Analytical Chemistry Chemical Cytometry Quantitates Superoxide

Figure 4. Comparison between simulated (curves) and experimental (symbols) steady-state concentration profiles along the vertical axis of
symmetry at disk electrodes of different radii when the electrode potential is poised on the oxidation plateau of Fe(CN)6 4- . Concentration profiles
simulated without (dashed curves) or with (solid curves) natural convection (δconv ) 200-250 µm). Experimental concentration profiles of the
substrate Fe(CN)6 4- (0) and product Fe(CN)6 3- (O). t ) 60 s. [Fe(CN)6 4- ] ) 10 mM in 1 M KCl.
The diagram is reported in Figure 3A, where the zones above
and below this limit correspond to the control of convection and
diffusion, respectively. In the lower zone, the equality between
eqs 7 and 10 discriminates by a vertical line located at r0/(πDt) 1/2
) 4/π two other domains where planar diffusion (i.e., r0/
(πDt) 1/2 > 4/π) and quasi-hemispherical diffusion (i.e., r0/
(πDt) 1/2 < 4/π) dominate.
One must note that this diagram is independent of the model
of natural convection since δ was calculated without considering
eq 6 and by only assuming δ ) δconv. In this context, the model
enables the transitions between the three regimes of the
diagram to be determined. For this purpose, the model is used
to evaluate δ and to compare its value to a given reference
thickness, δref, predicted by considering only one specific
regime: (1) δref ) δdiff for pure diffusion control without any
influence of convection, (2) δref ) δconv, (3) δref ) δplanar for
planar diffusion with δplanar ) (πDt) 1/2 , and (4) δref ) δhemisph
for hemispherical diffusion with δhemisph ) πr0/4. The transition
from one of these specific regimes to the others may then be
estimated by setting a relative threshold on δ such as
Note that eq 12 is equivalent to
|δ - δref |
) 0.1 (12)
δ
|
i - iref i | ) 0.1 (13)
ref
where iref is the reference current obtained from eq 8 with
i ref )( nFADc°
δ ref
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