Evolution of Mechanical Response of Sodium Montmorillonite

Jul 20, 2005 - The mechanical response of the interlayer of hydrated montmorillonite was evaluated using steered molecular dynamics. An atomic model o...
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Langmuir 2005, 21, 8069-8076

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Evolution of Mechanical Response of Sodium Montmorillonite Interlayer with Increasing Hydration by Molecular Dynamics Steven R. Schmidt, Dinesh R. Katti,* Pijush Ghosh, and Kalpana S. Katti Department of Civil Engineering and Construction, North Dakota State University, Fargo, North Dakota 58105 Received March 7, 2005. In Final Form: June 6, 2005 The mechanical response of the interlayer of hydrated montmorillonite was evaluated using steered molecular dynamics. An atomic model of the sodium montmorillonite was previously constructed. In the current study, the interlayer of the model was hydrated with multiple layers of water. Using steered molecular dynamics, external forces were applied to individual atoms of the clay surface, and the response of the model was studied. The displacement versus applied stress and stress versus strain relationships of various parts of the interlayer were studied. The paper describes the construction of the model, the simulation procedure, and results of the simulations. Some results of the previous work are further interpreted in the light of the current research. The simulations provide quantitative stress deformation relationships as well as an insight into the molecular interactions taking place between the clay surface and interlayer water and cations.

Introduction Clay minerals are commonly found in soils. They consist of alumina silicate crystals of colloidal dimensions stacked one upon another. A single particle has lateral dimensions of approximately 103-106 Å and a thickness of about 10 Å. The colloidal character and large surface area-tomass ratio give clay minerals highly reactive surfaces, high cation exchange capacities, and the ability to swell when exposed to water.1 These minerals are important in the petroleum and pharmaceutical industries, cosmetics, toxic and radioactive waste disposal, as additives for polymeric materials, and in geotechnical and geoenvironmental engineering. For the appropriate use of these materials in engineering applications, an understanding of the interaction between clay and water or other fluids is very important. Clay minerals belong to a group of minerals called phyllosilicates or “layer silicates”. The “layers” of these minerals are two-dimensional sheets of silica tetrahedra and aluminum or magnesium octahedra. These sheets can be stacked in various combinations. Clay minerals formed from one tetrahedral sheet and one octahedral sheet are called 1:1 clay minerals. The combination of two tetrahedral sheets and one octahedral sheet forms 2:1 clay minerals. The 2:1 clay minerals are called trioctahedral if the three octahedral positions are filled by three Mg atoms and dioctahedral if two of the octahedral positions are filled by Al atoms leaving the third unoccupied. Pyrophyllite and talc are the prototypical 2:1 dioctahedral and trioctahedral clay minerals. These prototypes are electroneutral. The structure of the minerals of the smectites group, including montmorillonite, is derived from pyrophyllite and talc by replacing Si atoms by Al atoms in the tetrahedral sheet and replacing Al atoms by Mg atoms in the octahedral sheet. These substitutions give an excess negative charge to the clay layer, which is compensated by the adsorption of cations such as sodium onto the surface of the clay.2 Ideal * Corresponding author. Telephone: (701) 231-7245. Fax: (701) 231-6185. E-mail: [email protected]. (1) van Olphen, H. An Introduction to Clay Colloid Chemistry; John Wiley & Sons: New York, 1977.

