Adsorption of Simple Fluid on Silica Surface and Nanopore: Effect of
Surface Chemistry and Pore Shape
Benoit Coasne,*,†Francesco Di Renzo,†Anne Galarneau,†and Roland J. M. Pellenq‡
Institut Charles Gerhardt Montpellier, CNRS (UMR 5253) and UniVersite ´ Montpellier 2,
Montpellier, France, and Centre Interdisciplinaire des Nanosciences de Marseille,
CNRS (UPR 7251), Marseilles, France
ReceiVed February 22, 2008. ReVised Manuscript ReceiVed May 9, 2008
This paper reports a molecular simulation study on the adsorption of simple fluids (argon at 77 K) on hydroxylated
silica surfaces and nanopores. The effect of surface chemistry is addressed by considering substrates with either
partially or fully hydroxylated surfaces. We also investigate the effect of pore shape on adsorption and capillary
condensation by comparing the results for cylindrical and hexagonal nanopores having equivalent sections (i.e., equal
section areas). Due to the increase in the polarity of the surface with the density of OH groups, the adsorbed amounts
isotherms for the cylindrical and hexagonal pores conform to the typical behavior observed in the experiments for
adsorption/condensation in cylindrical nanopores MCM-41. Capillary condensation occurs through an irreversible
discontinuous transition between the partially filled and the completely filled configurations, while evaporation occurs
through the displacement at equilibrium of a hemispherical meniscus along the pore axis. Our data are also used to
discuss the effect of surface chemistry and pore shape on the BET method. The BET surface for fully hydroxylated
surfaces is much larger (by 10-20%) than the true geometrical surface. In contrast, the BET surface significantly
underestimates the true surface when partially hydroxylated surfaces are considered. These results suggest that the
surface chemistry and the choice of the system adsorbate/adsorbent is crucial in determining the surface area of solids
using the BET method.
Fluids confined within nanometric pores (size of a few
molecular diameters) exhibit properties that are significantly
forces, and reduced dimension affect the phase transitions
(condensation, freezing, etc.). Significant shifts in transitions
(e.g., pressure, temperature) are observed, and in some cases,
new types of phase transitions (layering, wetting, etc.) can also
is of crucial interest for both fundamental research and potential
templated porous solids) are an important family of nanoporous
solids because of their uses as adsorbents or catalytic supports
for gas adsorption, phase separation, catalysis, preparation of
nanostructured materials, etc.1–3Among porous silicas, MCM-
41,4MCM-48,4and SBA-155attract a great deal of attention
because of their simple pore morphology (pore shape) and
topology (pore connectivity) compared to other porous silicas
by a template mechanism involving the formation of surfactant
or block copolymer micelles in a mixture composed of a solvent
and a silica source. Polymerization of the silica and removal of
the organic micelles lead to a material presenting an array of
regular pores. The pore diameter distribution is narrow with an
average value that can be varied from 2 up to 20 nm, depending
of nanoconfinement on the thermodynamics and dynamics of
in these solids (for a review, see refs 6 and 7).
In most simulation and theoretical studies, MCM-41 are
modeled as pores with a regular cylindrical geometry.8–14The
effect of surface roughness and morphological defects, such as
constrictions, on adsorption and capillary condensation of gases
of work, it is not clear whether the atomistic silica pores used
in the simulation studies mentioned above are realistic repre-
sentations of the morphology of MCM-41 pores, due to the lack
of conclusive experiments regarding their surface chemistry or
roughness and pore morphology. In particular, some properties
* To whom correspondence should be addressed. E-mail: bcoasne@
lpmc.univ-montp2.fr. Phone: +33 4 67 14 33 78. Fax: +33 4 67 14 42 90.
†Institut Charles Gerhardt Montpellier.
‡Centre Interdisciplinaire des Nanosciences de Marseille.
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Langmuir 2008, 24, 7285-7293
10.1021/la800567g CCC: $40.75
2008 American Chemical Society
Published on Web 06/04/2008
in theoretical and molecular simulation studies. For instance,
although MCM-41 pores are usually considered of a cylindrical
geometry, some authors have proposed that the pores in these
materials are of a hexagonal shape (see refs 16–19 and 20 for
instance). The surface chemistry of MCM-41 has also been
discussed in the literature. The density of silanol groups at the
pore surface is about 2-3 OH per nm2,21–25which is smaller
than that obtained for porous silica glasses such as Vycor (5-7
OH per nm2).26,27
The aim of the present work is to investigate by means of
molecular simulation the adsorption of a simple fluid (argon at
77 K) on atomistic silica surfaces or nanopores. The surfaces or
pores are generated from an initial silica block. The effect of
OH/nm2, respectively). We also compare adsorption on amor-
phous and crystalline substrates. We investigate the effect of
pore shape on the adsorption and capillary condensation by
comparing the results for cylindrical and hexagonal pores. The
two pores have equivalent sections (i.e., equal section areas),
which corresponds to a diameter of 3.2 nm for the cylindrical
pore and a width between opposite corners of 3.5 nm for the
hexagonal pore. The data are analyzed and compared in terms
also used to discuss the effect of surface chemistry and pore
shape on the routinely used characterization methods based on
the BET model. The remainder of the paper is organized as
MCM-41 used in this work and briefly discuss the details of the
and condensation on the silica surfaces and nanopores. Section
4 contains concluding remarks.
