Modeling Micelle-Templated Mesoporous Material SBA-15

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Modeling Micelle-Templated Mesoporous Material SBA-15: Atomistic Model and Gas Adsorption Studies Supriyo Bhattacharya,† Benoit Coasne,‡ Francisco R. Hung,§ and Keith E. Gubbins*,† †

Center for High Performance Computing and Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905, ‡Institut Charles Gerhardt Montpellier (UMR CNRS 5253), CNRS, Universit e Montpellier II, and ENSCM, Place Eug ene Bataillon, 34095 Montpellier, Cedex 5, France, and §Cain Department of Chemical Engineering, Louisiana State University, Baton Rouge, Louisiana 70803 Received May 21, 2008. Revised Manuscript Received September 10, 2008 We report the development of a realistic molecular model for mesoporous silica SBA-15, which includes both the large cylindrical mesopores and the smaller micropores in the pore walls. The methodology for modeling the SBA-15 structure involves molecular and mesoscale simulations combined with geometrical interpolation techniques. First, a mesoscale model is prepared by mimicking the synthesis process using lattice Monte Carlo simulations. The main physical features of this mesoscale pore model are then carved out of an atomistic silica block; both the mesopores and the micropores are incorporated from the mimetic simulations. The calculated pore size distribution, surface area, and simulated TEM images of the model structure are in good agreement with those obtained from experimental samples of SBA-15. We then investigate the adsorption of argon in this structure using Grand Canonical Monte Carlo (GCMC) simulations. The adsorption results for our SBA-15 model are compared with those for a similar model that does not include the micropores; we also compare with results obtained in a regular cylindrical pore. The simulated adsorption isotherm for the SBA-15 model shows semiquantitative agreement with the experimental isotherm for a SBA-15 sample having a similar pore size. We observe that the presence of the micropores leads to increased adsorption at low pressure compared to the case of a model without micropores in the pore walls. At higher pressures, for all models, the filling proceeds via the monolayer-multilayer adsorption on the mesopore surface followed by capillary condensation, which is mainly controlled by the mesopore diameter and is not influenced by the presence of the micropores.

1. Introduction 1,2

SBA-15 is one of the most important ordered mesoporous silicas synthesized after MCM-41, and numerous applications of this material have been reported in the literature. These applications include gas adsorption, catalysis and low dielectric constant materials,3-7 drug delivery,8,9 chemical and biological sensors,10,11 photonic band gap materials,12 and templates for other mesoporous substances.13-15 The structure of the SBA-15 consists of hexagonally arranged cylindrical pores (5-20 nm diameter) with siliceous pore walls. The hexagonal pore arrangement results from self-assembled surfactant micelles, which serve as templates for the polymerization of silica during synthesis. *To whom correspondence should be addressed. E-mail: [email protected]. (1) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Science 1998, 279, 548. (2) Zhao, D.; Huo, Q.; Feng, J.; Chmelka, B. F.; Stucky, G. D. J. Am. Chem. Soc. 1998, 120, 6024. :: (3) Ciesla, U.; Schuth, F. Microporous Mesoporous Mater. 1999, 27, 131. :: (4) Schuth, F.; Schmidt, W. Adv. Mater. 2002, 14, 629. (5) Selvam, P.; Bhatia, S. K.; Sonwane, C. G. Ind. Eng. Chem. Res. 2001, 40, 3237. (6) Soler-Illia, G. J. de A. A.; Sanchez, C.; Lebeau, B.; Patarin, J. Chem. Rev. 2002, 102, 4093. (7) Hoffmann, F.; Cornelius, M.; Morell, J.; Froba, M. Angew. Chem., Int. Ed. 2006, 45, 3216. (8) Song, S. W.; Hidajat, K.; Kawi, S. Langmuir 2005, 21, 9568. (9) Vallet-Regı, M; Balas, F.; Arcos, D. Angew. Chem., Int. Ed. 2007, 46, 7548. (10) Yamada, T.; Zhou, H.; Uchida, H.; Honma, I.; Katsube, T. J. Phys. Chem. B 2004, 108, 13341. (11) Hartmann, M. Chem. Mater. 2005, 17, 4577. (12) Liu, C. S.; Peng, L. M. Phys. Rev. B 2002, 66, 193407. :: (13) Lu, A.-H.; Schuth, F. Adv. Mater. 2006, 18, 1793. (14) Yang, H.; Zhao, D. J. Mater. Chem. 2005, 15, 1217. (15) Vinu, A.; Mori, T.; Ariga, K. Sci. Technol. Adv. Mater. 2006, 7, 753.

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Results from transmission electronic microscopy (TEM), Xray diffraction, and adsorption experiments suggest that microporous channels interconnect the cylindrical mesopores in SBA15 materials.13,16-18 In consequence, the regular cylindrical pore models that have been used in most simulation studies are unable to capture these structural features. As a result, it is usually difficult to link simulation results with experimental data for real materials. In addition, adsorption-based methods are insufficient or lead to inaccurate estimates of the surface roughness or microporosity, due to limitations in the classical models used to analyze the data.19,20 Despite extensive studies using a number of experimental techniques (e.g., TEM, X-ray diffraction, among others),3-6 it is still difficult to obtain a clear picture of the surface disorder of templated mesoporous silica materials. Many of these issues could be clarified by developing realistic molecular models for mesoporous silicas. Several models have been proposed, which include reconstruction models21-25 (models that are (16) Imperor-Clerc, M.; Davidson, P.; Davidson, D. A. J. Am. Chem. Soc. 2000, 122, 11925. (17) Ryoo, R.; Ko, C. H.; Kruk, M.; Antochshuk, V.; Jaroniec, M. J. Phys. Chem. B 2000, 104, 11465. (18) Galarneau, A.; Cambon, H.; Di Renzo, F.; Fajula, F. Langmuir 2001, 17, 8328. (19) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; 2nd ed.; Academic Press: London, 1982. (20) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by powders and porous solids; Academic Press: London, 1999. (21) Sonwane, C. G.; Jones, C. W.; Ludovice, P. J. J. Phys. Chem. B 2005, 109, 23395. (22) Feuston, B. P.; Higgins, J. B. J. Phys. Chem. 1994, 98, 4459. (23) Edler, K. J.; Raynolds, P. A.; White, J. W.; Cockson, D. J. Chem. Soc., Faraday Trans. 1997, 93, 199. (24) He, Y. F.; Seaton, N. A. Langmuir 2003, 19, 10132. (25) Solovyov, L. A.; Kirik, S. D.; Shmakov, A. N.; Romannikov, V. N. Microporous Mesoporous Mater. 2001, 44, 17.

