Tafel slope parameters

The slope of the Tafel curve drj/d log / is only one of the criteria that are required to determine the mechanism of the h.e.r., since different mechanisms, involving different r.d.s. often have the same Tafel slope. Parameters that are diagnostic of mechanism are the transfer coefficient, the reaction order, the stoichiometric number, the hydrogen coverage, the exchange current density, the heat adsorption, etc. 

The main purpose of this paper is to examine the real temperature dependence of the Tafel-slope parameter b for various processes and to discuss the mechanisms of activation in electrode processes in the light of the observed behavior of b as a function of temperature. 

Chapter 2, by B. E. Conway, deals with a curious fundamental but hitherto little-examined problem in electrode kinetics the real form of the Tafel equation with regard to the temperature dependence of the Tafel-slope parameter 6, conventionally written as fe = RT/ aF where a is a transfer coefficient. He shows, extending his 1970 paper and earlier works of others, that this form of the relation for b rarely represents the experimental behavior for a variety of reactions over any appreciable temperature range. Rather, b is of the form RT/(aH + ctsT)F or RT/a F + X, where and as are enthalpy and entropy components of the transfer coefficient (or symmetry factor for a one-step electron transfer reaction), and X is a temperature-independent parameter, the apparent limiting... 

Because of the logarithmic relation, polarization depends more strongly on parameter a than on parameter b. The parameter a, which is the value of polarization at the unit current density (1 mA/cm ), assumes values which for different electrodes and reactions range from 0.03 to 2-3 V. Parameter b, which is called the Tafel slope, changes within much narrower limits in many cases, at room temperature b 0.05 V and 0.115 V (or roughly 0.12 V). 

Elucidation of the actual values of key diagnostic parameters that have been used for a long time by ORR experimentahsts, including primarily the measured Tafel slope and the reaction order with regard to O2, and their predictive power regarding the ORR mechanism. 

The Tafel slope can be obtained from eqn. (153) by differentiation and substitution from eqn. (154) as a Br nsted slope. It should be noted that a is an empirical parameter defined in Sect. 2.1 and is not part of the theory. From eqns. (153) and (154), the transfer coefficient at constant Coulombic work terms is given by... 

This is the steady-state current which is theoretically predicted if stage 1 is the rate-determining step in the sub-stages sequence represented in Equations 4.8 1.12. An important parameter to compare both in theory and experimentally is the Tafel slope or the transfer coefficient which results from it. Therefore, Equation 4.30 has to be written in a form that contains only one exponential term. Since the considered I-E curve is an oxidation wave, the effect of the reduction (second term in the right-hand part of Equation 4.30) will be negligible with potentials that are situated sufficiently far away from the equilibrium potential, and for the anodic current the following applies ... 

First, when external current sources are used, the power consumption may be unpractically large. It all depends on the electrodic parameters of the electronation reaction—the larger its exchange-current density and the lower its Tafel slope, the larger will be the external protection current that must be used to achieve protection. 

Estimate the corrosion potential corr and the corrosion current density icorr of Zn in a deaerated HC1 solution of pH 1 at 298 K. In this solution Zn corrosion is accompanied by the hydrogen evolution reaction (h.c.r.). The parameters (standard electrode potential E°, exchange current density i0, Tafel slope b of Zn dissolution and the h.e.r. on Zn are... 

In practice, in all fuel cells that involve the utilization of 02 from air (Section 13.4.5), the oxygen reduction reaction [Eqs. (13.4) and (13.24)] is always rate determining for terrestrial applications. One can seejust how important it is to attempt to develop electrocatalysts for the cathodes of fuel cells on which the enhanced current density is high and Tafel slope is low and the efficiency of energy conversion, therefore, maximal. The direct relation of the mechanism of oxygen reduction and the associated Tafel parameters to the economics of electricity production and transportation is thus clearly seen. 

Relationships such as that in Eq. (12) offer convenient means of testing the validity of mixed potential models by comparing electrochemically determined parameters (in this case, a reaction order based on measured Tafel slopes) to values measured by other means. One such example would be the corrosion of U02 (nuclear fuel) in aerated neutral solutions containing added carbonate (6). In the presence of carbonate, corrosion product deposits are avoided, since the U02+ corrosion product is solubilized by complexation with the carbonate. Measured Tafel slopes yield a predicted reaction order of n0l = 0.67 with respect to 02 for the overall corrosion reaction ... 

The determination of a Tafel slope for 02 reduction illustrates some of the difficulties encountered in determining a value of this parameter and emphasizes the need for a thorough understanding of the reaction mechanism if the develop-... 

This equation simplifies the kinetic of a charge-transfer-controlled process to two parameters the exchange current density jo and the Tafel slope b. Both values do not depend not only on the electrochemical reaction but also on the electrode material and on the electrolyte composition. 

Figure 6.61 shows the four parameters (Rf, Rct, Rc. and f) with potential. In the region of 370-600 mV versus RHE, the inverse of the Faradaic resistance and charge-transfer resistance versus electrode potential gives the Tafel slope. The changing features in these plots indicate a change in the mechanism of methanol electrooxidation. 

Equipped with the assumption of quasi-equilibrium, we can now proceed to calculate the Tafel slopes and some other kinetic parameters for a few very simple hypothetical cases, to show how such calculations are made. In Section 15 we shall discuss the kinetics of several reactions that either have been important in the development of the theory of electrode kinetics or are of current practical importance. 

Some values of the Tafel slopes calculated for these two mechanisms for different values of the size parameter n are shown in Table 2J. 

---