Biomedical Engineering Reference
In-Depth Information
proximation when the dot is very small, this is not the case here
since the dot instead consists of a macroscopic volume of fluid. A
simple estimate for the self-capacitance of a 10 mL beaker of fluid
in a shielded enclosure yields a value in the range 1-10 pF, which
makes it by far the dominant contribution to
C
tot
. The predicted
peak spacing for Coulomb blockade is therefore several orders of
magnitude smaller than what was observed in the experiment. In
our opinion, this analysis indicates that the experimental observa-
tions of Ref. 127 cannot therefore be explained by the double-
junction Coulomb blockade model, and that the actual mechanism
remains undetermined. A hint of an alternative interpretation is
perhaps provided by the observation that the observed '
E
also
approximately corresponds to the potential needed to add a single
ion to the double layer at one of the electrodes.
IV. SINGLE-MOLECULE LIMIT
The ability to study single molecules is desirable for several rea-
sons. Studies of individual (macro)molecules at the nanoscale ena-
ble the unraveling of static and dynamic heterogeneities that are
characteristic at this scale. Static heterogeneity refers to the situa-
tion that static properties of different molecules constituting an
ensemble might be very different. Dynamic heterogeneity is used
to describe the time-dependent fluctuation of a property of an indi-
vidual molecule. Both these heterogeneities result in a broad dis-
tribution of molecular properties of ensembles.
128
Ensemble-
averaged measurements, as a consequence, probe only the averag-
es (or first moments) of these distributions. By contrast, single-
molecule measurements enable the construction of the entire prob-
ability distribution function of a particular parameter and all higher
moments, thereby revealing the full range of properties and their
relative significance.
129
From a metrology point of view, single
molecule measurements represent the ultimate sensitivity in any
kind of measurement, thus obviating the need for any artificial
means for enhancement of the signal. Single molecule studies have
contributed much to physics and chemistry, and are currently be-
ing intensely employed to the study of biological problems.
130
The advent of single molecule techniques owes to several
spectacular advances in the 1980s and -90s. In the 1980s, Binnig
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