2. Computational Details
2.1. Preparation of Silica Surfaces and Nanopores. In this
work, we consider a silica surface and two models of MCM-41
(Figure 1). The first model of MCM-41 is a regular cylindrical
nanopore having a diameter D ) 3.2 nm. The second model is a
regular tubular nanopore having a hexagonal cross-section. This
hexagonal pore has a section area equal to that of the cylindrical
pore so that the comparison between the two models is relevant as
they induce similar confinement effects. Due to the use of an initial
crystalline block to prepare these silica pores (see below), the
“cylindrical” pore corresponds to a pore with an octagonal section
rather than with a regular circular section. This octagonal section
planes of cristobalite. For the sake of clarity, the pores with a
hexagonal and octagonal section used in this work will be referred
to as “hexagonal” and “cylindrical” pores, respectively. We adopt
the following notation in the rest of this paper: P, C, and H indicate
the type of substrate (P ) planar surface, C ) cylindrical pore, H
) hexagonal pore), while the subscripts 1 and 2 denote fully and
partially hydroxylated surfaces, respectively. The characteristics of
in Table 1. We note that the size reported for the hexagonal pore
D ) 3.5 nm corresponds to the distance between opposite corners
(in contrast the distance between opposite sides is equal to 3.0 nm).
All the atomistic silica surfaces and pores used in this work were
generated according to the method by Pellenq and Levitz to prepare
numerical Vycor samples.28Coasne and Pellenq have shown that
and/or topologies, such as cylindrical, hexagonal, ellipsoidal, and
constricted pores.10,12,13Recently, He and Seaton used a similar
that equals 1 if (x,y,z) belongs to the silica wall and 0 if (x,y,z)
belongs to the void. The surfaces and nanopores used in this work
were obtained by carving out of an atomistic block of cristobalite
(cristalline silica), the void corresponding to η(x,y,z) ) 0. All the
pores are opened at both ends toward an external bulk reservoir, so
in contact with the external gas phase (this departs from infinitely
long pores for which there is no interface with the external phase).
To mimic the silica surface in a realistic way, we removed in a
second step the Si atoms that are in an incomplete tetrahedral
This procedure ensures that the remaining silicon atoms have no
dangling bonds and the remaining oxygen atoms have at least one
(16) Galarneau, A.; Cambon, H.; Di Renzo, F.; Fajula, F. Langmuir 2001, 17,
(17) Ottaviani, M. F.; Galarneau, A.; Desplantier-Giscard, D.; Di Renzo, F.;
Fajula, F. Microporous Mesoporous Mater. 2001, 44-45, 1.
(18) Galarneau, A.; Cambon, H.; Di Renzo, F.; Ryoo, R.; Choi, M.; Fajula,
F. New J. Chem. 2003, 27, 73.
(19) Fenelonov, V. B.; Derevyankin, A. Y.; Kirik, S. D.; Solovyov, L. A.;
Shmakov, A. N.; Bonardet, J. L.; Gedeon, A.; Romannikov, V. N. Microporous
Mesoporous Mater. 2001, 44, 33.
(20) Alfredsson, V.; Keung, M.; Monnier, A.; Stucky, G. D.; Unger, K. K.;
Schuth, F. J. Chem. Soc. Chem. Commun. 1994, 921.
(21) Ishikawa, T.; Matsuda, M.; Yasukawa, A.; Kandori, K.; Inagaki, S.;
Fukushima, T.; Kondo, S. J. Chem. Soc., Faraday Trans. 1996, 92, 1985.
(22) Landmesser, H.; Kosslick, H.; Storek, W.; Frick, R. Solid State Ionics
1997, 101-103, 271.
(23) Cauvel, A.; Brunel, D.; Di Renzo, F.; Fubini, B.; Garrone, E. Langmuir
1997, 13, 2773.
(24) Zhao, X. S.; Lu, G. Q.; et al. J. Phys. Chem. B 1997, 101, 6525.
(25) Sutra, P.; Fajula, F.; Brunel, D.; et al. Colloids Surf. A 1999, 158, 21.
(26) Low, M. J. D.; Ramasubramaniam, N. J. Phys. Chem. 1967, 71, 730.
(27) Huber, T. E.; Huber, C. A. J. Phys. Chem. 1990, 94, 2505.
(28) Pellenq, R. J. M.; Levitz, P. E. Mol. Phys. 2002, 100, 2059–2077.
Figure 1. Atomistic model of silica substrates: (left) a square plane surface, (middle) a regular cylindrical nanopore of a diameter D ) 3.2 nm, and
(right) a regular hexagonal nanopore of a section area equal to that of the cylindrical pore shown in the middle. Gray and white spheres are silicon
and oxygen atoms, respectively. Black spheres are the hydrogen atoms that delimit the pore surface. The silica surface and pores were carved out
from an initial silica block with the dimensions 10.7 nm × 10.7 nm × 32.1 nm. The hexagonal and cylindrical pores are 25.6 nm long and are opened
at both ends toward external bulk reservoirs.
