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regarded as negligible. The transfer coefficient, α, and the exchange current, i0, are obviously readily accessible from this kind of presentation, when it can be applied. Figure 9.3 – Tafel plots for anodic and cathodic branches of the current-overpotential curve for O+e=Rwithα=0.5,T=298K,andj0 =10-6 A/cm2. Some real Tafel plots are shown in Figure 9.4 for the Mn(IV)/Mn(III) system in concentrated acid. The negative deviations from linearity at very large overpotentials come from limitations imposed by mass transfer. The region of very low overpotentials shows sharp falloffs for the reasons outlined just above. Allen and Hickling suggested an alternative method allowing the use of data obtained at low overpotentials. Butler-Volmer equation can be rewritten as or (9.23) (9.24) (9.25) so a plot of log [i/(1-efn)] vs. η yields an intercept of log i0 and a slope of – αF/2.3RT. This approach has the advantage of being applicable to electrode reactions that are not totally irreversible, that is, those in which both anodic and cathodic processes contribute significantly to the currents measured in the overpotential range where mass-transfer effects are not important. Such systems are often quasi-reversible, because the opposing charge-transfer reactions must 219PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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