handbook of modern sensors

17.4 Direct Sensors 509
(A)
(B)
Fig. 17.7. Clark electrode (A) and the first-order one-dimensional model (B) of the oxygen
tension distribution throughout the system. (Adapted from Ref. [11].)
to act as a one-dimensional diffusion system with the partial pressure at the membrane
surface equal to the equilibrium partial pressure p 0 and that at the cathode equal to
zero. It can be shown that the steady-state electrode current is given by
I ≈ 4Fa mD m p 0
x m
, (17.7)
where A is the electrode area, αm is the solubility of oxygen in the membrane, F is
the Faraday’s constant, D m is the diffusion constant, and x m is the thickness of the
membrane. It should be noted that the current is independent of the electrolyte thickness
and diffusion properties. A Teflon ® membrane is used as an oxygen-permeable
film. We may define the sensor’s sensitivity as a ratio of the current to the oxygen
partial pressure:
S = I . (17.8)
p 0
For example, if the membrane is 25 µm thick and the cathode area is 2 × 10 −6 cm 2 ,
then the sensitivity is approximately 10 −12 A/mm Hg.
An enzymatic-type amperometric sensor can be built with a sensor capable of
measuring the relative oxygen deficiency caused by the enzymatic reaction by using
two Clark oxygen electrodes. The operating principle of the sensor is shown in Fig.
17.8. The sensor consists of two identical oxygen electrodes, where one (A) is coated
with an active oxidize layer and the other (B) with an inactive enzyme layer. An
example of the application is a glucose sensor, where inactivation can be carried out
either chemically, by radiation, or thermally. The sensor is encapsulated into a plastic
carrier with glass coaxial tubes supporting two Pt cathodes and one Ag anode. In the
absence of the enzyme reaction, the flux of oxygen to these electrodes and, therefore,
the diffusion-limiting currents are approximately equal to one another. When glucose
is present in the solution and the enzymatic reaction takes place, the amount of oxygen
reaching the surface of the active electrode is reduced by the amount consumed by
the enzymatic reaction, which results in a current imbalance.