Adsorption and Structure of Benzene on Silica Surfaces and in

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Adsorption and Structure of Benzene on Silica Surfaces and in Nanopores Benoit Coasne,*,† Christiane Alba-Simionesco,§, Fabrice Audonnet,§ Gilberte Dosseh,§ and Keith E. Gubbins‡ †

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Institut Charles Gerhardt Montpellier, UMR 5253 CNRS, Universit
e Montpellier 2, ENSCM, Place Eug ene Bataillon, 34095 Montpellier Cedex 05, France, §Laboratoire de Chimie Physique, UMR 8000 CNRS, Universit
e Orsay, 91405 Orsay Cedex, France, Laboratoire L
eon Brillouin, CEA Saclay, B^ atiment 563, 91191 Gif-sur-Yvette Cedex, France, and ‡Center for High Performance Simulation and Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905 Received March 20, 2009. Revised Manuscript Received June 22, 2009 Grand canonical Monte Carlo simulations are used to study the adsorption of benzene on atomistic silica surfaces and in cylindrical nanopores. The effect of temperature and surface chemistry is addressed by studying the adsorption of benzene at 293 and 323 K on both fully and partially hydroxylated silica surfaces or nanopores. We also consider the adsorption of benzene in a cylindrical nanopore of diameter D=3.6 nm and compare our results with those obtained for planar surfaces. The structure of benzene in the vicinity of the planar surface and confined in the cylindrical nanopore is determined by calculating orientational order parameters and examining positional pair correlation functions. The density profiles of adsorbed benzene reveal the strong layering of the adsorbate, which decays with the distance from the silica surface. At a given temperature and at low pressures, the film adsorbed at the fully hydroxylated silica surface is larger than that for the partially hydroxylated silica surface. This result is due to an increase in the density of silanol groups that induces an increase in the polarity of the silica surface, which becomes more attractive for the adsorbate. Our results also suggest that the benzene molecules prefer an orientation in which their ring is nearly perpendicular to the surface when fully hydroxylated surfaces are considered. When partially hydroxylated surfaces are considered, a second preferential orientation is observed where the benzene ring forms an angle of ∼50
with the silica surface. In this case, the average orientation of the benzene molecules appears disordered as in the bulk phase. These results suggest that determining the experimental orientation of benzene in the vicinity of a silica surface is a difficult task even when the surface chemistry is known. Capillary condensation in the nanopores involves a transition from a partially filled pore (a thin film adsorbed at the pore surface) to a completely filled pore configuration where the confined liquid coexists at equilibrium with the external gas phase. The disordered orientation of the adsorbed benzene molecules in the case of the partially hydroxylated surface favors the condensation of benzene molecules (the condensation pressure for this substrate is lower than that for the fully hydroxylated surface). Finally, these results are consistent with the structural analysis, showing that (1) benzene tends to relax its liquid structure a little in order to optimize its molecular arrangement near the pore wall and (2) the disordering of the liquid structure induced by the surface becomes stronger as the interaction with the pore wall increases.

1. Introduction The behavior of fluids in the vicinity of surfaces or confined within nanometric pores (size of a few molecular diameters) significantly differs from that of the bulk. In particular, the surface forces and nanoconfinement affect the phase transitions (condensation, freezing, etc.).1,2 Significant shifts in transitions (e.g., pressure, temperature, composition) are observed, and new types of phase transitions (layering, wetting, etc.) are often found for these inhomogeneous systems. Understanding such confinement and surface effects on the thermodynamics of fluids is of crucial interest for both fundamental research and potential applications. Among nanoporous solids, the siliceous MCM-413 and SBA154 are important materials because of their possible uses as adsorbents or catalytic supports for gas adsorption, phase *To whom correspondence should be addressed. E-mail: benoit.coasne@ univ-montp2.fr. Phone: +33 4 67 14 33 78. Fax: +33 4 67 14 42 90. (1) Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. Rep. Prog. Phys. 1999, 62, 1573. (2) Alba-Simionesco, C; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. J. Phys.: Condens. Matter 2006, 18, R15. (3) Beck, J. S.; Vartulli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C. T.-W.; Olson, D. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. J. Am. Chem. Soc. 1992, 114, 10834. (4) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Science 1998, 279, 548.

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separation, catalysis, preparation of nanostructured materials, drug delivery, and so forth.5-8 These materials are obtained by a template mechanism involving the formation of surfactant or block copolymers micelles in a mixture composed of a solvent and a silica source. After polymerization of the silica and removal of the organic micelles, one obtains a material made up of an array of regular pores. The pore diameter distribution is narrow with an average value that can be varied from 2 to ∼15-20 nm, depending on the synthesis conditions.7 From a fundamental point of view, MCM-41 and SBA-15 are considered as model materials to investigate the effect of nanoconfinement on the thermodynamic properties of fluids. In particular, the ideal geometry of the pores in these materials makes it possible to address in a simple way the effect of confinement on the adsorption, capillary condensation, and freezing/melting of fluids in nanopores. As a result, many experimental, theoretical, and molecular simulation studies have been reported on the thermodynamics and dynamics of fluids confined in these materials (for reviews, see refs 1. 2, and 9). (5) Corma, A. Chem. Rev. 1997, 97, 2373. (6) Ciesla, U.; Sch€uth, F. Microporous Mesoporous Mater. 1999, 27, 131. (7) Soler-Illia, G. J.; de, A. A.; Sanchez, C.; Lebeau, B.; Patarin, J. Chem. Rev. 2002, 102, 4093. (8) Galarneau, A.; Calin, A.; Iapichella, J.; Barrande, M.; Denoyel, R.; Coasne, B.; Fajula, F. Chem. Mater. 2009, 21, 1884. (9) Alcoutlabi, M.; McKenna, G. B. J. Phys.: Condens. Matter 2005, 17, R461.

Published on Web 08/11/2009

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Most simulation and theoretical studies on fluids confined in MCM-41 or SBA-15 have been performed for simple adsorbates, i.e., nonpolar and near-spherical molecules.10-18 These works have provided significant insights into the existence and nature of phase transitions for these simple probe molecules. In contrast, the behavior of more complex fluids confined in atomistic models of these materials has received considerably less attention19-23 and remains to be clarified. The aim of the present work is to investigate by means of molecular simulation the behavior of benzene adsorbed in the vicinity of silica surfaces or confined within silica nanopores such as MCM-41 and SBA-15. Both the planar surfaces and nanopores considered in this work are generated from an initial atomistic silica block. We address the effect of surface chemistry on the adsorption of benzene by considering two hydroxylated surfaces having different densities of OH groups (2.0 and 7.9 OH/nm2, respectively). We also address the effect of temperature by determining for these two planar surfaces the benzene adsorption isotherm at 293 and 323 K. Finally, we also investigate the adsorption of benzene in a cylindrical nanopore of diameter D = 3.6 nm. Again, for this system, we consider hydroxylated pore surfaces having different densities of OH groups. These results are compared with experimental data obtained at 298 K for a partially hydroxylated MCM41 silica sample with D=3.7 nm. The all-atom model developed by Jorgensen and Severance24 for benzene is used, so that we can address the orientation and conformation of the adsorbate near the silica surface of the planar substrates or of the cylindrical nanopores. Grand canonical Monte Carlo (GCMC) simulations are used to determine the adsorption isotherms of benzene. The orientation of benzene in the vicinity of the planar surfaces and confined in the cylindrical nanopores is determined by calculating orientational order parameters. We also compare the structure of the benzene confined in the silica nanopores with its bulk counterpart. The remainder of the paper is organized as follows. In section 2, we present the model of silica surfaces and cylindrical nanopores used in this work and briefly discuss the details of the simulation technique. In section 3, we report simulation results for adsorption of benzene on the silica surfaces and nanopores. Section 4 contains concluding remarks and suggestions for future work.

