Nanoelectrochemistry: Fundamentals and Applications in Biology and Medicine - Applications of Electrochemistry and Nanotechnology in Biology and Medicine - page 29

() De it () N t (13)

2

z

In this limit, measuring fluctuations in the faradaic current pro-
vides a way to directly resolve the particle number fluctuations.
Using thin-layer cells with electrode spacing z ~ 50 nm, we
recently observed these fluctuations. With sensitive electronics,
such that extrinsic sources of noise are minimized, the equilibrium
statistical fluctuations can easily become the dominant source of
noise in these systems. In this case they can be observed with
one's bare eyes on an oscilloscope screen; representative time
traces are shown in Fig. 5a . The figure also illustrates an important
signature of the fluctuations: because the reduction current at one
electrode is essentially identical to the oxidation current at the oth-
er electrode, the fluctuations in the two currents are perfectly anti-
correlated, contrary to what would be observed if the fluctuations
were caused by extrinsic noise in the two (independent) measure-
ment circuits.
Importantly for applications, statistical fluctuations thus place
a fundamental limit on the noise properties of electrochemical sen-
sors based on redox cycling. On the other hand, they also provide
an opportunity for observing the time evolution of microscopic
diffusive trajectories. Two types of information are available from
the noise time traces. First, the amplitude of the fluctuations is
dictated by Poisson statistics and is therefore universal (as long as
the molecules are essentially non-interacting). The scaling of the
amplitude with ¢ N ² 1/2 is directly verifiable, as shown in Fig. 5b .
Second, the speed at which the fluctuations take place depends on
how fast mass transport takes place between the inside and outside
of the cavity. For example, doubling the diffusion constant of the
redox molecules preserves the typical shape of the fluctuations in
i ( t ), but compresses the time axis by a factor of 2. Additional quan-
titative information can be gleaned from a detailed analysis of the
spectral density of the noise. 122 Because of the analogy with Fluo-
rescence Correlation Spectroscopy (FCS), we refer to this ap-
proach as Electrochemical Correlation Spectroscopy (ECS).