Published on Web 12/19/2008

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tailor-made to reproduce the experimentally observed structural features) and mimetic models.26-30 Effects of surface roughness on the adsorption behavior were studied by He and Seaton24 and Coasne et al.31-33 by introducing surface roughness or morphological defects in their models. On the other hand, a mimetic approach was used in developing atomistic models for MCM-4134-36 based on the mesoscale model of Siperstein and Gubbins.26,27 In contrast to the concept of surface roughness and defects in mesopores, microporosity in computer models has received considerably less attention.37 The aim of the present work is twofold. We address the effect of intrawall microporosity by developing a realistic model of SBA15 based on mimetic simulations. The method was first proposed for modeling MCM-41.35,36 Here, we use a modified version of the previous technique (improved surface roughness prediction) along with a recipe for including the micropores. As will be explained in detail below, we have used b-splines to get a smoother description of the pore surface (adsorption results from refs 35 and 36 suggest that our first version of the method leads to pore surfaces that are too rough at the atomistic scale). In the present paper, we also provide a procedure that allows one to include in a simple way micropores in our model of SBA-15. A preliminary account of this methodology was presented in earlier publications.38,39 A more detailed and complete account of our methods is presented here, together with extensive results of the characterization of our model materials (pore size distribution, pore surface area, simulated TEM measurements, and simulated adsorption results). In mimetic simulations (mimicking the material synthesis using simulation techniques), the pore structure evolves inside the simulation box in a way that is analogous to the real situation, thereby preserving the structural details that are observed in the experimental material (usually lost in reconstruction models, such as regular cylinders). We first simulated a mixture of surfactants, water, and silica using lattice Monte Carlo simulations. Similar to the experimental synthesis, the system self-assembled into cylindrical micelles impregnated by silica, wherein removal of the template (surfactants, water) resulted in a coarse-grained SBA15 model. Next, the mesopore surface was constructed using the surface coordinates from the coarse-grained model. This pore surface was then carved into a cristobalite block resulting in a fully atomistic cylindrical pore with rough pore walls. Finally, the micropores were carved into the pore walls using the coordinates of the surfactant chains. The physical properties of this pore model (pore size distribution, surface area transmission electron (26) Siperstein, F. R.; Gubbins, K. E. Mol. Simul. 2001, 27, 339. (27) Siperstein, F. R.; Gubbins, K. E. Langmuir 2003, 19, 2049. (28) Bhattacharya, S.; Gubbins, K. E. J. Chem. Phys. 2005, 123, 134907. (29) Schumacher, C.; Gonzalez, J.; Wright, P. A.; Seaton, N. A. J. Phys. Chem. B 2006, 110, 319. (30) Schumacher, C.; Gonzalez, J.; Perez-Mendoza, M.; Wright, P. A.; Seaton, N. A. Ind. Eng. Chem. Res. 2006, 45, 5586. (31) Coasne, B.; Grosman, A.; Ortega, C.; Pellenq, R. J. M. Stud. Surf. Sci. Catal. 2002, 144, 35. (32) Coasne, B.; Pellenq, R. J. M. J. Chem. Phys. 2004, 120, 2913. (33) Coasne, B.; Gubbins, K. E.; Pellenq, R. J. M. Part. Part. Syst. Charact. 2004, 21, 149. (34) Coasne, B.; Hung, F. R.; Siperstein, F. R.; Gubbins, K. E. Ann. Chim. Sci. Mater. 2005, 30, 375. (35) Coasne, B.; Hung, F. R.; Pellenq, R. J. M.; Siperstein, F. R.; Gubbins, K. E. Langmuir 2006, 22, 194. (36) Hung, F. R.; Coasne, B.; Gubbins, K. E.; Siperstein, F. R.; SliwinskaBartkowiak, M. Stud. Surf. Sci. Catal. 2006, 160, 153. (37) Coasne, B.; Galarneau, A.; Di Renzo, F.; Pellenq, R. J. M. Langmuir 2006, 22, 11097. (38) Bhattacharya, S.; Coasne, B.; Hung, F. R.; Gubbins, K. E. Stud. Surf. Sci. Catal. 2006, 160, 527. (39) Hung, F. R.; Bhattacharya, S.; Coasne, B; Thommes, M.; Gubbins, K. E. Adsorption 2007, 13, 425.

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micrograph, etc.) are compared with those of experimental SBA15.40 In the second part of this paper, Grand Canonical Monte Carlo (GCMC) simulations are used to simulate the adsorption of argon at 77 K inside our SBA-15 model. In addition to the microporous SBA-15 model (model A), we show adsorption results for two other pore models; one of them is the same SBA-15 model with the micropores removed (model B), and the other is a regular cylindrical pore (model C). Comparing the adsorption results between models A and B, we highlight the contributions of the micropores toward the adsorption characteristics, whereas the same analysis between models B and C elucidates the effects of surface heterogeneity on gas adsorption. We then discuss the contributions of the micropores to the adsorption behavior of model A. The remainder of this paper is organized as follows. In section 2, we describe the method used to generate a realistic model of SBA-15 (model A) as well as the other simpler pore models (B and C). Here, we also describe the methods used in characterizing the pore models and simulating the adsorption of argon. Then, in section 3, we first characterize the pore models using pore size distribution, pore surface area, and simulated TEM, and then discuss the results obtained for argon adsorption at 77 K in these pore models. When possible, comparison with the experiments is made. In section 4, we present our conclusions and suggestions for future work.

2. Computational Details In this section, we discuss the on-lattice and off-lattice techniques used in developing our model of SBA-15. We also provide details of the calculations done to characterize the structure of our model, and we describe the procedure used to simulate the adsorption of argon. 2.1. Development of a Model of SBA-15. Due to the large length and time scales involved in the processes taking place during the synthesis of periodic mesoporous silicas, coarse-grained simulation methods such as lattice Monte Carlo simulations41-43 have been shown to be efficient in modeling MCM-4126,27 and mesostructured cellular foams (MCFs).28 In our system, the surfactants are modeled as chains of beads on adjacent lattice sites and the rest of the molecules (water, silica) occupy single lattice sites. Each surfactant molecule is a triblock copolymer consisting of 11 lattice units, 5 of which are hydrophobic with 3 hydrophilic units on each end. The rationale behind this model is to mimic the experimental surfactant pluronic P123, which consists of hydrophobic polypropylene units in the center and hydrophilic polyethylene units at both ends. The lengths of the hydrophobic and hydrophilic segments of the surfactant were selected such that the simulated phase diagram qualitatively agrees with that of the experimental surfactant. A comparison of the quaternary phase diagram of the modeled surfactant to that of P123 has been presented in a previous work.28 The system is equilibrated in a NVT ensemble employing standard lattice Monte Carlo moves such as reptation, twist, and chain regrowth by configurational bias.44 Figure 1a represents the simulation box snapshot showing the mesoscale SBA-15 structure obtained through lattice simulations. Assuming a lattice unit of 0.5 nm, the lattice porous (40) Liu, J.; Zhang, X.; Han, Y.; Xiao, F. S. Chem. Mater. 2002, 14, 2536. (41) Larson, R. G.; Scriven, L. E.; Davis, H. T. J. Chem. Phys. 1985, 83, 2411. (42) Larson, R. G. J. Phys. II (France) 1996, 6, 1441. (43) Panagiotopoulos, A. Z.; Floriano, M. A.; Kumar, S. K. Langmuir 2002, 18, 2940. (44) Frenkel, D.; Smit, B. Understanding Molecular Simulation, 2nd ed.; Academic Press: San Diego, CA, 2002.

