If a Data Fitting has successfully terminated it may be useful to estimate how reliable the optimized parameters are. Provided the proposed mechanism is correct and the experimental data are not spoiled by systematic errors (such as IR-drop and/or double layer charging effects or errors resulting from incorrect electrode size or species concentrations) the reliability of the optimized parameters can be determined by executing a Chi²-Test analogously as described by Rudolph. The procedure starts with selecting the parameter for which the Chi²-Test is executed. The latter is done by means of the Edit command. The following picture refers to the CV example given the file "NiLExample.dep" which will be installed in the folder "Example Files" of the DigiElch directory
In the above example the heterogeneous rate constant of the charge transfer reaction has been selected and P becomes an abbreviation for ks(NiL + e = NiL-). In the above example, the optimized value found by the fitting procedure is ks(opt) = 1.4348 cm/s and the optimal standard deviation will be computed using parameter values which are varied from ks(min) = 0.14348 (log10[ks(min)/ks(opt)] = -1) to ks(max) = 4 cm/s (log10[ks(max)/ks(opt)] = 0.45) .
After running the Chi²-Test the user may use the Duplicate command for selecting another parameter for which the test is to be executed. The following picture shows the result of Chi²-Tests executed for the parametrer P = ks(NiL + e = NiL-) and P = D(NiL).
The diffusion coefficient is usually the parameter for which a realistic value of the error level can be best estimated most easily. Compared to the diffusion coefficient the effect of the heterogeneous rate constant on the overall standard deviation is much smaller an unsymmetrical. The minimum is very flat if lg(P/Popt) > -0.2. In other words, as far as the lower limit of ks(NiL + e = NiL-) concerned the accuracy is be about 3-4 times lower than that of the diffusion coefficient. The upper limit is hardly predictable because the speed of the charge transfer process seems to be beyond the limit that can be reliably determined by cyclic voltammetry on a macro-electrode.
