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Pore Structure of Imogolite Computer Models Phillip I. Pohl,*,†,‡ Jean-Loup Faulon,† and Douglas M. Smith‡,§ Energy and Environment Division, Sandia National Laboratories, Albuquerque, New Mexico 87185, UNM/NSF Center for Micro-Engineered Ceramics, University of New Mexico, Albuquerque, New Mexico 87131, and NanoPore Corporation, Albuquerque, New Mexico 87106 Received January 22, 1996. In Final Form: April 22, 1996X This study analyzes computer models of the microporous material imogolite. The purpose of this work is to validate computational methods developed for extracting pore size, pore volume, and surface area measurement of molecular level computer models. We accomplished this by comparing model properties with experimental data derived from N2 adsorption isotherms and by simulating CH4 and N2 adsorption and He/SF6 diffusion. Pore volume and pore size are easily determined and fit experimental data within reason for validation purposes. Surface area calculations are at first greater than those determined experimentally. Correcting for the curvature of the pore enables duplication of experimental data within the combined error of both methods. Simulations of adsorption and diffusion fit available experimental results reasonably well and along with previous conclusions allow identification of the most probable model structures. The computer-based method studied should be adequate for analyzing other silicate models such as sol-gel derived microporous membranes, aerogels, and zeolites.
Introduction Computer simulations in materials science have evolved steadily over the past decade with advances in hardware and software. For atomistic calculations, however, the size and complexity of models are currently limited by the available computer memory. One area that has been studied by atomistic computer simulations is the diffusion and adsorption of gases in microporous solids. Micropores are designated by IUPAC as having pore diameters or widths less than 2 nm;1 hence, the models required are usually less than a few thousand atoms. Computer studies reported on microporous materials run the entire range from lattice and molecular mechanics for studying gas diffusion and adsorption to detailed ab initio calculations primarily for precise thermodynamic data, i.e., adsorption enthalpy and acidity. The objective of this effort is to improve understanding of a material’s structural properties which control applications such as diffusion, adsorption, and catalysis and to provide sounder justification for assumptions made in predictive equations. Imogolite is a naturally occurring tubular aluminosilicate with inner pore diameter of 7-10 Å. Ackerman, et al.2,3 completed a study of the porosity associated with natural and synthetic imogolite which included N2, CO2, and CH4 adsorption, N2 temporal adsorption, and Xe NMR. In addition, it has been embedded into dense silica membranes having molecular sieving behavior4 and has been proposed as a shape-selective catalyst.5 The purpose of this paper is to explain the experimental results for * Corresponding author: Phillip I. Pohl P.O. Box 5800, Mail Stop 0720, Sandia National Laboratories, Albuquerque, NM 871850720; 505-844-2992 (voice); 505-844-2878 (fax);
[email protected] (e-mail). † Sandia National Laboratories. ‡ University of New Mexico. § NanoPore Corporation. X Abstract published in Advance ACS Abstracts, August 1, 1996. (1) Sing, K. S. W.; Everett, D. H.; Haul, R. A. W.; Moscou, L.; Pierotti, R. A.; Siemieniewska, T. Pure Appl. Chem. 1985, 57, 603. (2) Ackerman, W. C.;Smith, D. M.; Huling, J. C.; Kim, Y.-W.; Bailey, J. K.; Brinker, C. J. Langmuir 1993, 9, 1051-1057. (3) Ackerman, W. C.; Smith, D. M.; Kim, Y.-W.; Earl, W. C. Characterization of Porous Solids III; Rouquerol, J., Rodriguez-Reinoso, F., Sing, K. S. W., Unger, K. K., Eds.; 1994, p 735. (4) Sehgal, R.; Huling, J. C.; Brinker, C. J. Proceedings of the Third International Conference on Inorganic Membranes, Worcester, MA; Ma, Y., Ed.; 1995; p 85.
