Zeolites and Related Materials: Trends, Targets and Challenges
Proceedings of 4th International FEZA Conference
A. Gédéon, P. Massiani and F. Babonneau (Editors)
© 2008 Elsevier B.V. All rights reserved.
957
Pore shape affects the determination of the pore
size of ordered mesoporous silicas by mercury
intrusion
Anne Galarneaua, Benoît Lefèvrea, Hélène Cambona, Benoît Coasnea, Sabine
Valangeb, Zelimir Gabelicac, Jean-Pierre Bellatd, Francesco Di Renzoa
a
Institut Charles Gerhardt, UMR 5253 CNRS-UM2-ENSCM-UM1, ENSCM, 8 rue Ecole
Normale, 34296 Montpellier Cedex 5, France
b
Laboratoire de Catalyse en Chimie Organique, UMR CNRS 6503, ESIP, Université de
Poitiers, Poitiers, France
c
LPI-GSEC, ENSCMu, Université de Haute Alsace, F-68094 Mulhouse Cedex, France
d
Institut Carnot de Bourgogne, UMR 5209 CNRS-Université de Bourgogne, Dijon,
France
Abstract
The pore shape affects the pressure of mercury intrusion in ways not contemplated by
the usual Washburn-Laplace or Kloubek-Rigby-Edler models. These models have been
developed for cylindrical pores and correctly account for the penetration of mercury in
the cylindrical pores of MCM-41. The uneven surface of the cylindrical pores of SBA15 is responsible for a significant increase of the pressure of mercury intrusion and,
thereby, for a corresponding underevaluation of the pore size if the classical pressuresize correlations are applied.
Keywords: porosimetry, MCM-41, SBA-15, pore size, mesopores.
1. Introduction
Ordered mesoporous silicas present mesopores of appropriate size to be evaluated and
compared in their field of superposition (3-50 nm) of the methods of pore size
evaluation by N2 volumetry and Hg intrusion. The usual models to evaluate pore sizes
by Hg intrusion refer to cylindrical pores [1, 2]. Here we evaluate the influence of some
non ideal characteristics of the SBA-15 system, namely uneven pore walls, mesopore
interconnection or presence of micropores [3, 4], on the mercury intrusion.
2. Experimental
SBA-15 samples with diameters from 5 to 10 nm have been prepared by tuning the
temperature of the first step of the synthesis [5]. MCM-41 has been prepared in the
presence of hexadecyl trimethyl ammonium by using methylamine as pH-controlling
agent [6]. The pore size from N2 adsorption at 77 K has been evaluated by the
Broekhoff and de Boer method, shown to correctly evaluate the pore size of ordered
mesoporous silicas [7].
3. Results and discussion
The isotherms of N2 adsorption on MCM-41 and two samples of SBA-15 synthesized at
different temperatures are reported in Fig. 1. The curves of mercury intrusion-retraction
958
A. Galarneau et al.
800
600
3
adsorbed N2 / cm (STP) g
-1
on the same samples are reported in Fig. 2. In Fig. 2, only the high-pressure part of the
porosimetry curves is reported, to highlight the phenomena not related to powder
densification and intergranular porosity.
400
200
0
0
0.2
0.4
0.6
0.8
1
p/p°
Figure 1. Nitrogen adsorption-desorption isotherms at 77 K on (void squares) SBA-15
synthesized at 403 K, (void lozenges) SBA-15 synthesized at 343 K, (filled triangles)
MCM-41.
2
3
cumulative volume (cm /g)
2.5
1.5
1
0.5
0
50
100 150 200 250 300 350 400 450
pressure (MPa)
Figure 2. High-pressure part of the curves of intrusion-retraction of mercury on
(squares) SBA-15 synthesized at 403 K, (lozenges) SBA-15 synthesized at 343 K,
(triangles) MCM-41. Void symbols: first cycle. Filled symbols: second cycle. The
curves have been shifted along the y axis.
Two successive cycles of mercury intrusion in SBA-15 samples show an excellent
reproducibility of the intrusion and retraction pressure. A limited decrease of the
959
Pore shape affects the determination of the pore size by mercury intrusion
intruded volume in the second cycle is observed, due to retention of some mercury after
the first cycle [8]. In the case of MCM-41, the intrusion of mercury during the first
cycle induces a differential pressure between parallel pores, with partial collapse of the
pore walls and widening of the pores. The retraction of both cycles and the intrusion of
the second cycle correspond to a system of larger and less ordered pores, which retains
the volume of the parent structural porosity.
The comparison between pore sizes evaluated by Hg intrusion and N2 volumetry for
MCM-41 and SBA-15 samples are reported in Fig. 3. The data obtained from the two
techniques coincide for MCM-41, while Hg intrusion underevaluates the pore size of
the SBA-15 samples. The Washburn-Laplace model (Fig. 1a) [1] does not account for
the cavitation effects in the retraction of Hg [9], which are taken into account by the
Kloubek-Rigby-Edler model (Fig. 1b) [2]. The pore size evaluated by N2 adsorption is
not affected by the defects of the pore walls of SBA-15, as these defects have already
been filled when capillary condensation takes place [10].
D(Hg porosimetry) / nm
D(Hg porosimetry) / nm
12
18
a
15
12
9
6
3
0
b
10
8
6
4
2
0
0
2
4
6
8
10 12
D(N2 volumetry) / nm
0
2
4
6
8
10 12
D(N2 volumetry) / nm
Figure 3. Pore size from Hg porosimetry data calculated by the (a) Washburn-Laplace
equation or the (b) Kloubek-Rigby-Edler equations vs. the pore size from N2 volumetry.
Triangle: MCM-41; lozenges: SBA-15 samples; empty symbols: intrusion; filled
symbols: retraction. The solid lines correspond to equal diameters from Hg porosimetry
and N2 volumetry.
The higher than expected pressure required for mercury intrusion into the mesopores of
SBA-15 depends on the presence of side pockets, whose edge retains the advancement
of the mercury meniscus. According to the description of Kloubek [11], when a
meniscus advances with a contact angle ș1 and reaches the rim of an enlargement with
slope of the tapering wall ĭ, the contact angle with the tapering surface is ș2 = ș1-ĭ, too
small for further advancing. For further advancement, the pressure has to increase and
the meniscus radius to decrease until the contact angle with the tapering surface has
reached the value ș3 = ș2+ĭ = ș1. This effect is observed both in the presence of the
microporous pockets of low-temperature SBA-15 and the connections between
mesopores of high-temperature SBA-15.
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A. Galarneau et al.
ș2
ș1
r1
r1
R
r2
ĭ
ș3
Figure 4. Schematic representation of a meniscus of mercury in a cylindrical pore and at
the rim of an enlargment of the pore. Modified from Kloubek [11].
4. Conclusion
The penetration of mercury in MCM-41, a material with smooth cylindrical pores, takes
place at the pressure indicated by the Washburn-Laplace model, indicating that this
model is still valid at the scale of a few nanometers. When the pore surface is pitted
with micropores or when the pores are interconnected, like in the case of SBA-15, the
Washburn-Laplace model underevaluates the size of the pores, due to the excess energy
needed for advancement of the meniscus beyond the surface defects.
It is interesting to observe that a fair correlation can be found between the pore size
evaluated by the Washburn-Laplace model and the pore size evaluated by the BJH
model of nitrogen adsorption in the case of SBA-15 [12] and other materials with
interconnected pores [13]. In the case of gas adsorption, the surface defects are filled at
a lower pressure and do not affect the pressure of capillary condensation [10]. However,
the BJH model does not take into account the effects of curvature on condensation and
systematically underevaluates the size of the mesopores [7, 14].
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