Figure 12. 1 A hemispherical working electrode in cross section Figure 12.1 A hemispherical working electrode in cross section. The length d is the “superficial diameter” of the electrode, equal to πrhemi. Arrows show the direction taken by electroreactant on its way to the electrode surface, which has as area of A = 2πr2hemi.

Figure 12.2 The current predicted by equation 12:8 when a potential leap is applied to a hemispherical electrode of radius 10 μm. The sudden positive change in electrode potential causes the reaction R(soln) → e– + O(soln) to proceed with total transport polarization, so that R has zero concentration at the electrode. The R species is taken to have a bulk concentration of 1.00 mM and a diffusivity of 8 ; 10–10 m2 s–1.

Figure 12.3 Concentration profiles during potential-leap voltammetry at a hemispherical microelectrode. The concentration gradient close to the electrode (and hence the current) has become constant, though further away the concentration continues to deplete. The graphs illustrate equation 12:7 with the following values: rhemi = 10.0 μm, DR = 8  10–10 m2 s–1, t = 10 s and ∞.

Figure 12.4 Steady concentration profiles of the reactant and product at a hemispherical microelectrode following a potential step.

Figure 12.5 Logarithmic illustration of the reciprocal sum formula 12:20. On each diagram, the green line represents Ikin, the blue line represents Irem, and the red line represents Ilim. The fourth curve in each diagram logarithmically represents the reciprocal sum of the three straight lines. The three diagrams, scaled for α = ½, differ only in the magnitude of the reversibility index: (a) λ = 8, (b) λ = 1/2, (c) λ = 1/32.

Figure 12.6 Typical reversible, quasireversible and irreversible potential-step steady-state voltammograms from a hemispherical microelectrode. Each point represents a step to a different potential E. Data: cbR = 5 mM, DR = Do = 1 10–9 m2 s–1, rhemi = 5 μm, α = 0.5, λ’s as in Figure 12-5 corresponding to kº΄ values of 1.60 mm s–1, 0.100 mm s–1 and 6.25 μm s–1.

Figure 12. 7 Near-steady-state voltammetry Figure 12.7 Near-steady-state voltammetry. The red curve is obtained as the potential slowly becomes more positive. The blue curve is obtained after reversal, as the potential slowly returns to its starting value.

Figure 12. 8 A disk working electrode in cross section Figure 12.8 A disk working electrode in cross section. The length d is the “superficial diameter” of the electrode, equal to 2rdisk. Arrows show the direction taken by electroreactant on its way to the electrode surface, which has an area of A = πr2disk.

Figure 12.9 Different reversibility indices distinguish members of this family of α = ½ steady-state voltammograms. The λ of each curve differs by a factor of 2 from that of its neighbors. For λ ≥ 32, the reversible curves effectively overlap. For λ ≤ 1/32 the curves maintain their irreversible shape, but move to more positive potentials. The quasireversible curves are intermediate. This figure, as does 12-10, relates to steady-state voltammetry and is equally applicable to microhemispherical and rotating disk electrodes. The principles, though not the details, apply to microdisks and microelectrode arrays, too.

Figure 12.10 A logarithmic plot showing how, for three representative values of the transfer coefficient, the half-wave potential shifts away from Eh as the reversibility index decreases1231. The division of behavior into reversible, quasireversible, and irreversible regimes is very apparent in this graphical depiction.

Figure 12.11 Though the rotation speed may be varied only over a limited range, a plot of 1/I versus ω–1/2 provides a straight line of slope (ρ/η)1/6/vLFAcRD2/3 and intercept 1/Ikin. Repetition of the Koutecký-Levich experiment at a number of potentials provides access to a and to the term cited in 12:37.

Figure 12. 12 Anatomy of a one-electron reversible voltammetric wave Figure 12.12 Anatomy of a one-electron reversible voltammetric wave. The scaling of the abscissa is for 25ºC. Waves may be solely anodic as here, solely cathodic, or some of each, as in Figure 10-9.

Figure 12. 13 Anatomy of a reversible voltammetric peak Figure 12.13 Anatomy of a reversible voltammetric peak. The peak width is measured half-way to the summit. The peak has bilateral symmetry about the peak potential.

Figure 12.14 The reversible wave, the reversible hybrid, and the reversible peak.

Figure 12.15 Anatomy of a reversible hybrid.