Nanoelectrochemistry: Fundamentals and Applications in Biology and Medicine - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 31

3. QuantizationEffects
The double-layer and small-volume effects considered above were
mostly a consequence of employing electrode systems with na-
noscale critical dimensions. A separate class of mesoscopic effect
concerns redox species that are themselves mesoscopic entities.
The most common example is small clusters of metallic or semi-
conducting materials commonly referred to as quantum dots.
While the composition of these particles is similar to that of the
corresponding bulk materials, their small size can lead to qualita-
tively new behavior.
The free energy cost for adding an electron to a bulk conduc-
tor is given by the chemical potential for electrons in the conductor,
P. Adding electrons to a piece of conducting material leads to an
increase in P because the electrons in the conductor tend to occupy
the quantum states with the lowest energy; adding additional elec-
trons requires accessing electronic states with ever higher energy.
Extracting electrons similarly leads to a decrease in P. In a macro-
scopic conductor, the difference in energy between quantum states
is, however, extremely small. As a result, the shifts in P caused by
charge transfer normally remain small and do not need to be taken
into account in describing experiments. As the dimensions of the
conducting particle are reduced, however, this simplification ceas-
es to be valid. There are two main mechanisms through which this
occurs.
First, confinement of the electrons to smaller particles leads to
an increase in the energy level spacing. This is directly analogous
to the classic particle-in-a-box problem from quantum mechanics,
and leads to the energy level spacing scaling as V -1 , where V is the
volume of the particle. For small enough particles, the energy-level
spacing becomes comparable to k B T . When this occurs, the quanti-
zation of electronic levels becomes manifest in the form of discrete
states available for reduction or oxidation rather than a continuum
of states as in a conventional conductor. Electron transfer for each
of these discrete states then occurs at a different formal potential in
voltammetric experiments.
Second, reducing the dimensions of conducting particles leads
to discretization of the voltammetric response through the Cou-
lomb blockade effect, also commonly referred to as quantized
double-layer (QDL) charging in the electrochemical context. This