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Figure 1. (a) Mesoscale structure; (b) single pore with surface points shown in red; and (c) pore surface modeled as b-spline with surface points shown in red.

structure shown in Figure 1a was found to have a pore length of 15 nm and a mean pore radius of 2.7 nm. The choice of such a lattice spacing was motivated by the fact that it corresponds to a reasonable approximation for the size of the bead in the onlattice simulations (a few SiO2 tetrahedron units per bead). Moreover, similar values of lattice spacings were also used in previous lattice Monte Carlo studies of self-assembly of surfactants performed by our group.27,28,45,46 Atomistic levels of detail are then incorporated into this mesoscale model by following a methodology similar to that presented in our previous publications.34-36 However, our early silica models exhibited pore walls with excessive surface roughness at length scales below 10 A˚, as compared with real materials; on the other hand, the roughness at larger length scales was comparable to that exhibited by experimental samples.47,48 In order to reduce the surface roughness in our silica pore models, the following procedure was used. First, the silica particles that are located on the mesopore surface of the onlattice model were identified. The pore surfaces were then modeled as b-splines,49 where the control points were given by the coordinates of the silica particles that make up the mesopore surfaces (Supporting Information section S.1). Figure 1b shows an isolated single pore and typical surface points. Figure 1c shows the pore surface modeled as a b-spline using the surface points as control vertices. An atomistic SBA-15 pore model was then prepared by carving out of a crystalline silica block of cristobalite (in its β-form having a cubic structure) the mesoscale pore model obtained from the on-lattice simulations. The methodology followed here is the same as that used in our previous work to model MCM-41 pores.34-36 The atomistic model consists of two pores, one in the center of the box and one centered on the box edge. In fact, this constitutes a basic unit for the hexagonally ordered SBA-15, which can then be replicated to form a (45) Lısal, M.; Hall, C. K.; Gubbins, K. E.; Panagiotopoulos, A. Z. J. Chem. Phys. 2002, 116, 1171. (46) Scanu, L. F.; Gubbins, K. E.; Hall, C. K. Langmuir 2004, 20, 514. (47) Edler, K. J.; Reynolds, P. A.; White, J. W. J. Phys. Chem. B 1998, 102, 3676. (48) Sonwane, C. G.; Bhatia, S. K.; Calos, N. J. Langmuir 1999, 15, 4603. (49) Piegl, L.; Tiller, W. The NURBS Book; Springer: Berlin, 1995.

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repetitive structure. The resulting structure is shown in Figure 2a, where the violet regions represent the pore surface. By following the procedure described before, we ensure that features such as undulations and curvature of the mesopore surface from the mesoscale model are completely transferred to the pore surface of the atomistic model. The next step is to model the micropores, which are carved out using the coordinates of the surfactant chains (Supporting Information section S.2). Experimental evidence indicates that the micropores have diameters ranging from 0.5 to 1.5 nm.50 In our model, the micropore sizes are randomly selected from a Gaussian distribution with a mean value of 1 nm and are allowed to vary between 0.8 and 1.2 nm. The choice of a normal distribution differs from that expected for real SBA-15 solids, based on the observation that the micropores appear in the space left behind by the surfactant chain. However, the procedure proposed in this paper is an approximation that constitutes a first attempt to mimic in a simple way microporosity in these porous solids. The structure obtained after carving out the micropores is shown in Figure 2b. After carving out the mesoand micropores, the silicon atoms which are in an incomplete tetrahedral environment are first removed. The oxygen atoms with two dangling bonds are next removed, and those with one dangling bond are saturated with hydrogen atoms.51 This procedure ensures that the simulation box has no net electrical charge and that none of the silicon and oxygen atoms have dangling bonds. Finally, the pore surface was made amorphous by randomly displacing all the atoms in the system by a small distance. This procedure ensures that the model is consistent with the amorphous wall structure of SBA-15 reported in the experiments.1 The final structure (model A) is shown in Figure 2c, and the repetitive structure obtained by replicating the unit cell is shown in Figure 2d. We used a similar simulation protocol to generate two additional model materials (models B and C). No microporosity is present in model B, and the mesopores are similar to those in model A. Model C consists of a regular cylindrical mesopore with no microporosity. Front views and transverse cross sections of the three models are depicted in Figure 3. The mean mesopore diameter in all three models is D = 5.4 nm; nevertheless, by comparing the cross section views of pore models A and B (Figure 3), it is apparent that the elimination of microporosity leads to a small reduction in the mesopore diameter of model B. Model A represents a SBA-15 material, while model B represents a non-microporous silica material such as MCM-41; however, the silica walls in model B are about 2-4 times thicker than those observed in real MCM-41 materials (∼4.1 nm in model B, ∼1-1.5 nm in MCM-41 materials). Model C will be used to analyze how the adsorption properties of models A and B differ from those in an ideal, cylindrical pore model. 2.2. Characterization of the Model. Pore Size Distribution. The pore size distribution (PSD) of our silica pore models is obtained from the atomic coordinates in the model structure. The geometrical pore size at a given point is defined as the largest sphere that can be constructed encompassing the given point.52,53 The pore size distribution is calculated based on an algorithm published elsewhere.53 According to this technique, points are selected randomly inside the simulation box and the pore sizes are calculated at these points. Then, a cumulative (50) Galarneau, A.; Cambon, H.; Di Renzo, F.; Ryoo, R.; Choi, M.; Fajula, F. New J. Chem. 2003, 27, 73. (51) Pellenq, R. J. M.; Levitz, P. E. Mol. Phys. 2002, 100, 2059. (52) Gelb, L. D.; Gubbins, K. E. Langmuir 1999, 15, 305. (53) Bhattacharya, S.; Gubbins, K. E. Langmuir 2006, 22, 7726.