2. Methods 2.1. Preparation of Silica Surfaces and Nanopores. In this work, we prepared both silica planar surfaces and cylindrical nanopores (Figure 1). A pore diameter D=3.6 nm is considered in order to address the effect of confinement on benzene adsorption. We adopt the following notation in the rest of this paper: P and C indicate the type of substrate (P = planar surface, (10) Maddox, M. W.; Olivier, J. P.; Gubbins, K. E. Langmuir 1997, 13, 1737. (11) Ravikovitch, P. I.; Vishnyakov, A.; Neimark, A. V. Phys. Rev. E 2001, 64, 011602. (12) Gelb, L. D. Mol. Phys. 2002, 100, 2049. (13) Neimark, A. V.; Ravikovitch, P. I.; Vishnyakov, A. J. Phys.: Condens. Matter 2003, 15, 347. (14) Coasne, B.; Pellenq, R. J.-M. J. Chem. Phys. 2004, 120, 2913. (15) Coasne, B.; Pellenq, R. J.-M. J. Chem. Phys. 2004, 121, 3767. (16) Coasne, B.; Hung, F. R.; Pellenq, R. J. M.; Siperstein, F. R.; Gubbins, K. E. Langmuir 2006, 22, 194. (17) Coasne, B.; Galarneau, A.; Di Renzo, F.; Pellenq, R. J. M. Langmuir 2006, 22, 11097. (18) Bhattacharya, S.; Coasne, B.; Hung, F. R.; Gubbins, K. E. Langmuir 2009, 25, 5802. (19) Gallo, P.; Ricci, M. A.; Rovere, M. J. Chem. Phys. 2002, 116, 342. (20) Morineau, D.; Xia, Y.; Alba-Simionesco, C. J. Chem. Phys. 2002, 117, 8966. (21) Alba-Simionesco, C.; Dosseh, G.; Dumont, E.; Frick, B.; Geil, B.; Morineau, D.; Teboul, V.; Xia, Y. Eur. Phys. J. E. 2003, 19, 28. (22) He, Y.; Seaton, N. A. Langmuir 2003, 19, 10132. (23) Schumacher, C.; Gonzalez, J.; Wright, P. A.; Seaton, N. A. J. Phys. Chem. B 2006, 110, 319. (24) Jorgensen, W. L.; Severance, D. L. J. Am. Chem. Soc. 1990, 112, 4768.

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Figure 1. Atomistic model of silica substrates: (top) a square plane surface viewed from top, (bottom) a regular cylindrical nanopore of diameter D=3.6 nm. Gray and white spheres are silicon and oxygen atoms, respectively. Black spheres are the hydrogen atoms that delimit the pore surface. The planar silica surface and the cylindrical nanopore were carved out from an initial silica block with the dimensions 6.4 nm
6.4 nm
6.4 nm. C=cylindrical pore), while the subscripts 1 and 2 denote fully and partially hydroxylated surfaces, respectively. The characteristics of the silica planes and nanopores considered in the present work are reported in Table 1. All of these atomistic silica surfaces and pores were generated according to the method reported in ref 25. Coasne and Pellenq have shown that this technique can be used to prepare pores of various morphologies and/or topologies, such as cylindrical, hexagonal, ellipsoidal, and constricted pores.14-16 Recently, He and Seaton used a similar procedure to generate cylindrical silica pores.22 A porous silica material or silica surface can be defined using a mathematical function η(x, y, z) 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 (crystalline silica) the void corresponding to η(x, y, z) = 0. The initial silica block has the following dimensions 6.4 nm
6.4 nm
6.4 nm. The void is defined as η(x, y, z) = 0 if |z| < 2.0 nm for the planar surfaces and η(x, y, z) = 0 if (x2 +y2)1/2 < D/2 for the nanopores (with a diameter D = 3.6 nm). The thickness of the silica wall is g2.8 nm thick. Such a value is large enough that the interatomic interactions can be neglected beyond this value. In order to mimic the silica surface in a realistic way, we removed the surface Si atoms that are in an incomplete tetrahedral environment. We then removed all oxygen atoms that are nonbonded. This procedure ensures that the remaining silicon atoms have no dangling bonds and the remaining oxygen atoms have at least one 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 (2 OH/nm2) hydroxylated silica surfaces. (25) Pellenq, R. J. -M.; Levitz, P. E. Mol. Phys. 2002, 100, 2059–2077.

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Coasne et al. Table 1. Characteristics of the Silica Planes and Nanopores Considered in the Present Worka FOH (per nm2)

system

D (nm)

Vp (nm3)

Sint. (nm2)

Sext. (nm2)

fully hydroxylated

partially hydroxylated

2.0 (P2) plane substrate ---------114.4 7.9 (P1) 2.0 (C2) cylindrical pore 3.6 nm 65.3 72.6 ---7.3 (C1) a We adopted the following notation. P and C indicate the type of substrate (P = planar surface, C = cylindrical pore) while the subscripts 1 and 2 denote fully and partially hydroxydated surfaces, respectively. Pore size (D), pore volume (VP), internal surface (Sint.), external surface (Sext.), surface density of OH groups (FOH).

Figure 2. Cartoon showing the procedures used to prepare from a freshly cut silica substrate (left) a surface that is partially (right, bottom) or fully (right, top) hydroxylated. Red, gray, and white spheres are oxygen, silicon, 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 in order 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 in order to mimic an amorphous silica surface.

Fully Hydroxylated Silica. Fully hydroxylated silica surfaces and 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 A˚ (which corresponds to the OH bond length) from the unsaturated oxygen atom along the direction of the bond Si-O. It has been shown25 that the density 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 of the O, Si, and H atoms in order to mimic an amorphous silica surface (the maximum displacement in each direction x, y, and z is 0.7 A˚). Partially Hydroxylated Silica. Partially hydroxylated silica surface and nanopore were obtained by saturating with hydrogen atoms a fraction x of the oxygen atoms having a dangling bond. x was chosen so that the density of silanol groups at the pore surface equals 2 OH/nm2, which is close to the value reported for (26) Ishikawa, T.; Matsuda, M.; Yasukawa, A.; Kandori, K.; Inagaki, S.; Fukushima, T.; Kondo, S. J. Chem. Soc. Faraday Trans. 1996, 92, 1985. (27) Landmesser, H.; Kosslick, H.; Storek, W.; Frick, R. Solid State Ionics 1997, 101-103, 271. (28) Cauvel, A; Brunel, D.; Di Renzo, F.; Fubini, B.; Garrone, E. Langmuir 1997, 13, 2773. (29) Zhao, X. S.; Lu, G. Q..; et al. J. Phys. Chem. B 1997, 101, 6525. (30) Sutra, P.; Fajula, F.; Brunel, D..; et al. Colloids Surf., A 1999, 158, 21. (31) Brodie-Linder, N.; Dosseh, G.; Alba-Simionesco, C.; Audonnet, F.; Imperor, M. Mater. Chem. Phys. 2008, 108, 73. (32) Jentys, A.; Pham, N. H.; Vinek, H. J. Chem. Soc. Faraday Trans. 1996, 92, 3287.