7286 Langmuir, Vol. 24, No. 14, 2008 Coasne et al.
saturated bond with a Si atom. Then, the electroneutrality of the
simulation box was ensured using the procedures below that lead
to fully (∼ 7-8 OH/nm2) and partially hydroxylated silica surfaces
nanopores were obtained by saturating all oxygen dangling bonds
with hydrogen atoms (Figure 2). The latter are placed in the pore
void at a distance of 1 Å from the unsaturated oxygen atom along
of OH groups obtained using such a procedure (7-8 OH per nm2)
is close to that obtained experimentally for porous silica glasses
such as Vycor (5-7 OH per nm2). Then, we displace slightly and
randomly all the O, Si, and H atoms to mimic an amorphous silica
surface (the maximum displacement in each direction x, y, and z is
and nanopores were obtained by saturating with hydrogen atoms a
so that the density of silanol groups at the pore surface equals 2
OH/nm2, which is close to the value reported for MCM-41 obtained
after calcination of the material at 550 K.23A value of 2 OH/nm2
is in agreement with the experiments by Zhuravlev29on the surface
density of OH groups at the surface of amorphous silica thermally
atoms that were saturated with hydrogen atoms were chosen
randomly. The remaining oxygen dangling bonds Si-O* were then
saturated as follows (Figure 2). First, nearest unsaturated oxygen
atoms were paired together. Then, each pair was removed from the
simulation box and replaced by a unique oxygen atom that is placed
and randomly all the O, Si, and H atoms to mimic an amorphous
2.2. Grand Canonical Monte Carlo Simulation of Gas
at 77 K on the atomistic silica surfaces and MCM-41 (cylindrical
and hexagonal nanopores). The GCMC technique is a stochastic
method that simulates a system having a constant volume V (the
The absolute adsorption isotherm is given by the ensemble average
of the number of adsorbed atoms as a function of the pressure of
between the argon and substrate atoms were calculated using the
PN-TraZ potential as reported for rare gas adsorption in zeolite33
or in porous silica glass.28The intermolecular energy is written as
the sum of the dispersion interaction with a repulsive short-range
contribution and an induction term due to the interaction of the
adsorbed atom with the local field created by the partial charges of
the atoms in the substrate (qSi) +2e-and qH) +0.5e-, and qO
parameters as well as the details of the intermolecular potential
We calculated the adsorbate/substrate interaction using an energy
grid.34The potential energy is calculated at each corner of each
elementary cube (about 1 Å3). An accurate estimate of the energy
is then obtained by a linear interpolation of the grid values. Such
a procedure enables simulation of adsorption in mesoporous media
over matrix species in the course of GCMC runs.9,35–37The argon/
argon interaction was calculated using a Lennard-Jones potential
with εAr) 120 K and σAr) 0.34 nm.38Both the saturation pressure
of the solid and supercooled liquid can be used to calculate the
of argon. The saturation pressure P0 used in the present work
corresponds to that of the metastable liquid as given by the Kofke
by previous experiments,40density functional theory (DFT) calcula-
(29) Zhuravlev, L. T. Langmuir 1987, 3, 316.
(30) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical
Mechanics of Adsorption; Academic Press: New York, 1982.
(31) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford:
(32) Frenkel, D.; Smit, B. Understanding Molecular Simulation: From
Algorithms to Applications, 2nd ed.; Academic Press: London, 2002.
(33) Pellenq, R. J. M.; Nicholson, D. J. Phys. Chem. 1994, 98, 13339.
(34) Pellenq, R. J. M.; Nicholson, D. Langmuir 1995, 11, 1626.
(35) Gelb, L. D.; Gubbins, K. E. Langmuir 1998, 14, 2097.
(36) Pellenq, R. J. M.; Levitz, P. E. Mol. Simul. 2001, 27, 353.
(38) Streett, W. B.; Staveley, L. A. K. J. Chem. Phys. 1967, 47, 2449.
(39) Kofke, D. A. J. Chem. Phys. 1993, 105, 4149.
Table 1. Characteristics of the Silica Plane and Nanopores Considered in the Present Worka,b
fully hydroxylatedpartially hydroxylated
aPore size (D), pore volume (VP), internal surface (Sint.), external surface (Sext.), surface density of OH groups (FOH).bThe geometrical surface area and
pore volume were determined simply from the perimeter and cross-section area of the pore or surface. We adopted the following notation. P, C, and H indicate
the type of substrate (P ) planar surface, C ) cylindrical pore, H ) hexagonal pore). The subscripts 1 and 2 denote fully and partially hydroxydated surfaces,
respectively. The size reported for the hexagonal pore D ) 3.5 nm corresponds to the distance between opposite corners (in contrast, the distance between
opposite sides is equal to 3.0 nm).
and hydrogen atoms, respectively. The cyan sphere is an oxygen atom
forming a siloxane bridge. Fully hydroxylated surfaces are obtained by
saturating all oxygen dangling bonds with hydrogen atoms. Partially
hydroxylated surfaces are obtained by saturating with hydrogen atoms
a fraction x of the oxygen atoms having a dangling bond. Then, pairs
of nearest unsaturated oxygen atoms are replaced by a unique oxygen
atom that is placed at the center of mass of the pair to form a siloxane
bridge Si-O-Si. For both fully and partially hydroxylated materials,
we then displace slightly and randomly all the O, Si, and H atoms to
mimic an amorphous silica surface.
