Page 81 - Adsorbents - fundamentals and applications

66 PORE SIZE DISTRIBUTION

Table 4.1. Algorithm (pseudo-code) for obtaining effective pore size of slit-shaped pores
(from Rege and Yang, 2000)
(1) Guess slit width L corresponding to adsorbate relative pressure
P/P 0 .
(2) Calculate number of adsorbate molecular layers M (Eq. 4.16):
L − d S
M =
d A
(3) Calculate ε 1 , ε 2 , ε 3 and (Eqs. 4.17, 4.20, 4.21):

4 10 4 10
N S A S σ S σ S σ S σ S
ε 1 (z) = 4 − + − +
2σ
S d 0 d 0 L − d 0 L − d 0
4 10 4 10

N S A S σ S σ S N A A A σ A σ A
ε 2 (z) = − + + − +
2σ S 4 d 0 d 0 2σ A 4 d A d A

4 10

N A A A σ A σ A
ε 3 (z) = 2 · 4 − +
2σ
A d A d A
(4) If M< 2, then
ε = ε 1
Else (M ≥ 2)
2ε 2 + (M − 2)ε 3
ε =
M
(5) If [RT ln(P/P 0 ) = N Av ε], then
Effective pore width = (L − d S )
Else
Guess new L and iterate from (1) again.

at a still higher pore size in the new model. This again can be explained from the
fact that for the same interaction energy the new model predicts a higher pore
size compared with that predicted by the original model.
The adsorption isotherm of argon on faujasite zeolite at 87 K has been given by
Borghard et al. (1991). This type of zeolite actually has a spherical cavity, and the
results of using the modified HK model for spherical pores will be subsequently
shown. The slit-pore model was tried in the case of faujasite, particularly because
it has a comparatively larger pore structure than molecular sieve carbons. The
differences between the model predictions will become obvious. It has been
shown previously (Cheng and Yang, 1994) that the application of the original
HK model gives a highly underestimated pore-size distribution. Figure 4.6 shows
the predictions of the two original and two modified models. It can be seen that
while the original models predicted a pore size of 7 ˚ A, the modified models
gave a peak at much higher pore size of 13 ˚ A. It is interesting to note that the