Journal of Molecular Structure: THEOCHEM 729 (2005) 65–69
www.elsevier.com/locate/theochem
Molecular simulations of nitrogen adsorption
in pure silica MCM-41 materials
A.J. Palace Carvalhoa,b,*, T. Ferreirab, A.J. Estêvão Candeiasa,b, J.P. Prates Ramalhoa,c
a
Departamento de Quı́mica de Évora, Universidade de Évora, Rua Romão Ramalho 59, 7002-554 Évora, Portugal
b
Centro de Quı́mica de Évora, Universidade de Évora, Rua Romão Ramalho 59, 7002-554 Évora, Portugal
c
Centro de Fı́sica Teórica e Computacional, Av. Prof. Gama Pinto 2, 1649-003 Lisboa Codex, Portugal
Received 31 December 2004; accepted 28 January 2005
Available online 14 July 2005
Abstract
Nitrogen adsorption isotherms in infinite hexagonal shaped silica nanopores were obtained by Grand Canonical Monte Carlo simulations
and compared with experimental isotherms of this adsorptive on highly regular MCM-41 pure silica materials. The influence of surface
irregularity and pore size was analysed. The results indicate that the nitrogen adsorption in MCM-41 is well described by a model using
Lennard–Jones N2 spheres and amorphous hexagonal shaped pores.
q 2005 Elsevier B.V. All rights reserved.
Keywords: Grand canonical Monte Carlo; MCM-41; Nitrogen adsorption
1. Introduction
Since its discovery in 1992 by Beck et al. [1], MCM-41
silicate materials have been the subject of intense study by
the scientific community. What makes these materials so
interesting is their highly regular porous nanostructure with
hexagonal arrangement of parallel non-intersected uniform
tubular pores, the ease of their synthesis and pore size
control in the mesopore region and their high surface areas
and pore volumes [2,3]. The vast majority of the published
studies deal with its potential use in catalysis, which
include not only the modification of its surface properties
but also the incorporation of active species in the host
porous structure [4–9]. Several mechanisms have been
proposed for the synthesis of these materials [10–13] and
it is now well established that it involves the
interaction between silicate and surfactant species and its
self-assembly, which is controlled by charge density
matching [13].
* Corresponding author. Address: Departamento de Quı́mica de Évora,
Universidade de Évora, Rua Romão Ramalho 59, 7002-554 Évora,
Portugal. Tel.: C351 66745300; fax: C351 66745394.
E-mail address: [email protected] (A.J. Palace Carvalho).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.theochem.2005.01.057
MCM-41 materials have been characterised by several
techniques, particularly X-ray diffraction (XRD), transmission electron microscopy (TEM), NMR spectroscopy
and adsorption analysis. It was found that these materials are
composed of amorphous silica walls with silanol surface
concentrations ranging from 20 to 30% [1,14].
These materials have been used as model adsorbents in
fundamental studies concerning the criticality of the
condensation process [15–17], the development of theoretical models to describe the adsorption mechanism in
nanopores [17–19] and the evaluation and refinement of
empirical methods used in the analysis of adsorption
isotherms [20–22]. In particular, Grand Canonical Monte
Carlo (GCMC) simulations have been used to study the
adsorption of nitrogen and other gases in MCM-41 [23]. It
has been shown that models in which the fluid interacts with
a homogeneous non-discretised surface cannot reproduce
the shape of the adsorption isotherm of nitrogen in MCM-41
and the influence of pore wall heterogeneity was investigated. The results showed that heterogeneity effects play an
important role in the adsorption mechanism and its inclusion
allows a very good agreement with experimental data [23].
Similar findings were obtained for the adsorption of Ar and
Kr [24–26].
In all these works, it was generally assumed that these
materials have cylindrical pores. However, different studies
66
A.J. Palace Carvalho et al. / Journal of Molecular Structure: THEOCHEM 729 (2005) 65–69
aiming the elucidation of its structural properties have
shown that they have non-interconnected tubular hexagonal
shaped pores with amorphous silica walls with thicknesses
in the range of 0.8–1.2 nm [27–31].
The finding about the possible hexagonal pore shape is of
utmost importance, especially in studies concerning the
structural characterisation of these materials and its use as
model adsorbents. In this work, we present a comparative
study of simulated GCMC nitrogen adsorption isotherms on
hexagonal shaped pores with experimental data obtained on
pure silica MCM-41 samples with comparable pore widths.
The roles of surface irregularity and pore width were
investigated.
2. Simulation details
Two pure silica hexagonal nanopores, designated as A
and B, were generated with vertex to vertex distances of
4.246 and 3.717 nm, respectively.
