Convolution cyclic voltammetry

FIGURE 1.23. Variations of the transfer coefficient with the electrode potential derived from convolutive cyclic voltammetry of the following systems with double layer correction, t-nitrobutane in acetonitrile ( ), r-nitrobutane in DMF ( ), nitrodurene in acetonitrile + 2%H20 (a), nitrodurene in acetonitrile ( ), nitromesitylene in acetonitrile (y). Data from reference 64 and references therein. 

Fig. 9.11. Plots from convolution cyclic voltammetry for a reduction, (a) The current function (b) The convoluted current I( ip) (c) The logarithmic function in (9.39). All are plotted vs. , the dimensionless potential, where = (nF/RT) E - 1/2) (from Ref. 11 with permission).

Throughout the earlier chapters, we have tried to indicate the increasing role that mini- and microcomputers are playing in the control of electrochemical experiments, in data acquistion, as well as in data processing. Indeed, as we have seen, several new techniques have been developed recently that rely heavily on these capabilities (e.g. convolution cyclic voltammetry). 

All the above methods realistically require main-frame or minicomputers, but microcomputers are also having an impact on electrochemical experiments. They can take the tedium out the treatment of experimental data and, properly used, provide a much more critical test of the fit between experiment and theory. Moreover they make available new methods of data treatment, e.g. convolution cyclic voltammetry, and impedance analysis. 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

The variation of a with potential according to equation (13) may also be used to estimate the value of E°, from which the value of D may be inferred. This approach has been applied to organic peroxides,44 including endoperoxides of biological interest.37 Here again, convolution voltammetry proved to be more precise than plain cyclic voltammetry. 

The heterogeneous rates of electron transfer in eq 7 were measured by two independent electrochemical methods cyclic voltammetry (CV) and convolutive potential sweep voltammetry (CPSV). The utility of the cyclic voltammetric method stems from its simplicity, while that of the CPSV method derives from its rigor. 

In cyclic voltammetry, simple relationships similar to equations (1.15) may also be derived from the current-potential curves thanks to convolutive manipulations of the raw data using the function 1 /s/nt, which is characteristic of transient linear and semi-infinite diffusion.24,25 Indeed, as... 

These expressions are designed for cyclic voltammetry. The expressions appropriate for potential step chronoamperometry or impedance measurements, for example, are obtained by replacing IZT/Fv by the measurement time, tm, and the inverse of the pulsation, 1/co, respectively. Thus, fast and slow become Af and Ah I and -C 1, respectively. The outcome of the kinetic competition between electron transfer and diffusion is treated in detail in Section 1.4.3 for the case of cyclic voltammetry, including its convolutive version and a brief comparison with other electrochemical techniques. 

FIGURE 2.6. EC reaction scheme in cyclic voltammetry. Mixed kinetic control by an electron transfer obeying a MHL kinetic law (Xt — 0.7 eV, koo — 4 x 103 cms-1, implying that kg = 0.69 cms-1) and an irreversible follow-up reaction (from bottom to top, k+ = 103, 105, 107, 109s 1). Temperature, 25°C. a Potential-dependent rate constant derived from convolutive manipulation of the cyclic voltammetric data (see the text), b Variation with potential of the apparent transfer coefficient (see the text) obtained from differentiation of the curves in part a. 

In the electrochemical case, using, for example, cyclic voltammetry, one way of driving the potential toward more negative values is to increase the scan rate. This is true whether the linearization procedure or the convolution approach is followed. In the first case, equation (3.4) shows that the activation free energy at the peak, AG, is a decreasing function of the scan rate as a result of the kinetic competition between electron transfer and diffusion. The larger the scan rate, the faster the diffusion and thus the faster the electron transfer has to be in order to compete. This implies a smaller value AG, which is achieved by a shift of the peak potential toward more negative values. 

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. 

Equation (25) is general in that it does not depend on the electrochemical method employed to obtain the i-E data. Moreover, unlike conventional electrochemical methods such as cyclic or linear scan voltammetry, all of the experimental i-E data are used in kinetic analysis (as opposed to using limited information such as the peak potentials and half-widths when using cyclic voltammetry). Finally, and of particular importance, the convolution analysis has the great advantage that the heterogeneous ET kinetics can be analyzed without the need of defining a priori the ET rate law. By contrast, in conventional voltammetric analyses, a specific ET rate law (as a rule, the Butler-Volmer rate law) must be used to extract the relevant kinetic information. 