montmorillonite is formed by the substitution of one out of every six Al atoms by Mg.3 In the presence of water, the compensating cations between the layers are hydrated, causing montmorillonite to swell in a series of discrete steps. At increasing relative humidity, smectites adsorb water vapor to form one-, two-, and three-layer hydrates.4 This behavior is not seen in pyrophyllite or talc, which do not swell in the presence of water. This swelling phenomenon generates stresses that force the clay layers apart and increase the overall volume of the mineral. Swelling occurs in two stages, intracrystalline swelling, involving the adsorption of limited amounts of water in the interlayer space, and osmotic swelling, related to unlimited adsorption of water due to the difference between ion concentrations close to the clay surface and in the pore water. Intracrystalline swelling increases the volume of the mineral. Osmotic swelling causes macroscopic expansion of the clay.5 The experimental work of Katti and Shanmugasundaram6 showed that clay swelling is accompanied by the break down of the clay particles. This behavior cannot be modeled by current theories. The Stern-Guoy double layer theory has been used to model the interaction of clay particles and water.7 The DLVO theory (Derjaguin, Landau, Verwey, and Overbeek) can describe the stability of clay colloidal suspensions at spacings over 20 Å.8 However, these theories fail at smaller layer spacings and cannot accurately predict interlayer swelling. At this small scale the structure of the solvent must be explicitly modeled at the molecular level. (2) Grim, R. E. Clay Mineralogy; McGraw-Hill, New York, 1968. (3) Mitchell, J. K. Fundamentals of Soil Behavior; John Wiley & Sons: New York, 1993. (4) Brindley, G. W.; Brown, G. Crystal structures of clay minerals and their X-ray identification; Mineralogical Society: London, 1980. (5) McBride, M. B. Environmental Chemistry of Soils; Oxford University Press: New York, 1994. (6) Katti, D.; Shanmugasundaram, V. Influence of swelling on the microstructure of expansive clays. Can. Geotech. J. 2001, 38, 175-182. (7) Jo, H. Y.; Katsumi, T.; Benson, C.; Edil, T. B. Hydraulic Conductivity and Swelling of Nonprehydrated GCLs permeated with single species salt solutions. J. Geotech. Geoenviron. Eng. 2001, 127 (7), 557-560. (8) Verwey, E. J. K.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: New York, 1948.

10.1021/la050615f CCC: $30.25 © 2005 American Chemical Society Published on Web 07/20/2005

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To quantitatively describe the evolution of microstructure in swelling clays, it is necessary to study the claywater interactions in the interlayer. Steered molecular dynamics is a useful technique for this purpose. Many molecular dynamics studies of clay have recently appeared.9-13 With steered molecular dynamics, forces are directly applied to individual atoms in a molecular structure. The swelling pressure exerted by the hydrated interlayer can then be directly measured by applying an opposing pressure to the surface of the clay layers. The force deformation response of the montmorillonite and pyrophyllite interlayer has recently been studied by the authors in the dry condition and while hydrated by a single water layer.14,15 In the previous work,14 a molecular dynamics model of the Na-montmorillonite interlayer was developed. The stress deformation response of the interlayer was evaluated for clay in the dry state and when hydrated with one monolayer of water. A brief summary of the results is given here. First, under 0-3.11 GPa applied compressive stress, the stress deformation response of the interlayer is nearly linear. With the application of external stress the interlayer is compressed, while the clay layers remain almost rigid. Second, in dry Na-Mt, the Na cations are drawn to sites of isomorphous substitution by Mg in the clay crystal lattice. The cations remain in this position throughout the entire range of applied stress. In Na-montmorillonite hydrated with one water layer, Na-Mt[1], the Na cations reside midway between the clay layers surrounded by water molecules. The water oxygens point toward the Na and the water hydrogens generally point toward the clay surface, indicating hydrogen bonding, typical for the entire range of applied stress. Third, with increasing applied stress the thickness of the water layer remains constant. Compression of the interlayer is a result of compression of the space between the water and clay surface, defined as the silica-water interaction zone. The moduli of the interlayer and silica-water interaction zones, in the dry and hydrated conditions, are included here. The stressdeformation response, with increasing water content, is established. The nanoscale results of this work can be used to predict microscale swelling and particle size evolution. The previous experimental work6 used Na-montmorillonite from the clay repository, SWy-1, with the chemical formula (Ca0.12Na0.32K0.05)[Al3.01Fe(III)0.41Mn0.01Mg0.54Ti0.02][Si7.98Al0.02]O20(OH)4.16 This montmorillonite has both octahedral and tetrahedral substitutions. Due to the limited size of the montmorillonite model constructed in (9) Chang, F.-R.; Skipper, N. T.; Sposito, G. Computer simulation of interlayer molecular structure in sodium montmorillonite hydrates. Langmuir 1995, 11 (7), 2734-2741. (10) Shroll, R. M.; Smith, D. E. Molecular dynamics simulations in the grand canonical ensemble: Application to clay mineral swelling. J. Chem. Phys. 1999, 111 (19), 9025-9033. (11) Hwang, S.; Blanco, M.; Demiralp, E.; Cagin, T.; Goddard, W. A. MS-Q Force Field for Clay Minerals: Application to Oil Production. J. Phys. Chem. B 2001, 105 (19), 4122-4127. (12) Karaborni, S.; Smit, B.; Heidug, W.; Urai, J.; van Oort, E. The Swelling of Clay: Molecular Simulations of Hydration of Montmorillonite. Science 1996, 271 (5252), 1102-1104. (13) Teppen, B. J.; Rasmussen, K.; Bertsch, P. M.; Miller, D. M.; Schafer, L. Molecular Dynamics Modeling of Clay Minerals. 1. Gibbsite, Kaolinite, Pyrophyllite, and Beidellite. J. Phys. Chem. B 1997, 101 (9), 1579-1587. (14) Katti, D.; Schmidt, S.; Ghosh, P.; Katti, K. Steered molecular dynamics simulations of dry and hydrated sodium montmorillonite interlayer. J. Eng. Mechan. Submitted. (15) Katti, D. R.; Schmidt, S. R.; Ghosh, P.; Katti, K. S. Modeling response of pyrophyllite clay interlayer to applied stress using steered molecular dynamics. Clays Clay Miner. 2005, 53 (2), 171-178. (16) van Olphen, H., Fritpiat, J. J., Eds. Data Handbook for Clay Materials and other Nonmetallic Minerals; Pergamon Press: New York, 1979.

