Page 88 - Adsorbents fundamentals and applications

HORV ´ ATH–KAWAZOE APPROACH 73

estimates the pore size of the material as 45 ˚ A. By using the same model
parameters (shown in Table 4.2), the original HK and HK–CY models give a
grossly underestimated pore size of 12 ˚ Aand 9 ˚ A, respectively. It must be noted
that the corrected HK equation without the Cheng–Yang correction gives a highly
overestimated pore size value (beyond the limits of Fig. 4.9). This is because the
inflexion in the curve occurs at a high P/P S value (∼0.4). There is a severe
deviation from Henry’s law at this value. Further, Ravikovitch et al. (1997) have
reported that the BJH method systematically underestimated the pore size of the
MCM-41 materials studies by ∼10 ˚ A. Thus, the utility of the corrected HK–CY
model in predicting PSD for materials in the mesoporous (>20 ˚ A) size range is
demonstrated.
Like zeolitic materials, aluminophosphates also possess well-defined structure
and narrow PSD. Most aluminophosphates such as AlPO 4 -11 and VPI-5 have
a one-dimensional channel structure. Adsorption isotherms of argon on these
materials have been reported by Davis et al. (1988).
Figure 4.10 shows the computed PSD of VPI-5 aluminophosphate whose
isotherm is seen to have two sigmoidal bends, suggesting that it may have a
bimodal PSD. The currently accepted pore size of VPI-5 is 12.1 ˚ A(Daviset al.,
1988). It was shown previously by Cheng and Yang (1994) that VPI-5 gives two
peaks by use of the original HK–CY equation: a major peak at 8.6 ˚ Aand a
minor one at 11.7 ˚ A. In the work of Rege and Yang (2000) different parameters
were used for the kinetic diameter of argon and the oxide ion density in the
aluminophosphate framework. As a result the new peaks obtained by using the
original model were situated at 6.8 ˚ A and at 8.7 ˚ A. With the modified HK–CY
model the major peak was observed at 11.8 ˚ A and a minor peak was observed

Original HK
3.0 Original HK–CY
Corrected HK
2.5
Corrected HK–CY
2.0
d(W/W 0 )/dL 1.5

1.0

0.5

0.0
4 6 8 10 12 14 16 18
Effective channel size (Å)
Figure 4.10. Pore size distribution of VPI-5 as predicted by original HK models and the
corrected HK models for cylindrical pores (Rege and Yang, 2000, with permission).