Effect of Surface Chemistry and Pore Shape Langmuir, Vol. 24, No. 14, 2008 7287
tions,41and molecular simulations13in which it was found that
confined argon after capillary condensation in silica pores at 77 K
3. Results and Discussion
3.1. Effect of Surface Chemistry. The argon adsorption
isotherms at 77 K for the fully and partially hydroxylated silica
surfaces (P1and P2) are shown in Figure 3. Adsorbed amounts
have been converted into the number of adsorbed atoms per unit
of surface area of the silica surface (in µmol per m2). For all
pressures, the amount adsorbed at the surface of the silica plane
P1is larger by a factor 3 to 5 than that for the silica plane P2.
This result is due to the fact that an increase in the density of
silanol groups induces an increase in the polarity of the silica
amounts becomes smaller. This result is due to the decrease in
the interaction with the substrate as the distance to the silica
plane increases (i.e., when the adsorbed film becomes thicker).
We also report the simulation data obtained for a fully
hydroxylated plane similar to P1but with a crystalline structure.
This silica surface has been obtained by switching off the
amorphization procedure when preparing the silica amorphous
This result can be explained as follows. The OH bond length for
the silanol groups at the surface of the crystalline substrate is
substrate varies between dOH- δ and dOH+ δ, where δ ) 0.7
procedure. Given that the OH distance remains in average equal
at the surface of the amorphous substrate is identical to that at
for which dOH> dOHlead to induction terms Uind.) RE2(R is
dOH< dOH. As a result, the stronger induction interaction for the
amorphous surface leads to larger adsorbed amounts compared
to those for the crystalline surface. We also show in Figure 3
experimental data obtained by Sing and co-workers for a
a surface density of 7 OH/nm2for such a silica sample (which
is the value reported for nonporous silicas and porous silicas
such as Controlled Pore Glass or Vycor26,27), this result shows
surface used in this work are a reasonable model of the
groups is used.
The isosteric heats Qstof adsorption for argon at 77 K for the
fully and partially hydroxylated silica surfaces (P1and P2) are
shown in Figure 4. The data are reported as a function of the
from the fluctuations over the number of particles and energy
in the course of the simulations. These curves are typical of
adsorption on heterogeneous surfaces as they decrease rapidly
down to a plateau value that is close to the heat of liquefaction
coverage, Qst(0) ) 13.0 kJ/mol, is very similar for the two
substrates P1and P2. Due to its larger density of OH groups, the
than that for the susbtrate P2. As a result, the isosteric heat for
P1is always larger than that for the susbtrate P2; of course, this
result is consistent with the larger adsorbed amounts observed
for the planar surface P1. These results are relevant to a current
literature debate. In contrast with our findings, previous experi-
ments by Rouquerol et al.42showed a very similar isosteric heat
of adsorption for argon at 77 K on silica gel samples outgassed
no significant change of the argon adsorption isotherm on silica
samples activated at 423 and 1073 K.43According to the
experiments by Zhuravlev,29the expected surface densities of
OH groups are about 5.6, 0.7, and 0.4 OH/nm2after thermal
tratments at 423, 1073, and 1173 K, respectively. On the other
hand, more recent experimental data show the non-negligible
with our simulation results. For instance, Grillet and Llewellyn
found that the adsorption enthalpy for argon on functionalized
silica with alkyl chains is decreased compared to that on
that the argon/surface interaction for silica-based adsorbents
(Faujasite, ZSM, and Mordenite) depends on the strength of the
adsorption site.45,46Finally, these results are in agreement with
(40) Payne, D. A.; Sing, K. S. W.; Turk, D. H. J. Colloid Interface Sci. 1973,
(41) Neimark, A. V.; Ravkovitch, P. I.; Grun, M.; Schuth, F.; Unger, K. K.
J. Colloid Interface Sci. 1998, 207, 159.
(42) Rouquerol, F.; Rouquerol, J.; Sing, K. S. W. Adsorption by Powders and
Porous Solids; Academic Press: London, 1999; p 309.
(43) Aristov, B. G.; Kiselev, A. V. Colloid J. 1965, 27, 246.
(44) Grillet, Y.; Llewellyn, P. The surface properties of silica; Legrand, P.,
Ed.; Wiley: Chichester, 1998; p 62.
(45) Matsuhashi, H.; Arata, K. Phys. Chem. Chem. Phys. 2004, 6, 2529.
