electron transfer x is the distance away from the electrode surface. 

If the reaction (1.1) is controlled by the electrode kinetics, i.e., when the electrode reaction is not electrochemically reversible, the response depends on the dimensionless kinetic parameter k = and the transfer coefficient a [15-17],... 

The physical meaning of the kinetic parameter m is identical as for surface electrode reaction (Chap. 2.5.1). The electrochemical reversibility is primarily controlled by 03 (Fig. 2.71). The reaction is totally irreversible for log(m) < —3 and electrochemically reversible for log(fo) > 1. Between these intervals, the reaction appears quasireversible, attributed with a quasireversible maximum. Though the absolute net peak current value depends on the adsorption parameter. Fig. 2.71 reveals that the quasireversible interval, together with the position of the maximum, is independent of the adsorption strength. Similar to the surface reactions, the position of the maximum varies with the electron transfer coefficient and the amphtude of the potential modrrlation [92]. 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

Ve - Vo) is the overpotential, the potential required to initiate reactions at the electrode surface, the difference between the equilibrium potential Vo (no current flowing) and operating potential Ve (current flowing). The above kinetics indicate that the rate of electron transfer from the n-type semiconductor to the redox system depends on the surface electron concentration, while electron injection from the redox system into the conduction band is constant independent of applied potential [11,76,77]. If the Helmholtz layer potential (pn varies across the interface the description of electron transfer becomes considerably more complicated requiring a charge transfer coefficient in equation (3.4.34). 

The cadmium electrodeposition on the solid cadmium electrode from the sulfate medium was investigated [217]. The following kinetic parameters were obtained cathodic transfer coefficient a = 0.65, exchange current density Iq = 3.41 mA cm , and standard rate constant kg = 8.98 X 10 cm s . The electrochemical deposition of cadmium is a complex process due to the coexistence of the adsorption and nucleation process involving Cd(II) species in the adsorbed state. 

Thickness of thin layers, measured by ellipsometty, 1148,1151 Thin layer cells, 1146 adsorption in, 1103 in electrode kinetics, 1103 Ihiophcnol, adsorption, 979 Thirsk, clectrodcposition, 1310 Thompson, G. P., 1455 Thompson, J. J 1057, 1455 Throwing power, 1112 Throwing power, electrodeless, 1376 Titanium carbide, as dectrocatalyst, 1287 Transfer coefficient and symmetry factor, 1186, 1529... 

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