Nanoelectrochemistry: Fundamentals and Applications in Biology and Medicine - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 17

py. Besides inherent limitations of SEM in the sub-10 nm regime,
the problem is compounded by the fact that the small electrode is
buried in a thick layer of insulating material (for example, glass,
wax, or electrophoretic paint), which complicates imaging due to
sample instability and charging issues. A way to circumvent this
issue is to deposit a thin metal layer on the insulating part of the
electrode, but this is difficult to accomplish selectively, and further
the contrast between the deposited layer and the metal electrode
has to be high enough to yield useful images.
In conjunction with SEM as a general tool, most approaches
to characterization of nanoelectrodes rely on indirect means that
involve measuring electrochemical responses of the electrodes to
quantify their geometry and size. Generally, it is common in cases
where the dimensions of an electrode are not known a priori to
determine them by measuring the diffusion-limited current, i lim .
For example, by assuming that the electrode is a shrouded hemi-
sphere, one can determine an effective radius for an electrode us-
ing the relation R eff = i lim /2S FDC R b . In the notation introduced
above, this is exactly equivalent to an experimental determination
of the parameter b , since b = i lim / FDC R b = 2S R eff . Compared to a
hemisphere, the limiting current at a disk-shaped electrode is i lim =
4FDC R b R . It has been argued that if a shrouded hemispherical
electrode is mistaken for a disc-shaped electrode, then the error in
the determined R eff is at most 2/S, and therefore the error in an
electrochemical experiment will rarely be greater than a factor of
~2. 30 While this may indeed not be a problem for spherical-
segment electrodes (e.g., sphere, hemisphere, cone or disk) of the
same radius, the complications for a recessed electrode can be
more significant.
Problems can potentially arise if the value of R eff is in turn
used to estimate the true area of the electrode using A = S R eff 2 for
use in Eq. (6). Any discrepancy between the real and assumed ge-
ometry is further magnified by squaring and can lead to significant
uncertainties in the measured heterogeneous rate constants. For
instance, consider the case of a lagooned electrode with an orifice
of radius r , and a disk-shaped electrode of radius R embedded in
the lagoon as depicted in Fig. 3 .