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Figure 2. (a) Structure obtained by carving out the mesopores from a crystalline block of silica; (b) same structure as in (a) after carving out the micropores; (c) final structure after removing the unbonded atoms, saturating the dangling bonds with hydrogen and displacing all the atoms in the system by a small random distance; and (d) repetitive structure obtained by replicating the unit cell. Color code: yellow, silicon; red, oxygen; blue, hydrogen; violet, pore surface. Box sizes in (a-c) are 13.54  8.56  14.97 nm3.

histogram H(D) is constructed, where H(D) represents the probability of finding a point in the model space with a pore size greater than or equal to D. The pore size distribution P(D) is the negative of the differential coefficient of H(D) with respect to D, that is PðDÞ ¼ -

dHðDÞ dD

ð1Þ

While calculating the PSD, the porosity may be obtained as the ratio of the number of points with a nonzero pore size to that of the total number of trial points. Pore Surface Area. The pore surface area is obtained by rolling an adsorbate molecule over the pore surface and calculating the resulting surface area that is accessible to the adsorbate.54,55 Following a Monte Carlo scheme, many randomly oriented straight lines are constructed inside the simulation box. The points of intersection of these straight lines with the pore surface are then identified. Let l1, l2, l3..., ln be the lengths of the line segments and p1, p2, p3..., pn be the number of intersections for each segment. The surface area per unit volume is given by n P

SV ¼ 2 i ¼1 n P i ¼1

pi ð2Þ li

The proof of this expression is given in ref 56. A large number of line segments need to be sampled in order to get an accurate surface area estimate. This technique has been used in computing the surface areas of controlled pore glasses.52 (54) Connolly, M. L. Science 1983, 221, 709. (55) Connolly, M. L. J. Appl. Crystallogr. 1983, 16, 548. (56) Underwood, E. E. Quantitative Stereology; Addison-Wesley Publishing Company: Reading, MA, 1970.

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Simulated Transmission Electron Micrograph. High resolution TEM (HRTEM) of the model SBA-15 structure has been simulated following the multislice approach by Cowley and Moodie.57 The TEM simulations have been carried out using the CERIUSII software using a sample thickness of 15 nm. An accelerating voltage of 200 kV has been used for all the simulations. 2.3. Ar Adsorption in the Pore Models. Grand Canonical Monte Carlo (GCMC) simulations were used to simulate the adsorption of argon at 77 K inside the model SBA-15 pores. As noted by Neimark et al.,58 two different values for the saturation pressure, which correspond to the solid and to the supercooled liquid, are used in the adsorption literature. However, previous molecular simulations show that the density and saturation pressure of Ar at 77 K is close to the density and saturation pressure of the supercooled liquid Ar.32,58 The latter is obtained by extrapolating the liquid-gas saturation pressures below the triple point P ∼ 25 kPa. The argon-argon interaction was modeled using a Lennard-Jones potential with parameters, σ = 0.34 nm and ε = 121 K.59 The interaction between argon and the pore wall is modeled according to the PN-TrAZ potential (Transferable Potential for Adsorption in Zeolites) developed by Pellenq and Nicholson.60 The potential is made up of the following terms: (1) polarization interaction due to the electric field created by the partial charges carried by the atoms of the substrate, (2) dispersion interaction, and (3) repulsive interaction. This potential was originally developed for studying adsorption of rare gases in zeolites and/or mesoporous silicas, (57) Cowley, J. M.; Moodie, A. F. Acta Crystallogr. 1957, 10, 609. (58) Neimark, A. V.; Ravkovitch, P. I.; Grun, M.; Schuth, F.; Unger, K. K. J. Colloid Interface Sci. 1998, 207, 159. (59) Smith, J. M.; Van Ness, H. C.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics; McGraw Hill Science Eng.: New York, 2004. (60) Pellenq, R. J.-M.; Nicholson, D. J. Phys. Chem. 1994, 98, 13339.

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Figure 3. Front views and cross section views of the different models used in this study. Silicon, oxygen, and hydrogen are represented here in tan, gray, and black, respectively. Model A exhibits both mesoporosity and microporosity. Model B has mesopores that are similar to those of model A but has its microporosity removed. Model C is a regular cylindrical pore model. All three models have a mean mesopore diameter of 5.4 nm.

but it can be extended to cover the adsorption of more complex adsorbates.61,62 The model SBA-15 structure is placed in a simulation box with dimensions 13.55  8.566  14.97 nm3 with periodic boundary conditions in all directions. The system is then equilibrated at 77 K using Monte Carlo simulations in the Grand Canonical ensemble where the chemical potential ( μ), volume (V ), and temperature (T ) are kept constant. Starting from very low coverage, the chemical potential is increased in steps and the system is equilibrated at each step. The relation between the chemical potential and the system pressure is obtained from the equation of state for Lennard-Jones fluids by Kofke.63 While calculating the desorption branch, a similar procedure is followed. Starting from a maximum coverage, the chemical potential is decreased in steps until a sharp decrease in the adsorbed amount is observed. Variables such as the amount adsorbed (i.e., the number of adsorbate molecules in the simulation box) and the total energy of the system were monitored to ensure that our systems have reached equilibrium conditions. Afterward, thermodynamic properties were averaged over a minimum of 2  105 MC steps per particle (typical systems had up to N ∼ 22 000 particles); however, longer runs (of about 2 106 MC steps per particle) were considered near the phase transitions (the “jumps” in the isotherms). The isosteric heats of

(61) Puibasset, J.; Pellenq, R. J. M. J. Chem. Phys. 2003, 118, 5613. (62) Coasne, B.; Alba-Simionesco, C.; Audonnet, F.; Dosseh, G.; Gubbins, K. E. Adsorption 2007, 13, 485. (63) Kofke, D. A. J. Chem. Phys. 1993, 98, 4149. (64) He, Y.; Seaton, N. A. Langmuir 2005, 21, 8297.

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adsorption are calculated from the fluctuations in the internal energies of the adsorbate.64,65

3. Results and Discussion 3.1. Characterization of the Model. Pore Size Distribution. In Figure 4, we compare the pore size distribution of the model SBA-15 (model A) to that of an experimental SBA-15 material.17 The PSD of the model material was obtained by a geometrical method (2.2section 2.2), while in the experiments of Ryoo et al.17 the pore size distributions were calculated from the analysis of nitrogen adsorption measurements. It is important to note that the methods used to estimate PSD in the simulation and experimental approaches relate to the pore geometry in a different way. Moreover, the adsorption experiments were analyzed using the Barret, Joyner, and Halenda (BJH) algorithm (see, e.g., refs 19 and 20). The relation between the pore size and the capillary condensation pressure was calibrated in a previous study using MCM-41 silicas.66 The BJH method also introduces a degree of approximation in the PSD, and therefore, caution must be exercised when directly comparing the PSD results from our simulations and experiments. In Figure 4, both the model and the experimental PSD show qualitatively similar bimodal distributions, where the rightmost peak represents the mesopores and the leftmost peak the micropores. For the model SBA-15, the mean mesopore size is 5.4 nm (65) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: London, U.K., 1982. (66) Kruk, M.; Jaroniec, M.; Sayari, A. Langmuir 1997, 13, 6267.

