Tafel slope difference

If the first step would limit the reaction rate, the cathodic Tafel coefficient would be identical to that of the Volmer-Heyrovsky mechanism (the anodic Tafel coefficient would be different though). On the other hand, if the second step is rate determining the cathodic Tafel slope differs. The rate of the reaction determining step, Vn, is given by... 

Mg alloying elements do not have a significant effect upon the cathodic process. This is substantiated by the insignificant cathodic Tafel slope difference between Mg and its alloys (see Fig. 1.7), which is also indirect evidence for the normal cathodic hydrogen evolution. Nevertheless, alloying... 

The effects of adsorbed inhibitors on the individual electrode reactions of corrosion may be determined from the effects on the anodic and cathodic polarisation curves of the corroding metaP . A displacement of the polarisation curve without a change in the Tafel slope in the presence of the inhibitor indicates that the adsorbed inhibitor acts by blocking active sites so that reaction cannot occur, rather than by affecting the mechanism of the reaction. An increase in the Tafel slope of the polarisation curve due to the inhibitor indicates that the inhibitor acts by affecting the mechanism of the reaction. However, the determination of the Tafel slope will often require the metal to be polarised under conditions of current density and potential which are far removed from those of normal corrosion. This may result in differences in the adsorption and mechanistic effects of inhibitors at polarised metals compared to naturally corroding metals . Thus the interpretation of the effects of inhibitors at the corrosion potential from applied current-potential polarisation curves, as usually measured, may not be conclusive. This difficulty can be overcome in part by the use of rapid polarisation methods . A better procedure is the determination of true polarisation curves near the corrosion potential by simultaneous measurements of applied current, corrosion rate (equivalent to the true anodic current) and potential. However, this method is rather laborious and has been little used. 

Figure 19.10a shows a theoretical plot of the right-hand side of equation 19.16 vs. AE in which the cathodic Tafel slope has been assumed to be constant at 120 mV and the anodic Tafel slope to have the arbitrary slopes of 40, 60 and 120 mV. It can be seen that linearity over a range of positive and negative potentials AE is achieved only when b = and that linearity is confined to AE 0 when b and b differ. 

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. 

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). 

FIGURE 28.1 Relative reaction rates for a reaction with different Tafel slopes at two different electrodes. 

What is behind the apparent disagreements between Tafel slopes and reaction orders reported from recent investigations of the ORR at PEFC cathode catalysts and the slopes and reaction orders measured earlier for model systems of low Pt surface area Is the ORR process at a dispersed Pt catalyst possibly different in nature from the ORR process at low-surface-area Pt ... 

As described above, the mechanism for C02 reduction in aqueous solutions proposed by Eyring and co-workers45 has been widely accepted. However, there remains a rather large difference between theoretical and observed values for the Tafel slope,45 and... 

Because of the different potential distributions for different sets of conditions the apparent value of Tafel slope, about 60 mV, may have contributions from the various processes. The exact value may vary due to several factors which have different effects on the current-potential relationship 1) relative potential drops in the space charge layer and the Helmholtz layer 2) increase in surface area during the course of anodization due to formation of PS 3) change of the dissolution valence with potential 4) electron injection into the conduction band and 5) potential drops in the bulk semiconductor and electrolyte. 

In cathodic area, the Tafel slope in the presence of DDTC is bigger than that in the absence of DDTC, and the cathodic curves imder the conditions of different DDTC concentration are almost parallel and their Tafel slopes only change a little. These demonstrate that the chemisorption of DDTC on the surface of jamesonite electrode also inhibits the cathodic reaction, but the chemisorption amoimt of DDTC is a little and almost not affected by the DDTC concentration due to their negatively electric properties of DDTC anion and the electrode surface. This reveals that there is a little DDTC chemisorption on the mineral even if the potential is lower (i.e., negative potential). 

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. 

At pHsI, the Tafel slopes (Table I) for bare Cu emd Cu coated with PVI-1 or BTA are the same within experimental error. PVI-1 and BTA do not appear to affect the mechanism of 0 reduction on Cu. These results are supported by Heakal and Haruyama [12] who also found the Tafel slope of Cu with BTA present in a pH=3 solution of HNO ind 3% NaCl to be -0.18V/dec. These authors, however, do not cite a value for bare Cu. DDI-coated Cu shows a significantly different Tafel slope, -320mV/dec, indicating that a different mechetnlsm applies. 

Thus, there are four possible mechanisms for the hydrogen evolution in an acid solution (1) CT is RDS, CD fast (2) CD is RDS, CT is fast (3) CT is RDS, ED is fast and (4) ED is RDS, CT is fast. Different paths and different mechanisms have different Tafel slopes. Readers are referred to Refs. 11, 15, 21-23, and 26 for determination of the reaction mechanisms. 

The lower the slope, the lower the activation loss for the O2 reduction reaction in acid media, the observed slope is 0.060 V/ decade and it can be obtained theoretically by assuming the oxygen discharge step as the slowest one (the rate determining step, the r.d.s. ( 7)). For hydrogen the mechanism is different and the r.d.s. is the atomic dissociation and in this case a Tafel slope of 0.030... 

Equation (7.17) is the Tafel equation and expresses the way in which the applied potential difference operates to enhance the reaction rate [22]. Since the unit of q is volts, the units of a and b are also volts a is called the Tafel intercept, that is, the overpotential at 7 = 1 (which depends on the units of 7, A or mA or pA) b is known as the Tafel slope, that is, the variation of q per decade of current. 

---