Cyclic voltammograms shape

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). 

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. 

Figure 16.10 Photographs of nitrobenzene droplets. Vtias was fixed at 0.35 V and Eoffset was varied (a-d). The line in the photograph represents the position of the wetting boundary estimated from the shape of the droplets. Note that the current peak for the Fc /Fc reaction was observed at about —0.5 V in the cyclic voltammogram.

Another case of interest is the transition between no catalysis and the pure kinetic conditions leading to plateau-shaped responses. In the kinetic zone diagram of Figure 2.17, it corresponds to the extreme right-hand side of the diagram, where the cyclic voltammogram passes from the Nernstian reversible wave of the cosubstrate to the plateau-shaped wave, under conditions where the consumption of the substrate is negligible. The peak... 

In order to look at the multiple shapes that the cyclic voltammograms can assume as a function of the nature of the different electrode processes, let us begin by examining the case of a reversible reduction process, not complicated by homogeneous reactions ... 

Cyclic voltammetry at spherical electrodes. As discussed in Chapter 1, Section 4.2.3, diffusion laws at a spherical electrode must take into account the curvature r0 of the electrode. The mathematical treatment of diffusion at a spherical electrode becomes somewhat more complicated6 with respect to the preceding one for planar diffusion and we will not dwell on it. On the basis of what we will see in Chapter 11, Section 2, it is important to consider that, under radial diffusion, the cyclic voltammogram loses its peak-shaped profile to assume a sigmoidal profile, see Figure 6. 

It is conceivable that the presence of such complications must affect the shape of the cyclic voltammograms, and hence perturb to some extent the diagnostic criteria for the above-mentioned fundamental electron transfer processes. As these reactions proceed at their own rates, cyclic voltammetry will be able to detect them only if their rates fall within the time scale of the voltammetric technique (which ranges from a few tens of seconds to a few milliseconds). 

Therefore, given that a multi-electron process can be described as a series of one-electron transfers, more or less separated from each other, the shape of the cyclic voltammogram depends on the following factors 14... 

The cyclic voltammogram of PtdlO) in 0.5 M sulfuric add is shown in Fig. 2-16. Hs drogen adsorption-desorption current consisted of a lax e peak at 150 mV and a shoulder at 200 mV. The oxidation begins at 800 mV. Unlike PtClll), the shape of the voltammogram in the hydrogen region did not change much after the reconstruction of the surface by a sweep to an anodic potential of 1550 mV. 

The cyclic voltammograms for Pt(llO) and Pt(lOO) in 0.5 M perchloric acid are shown in Fig. 2-26 and Fig. 2—27 respectively. The shapes of the voltammograms for hydrogen adsorption-desorption were significantly different from those in sulfuric add. Although these anion... 

Experimental and simulated cyclic voltammograms for a solution that was 5 [iM in TMAFc and 0.5 mM in supporting electrolyte (sodium nitrate) are shown in Fig. 7 [25], The experimental data were obtained at a lONEE. In agreement with the above discussion, the experimental voltammograms are peak shaped, and peak current increases with the square root... 

Figure 6.13 shows a voltammogram for a simple solution-phase couple such a plot is known as a cyclic voltammogram (CV). The adjective cyclic arises from the closed loop drawn within the plot. The shape of the CV shown in Figure 6.13 is typical for a couple that is wholly reversible in the thermodynamic sense other simple diagnostic tests for electro-reversibility are listed in Table 6.3. 

In the case of an irreversible charge-transfer process the rate of electron transfer is insufficient to maintain the charge-transfer process at equilibrium. The shape of the cyclic voltammogram is modified and peak positions shift as a function of scan rate (unlike the reversible case). A more detailed discussion can be found elsewhere.93... 

Reduction of the solution temperature allows transition from steady-state to peak-shaped response simply by way of the marked diminution of D at low temperatures. Figure 16.5 shows slow-scan cyclic voltammograms obtained at two microdisk electrodes as a function of solution temperature. Between -120 and -140°C there is a particularly clear transition for the 25-pm-diameter electrode as the diffusion-layer thickness becomes less than the disk radius. Also illustrated here is the immense decrease in the limiting currents that is seen over this range of temperatures due to the 100-fold decrease in D. 

The most popular electroanalytical technique used at solid electrodes is Cyclic Voltammetry (CV). In this technique, the applied potential is linearly cycled between two potentials, one below the standard potential of the species of interest and one above it (Fig. 7.12). In one half of the cycle the oxidized form of the species is reduced in the other half, it is reoxidized to its original form. The resulting current-voltage relationship (cyclic voltammogram) has a characteristic shape that depends on the kinetics of the electrochemical process, on the coupled chemical reactions, and on diffusion. The one shown in Fig. 7.12 corresponds to the reversible reduction of a soluble redox couple taking place at an electrode modified with a thick porous layer (Hurrell and Abruna, 1988). The peak current ip is directly proportional to the concentration of the electroactive species C (mM), to the volume V (pL) of the accumulation layer, and to the sweep rate v (mVs 1). 

The constant /3 contains a partitioning coefficient of the analyte between the solution and the modifying layer, as well as the constants related to the bulk electrolysis in a small volume (i.e., thin) cell (Bard and Faulkner, 2001). If the electroactive species are confined to the electrode, if the couple is perfectly reversible, and if the extraction is fast on the time scale of the experiment, the peaks in the cyclic voltammogram occur at the same potential and the areas (charge) below the cathodic and anodic branches are equal, as is the case in Fig. 7.12. Obviously, any deviations from these conditions are reflected in the shape of the CV curve. Nevertheless, even then the relationship between the peak current iv and the bulk concentration of the electroactive species can be reproducible. In the determination of Fe2+ using the above procedure, the linear calibration between 5 x 10 8 and 5 x 10-6 M concentration has been obtained. 

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