Electrochemical Detection - Waterborne Pathogens: Detection Methods and Applications - page 155

not depend on the amount of metal present at the electrode, the size of
the electrode, and the concentration of ions in the solution. Consequently,
potential is scale-invariant. On the contrary, the electrical current and
charge are extensive properties. They depend on the size of the system,
only the current and charge densities are intensive. As a consequence, one
cannot expect improved performance when scaling down a potentiomet-
ric technique, while modifications will occur for voltammetric, coulomet-
ric, and impedimetric techniques where an electrical current flowing in
the system is monitored.
Going back to cyclic voltammetry to illustrate the effect of scaling
on an electrochemical technique, one should recall from Section 6.3
that the measured current is limited by analyte diffusion at the electrode
surface. The electrode geometry dictates the mass transport to and from
the electrode surface. The Cottrell equation describes how the current
decays as a function of time. The current at electrode is a sum of both
planar and spherical diffusion, and the magnitude of each depends on
time and the size of microelectrode. Planar diffusion is predominant at
short times, while spherical diffusion is predominant at sufficiently long
times. Indeed, at short times, the size of the diffusion layer is smaller
than that of the electrode, and planar diffusion dominates even if the
electrode has been miniaturized. On the contrary, at longer times, the
dimensions of the diffusion layer exceed those of the electrode, and the
diffusion becomes hemispherical. In this configuration, the analytes dif-
fusing to the electrode surface come from the hemispherical volume (of
the reactant-depleted region) that increases with time. A miniaturized
electrode can then be defined as an electrode that has a characteristic
surface dimension smaller than the thickness of the diffusion layer (i.e.
between hundreds of nanometers to several microns) on the timescale
of the electrochemical experiment. This means that the time required
to attain a steady state (i.e. plateau in cyclic voltammograms instead
of peaks) strongly depends on the electrode dimensions. Miniaturized
electrodes enable the study of very fast kinetics. Furthermore, capaci-
tive current (Ic) decreases in proportion to decreasing area of the elec-
trode, while the steady-state faradaic current (If ) is proportional to its
characteristic dimension. Therefore, the If /Ic ratio, which represents the
signal-to-noise ratio of the technique, increases with the reciprocal of
the characteristic length. 33,34 Analysis of noise in electrochemical sys-
tems can be an extremely sensitive technique to monitor biosystems. 35
With a miniaturized electrode, the absolute current level is small. A first