(46) Matsuhashi, H.; Arata, K. Catal. Today 2006, 111, 338.
Figure 3. Ar adsorption isotherm at 77 K on amorphous silica planes:
(black circles) fully hydroxylated, P1, and (gray circles) partially
silica plane similar to P1but with a crystalline structure. The solid gray
line corresponds to the experimental data by Sing and co-workers for
Ar adsorption at 77 K on nonporous amorphous silica (from ref 40).
Figure 4. Isosteric heat of adsorption as a function of the number of
adsorbed atoms for argon at 77 K on silica planes: (black circles) fully
hydroxylated, P1, and (gray circles) partially hydroxylated, P2.
7288 Langmuir, Vol. 24, No. 14, 2008Coasne et al.
those previously reported by Michot et al.47showing that argon
believe that the results reported in the present simulation work
show in a clear and simple way the effect of the surface polarity
of the adsorbent on the adsorption of argon, as seen in the large
set of experimens mentioned above. However, we do not reject
that the force field used in our study (charges carried by the
atoms of the substrate, repulsion/dispersion interaction param-
eters) may overestimate a little the effect of the surface
to clarify this issue.
The distribution of distances dArObetween the Ar adsorbed
atoms and the O atoms at the surface of the silica substrate is
shown in Figure 5 for the fully hydroxylated (P1) and partially
hydroxylated (P2) planes. For the plane P2, we distinguish the
distances to an O(OH)atom belonging to an OH group and those
to an O(OSi)atom belonging to a Si-O-Si bridge. All these
distributions were calculated at low loadings (P ) 2 × 10-4P0)
when less than one layer of argon atoms was adsorbed on the
silica surface. The Ar-O distance distribution for the fully
hydroxylated surface is unimodal: all the adsorbed atoms are
located at an equal distance, dArO∼ 3.7 Å, from four oxygen
is illustrated in Figure 5 where we report a typical molecular
configuration obtained during a simulation run. The Ar-O(OH)
distance distribution for the partially hydroxylated surface is
also unimodal if we consider only the distances to the O atoms
belonging to the OH groups. The average distance, dArO) 3.7
Å, is equal to that found for the substrate P1. On the other hand,
the Ar-O(OSi)distance distribution exhibits two peaks located
configurations reveals that (1) the first peak corresponds to an
Ar atom located between one O(OH)and three O(OSi)and (2) the
second peak corresponds to an Ar atom located between two
O(OH) and two O(OSi) or three O(OH) and one O(OSi). The first
situation is illustrated in the second typical molecular config-
uration shown in Figure 5.
3.2. Effect of Pore Shape. The argon adsorption isotherms
at 77 K for the fully and partially hydroxylated cylindrical pores
hysteresis). The argon adsorption isotherms for these two pores
conform to the typical behavior observed in the experiments for
adsorption/condensation in MCM-41:6the adsorbed amount
increases continuously in the multilayer adsorption regime until
a jump occurs due to capillary condensation of the fluid within
the pores. The condensation pressures are P ) 0.116P0for the
pressures, P ) 0.11P0(C1) and P ) 0.10P0(C2), are lower than
The larger condensation and evaporation pressures for the
density of OH groups for the pore C2, the thickness t(P) of the
film adsorbed for this pore is smaller at all pressures P than for
pore C1. As a result, the inner core radius R ) R0 - t(P),
corresponding to the pore radius R0 diminished by the film
thickness t(P), is larger at all pressures for the pore C2so that
capillary condensation will occur at a higher pressure for this
pore than for the pore C1. It is worth mentioning that this
explanation is independent of the model used (Kelvin equation,
Density Functional Theory, molecular simulation) to predict the
capillary condensation pressure as the latter is necessarily a
monotonous increasing function of the inner core radius R.
Figure 7 shows simulation snapshots of Ar atoms adsorbed
in the cylindrical nanopore C1 at the onset of capillary
condensation and evaporation. The surface of the nanopore is
covered by a molecularly thick cylindrical film at the onset of
condensation occurs through an irreversible and discontinuous
transition between the partially filled and the completely filled
configurations (see also the adsorption isotherm in Figure 6). In
agreement with previous works on adsorption/desorption in
length occurs through the displacement at equilibrium of a
hemispherical meniscus along the pore axis (Figure 7). This
result departs from what is observed for pores having an infinite
length for which the evaporation occurs necessarily through
cavitation as there is no interface between the confined liquid
and the external gas phase.13,14,37,48–53We also report in Figure
Louis Robert, J. -L. J. Phys. Chem. B 1998, 102, 3466.
(48) Sarkisov, L.; Monson, P. A. Langmuir 2001, 17, 7600.
