Digisim® Tutorials

6. Fitting Experimental Data Files

The ultimate goal of digital simulation of cyclic voltammetry is to be able to generate a simulated cyclic voltammogram that matches an experimental cyclic voltammogram. Although DigiSim^® can be used for this purpose, it is important to note that considerable input from the user is required. The user must provide the mechanism and initial estimates of the parameter values, and, once a good match between the simulated and experimental data has been obtained, the user must also determine whether the optimized parameter values are reasonable; that is, are they consistent with previously measured values?

It is important to note that there are two functions that are used to examine experimental data files in DigiSim. The Import function (in the File menu) is used to display experimental data files in DigiSim (e.g., for visual comparison with simulations). The Select Files function (also in the File menu) is used to read experimental data files into DigiSim to be used in the Fitting routine (which optimizes the values of user-selected parameters to give the best fit of the simulated data to the experimental data).

Data from BASi (.txt), EG&G (.dat), and Cypress (.dat) electrochemistry software can be read by DigiSim. In addition, there is the DigiSim text format, with the extension .use. Experimental data from other sources can be converted to any of the above formats and read into DigiSim, subject to three constraints:

1. the current values must obey the Classical (polarographic) convention; that is, cathodic currents are positive
2. the size of the potential step must be constant
3. the potential of the first data point must lie at Estart +/- x V, where x is the size of the potential step

One advantage of using the .use format is that additional information about the experiment (e.g., the electrode surface area, concentrations of redox species) can be included in the header, and these values can be read by DigiSim. Existing data files (either simulated (.cvs) or experimental) can be converted to the .use format using the Export function in the File menu.

One method for optimizing parameter values is to vary the parameters manually. The procedure for this method is as follows:

1. Import the experimental data into DigiSim
2. Enter a mechanism and appropriate parameter values in the CV-Properties dialog box
3. Run the Simulation, and compare the experimental and simulated voltammograms.
4. Vary the appropriate parameter values to obtain a good match between the experimental and simulated voltammograms.

The above method can be automated to a certain degree using the Fitting routine, which optimizes selected parameters. This routine also allows more than one experimental voltammogram to be fitted simultaneously. The procedure described below first generates and saves two simulated data files (a - c), and then uses these files as model files to illustrate how the Fitting routine is used (d - f). When fitting experimental files, only steps d - f should be used.

1. Enter the mechanism (O + e = R) and parameter values (Eo = 0 V, ks = 0.1 cm/s, [O] = 0.001 M) in the CV-Properties dialog box.

    

2. Running a simulation at this point will generated an idealized voltammogram. In order to generate a voltammogram that is less than ideal (i.e., one that is more similar to an experimental voltammogram) some "noise" can be introduced by enter a value of 1.6e-5 A for the Noise Level in the Model Parameters.

    

3. Run the simulation, and save as abn1.use using the Export function. Return to the CV-Properties dialog box, and change the scan rate to 10 V/s, and [O] to 0.002 M. Run the new simulation, and save as abn2.use. Clear the simulator by closing the window displaying the simulation.

    

4. The first stage of the Fitting routine is to select the "experimental" data files for fitting. This is achieved using Select Files from the File menu (F1). Click on files abn1.use and abn2.use, and then click Add (these files will be added to the Selected Files list). Click OK to exit this dialog box.

    

   
   Figure 1. Select Files dialog box.

    

5. Once the "experimental"data files have been selected, the mechanism and an initial estimate of the parameter values must be entered. Enter the mechanism and chemical parameter values shown in F2 (use default values for the CV parameters).

    

   
   Figure 2. Chemical Parameters dialog box for Fitting routine.

    

   There are three points to note:

   i) DigiSim will read the scan rate and concentrations from the experimental data files (provided that they have been included in the header, as is the case for the.use files). However, one non-zero concentration value must be entered.

   ii) The parameters to be optimized are selected by clicking the box to the left of that parameter. In this example, Eo and ks are to be optimized. When a box is checked, a Fitting Range dialog box will appear; click Select.

   iii) The optimized simulations are saved as .cvs files, and the optimized parameter set is saved as optimal.cvs (note that ONE parameter set is used to fit ALL the selected experimental data files).

6. Click Fitting in the Run menu to initiate the fitting routine. The optimization process will be shown as it occurs. The default number of iterations is 10, but this can be changed in the Fitting Parameters dialog box (if the number of iterations selected is insufficient to achieve optimization, rerun Fitting). The .use and .cvs files can be compared using Scan Selected Files in the View menu (F3).

    

   

    

    

   
   Figure 3. Comparison of experimental and simulated data.

    

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