This model describes an electrochemical reactant that can be electrolyzed both while adsorbed on the electrode and by diffusion through the solution to the electrode. This can be expressed by the electron transfer reactions in Box 12.1. Both O and R are adsorbed on the electrode, but O is adsorbed to a greater extent than R. The model as used for nonlinear regression is presented in Table 12.5.

-3 ' ' <><>''<< ' • . ■ ■ i ■ . . .

Figure 12.6 Results of regression analysis for background subtracted chronocoulometric data (Ei = -0.20 V vs. SCE; E,= 0.40 V vs. SCE) for 0.2 mAi ferrocyanide on 0.1 M KC1, pH 12: (a) background subtracted experimental charge (O); line from fit onto diffusion-kinetic model (Table 12.4); (b) plot of relative residuals from the analysis. (Reprinted with permission from [3], copyright by VCH.)

The surface concentration of O (T0) is of prime importance in studies of adsorption on electrodes. Pointwise analysis of variance showed that, for values of t > 50 ms, the most information about T0 is contained in the first 25 ms after t = 0, and the first 25 ms after the potential switch at t = r

O + e ^ R |
(12.5) | |

Oads + e ^ Rads |
(12.6) |

Box 12.1 Reactant adsorption, reversible electron transfer.

Box 12.1 Reactant adsorption, reversible electron transfer.

Table 12.5 Model for Reversible Electron Transfer with Reactant Adsorption in Double Potential Step Chronocoulometry [2]

Assumptions: Reversible electron transfer, linear + edge diffusion; D0 + DR; reactant adsorbed, product dissolves in solution (can modify for reactant + product adsorbed) [2]; electrolysis of adsorb species and double layer charging occur instantaneously Regression equation:

Q(t < r) = b^t1'2 - (t - r1'2] + b2t + b,(r - t) + b4(2/jt) sin'^i/r)1'2 b0 = Qdi + nFATo, bt = 2nFADmCTT-m; b2 = aFAD 0C(Trr)112; b3 = aFADRC{nr)V2\ b4 = nFAT0 Qdt = double layer charge; F = Faraday's constant; A = electrode area; D0, DH are diffusion coefficients; C = concentration of reactant; a = constant accounting for nonlinear diffusion; and r = radius of disk or spherical electrode Regression parameters: Data:

Special instructions: Logical statements required in subroutine for computing Q(t): IF t < t THEN (use) Q(t) = Q(t < r) IF t > t THEN (use) Q(t) = Q(t > t) Use t s 25 ms for accurate r0 estimates [2]; for solid electrodes, background may need subtraction or consideration in the model; obtain f0 from b4

[2]. When data are equally spaced on the t axis, accurate estimates of T0 require r < 25 ms. Data with larger values of r can be analyzed successfully by using an analysis schedule that includes data grouped in the regions of greatest significance; that is, immediately after t = 0 and t = t.

The model in Table 12.5 was used to analyze data for Cd(II) ions adsorbed onto mercury electrodes from aqueous sodium thiocyanate/sodium nitrate solutions [2], Thiocyanate induces adsorption of Cd(II), and both adsorbed and diffusing Cd(II) are reduced to Cd(Hg). When 50-data point sets using only the time regions of highest T0 information content were analyzed, excellent fits were obtained (Figure 12.7). Agreement of D and r0 was found [2] with a previous study done using a linear plot approximation [6]. Some of the results are summarized in Table 12.6. When 50-data point sets were analyzed for r > 100 ms with equal spacing on the t axis, large systematic errors in r0 resulted from both nonlinear regression and linear plot methods.

The residual plot obtained from fitting an unknown set of chronocoulo-metric data with the reversible model in Table 12.3 can be used as a test for adsorption. Figure 12.8 shows such a plot resulting from a fit of data for Cd(II) on a mercury electrode onto the reversible model. The experimental points fall along the lines for the theoretical deviation plot obtained by fitting data computed from the adsorption model onto the reversible model. The characteristic shape of this deviation plot suggests the presence of adsorbed reactant. This can be confirmed by fitting the data with the adsorp-

Q, jjlC

Figure 12.7 Double potential step chronocoulometry of 1 mM Cd(II) in 0.8 NaN03/ 0.2 M NaNO,: experimental charge (•); line from fit onto adsorption model (Table 12.5). (Reprinted with permission from [2], copyright by the American Chemical Society.)

tion model in Table 12.5. The resulting residual plot from such an analysis is random (Figure 12.9), confirming the hypothesis suggested by Figure 12.8.

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