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MCM-4126-31 (see also ref 32 for a discussion on hydroxyl groups in MCM-41). The oxygen 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 at the center of mass of the pair in order to form a siloxane bridge Si-O-Si. As for the fully hydroxylated silica materials, we then displace slightly and randomly all the O, Si, and H atoms in order to mimic an amorphous silica surface. The present atomistic model of MCM-41 provides a realistic description that allows us to address issues such as the effect of confinement (pore size), the effect of surface chemistry, and the effect of morphological disorder (pore shape) and topological disorder (the way the pores are spatially connected). For instance, this model was used in previous works to investigate the effect of surface roughness and disorder on the adsorption and condensation of simple fluids. The atomistic model adopted in the present work also allows consideration of different surface chemistries such as fully hydroxylated surfaces or partially hydroxylated surfaces with siloxane bridges (see, for instance, ref 33 for a molecular simulation study on the effect of surface chemistry on the adsorption of simple fluids). The present model can be improved by allowing for instance flexibility of the silanol groups at the pore surface. Other improvements16,18 include the preparation of similar pores with surface disorder that mimics the roughness of real templated-mesoporous silicas such as MCM-41 and SBA-15. Other models have been reported in the literature to model MCM-41 porous silicas. Several authors have described MCM-41 pores as simple regular cylindrical nanopores composed of an array of oxygen atoms.10,34,35 Although such an approach gives satisfactory results in predicting gas adsorption in pores provided that the substrate/fluid interaction is adjusted, it cannot provide a rigorous picture of the complex adsorption mechanism and local orientation effects at the pore surface, as it does not include the silicon atoms of the silica material and hydrogen atoms at the pore surface that saturates the dangling bonds of the oxygen atoms. Later, He and Seaton22 improves the latter model by proposing to carve the silica pore out of a quartz block (in a similar way to what is done in the present work with cristobalite). Nevertheless, these authors did not attempt to add silanol groups at the pore surface so that the surface of their MCM-41 model does not mimic real amorphous silica surfaces. Later, Seaton and co-workers further improved their model by adding silanol groups at the pore surface and allowing surface relaxation using kinetic Monte Carlo.23 More recently, other authors such as Shirono et al.36 and Hassanali and Singer37 also proposed models of MCM-41 pores that consist of regular cylindrical nanopores in which silanol groups are explicitely taken into account. The latter models are similar or equivalent to the model proposed in the present work, but they have not been used to investigate the effect of surface chemistry or morphological disorder. (33) Coasne, B.; Galarneau, A.; Di Renzo, F.; Pellenq, R. J. M. Langmuir 2008, 24, 7285. (34) Kuchta, B.; Llewellyn, P.; Denoyel, R.; Firlej, L. Colloids Surf., A 2004, 241, 137. (35) Cao, D.; Shen, Z.; Chen, J.; Zhang, X. Microporous Mesoporous Mater. 2004, 67, 159. (36) Shirono, K.; Daiguji, H. J. Phys. Chem. C 2007, 111, 7938. (37) Hassanali, A. A.; Singer, S. J. J. Phys. Chem. B 2007, 111, 11181.

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Table 2. Geometry and Parameters for Potential Functions for Benzene (from ref 24) r(CC) r(CH) q(C) q(H) σC εC σH εH

1.40 A˚ 1.08 A˚ -0.115e +0.115e 3.55 A˚ 0.07 kcal/mol 2.42 A˚ 0.03 kcal/mol

2.2. Intermolecular Potentials. Benzene was described in our simulations using the all-atom model of Jorgensen and Severance.24 In this model, each C and H atom of the rigid benzene molecule possesses a partial charge that interacts through Coulombic forces. In addition, each site of the molecule is a center of repulsion/dispersion interactions which interact through a Lennard-Jones potential. The geometry and interaction parameters of the benzene molecule used in this work are reported in Table 2. More recent benzene models have been reported in the literature. Errington and Panagiotopoulos proposed a model in which a united-atom description is employed; the CH groups are described as neutral single sites so that the atomic details of the CH bond are neglected and no electrostatic interaction is taken into account.38 Later, Bonnaud et al. developed a nine-sites potential for benzene with partial charges in order to account for the Coulombic interaction.39 The nine sites used by these authors correspond to those considered in the transferable potentials for phase equilibria (TraPPE):40 six CH groups, a positive charge in the ring center, and two negative charges representing the π-electron clouds perpendicular to the benzene ring. In contrast to the latter models that are based on the united-atom model, Cacelli et al. developed an all-atom model for benzene in which the interaction parameters including the atomic partial charges are estimated from ab initio calculations.41 The choice of using the model by Jorgensen and Severance24 in the present work was motivated by the fact that it provides, for reasonable time calculations, a realistic description of the thermodynamics of liquid benzene based on an all-atom description that includes electrostatic interactions. The all-atom description adopted in this model allows consideration of the atomic details of the molecular arrangement of the benzene molecules with respect to other molecules or porous substrate (although we note that the present model does not take into account the flexibility of the benzene molecule). Along the same line, the use of partial charges in the model by Jorgensen and Severance24 is crucial in the present work, as we expect the adsorption and structure of benzene on silica surfaces or nanopores to be strongly driven by the Coulombian interaction with the partial charges of the silica polar surface. Interactions between the C and H atoms of benzene and the Si, O, and H atoms of the silica nanopore were calculated using the PN-TraZ potential as reported for rare gas adsorption in zeolite42 or in porous silica glass.25 We assume that the flexibility of the chemical groups at the pore surface has a negligible effect on the adsorption of benzene, as all of the atoms of the silica substrate are kept rigid in the course of the simulation. The intermolecular energy is written as the sum of the Coulombic and dispersion interactions 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. The choice of the PN-TrAZ model to describe the benzene/silica interaction was motivated by the good (38) Errington, J. R.; Panagiotopoulos, A. Z. J. Chem. Phys. 1999, 111, 9731. (39) Bonnaud, P.; Nieto-Draghi, C.; Ungerer, P. J. Phys. Chem. B 2007, 111, 3730. (40) Wick, C. D.; Siepmann, J. I.; Koltz, W. L.; Schure, M. R. J. Chromatogr., A 2002, 954, 181. (41) Cacelli, I.; Cinacchi, G.; Prampolini, G.; Tani, A. J. Am. Chem. Soc. 2004, 126, 14278. (42) Pellenq, R. J.-M.; Nicholson, D. J. Phys. Chem. 1994, 98, 13339. (43) Puibasset, J.; Pellenq, R. J.-M. J. Chem. Phys. 2003, 118, 5613. (44) Puibasset, J.; Pellenq, R. J.-M. J. Phys.: Condens. Matter 2004, 16, S5329.

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Table 3. PN-TrAZ Potential Parameters for Benzene and Silica Species (a0 = 0.529 177 A˚ and Eh = 3.1578
105 K) benzene

silica

Aatom

C

H

Si

O

H

q (e) A (Eh) b (a0-1) R (a03) Neff

-0.115 142.505 1.910 12.820 2.772

þ0.115 91.837 2.900 4.320 0.709

+2 6163.4 2.395 2.36 1.529

-1 1543.5 2.19 8.03 4.656

+0.5 1.338 2.11 2.25 0.324

transferability of this model in the case of water in porous silica (Vycor).43,44 The adsorbate-surface energy Uk (rk of the atom k of an adsorbate molecule at a position rk is given by " # kj 5 X X C2n qi qk Uk ðrk Þ ¼ Akj expð -bkj rkj Þ f2n ðrkj Þ 2n þ 4πε0 rkj rkj n ¼3 j ¼fO;Si;Hg ð1Þ where rkj is the distance between the matrix atom j (O, Si, or H) and the atom k of the adsorbate molecule. The first term in eq 1 is a Born-Mayer term corresponding to the short-range repulsive energy due to finite compressibility of electron clouds when approaching the adsorbate to very short distance from the pore surface. The repulsive parameters Akj and bkj are obtained from mixing rules of like-atom pairs (see below). The second term in the above equation is a multipolar expansion series of the dispersion interaction that can be obtained from the quantum mechanical perturbation theory applied to intermolecular forces.45 It has been shown that two-body dispersion Ckj 2n coefficients for isolated or incondensed phase species can be derived from the dipole polarizability R and the effective number of polarizable electrons Neff of all interacting species,42 which are closely related to partial charges that can be obtained from ab initio calculations. f2n are damping functions that depend on the distance rkj and the repulsive parameter bkj f2n ðrkj Þ ¼ 1 -

