Quasi-reversible electrode reaction

Fig. 7.22 Quasi-reversible electrode reaction of a dissolved redox couple at a planar electrode. Dependence of the amplitude-based quasi-reversible maximum on the rate constant (a) and on the charge transfer coefficient (b). For panel (a), the simulations are conducted for two electrons and the frequencies (in Hz) 0.01 (1), 0.03 (2), 0.05 (3), and 0.06 (4). For panel (b), the simulation conditions are one electron, frequency 0.1 Hz, and a 0.2 (1), 0.3 (2), 0.4 (3), 0.5 (4), 0.6 (5), and 0.7 (6). A s = 5 mV. Reproduced from [33] with permission...

From Fig. 7.55c, d, it is clear that the converted charge-potential curves obtained with SWVC are much more sensitive than the SWV ones for quasi-reversible electrode reactions, although the response charge-potential (SWVC curves) is... 

For quasi-reversible electrode reactions it is not easy to say how much the peak potential difference can be to still allow a fairly reliable determination of the formal potential with the help of Eq. (1.2.40) however, differences up to 120 mV can be tolerated if a and fi are near to 0.5. 

The dimensionless peak current of a totally irreversible electrode reaction is a function of the variable y however, the relationship is not strictly linear. If a = 0.5, it can be described with two asymptotes Astraight lines are linear functions of the transfer coefficient a. The responses of quasi-reversible electrode reactions are complex functions of both the electrode radius and the kinetics parameter k = Hence, no linear relationship between A p and y was... 

Fig. 10. The complex impedance plot for several simple electrode processes at the electrode and their equivalent circuits (A) Ideally polarizable electrode. (B) Diffusion-controlled fast redox reaction. (C) Irreversible electrode reaction. (D) Quasi-reversible electrode reaction. Arrows indicate the increasing frequency.

Fig. 56. Location of the half-wave potential of a quasi-reversible electrode reaction according to Eq. (102). 1 and 1 forward and backward linear sweep voltammogram of 1.5 mM tert-nitrobutane in DMF, sweep rate 18mVs" 2 and 2 convoluted (vs. time) current transients potential is transferred vs. Ag/AgI electrode. Adapted according to [121].

An intermediate situation arises when the electron-transfer and mass-transport rates are comparable. Such quasi-reversible electrode reactions are quite common, and their analytical utility depends to a large extent on careful control of the mass-transfer rate in the electroanalytical method used for their study. 

Figure 1 shows a cyclic voltammogram at the RVC electrode of a 0.133 mM cofactor solution prepared by dilution of the oxidized form of FeMoco into acidic 0.1 M TBAPFe/NMF and recorded at the relatively fast sweep rate of 0.4 V s. Two quasi-reversible electrode reactions were observed at -0.30 and -0.98 V vs. NHE. These are assigned to sequential one-electron transfers involving conversion of FeMoco from its oxidized (ox) to semi-reduced (s-r) and semi-reduced to fully reduced (red) forms ... 

The effects of ultrasound-enlianced mass transport have been investigated by several authors [73, 74, 75 and 76]. Empirically, it was found that, in the presence of ultrasound, the limiting current for a simple reversible electrode reaction exhibits quasi-steady-state characteristics with intensities considerably higher in magnitude compared to the peak current of the response obtained under silent conditions. The current density can be... 

In this section, a non-reversible electrode reaction will be addressed. An exact definition of a slow charge transfer process is not possible because the charge transfer reaction can be reversible, quasi-reversible, or irreversible depending on the duration of the experiment and the mass transport rate. So, an electrode reaction can be slow or non-reversible when the mass transport rate has a value such that the measured current is lower than that corresponding to a reversible process because the rate of depletion of the surface species at the electrode surface is less than the diffusion rate at which it reaches the surface. Under these conditions, the potential values that reduce the O species and oxidize the R species become more negative and more positive, respectively, than those predicted by Nemst equation. 

Photogeneration of the charge carriers results in formation of quasi-Fermi levels, Fp and F in the space where light penetrates the semiconductor. Since Fp < F edox. and n = Fredox forward and the reverse electrode reactions in the redox couple are... 

