Potential digital simulation

Sokol et showed that the voltammetric response of cytochrome C3 arises from four relatively independent hemes with closely spaced formal potentials. Digital simulation results fitted to experimental data indicated four independent heme redox centers having formal potentials of -0.226, -0.278, -0.298, and -0.339 V. Each heme is apparently chemically unique and does not interact significantly with the other hemes in electron transfer. 

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... 

From the derivative of these plots, the potential dependence of a was obtained and the for each disulfide was estimated, using the approach described in Section 2. The double-layer uncorrected E° values and corresponding standard rate constants were optimized by reproducing the experimental curves by digital simulation. The data are reported in Table 11. By using the Eyring equation (4) with the pertinent pre-exponential... 

Digital simulation [37] has shown that the approximations made by Levich are valid under most conditions limits to his assumptions are given, particularly with regard to potential scan rates. 

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.]...

The real power of digital simulation techniques lies in their ability to predict current-potential-time relationships when the reactants or products of an electrode reaction participate in some intervening chemical reaction. These kinetic complications often result in a fairly difficult differential equation (when combined with the conditions for diffusion or convection encountered in electrochemical problems) that resists solution by ordinary means. Through simulation, however, the effect of any number of chemical steps may be predicted. In practice, it is best to limit these predictions to cases where the reactants and products participate in one or two rate-determining steps each independent step adds another dimensionless kinetics parameter that must be varied over the range of... 

Many problems involving competitive reaction kinetics may be treated by invoking the steady-state assumption within the digital simulation this has been done in at least two instances [29-34]. The first of these involves the development of a model for enzyme catalysis in the amperometric enzyme electrode [29-31]. In this model, the enzyme E is considered to be immobilized in a diffusion medium covering an electrode that is operated at a fixed potential such that the product (P) of enzyme catalysis is electroactive under diffusion-controlled conditions. (This model has also served as the basis for the simulation of the voltammetric response of the enzyme electrode [35].) The substrate (S) diffuses through the medium that contains the immobilized enzyme and is catalyzed to form P by straightforward enzyme kinetics ... 

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. 

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. 17 Double potential step chronoamperometric results at 23°C for the reduction of lucigenin (B +) in DMF containing BU4NBF4 (0.1 M). The circles are experimental values, and the lines show the results of digital simulation for the EEC mechanism (a) including, and (b) without the homogeneous redox equilibrium (eqn 51). Potential-step times varied between 1 and 100 ms. (Ahlberg, et al., 1981)...

---