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Figure 4. Pore size distributions: (a) model SBA-15 and (b) experimental SBA-15.17

and the mean micropore size is 1.2 nm, which are similar to the values obtained from the experimental PSD, 6 and 1.06 nm, respectively. In contrast to the smooth PSD for the experimental sample, three peaks can be distinguished in the mesopore region for the model SBA-15. This result is due to the small size of the simulation box, with only two mesopores; a smoother PSD would be obtained if a larger number of mesopores were modeled. The microporous volume in our model (assuming the micropores have pore sizes below 2 nm) represents 28% of the total porosity. Our model material has a higher micropore volume compared to the experimental material of Ryoo and coworkers;17 however, for other samples of SBA-15, it has been reported18 that the microporosity can represent 30% of the total porosity. Our model also shows some secondary porosity between 2 and 4 nm, which is a characteristic of experimental SBA-15 materials that are heated to high temperatures after synthesis. The experimental material from Ryoo et al. also shows some secondary porosity, although the amount is less than that of the model. The total pore volume in our model is 0.77 cm3/g, which is in fair agreement with the values obtained from the experiments (0.7-1.2 cm3/g).17,18 A summary of the comparison of these structural parameters between simulations and experiments is presented in Table 1. All the parameters listed here correspond to those determined from the adsorption of argon. We note that the validity of the comparisons between our data and those obtained from adsorption measurements for the real solid is based on the assumption that adsorption-based characterization methods provide accurate estimates of the material features (surface area, microporosity, pore size distribution). Pore Surface Area. The net surface area available for adsorption depends on the size of the test particle (adsorbate molecule). Figure 5a shows the internal surface area of the model SBA-15 as a function of the test particle radius rp. For rp = 0 nm, Langmuir 2009, 25(10), 5802–5813

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the surface area which corresponds to the true mathematical surface is approximately 3300 m2/g. The accessible surface area decreases rapidly with test particle radius until rp = 0.1 nm (zone 1). Between rp = 0.1 and 1.0 nm, the surface area varies nonlinearly with test particle radius (zone 2). Thereafter, the surface area shows a linear decay decreasing to zero around rp = 2.5 nm (zone 3). In zone 1 (rp < 0.1 nm), the surface area is contributed by the intermolecular spaces, in addition to the mesopores and the micropores. The additional surface area in zone 1 is not accessible to any adsorbate molecule (the van der Waals radius of hydrogen is 0.12 nm). In zone 2 (0.1 < rp 2.5 nm), the surface area is contributed by the mesopores only. From the PSD in Figure 4a, the majority of the micropores in the model SBA-15 have pore sizes below 1.25 nm. The surface area decreases to zero at rp = 2.5 nm which corresponds to the average mesopore radius (2.7 nm). Finally, zone 3 represents the surface area accessible to macromolecules (proteins and polymers) and metallic nanoparticles.67 Figure 5a can be used to predict the accessible surface area from the knowledge of the adsorbate size. For example, given the average mesopore and micropore radii of an experimental SBA-15 sample, one can estimate the specific surface area available for adsorption to a molecule of a particular size. In practice, this information will be helpful in designing SBA-15 materials tailored to have specific adsorption or catalysis properties. Radii of several common adsorbate molecules68 and the corresponding surface areas are given in Table 2. For the SBA15 model, the surface area for N2 adsorption is found to be 1035 m2/g, which is comparable to results obtained from adsorption experiments.2,17 Again, as noted above, the validity of the comparison between the simulated and experimental data is based on the assumption that accurate estimates of the surface area are obtained from adsorption measurements. We now compare the surface area of the model SBA-15 (model A) to that of a model without the micropores (model B). Figure 5b shows the total pore surface area with test particle radius for the two models. Only the zones 2 and 3 are considered here. Since the two models have different densities, surface areas per unit volume are compared instead of surface areas per unit mass. For adsorbate radii below 1 nm, model B shows less surface area compared to model A. For higher values of rp, the surface areas of both models are almost identical, indicating that adsorbate molecules with radii larger than 1 nm will not feel the presence of any micropore in the material. Simulated TEM. Figure 6 shows the simulated high resolution TEM images of two pore models, model A including both mesopores and micropores and model B without the micropores. In all of the figures, the darker areas represent the pore walls and lighter areas represent the pore voids and areas with low densities. Figure 6a and c shows the TEM images for models A and B taken in the axial direction (parallel to the mesopore axis), whereas Figure 6b and d shows the TEM images taken in the transverse direction (perpendicular to the mesopore axis). Comparing the TEM images in the axial direction, the model with micropores (Figure 6a) shows a lower wall density compared to the model without micropores (Figure 6c). This reduced pore wall density is due to the presence of the micropores in the pore walls. Model A also shows spatial variations in the wall :: (67) Yang, C. M.; Kalwei, M.; Schuth, F.; Chao, K. J. Appl. Catal., A 2003, 254, 289. (68) Bondi, A. J. Phys. Chem. 1964, 68, 441.

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Bhattacharya et al. Table 1. Parameters for Model A and Experimental Samples of SBA-1517,18 parameter

pore volume mesopore volume as % of total porosity specific surface area

model SBA-15 (model A)

experimental SBA-15 from ref 17

experimental SBA-15 from ref 18

0.77 cm3/g 72% 931.211 m2/g

0.96 cm3/g 94% 780-850 m2/g

0.6-1.2 cm3/g 63% 700-850 m2/g

Figure 5. (a) Variation of internal surface area per unit mass with test particle radius for the model SBA-15. The significances of the three zones are marked in the figure. (b) Comparison between the surface areas per unit volume of the model SBA-15 and the model without the micropores: (b) model with micropores; (O) model without micropores; and (1) contribution of the micropores toward the surface area. Table 2. Accessible Surface Area of the Model SBA-15 as a Function of Adsorbate Size adsorbate/van der Waals radius (nm) accessible surface area (m2/g) hydrogen/0.12 1178 nitrogen/0.155 1035 argon/0.188 931 krypton/0.202 898 xenon/0.216 865 metallic nanoparticles/between 1.0 and 2.0between 279 and 77

density due to a nonuniform distribution of micropores in the pore walls. In comparison, due to the absence of micropores, model B shows a uniform wall density. The granular patterns visible in both images are due to the diffraction around individual atoms and not due to the micropores. No significant difference in overall wall densities is observed between the TEM images taken in the transverse direction (Figure 6b and d), due to the small thickness of the samples in this direction. The wall density in model A is nonuniform, similar to the TEM images in the axial direction, whereas model B shows a uniform wall density. In high resolution TEM images of microporous structures, it is critical to distinguish between the real micropore features and 5808

