Convolution linear sweep voltammetry

Analysis of other mechanisms with coupled homogeneous reactions leads to plots of the same kind and which can be used for the determination of the relevant kinetic parameters. Details are given in the literature, for example Refs. 1, 2, and 4. 

Almost all the analysis of cyclic and linear sweep voltammograms has been done through peak currents and peak potentials. Unless digital simulation and curve-fitting by parameter adjustment is carried out, all the information contained in the rest of the wave is ignored this brings problems of accuracy and precision. Besides this, a kinetic model has to be proposed before the results can be analysed. 

An answer to this lies in the transformation of the linear sweep response into a form which is readily analysable, i.e. the form of a steady-state voltammetric wave. Two independent methods of achieving this goal have been described the convolution technique by Saveant and co-workers11,12, and semi-integration by Oldham13. In this section we describe the convolution technique, and demonstrate the equivalence of the two approaches at the end. 

Electrode reactions with slower kinetics and with coupled homogeneous reactions have been considered by Saveant et al.14. A logarithmic equation of the type of (9.39) is obtained in all cases. 

If a convoluted voltammogram is to be utilized effectively and efficiently, much data transformation is required. It is necessary to use a computer, preferably linked directly to the experiment. 

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We deemed it necessary to confirm the CV results by the alternate method using convolutive potential sweep voltammetry, which requires no assumptions as to the form of the free energy relationship and is ideally suited for an independent analysis of curvature revealed in Figure 7. In convolutive linear sweep voltammetry, the heterogeneous rate constant ke is obtained from the cur-... 

Convolutive linear sweep voltammetry (CLSV) The convolutive transformation of a LSV curve yields the expression for surface concentration of the electroactive species A (in a reversible reduction process) as... 

The systematic application of modern electrochemical methodology proved in a first instance to be a very useful tool to gather thermodynamic information, as Gibbs energies of transfer from half-wave potential measurements. Then, in 1981, Samec et al used convolution linear sweep voltammetry to address experimentally the fundamental aspects of ion transfer reactions. The main advantage of this technique when studying charge trans-... 

In 1990, Shao and Girault started a series of investigations based on the kinetic study of the transfer of acetylcholine Ac = CH3C02CH2CH2N (CH3)3 in which the physical properties of one of the solvents were varied. The experimental approach for the measurement of the kinetic parameters was chronocoulometry, a technique which, like convolution linear sweep voltammetry, does not impose any prerequisites on the potential dependence of the rate constants. To verify the suitability of the experimental method, they studied the potential dependence of the rate constant for Ac transfer from water to oil and from oil to water. As illustrated in Fig. 7, the results obtained show that the apparent rate constants obey the Butler-Volmer relationship, expressed by Eq. 10. Note that Fig. 7 has been obtained from two independent experiments. In the first experiment, acetylcholine was only present in the aqueous phase as a chloride salt and forced to cross to the organic phase, whereas in the second, acetylcholine was only present in the organic phase as a tetraphenylborate salt and forced to transfer to the aqueous phase. 

Linear sweep voltammetry Ep measurements have not been applied extensively for the study of heterogeneous charge transfer kinetics. A serious problem with the use of this method is that Ep in itself is not significant in this respect but rather Ep — Etev is the quantity of interest. While AEP in CV is readily measured, this cannot be said for Etev using only LSV as a measurement technique. Therefore, there does not appear to be any advantage in LSV for the study of electrode kinetics. A more detailed analysis of the LSV wave, by convolution potential sweep or normalized potential sweep voltammetry (both to be discussed later) can provide both a and k°. 

Aalstad and Parker, 1980, 1981 Linear current potential analysis df/df/Z/P) p Normalized potential sweep voltammetry Convolution potential sweep voltammetry... 

When the transport of reactants is controlled by linear diffusion, the kinetic analysis can be performed using convolution potential sweep voltammetry [182]. Here it is more convenient to choose one of the reactant concentrations to be equal to zero, i.e., the initial conditions are recovered at sufficiently negative or positive potentials as in linear potential sweep voltammetry. By using the Laplace transform and the convolution theorem in solving the second Fick equation for each reactant, the convolution current m. 

Most of the more advanced techniques have only rarely been used outside the laboratories where they have been developed, and for that reason it is not easy to give recommendations. Examples include normalized sweep voltammetry [34,35,157,158], linear current-potential analysis [33], and the so-called global analysis and related techniques [159-161]. However, one such technique, convolution potential sweep voltammetry, has gained some popularity, and is introduced briefly here. 

Linear sweep voltammetry was used, with the convolution technique. A silver chloride-silver reference electrode was employed. The working electrode was a tungsten wire (I mm in diameter). The counter electrode was either a carbon rod or the graphite crucible. 

In the case of semiinfinite linear diffusion the semiintegration coincides with the simplest case of convolutive potential sweep voltammetry ... 

In the more advanced kinetic measurements, which were carried out by using chronopotentiometry [118], chronocoulometry [124, 139], linear [146] and convolution [18, 147] potential sweep voltammetry, or phase-sensitive ac polarography [142, 143], the ohmic drop was either numerically subtracted [118], or compensated [124, 139, 142, 143, 146, 147] with the help of the positive feedback. The feedback adjustment was based either on the assumption that the separation of the current peaks measured by the slow potential sweep voltammetry should reach the value of (59/z)mV [124, 139, 146, 147], or on the value of the solution resistance obtained by an ac bridge technique [142, 143]. However, the former adjustment is not very sensitive, whereas the estimated accuracy of 10 Q [142] in the latter case may not be... 

Solution of the transport problem when the process is controlled by both the interfacial electron transfer and the steady-state or linear diffusion of reactants was derived by Samec [181, 182]. These results represent the basis for the kinetic analysis, e.g., in dc polarography or convolution and potential sweep voltammetry. Under the conditions of steady-state diffusion, Eq. (60) can be transformed into a dimensionless form [181],... 

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