Voltammetric response

The cyclic voltammogram is characterized by several important parameters. Four of these observables, the two peak currents and two peak potentials, provide the basis for the diagnostics developed by Nicholson and Shain (1) for analyzing the cyclic voltammetric response. 

Explain clearly why and how a change of the scan rate affects the shape of the cyclic voltammetric response of an ultramicroelectrode. 

Reversing the previous reasoning, the presence of a conformational relaxation control in voltammetric responses can be detected in a single... 

This reaction has been associated with anomalous voltammetric responses during ET reactions in the presence of aqueous redox couples [71,84]. However, as indicated in Fig. 3, the redox potential of TPB is considerably more positive than Fc in DCE, therefore the reaction in Eq. (20) must involve a complex interfacial catalytic mechanism to indeed take place. On the other hand. Ding et al. have studied the oxidation of 1,1-dimethylferrocene (DMFc) and the reduction of TCNQ by Fe(CN)g at the water-... 

No steady-state theory for kinetically controlled heterogeneous IT has been developed for micropipettes. However, for a thin-wall pipette (e.g., RG < 2) the micro-ITIES is essentially uniformly accessible. When CT occurs via a one-step first-order heterogeneous reaction governed by Butler-Volmer equation, the steady-state voltammetric response can be calculated as [8a]... 

Figure 5. Cyclic voltammetric response of Ferrocene - (A) in CH2CI2, (B) with added CN-[P], (C) after addition of Cr(CN-[P])6.

In neither case - Cr(CN-[P])g or Ni(CN-[P])4 - was a cyclic voltammetric response observed directly for the metal center at a Pt electrode, for either solution phase or surface-confined materials. The solution phase behavior in this respect is very similar to the situation encountered with many biological macromolecules (23). 

Bradley et al.109 have combined a p-Si photocathode and homogeneous catalysts (tetraazamacrocyclic metal complexes, which had been shown to be effective catalysts for C02 reduction at an Hg electrode110) to reduce the applied cathode potential. The catalysts showed111 reversible cyclic voltammetric responses in acetonitrile at illuminated p-Si electrodes at potentials significantly more positive (ca. 0.4 V) than those required at a Pt electrode, where the p-Si used had surface states in high density and Fermi level pinning112 occurred. Electrolysis of a C02-saturated solution (acetonitrile-H20-LiC104 1 1 0.1 M) in the presence of 180 mM... 

If the electrochemical kinetics of the process are facile then the overall process will be dominated entirely by mass transport. Kinetic parameters such as the exchange current cannot, therefore, be obtained from such a system by analysis of the cyclic voltammetric response. Systems which satisfy this condition are normally referred to as reversible . This is slightly unfortunate... 

Type II (see Figure 3.89(b)) yielded extremely poor voltammetric responses k° 0.1 x 10 3cms i) with the activity quickly declining to zero. 

Figure 6.7 illustrates the voltammetric response of the third-generation SOD-based 02 biosensors with Cu, Zn-SOD confined onto cystein-modified Au electrode as an example. The presence of 02" in solution essentially increases both the cathodic and anodic peak currents of the SOD compared with its absence [150], Such a redox response was not observed at the bare Au or cysteine-modified Au electrodes in the presence of 02". The observed increase in the anodic and cathodic current response of the Cu, Zn-SOD/cysteine-modified Au electrode in the presence of 02 can be considered to result from the oxidation and reduction of 02, respectively, which are effectively mediated by the SOD confined on the electrode as shown in Scheme 3. Such a bi-directional electromediation (electrocatalysis) by the SOD/cysteine-modified Au electrode is essentially based on the inherent specificity of SOD for the dismutation of 02", i.e. SOD catalyzes both the reduction of 02 to H202 and the oxidation to 02 via a redox cycle of its Cu (II/I) complex moiety as well as the direct electron transfer of SOD realized at the cysteine-modified Au electrode. Thus, this coupling between the electrode and enzyme reactions of SOD could facilitate the development of the third-generation biosensor for 02". ...

The cyclic voltammetric responses depend on the manner in which the rate constants are related to the electrode potential. We start with cases in which the Butler-Volmer law applies ... 

As the kinetic parameter Ahset decreases, either because the standard rate constant decreases or because the scan rate is increased, the cyclic voltammetric response passes rapidly from the symmetrical reversible Nernstian pattern described in Section 1.2.1 to an asymmetrical irreversible curve, while the cathodic peak shifts in the cathodic direction and the anodic peak shifts in the anodic direction. 

We examine next the cyclic voltammetric responses expected with nonlinear activation-driving force laws, such as the quasi-quadratic law deriving from the MHL model, and address the following issues (1) under which conditions linearization can lead to an acceptable approximation, and (2) how the cyclic voltammograms can be analyzed so as to derive the activation-driving force law and to evidence its nonlinear character, with no a priori assumptions about the form of the law. 

FIGURE 1.18. Deriving the rate law of an electron transfer involving immobilized reactants from the cyclic voltammetric responses, a Voltammograms recorded at 1 ( ), 10 (A), 100 (O), 1000 (v), 10,000 (O) V/s. b Derivation of the surface concentrations from the current responses, c Potential-dependent rate constant from the combination of a and b. MHL kinetics with /., = 0.85 eV. Adapted from Figure 4 in reference 43, with permission from the American Chemical Society. 

