Kinetic parameters cyclic voltammetry

Voltammetric methods produce current-voltage curves with features characteristic of the reaction mechanism and kinetic conditions. Combining this with the ease of changing the waveform parameters, cyclic voltammetry is nearly always the first technique used to study a new systan. It is particularly usefril for assessing reaction mechanisms, even when there are additional complications such as coupled homogeneous reactions, or surface adsorption. These techniques also provide quantitative information as will be shown below with a selection of theoretical expressions. 

Thus, cyclic or linear sweep voltammetry can be used to indicate whether a reaction occurs, at what potential and may indicate, for reversible processes, the number of electrons taking part overall. In addition, for an irreversible reaction, the kinetic parameters na and (i can be obtained. However, LSV and CV are dynamic techniques and cannot give any information about the kinetics of a typical static electrochemical reaction at a given potential. This is possible in chronoamperometry and chronocoulometry over short periods by applying the Butler Volmer equations, i.e. while the reaction is still under diffusion control. However, after a very short time such factors as thermal... 

The one-electron reduction potentials, (E°) for the phenoxyl-phenolate and phenoxyl-phenol couples in water (pH 2-13.5) have been measured by kinetic [pulse radiolysis (41)] and electrochemical methods (cyclic voltammetry). Table I summarizes some important results (41-50). The effect of substituents in the para position relative to the OH group has been studied in some detail. Methyl, methoxy, and hydroxy substituents decrease the redox potentials making the phe-noxyls more easily accessible while acetyls and carboxyls increase these values (42). Merenyi and co-workers (49) found a linear Hammett plot of log K = E°l0.059 versus Op values of substituents (the inductive Hammett parameter) in the 4 position, where E° in volts is the one-electron reduction potential of 4-substituted phenoxyls. They also reported the bond dissociation energies, D(O-H) (and electron affinities), of these phenols that span the range 75.5 kcal mol 1 for 4-amino-... 

FIGURE 1.17. Cyclic voltammetry of slow electron transfer involving immobilized reactants and obeying a Butler Volmer law. Normalized current-potential curves as a function of the kinetic parameter (the number on each curve is the value of log A ) for a. — 0.5. Insert irreversible dimensionless response (applies whatever the value of a). 

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. 

We start with the case where the initial electron transfer reaction is fast enough not to interfere kinetically in the electrochemical response.1 Under these conditions, the follow-up reaction is the only possible rate-limiting factor other than diffusion. The electrochemical response is a function of two parameters, the first-order (or pseudo-first-order) equilibrium constant, K, and a dimensionless kinetic parameter, 2, that measures the competition between chemical reaction and diffusion. In cyclic voltammetry,... 

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. 

As with the other reaction schemes involving the coupling of electron transfer with a follow-up homogeneous reaction, the kinetics of electron transfer may interfere in the rate control of the overall process, similar to what was described earlier for the EC mechanism. Under these conditions a convenient way of obtaining the rate constant for the follow-up reaction with no interference from the electron transfer kinetics is to use double potential chronoamperometry in place of cyclic voltammetry. The variations of normalized anodic-to-cathodic current ratio with the dimensionless rate parameter are summarized in Figure 2.15 for all four electrodimerization mechanisms. 

Although separate determination of the kinetic and thermodynamic parameters of electron transfer to transient radicals is certainly important from a fundamental point of view, the cyclic voltammetric determination of the reduction potentials and dimerization parameters may be useful to devise preparative-scale strategies. In preparative-scale electrolysis (Section 2.3) these parameters are the same as in cyclic voltammetry after replacement in equations (2.39) and (2.40) of Fv/IZT by D/52. For example, a diffusion layer thickness S = 5 x 10-2 cm is equivalent to v = 0.01 V/s. The parameters thus adapted, with no necessity of separating the kinetic and thermodynamic parameters of electron transfer, may thus be used to defined optimized preparative-scale strategies according to the principles defined and illustrated in Section 2.4. 

The governing dimensionless partial derivative equations are similar to those derived for cyclic voltammetry in Section 6.2.2 for the various dimerization mechanisms and in Section 6.2.1 for the EC mechanism. They are summarized in Table 6.6. The definition of the dimensionless variables is different, however, the normalizing time now being the time tR at which the potential is reversed. Definitions of the new time and space variables and of the kinetic parameter are thus changed (see Table 6.6). The equation systems are then solved numerically according to a finite difference method after discretization of the time and space variables (see Section 2.2.8). Computation of the... 

Cyclic voltammetry is probably the most commonly encountered technique for studying dynamic electrochemistry. It is useful for discerning kinetics, rates and mechanisms, in addition to thermodynamic parameters which are usually obtained at equilibrium. 

Determination of the kinetic parameters by using cyclic voltammetry is conceptually very similar to this t = 0 is taken to be the time at the formation of the intermediate (here Br2), i.e. at the forward current peak Ipa, and the time when it is monitored at t = t, i.e. at the current peak for the reverse electrode process, pc. The time-scale of the reaction, r, is given by the following equation ... 

For the rapid electron transfer process, which follows a reversible chemical step (CE), a procedure is presented for the determination of chemical and electrochemical kinetic parameters. It is based on convolution electrochemistry and was applied for cyclic voltammetry with digital simulation [59] and chronoamperometric curves [60]. The analysis was applied to both simulated and experimental data. As an experimental example, the electroreduction of Cd(II) on HMDE electrode in dimethylsulphoxide (DM SO) [59] and DMF [60] with 0.5 M tetraethylammonium perchlorate (TEAP) was investigated. 

