Voltammogram shape

To check this behavior, in Fig. 5.5 are plotted the voltammograms corresponding to a planar electrode calculated from Eq. (5.50) (Fig. 5.5a), those calculated from Eq. (5.63) for different values of the electrode radius (Fig. 5.5b), and, finally, the current corresponding to a spherical electrode, calculated as the sum of these two contributions (Fig. 5.5c). Thus, the decrease of the electrode size leads to an increase of the dimensionless current of the spherical electrode and to a change of the voltammogram shape in the way indicated above. For small electrodes (see curves in Fig. 5.5c for a radius rs = 10 microns), the peak of the second scan has disappeared and that corresponding to the first scan is poorly defined. Therefore, in these conditions the determination of thermodynamic parameters of the experimental systems under study lies in the study of the half-wave potential of the voltammograms (see below). 

A dramatic effect of v on the voltammogram shape can be seen in Figure 15.8. 

Generally, the shape of background-corrected voltammograms varies with different chemical species. At the scan rates used in fast-scan cyclic voltanune-try, voltammogram shapes are kinetically controlled. As a result, most electroac-... 

The initial segregation of B component in the surface layer of an A,B-alloy only insubstantially influence the current along the whole length of the lA,r (t)-curve via the constant parameter O. The voltammogram shape is not changed but the maximum current is changed because O 1. 

The shape of a voltammogram is determined by several experimental factors, the most important of which are how the current is measured and whether convection is included as a means of mass transport. Despite an abundance of different voltam-metric techniques, several of which are discussed in this chapter, only three shapes are common for voltammograms (figure 11.33). 

The current during the stripping step is monitored as a function of potential, giving rise to peak-shaped voltammograms similar to that shown in Figure 11.37. The peak current is proportional to the analyte s concentration in the solution. 

C o(0, /)/CR(0, /) = 1/10,n = 1). The decrease in Co(0, t) is coupled with an increase in the diffusion layer thickness, which dominates the change in the slope after Co(0, /) approaches zero. The net result is a peak-shaped voltammogram. Such... 

The resulting voltammogram thus has a sigmoidal (wave) shape. If the stirring rate (U) is increased, the diffusion layer thickness becomes thinner, according to... 

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 63. Theoretical simulation of voltammograms obtained from -2500 to 300 mV, showing the effect of the temperature on the shape of the curve and the position of the maximum. (Reprinted from T. F. Otero, H.-J. Grande, and J. Rodriguez, J. Phys. Chem. 101, 8525, 1997, Figs. 3-11, 13. Copyright 1997. Reproduced with permission from the American Chemical Society.)...

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.

The shape of the hydrogenase catalytic voltammograms shown in Fig. 17.14 also changes as the temperamre is raised. At 10 °C, the current tends towards a plateau at high overpotential as catalysis becomes limited by the inherent turnover frequency of the enzyme, but at higher temperamres, the current continues to increase linearly with electrochemical driving force. This has been attributed to a range of different... 

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 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]. 

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