## B1 Reversible Electron Transfer Single Potential Step

In principle, it should be possible to pulse the potential to values for which conversions of O to R, or R to O, are rapid and diffusion controlled. The diffusion coefficient can be determined from a single potential step

Table 12.1 Model for Reversible Electron Transfer in Single Potential Step Chronocoulometry [2, 3]

Assumptions: Reversible electron transfer, linear and edge diffusion Regression equation:

2(0 = b0 + b^112 + b2t bo = Qai, b, = 2FADmCn-y2; b2 = aFADC(itr)-m

Qii = double layer charge; F = Faraday's constant, A = electrode area; D = diffusion coefficient; C = concentration of reactant; a = constant accounting for nonlinear diffusion; and r = radius of disk or spherical electrode Regression parameters: Data:

Special instructions: Compute D from b\. background, especially on solid electrodes, may need subtraction experiment of this sort. The semi-infinite linear diffusion model for a solid disk or mercury drop (spherical) electrode with a correction for nonlinear diffusion is given in Table 12.1. Although linearization of the model is often used to analyze chronocoulometric data, this means that the nonlinear diffusion term must be ignored, which can lead to significant errors [2, 4].

The characteristic response of the model in Table 12.1 is shown in Figure 12.2. The single-step response is shown along with that for the reversible double potential step experiment to be discussed later. In this chapter, we shall consider the charge generated on the forward potential pulse to be Figure 12.2 Theoretical responses for an arbitrary reversible, diffusion-controlled electrochemical reaction. Forward response for single potential step is shown over 50 ms. Forward and reverse responses are shown for a double potential step and a switching time (t) of 25 ms. In the latter case, the forward response is observed for only 25 ms, where the reverse response begins.

Figure 12.2 Theoretical responses for an arbitrary reversible, diffusion-controlled electrochemical reaction. Forward response for single potential step is shown over 50 ms. Forward and reverse responses are shown for a double potential step and a switching time (t) of 25 ms. In the latter case, the forward response is observed for only 25 ms, where the reverse response begins.

positive in sign. In this way, the models presented are applicable to both oxidations and reductions without changes in signs.

If the charging of the double layer at the electrode is the only component of background charge, then this model can be used without background subtraction. This is sometimes the case for mercury electrodes , but background subtraction is usually necessary for solid electrodes . Evaluations showed that the background correction was most important for glassy carbon, less so for platinum, and could often be omitted for carbon paste electrodes. Background corrected data can be analyzed with the model in Table 12.1, realizing that the parameter b0 is now AQdi, which represents the difference between electrode double layer charges in the electrolyte and in the solution containing the analyte. This term remains because Q& in the presence and absence of solutes may be different.

The importance of background subtraction on solid electrodes is illustrated by a study of the reduction of the Co(II) corrin complex vitamin B|2r . In acetonitrile/water (1:1) buffered with phosphate at pH 2-3, the Co(II)L form of the vitamin undergoes the following reaction at glassy carbon electrodes:

Co(II)L + e" ^ Co(I)L E°' = -0.77 V vs. SCE. (12.3)

The heterogeneous rate constant for this reaction in 0.02 cm s_1 and a single potential pulse to a value well negative of E°' would be expected make the reaction quite rapid.

Figure 12.3 shows the results of single potential step experiments to -1.0 V on a glassy carbon electrode in solutions of vitamin B12r and in the buffer solution used to dissolve it. This figure suggests that the background charge is a large component of the response curve for vitamin B)2r. From

 Species Method Data Electrode' KfD, cm2 s"1 Ref. Vitamin B12r» CV I VS. V GC 2.7 [31 Vitamin B12r" Single-step CC Raw Q vs. t GC 11.5  Vitamin B12r» Single-step CC Background GC 2.3 13] Corrected Q vs. t T1(I)/0.1 M HCl Polarography h DME 15.5 P] T1(I)/0.1 M HCl Double-step CC Raw Q vs. i Hg drop 15.2 ± 0.7 12] U(VI)/0.1 M HCl Polarography h DME 6.5  U(VI)/0.1 M HCl Double-step CC Raw Q vs.i Hg drop 6.5 ± 0.2 12]

" In pH 2.3-2.4 phosphate buffer in 1:1 acetonitrile/water. b Electrodes: GC = glassy carbon; DME = dropping mercury.

" In pH 2.3-2.4 phosphate buffer in 1:1 acetonitrile/water. b Electrodes: GC = glassy carbon; DME = dropping mercury.

7.00

3.50

0.00

7.00

3.50 0.00 0.05 0.10 0.15 0.20 0.25

Figure 12.3 Single potential step chronocoulometry of l mM vitamin Bni in pH 2.4 phosphate buffer in water/acetonitrile (1:1) E, = -0.35 V vs. SCE; Ef= -1.0 V vs. SCE: (a) raw data for 1 mM vitamin B]2r; (b) background charge for solution not containing vitamin B12r. (Reprinted with permission from , copyright by VCH.)

Table 12.2, we see that when the raw chronocoulometric data were analyzed by using the model in Table 12.1, a value of the diffusion coefficient (D) much larger than that obtained by cyclic voltammetry was obtained. However, when the background subtracted data for vitamin B12r were analyzed, a value similar to that from CV was obtained. An excellent fit of the reversible model to the data was obtained (Figure 12.4). This example Figure 12.4 Chronocoulometry of 1 mM vitamin B12r in pH 2.5 phosphate buffer in water/ acetonitrile (1:1) after background subtraction. = -0.35 V vs. SCE; Ef = -1.0 V vs. SCE. Points are experimental data; line results from fit onto reversible model, Table 12.1. (Reprinted with permission from , copyright by VCH.)

Figure 12.4 Chronocoulometry of 1 mM vitamin B12r in pH 2.5 phosphate buffer in water/ acetonitrile (1:1) after background subtraction. = -0.35 V vs. SCE; Ef = -1.0 V vs. SCE. Points are experimental data; line results from fit onto reversible model, Table 12.1. (Reprinted with permission from , copyright by VCH.)

illustrates the importance of background subtraction when using solid electrodes with chronocoulometry to obtain diffusion coefficients.