Cyclic voltammetry is perhaps the most widely used electrochemical technique, and is frequently used for the initial characterization of a redox system. It can provide information about the number of oxidation states, as well as qualitative information about the stability of these oxidation states and the electron transfer kinetics. There are also simple models that can be used to calculate the rate of electron transfer (represented by ksh) and the rate of chemical reactions coupled to the electron transfer for simple systems (those where the cyclic voltammetric behavior is controlled by only one of these parameters). However, these simple models cannot be used for more complicated systems, since the effects of, for example, slow electron transfer kinetics and a coupled chemical reaction cannot be readily separated.
Quantitative measurements can be made using digital simulation programs. A mechanism and the appropriate parameters are entered into the program, and the software calculates the cyclic voltammogram for the entered data. However, the computational problems associated with digital simulation of cyclic voltammograms are formidable, and until recently there was no software available that was user-friendly and truly general. Typical problems included the following:
In 1993, BASi introduced DigiSim®, a cyclic voltammetry simulation program based on the Fast Implicit Finite Difference (FIFD) method originally developed by Rudolph, and adapted for commercial use by Rudolph, Feldberg and BAS. This software is truly general, and can accept any mechanism that can be entered in terms of single- or multiple-electron transfer reactions and first- or second-order chemical reactions. It is also efficient, and can rapidly calculate the simulated voltammograms for a wide range of kinetic parameter values. Furthermore, it requires little mathematical sophistication or computational expertise from the user.
In addition to the basic simulation operation, there are two additional functions available on DigiSim. The first of these is CV - the Movie™ , which shows the concentration profiles of the various species involved in the electrochemical mechanism as they change during the cyclic voltammetry experiment. The other is a least-squares fitting routine, which is used to match experimental voltammograms to simulated voltammograms through the variation of user-specified parameter values.
It is important to note that any given cyclic voltammogram can often be accurately simulated by more than one mechanism and/or set of parameter values. Experimental measurements should therefore be made over a wide range of parameter values (the most common variables are scan rate and concentration, although variation of temperature can also be used). If one set of parameter values can provide a good match between the experimental voltammograms measured over a wide range of scan rates (and/or concentrations) and the respective simulated voltammograms, then this is good evidence that these parameter values are correct. However, it does not prove that the correct mechanism and parameter values have been selected; it is up to the user to determine whether the selected mechanism and parameter values are chemically and electrochemically reasonable (i.e., are they consistent with the results of electrochemical studies on similar systems?). The sensitivity of the fit to variations in the parameters values must also be investigated.
The fitting routine in DigiSim can be used to fit more than one voltammogram. The basic procedure is as follows. The experimental data (text) files are selected and loaded into DigiSim. The mechanism and parameter values are then entered, and the parameters to be varied are selected. Once this has been done, the fitting operation can be started. If the experimental cyclic voltammograms are run using different concentrations and/or different electrode geometries, then this information must be added to the text files (this is discussed in a later note).
DigiSim can be used not only for investigating the electrochemical mechanisms of real redox systems, but it can also be used for understanding the basic concepts and behavior of cyclic voltammetry. It is therefore a highly effective tool for teaching cyclic voltammetry. These applications will be discussed in future notes.
DigiSim is a registered trademark and CV - the Movie is a trademark of Bioanalytical Systems, Inc.
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