Scan rate variation

Figure 3.13 Curve A Cyclic voltammogram for a Pt electrode in 0.5 M H2S04. Electrodes are 1.13cm2. scan rate 0.1 cycles per second. Curve B corresponding variation in the charge passed (in pC) vs. potential. Each point on the A and plots is the average of points obtained from four successive sweeps From Greef (1969),...

The same family of compounds shows another interesting feature, namely, the existence of borderline cases exhibiting an intermediate behavior between the concerted and stepwise mechanisms. More precisely, the width of the cyclic voltammetric peak and the variation of its location with scan rate change from a concerted to a stepwise behavior as the scan rate is raised (Fig. 4 and Scheme 6). 

Another striking example, recently discovered, is the reduction of iodoben-zene in DMF.61 The variation of the apparent transfer coefficient with the scan rate indicates that the mechanism passes from concerted to stepwise as the driving force increases (Fig. 5). As expected, the zone where the concerted mechanism prevails enlarges as one raises the temperature. In contrast, bromobenzene and 1-iodonaphthalene exhibit the characteristics of a stepwise mechanism over the whole range of scan rate. 

Fig. 5 Electrochemical reduction of aryl halides showing the variation of the apparent transfer coefficient with the scan rate. iodobenzene, O bromobenzene, V 1-iodonaphthalene, O 4-methyliodobenzene, at 298 K, iodobenzene at 329 K.

The variation in driving force that can be induced by a change in scan rate cannot be larger than a few hundred meV. The observation of the mechanism... 

Atienza et al. [657] reviewed the applications of flow injection analysis coupled to spectrophotometry in the analysis of seawater. The method is based on the differing reaction rates of the metal complexes with 1,2-diaminocycl-ohexane-N, N, N, A/Metra-acetate at 25 °C. A slight excess of EDTA is added to the sample solution, the pH is adjusted to ensure complete formation of the complexes, and a large excess of 0.3 mM to 6 mM-Pb2+ in 0.5 M sodium acetate is then added. The rate of appearance of the Pbn-EDTA complex is followed spectrophotometrically, 3 to 6 stopped-flow reactions being run in succession. Because each of the alkaline-earth-metal complexes reacts at a different rate, variations of the time-scan indicates which ions are present. 

In addition to possible variations between methods, there may also be variations in Tg within a method, depending on the measurement protocol employed. For example, the DCS Tg midpoint for a quench-cooled ( 100 K/min) maltose sample, heated at a scanning rate of lOK/min, was 43.1 0.21 °C, whereas for a maltose sample prepared using equal heating and cooling rates of lOK/min the Tg was 41.2 0.10°C (Schmidt and Lammert, 1996). For the same samples, DSC Tg Active temperatures were also calculated. Tg Active for the quench-cooled sample was 41.0 0.20 °C, whereas for the equal-rate sample, Tg Active was 38.6 0.06 °C. 

Figures 12a, 12b and 12c give on a logarithmic scale the variations of the peak current of the cyclic voltammograms obtained from Pt/polished A1203, Pt/etched Ni and Pt/unpolished A1203 electrodes, respectively, as a function of the scan rate. For the very flat Pt/polished A1203 electrode, the peak current in Figure 12a was linearly proportional to the scan rate with the slope...

The Faradaic and capacitive components of the current both increase with the scan rate. The latter increases faster (proportionally to v) than the former (proportionally to y/v), making the extraction of the Faradaic component from the total current less and less precise as the scan rate increases, particularly if the concentration of the molecules under investigation is small. The variations of the capacitive and Faradaic responses are illustrated in Figure 1.7 with typical values of the various parameters. The analysis above assumed implicitly that the double-layer capacitance is independent of the electrode potential. In fact, this is not strictly true. It may, however, be regarded as a good approximation in most cases, especially when care is taken to limit the overall potential variation to values on the order of half-a-volt.10 13... 

The free energy of activation or the forward rate constant may thus be obtained as a function of Ep for each scan rate. The nonlinear character of the rate law, if any, will then become apparent in the way in which AG p varies with the peak potential, which provides a point-by-point description of the activation-driving force relationship (one point per scan rate). The nonlinear character of the rate law will also transpire in the variation of ap, derived from ctp = 2A2 1ZT/F)(Ep/2 — Ep) with the scan rate. 

