Quasireversible systems

When the heterogeneous electron transfer (ET) between the electrode and the molecule in solution is slow, dramatic changes may be exhibited in the CV diagnostic criteria. Modest decreases in kf and kb (a quasireversible system) cause a modest increase in AEp, the change of which with v may be used to calculate ks, the standard heterogeneous ET rate (ks = kf = kb at E = E° ). As the ET rates become smaller, the waves are more likely to reflect the influence of the transfer coefficient, a, on the wave shape. The forward and reverse branches are shaped as mirror images only if a = 0.5. If a < 0.5, the cathodic branch is broader the converse is true if a > 0.5 (Fig. 23.7). 

Example Determination of ks from AEp Measurements The ks value of a quasireversible system is conveniently determined by monitoring the peak separation of the CV wave as a function of sweep rate, using the results of calculations by Nicholson [12] that relate AEp to the dimensionless parameter vj/, through Equation 23.12 ... 

In Fig. 4.18, the influence of the kinetic parameters (k°, a) on the ADDPV curves is modeled at a spherical microelectrode l /Dr /r, = 0.2). In general terms, the peak currents decrease and the crossing and peak potentials shift toward more negative values as the electrode processes are more sluggish (see Fig. 4.18a). For quasireversible systems (k° 10-2 — 10 4 cm s ). the peak currents are very sensitive to the value of the heterogeneous rate constant (k°) whereas the variation of the crossing potential is less apparent. On the other hand, for totally irreversible... 

Summarize the different features of cyclic voltammetric response for reversible and quasireversible systems. 

A quasireversible system is characterised by the Butler-Volmer equation, here in dimensionless form,... 

As mentioned, the procedure has the advantage that the time variable T is part of the solution expression, so that if solutions at only a few time values, or even just one such T, are sought, the method might be competitive with the more usual time-marching schemes. Also, although the above description has been simplified by leaving out the boundary condition vector in (9.104), its addition still leaves the method intact. As shown in the second paper [332], LSV simulations and quasireversible systems can be handled. For some reason, however, the method has not seen any use in electrochemistry since these two seminal papers. 

The -> polarization curves for irreversible and quasireversible systems are shown in Figure (a). The respective -> Tafel plots are presented in Figure (b). Tafel plots can be constructed only for electrochemically irreversible systems, and kinetic parameters can be determined only when irreversible kinetics prevails. A switching from reversible to irreversible behavior and vice versa may occur. It depends on the relative values of ks and the -> mass transport coefficient, km. If km ks irreversible behavior can be observed. An illustration of the reversibility-irreversibility problem can be found in the entry -> reversibility. 

Optically transparent electrode — (OTE), the electrode that is transparent to UV-visible light. Such an electrode is very useful to couple electrochemical and spectroscopic characterization of systems (- spectroelectro-chemistry). Usually the electrodes feature thin films of metals (Au, Pt) or semiconductors (In203, SnCb) deposited on transparent substrate (glass, quartz, plastic). Alternatively, they are in a form of fine wire mesh minigrids. OTE are usually used to obtain dependencies of spectra (or absorbance at given wavelengths) on applied potentials. When the -> diffusion layer is limited to a thin layer (i.e., by placing another, properly spaced, transparent substrate parallel to the OTE), bulk electrolysis can be completed in a few seconds and, for -> reversible or - quasireversible systems, equilibrium is reached for the whole solution with the electrode potential. Such OTEs are called optically transparent thin-layer electrodes or OTTLE s. 

Because a reversible system will show cot 4> = 1-0 at all a.c. frequencies, increases of cot 4> above unity can be used to measure the degree of quasireversibility of the couple, i.e., its kj value. The in-phase and out-of-phase peak heights are measured at a series of different a.c. frequencies and cot (f> vs. a> is plotted. For a quasireversible system, this plot should be linear with an intercept at 1.00. If the a value is 0.5, the slope of the plot will have the value ... 

Cyclic-voltammetry measurements of quasireversible systems yield more easily to interpretation. Both the cathodic and anodic peak potentials shift as a function of scan rate, resulting in an increasing AE as v increases. This dependence of AEp on electron-transfer rate is used to measure the k value of the system, but AE also increases monotonically with v from the effects of uncompensated resistance, and the two effects are difficult to separate. The absence of appreciable resistance effects must be insured when making these measurements. Many reported rate constants are erroneous because of improper attention to this problem ... 

If the former mechanism were correct (low k ), E would be given by Ep, + Ep /2. A similar procedure would give an incorrect number for the latter mechanism. Therefore, a redox mechanism must be understood if meaningful E values are to be obtained. In the above case in which a followup reaction (to produce Z) occurs, this could be diagnosed by bulk coulometric reduction of the molecule, followed by voltammetric measurements on the reduced solution. Then only the oxidation wave for Z would be observed in the electrolyzed solution. Another method of distinguishing these two mechanisms is from the scan-rate dependence of the AE value, which must follow that of a quasireversible system if Eq. (d) describes the mechanism. 

Exactly as in the reversible case, the plateau of an irreversible or quasireversible wave is controlled entirely by diffusion and can be used to determine any variable that contributes to /(j- The most important applications involve the evaluation of C, but it is sometimes useful to determine n. A, D, or tq from i. Section 5.4.4(a), which covers these ideas, is wholly applicable to irreversible and quasireversible systems. 

Equation 5.5.11 for early transients in a quasireversible system having only species O present in the bulk. 

Figure 6.7.3 Experimental cyclic voltammogram and convolution of (a) 1.84 mM p-nitrotoluene in acetonitrile containing 0.2 M TEAP at HMDE, v = 50 V/s. [Reprinted with permission from P. E. Whitson, H. W. Vanden Bom, and D. H. Evans, Anal. Chem., 45, 1298 (1973). Copyright 1975, American Chemical Society.] (b) 0.5 mM fert-nitrobutane in DMF containing 0.1 M TBAI, v = 17.9 V/s. E1/2 determined for quasireversible system from E1/2 =...

The previous two sections have dealt generally with ac voltammetry as recorded by the application of successive steps and with a renewal of the diffusion layer between each step. The DME permits the most straightforward application of that technique, but other electrodes can be used if there is a means for stirring the solution between steps so that the diffusion layer is renewed. On the other hand, this requirement for periodic renewal is inconvenient when one wishes to use stationary electrodes, such as metal or carbon disks, or a hanging mercury drop. Then one prefers to apply as a ramp and to renew the diffusion layer only between scans. In this section, we will examine the expected ac voltammograms for reversible and quasireversible systems when is imposed as a linear sweep and we will compare them with the results obtained above for effectively constant... 

Using a computer, carry out simulations of cyclic voltammetry for a quasireversible system. Let = 50 and Dm = 0.45, Take a = 0.5 and let the diffusion coefficients of the oxidized and reduced forms be equal. Cast your dimensionless intrinsic rate parameter in terms of the function ij/ defined in (6.5.5), and carry out calculations for ip = 20, I, and 0.1. Compare the peak splittings in your simulated voltammograms with the values in Table 6.5.2. 

Blitz D (1987) Investigation of the relative merit of some n-point current approximations in digital simulations. Application to an improved algorithm for quasireversible systems. Anal Chim Acta 193 277-285... 

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