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Figure 6. Simulated TEM images of model structures. Model A represents the entire microporous-mesoporous structure, and model B only the mesoporous structure. (a) Axial view of model A; (b) transverse view of model A; (c) axial view of model B; and (d) transverse view of model B. The axial and the transverse views are explained in the schematic. Defocus values for the individual images are tabulated.

the artifacts arising due to atomic diffraction. Usually a slight under-focusing of the electron beam helps to suppress the atomic diffraction patterns, at the same time emphasizing the structural details in the pore walls. The amount of under-focusing, also called defocus (measured in A˚), is an important parameter that must be fine-tuned to obtain an optimal TEM image. TEM images (axial direction) of the microporous SBA-15 model are shown in Figure 7 for several defocus values d. Above d = -400 A˚, spurious details in the TEM images in the form of bright fringes overshadow the micropore contrast in the pore walls. On the other hand, decreasing the defocus below d = -550 A˚ does not affect the image contrast. Therefore, we select d = -550 A˚ as the optimum defocus. Similar procedures have been followed for all the other TEM images shown in Figure 6. The individual defocus values of the different images are listed at the bottom right corner of Figure 6. The images in Figure 7 show the key role of the effect of defocus to reveal the details of the pore structure and morphology from TEM images. In Figure 8, we compare the TEM images of the model SBA15 with the high resolution TEM images of an experimental SBA-15 from Liu et al.40 Figure 8a and b show the TEM images of the model SBA-15 structure along the axial and transverse directions, respectively. In Figure 8a, the unit cell has been replicated in order to show the repetitive ordering of the SBA-15 porous structure. Figure 8c and d represent the TEM images for the experimental structure. Figure 8e represents the TEM image for the non-microporous model (model B). A qualitative comparison between Figure 8a and c indicates that the pore walls of Langmuir 2009, 25(10), 5802–5813

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Figure 7. Effect of defocus on the image contrast in the simulated TEM images of SBA-15. Defocus values are listed below the individual images.

Figure 8. Comparison between experimental40 and model TEM images: (a) model SBA-15 (axial direction); (b) model SBA-15 (transverse direction); (c) experimental SBA-15 (axial direction); (d) experimental SBA-15 (transverse direction); and (e) model without the micropores (axial direction). White boxes represent regions showing similar contrast patterns.

structures A and B exhibit similar granular features, as shown by the white boxes in the images. These granular features were interpreted by the authors (Liu et al.40) as direct experimental evidence of the micropores. It is important to note here that we are only attempting to make a qualitative comparison, since the experimental and calculated TEM images do not have the same underfocus. We note that the pore walls of the non-microporous model also show granularities to some extent (Figure 8e). However, the sizes of the grains in Figure 8e are smaller compared to those of the grains in Figure 8a and are due to the atomic contrast. On the other hand, both panels a and c in Figure 8 show similar sized grains in the pore walls, which suggests that they are due to the micropores. 3.2. Adsorption of Argon at 77 K. Adsorption Isotherm. The adsorption isotherm of argon at 77 K in the three atomistic silica mesopore models A, B, and C (Figure 3) are presented in Figure 9. The adsorbed amounts have been normalized to the total number of atoms, N0, when the pores are filled. The adsorption curves as a function of relative pressure P/P0 exhibit different features and are significantly affected by the pore morphology. For the regular cylindrical pore model Langmuir 2009, 25(10), 5802–5813

(model C), we observe one small vertical jump in the adsorption curves, which is due to capillary condensation inside the pore. In contrast, two small jumps are observed in the adsorption isotherms for pore models A (with micropores) and B (without micropores). On the one hand, the surface area of pore model A is larger than that of model B due to the presence of microporosity and surface roughness, where the molecules of adsorbate can be preferentially adsorbed at lower values of P/P0. On the other hand, pore undulations and other morphological features on the mesopores cause the surface area of model B to be larger than that of model C. As a result, at low pressures (P/P0 < 0.4 for Ar at 77 K), pore model A exhibits the largest amount adsorbed, followed by models B and C. A small increase in P/P0 leads to the first small jump in the adsorption isotherm of model B. This is due to the fact that elimination of microporosity in model B leads to a small reduction in its mesopore diameter, as compared to the other pore models (Figure 3). Further increases in P/P0 leads, in order, to the following features in the adsorption isotherms: first jump (model A), second jump (model B), single jump (model C), and second jump (model A). The three pore models fill at similar DOI: 10.1021/la801560e

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Figure 9. Argon adsorption isotherm at T = 77 K. Simulation results for pore models (0) A, (4) B, and (]) C. (b) Experimental results for Ar adsorption at 77 K on SBA-15 with a mean mesopore diameter of D = 5 nm.50 Inset represents adsorption data, in cm3, of Ar at standard T and P per gram of adsorbent, as a function of relative pressure P/P0.

values of P/P0, around 0.60-0.65 for Ar at 77 K (Figure 9). As will be discussed in the following section, the two jumps for model A and model B correspond to capillary condensation in each mesopore (the simulation box for both models contains two mesopores). In Figure 9, we compare our simulation results with experimental data50 for gas adsorption on SBA-15 with a mean mesopore diameter of D = 5 nm (similar to that used in our models, D = 5.4 nm) and a micropore volume of about 30% (similar to that of our model, 28%). In the experiments,50 the mesopore diameter was obtained from the desorption branch of N2 adsorption isotherms using the Broekhoff and de Boer (BdB) method (see, e.g., refs 19 and 20); afterward, the mesopore and micropore volumes were estimated using numerical relations developed in their earlier studies.18,48 Although the properties of the porous samples used in experiments and simulations seem to be similar, one must exercise caution when comparing adsorption results from simulations and experiments. As we discussed before (3.1section 3.1), the geometrical methods that we used to characterize our simulated porous samples relate to the pore geometry in a different way than the methods used to characterize the physical properties of porous samples from experimental adsorption measurements. Moreover, characterization methods based on adsorption measurements usually introduce a degree of approximation in the results. Capillary condensation in model A takes place at relative pressures closer to those observed in experiments, and the amount adsorbed is overestimated in all our models at P/P0 < 0.7. In the inset of Figure 9, we compare the adsorption of Ar, in cm3, of adsorbate (at standard T and P) per gram of adsorbent, between simulations and experiments. The amounts adsorbed in the experimental isotherm are close to those obtained from simulated Ar adsorption on pore model A; models B and C provide significantly lower adsorption at any given value of P/P0. At 100% loading (high-pressure regime, P/P0 > 0.7), there is agreement between the experiment and the simulated adsorption isotherm on pore model A. In the experimental isotherm, capillary condensation takes place at values of P/P0 between 0.55 and 0.74, which are comparable to those observed for the pore filling in model A (P/P0 ∼ 0.60-0.67). Nevertheless, the adsorption on pore model A at P/P0 < 0.7 is larger than that reported in the experimental isotherm. The lack 5810

