Tafel slope coefficient

Tafel slope (Napieran loop) transfer coefficient diffusion layer thickness dielectric constant, relative electric field constant = 8.85 x 10 F cm overvoltage, polarization ohmic voltage drop, resistance polarization specific conductance, conductivity electrochemical potential of material X,... 

These are the coefficients that determine the Tafel slope of the log / against q curve of a multistep reaction, and they are of fundamental importance in providing information on the mechanism of the reaction. Equations 20.86 and 20.87 are of the same form as equations 20.59 and 20.58 that were derived for a simple one-step reaction involving a symmetrical energy barrier, and under these circumstances equations 20.90 and 20.91 simplify to... 

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. 

Tafel s equation (eqn (30)) is accurate at large overpotentials, but fails as q approaches zero. The Tafel plot is obtained by plotting rj vs. log i, with b referred to as the Tafel slope. The Tafel slope is a function of the transfer coefficients and temperature, where... 

Figure 7.12 Schematic Tafel plot of log / (as y ) against overpotential rj (as x ). The linear regions yield the Tafel slopes, from which the transfer coefficients a can be determined. The intersection between the two Tafel regions occurs on the y-axis at log /o. ...

In this equation, SLm represents the Tafel slope for the mixture of X plus Y, and Slx,Siy represents the Tafel slopes for the individual components. This equation enables a determination of / from Tafel representations, providing that the quotients between the individual electrochemical rate constants, kx and ky, and the electron transfer coefficients, ocxnax,ocYnaY, are known. 

These are the coefficients that determine the slope of the log i versus T curve (i.e., the Tafel slope of a multistep reaction) and are of primary importance in mechanism determinations. 

In the above analysis, it has been considered that the transfer coefficient, a, was independent of temperature the temperature dependence of Tafel slopes is then given by... 

In some cases, however, anomalous Tafel slopes have been observed for strongly catalytic processes [40—42] if the transfer coefficient is temperature-dependent an extra term, d a/d(l/T), must be considered in eqn. (101). 

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... 

The transfer coefficients are the ones determining how the electrode potential influences the electrochemical reaction rate or, in other words, the inclination of the relation between log I and the over-potential, also called the Tafel slope, of a multistep reaction. The coefficients are an important aid when unravelling the electrochemical reaction mechanisms, because the experimentally determined Tafel slope should correspond to the value that is calculated for the postulated sub-step sequence and RDS. 

A key element in the analysis is the correspondence between the observed and the theoretical dependence of the current on the potential. In other words, one compares the theoretical Tafel slope for the postulated mechanisms, or the transfer coefficients which are derived from these, to the experimentally obtained values. 

The experimental Tafel slope does not appear to deviate significantly from 120mV/decade, which corresponds to a transfer coefficient of 0.5, and this over the complete investigated range of hydrogen peroxide concentration and pH (Fig.4.6). This Tafel slope is found within a potential range restricted from ca. -0.10 to 0.20V vs. SCE. Above =0.20 V vs. SCE, the inclination of the current-potential curve appears to decrease. In Fig. 4.7,... 

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 ... 

The Tafel slopes are given in Table 9. The first slope (bx) is the lower one and it occurs at more positive potentials the second (b2) has higher values and occurs at slightly positive potentials, i.e., at lower coverages (8). Two slopes were not observed at all temperatures. Table 9 also contains corresponding coverages and the charge transfer coefficient, a ... 

Table 9 Experimental Tafel Slopes, Charge Transfer Coefficients and Surface Coverages for Halogen-Active Carbon Electrodes at Various Temperatures and Coverages... 

The Tafel slope for this mechanism is 2.3RT/PF, and this is one of the few cases offering good evidence that P = a, namely, that the experimentally measured transfer coefficient is equal to the symmetry factor. A plot of log i versus E for the hydrogen evolution reaction (h.e.r.), obtained on a dropping mercury electrode in a dilute acid solution is shown in Fig. 4F. The accuracy shown here is not common in electrode kinetics measurements, even when a DME is employed. On solid electrodes, one must accept an even lower level of accuracy and reproducibility. The best values of the symmetry factor obtained in this kind of experiment are close to, but not exactly equal to, 0.500. It should be noted, however, that the Tafel line is very straight that is, P is strictly independent of potential over 0.6-0.7 V, corresponding to five to six orders of magnitude of current density. 

This leads to a Tafel slope of b = 2.3RT/PF = - 0.12 V for P = 0.5, and a reaction order (at constant potential) of unity. The transfer coefficient is equal to the symmetry factor P as in the case of mercury, but we recall that the Tafel slope is calculated here assuming essenti illy full coverage, whereas that on mercury was obtained assuming a very low value of the coverage. The Tafel plot observed on platinum in acid solutions is shown in Fig. 5F. 

For this mechanism, the transfer coefficient a is 4 and the Tafel slope b is 15 mV. The reaction order at constant potential is 4, and the stoichiometric number is unity. 

Either Eq. 5F or 6F can be considered to be a definition of the transfer coefficient a. Equation 5F relates it directly to the measured quantity (ar /alog i), while Eq. 6F can be regarded as a formal definition, indicating that the transfer coefficient a, is simply the reciprocal Tafel slope in dimensionless form. 

The transfer coefficient a is an experimental parameter obtained from the current-potential relationship. Just that and nothing more It is equal to the inverse of the Tafel slope b expressed in units of (2.3RT/F), that is, to the inverse Tafel slope in dimensionless form. It is shown later that the relationship between a and p depends on the mechanism of the reaction. The transfer coefficient is therefore one of the parameters that allow us to evaluate the mechanism of electrode... 

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