Figure 5. (top) Histograms of the distances between the Ar adsorbed
atoms and the O atoms at the surface of the silica substrate. The dotted
and solid lines are for the fully hydroxylated (P1) and partially
hydroxylated (P2) planes, respectively. For the plane P2, the black line
is the distance to an O(OH)atom in an OH group, while the gray line is
the distance to an O(OSi) atom in a Si-O-Si bridge. (right) Typical
configurations of an argon atom adsorbed on the silica plane P1(left)
and P2(right). The argon atom is shown as a big white sphere. Gray and
black spheres are oxygen atoms belonging to an OH and Si-O-Si
group, respectively. The small white sphere is the hydrogen atom (OH
with D ) 3.2 nm: (black symbols) fully hydroxylated, C1, and (gray
to the adsorption and desorption data, respectively. Adsorbed amounts
have been normalized to the total number of adsorbed atoms when the
pores are completely filled, N0.
Effect of Surface Chemistry and Pore ShapeLangmuir, Vol. 24, No. 14, 2008 7289
8 molecular configurations of Ar adsorbed in the cylindrical
nanopore C2at the onset of capillary condensation and evapora-
tion. As for the pore C1, the surface of the nanopore is covered
by a molecularly thick cylindrical film at the onset of capillary
condensation. However, the film adsorbed at the surface of the
pore C2is less homogeneous compared to that for the nanopore
molecules (Figure 8). This result is due to the larger surface
heterogeneity of pore C2, which possesses different surface
bridges, respectively. Despite this difference in the filling of
through an irreversible discontinuous transition between the
partially filled and the completely filled configurations (see also
the adsorption isotherm in Figure 6). In addition, as for the
the displacement at equilibrium of a hemispherical meniscus
along the pore axis. However, the emptying mechanism for the
pore C2also reflects its larger degree of surface heterogeneity
as the recession of the hemispherical meniscus along the pore
axis is asymmetrical (as shown in Figure 8, the left part of the
pore empties more rapidly than the right part).
The hysteresis loops for the nanopores C1and C2are of a
similar width (we assume in what follows that they are identical
given the uncertainty over the capillary condensation and
evaporation pressures). We know from previous experimen-
tal,54–57theoretical,58–61and molecular simulation9,62,63works
that there is a temperature, the so-called capillary condensation
temperature Tcc, above which capillary condensation in nan-
oporous solids becomes reversible and continuous. This pseud-
ocritical temperature, which increases as the pore diameter
increases, corresponds to the threshold of reversible capillary
Tcc, the width of the hysteresis loop decreases and, finally,
disappears for T ) Tcc. The fact that the width of the hysteresis
loops for C1 and C2 is identical suggests that Tccis independent
with our previous works which suggest that Tccis independent
of the shape (cylindrical, ellipsoidal, constricted) of the pore.62
The argon adsorption isotherms at 77 K for the fully
hydroxylated cylindrical and hexagonal pores (C1and H1) are
shown in Figure 9. Again, the adsorbed amounts have been
hysteresis). The adsorption isotherms for these two regular
nanopores resemble their experimental counterpart for MCM-
41 samples, which suggests that these materials are made up of
cylindrical or hexagonal pores having no or only very smooth
morphological defects. Inspection of molecular configurations
taken upon adsorption and desorption (not shown) reveal that
(49) Ravikovitch, P. I.; Neimark, A. V. Langmuir 2002, 18, 1550.
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E.; Fajula, F.; Di Renzo, F. Langmuir 2005, 21, 8560.
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(59) Evans, R.; Marini Bertollo Marconi, U.; Tarazona, P. J. Chem. Phys.
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Science Catalysis; Elsevier Science: New York, 2006; Vol. 160; 1-8.
Figure 7. Configurations of argon atoms adsorbed at 77 K on a fully
hydroxylated silica cylindrical nanopore C1: (top) onset of capillary
condensation, P ) 0.12P0, and (bottom) onset of capillary evaporation,
P ) 0.10P0. Black spheres correspond to the hydrogen atoms, which
delimit the pore surface, and the light colored spheres are Ar atoms.
Figure 8. Configurations of argon atoms adsorbed at 77 K on a fully
hydroxylated silica cylindrical nanopore C2: (top) onset of capillary
condensation, P ) 0.12P0, and (bottom) onset of capillary evaporation,
P ) 0.11P0. Black spheres correspond to the hydrogen atoms, which
delimit the pore surface, and the light colored spheres are Ar atoms.
Figure 9. Ar adsorption isotherm at 77 K on fully hydroxylated silica
hexagonal pore, H1. Open and closed symbols correspond to the
adsorption and desorption data, respectively. Adsorbed amounts have
been normalized to the total number of adsorbed atoms when the pores
are completely filled, N0.
7290 Langmuir, Vol. 24, No. 14, 2008Coasne et al.
the filling and emptying mechanisms for the hexagonal pore are
identical to those for the cylindrical pore. Condensation occurs
at the pore surface, while evaporation occurs through the
displacement at equilibrium of a hemispherical meniscus along
the pore axis. Prior to capillary condensation, the adsorbed
amounts for the pore H1are very similar to those for pore C1.
This result suggests that the slight difference between the shape
of the cylindrical and hexagonal pores has no or very little
the condensation and evaporation pressures for the pore H1are
larger than those for the pore C1.