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pore size and volume and the micropore surface area using various imogolite molecular models and to present a finite element program for predicting these properties. We intend to use this methodology in comparing experimental data with future computer models. Imogolite was originally described in 1962.6 The composition, (OH)2Al2O3SiOH, and atomic coordinates provided by X-ray diffraction analysis of natural imogolite were reported in 1972,7 and the material was synthesized in 1977 from dilute solutions of Al(ClO4)3 and Si(OH)4.8 In 1983, the tube diameters were enlarged by synthesis using Ge in place of Si.9 Huling et al. developed a procedure to align the tubes into a “fabric” of hydrated bundles.10 The material thus synthesized contains little, if any, mesoporosity associated with the random twisting of tube bundles found in all previous samples.1,2 On the basis of electron diffraction measurements of the tube to tube distance, Cradwick et al. suggested that a model with 10 gibbsite units around the circumference was the most likely structure of natural imogolite.7 A gibbsite unit is an octahedral Al(OH)3 sheet with nominal unit cell dimensions of 8.6 Å × 5.1 Å and used in describing imogolite since it may make up the Al layer of the material. Farmer and Fraser, on the other hand, concluded that the natural material was composed of the 12 unit structure and synthetic imogolite of the 14 unit structure.8 Wada and Wada concluded that for 100% Ge replacement, the tube contained up to 18 units based on an interaxial separation of ∼30 Å.9 Hence, the analysis that follows considers models with 10, 12, 14, and 16 gibbsite units. Molecular models of the 10 and 14 unit imogolite structures are given in Figure 1. Using imogolite (a hydrated paracrystalline material) rather than a zeolite gives some flexibility in the modeled (5) Imamura, S.; Hayashi, Y.; Kajiwara, K.; Hoshino, H.; Kaito, C. Ind. Eng. Chem. Res., 1993, 32, 600. (6) Yoshinaga, N.; Aomine, S. Soil Sci. Plant Nutr. 1962, 8, 6 and 14. Abstr. Am. Mineral. 1963, 48, 434. (7) Cradwick, P. D. G.; Farmer, V. C.; Russell, J. D.; Masson, C. R.; Wada, K.; Yoshinaga, N. Nature, Phys. Sci. 1972, 240, 187. (8) Farmer, V. C.; Fraser, A. R. In International Clay Conference 1978; Mortland, M. M., Farmer, V. C., Eds.; Elsevier Science Publishers: Amsterdam, 1979; pp 547-553. (9) Wada, S.; Wada, K. Clays Clay Miner. 1982, 30, 123. (10) Huling, J. C.; Bailey, J. K; Smith, D. M.; Brinker, C. J. Better Ceramics through Chemistry V; Hampden-Smith, M. J., Klemperer, W. G., Brinker, C. J., Eds.; Materials Research Society: Pittsburgh, PA, 1992; no. 271, p 511.
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Figure 1. Molecular model of imogolite structures with 10 (top) and 14 (bottom) gibbsite units, composition from outside to inside (OH)2Al2O3SiOH.
Pore Structure of Imogolite Computer Models
structure and therefore provides a challenging task for the computational methodology. For instance, although the atomic positions around the circumference of the tube are known from X-ray diffraction, the center-to-center distance is known less accurately from electron diffraction or microscopy. The size of the tube also varies as per the synthesis scheme. In addition, depending upon the outgassing temperature, which drives off bound water, pores can take still different shapes (inter- and intratubular pores) and sizes. These variables enable one to make numerous, differing structures yet of the same general cylindrical material. Determining pore volume and surface area of porous materials has a long history described well by Gregg and Sing.11 For pore volume calculations from adsorption isotherms, the Gurvitsch rule is used. Gurvitsch states that the amount adsorbed along the isotherm plateau, when expressed as a volume of liquid (by use of the normal liquid density), is the pore volume. The surface area of materials is often given by the monolayer number nm, the average cross-sectional area of the adsorbate, am, and Avogadro’s number, L
