C 1 Reversible and Diffusion Kinetic Control

Cyclic voltammetry is the combination of two linear sweep experiments. The potential is initially swept in a forward direction, and the second scan is the reverse of the first. CV provides signals from the electrolysis of reactants on the forward scan and gives signals from the electrolysis products on the reverse scan [1, 2, 19]. Figure 11.14 shows a typical cyclic voltammogram for a Co(II) complex controlled by electrode kinetics and diffusion. On the forward scan, a peak for the Co(II)/Co(I) reduction is observed. On the reverse scan, the Co(I) that has been formed at the electrode in the forward scan is oxidized back to Co(II).

Cyclic voltammograms (CVs) are rich in information about the mechanism and kinetics of the electrode reaction. Parameters such as D, a, k°', and E°' can be obtained by nonlinear regression analysis of CVs controlled by diffusion and electrode kinetics [5]. CVs can also be employed to examine heterogeneous electron transfer kinetics as well as estimate rate constants (^chem) for a wide variety of chemical reactions coupled to electron transfer steps, such as for the catalytic mechanism in Box 11.2 [5], Chemical reactions may precede or follow electron transfer at the electrode. Discussion of this vast subject is beyond the scope of this chapter, and the reader is directed to several excellent books [1, 2, 19].

Caled.

Caled.

0.80

0.30

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Figure 11.14 Cyclic voltammogram (background subtracted) of 1 mM Co(II)tetraphenyl-porphyrin in 0.1 M TBABr at 25°C showing the results of fitting the data using the CVSIM/ CVFIT package.

CVs can be more difficult to analyze by nonlinear regression than steady state voltammograms. First, closed form equations describing the CV responses exist for only a few special cases. In general, numerical simulation techniques must be used to solve the models, which begin as sets of differential equations describing the relevant diffusion and kinetics of the species involved [1, 2]. However, successful solutions to this problem have been devised such that regression analysis using numerically simulated models can now be done on small computers [13, 19, 20].

A more serious problem is that of accounting for the background in CV. The signal to noise ratio is often less than optimum, and background currents may be curved and dependent on a complex set of conditions. Although steady state voltammograms involve background for a single scan, CV background currents occur on both oxidation and reduction cycles. Background subtraction remains a possibility, but background scans on solid electrodes are often not very reproducible.

We are currently aware of three commercially available general programs employing numerically solved or digitally simulated models for nonlinear regression analyses of voltammetric data (Table 11.9). The programs assume linear diffusion and can be used for any system for which this condition applies.

Major advantages of all of the commercial programs are that they allow the analysis of a wide variety of reaction types. The simulation models can generally be used independent of regression analysis. At the time of this writing, limitations in versatility of handling of the backgrounds of CVs existed in all of them. Backgrounds of CVs with irregularly shaped residual currents must be accurately subtracted if good fits are to be obtained. The first program in the list accompanies an excellent book by Gosser [19]. The

Table 11.9 Commercially Available Programs for Digital Simulation-Nonlinear Regression Analyses of Cyclic Voltammograms

Program

Vendor

Capabilities

Limitations"

CVSIM/CVFIT

VCH Publishers (with

Many second-order

Slow for large £chem;

book on CV [19])

chemical reactions

slow regression

COOL

PARC''

Reliable regression;

Pseudo-first-order

fast

chemical reactions

only

DIGISIM

BASC

Many second-order

Regression conver

chemical reactions;

gence poor for very

fast

complex mechanisms

" Limitations at the time of this writing, which may be corrected in future. b Princeton Applied Research Corp., Princeton, NJ. COOL algorithm also accommodates NPV, SWV, and other digital electrochemical methods. c Bioanalytical Systems, Lafayette, IN.

" Limitations at the time of this writing, which may be corrected in future. b Princeton Applied Research Corp., Princeton, NJ. COOL algorithm also accommodates NPV, SWV, and other digital electrochemical methods. c Bioanalytical Systems, Lafayette, IN.

other two programs are marketed by electrochemical instrument manufacturers.

A comparison of results from commercial programs is illustrated for the CV of Co(II)tetraphenylporphyrin [Co(II)TPP] in N,N-dimethylform-amide containing tetrabutylammonium bromide (TBABr) on a glassy carbon electrode. This is a simple one-electron transfer reaction, represented by

Data were successfully fit using a quasireversible model. Results are expressed graphically in Figures 11.14 and 11.15. Although the fits are reasonably good, small systematic deviations of the model and the data can be seen. These deviations are especially apparent on the oxidation scan and may be caused by an inaccurate consideration of the background. As mentioned previously, none of the programs have versatile background models and rely mainly on background subtraction. The situation is not too bad with the Co(II)TPP data, for which S/N is large, but will become more serious for signals that are relatively small with respect to background currents.

Results from different regression-simulation packages agree well. This is illustrated by the parameter values in Table 11.10 for Co(II)TPP, which exhibits reasonably fast electron transfer in DMF. The COOL package gave comparable results.

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