Page 87 - Adsorbents fundamentals and applications

72 PORE SIZE DISTRIBUTION

visible for both the original HK as well as the HK–CY model, as no solution for
the pore size existed for the first few points of the isotherm. However, a peak
was obtained at 5.7 ˚ A by using the modified HK model. On using the modified
HK–CY model, a sharper peak was observed at 5.6 ˚ A, which agrees well with
the crystallographic dimension of the ZSM-5 channel.
MCM-41 materials belong to the family of large pore (mesoporous) molecular
sieves and are increasingly becoming popular as catalyst supports. These synthetic
materials possess a regular array of hexagonal, uniform unidimensional meso-
pores, which can be systematically varied from 16 to 100 ˚ A. Due to their narrow
pore size distribution, minimal network effects, and well-known surface chem-
istry, they are ideal candidates for testing pore-size models. Numerous studies
have been conducted for studying the PSD of MCM-41 materials by using vari-
ous techniques such as the BJH method (Ravikovitch et al., 1997; Sayari et al.,
1999), X-ray diffraction (XRD) (Ravikovitch et al., 1995), H-NMR (Schmidt
et al., 1995), and non-local density functional theory (NLDFT) (Ravikovitch
et al., 1995, 1997).
In order to test the corrected HK model, N 2 adsorption data at 77.4 K
on a MCM-41 material denoted “Sample C” in a previously published work
(Ravikovitch et al., 1995) was used. The XRD results and the NLDFT simulation
studies reported in the latter work show the pore size of the material as 45 ˚ A.
Figure 4.9 shows the PSD for the MCM-41 material predicted from the N 2
adsorption data by using the corrected and original HK cylindrical pore models.
Because the isotherm does not follow Langmuirian behavior, the Cheng–Yang
correction was computed by fitting the data to a Langmuir isotherm as much
as possible. The figure shows that the corrected HK–CY equation accurately

1.2
Original HK
1.0
Original HK–CY
Modified HK
d(W/W 0 )/dL 0.8
Modified HK–CY
0.6

0.4

0.2

0.0
0 10 20 30 40 50 60
Effective channel size (Å)

Figure 4.9. Pore size distribution of MCM-41 material as predicted by original HK models and
the corrected HK models for cylindrical pores (Rege and Yang, 2000, with permission).