The possible use of Γ-functions for the determination of microporosity–mesoporosity and the pore size in materials with ordered (MCM) and quasi-ordered pore structure

Abstract

The purpose of this work is to examine the possibility to apply Γ-functions for the description of pore size distribution (PSD) as well as for the distinction between the microporosity and mesoporosity in materials with ordered and/or quasi-ordered pore structure. The group of materials used were six (6) MCM-Al x solids ( x=0, 5, 10, 15, 20, 50) in which the ordered mesoporosity ( x=0) was gradually destroyed by increasing the percentage substitution x of Si by Al. All samples were characterized by N 2 adsorption–desorption porosimetry. Then the estimation of PSD took place by using two Γ-functions, one for the micropore region (0< D p<2 nm) and another for the mesopore region (2< D p<50 nm). As a benchmark for the choice of Γ-functions their fitting to the N 2-adsorption loop was used. Consequently the PSD from those chosen Γ-functions was calculated and the results were compared with the method of Horvath–Kawazoe (HK). The specific surface areas S p, the specific pore volumes V p and the maximum D p of the PSDs calculated by the standard methodologies (HK and BET) are perfectly compared to the ones obtained with the methodology of Γ-functions. In addition the use of Γ-functions methodology provides the possibility to distinguish the percentage of microporosity in such quasi-ordered, amorphous mesoporous, or quasi-mesoporous, materials which is zero for the pure siliceous MCM-Al 0 but increases gradually with the addition of Al atoms and reaches ∼32% for the highly substituted solids MCM-Al 50.