Improvement of the Derjaguin−Broekhoff−de Boer Theory for Capillary Condensation/Evaporation of Nitrogen in Mesoporous Systems and Its Implications for Pore Size Analysis of MCM-41 Silicas and Related Materials

Abstract

In this work, we propose an improvement of the classical Derjaguin-Broekhoff-de Boer (DBdB) theory for capillary condensation/evaporation in mesoporous systems. The primary idea of this improvement is to employ the Gibbs-Tolman-Koenig-Buff equation to predict the surface tension changes in mesopores. In addition, the statistical film thickness (so-called t-curve) evaluated accurately on the basis of the adsorption isotherms measured for the MCM-41 materials is used instead of the originally proposed t-curve (to take into account the excess of the chemical potential due to the surface forces). It is shown that the aforementioned modifications of the original DBdB theory have significant implications for the pore size analysis of mesoporous solids. To verify our improvement of the DBdB pore size analysis method (IDBdB), a series of the calcined MCM-41 samples, which are well-defined materials with hexagonally ordered cylindrical mesopores, were used for the evaluation of the pore size distributions. The correlation of the IDBdB method with the empirically calibrated Kruk-Jaroniec-Sayari (KJS) relationship is very good in the range of small mesopores. So, a major advantage of the IDBdB method is its applicability for small mesopores as well as for the mesopore range beyond that established by the KJS calibration, i.e., for mesopore radii greater than approximately 4.5 nm. The comparison of the IDBdB results with experimental data reported by Kruk and Jaroniec for capillary condensation/evaporation as well as with the results from nonlocal density functional theory developed by Neimark et al. clearly justifies our approach. Note that the proposed improvement of the classical DBdB method preserves its original simplicity and simultaneously ensures a significant improvement of the pore size analysis, which is confirmed by the independent estimation of the mean pore size by the powder X-ray diffraction method.

The role of accessibility in the characterization of porous solids and their adsorption properties

“…Indeed a number of reviews have been presented in the literature, dealing almost exclusively with these simple molecular probes (Kaneko 1994;Kaneko et al 1998b; Thommes et al 2000;Thommes 2004;Do et al 2008a). With the recent discovery of well defined mesoporous solids such as MCM-41, SBA-15, SBA-16, etc., there has been a surge of interest in characterization with numerous papers on experimental, theoretical and simulation aspects of characterization (Kruk and Jaroniec 2000;Kowalczyk et al 2005;Ustinov et al 2005Ustinov et al , 2006; Thommes et al 2006;Jaroniec et al 1999;Kruk and Jaroniec 2003). Classical theories such as the BJH method (Barrett et al 1951;Jaroniec et al 2002), the Broekhoff and de Boer (BdB) theory (Broekhoff and de Boer 1967, 1968a, 1968bUstinov et al 2005), the Cole and Saam (CS) theory (Cole and Saam 1974) have been challenged by modern methods that have a basis in statistical mechanics (Thommes et al 2006;Kanda et al 2000;Neimark et al 1998Neimark et al , 2003Visnyakov and Neimark 2003;Neimark 2001, 2002;Neimark and Ravikovitch 2001;Ravikovitch et al 1995Ravikovitch et al , 1998Ravikovitch et al , 2000.…”

Thermodynamics and Modeling of Sorption Isotherms

“…However, together with Churaev the author showed already in [10], that a sum of two exponential functions is helpful for the description of wetting phenomena in very large pores with pores sizes of several microns, but not necessarily for micropores as in MCM-41 zeolites. Further in the results ( [9] Tab. 1 in [9]) the l 1 values for nitrogen differ too much within a range of 0.173 nm and 0.154 nm.…”

“…Further in the results ( [9] Tab. 1 in [9]) the l 1 values for nitrogen differ too much within a range of 0.173 nm and 0.154 nm. One would expect a constant monolayer thickness of 0.3575 nm, and not half the size.…”

“…Shkolnikov et al [8] applied the DBdB approach for benzene adsorption on MCM-41 with a Frenkel-Halsey-Hill equation in order to compute the thickness of adsorbed layers. Based on the work of Churaev et al [2], Kowalczyk et al [9] proposed an improved IDBdB, where again for desorption the Derjaguin disjoining pressure approach was used. Further, for adsorption the sum of two exponential functions for the film thickness was applied, and the surface tension dependence on the pore size was considered.…”

Effects of surface structure on the molecular projection area. Adsorption of argon and nitrogen onto defective surfaces

“…Traditionally, the determination of the surface area of a porous solid with adsorption methods requires the molecular projection area of the fluid molecule used (a m ) as it is one of the most important information for solid characterization (Gregg and Sing 1982;Jaroniec et al 1999Jaroniec et al , 2003Kowalczyk et al 2005;Kaneko et al 1998;Cascarini de Torre et al 1996). Among the various probe molecules used, argon and nitrogen are the most widely used, and the recommended values for the molecular projection area of nitrogen and argon are 0.162 and 0.138 nm 2 , respectively (Gregg and Sing 1982).…”