The normalized current-potential curves are thus a function of the two parameters A and oc. An example corresponding to a = 0.5 is shown in Figure 1.19. Decreasing the parameter A as a result of a decrease in the rate constant and/or an increase in scan rate triggers a shift of the cathodic potential toward negative values and of the anodic potential in the reverse direction, thus increasing the irreversibility of the cyclic voltammetric response. When complete irreversibility is reached (i.e., when there is no anodic current underneath the cathodic current, and vice versa), a limiting situation is reached, characterized by... 

Before depicting these examples, we examine two questions. One deals with the cyclic voltammetric responses of systems reversibly exchanging two electrons with the electrode as a function of the standard potential separation, having in mind the use of these signals to determine the difference between the two standard potentials. The other concerns the response of a molecule containing two or more identical and independent reducible or oxidizable groups. 

The EC mechanism (Scheme 2.1) associates an electrode electron transfer with a first-order (or pseudo-first-order) follow-up homogeneous reaction. It is one of the simplest reaction schemes where a heterogeneous electron transfer is coupled with a reaction that takes place in the adjacent solution. This is the reason that it is worth discussing in some detail as a prelude to more complicated mechanisms involving more steps and/or reactions with higher reaction orders. As before, the cyclic voltammetric response to this reaction scheme will be taken as an example of the way it can be characterized qualitatively and quantitatively. 

FIGURE 2.1. EC reaction scheme in cyclic voltammetry. Kinetic zone diagram showing the competition between diffusion and follow-up reaction as a function of the equilibrium constant, K, and the dimensionless kinetic parameter, X. The boundaries between the zones are based on an uncertainty of 3 mV at 25°C on the peak potential. The dimensionless equations of the cyclic voltammetric responses in each zone are given in Table 6.4. 

A reaction scheme frequently encountered in practice, the so-called square scheme mechanism, consists of the association of two EC reaction schemes as shown in Scheme 2.3 (which may as well be viewed as an association of two CE mechanisms). In the general case, the cyclic voltammetric response may be analyzed by adaptation and combination of the treatments given in Sections 2.2.1 and 2.2.2. A case of practical interest is when the follow-up reactions are fast and largely downhill. A and D are then stable reactants, whereas B and C are unstable intermediates. When the starting reactant is A (reduction process), the reaction follows the A-B-D pathway. The reoxidation preferred pathway is D-C-A. It is not the reverse of the forward... 

The simplest electrodimerization mechanism occurs when the species formed as the result of a first electron transfer reaction reacts with itself to form a dimer (Scheme 2.7). This mechanism is usually termed radical-radical dimerization (RRD) because the most extensive studies where it occurs have dealt with the dimerization of anion and cation radicals formed upon a first electron transfer step as opposed to the case of radical-substrate dimerizations, which will be discussed subsequently. It is a bimolecular version of the EC mechanism. The bimolecular character of the follow-up reaction leads to nonlinear algebra and thus complicates slightly the analysis and numerical computation of the system. The main features of the cyclic voltammetric responses remain qualitatively similar, however. Unlike the EC case, however, the dimensionless parameter,... 

TABLE 2.1. Characteristics of the Irreversible Cyclic Voltammetric Responses (Pure Kinetic Conditions) for the Main Mechanisms That Involve the Coupling of a Fast Electron Transfer and a Homogeneous Rate-Determining Follow-up Reaction... 

FIGURE 2.16. Homogeneous catalysis electrochemical reactions. Reaction scheme and typical cyclic voltammetric responses. The reversible wave pertains to the mediator alone. The dotted curve is the response of the substrate alone. The third voltammogram corresponds to the mediator after addition of the substrate. 

A completely opposite situation is reached when Xe is large, but the excess factor is small, so that the substrate is consumed to a large extent. Its concentration at the electrode surface is then much smaller that in the bulk, implying that diffusion of the substrate toward the electrode surface may become the slow step of the catalytic process. Under these conditions (left-hand part of the zone diagram in Figure 2.17), the cyclic voltammetric responses are governed by the parameter... 

When Xe/y —> 0, catalysis vanishes. In the converse situation, where Xe/y oo, an interesting extreme behavior is observed. Substrate consumption is so rapid that substrate diffusion from the bulk of the solution to the electrode substrate becomes rate limiting. The cyclic voltammetric response... 

When the B/C conversion is fast, C is produced close to the electrode surface and is likely to diffuse back and be oxidized there. The situation is similar to the ECE case in the ECE-DISP problem discussed in Section 2.2.5. In the ECE case, the cyclic voltammetric responses depend essentially on the dimensionless rate constant, 2 = (7ZT/F)(k/v), of the B/C reaction in the framework of two subcases according to the order in which the two standard potentials, Z yBand c, lie (note that in the D/C couple, D is the oxidized form). Typical cyclic voltammograms are shown in Figure 2.25a and b for the two subcases. 

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