DigiSim

Simulation through DigiSim software was used to help in elucidating mechanism. 

Figure 6,16 Cyclic voltammograms as a function of scan rate. This figure comprises traces simulated by the DigiSim program for a reversible one-electron couple, with the fastest scan rate being shown outermost. Reprinted with permission from Current Separations, Vol. 15, pp. 25-30, copyright Bioanalytical Systems, Inc., 1996.

Wfe can be satisfied that the variables we have (e.g. A, D, etc., as above) are accurate if they allow us to model a system precisely. Vie say that the variables fit the data. Figure 10.1 shows a cyclic voltammogram (CV), with superimposed on this current-potential data simulated with the DigiSim package (as described in more detail below). The fit between theory and experiment is seen to be good, so we say that the derived variables fit the data. 

The programs described above are limited in scope, and a superior approach is to employ a simulation package. There are three commercial programs at the forefront of the market, namely DigiSim, Condecon and GPES. 

The DigiSim simulation package was compiled by Manfred Rudolph and Stephen Feldberg, in collaboration with Bioanalytical Systems, Inc. (BAS). 

The DigiSim program probably represents the current state of the art which is achievable for simulating and analysing cyclic voltammograms. This package can perform cyclic voltanunetry for a wide range of mechanisms at planar, spherical, cylindrical or rotated disc electrodes. It also computes concentration profiles. 

Carlo Nervi considers DigiSim to be presently the best simulation package available , even though he has produced a package of his own, namely ESP, as described below. 

The DigiSim software is presently available in Version 3 for Windows 95/98... 

The DigiSim program enables the user to simulate cyclic voltanunetric responses for most of the common electrode geometries (planar, full and hemispherical, and full and hemicylindrical) and modes of diffusion (semiinfinite, finite and hydrodynamic diffusion), with or without inclusion of IR drop and double-layer charging. 

Figure 10.3 shows the CV of a nickel(n) complex as a function of scan rate (continuous lines), together with data simulated by the DigiSim package (solid and open circles). The agreement between experiment and theory is seen to be very close. 

Although the theoretical basis of the technique is different from other electrochemical-simulation packages, in operation it is just as powerful as DigiSim, allowing parameters to be computed for a variety of mechanisms, electrode geometries and experiment types. More information and representative references to Condecon, can be found at its website ... 

While several sample programs are available, nowadays a preferred and simpler process is to simulate the system via the use of more sophisticated packages such as DigiSim, Condecon or GPES. 

The following articles in the Current Separations Series are an excellent introduction to the topic of simulation Bott, A. W., Fitting experimental cyclic voltammetry data with theoretical simulations using DigiSim 2.1 , Current Separations, 15, 67-71 (1996) Bott, A. W. and Jackson, B. P., Study of ferri-cyanide by cyclic voltammetry using the CV-50w, Current Separations, 15, 25-30(1996). 

I also wish to thank Dr Lou Coury and Dr Adrian Bott of Bioanalytical Systems, Inc. for their enthusiasm, and permission to reproduce Figures 6.16, 6.18, 6.19, 10.1 and 10.3.1 gladly thank Dr Manfred Rudolph for his description of the DigiSim program. Dr Mike Dawson of E G G for his help concerning the Condecon program, and Dr Keith Dawes of Windsor Scientific for his help, and the permission to reproduce Figure 10.2. 

Figure 3.19 Voltammograms and concentration-distance profiles for (a) fast, and (b) slow scan rate. Simulation by DigiSim. ...

Figure 3.22 Cyclic voltammogram of 1 mM O in supporting electrolyte. Scan initiated at 0.6 V vs. SCE in negative direction at 200 mV s1. Concentration-distance profiles a-h keyed to voltammogram. Eq R = 0 V vs. SCE. Simulation by DigiSim. ...

Figure 3.25 (A) Cyclic voltammograms exhibiting electrochemical reversibility effect of variation of ks kj = 1 (solid lines), 0.01 (dashed lines), 0.001 (dotted lines). Scan rate = 1 V s1. [Simulation by DigiSim .] (B) Dependence of AEpon ks and vl/2. [From Ref. 45, reprinted with permission.]...

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. 

Fig. 6.9 Cyclic voltammogram for a reversible one-electron reduction v = 1 V s 1 (DigiSim ).

Fig. 6.10 Concentration profiles corresponding to (a) the forward sweep, and (b) the reverse sweep in cyclic voltammetry. O full line R dots. The values of E — E° corresponding to each set of profiles are given in the figure (DigiSim ).

Fig. 6.17 Cyclic voltammetry data (solid line) for the oxidation of 2,4-dimethyl-3-ethylpyrrole in MeCN at v = 0.2 V s-1 and the simulated curve (dash-dot, DigiSim ) corresponding to the reaction sequence in Scheme 6.10. Reprinted with permission [39].

Fig. 6.25 Cyclic voltammograms for an eCeh mechanism with k = 20 s 1 at v = 100 V s 1 (solid) and v = 0.1 Vs-1 (dots). Note that the y-axis shows values of i/ /v (DigiSim ).

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... 

See also http //www.basinc.com/products/ec/digisim/ and http //www.gamry.com/products/ digielch-electrochemical-simulation-software/... 

The question arises of how low an N value it is possible to work with and still get good results. The simulation package DigiSim due to Rudolph and Feldberg [482] routinely uses as few as 14 and is able to achieve sufficient accuracy in the current. This depends on one s definition of sufficient . If 0.1% accuracy is wanted, about 40 points in space might be optimal. 

The Feldberg approach to digital simulation [229] uses a somewhat different method of discretisation, and the method is alive and well it is, for example, the basis for the commercial program DigiSim [482], It begins with Fick s first diffusion equation, using fluxes between boxes or finite volumes, rather than concentrations at points in the discretisation process (see below). 

One of the authors of DigiSim has now produced his own separate program, DigiElch, available through a web site [14]. Presumably it functions much like DigiSim. 

Britz D., Anal. Chem. 67, 600A-601A (1995), review of DigiSim. 

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