14140 J. Phys. Chem., Vol. 100, No. 33, 1996
Demaille et al.
In this case, when the tip approaches the substrate, the tip current
decreases as a result of the hindered diffusion of A to the
electrode surface. The approach curve is then identical to that
corresponding to a two-electron pure negative feedback.
For intermediate values of K, the approach curve is located
between the limiting curves corresponding to the one-electron
positive feedback (upper limit at short tip-substrate separation)
and the n-electron (1 < n e 2) negative feedback (lower limit
at infinite tip-substrate separation). As the tip approaches the
substrate, a competition is established between the diffusion of
B across the gap and the rate of the homogeneous chemical
reaction. This diffusion time is related to the tip-substrate
distance rather than to the electrode radius and is defined by
d2/D. At very close tip-substrate separation (when d2/D ,
1/k) the flux of B leaving the electrode surface reaches the
substrate surface before reacting, and it is therefore entirely
converted into an equal flux of A that is fed back to the tip.
The approach curve then tends toward the upper dashed curve
corresponding to a pure one-electron positive feedback. The
portion of the approach curve corresponding to the transition
between the n-electron (1 < n e 2) negative feedback and the
one-electron positive feedback contains the kinetic information.
As can be seen in Figure 2a, such a transition can always be
observed no matter how high the value of K if the tip-substrate
distance is made small enough. However, in our experience,
the minimum dimensionless tip-substrate separation routinely
attainable is about d/a ) 0.2-0.1. So evaluating the maximum
kinetic constant that can be measured by the SECM technique
in this case means evaluating the minimum deviation from the
negative feedback behavior that can be observed for d/a ≈ 0.1.
From Figure 2a, one can estimate that this corresponds to about
K ) 50, so the maximum value of k measurable with an
electrode of radius a is given by k ) 50D/a2.
Figure 3. ECE pathway. Theoretical variation of the dimensionless
tip and substrate current with the tip-substrate dimensionless distance
d/a for several values of K ) ka2/D: K ) 1 (]), 2 (4), 5 (O), 10 (0),
20 (3), and 50 ([). Part a shows the tip current, where the upper dashed
line represents the one-electron pure positive feedback (K ) 0). Part b
shows the substrate current, where the dashed line represents the one
electron pure positive feedback. The inset shows the substrate current
for K ) 100.
Figure 2b presents the variation of the substrate current with
the tip-substrate separation (i.e., a tip generation-substrate
collection experiment). The main feature of this variation is
that the substrate current remains equal to zero until the tip is
close enough for species B to reach the substrate and be
oxidized. The substrate current is therefore either equal to zero
or of the opposite sign of the tip current. As the tip-substrate
separation is made smaller, the substrate current tends toward
the value corresponding to the one-electron positive feedback
represented by the dashed line in Figure 2b.
separation, the substrate current has the same sign as the tip
current because the dominant electrochemical reaction at the
substrate is the reduction of C. As the tip approaches the
substrate, the oxidation of B occurs to a greater extent, and at
a certain distance, these two currents cancel one another. At a
shorter tip-substrate distance, the oxidation of B dominates and
the substrate current is of the opposite sign to the tip current.
One can therefore consider that the chemical reaction is “sensed”
at a much greater tip-substrate separation in the ECE case
through the production of the species C, which has, unlike in
the DISP1 case, a long lifetime and must diffuse to one of the
electrodes to be consumed. This change of sign of the substrate
current is not observed in the DISP1 case and can therefore be
used as a powerful experimental diagnostic to establish the
occurrence of an ECE pathway.
From the approach curves presented in Figure 3, one can
estimate that the maximum value of the chemical rate constant
that is possible to measure in the ECE case is about the same
as in the DISP1 case, ca. k ) 50D/a2. If the only purpose is to
discriminate between an ECE and a DISP1 pathway, however,
this can be achieved for much faster chemical reactions because,
in the ECE case, the substrate consumes the species C at large
tip-substrate separation, even for very large values of K (see
the inset in Figure 3b, where even for K ) 100, the substrate
current is clearly greater than zero for 0.2 < d/a e 1.6).
ECE Case. Typical tip and substrate currents corresponding
to the ECE case are presented in Figure 3. At long tip-substrate
separation, the n-electron (1 < n e 2) tip current decreases with
decreasing tip-substrate distance as a result of the hindered
diffusion of A. In this part of the approach curve, the tip current
for the ECE case is, however, always smaller than the one
obtained in the DISP1 case for a given value of K, as illustrated
in Figure 4. The reason for this is that, as shown in Figure 1,
not only does species C diffuse back to the tip to exchange the
second electron, but it can also exchange this second electron
with the substrate, leading to an overall tip current that is smaller
than the expected n-electron (1 < n e 2) negative feedback
current (see Figure 4). This characteristic variation of the tip
current with the tip-substrate distance can therefore be used
to discriminate between an ECE and a DISP1 pathway. As in
the DISP1 case, when the tip is brought closer to the substrate,
the current tends toward the value corresponding to one-electron
positive feedback.
Another particularly interesting consequence of the ability
of C to be reduced at the substrate is that, for the ECE case, the
substrate current changes sign as the tip-substrate separation
decreases (see Figures 3 and 4). At long tip-substrate