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Figure 10. Isosteric heat of adsorption Qst as a function of coverage fraction N/N0 for Ar at 77 K: (top) total Qst and (bottom) adsorbate-wall (filled symbols) and adsorbate-adsorbate (open symbols) contributions to Qst. Simulation results for pore models (9/0) A, (2/4) B, and ([/]) C. Experimental results for Ar at 87 K on MCM-41 with mesopores of about 4.5 nm58 are depicted by filled circles (b) in the top figure.

of quantitative agreement between simulations and experiments for these pressure regimes could be due to several possible reasons. First, the intermolecular potential adsorbate-wall may be overestimating the attractive energy: for simulated Ar adsorption in regular cylindrical silica pores, it has been reported32,69 that a reduction of 3% in selected parameters can lead to quantitative agreement in film thickness (t-plot) with experimental results. Second, it has been found70 that the density of OH groups obtained in our models is about 7-8 OH per nm2, which is larger than that for real MCM-41/SBA-1571-75 (2-3 OH per nm2). This quantitative difference in the surface chemistry of the numerical and real samples leads to a significant increase in the adsorbed amount for the simulated material (69) Coasne, B.; Pellenq, R. J. M. J. Chem. Phys. 2004, 121, 3767. (70) Coasne, B.; Galarneau, A.; Di Renzo, F.; Pellenq, R. J. M. P. J. Phys. Chem. C 2007, 111, 15759. (71) Ishikawa, T.; Matsuda, M.; Yasukawa, A.; Kandori, K.; Inagaki, S.; Fukushima, T.; Kondo, S. J. Chem. Soc., Faraday Trans. 1996, 92, 1985. (72) Landmesser, H.; Kosslick, H.; Storek, W.; Frick, R. Solid State Ionics 1997, 101-103, 271. (73) Cauvel, A.; Brunel, D.; Di Renzo, F.; Fubini, B.; Garrone, E. Langmuir 1997, 13, 2773. (74) Zhao, X. S.; Lu, G. Q.; Whittaker, A. K.; Millar, G. J.; Zhu, H. Y. J. Phys. Chem. B 1997, 101, 6525. (75) Sutra, P.; Fajula, F.; Brunel, D.; Lentz, P.; Daelen, G.; Nagy, J. B. Colloids Surf., A 1999, 158, 21.

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Figure 11. Representative simulation snapshots of Ar adsorbed at 77 K on pore model A: front views (left), side views (center), and transverse section views of the center pore (right). Different values of relative pressure P/P0 are depicted: (a) P/P0 = 0.001, (b) P/P0 = 0.67, and (c) P/P0 = 0.7. Silicon, oxygen, hydrogen, and argon atoms are depicted in tan, white, black, and purple, respectively.

compared to the experiments.76 Finally, the micropore volume and the degree of surface roughness for pore model A may be high when compared to the sample of SBA-15 used in the experimental measurements. We believe that tuning the micropore volume and/or the micropore size distribution in our model materials can lead to a better agreement with the experimental adsorption results. Isosteric Heat of Adsorption. Results for the isosteric heat of adsorption Qst are presented in Figure 10 for Ar at 77 K in the SBA-15 models A, B, and C. These curves are typical of adsorption on heterogeneous surfaces, as they decrease down to a plateau value that is close to the heat of liquefaction of bulk Ar. In Figure 10, we also show experimental data for Ar at 87 K on MCM-41 with mesopores of about 4.5 nm.63 We note that the simulated and experimental data are taken at different temperatures; however, the comparison remains relevant, as (1) both temperatures are far from the critical point of argon (158 K for Lennard-Jones argon) and (2) pressures are reduced with respect to the corresponding bulk saturating vapor pressure, P0(T ). The experimental data for Qst matches better our simulation results in pore model C. At low pore filling fractions (N/N0 < 0.3), the total Qst in pore model A is larger than that observed for model B, which in turn is larger than that for model C (Figure 10, top). The reason behind this observation is that the adsorbatewall contribution to Qst for pore model A is significantly larger than that for model B; model C exhibits the lowest adsorbatewall contribution to Qst (Figure 10, bottom). As a result, the largest adsorption at a given pressure prior to capillary condensation is given by pore model A, followed by models B and C. Our results for Qst, as well as the comparison with experimental results, corroborate our prior conclusion that the micropore volume and the degree of surface roughness for pore model A is somewhat high, when compared to the two experimental samples of mesoporous silica used in the experimental (76) Coasne, B.; Galarneau, A.; Di Renzo, F.; Pellenq, R. J. M. P. Langmuir 2008, 24, 7285-7293.

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measurements. As noted above, the disagreement between the experimental results and those from models A and B, can also be explained by the large density of OH groups in the simulation models (7-8 OH/nm2) that leads to a surface that is somewhat too attractive energetically. For instance, it has been shown76 that the adsorbed amount at a given pressure is reduced by a factor of 2 or 3 when the surface density of OH groups is decreased from 7 to 2 OH/nm2. We also note that in our previous work35 we obtained simulated SANS results for a similar silica mesopore model, and found that its roughness at length scales between 10 and 50 A˚ is in agreement with experimental measurements for templated mesoporous silica materials.47,48 Pore Filling Mechanisms. We have used our pore models to discuss the effect of surface roughness and structural defects on the pore filling mechanism. In Figures 11 and 12, we present plots of representative simulation snapshots for Ar adsorption at 77 K on pore models A and B, respectively, at different values of P/P0. The pore filling mechanism on model C corresponds to the classical picture of capillary condensation in regular mesopores: the thickness of the adsorbed film increases with P/P0 until it reaches its stability limit [P/P0 = 0.58, Figure 9]. A slight increase in P/P0 induces a transition to a condensed phase, and a vertical jump is observed in the adsorption isotherm [P/P0 = 0.60, Figure 9]. For pore model A, at low relative pressures, the Ar atoms are mainly adsorbed inside the micropores, whereas little adsorption takes place on the surface of the mesopores [P/P0 = 0.001, Figure 11a]. As the pressure increases, the micropores fill and a monolayer of Ar covers the mesopore surface. The thickness of the Ar film adsorbed in the mesopores increases gradually with P/P0, until it reaches the onset of capillary condensation in the mesopore at the center of the simulation box [P/P0 = 0.67, Figure 11b]. A further increase in pressure causes capillary condensation to occur in both mesopores [P/P0 = 0.7, Figure 11c]. The adsorption mechanism on model B is similar to what was described for the mesopores in model A: as P/P0 increases, the pore walls are covered by an adsorbate film [P/P0 = 0.001, Figure 12a], whose thickness increases gradually DOI: 10.1021/la801560e

