(Figure 1) The schematic of limiting current oxygen sensor
When voltage is applied between electrodes constructed on both sides of Yittria stabilized zirconia (YSZ), the oxygen gas reacts with the electrons at the cathode side, as shown below,
The oxygen ion is transferred through the YSZ, an oxygen ion conductor,
and is oxidized to the oxygen gas at the anode side as follows. As a results, oxygen is pumped from the cathode to anode.
In this kind of sensor, a narrow hole constructed as depicted in Figure 1 is used as a diffusion barrier, the oxygen gas escapes to anode of the pumping cell, and then the diffusion takes place through the diffusion hole to cathode by means of Fick’s 1st law. If the amount of oxygen pumped by applied voltage is larger enough than that of oxygen entering the diffusion hole, the diffusion process of oxygen gas through the diffusion hole is the rate determining step. This restriction in the amount of oxygen flowing through YSZ due to the diffusion process of oxygen is referred to as the limiting current. A sensor using this phenomenon that the oxygen ionic current is limited by the gas diffusion is called a limiting current type oxygen sensor.
Figure 2 shows a current as a function of applied voltage across the oxygen pumping cell. These current(I)-voltage(V) curves can be divided into three regions.
In region (I), the amount of pumped oxygen is less than that of oxygen supplied by diffusion. So, with increasing applied voltage, the amount of pumped oxygen increases linearly. The slope is then determined by the resistance of the electrode and solid electrolyte.
In region (II), the amount of pumped oxygen is determined by the diffusion of oxygen,
so the amount of current is constant regardless of the applied voltage. As mentioned earlier, the diffusion of oxygen in these restricted current region is proportional to the difference of oxygen concentration between inside and outside of the chamber on the basis of the diffusion process. Moreover, the oxygen concentration inside the chamber is negligible enough compared to the concentration of measured gas, so the amount of the limiting current is proportional to the concentration of oxygen contained in measured gas.
(Figure 2) I-V Characteristics of the limiting current oxygen sensor
In region (III), as the applied voltage becomes larger, the YSZ solid electrolyte will be
electrically decomposed, resulting in a greater concentration of oxygen ions, which in turn increases the current.
Gas diffusion through narrow hole is classified into two types, normal diffusion and
Knudsen diffusion. When the size of the diffusion hole is much larger than the mean free path of the gas, gas diffusion becomes more affected by collisions between gas molecules without being affected by the wall of narrow hole. This is defined as normal diffusion. If the size of the diffusion hole is less than the mean free-path of the gas, the effect between the gas and the diffusion barrier is more important than the effect between the gases, which is called the Knudsen diffusion.
Here λ and d refer to mean free path of the gas and the diameter of diffusion hole, respectively.
Generally, the dominant diffusion type is determined by means of Knudsen number, Kn as follows.
Kn≫1 : Knudsen Diffusion
Kn≪1 : Normal Diffusion
(Table 1) The comparison of Knudsen diffusion and normal diffusion
As shown in Table 1, in Knudsen diffusion type oxygen sensor, a quantity of limiting current is
proportional to oxygen partial pressure (or concentration) under the condition of constant applied voltage.
Limiting current type oxygen sensor has longer life time than electrochemical oxygen sensor since there is no electroyte dissipation. In addition, it can be fabricated as a small chip unlike zirconia oxygen sensor because there is no need to construct reference electrode. And it is possible to make more precise measurement at the high oxygen concentration since the change in the sensor output signal is greater than the zirconia oxygen sensor's.