Nanoelectrochemistry: Fundamentals and Applications in Biology and Medicine - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 3

diffusion length being much larger than the dimension of the elec-
trode) that came with the advent of UMEs will be further amplified
as the electrode is made smaller still. While this is undoubtedly
true, it is merely one among many other interesting possibilities
that result from nanoscale electrodes.
Besides the critical dimension of the electrode itself, two other
crucial scales are the double-layer thickness (or Debye length ( vide
infra )) and the number of molecules being probed at the electrode.
An interesting question is what happens when the size of the elec-
trode is of the same order or smaller than the Debye length. For a
typical 0.1 M, 1:1 electrolyte at 25qC, the Debye length is about 1
nm. It is thus readily apparent that in order for the scale of the
electrode to approach that of the double layer thickness, at least
one dimension of the electrode will have to be on the order of
1 nm! This points to the fundamental difficulty in approaching
truly nanoscale phenomena via the means of electrochemistry.
Another interesting scale that opens up for investigation, particu-
larly in the context of nano-gap electrodes, is the number of mole-
cules being probed. As electrode dimensions shrink, it becomes
possible to utilize them to electrochemically detect molecules in
and across confined spaces such as membranes and cells. Thus,
when dealing with a small, finite number of molecules, one enters
a regime where the discreteness of individual molecules cannot
always be ignored. The culmination of this scale is the single-
molecule limit where individual molecules are probed, and inter-
esting dynamical properties masked by ensemble averages can be
revealed.
The present chapter is structurally organized on the basis of
these disparate scales. Although in all instances our focus will be
on nano-sized electrodes, we start off with the classical regime,
wherein the Debye length is still shorter than the dimension of the
electrode and ensemble averages of molecules are being probed.
We briefly introduce some key concepts related to the double layer,
mass transport and electrode kinetics and their dependence on the
dimension and geometry of the electrode. We review various fab-
rication schemes utilized in making nano-sized electrodes, and
discuss the inherent challenges in characterizing them accurately.
We then move to discuss the mesoscopic regime—dimensions in
which one or more of the assumptions of the classical regime
break down. In particular, we discuss what happens when the De-