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