Tafel relationship

If it is assumed that anodic polarisation of the more negative metal of the couple is insignificant, then it can be shown from the Tafel relationship for the hydrogen evolution reaction that... 

Figure 8-7 shows the anodic and cathodic polarization curves observed for a redox couple of hydrated titanium ions Ti /Ti on an electrode of mercury in a sulfuric add solution the Tafel relationship is evident in both anodic and cathodic reactions. FYom the slope of the Tafel plot, we obtain the symmetry factor P nearly equal to 0.5 (p 0.5). 

Tafel relationship The equation which relates the current I and overpotential r], as log / a T). 

The Tafel relationship as expressed in eqns. (82b) and (83b) is a linear free energy relation of the rate coefficient of a net electrode reaction (neglecting the back reaction). From eqn. (78)... 

The Tafel expressions for both the anodic and the cathodic reaction can be directly incorporated into a mixed potential model. In modeling terms, a Tafel relationship can be defined in terms of the Tafel slope (b), the equilibrium potential for the specific half-reaction ( e), and the exchange current density (70), where the latter can be easily expressed as a rate constant, k. An attempt to illustrate this is shown in Fig. 10 using the corrosion of Cu in neutral aerated chloride solutions as an example. The equilibrium potential is calculated from the Nernst equation e.g., for the 02 reduction reaction,... 

Figure 10 Schematic Tafel relationships showing the key parameters, Ee, and b, which define them. The sets of lines indicate the expected influence of concentration on the anodic and cathodic reactions.

Also shown in Fig. 10 are additional lines indicating the influence of 02 and Cl concentrations on the Tafel relationships. The lines allow the determination of reaction orders with respect to these reaction participants and yield the following expressions for the anodic and cathodic Tafel lines ... 

This fact, and the more complicated two-step nature of the anodic reaction [via steps (3) and (4)], could be incorporated into the Tafel relationship to yield... 

Figure 15 Procedure used to obtain a database of nuclear fuel (U02) corrosion rates (currents) (B) from a Tafel relationship for the anodic dissolution currents for U02 and a series of EC0Rr values measured in radiolytically decomposed solutions (A).

For a reversible electron-transfer process, the Tafel relationship corrected for mass transport holds in the central region of the voltammogram (Brett and Oliveira-Brett, 1993). Therefore, for a reversible one-electron process, a plot of - Euz versus logio(/ - Zi7m) will have a slope of 59/n mV per decade at 25°C. 

The partial current of CH4 formation is widely scattered when plotted against the potential. With an assumption that the partial current is proportional to proton activity, a linear Tafel relationship is obtained as shown in Fig. 25.The transfer coefficient is determined as 1.33. These facts indicate that the rate determining step of CH4 formation is involved with the second electron transfer to a hypothetical intermediate species such as COH in an electrochemical equilibrium with a CO adsorbed on the electrode and a proton from the electrolyte,... 

The boimdary conditions are described in more detail elsewhere. A zero-flux condition is imposed on the electrode for all species except the reactant Cu. A Tafel relationship with a concentration-dependent exchange current density was used to describe the electrode kinetics. The exchange current density was found from rotating disk experiments, and all other model parameters were taken from the literature. No parameters were adjusted for the simulations in the cell. 

Fig. 3.2 Deviation in the linear Tafel relationships at higher current densities dueto diffusion or other current limiting processes...

Equations 3.41 and 3.42 give the current density of the oxidation and reduction components of the interface electrochemical reaction as a function of the overpotential, r CT, with i0 M and the P s as kinetic parameters characterizing the reaction mechanism. To obtain the Tafel relationship (Eq 3.2),which expresses the overpotential as a function of the current density, Eq 3.41 and 3.42 are changed to make the current density the independent variable ... 

Fifi. 3.9 (a) Tafel relationships for the individual anodic and cathodic com- ponents of the interface reaction, (b) Net oxidation and reduction... 

Substituting the appropriate Tafel relationships into Eq 4.55 and 4.56 gives ... 

At potential ranges where Iex < 0, that is, when E < Ecorr, the external current is cathodic (net reduction), and at potential ranges where Iex > 0, that is, when E > Ecorr, the external current is anodic (net oxidation). Thus, the sign of Iex is sufficient to identify whether it is an external cathodic or anodic current. An expression for the external current is obtained on substitution ofthe individual Tafel relationships in Eq 4.66 ... 

This relationship called Tafel relationship was proposed empirically in 1905. 

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