To gain more insight on the origin of the shift in the
and hexagonal (H1) pores, we show in Figure 10 density maps
of argon adsorbed in these pores at the onset of capillary
condensation in the pore C1(P ) 0.12P0). We estimated from
the density profiles of argon in these pores when a gas/liquid
interface exists (not shown) that regions with a density larger
than Fc) 1 atom/nm3correspond to the adsorbed liquid-like
phase (the bulk liquid density at this temperature is ∼22 atom/
nm3). For the sake of clarity, the density maps in Figure 10 do
not report the gaslike phase, i.e., regions with F < Fc. The effect
of such an arbirtrary choice will be discussed below. To avoid
considered in the calculations of these density maps (the total
pore length is 25.6 nm). While the gas/liquid interface for the
nanopore C1is of a regular cylindrical geometry, that for the
nanopore H1is of a hexagonal geometry (i.e., a collection of
The slight shift in the condensation/evaporation pressures for
the shape of the hexagonal gas/liquid interface is rotated with
respect to the hexagonal pore wall section (i.e., the corners of
the gas/liquid interface point toward the planar sides of the pore
pore. If another value is chosen for Fc, the gas/liquid interface
remains hexagonal so that the reasoning above is still valid. For
instance, for Fc) 5 atom/nm3(the corresponding density maps
are readily obtained by removing the blue regions in Figure 10),
the gas/liquid interface for the pore H1remains hexagonal but
not rotated with respect to the pore section. The interpretation
pressures to the delay in the formation of a regular cylindrical
gas/liquid interface for pore H1, is supported by the fact that
planar gas/liquid interfaces are theoretically stable up to the
interfaces are stable up to a pressure above that for a curved
interface (for a given pore size) and collapse when the system
becomes unstable, i.e., when the Laplacian capillary pressure
corresponding to the pressure difference between the liquid and
gas phases cannot counterbalance the sum of the surface free
energy (surface tension) and disjoining pressure (caused by
The argon adsorption isotherms at 77 K for the partially
hydroxylated cylindrical and hexagonal pores (C2and H2) are
shown in Figure 11. Again, the adsorbed amounts have been
hysteresis). The adsorption isotherms are very similar to those
for the fully hydroxylated cylindrical and hexagonal pores. The
(64) Crassous, J.; Charlaix, E.; Loubet, J. L. Europhys. Lett. 1994, 28, 37.
Sci. 2002, 96, 143.
Figure 10. Density map F(x,y) of argon adsorbed at 77 K and 0.12P0on fully hydroxylated silica nanopores with D ) 3.2 nm: (left) cylindrical pore,
C1, and (right) hexagonal pore, H1. To avoid the effect of the pore openings, only atoms with |z| < 10 nm were considered in the calculations of
the density maps (the total pore length is 25.6 nm). x and y are the algebraic distances to the pore axis. The density increases from blue f green
f yellow f orange f red. Only pore regions occupied with an adsorbate density F > 0.001σ3are shown (lower densities correspond to the gas
Figure 11. Ar adsorption isotherm at 77 K on partially hydroxylated
silica nanopores with D ) 3.2 nm: (circles) cylindrical pore, C2, and
(squares) hexagonal pore, H2. Open and closed symbols correspond to
the adsorption and desorption data, respectively. Adsorbed amounts
have been normalized to the total number of adsorbed atoms when the
pores are completely filled, N0.
Effect of Surface Chemistry and Pore ShapeLangmuir, Vol. 24, No. 14, 2008 7291
and partially hydroxylated pores, which shows that the surface
chemistry does not affect these mechanisms. Again, the larger
to those for the nanopore C2are probably due to the delay in the
formation of a regular cylindrical gas/liquid interface for this
for the nanopore H2 and C2 compared to that between the
nanopores C1and H1can be qualitatively explained as follows.
In the case of the nanopores C1 and H1, the delay in the
of a cylindrical gas/liquid interface) is partially compensated by
the more attractive surface for this pore as its surface density of
OH groups (7.9 OH/nm2) is larger than that for the nanopore C1
(7.4 OH/nm2). In contrast, the surface density of OH groups for
the nanopores C2and H2are identical so that the delay in the
formation of a regular circular gas/liquid interface is not
study is needed to fully clarify this issue.
3.3. Test of the BET Method. The BET method is routinely
used to characterize porous solids as it allows the estimation of
specific surfaces from adsorption isotherms on the basis of a
model developed to describe multilayer adsorption. The hy-
homogeneous sites having an energy ?1(the surface density of
on each other. In this case, the adsorption energy ?0 for all
molecules adsorbed above the first layer is constant and equal
it can be shown that adsorption data (adsorbed amount N versus
the relative pressure P/P0) must obey the following equation
where Nmis the monolayer capacity, i.e., the number of atoms
needed to uniformly cover the substrate with one monolayer.
