Nanoelectrochemistry: Fundamentals and Applications in Biology and Medicine - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 20

the glass during cathodic scans in 0.5 M H 2 SO 4 and can be subse-
quently re-oxidized during anodic scans. While the spill-over ef-
fect is fundamentally interesting, it also illustrates that glass might
not be impervious to small molecules and ions. This could lead to
significant complications, especially through the double layer ef-
fects of the adsorbed ions on electrode kinetics.
A more reliable method for characterizing the shape and size
of electrodes involves the measurement of approach curves in an
SECM-type measurement. An approach curve is obtained by plot-
ting the tip current as a function of the tip-substrate distance as the
tip is moved a distance several tip diameters away towards the
substrate. Because the diffusional flux of molecules in the volume
between the nanoelectrode and the substrate is very sensitive to the
geometry of the electrode, one can obtain information about the
geometry of the electrode. Normally, the theoretical approach
curve is calculated numerically for both a conducting as well as an
insulating substrate, and the experimental curve is compared to the
theoretical curve to assess the accuracy of the expected geome-
try. 34, 102, 109
4. ExperimentalResults
As stated earlier, the shrinking of electrode dimensions is expected
to enable measurements in regimes which are not ordinarily acces-
sible through larger electrodes. Since we are dealing with the so-
called classical regime, we focus in this Section on results where
much of the conceptual framework that underpins our understand-
ing of macroscale electrodes continues to be relevant also at nano-
electrodes. As mentioned earlier, due to enhanced mass-transport
and consequently much higher current densities, nanoelectrodes
become sensitive to electrode kinetics. We recall from Eq. (7) that
the dimensionless rate constant Ȝ determines the relative im-
portance of heterogeneous electrode kinetics compared to mass
transport. As a rule of thumb, in the limit that Ȝ 10, the electron
transfer step becomes the rate-limiting step in the overall voltam-
metric response. For the case of a spherical electrode of radius r ,
O = k 0 r / D . Thus, for a typical value of diffusion constant D = 10 -5
cm 2 /s and an electrode of radius r = 10 nm, one can in principle
measure rate constants as high as k 0 = 100 cm/s. It is not surprising,
therefore, that the most extensive application of nanoelectrodes has