Tafel plots from Butler-Volmer equation

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

As already shown in Fig. 1, a general feature of electrocatalysis is that the current passing through an electrode-electrolyte interface depends exponentially on overpotential, as described by the Butler-Volmer equation discussed in Sect. 2.4.1, so that logi versus r] U — C/rev) gives straight lines, termed Tafel plots (Fig. 1). On this basis, one would expect an exponential-type dependence of current on overpotential in Fig. 12 (curve labeled 7ac). Such a curve would correspond to pure activation control, that is, to infinitely fast mass-transport rates of reactants and products to and from the two electrodes. 

The usual procedure for extracting the exchange current Iq is then to measure q as a function of I and to plot Inl vs q (Tafel plot). Such plots are shown in Figures 3 and 4 for Pt and Ag catalyst electrodes deposited on YSZ and acting as catalyst for C2H4 oxidation. Throughout the rest of this discussion, we omit the subscript "W" from q and simply write q, since the only overpotential of interest is that of the catalyst film. When Iql >100 mV, then the Butler-Volmer equation (16) reduces to its "high field approximation" form, i.e.. 

The usual procedure for measuring the exchange current density ig is then to measure t] as a function of I and to plot In I vs. (Tafel plot). Such plots are shown in Figure 13.3 for Pt and Ag electrodes deposited on YSZ. From the slopes of the linear part of these plots ( ri > 200 mV, in which case Equation 13.15 are valid) one obtains the transfer coefficients and a. By extrapolating the linear part of the plot to r] = 0, one obtains io. One can then plot i vs. T] and use the low field approximation of the Butler-Volmer equation which is valid for < 10 mV, i.e.. 

For low voltage, the Tafel line deviates from the Butler-Volmer relation. A method given by Allen and Flickling (1957) allows plotting of i versus q, even at low voltages. The simple form of the BV equation (Equation 5.77) can be cast into the following form ... 

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