Potential or current step transients seem to be more appropriate for kinetic studies since the initial and boundary conditions of the experiment are better defined unlike linear scan or cyclic voltammetry where time and potential are convoluted. The time resolution of the EQCM is limited in this case by the measurement of the resonant frequency. There are different methods to measure the crystal resonance frequency. In the simplest approach, the Miller oscillator or similar circuit tuned to one of the crystal resonance frequencies may be used and the frequency can be measured directly with a frequency meter [18]. This simple experimental device can be easily built, but has a poor resolution which is inversely proportional to the measurement time for instance for an accuracy of 1 Hz, a gate time of 1 second is needed, and for 0.1 Hz the measurement lasts as long as 10 seconds minimum to achieve the same accuracy. An advantage of the Miller oscillator is that the crystal electrode is grounded and can be used as the working electrode with a hard ground potentiostat with no conflict between the high ac circuit and the dc electrochemical circuit. 

Basically, experimental approaches to ion transfer kinetics rely on classical galvanostatic [152] or potentiostatic [146] techniques, such as chronopotentiometry [118, 138], chronocoulometry [124], cyclic voltammetry [146], convolution potential sweep voltammetry [147], phase selective ac voltammetry [142], or equilibrium impedance measurements [148]. These techniques were applied mostly to liquid-liquid interfaces with a macroscopic area (typically around 0.1 cm ). However, microelectrode methodology has been successfully introduced into liquid-liquid electrochemistry as a novel electroanalytical tool by Senda and coworkers [153] and... 

The electrochemistry of a square-planar gold(III) complex with 2-(diphenylphosphino) benzenethiolate (21) was reported by Dilworth and coworkers35. Cyclic voltammetry experiments on [Au(21)2]BPh4 indicate a reversible redox couple at —0.862 V (vs the Fc/Fc+ reference couple) in 0.2 M [Bu4N]BF4/MeCN solution. Peak-to-peak separation of the redox waves was 84.2 mV and convolution methods were used to establish that the redox couple was reversible and involved the same number of electrons as the ferrocene/ferrocenium couple under identical conditions. The reductive scan was assigned... 

No analytical closed form has been derived for combined PBD and cyclic voltammetry (cyclic voltadeflectometry). Either numerical simulation or convolution of the experimental signal is applied [10,280,281]. 

The advantages of using EIS are numerous. First of all, it provides a lot of useful information that can be further analyzed. In practical applicatiOTis of cyclic voltammetry, simple information about peak currents and potentials is measured. These parameters contain very little information about the whole process especially when hardware and software is able sampling the current-potential curve producing thousands of experimental points every fraction of mV. On the other hand, one can use voltammetry with convolution, which delivers information at each potential, although very few people know and use this technique in current research. EIS contains analyz-able informatimi at each frequency. This is clearly seen from the examples that follow. 

For the elucidation of electrode mechanisms involving chemical steps various digital and analogous procedures are now the centre of attention. The fully automatized method applying artificial intelligence was presented in [5]. An expert system for the electrode mechanism is coupled to the electrochemical device. The presented set of rules allows identification of 10 mechanisms using cyclic voltammetry, chronocou-lometry, chronoamperometry and convolution voltammetry, respectively. 

A further advantage of the convolution method is that iR drop is very easily accounted for. In the case of conventional cyclic voltammetry, the nonlinearity of the sweep makes data analysis difficult however, in convolution voltammetry all that is necessary is to replace E by E + when plotting the voltammogram [43]. 

A necessary pre-requisite to such a study required accurate assessment of Ae formal potentials involved this in turn demanded careAl appraisal of adherence to a suitable mechanistic scheme. This criterion was satisfied by a combination of convolution techniques applied to cyclic voltammetry direct comparison wiA simulation results normally via Ae symmetrical deconvolution or dl /dE peaks produced when Ae time-scales are such Aat Ae system appeared electrochemically reversible. 

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