The factor C ) exp(ε1- ε0) is related to the energetics of the
system. The parameters CBETand N0can be estimated from the
A comparison between the BET surface and the geometrical
considered in this work. The BET plot was found to describe
quite well the Ar adsorption isotherm for the planar substrates
over the range of reduced pressures [0.1, 0.3] (as typically
at low temperature). On the other hand, the linear region of the
BET plot for the cylindrical and hexagonal pores was limited to
a small range of relative pressures from [0.01 to 0.1] as the
capillary condensation occurs at very low pressures. The
the common value for atomic surface area for an Ar atom at 77
K a(Ar) ) 0.138 nm2(this value has been chosen as its use is
recommended when applying the BET method to estimate the
significantly depends on the surface chemistry as it is about
twice as large for the fully hydroxylated substrates than for the
seems to be sensitive to the confinement as it is much larger for
the cylindrical and hexagonal pores than for the silica surface.
In contrast, our results suggest that the parameter CBETcannot
be used to distinguish the hexagonal and cylindrical pores as it
is, for a given surface chemistry, very similar for these two
geometries. The BET surface for fully hydroxylated surfaces is
much larger (by 10 to 20%) than the true geometrical surface,
in agreement with our previous work on adsorption of argon in
silica pores of various morphologies and topologies.37On the
other hand, it is found that the BET surface significantly
underestimates the true surface when partially hydroxylated
surfaces are concerned. These results suggest that the surface
chemistry and the choice of the system adsorbate/adsorbent are
who observed that the fraction of covered surface at the BET
monolayer depends on the value of CBET. In agreement with the
the fraction of the second monolayer already filled at the BET
monolayer are expected to increase with a decrease of the wall/
fluid (CBET) interaction.66Such a result is also consistent with
the effective surface area occupied by Ar atoms on different
materials when the substrate is supposedly covered by a
monolayer. These authors found that such an effective atomic
surface area can vary by a factor 2 depending on the surface
and the BET surface obtained from our simulation data, a(Ar)
) 0.115 nm2and a(Ar) ) 0.230 nm2should be used for argon
reported in Table 2 show that the ratio of the BET surface to the
true surface is not very sensitive to the confinement effect and
cylindrical and hexagonal nanopores are very similar (provided
the surface chemistry is identical).
of argon at 77 K on hydroxylated silica surfaces and nanopores.
We address the effect of surface chemistry by considering
substrates with either partially or fully hydroxylated surfaces.
is also addressed by comparing the results for cylindrical and
hexagonal nanopores having equivalent sections (i.e., equal
section areas). All the pores considered in this work are of a
finite length and are connected to bulk reservoirs so that they
mimic real materials for which the confined fluid is always in
(66) Hill, T. L. J. Chem. Phys. 1946, 14, 268.
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Table 2. BET Surface and Parameter (SBETand CBET) for the Different Substrates Considered in the Present Worka
plane substrate cylindrical porehexagonal pore
aWe also report the ratio of the BET surface assessed from argon adsorption at 77 K and the true geometrical surface SGEO. The monolayer capacity has
been converted into a surface area using the common value for atomic surface area for an argon atom at 77 K, σ(Ar) ) 0.138 nm2.
7292 Langmuir, Vol. 24, No. 14, 2008 Coasne et al.
contact with the external gas phase (this departs from infinitely Download full-text
long pores for which the evaporation of the confined liquid
necessarily occurs through cavitation as there is no interface
with the external phase). The data are analyzed and compared
molecular configurations are also used to monitor the filling and
emptying mechanisms of the pores. Finally, we also discuss the
effect of surface chemistry and pore shape on the routinely used
characterization method based on the BET model.
Our findings can be summarized as follows. For a given
substrate (plane, cylindrical, or hexagonal nanopores), the
adsorbed amounts are larger for the fully hydroxylated surface
than those for the partially hydroxylated surface. This result is
due to the fact that an increase in the density of silanol groups
induces an increase in the polarity of the silica surface, which,
of the surface chemistry is also reflected in the isosteric heat of
adsorption Qst which increases as the surface density of OH
The argon adsorption isotherms for the cylindrical and
MCM-41. The adsorbed amount increases continuously in the
are observed. For both the cylindrical and hexagonal pores,
capillary condensation occurs through an irreversible discontinu-
ous transition between the partially filled and the completely
filled configurations (collapse of the cylindrical adsorbed film),
of a hemispherical meniscus along the pore axis. For a given
surface chemistry (fully or partially hydroxylated surfaces), the
condensation and evaporation pressures for the hexagonal pore
are larger than those for the cylindrical pore. This result is due
to the delay in the formation of a regular circular gas/liquid
keeps memory of the pore shape up to a pressure slightly above
the condensation pressure for the regular cylindrical pore).
Our results show that the parameter CBETdepends on both the
surface chemistry and confinement. The BET surface for fully
hydroxylated surfaces is much larger (by 10 to 20%) than the
true surface. In contrast, the BET surface significantly under-
estimates the true surface when partially hydroxylated surfaces
are concerned. These results suggest that the surface chemistry
and the choice of the system adsorbate/adsorbent is crucial in
determining the surface area of porous solids using the BET
method. In contrast to the factor CBET, the ratio of the BET
surface to the true surface is found to not be very sensitive to
the confinement effect and the pore shape.
Effect of Surface Chemistry and Pore ShapeLangmuir, Vol. 24, No. 14, 2008 7293