Page 86 - Adsorbents fundamentals and applications

HORV ´ ATH–KAWAZOE APPROACH 71

Thus the average interaction energy ε can now be written down by a popula-
tion-weighted average as follows:

M

N i ε i
i=1
ε = (4.32)
M

N i
i=1
The PSD for the cylindrical pore model can now be easily determined by using
either the HK Eq. 4.23, or the HK–CY Eq. 4.24. The algorithm for determining
pore size by using the corrected HK equation for cylindrical pores was also given
by Rege and Yang (2000).
The modified HK model for spherical pores has also been derived by Rege
and Yang (2000). The HK–CY version for the spherical pore was given earlier
by Cheng and Yang (1994).
Rege and Yang (2000) have compared the PSD predicted from the four HK
type models to assess a number of molecular sieves with well-defined shapes
and sizes. In all cases, the modified or corrected HK–CY models gave sig-
nificantly better results than all other models. Some of the comparisons are
shown here.
The ZSM-5 zeolite is an aluminosilicate with three-dimensional channels mea-
suring 5.6 × 5.3 ˚ A size. High-resolution isotherm of Ar on ZSM-5 at 87 K has
been measured by Venero and Chiou (1988). The pores are approximately cylin-
drical. The PSD of ZSM-5 predicted by the four models is shown in Figure 4.8.
It is seen that for the parameters chosen (Table 4.2), no prominent peak was

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

1.0

0.5

0.0
4 5 6 7 8 9 10
Effective channel size (Å)
Figure 4.8. Pore-size distribution of ZSM-5 zeolite as predicted by original HK models and the
corrected HK models for cylindrical pores (Rege and Yang, 2000, with permission).