 2n  X bkj rkj m ¼0

m!

expð -bkj rkj Þ

ð2Þ

The role of these damping functions is to avoid divergence of the dispersion interaction at short distances where the wave functions of the two species overlap (i.e., when the interacting species are in contact).46 Each pair of interacting species is parametrized with the single bkj repulsive parameter. The third term in eq 1 is the Coulombic interaction between the charge of atom k and that of the substrate atom j. The Coulomb energy was computed using the Ewald summation technique. The atomic parameters and coefficients for the benzene/silica substrate interactions are given in Tables 3 and 4. The repulsive parameters for like pairs are taken from the previous work by Pellenq and Nicholson on the simulation of rare gases in silicalite42 using the Bohm and Ahlrichs combination rules.47 This type of potential function based on the PN-TrAZ parametrization method was used in various studies of molecular and covalent fluids at interfaces from open surfaces43,48 to microporous zeolites49-53 and more recently in the case of mesoporous silica materials.14,15,43,44,54 (45) Stone, A. The Theory of Intermolecular Forces; Oxford: Clarendon, 1996. (46) Tang, K. T.; Toennies, J. P. J. Chem. Phys. 1984, 80, 3726. (47) Bohm, H. J.; Ahlrichs, R. J. Chem. Phys. 1982, 77, 2028. (48) Marinelli, F.; Grillet, Y.; Pellenq, R. J. M. Mol. Phys. 1999, 97, 1207. (49) Lachet, V.; Boutin, A.; Tavitian, B.; Fuchs, A. H. J. Phys. Chem. B 1998, 102, 9224. (50) Nicholson, D.; Pellenq, R. J. M. Adv. Colloid Interface Sci. 1998, 76-77, 179. (51) Fuchs, A. H.; Cheetham, A. K. J. Phys. Chem. B 2001, 105, 7375. (52) Grey, T. J.; Nicholson, D.; Gale, J. D.; Peterson, B. K. Appl. Surf. Sci. 2002, 196, 105. (53) Bichara, C.; Raty, J. Y.; Pellenq, R. J. M. Phys. Rev. Lett. 2002, 89, 016101. (54) Pellenq, R. J. M.; Rousseau, B.; Levitz, P. E. Phys. Chem. Chem. Phys. 2001, 3, 1207.

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Table 4. Dispersion and Repulsion Parameters Obtained in the Framework of the PN-TrAZ Model with Bohm and Ahlrichs Combination Rules for Repulsive Interactions benzene species C C C H H H

silica species O Si H O Si H

C8 C6 (Eh.a06) (Eh.a08) 44.580 13.376 9.041 13.760 4.121 2.857

C10 (Eh.a010)

b A (Eh) (a0-1)

1026.487 25400.075 468.995 2.041 266.007 ; 937.185 2.125 151.148 ; 13.808 2.005 225.098 5216.221 376.497 2.495 54.469 ; 752.347 2.623 27.005 ; 11.085 2.443

2.3. Grand Canonical Monte Carlo Technique. We performed GCMC simulations of benzene adsorption at 293 and 323 K on the atomistic models of silica surface and nanopores. The GCMC technique is a stochastic method that simulates a system having a constant volume V (the pore with the adsorbed phase), in equilibrium with an infinite reservoir of particles imposing its chemical potential μ and temperature T.55-57 The adsorption isotherm is given by the ensemble average of the number of adsorbed atoms as a function of the pressure of the gas reservoir P (the latter is obtained from the chemical potential μ according to the bulk equation of state for an ideal gas). P0 = 10 158 Pa at 293 K and P0 = 36 575 Pa at 323 K have been chosen equal to the experimental saturation vapor pressure.58 We calculated the adsorbate/substrate interaction using an energy grid;59 the potential energy is calculated at each corner of each elementary cube (about 1 A˚3). 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 of complex morphology and/or topology without a direct summation over matrix species in the course of GCMC runs.12,14,15,60,61 The system was first allowed to equilibrate in the course of a first GCMC run. Afterward, data such as the number N of adsorbed molecules were estimated by averaging over 2000 MC configurations. The uncertainty in N was estimated for each pressure from the statistical error 1/[(Nr)1/2] for a Gaussian distribution of Nr values centered around its average value. The maximum uncertainty, which is found for the low pressure range, is at most a few percent. Of course, such an estimate does not include the error in the condensation/evaporation pressures, which is related to the use of a finite number of attempted configurations in the simulations.

3. Results and Discussion 3.1. Effect of Surface Chemistry and Temperature: Adsorption on Planar Surfaces. The benzene adsorption isotherms at 293 and 323 K for the fully (P1) and partially (P2) hydroxylated silica surfaces are shown in Figure 3. Adsorbed amounts have been converted into the number of adsorbed atoms per unit of surface area (μmol/m2). For both surfaces, we checked that the data follow the Polanyi plot, i.e., the adsorbed amounts fall on the same master curve when plotted as a function of the chemical potential, μ - μ0 = kBT ln(P/P0) (μ0 is the chemical potential at the gas/liquid bulk coexistence pressure P0). Our data (55) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: New York, 1982. (56) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford: Clarendon, 1987. (57) Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed.; Academic Press: London, 2002. (58) Williamham, C. B.; Taylor, W. J.; Pignocco, J. M.; Rossini, F. D., J. Res. Natl. Bur. Stand. (U.S.), 1945, 35, 219. The Antoine equation parameters taken from this paper to determine P0 can be found on the website of the National Institute of Standards and Technology: http://webbook.nist.gov/chemistry/ (59) Pellenq, R. J. -M.; Nicholson, D. Langmuir 1995, 11, 1626. (60) Gelb, L. D.; Gubbins, K. E. Langmuir 1998, 14, 2097. (61) Pellenq, R. J.-M.; Levitz, P. E. Mol. Sim. 2001, 27, 353.

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show that temperature does not affect significantly the adsorption of benzene on the silica surfaces. In particular, this result suggests that one has to cover a much larger temperature range to see a significant effect of temperature on adsorption. It must be emphasized that the difference between the two temperatures considered in this work (293 and 323 K) corresponds to a small change when plotted in reduced units with respect to the critical temperature Tc for bulk benzene (0.52 and 0.58). Such a small difference in reduced temperatures may explain the absence of any significant effect on adsorption of benzene in our simulation results. At a given temperature, the film adsorbed at the surface of the silica plane P1 for pressures lower than 0.6P0 is larger than that for the silica plane P2. This result cause by an increase in the density of silanol groups that induces an increase in the polarity of the silica surface, which, in turn, becomes more attractive for the adsorbate. As the pressure increases, the difference between the two film thicknesses 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). These results are consistent with previous work62 on the adsorption of a simple fluid (argon) on silica surfaces with different densities of silanol groups. In contrast, at pressures larger than 0.6 P0, the adsorbed amount is larger for the silica plane P2 than for the silica plane P1. Such an inversion, which occurs as a second layer of benzene starts to form on the surface, is due to the difference in the orientation of the adsorbed benzene molecules between the two substrates. On one hand, as will be discussed in detail below, the benzene molecules in the first layer adsorbed on the silica plane P1 tend to be perpendicular to the surface. On the other hand, the orientation of the benzene molecules in the first layer adsorbed on the silica plane P2 is more disordered. As a result, adsorption of a second layer of benzene molecules is more favorable in the case of the substrate P2 due to the disordered structure of the first layer which resembles the bulk liquid configuration for the subsequent adsorbed molecules. The density profiles of benzene adsorbed at low and high pressures on the fully hydroxylated silica surface P1 are shown in Figure 4. We report the density profile for the center of mass of the molecules and those for the C and H atoms. The density profiles show that a molecular layer of benzene is adsorbed on the silica surface at low pressure. The position of the peaks for the density of the C and H atoms suggests that the benzene molecules tend to orientate themselves perpendicularly to the silica surface (since these density profiles exhibit two distinct peaks located at equal distance from the center of mass). The precise arrangement of the benzene molecules toward the O and H atoms of the silica substrate will be discussed in detail below. The density profile for the center of mass of the benzene molecules when several layers are adsorbed shows density oscillations that are characteristic of heterogeneous fluids. Such a spatial ordering of fluids in the vicinity of surfaces or confined in porous materials have been discussed in detail in the literature (for a review, see ref 63). As for the case of the density profile obtained at low pressure, the density profiles for the C and H atoms of the benzene molecules adsorbed in the first layer at high pressure show that these molecules remain significantly oriented perpendicular to the silica surface. On the other hand, the density profiles for the C and H atoms of the benzene molecules adsorbed in the second and subsequent layers show that these molecules do not exhibit orientational order (62) Coasne, B.; Galarneau, A.; Di Renzo, F.; Pellenq, R. J. M. J. Phys. Chem. C 2007, 111, 15759. (63) Evans, R. J. Phys.: Condens. Matter 1990, 2, 8989.

