handbook of modern sensors

508 17 Chemical Sensors
The equivalent conductance of the solution at any concentration, C in mol/L or any
convenient units, is given by
= 0 − βC 0.5 , (17.5)
where β is a characteristic of the electrolyte and 0 is the equivalent conductance of
the electrolyte at an infinite dilution.
Measurement techniques of electrolytic conductance by an electrochemical conductivity
sensor has remained basically the same over the years. Usually, a Wheatstone
bridge (similar to Fig. 17.4) is used with the electrochemical cell (the sensor) forming
one of the resistance arms of the bridge. However, unlike the measurement of
the conductivity of a solid, the conductivity measurement of an electrolyte is often
complicated by the polarization of the electrodes at the operating voltage. A faradic
or charge-transfer process occurs at the electrode surfaces. Therefore, a conductivity
sensor should be operated at a voltage where no faradic process could occur. Another
important consideration is the formation of a double layer adjacent to each of the
electrodes when a potential is imposed on the cell. This is described by the so-called
Warburg impedance. Hence, even in the absence of the faradic process, it is essential
to take into consideration the effect of the double layers during measurement of
the conductance. The effect of the faradic process can be minimized by maintaining
the high cell constant L/A of the sensor so that the cell resistance lies in the region
between 1 and 50 k. This implies using a small electrode surface area and large interelectrode
distance. This, however, reduces the sensitivity of the Wheatstone bridge.
Often the solution is in the use of a multiple-electrode configuration. Both effects of
the double layers and the faradic process can be minimized by using a high-frequency
low-amplitude alternating current. Another good technique would be to balance both
the capacitance and the resistance of the cell by connecting a variable capacitor in
parallel to the resistance of the bridge area adjacent to the cell.
17.4.6 Amperometric Sensors
An example of an amperometric chemical sensor is a Clark oxygen sensor which was
proposed in 1956 [10,11]. The operating principle of the electrode is based on the
use of an electrolyte solution contained within the electrode assembly to transport
oxygen from an oxygen-permeable membrane to the metal cathode. The cathode
current arises from a two-step, oxygen-reduction process that may be represented as
O 2 + 2H 2 O + 2e − → H 2 O 2 + 2OH −
H 2 O 2 + 2e − → 2OH − .
(17.6)
Figure 17.7A shows the membrane which is stretched across the electrode tip, allowing
oxygen to diffuse through a thin electrolyte layer to the cathode. Both anode and
cathode are contained within the sensor assembly, and no electrical contact is made
with the outside sample. A first-order diffusion model of the Clark electrode is illustrated
in Fig. 17.7B [11]. The membrane–electrolyte–electrode system is considered