Digital simulation software, which is now commercially available, is useful in analyzing cyclic voltammograms of complicated electrode reactions [67]. If we assume a possible reaction mechanism and can get simulated CV curves that fit the experimental CV curves, we can confirm the reaction mechanism and obtain thermodynamic and kinetic parameters concerning the electron transfer and chemical processes. By the development of simulation softwares, cyclic voltammetry has become a very powerful technique. On the contrary, without a simulation software, cyclic voltammetry is not as convenient.14)... 

Variation of cyclic voltammetry peak potential separation with the heterogeneous kinetic parameter i//... 

Because cyclic voltammetry was chosen as the method for quantitative evaluation of the kinetic parameters, close attention to the effects of solution... 

Recent studies describe the use of cyclic voltammetry in conjunction with controlled-potential coulometry to study the oxidative reaction mechanisms of benzofuran derivatives [115] and bamipine hydrochloride [116]. The use of fast-scan cyclic voltammetry and linear sweep voltammetry to study the reduction kinetic and thermodynamic parameters of cefazolin and cefmetazole has also been described [117]. Determinations of vitamins have been studied with voltammetric techniques, such as differential pulse voltammetry for vitamin D3 with a rotating glassy carbon electrode [118,119], and cyclic voltammetry and square-wave adsorptive stripping voltammetry for vitamin K3 (menadione) [120]. 

Cyclic voltammetry is of particular value for the study of electrochemical processes that are limited by finite rates of electron transfer. The quantitative relationships derived by Nicholson and Shain7 allow the evaluation of kinetic parameters for such rate-limited processes via cyclic voltammetry. A particularly useful function for such measurements is given by the relation... 

The chronocoulometry and chronoamperometry methods are most useful for the study of adsorption phenomena associated with electroactive species. Although less popular than cyclic voltammetry for the study of chemical reactions that are coupled with electrode reactions, these chrono- methods have merit for some situations. In all cases each step (diffusion, electron transfer, and chemical reactions) must be considered. For the simplification of the data analysis, conditions are chosen such that the electron-transfer process is controlled by the diffusion of an electroactive species. However, to obtain the kinetic parameters of chemical reactions, a reasonable mechanism must be available (often ascertained from cyclic voltammetry). A series of recent monographs provides details of useful applications for these methods.13,37,57... 

Digital simulation — Data from electrochemical experiments such as cyclic voltammetry are rich in information on solution composition, diffusion processes, kinetics, and thermodynamics. Mathematical equations describing the corresponding parameter space can be written down but can be only very rarely solved analytically. Instead computer algorithms have been devised to ac-... 

The time domain on a window accessed by a given experiment or technique, e.g., femtosecond, picosecond, microsecond, millisecond. The time scale (or domain) is often characterized by a set of physical parameters associated with a given experiment or technique, e.g., r2 ]/1) (for - ultramicroelectrode experiments) - thus if the electrode radius is 10-7 cm and the - diffusion coefficient D = 1 x 10-5 cm2/s-1 the time scale would be 10 9s. Closely related to the operative kinetic term, e.g., the time domain that must be accessed to measure a first-order -> rate constant k (s-1) will be l//ci the time domain that must be accessed to measure a given heterogeneous rate constant, k willbe /)/k2. In - cyclic voltammetry this time domain will be achieved when RT/F v = D/k2 with an ultramicroelectrode this time domain will be achieved (in a steady-state measurement when r /D = D/k2 or ro = D/k at a microelectrode [i-ii]. 

Rashid and Kalvoda examined this reaction using cyclic voltammetry by measuring the current enhancement for the electro-oxidation of potassium ferricyanide on addition of the amine. Using working curves derived by Nicholson and Shain (1964) relating the ratio of the peak current measured in the presence and absence (i.e. the diffusion-controlled peak current for oxidation of ferricyanide) of the amine to the parameter kfRTInFvioT an EC mechanism, the kinetic parameter, kf, could be calculated. 

The development of ultramicroelectrodes with characteristic physical dimensions below 25 pm has allowed the implementation of faster transients in recent years, as discussed in Section 2.4. For CA and DPSC this means that a smaller step time x can be employed, while there is no advantage to a larger t. Rather, steady-state currents are attained here, owing to the contribution from spherical diffusion for the small electrodes. However, by combination of the use of ultramicroelectrodes and microelectrodes, the useful time window of the techniques is widened considerably. Compared to scanning techniques such as linear sweep voltammetry and cyclic voltammetry, described in the following, the step techniques have the advantage that the responses are independent of heterogeneous kinetics if the potential is properly adjusted. The result is that fewer parameters need to be adjusted for the determination of rate constants. 

Indeed, in cyclic voltammetry, peak potentials Ep play a role identical to that of halfwave potentials E1/2 in steady-state methods. As for the later methods, peak potentials vary linearly with the logarithm of dimensionless kinetic parameters A. or A in Table 5, provided these latter have values sufficiently large when compared to unity [94]. These linear variations, which may be used for determination of reaction orders, stem from the same mathematical reasons as explained in the case of E1/2. Yet the physical reason is quite different as evidenced by the case of the simple EC sequence in Eqs. (222) and (223) ... 

Electrocatalysts are produced in different ways, on different substrates, and for different purposes,10,64-72 but almost in all cases the electrochemical characterization was performed by using the cyclic voltammetry observations. In this way, it was not possible to analyze the effects of the mass-transfer limitations on the polarization characteristics of electrochemical processes. As shown recently,7,9 the influence of both kinetic parameters and mass-transfer limitations can be taken into account using the exchange current density to the limiting diffusion current density ratio, jo/ju for the process under consideration. Increased value of this ratio leads to the decrease of the overpotential at one and the same current density and, hence, to the energy savings. 

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