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Figure 3. (left) Adsorption isotherms of benzene at 293 K (circles) and 323 K (squares) on amorphous silica surfaces: (open symbols) fully hydroxylated, P1 and (filled symbols) partially hydroxylated, P2. (right) Same data for T = 293 K but on a semilogarithmic scale.

Figure 4. Density profile of benzene adsorbed at 293 K on the fully hydroxylated surface (P1): (left) P = 10-4P0 and (right) P = 0.98P0. The circles correspond to the overall density that was calculated by considering the center of mass of the molecules. The black and gray lines are the density profiles of the C and H atoms of the molecules, respectively.

Figure 5. Density profile of benzene adsorbed at 293 K on the partially hydroxylated surface (P2): (left) P = 0.1P0 and (right) P = 0.98P0. The circles correspond to the overall density that was calculated by considering the center of mass of the molecules. The black and gray lines are the density profiles of the C and H atoms of the molecules, respectively.

(in the sense that corresponding density peaks do not subdivide into peaks at well-defined positions). The density profiles of benzene adsorbed at low and high pressures on the partially hydroxylated silica surface P2 are shown in Figure 5. Again, we report both the density profile for the center of mass of the molecules and those for the C and H atoms. The density profiles for this partially hydroxylated surface show that a molecular layer of benzene is adsorbed on the silica surface at low pressure. The positions of the peaks for the density of the C and H atoms do not seem to follow the perpendicular orientation observed for the benzene molecules in the case of the fully hydroxylated silica surface. At higher pressures, the density profile for the center of mass of the benzene molecules shows that several layers are adsorbed. Again, as for the results obtained at low pressure, the density profiles for the C and H atoms of the benzene molecules adsorbed in the second layer show that these molecules do not exhibit any particular orientational order. In order to investigate the orientation of the benzene molecules with respect to the fully and partially hydroxylated silica surface, Langmuir 2009, 25(18), 10648–10659

we calculated the following orientational order parameter for each layer of adsorbate: S ¼

Æ 32 cos θ - 12 æ 2

ð3Þ

where θ is the angle between the normal vector to a benzene molecule and the normal vector to the silica surface. The brackets in the equation above denote an average over all of the adsorbed molecules. S ∼-0.5 and ∼1 for benzene molecules perpendicular and parallel to the silica surface, respectively, whereas S ∼0 for adsorbed molecules having no particular orientation with respect to the surface. Table 5 reports the values of the order parameter S for the layers of benzene adsorbed at different pressures on the fully (P1) and partially (P2) hydroxylated surfaces. For all loadings, S∼-0.3 for the molecules located in the contact layer of the fully hydroxylated silica surface P1. This result confirms that the molecules prefer an orientation in which their ring is nearly perpendicular to the pore surface. The fact that S is not strictly DOI: 10.1021/la900984z

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Table 5. Order Parameter S for the Layers of Benzene Adsorbed at Different Pressures and a Temperature T = 293 K on a Fully (P1) and Partially (P2) Hydroxylated Silica Surfacea P/P0

no of layers

S (contact layer)

S (second layer)

Fully Hydroxylated Surface P1 -4

10 0.98

1 2

-0.26 -0.28

-0.03

Partially Hydroxylated Surface P2 0.01 1 0.07 0.98 2 0.04 0.12 a Contact layer corresponds to the layer in contact with the silica surface.

equal to -0.5 is due to the thermal activity of the molecules which introduces some disorder in the organization of the adsorbate. In addition, the thermal mismatch between the confined fluid and the host material (which is considered as frozen in the simulations) may disturb the orientation of the molecules (see ref 64 for a discussion on the effect of the thermal mismatch on the dynamics of confined fluids). In contrast, S ∼0 for the benzene molecules adsorbed in the contact layer of the partially hydroxylated surface P2. As will be discussed in detail below, this is due to the surface heterogeneity for this silica substrate, which favors different orientations for the molecules so that S ∼0 on average. On the other hand, for both silica surfaces, the molecules adsorbed in the second layer tend to have a disordered orientation close to that in the bulk liquid phase (S∼0 for the fully hydroxylated surface and S∼0.1 for the partially hydroxylated surface). This result suggests that the influence of the silica surface on the orientation of the adsorbed molecules rapidly drops off beyond the contact layer. In order to further characterize the orientation of benzene in the vicinity of the fully and partially hydroxylated silica surfaces, we calculated the distribution of angles, R = (CH, z), between the CH bond of a benzene molecule and the normal vector to the silica surface. R can be seen as a chemical orientational order parameter (while the parameter S defined above is an order parameter related to the physical orientation of the molecules). Calculations for the angle R were limited to benzene molecules located at a distance of less than 4 A˚ from the silica surfaces in order to consider only molecules within the first layer. The probability distribution P(R) is shown in Figure 6 for both the fully (P1) and partially (P2) hydroxylated silica surfaces. The data are reported at low loading when about one monolayer is adsorbed on the silica surface. On the one hand, the largest probability is located at R = 0
for the surface P1. This result is consistent with the fact that the benzene molecules tend to have their ring perpendicular to the silica surface when adsorbed on this substrate (see the discussion above). This particular orientation is also illustrated in Figure 7 where a typical molecular configuration of benzene adsorbed at low pressure on the fully hydroxylated surface P1 is shown. The maximum in the distribution P(R) for the surface P2 is also located at R ∼0
, which suggests that the benzene molecules tend to have their ring perpendicular to the silica surface as for the silica surface P1. In addition, a shoulder in the distribution is observed at a value about 50
for the partially hydroxylated silica surface. This other probable value for R shows that a second preferential orientation is observed for the heterogeneous surface. The two possible orientations for the substrate P2, which can be seen in the typical molecular configuration shown in Figure 7, (64) Koppensteiner, J.; Schranz, W.; Puica, M. R. Phys. Rev. B 2008, 78, 054203.