Experimentally, the determination of the pore widths
assumes a cylindrical pore shape. Therefore, for comparison
purposes, vertex to vertex widths of hexagonal shaped
nanopores have to be converted to an equivalent pore width
of a cylindrical pore model with the same internal surface
area. Simple calculation shows that the equivalent cylindrical pore radius is given by
rZ
3
ðd K sO Þ
2p h
(1)
where dh stands for the vertex to vertex distance of the
hexagonal section and sO is the wall’s oxygen atom
diameter. Using the oxygen’s van der Waals diameter of
0.304 nm, the equivalent cylindrical pore radii of 1.882 and
1.630 nm are obtained for hexagonal nanopores A and B,
respectively. These distances allow comparison of isotherms with available experimental data obtained on pure
silica MCM-41 materials with average pore radii of 1.89 and
1.65 nm when estimated by DFT method, or 1.84 and
1.60 nm when estimated by geometrical considerations
[22].
A set of GCMC simulations was performed for systems
consisting of the pure silica periodic hexagonal nanopores
containing nitrogen at 77 K and at different pressures. The
regularity of the silica structure was modified in some
simulations to take into account the amorphous nature of
mesostructured silica materials by introducing displacements randomly in the positions of the matrix atoms (Fig. 1).
Nitrogen adsorption simulations were carried out using a
GCMC code developed in our group.
The Monte Carlo moves consisted of centre of mass
translation of the N2 molecules and the creation and
annihilation steps inherent to the GCMC algorithm.
The chemical potentials of the nitrogen were calculated,
for a given pressure, using the Peng-Robinson equation of
state defined by its gas’ critical properties [32].
Fig. 1. Structures of the pure silica model hexagonal nanopores. (a) Periodic
(b) with 0.25 Å random displacements (c) with 0.5 Å random
displacements.
The nitrogen molecules were modelled as single
Lennard–Jones spheres and the adsorbent was modelled
by Lennard–Jones potentials centred on the oxygen atoms.
Several parameters available in the literature were tested
[23,33,34] (Table 1). The dispersive interactions with the
silicon atoms were neglected due to their reduced polarizability, which results in very weak dispersive interactions.
Lorentz–Berthelot mixing rules were employed to obtain
the parameters for the oxygen–adsorbate interactions.
Periodic boundary conditions were used in the simulations lengthwise. The dispersive interactions were neglected past a cutoff of 20 Å.
Averages were calculated for 106 simulation steps after a
equilibration run of the same length. In addition to the
adsorption isotherms, the isosteric heats of adsorption have
also been calculated. The isosteric heats of adsorption can
be computed in a GCMC simulation from the particle
number and energy fluctuations [35]
qst Z kT K
hUNi K hUihNi
hN 2 i K hNi2
(2)
where qst is the isosteric heat of adsorption per molecule, N
is the number of adsorbed atoms and U is the total potential
energy of the system.
3. Simulation results and discussion
The periodic hexagonal silica nanopore A was used to
test the different sets of Lennard–Jones parameters.
The simulated isotherms were compared with an
experimental isotherm obtained on a mesostructured pure
silica MCM-41 with equivalent average pore width [22].
The results are shown in Fig. 2. It can be seen that
Table 1
Published Lennard–Jones parameters used in this work
Reference
Species
3kb (K)
s (Å)
Maddox et al. [23]
O
N2
O
N2
O
N2
164.13
95.2
229.95
95
80.507
95.2
3.2
3.75
2.7
3.7
3.033
3.75
Miyahara et al. [33]
Ravikovitch et al. [34]
28
24
24
20
20
67
–1
28
nads/ mmol.g
nads/ mmol.g–1
A.J. Palace Carvalho et al. / Journal of Molecular Structure: THEOCHEM 729 (2005) 65–69
16
12
experimental
Maddox et al
Ravikovitch et al
Miyahara et al
8
4
16
12
experimental
crystalline
distort. 0.25 A
distort. 0.50 A
8
4
0
0.0
0.2
0.4
0.6
0.8
1.0
p/p0
0
0.0
0.2
0.4
0.6
0.8
1.0
p/p0
Fig. 2. Simulated isotherms obtained in silica nanopore A using different
Lennard–Jones parameters. Solid line represents the experimental isotherm
obtained on a MCM-41 sample with equivalent mean pore width [22].
the parameters proposed by Maddox et al. [23] show a better
fit, thus allowing a better description of the system.
