Peak current ratios

FIGURE 2.4. EC reaction scheme in cyclic voltammetry. Derivation of the rate constant from the anodic-to-cathodic peak current ratio in zone KO. In this example the scan is reversed 200 mV (at 25° C) after the peak. 

FIGURE 2.13. Radical-radical electrodimerization (Scheme 2.7). a Variations of the peak potential with the kinetic parameter, aj. h Procedure for determining the dimerization rate constant from the anodic-to-cathodic peak current ratio. 

Irreversible follow-up reactions (most simple case EC mechanism) decrease the concentration of the primary redox product. This is again diagnosed in CV (Figure 9) and also in chronocoulome-try. Timescale variation in CV allows to modulate the importance of the C-step at fast v the chemical reaction will have no influence on the curves, while at slower v all product has reacted and the reverse peak disappears. A governing factor is k/a (k = rate constant of C-step, a = nFv/RT). Thus, for a qualitative interpretation, the peak current ratio in CV is evaluated as a function of V (and E ) in order to calculate k [49]. Also, p and ip depend on k/a [28]. 

The voltammetric features of a reversible reaction are mainly controlled by the thickness parameter A = The dimensionless net peak current depends sigmoidally on log(A), within the interval —0.2 < log(A) <0.1 the dimensionless net peak current increases linearly with A. For log(A )< —0.5 the diSusion exhibits no effect to the response, and the behavior of the system is similar to the surface electrode reaction (Sect. 2.5.1), whereas for log(A) > 0.2, the thickness of the layer is larger than the diffusion layer and the reaction occurs under semi-infinite diffusion conditions. In Fig. 2.93 is shown the typical voltammetric response of a reversible reaction in a film having a thickness parameter A = 0.632, which corresponds to L = 2 pm, / = 100 Hz, and Z) = 1 x 10 cm s . Both the forward and backward components of the response are bell-shaped curves. On the contrary, for a reversible reaction imder semi-infinite diffusion condition, the current components have the common non-zero hmiting current (see Figs. 2.1 and 2.5). Furthermore, the peak potentials as well as the absolute values of peak currents of both the forward and backward components are virtually identical. The relationship between the real net peak current and the frequency depends on the thickness of the film. For Z, > 10 pm and D= x 10 cm s tlie real net peak current depends linearly on the square-root of the frequency, over the frequency interval from 10 to 1000 Hz, whereas for L <2 pm the dependence deviates from linearity. The peak current ratio of the forward and backward components is sensitive to the frequency. For instance, it varies from 1.19 to 1.45 over the frequency interval 10 < //Hz < 1000, which is valid for Z < 10 pm and Z) = 1 x 10 cm s It is important to emphasize that the frequency has no influence upon the peak potential of all components of the response and their values are virtually identical with the formal potential of the redox system. 

Similar to the surface electrode processes (Chap. 2.5.1) the peak current ratio of the split peaks ( fp,c/ lp,a) is a function of the electron transfer coefficient o. Note that the anodic and the cathodic peak is located at the more negative and more positive potentials, respectively. This type of dependence is given in Fig. 2.98. Over the interval 0.3 < < 0.7 the dependence vs. is hnear, associated with the... 

Table 3.2 Peak current ratios for commercial iron oxide (FeiO-, Aldrich) and earth pigments from Kremer. From square-wave voltammograms of sample-modified PlGEs immersed into 0.10 M HCl. Potential step increment 4 mV square wave amplitude 25 mV frequency 5 Hz. Adapted from ref. [139]...

The peak potertial on the reverse scan of a CV depends upon the switching potential, Ex, which results in some variation of the peak potential separation AEp. Some values are tabulated in Table 2. These, along with the peak current ratio, (/p)r/(/p)f, where the subscripts refer to the reverse (r) and forward (f) scans, provide additional criteria for the reversible charge transfer. 

Cyclic voltammetry peak currents and peak current ratios for reversible one-electron transfer as a function of E a... 

The precision problems in measuring CV peak current ratios is effectively eliminated by redefining the ratio so that the current, after subtracting /c, is measured from the same base line for the reverse scan as for the forward [27], The problem is also eliminated using derivative techniques [49, 50], Precision during the measurement of LSV and CV electrode potentials will be discussed in some detail with practical examples in the following sections. 