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Figure 6. Probability distribution P(R) of the angle R = (CH, HO) between the CH bond of a benzene molecule and the closest OH group of the silica surface at T = 293 K: The black and gray lines are for the fully hydroxylated, P1, and partially hydroxylated, P2, silica surfaces.

explains why the average orientation of the adsorbed benzene molecules appears disordered as in the bulk phase (see the S parameter value for this system in Table 5). 3.2. Adsorption in a Cylindrical Nanopore. The benzene adsorption isotherms obtained at 293 K for the fully and partially hydroxylated cylindrical silica nanopores with D = 3.6 nm (C1 and C2) are shown in Figure 8. Adsorbed amounts have been normalized to the total number of adsorbed atoms when the pores are completely filled, N0. We also report in Figures 9 and 10 typical molecular configurations of benzene adsorbed at different pressures in the two pores. The filling of these nanopores starts with the formation of a homogeneous monolayer of benzene adsorbed at the pore surface. As the pressure increases, the thickness of the film adsorbed increases up to a value for which the pore surface is uniformly covered by layers of benzene molecules. A sharp increase in the adsorbed amounts is observed at P = 0.32 P0 and P = 0.27P0 for the nanopores C1 and C2, respectively. The latter corresponds to capillary condensation of benzene within the pores that occurs through the collapse of the cylindrical film adsorbed at the pore surface. It is surprising that capillary condensation for the partially hydroxylated nanopore occurs at a pressure lower than that for fully hydroxylated nanopore. Indeed, we have shown in the previous section that the adsorbed amount at a given pressure is larger for the fully hydroxylated nanopore than for the partially hydroxylated (due to the stronger silica/fluid interaction in the case of the fully hydroxylated surface). As a result, based on the classical picture of capillary condensation in nanopores, one expects that condensation in the fully hydroxylated nanopore occurs at a lower pressure; the adsorbed film in this nanopore should be thicker so that its collapse/unstability of the cylindrical film occurs at lower pressure. A possible explanation for the fact that capillary condensation in the partially hydroxylated nanopore occurs at a lower pressure than in the fully hydroxylated nanopore is as follows. As will be discussed in more detail below, the benzene molecules have a disordered orientation in the partially silica nanopore C2, while a strong perpendicular orientation is observed for the benzene molecules confined in the fully silica nanopore C1. Consequently, because of less efficient packing in the disordered adsorbed layer, the density of the adsorbed film in the partially hydroxylated nanopore is smaller than that in the fully hydroxylated nanopore. This, in turn, imples that, for a given adsorbed amount prior to capillary condensation, the core radius where capillary condensation occurs through the collapse of the adsorbed film is smaller for the partially hydroxylated nanopore than for the fully hydroxylated nanopore. This result is supported by the fact that, for similar adsorbed amounts, the density profile Langmuir 2009, 25(18), 10648–10659

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Figure 7. Typical configurations of benzene adsorbed at 293 K on (left) fully P1 and (right) partially P2 hydroxylated surfaces. The pressure in both cases is P = 10-3P0. The white and gray spheres are the carbon and hydrogen atoms of the benzene molecules. Orange and red spheres are the silicon and oxygen atoms of the silica substrate. For each configuration, we also show a magnified view illustrating the perpendicular orientation of the benzene molecules in the case of surface P1 and the perpendicular and nonperpendicular orientations of the benzene molecules in the case of surface P2.

Figure 8. Adsorption isotherm of benzene at 293 K for cylindrical nanopores with D = 3.6 nm: (circles) fully hydroxylated nanopore, C1, and (triangles) partially hydroxylated nanopore, C2. Adsorbed amounts have been normalized to the total number of adsorbed atoms when the pores are completely filled, N0. Open and closed symbols are for the adsorption and desorption processes, respectively. The squares are experimental data obtained for benzene adsorption at T = 298 K for a MCM-41 sample with D = 3.7 nm corresponding to the simulated nanopore C2.70 Experimental adsorbed amounts have been normalized to the adsorbed amount when the pores are filled at a pressure P = 0.4P0.

for the partially hydroxylated nanopore extends over longer distances within the pore than that for the fully hydroxylated nanopore (see the discussion below). Consequently, given that the adsorbed amounts at the onset of capillary condensation are similar for the partially and fully hydroxylated nanopores (see Figure 8), the smaller core radius for the partially hydroxylated nanopore implies that capillary condensation occurs at lower pressure for this nanopore. The evaporation pressures, P = 0.15 P0 for the nanopore C1 and P = 0.10 P0 for the nanopore C2 are lower than the condensation pressures so that a hysteresis loop is observed. Such a hysteresis loop observed upon adsorption of benzene at ambient temperature can be explained as follows. We know from previous experimental, theoretical, and molecular simulation works that there is a temperature, the so-called hysteresis critical temperature Tcc, below which capillary condensation in nanoporous solids is (65) (66) (67) (68)

Ball, P. C.; Evans, R. Langmuir 1989, 5, 714. Coasne, B.; Gubbins, K. E.; Pellenq, R. J. M. Adsorption 2005, 11, 289. Morishige, K.; Fujii, H.; Uga, M.; Kinukawa, D. Langmuir 1997, 13, 3494. Morishige, K; Ito, M. J. Chem. Phys. 2002, 117, 8036.

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irreversible.65-69 This pseudocritical temperature corresponds to the threshold of reversible capillary condensation of the confined fluid (as the temperature approaches Tcc, the hysteresis loop shrinks and, finally, disappears for T = Tcc). We also know that Tcc(D) increases as the pore diameter D increases. Consequently, for a given temperature T, the hysteresis loop decreases as D decreases and eventually disappears when D is such that T > Tcc(D). Hence, the presence of a hysteresis loop for benzene confined at 293 K in the nanopores with D = 3.6 nm suggests that Tcc(3.6 nm) > 293 K. We also show in Figure 8 experimental data obtained for benzene adsorption at T = 298 K for a MCM-41 sample with D = 3.7 nm corresponding to the simulated nanopore C2.70 The latter were found to be consistent with the benzene adsorption isotherm reported by Ribeiro Carrott et al.71 for a MCM-41 sample with D = 3.7 nm. These results are also consistent with the experimental works reported by Nguyen et al.72 and Zhao and Lu.73 The experimental data in Figure 8 should be compared with the simulation data for the nanopore C2, as the silanol surface density in real MCM-41 is usually close to that used for the partially hydroxylated silica surface (see section 2 for a discussion of the degree of surface hydroxylation in MCM-41). The simulated adsorbed amounts prior to capillary condensation are much larger than the experimental values. This result suggests that the interatomic potential functions used in the molecular simulations overestimate the interaction between the benzene molecules and the silica surface. Such a discrepancy between the simulated and experimental data indicates that the agreement between the experimental condensation pressure and that observed in the simulations for the partially hydroxylated nanopore, P ∼0.3P0, is fortuitous. Nevertheless, we believe that the pore filling mechanism found in the simulations qualitatively reproduces what is observed in the experiments (i.e., formation and growth of (69) Thommes, M. Physical Adsorption Characterization of Ordered and Amorphous Mesoporous Materials In Nanoporous Materials, Science & Engineering, Lu, G. Q., Zhao, X. S., Eds.; Imperial College Press: London, 2004. (70) Alba-Simionesco, C.; Audonnet, F.; Dosseh, G. , To be published, 2009. (71) Ribeiro Carrott, M. M. L.; Candeias, A. J. E.; Carrott, P. J. M.; Ravikovitch, P. I.; Neimark, A. V.; Sequeira, A. D. Microporous Mesoporous Mater. 2001, 47, 323. (72) Nguyen, C.; Sonwane, C. G.; Bhatia, S. K.; Do, D. D. Langmuir 1998, 14, 4950. (73) Zhao, X. S.; Lu, G. Q. J. Phys. Chem. B 1998, 102, 1556.

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Figure 9. Typical configurations of benzene adsorbed at 293 K in the cylindrical nanopore with D = 3.6 nm having a fully hydroxylated surface (C1): (from left to right and top to bottom) P is 10-8P0, 10-6P0, 10-4P0, 0.10P0, 0.30P0, 0.40P0. The white and gray spheres are the carbon and hydrogen atoms of the benzene molecules. Orange and red spheres are the silicon and oxygen atoms of the silica substrate.

