Voltammetry kinetic parameter

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]. 

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... 

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). 

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. 

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... 

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. 

While the above technique can be used in many cases, it does require uncomplicated voltammetry and that significant Ey2 shifts are observed at guest concentrations >10 times the host concentration. If these conditions are not met, then an alternative strategy is needed. The most powerful is to use CV simulation software to fit the experimental CVs to the square scheme or a more complicated mechanism if necessary. This method allows determination of the thermodynamic parameters and possibly the kinetic parameters as well. 

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//... 

An interesting way of evaluating rate constants and charge transfer coefficients is the technique of iso-surface concentration voltammetry (ISCVA) [164] where the surface concentration of reactant is held constant over the electrode surface. A uniformly accessible electrode such as the RDE is therefore a prerequisite. At the RDE, the value of Hto1/2 is kept constant and disc potential plotted against current for different ratios of i/co1/2. This yields the kinetic parameters as well as E and the number of electrons transferred. 

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

In voltammetry, the relevant kinetic parameters for the electrode process (in addition to v) are k° and a (see Equations 6.10-11). The mutual dependence of k° and v is conveniently expressed through the magnitude of a dimensionless parameter, A, defined in Equation 6.37, in which the diffusion coefficients for O and Rare assumed to be identical (Do = Dr — D) ... 

Table 5.2 Kinetic parameters obtained from the fitting of experimental voltammetry at mercury hemispherical microelectrode and platinum disc microelectrode with the asymmetric MH model...

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... 

Fortunately, kinetics makes corrosion more difficult, so that it is much less prejudicial than predicted thermodynamically. In the electrochemistry laboratory corrosion can be studied by voltammetry and kinetic parameters can be predicted from Tafel plots and from impedance data. 

Kinetic parameters of dimerization can be determined by polarography, -> chronoamperometry, -> linear potential scan and -> convolution voltammetry, -> rotating disc voltammetry, and alternating current sinusoidal polarography. See also -> association. 

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. 

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) ... 

In electrochemistry, electron transfer reactions are classified as reversible, quasi-reversible, or irreversible, depending on the ability of the reaction to respond to changes in E. In voltammetry the relevant kinetic parameters are k°, a, and v. The mutual influence of k° and v is conveniently expressed through the magnitude of the dimensionless para-... 

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. 

Slow ET between redox species confined to two immiscible solvents was first observed by Guainazzi et al. (18). Several different theoretical and experimental studies of ET between redox species at the ITIES have been reported in the last several years (6-8,15,19-21). Severe experimental problems complicate extraction of the kinetic parameters from conventional electrochemical measurements at the ITIES (e.g., by cyclic voltammetry). Besides the difficulty of discrimination between ET and IT, there are also distortions from the double-layer charging current and /R-drop in the highly resistive nonaqueous solvents, and the limited potential window for studying ET in the absence of currents controlled by IT (1,16). 

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