Rate constant-overpotential plot

Figure 2. The electrochemical free energy of activation, AGe, for Cr(OHt)6s+/2+ at the mercury-aqueous interface, plotted against the electrode potential for both anodic and cathodic overpotentials. Solid lines are obtained from the experimental rate constant-overpotential plot in Ref. 14, using Eq. 6 (assuming A = 5 X 10s cm S1). Dashed lines are the predictions from Eq. 16.

Figure 10.11 Arrhenius plots of the ORR rate constants obtained at various electrodes. The symbols are the same as those in Fig. 10.10. Each solid line is the least squares fit of all the data at the constant applied potential. Since the standard potential E° and [RHE(r)] shift to less positive values in a different maimer, the corrected potential E is applied so as to keep a constant overpotential for the ORR at each temperature. The applied potentials of -0.485, -0.525, and -0.585 V vs. E° correspond to 0.80, 0.76, and 0.70 V vs. RHE, respectively, at 30 °C. (From Yano et al. [2006b], reproduced by permission of the PCCP Owner Societies.)...

To learn how to calculate the rate constant of electron transfer, kd, from a Tafel plot of log I o (as y ) against overpotential r) (as x ). 

Figure 11. Tafel plot of flooded porous-electrode simulation results for the cathode at three different values of xp = 2.2nFIfQ 2 02, z=dbK. The z coordinate ranges from 0 (catalyst layer/membrane interface) to L (catalyst layer/diffusion medium interface), the dimensionless overpotential is defined as // = —o FIRT r]oRR, - ), and the ORR rate constant is defined as A = hFFq 2 (Reproduced with permission from ref 36. Copyright 1998 The Electrochemical Society, Inc.)...

Calculating Exchange Current Densities and Rate Constants from Impedance Plots. If one takes the Butler-Volmer equation (7.24) under the reversible condition, i.e that in which the overpotential, rj, tends to zero, then,... 

Figure 5.2 Tafel plots of In k versus overpotential for a mixed self-assembled monolayer containing HS(CH2)i600C-ferrocene and HS(CH2)isCH3 in 1.0 M HCIO4 at three different temperatures V, 1 °C O/ 25 °C , 47°C. The solid lines are the predictions of the Marcus theory for a standard heterogeneous electron transfer rate constant of 1.25 s-1 at 25 °C, and a reorganization energy of 0.85 eV (= 54.8 kj moh1). Reprinted with permission from C. E. D Chidsey, Free energy and temperature dependence of electron transfer at the metal-electrolyte interface, Science, 251, 919-922 (1991). Copyright (1991) American Association for the Advancement of Science...

Given that electrochemical rate constants are usually extremely sensitive to the electrode potential, there has been longstanding interest in examining the nature of the rate-potential dependence. Broadly speaking, these examinations are of two types. Firstly, for multistep (especially multielectron) processes, the slope of the log kob-E plots (so-called "Tafel slopes ) can yield information on the reaction mechanism. Such treatments, although beyond the scope of the present discussion, are detailed elsewhere [13, 72]. Secondly, for single-electron processes, the functional form of log k-E plots has come under detailed scrutiny in connection with the prediction of electron-transfer models that the activation free energy should depend non-linearly upon the overpotential (Sect. 3.2). 

Figure 4. Plot of the rate of methane formation at a Ru electrode as a function of pH at 60-63 C and a constant overpotential.

The sign holds for anodic and cathodic overpotentials respectively. A plot of electrode potential versus the logarithm of current density is called the Tafel plot and the resulting straight line is the Tafel line" The linear part (5=2.3 RT/anF) is the Tafel slope that provides information about the mechanism of the reaction, and "a" provides information about the rate constant of the reaction. The intercept at r =0 gives the exchange current density... 

Then A versus log(/ f results in a single kinetic working curve, as shown in Fig. 8, and provides a convenient way of determining Xf h- A plot of log Xf h against overpotential (17) yields the formal heterogeneous electron transfer rate constant (X h) from the intercept and the value of the electrochemical transfer coefficient (a) from the slope. - ... 

Although standard electrode reaction rate constants k are in principle obtainable from peak-to-peak separations in CVs or from extrapolations of Tafel plots to zero overpotential, the precision needed for measurement of AFei demands alternating eurrent voltammetry (ACV), in which a small AC potential of angular frequency lj is superimposed upon a DC potential ramp and the phase angle (p is extracted from measurements of the maximum in-phase and 90° out-of-phase currents.if the diffusion coefficients of the oxidized and redueed speeies are taken to be the same (D),... 

In Fig. 6, the effects of temperature on Tafel behavior are shown with the assumption that X and Vp are independent of temperature. Again, at large overpotentials, the Tafel plots converge to a temperature-independent value, while ln( °) at r] = 0V is sensitive to temperature. If the entropy of activation is zero, an Arrhenius plot of the standard rate constant is related to the reorganization energy via Eq. (8) ... 

Experimental kinetic measurements at SAM-coated electrodes yield two parameters, the standard rate constant and the reorganization energy X. The latter can be obtained either by measuring the rate constant versus the overpotential and fitting a Tafel plot to the theoretical curves or by meastiring the standard rate constant versus temperature and using Eq. (8). Once... 

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