Nanoelectrochemistry: Fundamentals and Applications in Biology and Medicine - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 18

Figure 3. Sketch of a section of a disk electrode of
radius R , embedded in a lagoon with an orifice of
radius r .

The limiting current in the voltammogram will yield a value
of R eff | r, that corresponds to the radius of the orifice of the la-
goon. The area of the electrode, however, is S R 2 . Therefore, if the
true area is instead expressed as S r 2 , then the measured rate con-

2

R
kk r

§·

0 0 0

m

stant will be

¨ ©¹ , where

k is the measured rate con-

m

stant and k 0 is the true heterogeneous rate constant. It is readily
apparent that in the limit R >> r , the measured rate constant will
be highly overestimated. It has been argued that the unusually high
rate constant (220 cm/s) for ferrocene oxidation in acetonitrile
measured by Penner et al. 33 was likely an overestimation due to the
formation of a lagoon around the conductive tip of the nanoelec-
trode. 19, 107, 108
An ingenious approach to determining the electrode area was
employed by White and co-workers, 44 wherein the active areas
were determined by measuring the electrical charge ( Q ) associated
with oxidation of adsorbed bis(2,2'-bipyridine)chloro(4,4'-
trimethylenedipyridine)osmium(II) on Pt electrodes in fast-scan