Tomes criteria

The shape of the current-voltage curve is easily analysed with the Tomes criteria ... 

To determine between reversible, quasi-reversible and irreversible, a useful approach is the Tomes criteria [7] see Ref. [6] for a full overview of the various diagnostic approaches. 

The voltammograms at the microhole-supported ITIES were analyzed using the Tomes criterion [34], which predicts ii3/4 — iii/4l = 56.4/n mV (where n is the number of electrons transferred and E- i and 1/4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufficient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler-Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. 

The results obtained in both acetonitrile and dichloromethane solutions are similar. Normally, the voltammograms included two reversible or quasi-reversible waves with a Tomes criterion AE = E3/4 - Ei/4, characterizing the reversibility of electrochemical processes [335], of ca 60 mV and a distance between them of 855 20 mV. The first and more intensive wave was attributed to the oxidation of two independent ferrocenylboron caps. A substantial (100 200 mV) cathodic shift of this wave versus the Fc /Fc potential is caused by the donor effect of the macrobicyclic substituent in cyclopentadienyl rings. 

The electrochemical properties of the clathrochelate Ca-nonsymmetric FeDnD 3-n(BX)2 and Ca-nonsymmetric FeD3(BX)(BY) tris-dioximates and their dependence on electronic characteristics of the substituents in the dioximate fragments and ones at capping atoms are discussed in Refs. 64 and 68. Table 36 lists the E1/2 and the Tomes criterion values for these complexes. As seen from this table, the oxidation process for most of the boron-capped iron(II) clathrochelates is reversible or quasi-reversible. 

The electrochemical behaviour of the ribbed-functionalized iron(II) [65, 68] and ruthenium(II) [78] clathrochelates with alkylamine, thioaryl, thioalkyl, phenoxyl and crown ether substituents in a-dioximate fragments was characterized by E1/2 values for Fe3+/2+ and Ru3+/2+ couples (Table 37). The Tomes criterion values of most complexes exhibited reversible or quasi-reversible anodic processes. Moreover, the quasi-reversible oxidation processes are accompanied by the formation of insoluble products followed by passivation of the working electrode. The Ev2 values depend on the electron-donating properties of the substituents in the ribbed fragments. The correlations of E1/2 values for Ru3" 2+ and Fe + 2+ couples with these substituents Hammet s Opara constants were observed in Refs. 65, 68, and 78. These correlations are rather qualitative, but they enable one to conclude that ruthenium complexes are less sensitive to the change of substituents in dioximate fragments. There was no correlation between the Em values and the inductive Taft s (cr,) constants for substituents in dioximate fragments. 

Note also that E vs. log [(/ OM should be linear with a slope of 2.303RTInF or 59.1/n mV at 25°C. This wave slope is often computed for experimental data to test for reversibility. A quicker test [the Tomes criterion (25)] is that IE3/4 — Ey l = 56.4/n mV at 25°C. The potentials Ey4 and E1/4 are those for which i = 3iJ4 and / = iJ4, respectively. If the wave slope or the Tomes criterion significantly exceeds the expected values, the system is not reversible. (See also Section 5.5.4). 

Tomes criterion and half-wave potential. As one can see from Table 5.5.1, 3/4 — 1/4 for a totally irreversible system provides a directly. That figure can then be used in conjunction with (5.5.30) [for early transients] or 5.5.49 [for steady-state voltammetry] to obtain l. Butler-Volmer kinetics are implicit and E must be known. 

Derive the Tomes criterion for (a) a reversible sampled-current voltammogram based on semi-infinite linear diffusion, (b) a totally irreversible sampled-current voltammogram based on semi-infinite hnear diffusion, and (c) a totally irreversible steady-state voltammogram. 

Since a is usually between 0.3 and 0.7, both the wave slope and the Tomes criterion for a totally irreversible system are normally significantly larger than for a reversible system. These figures of merit are not without ambiguity, however. Consider the predicted wave slope of 63.8 mV for a = 0.85. Within the precision of normal measurements, one could diagnose the system as either reversible or irreversible. It is always a good idea to examine reversibility by a method, such as cyclic voltammetry, that allows a view of the electrode reaction in both directions. 

Conventional log-plot analysis, variation of E1/2 and Ep values towards more negative potential with increase of concentration of depolariser, disobedience of Tomes criterion, the non-linearity between m vs where polarographic half-wave potential (E1/2) show that the electrode process related to the reduction of EPN is irreversible. The irreversibility of the electrode process is also evidened from the absence of anodic peak in the cyclic voltammogram and the variation of peak potential with the scan rate. 

The first wave corresponds to a one-electron reversible process as suggested by the Tomes criterion, i.e., IE3/4-E1/4I = 60 mV. The diffusion coefficient, determined by the limiting current and for n=l, was 1.4x10 cm s in agreement with the value obtained in cyclic voltammetry for scan rates above 300 mV/s, when the process is reversible. Furthermore, the Ei/2 values were the same ( 5 mV) when different electrode radii were used (5, 12.5 and 25 xm) confirming the reversibility of the process (5). 

Alternatively, from the difference of two quartile potentials lfi3/4 - 1/4 , where 1/4 and - 3/4 are the potential values at which i and i = jh, respectively, one can find a using Tomes criterion ... 

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