Control voltammograms

Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

For quasi-reversible systems (with 10 1 > k" > 10 5 cm s1) the current is controlled by both the charge transfer and mass transport. The shape of the cyclic voltammogram is a function of k°/ JnaD (where a = nFv/RT). As k"/s/naD increases, the process approaches the reversible case. For small values of k°/+JnaD (i.e., at very fast i>) the system exhibits an irreversible behavior. Overall, the voltaimnograms of a quasi-reversible system are more drawn-out and exhibit a larger separation in peak potentials compared to those of a reversible system (Figure 2-5, curve B). 

Figure 4. Log intensity vs. potential plots (Tafel plots) obtained from the voltammograms of a platinum electrode submitted to a 2 mV s l potential sweep polarized in a 0.1 M LiC104 acetonitrile solution having different thiophene concentrations. (Reprinted from T. F. Otero and J. Rodriguez, Parallel kinetic studies of the electrogeneration of conducting polymers mixed materials, composition, and kinetic control. Electrochim, Acta 39, 245, 1994, Figs. 2, 7. Copyright 1997. Reprinted with permission from Elsevier Science.)...

Equations (57) and (58) describe the electrochemical oxidation of conducting polymers during the anodic potential sweep voltammograms (/f vs. q) or coulovoltagrams (Qr vs. tj) under conformational relaxation control of the polymeric entanglement initiated by nucleation in the reduced film. They include electrochemical variables and structural and geometric magnitudes related to the polymer. 

Thus, at constant temperature and at a constant sweep rate, the influence of the cathodic overpotential (tjc) on the peak overpotential (t]p) of the voltammogram obtained under conformational relaxation control of the polymeric structure is described by... 

So a linear dependence between the potential of the voltammetric peak and the increasing cathodic initial potential for the voltammograms (Fig. 57) points to an oxidation process occurring under conformational relaxation control of the electrode structure. 

If the film is nonconductive, the ion must diffuse to the electrode surface before it can be oxidized or reduced, or electrons must diffuse (hop) through the film by self-exchange, as in regular ionomer-modified electrodes.9 Cyclic voltammograms have the characteristic shape for diffusion control, and peak currents are proportional to the square root of the scan speed, as seen for species in solution. This is illustrated in Fig. 21 (A) for [Fe(CN)6]3 /4 in polypyrrole with a pyridinium substituent at the 1-position.243 This N-substituted polypyrrole does not become conductive until potentials significantly above the formal potential of the [Fe(CN)6]3"/4 couple. In contrast, a similar polymer with a pyridinium substituent at the 3-position is conductive at this potential. The polymer can therefore mediate electron transport to and from the immobilized ions, and their voltammetry becomes characteristic of thin-layer electrochemistry [Fig. 21(B)], with sharp symmetrical peaks that increase linearly with increasing scan speed. 

The cyclic voltammograms of ferrlcyanlde (1.0 mM In 1.0 M KCl) In Fig. 2 are Illustrative of the results obtained for scan rates below 100 mV/s. The peak separation is 60 mV and the peak potentials are Independent of scan rate. A plot of peak current versus the square-root of the scan rate yields a straight line with a slope consistent with a seml-lnflnlte linear diffusion controlled electrode reaction. The heterogeneous rate constant for the reduction of ferrlcyanlde was calculated from CV data (scan rate of 20 Vs using the method described by Nicholson (19) with the following parameter values D 7.63 X 10 cm s , D, = 6.32 X 10 cm s, a 0.5, and n =1. The rate constants were found to be... 

Before the measurement of HOR activity, a pretreatment of the alloy electrode was carried out by potential sweeps (10 V s ) of 10 cycles between 0.05 and 1.20 V in N2-purged 0.1 M HCIO4. The cyclic voltammograms (CVs) at all the alloys resembled that of pure Pt. As described below, these alloy electrodes were electrochemically stabilized by the pretreatment. Hydrodynamic voltammograms for the HOR were then recorded in the potential range from 0 to 0.20 V with a sweep rate of 10 mV s in 0.1 M HCIO4 saturated with pure H2 or 100 ppm CO/H2 at room temperature. The kinetically controlled current 4 for the HOR at 0.02 V was determined from Levich-Koutecky plots [Bard and Faulkner, 1994]. 

FIG. 23 Cyclic voltammograms for ET between 0.2 mM TOAAuCfi and 0.1 mM K4Fe(CN)g at the water-DCE interface at 0.05 V (a). The control experiments in the absence of the aqueous couple (b) and the metal complex (c) are also displayed. (From Ref. 89. Reproduced by permission of The Royal Society of Chemistry.)... 

The shape of steady-state voltammograms depends strongly on the geometry of the microhole [13,14], Wilke and Zerihun presented a model to describe diffusion-controlled IT through a microhole [15], In that model, a cylindrical microhole is assumed to be filled with the organic phase, so that a planar liquid-liquid interface is located at the aqueous phase side of the membrane. Assuming that the diffusion is linear inside the cylindrical pore and spherical outside [Fig. 2(a)], the expression for the steady-state IT voltammo-gram is... 

The mathematical formulations of the diffusion problems for a micropippette and metal microdisk electrodes are quite similar when the CT process is governed by essentially spherical diffusion in the outer solution. The voltammograms in this case follow the well-known equation of the reversible steady-state wave [Eq. (2)]. However, the peakshaped, non-steady-state voltammograms are obtained when the overall CT rate is controlled by linear diffusion inside the pipette (Fig. 4) [3]. 

The facilitated ion transfers of some alkaline earth metals have been also studied in the DCE systems by the cyclic voltammetry. These systems perhaps have not been studied by any solvent extraction methods yet. Typical voltammograms in the N15C5 diffusion-control systems are shown in Fig. 6. The aqueous supporting electrolyte was MgCl2 instead of MgS04 in these measurements because BaS04 precipitated. 

This equation describes the cathodic current-potential curve (polarization curve or voltammogram) at steady state when the rate of the process is simultaneously controlled by the rate of the transport and of the electrode reaction. This equation leads to the following conclusions ... 

Melendres et ai (1991) reported the in-situ study of the electrode/oxide and oxide/electrolyte interfaces for a copper electrode in pH 8.4 borate buffer under potential control. The grazing-angle incidence arrangement employed by the authors is shown in Figure 2.81(a) and a cyclic voltammogram of the Cu electrode in the buffer is shown in Figure 2.81(b). 

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