Tafel plots theory

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...

The linear Tafel plots and a values close to 0.5 indicate that conventional ET theory, e.g., Buttler-Volmer model, is applicable to heterogeneous reactions at the ITIES. ... 

The following problem is designed to provide understanding of Tafel plots for individual half-cell reactions and the form of experimental polarization curves to be expected based on the theory. Assume that for a given metal, M,... 

An additional test of the theory is given by the comparison of the data for different electrode materials. Experimentally the reduction of the same anion at different metals leads to quite different patterns for the polarization curve, in particular, a drastic variation of the interval in which the diffuse-layer minimum is observed. According to the theory (24), if the reacting species do not enter the compact layer and the possible change of the electron-tunneling factor does not influence the reaction rate (e.g. for adiabatic electrochemical reactions [58]) the corrected Tafel plots must be independent of the electrode material. This prediction has also been confirmed experimentally for the persulfate reduction at Hg (amalgams), Bi, Sn,... 

Eor ferrocene sites at the end of long alkanethiols self-organized at gold electrodes and diluted with unsubstituted thiols with the redox moiety in contact with the electrolyte (Fig. 4a), Chidsey has reported [34] curved Tafel plots (Fig. 4b), which could be fitted by equations derived from Marcus theory with values of k = 0.85 eV and Z = 6.73 x 10 s"l eV" for a reaction rate of A = 2.5 s at in Fig. 4(b). Similar curvature in Tafel plots has been reported by Faulkner and coworkers [35] for adsorbed osmium complexes at ultramicro-electrodes (UME). The temperature dependence of the rate coefficient could also be fitted from Marcus equation and electron states in the metal and coupling factors given by quantum mechanics. 

Methods for assessing the degree of kinetic heterogeneity are based on measuring the kinetics of a subset of the entire ensemble of redox centers. In CA and CV experiments, k(t) and r)(t) data pairs are obtained for a fixed fraction of the remaining reactant redox centers (Q(t)/Qtot > see Eq. 16). Tafel plots are generated and fitted to the theory for each fixed fraction (or percentage) [83,116,117,... 

Figure 1. Tafel plots for different reactions reduction of benzene/ oxidation of Cu in solid electrolyte/ reduction of Fe "(CN)6/ H2 evolution reaction/ O2 evolution reaction/ Cr(OH2)sOSO reduction/ and the theoretical plots from the continuum theory expression (----) for various values, i.e., 0.5,1.0, and 2.0 eV.

Quantitative comparison of the experimental results with theory should be made preferably by the method of corrected Tafel plots (C.T.P.), proposed by Delahay et or by the graphical method of constructing polarization... 

Several theories exist on the mechanism of dissolution of this type of metal, which explain the experimentally observed linearity of the Tafel plots. 

This result is important it shows us that a is predicted by Marcus theory to be 0.5 for a one-electron process if A AG, i.e. if the reaction is irreversible. Of further importance is the fact that AG as discussed above is not a standard Gibbs energy since it is dependent upon the electrode potential. Ckinsequently, a is not constant and this may lead to curved Tafel plots if a is measured over a wide potential range. 

Viswanathan V, Norskov JK, Speidel A et al (2013) Li-02 kinetic overpotentials Tafel plots from experiment and first-principles theory. J Phys Chem Lett 4 556-560. doi 10.1021/ jz400019y... 

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