W C Maskell
pumping time. Clearly the response time in this mode cannot be shorter than the cycle time.
These sensors employ appropriate ionic conductors in both the pumping (equation (34)) and sensing modes (equation (4)). Arrangements are shown schematically in figures 1l(a) and (b). The device consists of an enclosed volume, VI,and two ionically conducting materials each in contact with both the internal and external gases with partial pressures of the gas to be sensed ofp, andp, respectively. There may also be a pore or porous material connecting the inner and outer regions. These arrangements allow the measurement of p, via a number of operating modes as discussed below.
5.2. Coulometric Haaland (1977) constructed a device of the type shown in figure 1l(a) and operated it as an oxygen sensor as follows. The device was placed into the sample gas of unknown oxygen partial pressure. Oxygen was electrochemically pumped out of the volume VI until the gauge EMFE, reached a sufficiently high value to indicate that p2 was close to zero. (The EMF E is approximately 50 mV for each decade of the ratio of pI/p2at 1000 K.) The current to the pump was then reversed and the charge passed, q, determined to achieve p2=pI (E=O). This
enabled calculation ofp, according to equation (36) pi =RTq/4FVl.
If the magnitude of the applied current is constant then the pressure p1 is proportional to the time of pumping and to T. Clearly the determination is intermittent and the response time cannot be less than the cycle time of the device. The latter may be reduced by minimising V, and maximising the pump current. Cells may be constructed with VI < 1 mm3 (Maskell et a1 1987b).
The oscillatory mode of operation has been further developed by Hetrick et a1 (1982) and by De Jong (1983) using
Figure 11. Pump-gauge devices. (a)internal volume totally sealed. (b)capillary joining inner volume with outer gas. Apart from capillary. devices (a) and (6) are identical.
cells of the type in figures 1l(b) and (a) respectively. In this mode pumping may be carried out between any two predetermined gauge EMFS,EY and E Z , in the range from - 1 to + 1 V although in practice normally of magnitude <100 mV. Thus the. internal partial pressure is pumped between p y and pz
respectively. Using equation (4)
P ~ = Pexp(4FEY/RT) PZ=PI exp ( ~ F E z I T). The ideal gas equation may be applied:
where An is the number of moles of gas pumped between the EMF values EYand EZ and is related to the charge, Aq, by Faraday’s law (assuming leakage rates to be small compared with the current): for a reaction involving 4 faradays/mole (e.g. oxygen reaction)
Aq =4FAn. Simplifying the above equations,
pl(exp(4FEY/RT)-exp(4FEZ/R T)) =RTIy/8FV1 (40)
where y is the cycle time and I is the current. Equation (40) shows that for fixed EYand EZ values, the cycle time. 7, is proportional to p,. In the particular case where IEYI and
lEzl <RT/4F (i.e.
25 mV) then
the higher-order term
exponentials may be ignored to reveal p I =(R ~-/4F)~[IyV2I(EY-E z ) ] .
This equation contains T to the second power indicating that attention must be paid to the control of temperature for accurate results. Interestingly where E y = 0 and EZ> 50 mV, equation (36) is applicable and temperature control is less critical.
In the above discussion, as it relates to oxygen sensing, it has been assumed that the enclosed volume contains only oxygen as a reducible gas. This can be a reasonable assumption for the arrangement of figure 1l(a) but not for that in figure 1l(b). In the latter case this would result in uncertainty of the sample gas composition for the reasons presented in 5 3.5.
5.3. Amperometric withoutfixed reference The arrangement for this mode of operation is that shown in figure 1l(b) with the circuit shown in figure 12 (Hetrick et a1 1981). The pump current is automatically adjusted continuously
to hold the gauge EMF at some predetermined value E,.
I , =4FUL(P1 -p2)
where OL is the leak conductance of the diffusion barrier. It can be quantified for a cylindrical pore of cross-sectional area A I and length l
01.=DA I / RTI.
E, =(RT/4F) l n ( ~ d ~ 2 ) . In the steady-state situation the current, Ipis given by
1 , = 4 F u ~ p l ( l-exp(-4FES/RT)).
For a given gauge EMF,E,, the current is proportional to the oxygen partial pressure in the sample gas. Hetrick et a1 (1981) suggested that by an appropriate choice of E , the temperature dependence of the sensor in this mode can be small.
Again this sensor is satisfactory in the region lean of stoichiometry but is inevitably deficient where a combustion system has the possibility of crossing stoichiometry into the rich region. This is a serious drawback for operation in boilers where