Tafel expression

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,... 

Returning to the forward bias (cathodic) current flow, Eq. 17 bears some analogy to the famous Tafel expressions in electrochemical kinetics. Thus, ignoring the unity term within the square brackets, Eq. 17 predicts a Tafel slope of 60 mV per decade at 298 K. In many instances (see, e.g.. Refs. [157, 158]), such a slope indeed is observed. In many cases, however, the slopes are higher than the ideal value [14, 159-163]. 

There are two types of problems in the analysis of electrocatalytic reactions with mixed control kinetics reactant adsorption and combined considerations of mass and charge transfer processes in the current vs. potential profiles. The dependence of the current density, j, with the overpotential, x, can be expressed under r values larger than 0.12 V (in absolute values) through the Tafel expression corrected by the mass transfer effects ... 

The theoretical Tafel expression for polarization of the oxidation reaction was given as Eq 3.47, into which iox M from Eq 3.54 is now substituted to give ... 

WE established by the potentiostat, the external current, Iex, is the difference between Iox M and Ired M. This difference, in terms of the Tafel expressions for the individual reactions (see Eq 4.69), is ... 

The net (or experimental) anodic and cathodic polarization curves in Fig. 6.2 also can be expressed with Ecorr and Icorr as parameters. This form is used in establishing expressions that provide the basis of one of the experimental techniques for determination of Icorr. At the specific condition that E = Ecorr and Iex = 0, Iox M = Ired x = Icorr therefore, the Tafel expressions for the currents of the individual anodic and cathodic reactions can be equated, or... 

In the cases where the potential is controlled via the common-ion, it has been widely assumed that a simple coupling of the potential established via the ion partition and ET equilibria occurs [146, 148] hence combining Eqs. (5) and (48) yields a Tafel expression for ET coupled to the distribution of a common-ion (of charge number n) at the ITIES ... 

Next, one should estimate and. Because the two Tafel expressions for and are... 

The relationship between the potential and the logarithmic current density is not always linear (Tafel expression). In the case of a reacting species that is difiusion controlled, the logarithm of current density does not increase proportionally beyond a certain value of... 

The second term of the expression (C dEldt) approaches 0 at low voltage scan rates dEldt. Steady state is desirable, since the goal is to obtain at E, Note that t app becomes approximately equal to either or at large Ti, where tp = (E-E ). At very large anodic or cathodic overpotentials, Eq 19 can be rearranged in the form of the Tafel expression [1-3,5,7,18,19]... 

Fig. 18.6 Dimensionless concentration profiles of oxygen in an agglomerate for different overpotentials with full Butler-Volmer expression accounting for concentration overpotential (a) and Tafel expression (b). The reaction rate close to the middle of the agglomerates in (a) is...

When the current-potential relationship of the anodic branch of the corroding metal and the cathodic branch of the oxidising agent are expressed in their logarithmic form then one obtains the familiar Tafel expressions ... 

These polarization curves were deduced using Tafel kinetics at a single electrode only and no other losses. Note that the Tafel expression results in zero losses (mathematically, it will actually predict negative polarization, which is physically unrealistic) until i > io. The exact solution shown for io = 0.3 A/cm shows the error associated with the Tafel approximation with a higher exchange current density. 

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