Figure 10. Typical configurations of benzene adsorbed at 293 K in the cylindrical nanopore with D = 3.6 nm having a partially hydroxylated surface (C2): (from left to right and top to bottom) P is 10-8P0, 10-6P0, 10-4P0, 0.10P0, 0.25P0, 0.30P0. The white and gray spheres are the carbon and hydrogen atoms of the benzene molecules. Orange and red spheres are the silicon and oxygen atoms of the silica substrate.

an adsorbed film at the pore surface followed by capillary condensation of benzene at a pressure lower than the bulk saturating vapor pressure). It must be noted that the effect of confinement and surface chemistry on the orientation and structure of adsorbed benzene molecules has not received sig10656 DOI: 10.1021/la900984z

nificant attention in the literature. In particular, no molecular simulation study of benzene adsorption in atomistic silica nanopores with a realistic description of the surface chemistry has been reported. As a result, we believe that the present work provides new interesting and useful insights although our model does not Langmuir 2009, 25(18), 10648–10659

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Figure 11. Radial density profile of benzene adsorbed at 293 K in the cylindrical nanopore with D = 3.6 nm having a fully hydroxylated surface (C1): (left) P = 0.32P0 and (right) P = 0.40P0. The circles correspond to the overall density that was calculated by considering the center of mass of the molecules. The black and gray lines are the density profiles of the C and H atoms of the molecules, respectively.

Figure 12. Radial density profile of benzene adsorbed at 293 K on the partially hydroxylated surface (P2): (left) P = 0.1P0 and (right) P = 0.25P0. The circles correspond to the overall density that was calculated by considering the center of mass of the molecules. The black and gray lines are the density profiles of the C and H atoms of the molecules, respectively.

capture all the features of adsorption of benzene in real MCM-41 materials. As will be discussed below, our approach is also supported by the fact that the present simulations, showing that confined benzene is composed of a superficial phase and a bulk phase in the pore center, corroborates with experimental results. In fact, given the lack of conclusive experiments on the exact pore morphology, surface roughness, and surface chemistry in MCM41, we decided to adopt a fundamental approach in which molecular simulations of benzene adsorption are performed for ideal cylindrical nanopores with well-defined surface chemistries. Although more realistic models of MCM-41 or SBA-15 have been reported,16,18,23 we thought that one should start with a simple ideal model before considering more complex models incorporating many features of the real materials (chemical defects, surface roughness on different length scales, etc.). For the different reasons listed above, we believe that the interpretation and comparison of the simulation data reported in the present work are meaningful, although it cannot be claimed that the experimental behavior is fully captured. Following previous molecular simulation works74,75 on the adsorption and condensation of aromatic molecules (p-xylene) in MCM-41 nanopores, we looked at the structure of confined benzene by calculating radial density profiles. The density profiles of benzene confined at the onset of capillary condensation and when the pore is filled are shown in Figure 11 for the fully hydroxylated silica nanopore C1. We report the density profile for the center of mass of the molecules and those for the C and H atoms. The density profiles show that a molecular layer of benzene is adsorbed on the silica surface prior to capillary condensation. At this pressure, only a few molecules start being adsorbed in the second layer, so that the density is not exactly zero. Again, the position of the peaks for the density of the C and (74) Nanok, T.; Bopp, P. A.; Limtrakul, J. Z. Naturforsch. 2005, 60a, 805. (75) Sangthong, W.; Probst, M.; Limtrakul, J. Chem. Eng. Commun. 2008, 195, 1486.

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Table 6. Order Parameter S for the Layers of Benzene Confined at Different Pressures in Silica Nanopores with D = 3.6 nm (C1 and C2)a P/P0

no of layers

S (contact layer)

S (second layer)

S (inner layers)

Fully Hydroxylated Nanopore C1 -4

10 0.32 0.39

1 2 4

-0.21 -0.32 -0.28

;; 0.11 0.01

;; ;; 0.00

Partially Hydroxylated Nanopore C2 10-4 1 0.36 ;; ;; 0.25 2 0.09 0.04 ;; 0.30 4 0.10 -0.02 0.03 a Contact layer corresponds to the layer in contact to the silica surface.

H atoms suggests that the benzene molecules tend to orientate themselves perpendicular to the silica surface. When the pore is filled by the confined liquid, the density profile for the center of mass of the benzene molecules exhibits density oscillations that are characteristic of confined fluids. As for the case of the density profile obtained at low pressure, the density profiles for the C and H atoms of the benzene molecules adsorbed in the first layer at high pressure show that these molecules remain significantly oriented perpendicular to the silica surface. On the other hand, the density profiles for the C and H atoms of the benzene molecules adsorbed in the second and subsequent layers show that these molecules do not exhibit orientational order. The density profiles of benzene confined at the onset of capillary condensation and when the pore is filled are shown in Figure 12 for the partially hydroxylated silica nanopore C2. Again, we report both the density profile for the center of mass of the molecules and those for the C and H atoms. The density profiles for this partially hydroxylated nanopore show that two molecular layers of benzene are adsorbed on the silica surface at the onset of DOI: 10.1021/la900984z

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Figure 13. (left) Pair correlation function g(r) for the center of mass of the benzene molecules: (black line) benzene in the fully hydroxylated nanopore with D = 3.6 nm, (gray line) benzene in the partially hydroxylated nanopore with D = 3.6 nm, and (squares) bulk benzene. The data for bulk benzene correspond to the simulations by Jorgensen and Severance (ref 24). (right) Partial C-H pair correlation function g(r) for confined benzene (the legend in the same as in left). The C-C and H-H contributions are not shown. The data for bulk benzene correspond to the simulations by Jorgensen and Severance (ref 24).

capillary condensation pressure. As for the partially hydroxylated planar surface P2, the positions of the peaks for the density of the C and H atoms do not seem to follow the perpendicular orientation observed for the benzene molecules in the case of the fully hydroxylated silica surface. At larger pressures, the density profile for the center of mass of the benzene molecules show that several layers are confined when the pore is filled. The density profiles for the nanopores C1 and C2 at the onset of capillary condensation correspond to about the same number of adsorbed benzene molecules, N ∼0.6 μmol/m2. It is therefore interesting that, for similar adsorbed amounts, the density profile for the partially hydroxylated nanopore extends to a larger coverage than that for the fully hydroxylated nanopore. On one hand, the second adsorbed layer is almost empty for the fully hydroxylated nanopore, as only a few molecules are adsorbed on the top of those in the contact layer. On the other hand, the second adsorbed layer is almost complete for the partially hydroxylated nanopore. This difference between the two nanopores is due to the fact that the molecules adsorbed in the partially hydroxylated nanopore have disordered orientations (see the disccussion below on the orientation of the confined molecules). This disordered orientation of the benzene molecules results in a less efficient packing for this pore. Consequently, the density of the confined benzene molecules in the partially hydroxylated nanopore is smaller than that for the fully hydroxylated nanopore and the film corresponding to a given adsorbed amount is thicker. Table 6 reports the orientational order parameter S calculated according to eq 3 for the layers of benzene confined at different pressures in the fully and partially hydroxylated nanopores C1 and C2. We show the results for the contact, second, and third and fourth layers (these two last layers are considered together as “inner layers”). For all loadings, S ranges from -0.2 to -0.3 for the molecules located in the contact layer of the fully hydroxylated nanopore C1. As for the planar surface P1 (see results in Table 5), this result shows that the molecules prefer an orientation in which their ring is nearly perpendicular to the pore surface. Again, the fact that S is not strictly equal to -0.5 is due to the thermal activity of the molecules which introduces some disorder in the organization of the adsorbate. Interestingly, S for the contact layer decreases when molecules get adsorbed in the second, third, and fourth layers, i.e., the molecules that are not located in the vicinity of the silica surface strengthen the perpendicular anchoring of benzene at the pore surface. In contrast, S ∼0.4 for the benzene molecules adsorbed in the contact layer of the partially hydroxylated surface P2. As was discussed above for the partially hydroxylated surface P2, this is due to the surface heterogeneity for this silica substrate which favors different orientations for the molecules, so that S takes, on average, a value that is not 10658 DOI: 10.1021/la900984z

