Nanoelectrochemistry: Fundamentals and Applications in Biology and Medicine - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 9

This occurs because, in this case, both the area A, and the mass
transport parameter b, are proportional to R 2 . Nonetheless, as dis-
cussed above, isotropic downscaling of the device dimensions also
leads to enhanced mass transport, since in this case the parameter l
is also scaled down.
The above discussion was meant as a simple introduction to
BV kinetics at electrodes with non-trivial geometries. Strictly
speaking, this treatment only holds for cases where the symmetry
of the electrode is such that the concentrations at the electrode sur-
face, C O e and C R e , are uniform over the electrode surface. In cases
where this is not strictly true, such as the system of Eq. (10), a
slight numerical error is introduced (which becomes increasingly
negligible as l / R increases in that particular example). For a far
more general treatment that extends to non-uniform current densi-
ties, we refer the reader to the work of Oldham. 19

2. Experimental Approaches to Nanoelectrochemistry

( i ) Fabrication of Nanoelectrodes

As mentioned in the introduction, the efforts to miniaturize
electrodes began in the early 1980s with the advent of microelec-
trodes and, later, ultra-microelectrodes (UMEs). 20,21
Many of the advantages that accrued from shrinking electrode
sizes from millimeter to micrometer dimensions are also expected
to hold as the dimensions are further reduced into the nanometer
regime. Nanoscale electrodes allow the extension of electrochemi-
cal measurements into new realms of space (cells, nanogaps, etc.)
and time. The uncompensated resistance, R u , scales with 1/ r , where
r is the radius of the electrode, and the capacitance scales with the
area ( r 2 ). Thus, the RC time constant of the cell scales with r and,
hence, reduces with smaller electrode sizes. With electrodes of
r ~ 100 nm, one can in principle reduce the cell time constant to
lower than 1 ns. Further, the complications arising from uncom-
pensated solution resistance, iR u , are significantly minimized. This
feature makes it easier to do electrochemical experiments in media
of low conductivity such as highly resistive organic solvents and
solutions devoid of any supporting electrolyte. Lastly, the high