Nanoelectrochemistry: Fundamentals and Applications in Biology and Medicine - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 32

is a classical effect in the sense that quantum mechanics does not
play an explicit role; the effect arises solely from the fact that elec-
trons are discrete particles with a fixed charge e . Consider a quan-
tum dot in solution to which a single electron is added; in response,
the double layer around the particle adjusts itself to screen this
change in the charge. The electrostatic potential of the dot thus
changes by an amount ' E dot = - e / C tot , where C tot is the total ca-
pacitance between the quantum dot and its environment. The suc-
cessive addition of multiple electrons thus results in a correspond-
ing step-wise increase in the electrostatic potential of the dot with
respect to the solution. Furthermore, the change in electrostatic
energy stored in C tot due to electron transfer must ultimately be
supplied by the electrode. This leads to a corresponding shift in the
formal potential toward higher overpotential for the addition of
each successive electron. To a first approximation, the magnitude
of this shift is simply given by ' E | ' E dot = - e / C tot . Smaller sys-
tems have a smaller C tot ; once a system becomes sufficiently small
that |' E | | k B T / e , the different waves for each charge state can be
resolved in voltammograms.
Electron confinement and Coulomb blockade effects are not
mutually exclusive, and in practice they often coexist in electro-
chemical experiments. As a rough approximation, C tot scales ap-
proximately with the surface area of the dot or, equivalently, as
V -2/3 . Therefore, confinement, which as we have seen scales as V -1 ,
tends to dominate for the smallest particles. For intermediate size
nanoparticles, on the other hand, Coulomb blockade can become
the dominant effect. This is further facilitated by the layer of lig-
ands that is often necessary to stabilize conducting nanoparticles,
and which essentially acts as a non-conducting dielectric shell. The
increased distance between the conductor and the double layer in
solution leads to a smaller value of C tot and a corresponding in-
crease in the relevance of Coulomb blockade.
First reported in Au nanoparticle voltammetry in 1997, 124 ad-
vances in the preparation of monodisperse nanoparticles have ena-
bled increasingly sophisticated and quantitative studies of Cou-
lomb blockade in electrochemical systems. Its dramatic impact on
the properties of metal nanoparticles is illustrated in Fig. 6 , where
each of the 15 equally-spaced peaks corresponds to the transfer of
one additional electron per particle. The data also illustrate the
cross-over from pure Coulomb blockade behavior to more com-