conditions is expressed as follows for a straight round pore [89],

where r is the pore radius, T the absolute temperature (K) and M the molecular weight of the gas. As the gas molecules diffuse into the film, they react with the adsorbed oxygen ions (O-) on the way. This process is expressed by the following transport equation:

where x is the distance from the film surface, CA the concentration of an inflammable gas at x, and k the rate constant of the surface reaction. When the steady state is reached, CA no longer changes with time:

The concentration profile of the reducing gas molecules (A) can be obtained by solving this equation. Two boundary conditions are required to determine the two integration constants involved. These are CA = CA S at x = 0 and x = 2L. Under these boundary conditions, Eq. (10) can be solved to give

Ca = Cas[sinh(x(kD)1/2) + sinh((2/ - x)(k/DK)1/2)] /sinh(2/(k/DK )1/2) (16)

Figure 19 is a generalized profile, which gives the relations between CA/CK S and x/l for changing l(k/DK)1/2 as a parameter. It is clearly observed that for fixed k/DK, the flat profile is exhibited by thin films (low l(k/DK)). On the other hand, for thick films (high l(k/DK)), the concentration of the gas molecules within the film is restricted to the near surface region. As the gas molecules are likely to diffuse throughout the film thickness, thin films exhibit large sensitivity relative to thick films. For a given film thickness, large pore radius would increase the Knudsen diffusion coefficient, and hence, would favor the flat concentration profile, thus enhancing the gas sensitivity. Figure 20 shows the effect of the amount of porosity on the gas sensitivity of the sol-gel derived nanocrystalline SnO2 thin films [8, 12]. It is observed that the increased amount of porosity within the thin films also increases the gas sensitivity, which is in accordance with the above model.

Further, the molecular weight of the gas molecules also tends to affect the Knudsen diffusion coefficient, Eq. (8). Hence, the gases having lower molecular weight, such as H2, are likely to exhibit higher sensitivity than those having higher molecular weight (for example, CO, NO, and CH3OH). In Figure 21 [5, 9, 21, 22], the maximum sensitivity reported for these gases is plotted as a function of their molecular weights. Decrease in the maximum gas sensitivity with increasing molecular weight is evident in Figure 21, which also supports the prediction of the above model.

The effect of operating temperature on the response and recovery time, for the sol-gel derived nanocrystalline SnO2 thin-film sensor, is shown in Figures 22 [5, 8, 9, 12, 13, 18, 21] and 23 [5, 9, 12, 18, 21], respectively. It is observed that both the response and recovery time decrease with increasing operating temperature and this behavior is primarily attributed to the reduced activation energy for the involved chemical reactions at higher operating temperatures. In agreement with this, the recovery time is observed to increase with increasing response time, Figure 24.

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