A ) nmamL The cross-sectional area of many adsorbates has been studied extensively, yet has not been exactly determined.12 Furthermore, the monolayer number for microporous solids is not equivalent to the surface area requiring approximations to be made. In these cases, comparison with a statistical monolayer curve provides an empirical means of obtaining the surface area. In the experimental results of Ackerman et al.,2 the BET surface area, micropore surface area, and pore volume were calculated along with approximations of the pore size distribution. From Cradwick et al.,7 we can generate computer models of the most probable structures of the imogolite material and use a geometric finite element method to measure the pore size distribution, the pore surface area, and the pore volume. The aim of this work is to provide confidence in using this protocol for evaluating the pore structure of computer models for less defined materials such as ultramicroporous silica membranes described by Brinker et al.13 or aerogels, which have considerable porosity over large length scales.14 In addition, this methodology should complement the more rigorous computational evaluations of porous materials including grand canonical ensemble Monte Carlo and density functional theory for adsorption isotherm prediction.15,16 Methodology The method for pore analysis of computer models was developed for comparing various models of the structure of coal.17 It begins by forming a 3-D grid that encompasses all of the atomic coordinates of the model of interest. Following, the nature of each grid cell is determined, i.e., it is defined as an atomic cell, an internal cell, or a closed cell. An atomic cell is a cell included in the van der Waals sphere of any atom. The sum of the volume of all atomic cells defines the atomic volume. Internal cells are cells (11) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: London, 1982. (12) McClellen, A. L.; Harnsberger, H. F. J. Colloid Interface. Sci., 1967, 23, 577-599. (13) Brinker, C. J.; Ward, T. L.; Seghal, R.; Raman, N. K.; Hietala, S. L.; Smith, D. M.; Hua, D.-W.; Headley, T. L. J. Membr. Sci. 1993, 77, 165-179. (14) Schaefer, D. W. MRS Bull. 1994, xix(4), 49. (15) Cracknell, R. F.; Gubbins, K. E. Langmuir 1993, 9, 824. (16) Lastoskie, C.; Gubbins, K. E.; Quirke, N. Langmuir 1993, 9, 2693. (17) Faulon, J.; Mathews, J. P.; Carlson, G. A.; Hatcher, P. Energy Fuels 1994, 8, 408-414.
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Figure 2. Grid method used in computing the pore volume and surface area of molecular models.
not accessible to nitrogen because they are located between two or more atoms having an interatomic distance less than a critical value corresponding to N2. The sum of all internal cells defines the internal volume. Closed cells are identified after determining atomic and internal cells and represent closed volumes (i.e., cells surrounded by atomic and internal cells). The sum of all closed cells defines the closed porosity volume. Next, the number of pore surface elements is determined and counted. Since atomic and internal cells are inaccessible to adsorbate molecules, the total surface area is computed by summing all the areas of cell faces between an atomic or internal cell and a nonatomic or noninternal cell (not including closed cells). The pore surfaces area is the surface of the micropore volume. A schematic of this procedure is shown in Figure 2. Each computation is carried out using periodic boundary conditions, which eliminates edge effects allowing better comparison with real materials. Another variable in this methodology is the size of the atoms used in describing the models and deciding which van der Waal’s radii is adequate for predicting the surface of aluminosilicate materials. If the material is ionic, then the values of the atomic radii for Si and Al are 0.41 and 0.39 Å respectively, having little effect on the overall pore structure if surrounded by O atoms. The O atoms and OH groups, on the other hand, as well as the bound water molecules will dictate the pore structure of the imogolite models. Israelachvili gives several values of the size for O (1.5 Å), H (1.1 Å), and OH (1.45 Å).18 The value for OH was used in the calculations since the hydroxylated surface is the most likely condition of the imogolite surface as shown by both Fourier transform IR and 29Si magic angle spinning NMR.2 In addition to pore structure, the adsorption isotherms were simulated by using grand canonical Monte Carlo (GCMC) simulations for CH4 adsorption at 273 K and up to 1.2 atm.19 CH4 was structureless and its interactions with an individual oxygen atom within the imogolite framework was modeled with the Lennard-Jones (12-6) potential. The Si and Al were not included in the simulations as they are effectively screened by the oxygens. The interaction parameters for the bridging oxygens (/k ) 184K, σ ) 2.7 Å) were only slightly different from the surface hydroxyls (/k ) 184K, σ ) 3.0 Å).20 The chemical potential related to each pressure (and corresponding number of adsorbed methanes) was calculated over 1 × 105 Monte Carlo steps. This method sampled only the (18) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1992. (19) Catalysis & Sorption User Guide, version 5; Biosym Technologies: San Diego, CA, 1994. (20) MacElroy, J. M. D.; Raghavan, K. J. Chem. Phys. 1991, 93 (3), 2068.