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Figure 12. Representative simulation snapshots of Ar adsorbed on pore model B: front views (left), side views (center), and transverse section views of the center pore (right). Different values of relative pressure P/P0 are depicted: (a) P/P0 = 0.001, (b) P/P0 = 0.45, (c) P/P0 = 0.5, and (d) P/P0 = 0.65. Silicon, oxygen, hydrogen, and argon atoms are depicted in tan, white, black, and purple, respectively.

with pressure [P/P0 = 0.45, Figure 12b]. A small increase in P/P0 induces capillary condensation in the central pore, while the second pore still maintains a low density region in the center [P/P0 = 0.5, Figure 12c]. Larger pressures are needed to fill the second pore with condensed Ar [P/P0 = 0.65, Figure 12d]. These results are in agreement to what we observed in our previous work on krypton adsorption in the same silica models,39 where capillary condensation in the two mesopores of models A and B took place at slightly different values of P/P0. Capillary condensation in the mesopores of model B take place at smaller values of relative pressure than in the case of model A. Again, this is due to the fact that elimination of microporosity in model B leads to a small reduction in its mesopore diameters, as compared to those of model A (Figure 3). The two jumps observed in the adsorption isotherms for model A and B (Figure 9) are therefore due to capillary condensation in the two pores, which take place at different values of P/P0 due to small differences in the pore morphologies. The adsorption isotherm is therefore expected to become smoother for a larger porous sample with a number of pores exhibiting small differences in their morphologies. In our previous studies of gas adsorption on a single silica mesopore with significant surface roughness at length scales below 10 A˚,34-36 we observed phases that involved coexistence of liquidlike “bridges” and gaslike regions, just before capillary condensation took place, in analogy to what was found in past (77) Bock, H.; Schoen, M. Phys. Rev. E 1999, 59, 4122. (78) Sarkisov, L.; Monson, P. A. Langmuir 2001, 17, 7600. (79) Puibasset, J. J. Chem. Phys. 2005, 122, 134710.

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studies for adsorbents with distinct chemical and morphological heterogeneities.32,51,69,77-81 In the present study, however, we did not observe any evidence of such intermediate phases. The filling of the mesopores in model materials A and B proceeded via a classical capillary condensation mechanism, where the pores fill at slightly different pressures. These results suggest that pore surface roughness, and other morphological features such as mesopore constrictions, play an important role in determining the mechanism of filling of the mesopores during gas adsorption.

4. Conclusions The present work focuses on the effect of intrawall microporosity by developing a realistic model of SBA-15 based on mimetic simulations. We first simulated a mixture of surfactants, water, and silica using lattice Monte Carlo simulations. Similar to the experimental synthesis, the system self-assembled into cylindrical micelles impregnated by silica, wherein removal of the template (surfactants, water) resulted in a coarse-grained SBA-15 model. Next, the mesopore surface was constructed using the surface coordinates from the coarse-grained model. This pore surface was then carved into a cristobalite block resulting in a fully atomistic cylindrical pore with rough pore walls. Finally, the micropores were carved into the pore walls using the coordinates of the surfactant chains. The physical properties of this pore model (pore size distribution, surface area and transmission electron (80) Vishnyakov, A.; Neimark, A. V. Langmuir 2003, 19, 3240. (81) Detcheverry, F.; Kierlik, E.; Rosinberg, M. L.; Tarjus, G. Phys. Rev. E 2003, 68, 061504.

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micrograph) are found to be in general agreement with those of experimental samples of SBA-15. In the second part of this paper, Grand Canonical Monte Carlo simulations (GCMC) are used to simulate the adsorption of argon at 77 K inside our SBA-15 model. Besides the microporous SBA-15 model (model A), we show adsorption results for two other pore models, one of them being the same SBA-15 model but with the micropores removed (model B) and the other one a regular cylindrical pore (model C). The gas adsorption isotherm on model A is in reasonably good agreement with experimental data, while the isotherms obtained from models B and C seem to underestimate the adsorbed amounts (in cm3 of adsorbate at standard T and P, per gram of adsorbent). For model A, we found excellent agreement in the adsorption at high pressures (100% loading) and in the capillary condensation pressure; however, the simulated adsorption at low and intermediate pressures was overestimated when compared with experiments. We argue that the micropore volume and the degree of surface roughness for pore model A may be somewhat high when compared to the samples of SBA-15 used in the experimental measurements. Results for the isosteric heat provide additional support for that conclusion. We believe that either finetuning the amount of microporosity or changing the surface chemistry (by decreasing the density of OH groups at the pore surface) in our model can lead to a better agreement with experiment, especially at low and intermediate pressures. Our results also suggest that microporosity, surface roughness, and structural defects (such as undulations in the mesopore surface and pore constrictions) can affect significantly the gas adsorption. We observed marked differences in the adsorption isotherms, isosteric heat curves, and pore filling mechanisms among the three model materials. For models A and B, which exhibit two

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mesopores each, we observed that small differences in their morphology lead to slightly different capillary condensation pressures. In particular, the slightly small pore diameter for model B, which arises from the elimination of microporosity for this sample, causes capillary condensation to take place at pressures that are slightly lower than those observed for model A. The mesopore filling in these models proceeded via a classical capillary condensation mechanism, which contrasts to what was observed in our previous studies,34-36 where the pore filling of a silica mesopore with an important degree of surface roughness at length scales below 10 A˚ took place via a quasi-continuous pore filling involving coexistence of liquidlike “bridges” and gaslike regions. These results suggest that pore surface roughness, and other morphological features such as mesopore constrictions, play an important role in determining the mechanism of filling of the mesopores during gas adsorption. Acknowledgment. This work was funded by the Department of Energy (DOE) under Grant DE-FG02-98ER14847. High performance computational resources for this research were provided by the San Diego Supercomputer Center (Grant NSF/MRAC CHE050047S), Louisiana State University (http://www.hpc.lsu.edu), and the Louisiana Optical Network Initiative (http://www.loni.org). Supporting Information Available: (1) Details of the method used in the selection of control points for the b-spline procedure used to model the mesopore surfaces in the atomistic silica pores. (2) Details of the method used to carve the micropores in the atomistic silica pores. This material is available free of charge via the Internet at http://pubs.acs.org.

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