The Butler-Volmer rate law has been used to characterize the kinetics of a considerable number of electrode electron transfers in the framework of various electrochemical techniques. Three figures are usually reported the standard (formal) potential, the standard rate constant, and the transfer coefficient. As discussed earlier, neglecting the transfer coefficient variation with electrode potential at a given scan rate is not too serious a problem, provided that it is borne in mind that the value thus obtained might vary when going to a different scan rate in cyclic voltammetry or, more generally, when the time-window parameter of the method is varied. 

FIGURE 2.5. EC reaction scheme in cyclic voltammetry. Mixed kinetic control by an electron transfer obeying the Butler-Volmer law (with a = 0.5) and an irreversible follow-up reaction, a Variation of the peak potential with the scan rate, b Variation of the peak width with scan rate. Dots represent examples of experimental data points obtained over a six-order-of-magnitude variation of the scan rate. 

Once a DISP mechanism has been recognized, the procedures for determining the rate constant of the follow-up reaction and the standard potential of the A/B couple from peak current and/or peak potential measurements are along the same lines as the procedures described above for the ECE mechanism. A distinction between the ECE and DISP mechanisms cannot be made when the pure kinetic conditions are achieved since the peak height, peak width, and variations of the peak potential with the scan rate and rate constant are the same, and so is its independence vis-a-vis the concentration of substrate. The only difference is then the absolute location of the peak, which cannot be checked, however, unless the standard potential of the A/B couple and the follow-up rate constant are known a priori. 

The peak current is proportional to the substrate concentration and to the square root of the scan rate as for a simple diffusion-controlled wave. The proportionality coefficient is slightly larger, 0.527 instead of 0.446. Correspondingly, the wave is thinner, in the ratio 1.51/1.86. As with the EC mechanism, the peak potential is more sensitive to the follow-up reaction. It varies linearly with the logarithm of the scan rate, of the rate constant of the dimerization reaction, and of the substrate concentration. The rates of these variations are summarized in Table 2.1, where they can be compared to the values characterizing other mechanisms, hence serving as diagnostic... 

Equation (3.5) also shows that the activation free energy at the peak, AGj, is an increasing function of temperature, taking into account the explicit presence of T and also the variation of k, [equation (1.34)] and Dh. Thus, increasing scan rate and decreasing temperature favor the transition between concerted and stepwise mechanisms, and vice versa. 

FIGURE 5.25. Avidin-biotin construction of a monolayer glucose oxidase electrode with an attached ferrocenium cosubstrate and cyclic voltammetric response in a phosphate buffer (pH 8) at 25°C and a scan rate of 0.04 V/s. a attached ferrocene alone, h In the presence of 0.5 M glucose, c Variation of the inverse of the plateau current with the inverse of substrate concentration. Adapted from Figure 1 in reference 24, with permission from the American Chemical Society. 

There are two ways in which one can calculate the kinetic parameter k2. The first is based on the measurement of the variation of the forward peak Ep with the scan rate. As can be seen in Figure 17, the shift of the peak potential is particularly marked at low scan rates, whereas at high scan rates it tends to disappear. 

Figure 17 Variation of the forward peak potential with the scan rate for a dimerization reaction following an electron transfer... 

This mechanism has some analogy with the dimerization complication. The parameter which distinguishes them is the variation of the peak current with the scan rate. In fact, decreasing the scan rate will allow the chemical reaction to regenerate the initial species Ox, thus causing a significant increase in the forward peak current. 

These diagrams should be considered from a qualitative point of view. Furthermore, it is often not necessary to determine the trends of all the forward and reverse peaks, but only those that one judges to be the most significant. The scale of the potential scan rate in these plots is only illustrative and chosen to highlight the variations of the parameters that become evident on passing from slow to high scan rate. 

Figure 26 Diagnostic criteria showing the variation of the parameter ip v v 2 as a function of the scan rate. AE° = —180 mV n2/nt = 1.0...

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