In practice, the values of v necessary to hold Rx or Rj at a constant value, most commonly equal to 0.500, are determined and defined as vc, i.e. f o.s when the peak current ratio is held constant at 0.500. Under these conditions, z can conveniently be determined by the logarithmic relationship... 

As mentioned above, the characteristic feature of processes in this kinetic region is that the peak current ratio — z°x/Zped varies from about unity to zero. Thus, a procedure for studying the kinetics would be to record values of —/°x//ped at different sweep rates and compare these with a working curve for the proposed mechanism in a way analogous to that discussed for DPSCA above. However, a problem with this approach is the difficulty of defining a baseline for the reverse sweep (see below) and, for that reason, CV suffers from some limitations when used in quantitative work. This has led to the development of derivative cyclic voltammetry (DCV) [37]. 

The ratio of the peak current for the cathodic process relative to the peak current for the anodic process is equal to unity (ip>(/ p,a = 1) for a reversible electrode process. For measurement of the peak current for the anodic process, the extrapolated baseline going from the foot of the cathodic wave to the extension of this cathodic current beyond the peak must be used as a reference, as illustrated by Figure 3.9. Another approach to measuring peak-current ratios is illustrated by Figure 3.10. 

The variation of the cathodic peak potential with the scan rate (0.3-0.4 mV precision on each determination, 1 mV reproducibility over the whole set of experiments) allows the determination of the rate constant with a relative error of 3-11%. The results are consistent with those derived from anodic-to-cathodic peak current ratios. Simulation of the whole voltammogram confirms the absence of significant systematic errors that could arise from the assumptions underlying the analysis of kinetic data. Activation parameters derived from weighted regression Arrhenius plots of the data points taken at 5 or 6 tern-... 

Fig. 5 Influence of incubation time on average SWV peak current ratios for (PDDA/ds-DNA)2 films in 20 pM Co(bpy)3 + at pH 5.5 after incubations with styrene oxide, toluene, or pure buffer. /p,final corresponds to the peak current after each incubation /p.initial corresponds to peak current before incubation. (From Ref. [46] with permission. Copyright 2002 Wiley-VCH.) (View this art in color at www.dekker.com.)...

The peak current ratio —ip /ip is unity and independent of v. For a simple electron transfer process, measurements of the peak current ratio serve to control the assumption that B is indeed stable in the solution on the time scale of the experiment. 

As mentioned earlier, the characteristic features of processes in this category are that Ep is close to that for the no-reaction case, Eq.(l), and that the peak current ratio —ip /ip varies from approximately unity to zero. The observation of oxidation current for B during the backward sweep shows that the material conversion is low. By comparison of the voltammograms for the eC and the eCen mechanisms in Fig. 8, it is seen that the second electron transfer reaction in the eCeh mechanism gives rise to only little additional current, illustrating that only a small fraction of B has been converted to C. 

Figure 14.3.12 Peak current ratio v.y. scan rate for cyclic voltammetry when the reactant (A) or the product (B) is weakly adsorbed. Curve A Fi = Fq,s, PqCq = 1. Curve R F[ = Fr, PrCq = 1. Reversal potential = Ey2 (ISO/n) mV. [Reprinted with permission from R. H. Wopschall and I. Shain, Anal. Chem., 39, 1514 (1967). Copyright 1967, American Chemical Society.]...

This equation is often used to determine the formal potential of a given redox system with the help of cyclic voltammetry. However, the assumption that mid-peak potential is equal to formal potential holds only for a reversible electrode reaction. The diagnostic criteria and characteristics of cyclic voltammetric responses for solution systems undergoing reversible, quasi-reversible, or irreversible heterogeneous electron-transfer process are discussed, for example in Ref [9c]. An electro-chemically reversible process implies that the anodic to cathodic peak current ratio, lpa/- pc equal to 1 and fipc — pa is 2.218RT/nF, which at 298 K is equal to 57/n mV and is independent of the scan rate. For a diffusion-controlled reduction process, Ip should be proportional to the square root of the scan rate v, according to the Randles-Sevcik equation [10] ... 

Values for d and D are chosen according to those in reality. As layer thickness decreases [Table 6.1 (ar-e)], the peak current ratio Hip tends toward 1.00. As the number of points increases [Table 6.1(f)], the Hip changes only a little. If hll rather than h is used for the first distance element, it does not make any difference, as seen inTable6.1(g, h). 

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