Maddox et al. [23] parameters were used to generate
simulated isotherms on both nanopores and compared with
those obtained for the MCM-41 materials. Fig. 3 shows the
simulated and the experimental isotherms. Comparison of
these isotherms shows that the simulated ones exhibit the
same general features as the experimental ones obtained on
MCM-41. These isotherms show initially a rapid increase in
the adsorbate amount at very low relative pressures
corresponding to the monolayer formation; as the pressure
is increased additional multilayers are gradually adsorbed
followed by a sudden step in the same range of p/p0
corresponding to capillary condensation in uniform and
regular pores. Even though the simulated isotherms can
reproduce fairly the adsorption of nitrogen in MCM-41
28
24
nads/ mmol.g–1
20
16
12
8
4
0
0.0
0.2
0.4
0.6
0.8
1.0
p/p0
Fig. 3. Simulated isotherms (B) obtained on hexagonal nanopores A and B
and experimental isotherms (—) obtained on MCM-41 materials with
equivalent mean pore widths [22].
Fig. 4. Simulated isotherms obtained on silica nanopore B and with
different random distortions in the crystalline structure of the silica walls.
Solid line represents the experimental isotherm obtained on a MCM-41
sample with equivalent mean pore width [22].
the fit is still poor in the mono-multilayer region (before the
pore filling step), which is probably due to the structural
differences between the amorphous pore wall of the real
adsorbent and the crystalline structure used in the
theoretical model.
To overcome this situation, simulated isotherms were
made on silica nanopores with different distortions in the
crystalline structure of the silica walls. Fig. 4 shows the
simulated isotherms along with the experimental isotherm.
It can be seen that the incorporation of surface irregularity
provides a good agreement with the experimental isotherm,
which extends into the mono-multilayer region. This
observation is consistent with the amorphous nature of
synthesized mesoporous silicas and shows that the discretised silica model with hexagonal shaped pores can
reproduce the adsorption of nitrogen in pure silica MCM-41.
The results also show that the capillary condensation
pressure is not influenced significantly by the pore wall
irregularity mainly because the solid–fluid interactions are
short-ranged. This can be illustrated by the average particle
density for nitrogen in nanopore A and by the variation of
the isosteric heats of adsorption as a function of coverage in
the same pore with and without structural distortion (Figs. 5
and 6). The results clearly show that the nitrogen molecules
in the monolayer adsorb strongly at the surface and remain
localized in the adsorption centers, which correspond to
higher isosteric heats. On the other hand, when the pressure
increases, a more diffuse second layer is formed, corresponding to lower isosteric heats, followed by capillary
condensation. The isosteric heats of adsorption of the
crystalline structure also show that, during the formation of
the monolayer the heat of adsorption increases slightly due
to the contribution of fluid–fluid interactions. This result is
similar to the ones obtained by Maddox and Gubbins for
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A.J. Palace Carvalho et al. / Journal of Molecular Structure: THEOCHEM 729 (2005) 65–69
Fig. 5. Average particle density for nitrogen obtained in nanopore A at different relative pressures: (a) 0.00082 (b) 0.082 (c) 0.247 (d) 0.345.
argon adsorption in a Buckytube [18]. However, in the case
of the nanopore with amorphous walls the heat of adsorption
decreases during formation of the monolayer reflecting
the surface energetic heterogeneity. In fact, at low coverage
nitrogen molecules adsorb firstly in the centers with higher
energy (outer oxygen atoms) and progressively in the
centers with decreasing energies. After the formation of the
monolayer the isosteric heat curves are identical for both
structures showing that for higher pressures the adsorbate
molecules interact mostly with each other and are not
influenced by the surface nature of the adsorbent.
14000
crystalline
distort. 0.5 A
qst / Jmol–1
12000
4. Conclusions
We have simulated a series of adsorption isotherms of
nitrogen in MCM-41 and compared it to experimental data.
Several models for the interaction potential were tested. We
adopted a silica crystalline description of the MCM-41
structure with a hexagonal section. Modelling the nitrogen
molecule as a Lennard–Jones sphere can give good results
when the potential parameters are carefully chosen.
The influence of surface roughness in the MCM-41
structures was also studied. In general, the introduction of
surface roughness improved the agreement with the
experimental data, particularly in the low pressure region
corresponding to the mono-multilayer coverage.
Considering the encouraging results obtained in this
work, we hope to improve and extend the present approach
to other adsorptives and adsorbents.
10000
8000
References
6000
4000
0
100
200
300 400 500
N / molec.
600
700
800
Fig. 6. Isosteric heats of adsorption as a function of coverage in the silica
nanopore A with and without structural distortion.
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