This equation is often used to determine the formal potential of a given redox system with the help of cyclic voltammetry. However, the assumption that mid-peak potential is equal to formal potential holds only for a reversible electrode reaction. The diagnostic criteria and characteristics of cyclic voltammetric responses for solution systems undergoing reversible, quasi-reversible, or irreversible heterogeneous electron-transfer process are discussed, for example in Ref [9c]. An electro-chemically reversible process implies that the anodic to cathodic peak current ratio, lpa/- pc equal to 1 and fipc — pa is 2.218RT/nF, which at 298 K is equal to 57/n mV and is independent of the scan rate. For a diffusion-controlled reduction process, Ip should be proportional to the square root of the scan rate v, according to the Randles-Sevcik equation [10] ... 

Yeh and Kuwana " were the first to report on the electrochemistry of cytochrome c at doped metal oxide semiconductor electrodes. A nearly reversible electrode reaction was indicated by the cyclic voltammetry and differential pulse voltammetry of cytochrome c at tin-doped indium oxide electrodes. Except for the calculated diffusion coefficient, all of the characteristics of the electrochemistry of cytochrome c at this electrode indicated that the electrode reaction was well-behaved. A value of 0.5 x 10" cmVs was determined for the diffusion coefficient which, like previously determined values at mercury, is lower than the value obtained by nonelectrochemical methods (i.e., 1.1 X 10 cm /s " " ). The electrochemical response of cytochrome c at tin oxide semiconductor electrodes was reported to be quasi-reversible, although no details were given. " ... 

Fig. 48. Dependence of the ratio Ip qr/Ip.rev on the kinetic parameter A (defined in Eq. (88a)) under equal experimental conditions. Electron transfer coefficients for the forward process (xf (1) 0.3, (2) 0.5, (3) 0.7 IZ zone of total irreversibility, QZ zone of quasi-reversible processes, RZ zone of reversible electrode reaction.

As stated above, the background current density observed for diamond electrodes was lower than those for the other types of carbon-based electrodes in non-aqueous as well as aqueous electrolytes. Utilizing this characteristic, the electrochemical sensing processes have been investigated. For example, the Ceo molecule, which shows five reversible reductions at the GC electrode, has been reported to exhibit six waves at the diamond electrode [ll]. Moreover, ascorbic acid, an essential vitamin, has been shown to exhibit a particular reaction in non-aqueous electrolytes. A quasi-reversible redox reaction to produce the ascorbic acid radical anion occurs in non-aqueous electrolytes, while only an irreversible anodic oxidation reaction occurs in aqueous electrolytes [12]. 

Figure Bl.28.7. Schematic shape of steady-state voltaimnograms for reversible, quasi-reversible and irreversible electrode reactions.

Conducted in 10% CH2Cl2-90% acetonitrile for compounds [54] and [56] and in acetonitrile [55] upon addition of 2 equiv of the respective cation supporting electrolyte, 0.10 mol dm-3 TBABF4. The potential of the reduction current peak r, reversible q, quasi-reversible s, single reduction peak without corresponding reoxidation peak ec, electron transfer followed by a chemical reaction ec, ad, electron transfer followed by a chemical reaction with insoluble product which adsorbs on to the electrode surface. Prewaves are in parentheses. 

The key parameters from a CV measurement include the wave shape, the peak potential(s), pa and pc, and, more importantly, their dependence on the scan rate. For reversible and many quasi-reversible systems, the average of pa and equals or closely approximates EV2. Forjudging the reversibility of an electrode reduction like reaction (A.l) at 25°C, the useful criteria are ... 

The electrochemical oxidation of 4-dimethylaminoantipyrine (4-dimethyl-amino-2,3-dimethyl-l-phenyl-A3-pyrazolin-5-one) has been investigated in CH3CN-NaC104 at a glassy carbon electrode.421 The first step is a quasi-reversible electron transfer from the lone-pair electrons on the 4-dimethyl-amino nitrogen to form the radical-cation. The second-order disappearance of the radical-cation is presumably due to a disproportionation reaction. The oxidation at the potential of the plateau of the first wave gave the protonated 4-dimethylaminoantipyrine in 60% yield, but other products were not identified. 

In the absence of coupled homogeneous reactions, the current observed at an electrode is controlled by mass transport, electrode kinetics, or a mixture of the two. Control is wholly by mass transport at all points of a current—voltage curve for a reversible reaction and at the limiting current for quasi-reversible and irreversible reactions. 

Reversible, quasi-reversible and irreversible electrode processes have been studied at the RDE [266] as have coupled homogeneous reactions without [267] and with the effect of electrode kinetics [268], The theoretical results are very similar to those of a.c. polarography, being very phase-angle sensitive to coupled chemical reactions in the rotation speed range where convection can be neglected, the polarographic results may be directly applied [269]. 

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