representative of any particular orientation. On the other hand, for both silica surfaces, the molecules adsorbed in the subsequent layers (second, third, and fourth layers) tend to have a disordered orientation close to that in the bulk liquid phase (S∼0 for the fully hydroxylated surface and S ∼0.1 for the partially hydroxylated surface). These results are compatible with the experimental data obtained by Findenegg and co-workers, which show that confined benzene is composed of one surperficial phase at the pore surface and a bulk-like phase located at the inner part of the pore.76,77 We now discuss the structure of benzene adsorbed in the silica nanopores C1 and C2. The pair correlation functions g(r) of the center of mass of the confined benzene molecules when the nanopores are completely filled are shown in Figure 13. We also report the pair correlation function of the bulk liquid at the same temperature, as calculated by Jorgensen and Severance for the same model of benzene molecules.24 We also show in Figure 13 the partial pair correlation corresponding to the C-H contribution to the total g(r). Again, this curve is compared with its bulk counterpart (liquid phase at 293 K).24 All the pair correlation functions for the confined fluid have been corrected for excluded volume effects19,21,78 according to the method proposed by Gallo et al.19 The pair correlation function for the center of mass of the molecules in the pores shows that the confined fluid has a liquidlike structure, as only short-range positional order is observed. This result is consistent with experimental data for benzene confined in MCM-41 pores having a diameter smaller than 4.7 nm.79 Also, it is found that the peaks of this g(r) function for the confined molecules are located at the same position as those for the bulk fluid. On the other hand, the amplitude of these peaks for the fluid in the fully and partially hydroxylated nanopores are smaller than those for the bulk. This result shows that the confined fluid is less ordered than in the bulk phase, due to the interaction with the pore wall. The confined fluid tends to disorganize its liquid structure a little in order to optimize its molecular arrangement near the pore wall. We note that this effect is more pronounced for the fluid in the fully hydroxylated nanopore C1 than for the fluid in the partially hydroxylated nanopore C2. This result is consistent with our previous result above showing that the orientation of benzene molecules in the case of the nanopore C2 is closer to that of bulk benzene. In contrast to these results for the center of mass, the partial (76) Gedat, E.; Schreiber, A.; Albrecht, J.; Emmler, Th.; Shenderovich, I.; Findenegg, G. H.; Limbach, H.-H.; Buntkowsky, G. J. Phys. Chem. B 2002, 106, 1977. (77) Masierak, W.; Emmler, Th.; Gedat, E.; Schreiber, A.; Findenegg, G. H.; Buntkowsky, G. J. Phys. Chem. B 2004, 108, 18890. (78) Morineau, D.; Alba-Simionesco, C. J. Chem. Phys. 2003, 188, 9389. (79) Dosseh, G.; Xia, Y.; Alba-Simionesco, C. J. Phys. Chem. B 2003, 107, 6445.

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correlation function for the C-H pair is very similar to that for the bulk liquid, independent of the degree of hydroxylation of the silica surface. The same conclusion was reached for the C-C and H-H contributions (not shown). This result suggests that confined benzene retains the local details of its liquid-like ordering. Finally, in order to determine the correlation length ξ of the bulk and confined fluids, we fitted the successive maxima gmax(r) in the pair correlation functions shown in Figure 13 using the following expression:   r gmax ðrÞ ∼ exp ξ0

ð4Þ

We found ξ0 = 2.0 and 1.7 nm for the fluid confined in the fully and partially hydroxylated nanopore, respectively (while ξ0 = 0.9 nm for the bulk fluid). These results suggest that the correlation length for the bulk and confined fluids are both of a few molecular diameters.

4. Conclusion This work reports a molecular simulation study of the adsorption of benzene on atomistic silica surfaces and nanopores (MCM-41). Both the planar surfaces and the nanopores are generated from an initial atomistic silica block. The effect of surface chemistry is addressed by studying the adsorption of benzene on both partially and fully hydroxylated silica surfaces (2.0 and 7.9 OH/nm2, respectively). We also address the effect of temperature by determining the benzene adsorption isotherm at 293 and 323 K. Finally, we also investigate the adsorption of benzene in a cylindrical nanopore of diameter D=3.6 nm. At a given temperature, the film adsorbed at the surface of the fully hydroxylated substrate for pressures lower than 0.6 P0 is slightly larger than that for the partially hydroxylated silica substrate, due to the fact that an increase in the density of silanol groups induces an increase in the polarity of the silica surface. On the other hand, for larger pressures, the adsorbed amount is larger for the partially hydroxylated silica surface than for the fully hydroxylated silica surface. This change in the adsorption behavior when a second layer starts to form is due to the different orientation of the benzene molecules in the first adsorbed layer. The benzene molecules in the first layer tend to be perpendicular to the substrate in the case of the fully hydroxylated surface, while they adopt a more disordered orientation in the case of the partially hydroxylated surface. These results are confirmed by our calculations of bond angles with the silica surfaces and orientational order parameters. For both substrates, the density

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profiles of adsorbed benzene reveal the strong layering of the adsorbate in the vicinity of the silica surface. Using suitable orientational order parameters, we confirm that the molecules in contact with the fully hydroxylated silica substrate prefer an orientation in which their ring is nearly perpendicular to the pore surface. In contrast, different orientations of the adsorbed benzene molecules are favored when partially hydroxylated silica surfaces are considered. Thus, it seems that surface chemistry is a key parameter in describing the orientation and ordering of adsorbed benzene molecules. The filling of the nanopores starts with the formation of a homogeneous monolayer of benzene adsorbed at the pore surface. As the pressure increases, a sharp increase in the adsorbed amount is observed, due to capillary condensation of benzene, which occurs through the collapse of the cylindrical film adsorbed at the pore surface. Condensation in the partially hydroxylated nanopore occurs at a lower pressure than in the fully hydroxylated nanopore, due to the less efficient packing of benzene molecules (arising from their disordered orientation), which favors condensation because the core radius (the pore radius diminished by the film thickness) is smaller. The positional pair correlation function, g(r), shows that confined benzene remains liquid-like, as only short-range order is observed. On the other hand, the amplitude of the peaks for the confined fluid are slightly smaller than those for the bulk, which suggests that benzene adsorbed in the vicinity of the silica surface shows a less organized liquid structure, thus optimizing its molecular arrangement near the pore wall. Such an effect is more marked for the fully hydroxylated nanopore than for the partially hydroxylated nanopore, which is consistent with the fact that the orientation of the benzene molecules in the second situation resembles that of bulk benzene. In future work, we plan to address the following issues. First, we will take into account the effect of the flexibility of silanol groups at the pore surface in order to estimate its effect on the adsorption and structure of benzene in nanopores. The effect of surface disorder or roughness will also be addressed by considering the realistic samples of porous MCM-41 and SBA-15. Such models, which have been compared with experimental samples in terms of pore size distribution, surface area, gas adsorption, and neutron scattering, are available in the literature.16,18 Finally, we also investigate the freezing of benzene and other aromatic liquids (cyclohexane, bromobenzene, etc.) confined in similar silica nanoporous materials. Acknowledgment. KEG thanks the U.S. Department of Energy for partial support of this work under grant no. DEFG02-98ER14847.

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