Cyclic digital simulation

The cyclic voltammograms of these systems display quasi-reversible behavior, with AEv/v being increased because of slow electrochemical kinetics. Standard electrochemical rate constants, ( s,h)obs> were obtained from the cyclic voltammograms by matching them with digital simulations. This approach enabled the effects of IR drop (the spatial dependence of potential due to current flow through a resistive solution) to be included in the digital simulation by use of measured solution resistances. These experiments were performed with a non-isothermal cell, in which the reference electrode is maintained at a constant temperature... 

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. 

Figure 13.27 Dual-pathway square scheme mechanism that accounts for the rearrangements induced by the monoelectronic reduction of deprotonated rotaxane 92+. The species A and C represent the stable structure of the deprotonated rotaxane and its monoreduced form, respectively, whereas and D are metastable intermediates. Note that the exact position of the macrocycle along the axle in the reduced forms and C is not known. From a simple digital simulation of the cyclic voltammetric patterns, the following values have been obtained = - 0.59V, E°dc = - 0.34V, /cAD 0.15S- da<2.5s kBC > 100 s and kCB 1 s V...

The reach of cyclic voltammetry is vast. It has been applied to the investigation of simple electron-transfer reactions those with two successive electron transfers (so-called EE reactions) and with multiple electron transfers (EEE) involving electron transfer to and from compounds, say, with several benzene rings. The technique has been applied to complex sequences in which an electron transfer is followed by a chemical reaction step, and then by another electron transfer (ECE reactions), etc. The complexity of some of the reaction sequences investigated by cyclic voltammetry lends itself well to calculations that need computers the classic work of Feldburg in this direction (digital simulation) has been already mentioned (Section 7.5.19.2). 

This could be explained in terms of disproportionation of the radical-anion to dianion with subsequent protonation. However, a much more complete explanation followed the realisation that, in most cases, the radical-anion acts not only as a base but also as a single electron-transfer agent (the so-called DISP mechanisms). In particular a comparison of observed cyclic voltammetric behaviour of substituted azobenzenes in the presence of weak acids with that predicted using digital simulation based on various mechanistic possibilities has established the DISPl route given in Eq. (3) (reactions 1-4). 

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)... 

Clearly, the data contain information about both the equilibrium constant and the rate constants for the conformational interconversion. In this instance, the quantitative analysis was based upon the cyclic voltammetric data. The points in Figure 16.3 are the background-corrected experimental data, and the curves were computed by digital simulation with values of the equilibrium and rate constants selected to achieve best agreement with the experimental data. A given set of parameters was found to account for the data at a variety of scan rates, a necessary condition if the kinetic model is to be judged adequate. 

Figure 16.4 Cyclic voltammogram of 4.5 mM 2,3-dinitro-2,3-dimethylbutane in N,N-dimethylformamide/0.20 M Bu4NPF6 at a 25-pm-diameter mercury electrode. Curves experimental voltammograms after subtraction of background current. Points digital simulations. Potentials referred to cadmium reference electrode [cadmium amalgam/CdCl2 (sat d) in DMF]. [Reprinted with permission from W.J. Bowyer and D.H. Evans, J. Org. Chem. 53 5234 (1988). Copyright 1988 American Chemical Society.]...

Attempts to develop a model for the digital simulation of the cyclic voltammetric behaviour of PVF films on platinum62 electrodes required inclusion of the following features (a) environmentally distinct oxidized and reduced sites within the film (b) interconversion of the above sites and interaction between them (c) rate of electrochemical reactions to depend on the rate of interconversion of redox sites, the rate of heterogeneous electron transfer between film and substrate, intrafilm electron transfer and the rate of diffusion of counter ions and (d) dependence on the nature of the supporting electrolyte and the spacing of electroactive groups within the film. 

The task now at hand is to find solutions to these second-order differential equations under theboundary conditions defined by the electroanalytical method in question. Nowadays, this is most often accomplished by numerical integration, known in electroanalytical chemistry as digital simulation. It is beyond the scope of this chapter to go into the mathematical details, and the interested reader is referred to the specialist literature [33]. Commercial user-friendly software for linear sweep and cyclic voltammetry is available (DigiSim ) software for other methods has been developed and is available through the Internet. 

Digermanes, unsymmetrically substituted, 3, 787 Digermenes, preparation, 3, 796 Digestion studies, stability, 12, 612-613 DIGISIM, in cyclic voltammetry, 1, 282-283 Digital simulations, in cyclic voltammetry, 1, 282 Dihalides, in chromium mononitrosyl complexes, 5, 302 Dihaloarenes, cross-coupling polymerization, 11, 659... 

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. 

One of the main uses of digital simulation - for some workers, the only application - is for linear sweep (LSV) or cyclic voltammetry (CV). This is more demanding than simulation of step methods, for which the simulation usually spans one observation time unit, whereas in LSV or CV, the characteristic time r used to normalise time with is the time taken to sweep through one dimensionless potential unit (see Sect. 2.4.3) and typically, a sweep traverses around 24 of these units and a cyclic voltammogram twice that many. Thus, the explicit method is not very suitable, requiring rather many steps per unit, but will serve as a simple introduction. Also, the groundwork for the handling of boundary conditions for multispecies simulations is laid here. 

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-... 

It is evident from these considerations that the use of a less hydrophobic redox species in the O phase makes the homogeneous ET occur more favourably. Another example of the IT mechanism has been found in the ET between L-ascorbic acid in W and chloranil (with Ko = 900) in NB or DCE. This has been confirmed using potential-controlled polarography [47], potential modulated reflectance spectroscopy [46], microflow coulometry [39], ECSOW system [38] and digital simulation of cyclic voltammograms [48]. 

Fig. 16 Working curve for the EC dimerization mechanism during cyclic voltammetry. Calculated by digital simulation. (Ahiberg et al., 1980b)...

The general behavior expected in LSV may then be computed by digital simulations [20] and the results can be conveniently visualized in a zone diagram as shown in Figure 9. For log 2 < — 1, the dimerization reaction has no effect whatsoever, and the cyclic voltammetric behavior pertains to the reversible, quasi-reversible (QR), or totally irreversible charge transfer (IR), depending on the value of A. For very large... 

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