Page 91 - Adsorbents fundamentals and applications

76 PORE SIZE DISTRIBUTION

The constants β, k and u can be determined by using data with a probe molecule
(Baksh et al., 1992). The PSD function, G(x), can then be calculated from
Eq. 4.36 by using N 2 isotherm at 77 K.
However, despite its experimental and theoretical simplicity, the above proce-
dure was undermined by the empiricism and assumptions involved. Recently new
statistical mechanics approaches by using either Monte Carlo techniques or the
density functional theory have been proposed and are steadily gaining acceptance.
In this approach, the local or individual pore isotherm, f(x, P ), is calculated by
using any of the statistical mechanics techniques. These techniques enable the
calculation of the isotherm (dependent on pore size and geometry) in conjunction
with PSD functions with assumed mathematical forms. A large amount of litera-
ture has been published regarding the application of this theory for studying gas
adsorption and, in particular, evaluation of PSD of microporous materials (e.g.,
Seaton et al., 1989; Lastoskie et al., 1993; Olivier, 1995; Webb and Orr, 1997;
Ravikovitch et al., 1998). The advantage of the technique is that it is a unified
method applicable to both microporous as well as mesoporous types of materials.
However, the empirical parameters used in these models are difficult to obtain
from the literature except for a few well-studied systems. This is a common prob-
lem with the HK approach. The results are highly sensitive to the empirically
parameters that are used. Moreover, the calculations involved in the statistical
mechanics approach are highly intensive and require an elaborate computer code.
A common drawback for all three approaches (i.e., the Kelvin equation,
the Horv´ ath–Kawazoe approach, and the integral equation approach) is that
non-intersecting pores are assumed. This problem of intersecting pores remains
unsolved. There exists an interesting conceptual difference between the statisti-
cal mechanics approach and the two former approaches. In the Kelvin equation
and the HK approaches, a pore is either filled or empty; whereas in the statistical
mechanics approach, all pores are partially and gradually filled. The experimental
data in the literature on high-resolution isotherms cannot distinguish, unambigu-
ously, which is the correct picture. Obviously the actual picture of the pore filling
also depends on the homogeneity of the sites on the pore walls.

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