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inner tubular space, giving less pore volume but corresponding only to the cylindrical microporosity. Finally, we computed the diffusivities of gases in the pore spaces using canonical molecular dynamics. Recently, Seghal et al. reported the permeation of He and SF6 using composite silica-imogolite membranes made with the 100% Si imogolite.4 The ideal separation (ratio of individual gas permeabilities) of these two gases ranged from 15 at 298 K and with a transmembrane pressure drop of 20 psi to 33 at 298 K and 80 psi differential pressure. To simulate this experiment, Lennard-Jones atoms were placed in the tubular region of each model using a cell 33 Å long with periodic boundary conditions and encompasing the cylindrical imogolite walls. The Lennard-Jones interaction parameters were the same as above for GCMC and those for He and SF6 were /k ) 10K, σ ) 2.6 Å and /k ) 200K, σ ) 5.51 Å, respectively.21 For the simulations, only the oxygens in the imogolite structure were used to model the framework, and they were fixed. Ten atoms each of He and SF6 were then allowed to diffuse for ∼50 ps using time steps of 1 fs. The trajectories were recorded every 10 steps and later used to predict the self-diffusivity based on the Einstein equation, that is, the slope of the mean square displacement vs time plots. These diffusivities were meant to be a first approximation to the membrane permeatility. We currently use a grand canonical molecular dynamics technique to simulate the gas permeation across model membranes.22 The ratio of these self-diffusivity values is reported below and should be comparable with the ideal separation of Seghal et al.
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Figure 3. Pore size profile. Sharp canyon gives rise to higher than expected surface areas.
Results The simplest task carried out was measuring the pore size. Figure 3 shows the pore profile experienced as one travels down the cylindrical pores. The pore is less cylindrical than one might first imagine. This heterogeneity gives rise to large pore volume and even larger surface areas for the models as described below. The experimentally determined pore diameters for synthetic imogolite were ∼7 and ∼10 Å for the 100% Si and 50% Si/50% Ge materials.2 On the basis of this information and Figure 3, one might conclude that these two materials have structures consisting of 10 and 12 gibbsite units, respectively. The experimental values, however, are based on theory that has not been completely validated, so comparison must be done with caution. As a standard for comparison of the pore volume calculation, VPI-5, a crystalline aluminophosphate with pore diameter ∼1 nm was first analyzed. Its pore volume was calculated using the scheme above and a unit cell of 37 Å × 64 Å × 16 Å and micropore entrance critical diameter for H2O (2.65 Å). The value found (0.37 cm3/g) matched within 1% of the equivalent liquid volume at P/P0 ) 0.4 for H2O adsorption.23 This exemplifies the accuracy of the finite element method for pore volume calculations in relation to gas adsorption. For the imogolite models, atomic positions were constructed using the crystallographic data given in ref 7. These models assumed hexagonal close packing with center-to-center distances of 20-30 Å, depending on the model size, the optimum separation based on a minima in the intertubular potential energy, and the use of intertubular water or not. This value is often obtained experimentally by electron diffraction. (The resultant (21) Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; John Wiley & Sons: New York, 1954. (22) Pohl, P. I.; Heffelfinger, G. S.; Smith, D. M. Molecular Dynamics Computer Simulation of Gas Permeation in Thin Silicalite Membranes. Mol. Phys., in press. (23) Davis, M. E.; Saldarriage, C.; Montes, C.; Garces, J.; Crowder, C. Zeolites 1988, 8, 362.
Figure 4. Cross sectional view of imogolite tubes packed in hexagonal close packing arrangement. The center to center distance or cell size is marked with an arrow.
model from this procedure is shown in the cross-sectional view in Figure 4.) The depth of the box was 33.6 Å, to ensure adequate sampling of the periodic structure by the cubic finite element method. In calculating the parameters to remove both statistical and fractal variations, over 20 different cell sizes (from 1 to 4 Å) were used to calculate the surface area and pore volumes. The pore volumes were averaged over all the cell sizes. For surface areas, a least-squares fit of area vs cell size was found and, from this, the surface area corresponding to the N2 size (am ) 16.2 Å2) reported. An example of this latter procedure is shown in Figure 5 for a 12 unit model. The peaks and valleys are likely a function of the axial repeat distance of 4.2 Å. The difficulty with reporting surface areas may be seen in Figure 6, where the N2 adsorption in the 10 unit imogolite pore is shown. As can be seen, the curvature of the surface and the finite size of N2 cause the surface area to be quite different from that of a flat surface. Next,
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Langmuir, Vol. 12, No. 18, 1996 4467 Table 1. Micropore Surface Area (m2/g) and Pore Volumes (cm3/g) from Ackerman et al.2 275 °Ca 250 °Ca 225 °Ca synthetic (100% Si), BET area micropore surface area pore volume micropore volume (
