Kinetics of electron transfer involving electroactive films are important for their characterization and performance [15]. For films of micrometer thickness, diffusion within the film and electron transfer kinetics may influence NPV data. In such cases, it is possible to estimate k°' from NPV data obtained under diffusion-kinetic control. The key requirement is that the diffusion layer developed at the electrode during electrolysis should be a small fraction of the film thickness so that semi-infinite linear diffusion applies [1],

The model in Table 11.8 was used to obtain electrochemical parameters for 20 (xm thick films of the protein myoglobin (Mb) and surfactant didode-cyldimethylammonium bromide (DDAB) on graphite electrodes. NPV pulse widths of 4-60 ms were used, and the voltammograms featured relatively low signal to noise ratios. From the relation between root mean square displacement A2 and diffusion coefficient [1]

A2 = 2 D t we find for D = 4 X 10"7 cm2 s"1 for Mb-DDAB films [10] the diffusion layer is only 10% of film thickness at the end of a 60 ms pulse and proportionately less at 4 ms. Therefore, the conditions of linear diffusion pertain.

Typical results for Mb-DDAB at small (Figure 11.11) and large (Figure 11.12) pulsewidths show good agreement with the model. Only the rising portion of the curve, between about 2% and 98% of id, needs to be analyzed. The small pulsewidth voltammogram is broader than that for the larger pulsewidth because of the increased influence of electrode kinetics at shorter times. Residual plots were nearly random. Relative standard devia-

pH/method |
WD', cmzs_1 |
103*«", cm |
-E°', V/SCE |
a |
%RSDC |

5.5/NPV |
7.1 ± 1.5 |
0.31 ± 0.04 |
0.26 | ||

5.5/NPV |
5.7 ± 1.6 |
0.18 ± O.OS'' |
0.46 | ||

5.5/CV |
5.1 |
6.7 ± 0.7 |
0.124 | ||

7.5/NPV |
7.8 ± 1.5 |
0.27 ± 0.02 |
0.34 | ||

7.5/NPV |
4.5 ± 1.1 |
0.18 ± 0.066 |
0.53 | ||

7.5/CV |
3.7 |
9.0 ± 0.3 |
0.194 |

" NPV results obtained on two electrodes by analysis with the model in Table 11.7, see [10], Values of k°' obtained as average from data at 4-10 ms pulsewidth; D, from data with 30-60 ms pulsewidth.

b Estimated as average from 11 data sets with 4-60 ms pulsewidths e Average standard deviation of regression relative to

" NPV results obtained on two electrodes by analysis with the model in Table 11.7, see [10], Values of k°' obtained as average from data at 4-10 ms pulsewidth; D, from data with 30-60 ms pulsewidth.

b Estimated as average from 11 data sets with 4-60 ms pulsewidths e Average standard deviation of regression relative to

Figure 11.11 The NPV at a 4 ms pulsewidth of Mb-DDAB film on pyrolytic graphite electrode in pH 5.5 buffer. The line shows experimental NPV; the circles are points computed from a nonlinear regression using the model in Table 11.7 for the parameters found: k°' = 8.1 x 1(T3 cm s-1, id = 363.7 /j.A, E<" = -0.261 V vs. SCE, a = 0.28. (Reproduced with permission from [10], copyright by the American Chemical Society.)

Figure 11.11 The NPV at a 4 ms pulsewidth of Mb-DDAB film on pyrolytic graphite electrode in pH 5.5 buffer. The line shows experimental NPV; the circles are points computed from a nonlinear regression using the model in Table 11.7 for the parameters found: k°' = 8.1 x 1(T3 cm s-1, id = 363.7 /j.A, E<" = -0.261 V vs. SCE, a = 0.28. (Reproduced with permission from [10], copyright by the American Chemical Society.)

tions of the regression were less than the estimated absolute error in the data of ±0.5% of id.

The NPV results for Mb-DDAB films are in good agreement with those obtained from cyclic voltammetry (CV) by conventional peak separation analysis [1, 2], Nonlinear regression of NPV data for Mb-DDAB films has the advantage over the CV peak separation method of providing a direct test of each voltammogram against the model. Pulsewidths <10 ms were required for reliable k°' values, and longer pulsewidths gave reliable D' values. Nonlinear regression analyses of CV data for Mb-DDAB by using

Figure 11.12 The NPV at a 30 ms pulsewidth of Mb-DDAB film on PG electrode in pH 5.5 buffer. The line shows experimental NPV; the circles are points computed from a nonlinear regression using the model in Table 11.7 for the parameters found: id = 41.3 (jlA, E°' = -0.162 V vs. SCE (k was not obtainable for this reversible data, see the text). (Reproduced with permission from [10], copyright by the American Chemical Society.)

Figure 11.12 The NPV at a 30 ms pulsewidth of Mb-DDAB film on PG electrode in pH 5.5 buffer. The line shows experimental NPV; the circles are points computed from a nonlinear regression using the model in Table 11.7 for the parameters found: id = 41.3 (jlA, E°' = -0.162 V vs. SCE (k was not obtainable for this reversible data, see the text). (Reproduced with permission from [10], copyright by the American Chemical Society.)

the regression-simulation method were not successful because of the difficulty of modeling the large, nonlinear background currents [10].

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