Analytical Chemistry Chemical Cytometry Quantitates Superoxide

The zone diagram built from eq 12 or 13 is reported in Figure
3B. Thus, three curves (curves 2-4) delineate a new domain
corresponding to a mixed regime between the limiting ones
previously identified (Figure 3A). In particular, the transitions from
hemispherical diffusion to convection (i.e., vertical displacement
on the diagram) and from hemispherical diffusion to planar
diffusion (i.e., horizontal displacement) are relatively broad since
they occur approximately over 2 orders of magnitude on the r0/
δconv and r0/(πDt) 1/2 scales, respectively. Only the transition
from planar diffusion to convection is very sharp. Indeed, as
soon as δplanar ≈ δconv, the diffusion layer reaches its steadystate
limit and mass transport is fully controlled by convection.
In contrast, when the condition δz ≈ δconv is met for hemispherical-type
diffusion, the layer may still expand laterally
along the r axis until reaching its steady-state limit (see Figure
2A-C). This latter condition corresponds to curve 1 in Figure
3B when |δ - δdiff|/δ ) 0.1 or |i - idiff|/|idiff| ) 0.1. It allows
delineating the upper zone of the diagram where convection
starts to interfere in the mass transport.
A chronoamperometric experiment can be represented on the
diagram by a horizontal straight line described from the right to
the left when the time duration increases. According to the size
of the electrode, r0, and thickness, δconv, the nature of the steadystate
regime reached at longer time may be different. On the
one hand, if log(r0/δconv) > 0.95, a sharp transition from planar
diffusion to convection occurs. On the other hand, if log(r0/
δconv) < -0.7, a broad transition with a mixed regime from
planar diffusion to quasi-hemispherical diffusion operates
without any influence of natural convection. When log(r0/
(πDt) 1/2 ) < -0.75, a steady-state regime is always observed
though its nature (diffusional or convective) only depends on
the ratio r0/δconv.
Under given experimental conditions (i.e., the same position
of the electrode in the cell, temperature, viscosity of the electrolyte,
environment, etc.), δconv is approximately constant so that the
mass transport regime under steady state depends only on the
electrode dimension. This was checked experimentally by
mapping diffusion layers in the vicinity of electrodes of various
radii. Figure 4 shows the concentration profiles along the vertical
axis of symmetry of the electrodes for both the reactant and
product. δconv was evaluated independently by chronoamperometry
at a large electrode 18 and was found to range from 200
to 250 µm. It was thus possible to compare the experimental
data with concentration profiles predicted with or without
natural convection. A very good agreement was observed in
Figure 4 whatever the size of the electrodes between experimental
data and predictions issued from the model when natural convection
was taken into account. Alterations on the concentration
profiles due to convection were apparent as soon as r0 ) 25 µm.
The experimental conditions pertaining to each concentration
profile in Figure 4 are reported as symbols in the zone diagram
of Figure 3B. According to the threshold previously defined with
|δ - δhemisph|/δ ) 0.1 or |i - ihemisph|/|ihemisph| ) 0.1, the results
show that a hemispherical diffusion regime was reached for r0
) 12.5 and 25 µm while a mixed regime was achieved for the
other radii (r0 ) 62.5-500 µm).
These experimental data validate the predictions of the present
model, yet they involved only the effect of natural convection along
6938 Analytical Chemistry, Vol. 82, No. 16, August 15, 2010
Figure 5. Comparison between simulated (curves) and experimental
(symbols) steady-state concentration profiles at a disk electrode of
radius r0 ) 25 µm when the electrode potential is poised onto the
oxidation plateau of FeCH2OH. (A) Experimental concentration profiles
of the product FcCH2OH + along the vertical axis of symmetry (circles).
(B) Experimental concentration profiles of FcCH2OH + along the r axis
at various vertical distances z: z ) 6(O), 16 (0), 26 (]), 36 (×), 46
(+), and 56 µm (∆). The black area indicates the extent of the
electrode coordinates along the r axis. The concentration profiles are
simulated without (dashed curves) and with (solid curves) consideration
of the influence of natural convection (δconv ) 200 µm).
[FeCH2OH] ) 2 mM in 0.1 KNO3.
the axis of symmetry of the electrodes. Conversely, we showed
above (see Figure 2) that this effect is also effective along lateral
directions due to the compensation of transport between vertical
and lateral fluxes. In the following, we investigated this latter issue
experimentally by performing 2D imaging. Figure 5 reports the
mapping of concentration profiles established in the steady-state
regime along the z axis and r axis when r0 ) 25 µm. As in Figure
4, the concentration profiles were compared to the predictions
established with and without the influence of convection. Apart
from the good agreement obtained between the data and predictions,
these results clearly illustrate the fact that convection may
still alter the diffusion layers even when quasi-hemispherical
diffusion is expected to prevail (Figure 3B). In the present case,
the concentration profiles are distorted over distances z equivalent
to 10 times the electrode radius, r0. Simultaneously, the relative