Biomedical Engineering Reference
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from predicted classical theories of mass transport have been
qualitatively attributed to dynamic changes within the diffuse dou-
ble layer when the size of the diffusion region becomes compara-
ble to O
d
. Similarly, Krapf et al.
70
studied oxidation of TMAFc
+
and found that transport to sub-10 nm electrodes increased sub-
linearly with concentration of the charged TMAFc
+
. A similar de-
pendence was not observed for the neutral FcCH
2
OH. This obser-
vation is not captured by the Poisson-Nernst-Planck equations, and
it was suggested that the discrepancies originate from the very
high current densities at nanoelectrodes.
2. Small Volumes
A second way in which nanometer-scale systems can lead to quali-
tatively different behavior is in cases where very small volumes
are being probed. Once again, this can influence electrochemical
experiments in two different manners.
First, liquid-filled cavities with nanometer-scale dimensions
have a higher surface-to-volume ratio than larger systems with the
same geometry. Consequently, surface processes have a higher
propensity to influence the properties of the bulk solution present
in the cavity. In particular, changing the potential of an electrode
can lead to different level of adsorption as well as the localization
of charged species near the electrode surface through double-layer
formation. At sufficiently high surface-to-volume ratios, this can
lead to significant, potential-dependent changes in concentration in
the solution if the nanoscopic volume is not connected to a bulk
reservoir.
A dramatic manifestation of this effect was reported by Sun
and Mirkin,
121
who studied redox cycling of FcCH
2
OH
+/0
in nano-
scopic cells at different concentrations of KNO
3
supporting elec-
trolyte. Significant variations in the limiting current were already
observed when the salt concentration was decreased to 100 times
that of the redox species, and the wave disappeared entirely for a
salt concentration 3 times that of the redox species. Even more
pronounced changes in the limiting current were observed for the
Ru(NH
3
)
6
3+/2+
couple. These observations were attributed to deple-
tion of ions in solution due to the charging of the double layers.
Once the bulk solution in the cell is essentially depleted of ions,
the electric field penetrates from the electrodes into the bulk of the
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