Tafel-limit

Assuming a phenomenological model, anodic polarisation can be described using the Butler-Volmer equation, and its low current density (linear) and high current density (Tafel) limits. Experimental results for some selected cases can be... 

Overvoltage. Overvoltage (ti. ) arises from kinetic limitations or from the inherent rate (be it slow or fast) of the electrode reaction on a given substrate. The magnitude of this value can be generally expressed in the form of the Tafel equation... 

This limit is called linear kinetics. On the other hand, if the surface overpotential is large, one of the exponential terms is negligible. This limit is called Tafel kinetics. The relationship was found empirically. In the anodic Tafel region... 

In oxygen-free seawater, the J(U) curves, together with the Tafel straight lines for hydrogen evolution, correspond to Eq. (2-19) (see Fig. 2-2lb). A limiting current density occurs with COj flushing for which the reaction ... 

Turning now to the acidic situation, a report on the electrochemical behaviour of platinum exposed to 0-1m sodium bicarbonate containing oxygen up to 3970 kPa and at temperatures of 162 and 238°C is available. Anodic and cathodic polarisation curves and Tafel slopes are presented whilst limiting current densities, exchange current densities and reversible electrode potentials are tabulated. In weak acid and neutral solutions containing chloride ions, the passivity of platinum is always associated with the presence of adsorbed oxygen or oxide layer on the surface In concentrated hydrochloric acid solutions, the possible retardation of dissolution is more likely because of an adsorbed layer of atomic chlorine ... 

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). 

It can be seen from Fig. 14.7 that the polarization curve for this reaction involving p-type germanium in 0.1 M HCl is the usual Tafel straight-line plot with a slope of about 0.12 V. For -type germanium, where the hole concentration is low, the curve looks the same at low current densities. However, at current densities of about 50 AJvcF we see a strong shift of potential in the positive direction, and a distinct limiting current is attained. Thus, here the first reaction step is inhibited by slow supply of holes to the reaction zone. 

The surface concentration Cq Ajc in general depends on the electrode potential, and this can affect significantly the form of the i E) curves. In some situations this dependence can be eliminated and the potential dependence of the probability of the elementary reaction act can be studied (called corrected Tafel plots). This is, for example, in the presence of excess concentration of supporting electrolyte when the /i potential is very small and the surface concentration is practically independent of E. However, the current is then rather high and the measurements in a broad potential range are impossible due to diffusion limitations. One of the possibilities to overcome this difficulty consists of the attachment of the reactants to a spacer film adsorbed at the electrode surface. The measurements in a broad potential range give dependences of the type shown in Fig. 34.4. 

Can an ORR mechanism at Pt metal in an acid electrolyte with the Reaction (1.2) as the first and rate-limiting step be defended in light of the recently reported apparent Tafel slope and reaction order for ORR in the PEFC cathode ... 

Applying the Tafel equation with Uq, we obtain the polarization curves for Pt and PtsNi (Fig. 3.10). The experimental polarization curves fall off at the transport limiting current since the model only deals with the surface catalysis, this part of the polarization curve is not included in the theoretical curves. Looking at the low current limit, the model actually predicts the relative activity semiquantitatively. We call it semiquantitative since the absolute value for the prefactor on Pt is really a fitting parameter. 

The above-described theory, which has been extended for the transfer of protons from an oxonium ion to the electrode (see page 353) and some more complicated reactions was applied in only a limited number of cases to interpretation of the experimental data nonetheless, it still represents a basic contribution to the understanding of electrode reactions. More frequently, the empirical values n, k° and a (Eq. 5.2.24) are the final result of the investigation, and still more often only fcconv and cm (cf. Eq. 5.2.49) or the corresponding constant of the Tafel equation (5.2.32) and the reaction order of the electrode reaction with respect to the electroactive substance (Eq. 5.2.4) are determined. 

The method permits the simultaneous determination of reaction order, m, and reaction rate constant, k, from the slope and the intercept of the straight line. The procedure can be repeated for various potential values below the limiting current plateau to yield k as a function of electrode potential. The exchange current density and the Tafel slope of the electrode reaction can be then evaluated from the k vs. potential curves. 

Butler27 and Volmer28 advanced Tafel s equation by relating overpotentials to activation barriers. The quantitative relationship between current and overpotential is called the Butler-Volmer equation (eqn (32)), and is valid for electrochemical reactions that are rate limited by charge transfer. 

To learn that when the rate of electron transfer is slow, a useful approach is to construct Koutecky-Levich plots of (/(current) against l/Tafel plot from these mass-transport-limiting values of the current. 

Care The Tafel equation is different to all the other equations we have discussed so far in this chapter, because in this case I is not a limiting current. 

The equations used in these models are primarily those described above. Mainly, the diffusion equation with reaction is used (e.g., eq 56). For the flooded-agglomerate models, diffusion across the electrolyte film is included, along with the use of equilibrium for the dissolved gas concentration in the electrolyte. These models were able to match the experimental findings such as the doubling of the Tafel slope due to mass-transport limitations. The equations are amenable to analytic solution mainly because of the assumption of first-order reaction with Tafel kinetics, which means that eq 13 and not eq 15 must be used for the kinetic expression. The different equations and limiting cases are described in the literature models as well as elsewhere. 

---