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Figure 1. Starting structure of Na-montmorillonite with two water layers.

Figure 2. Starting structure of Na-montmorillonite with three water layers.

the current study, as well as the previous study,14 the chemical formula was simplified to NaSi16(Al6FeMg)O40(OH)8. Only the octahedral substitutions were made. The response of sodium montmorillonite hydrated with two water layers (Na-Mt[2]) and three water layers (NaMt[3]) under externally applied loads are described in this work. For continuity and clarity, some results from the previous work are also incorporated into this paper. Modeling Approach The models of sodium montmorillonite with two (NaMt[2]) and three (Na-Mt[3]) water layers are shown in Figures 1 and 2, respectively. The deformations of the interlayer, clay layers, and interlayer water are studied under externally applied loads. To perform this study molecular dynamics (MD) in the isobaric-isothermal ensemble, constant number, pressure, and temperature (NPT), were applied. Forces of gradually increasing magnitude were applied in each simulation, and the resulting deformation of the interlayer and clay layers was measured. This work quantitatively evaluates the interactive forces existing in the interlayer between two clay layers, interlayer water, and cations. This was accomplished by applying opposing forces to the surface of Na-montmorillonite as shown in Figure 3. After the force had been applied and the simulation had come to equilibrium, the interlayer spacing, Li, was measured. This was done by

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were completed using the software NAMD2.5. The software NAMD was developed by the Theoretical and Computational Biophysics Group in the Beckman Institute for Advanced Science and Technology at the University of Illinois at UrbanasChampaign.18 Atom types and parameters used with the current model are given in the previous work.14,15 The TIP3P parameters were used for water.19 Simulation Details NAMD2.518

Figure 3. Forces applied normal to the clay layers.

tracking the coordinates of the oxygen atoms on the top and bottom surfaces of each clay layer. Stress-interlayer spacing and stress-interlayer strain relationships were developed. “Interlayer strain” is the strain in the void space between clay layers and is analogous to the strain in solids. The “silica-water interaction zone”, Lsw, is defined here as the space between the surface of the silica tetrahedrons and the surface of the interlayer water also seen in Figure 3. “Interlayer water strain” is the strain measured by the change of thickness of the interlayer water. Model Construction The previous MD study14 simulated clay with the composition NaSi16(Al6FeMg)O40(OH)8 in the dry state and hydrated with one monolayer of water. The layer charge of this clay is 0.5|e| due to isomorphous substitution in the octahedral sheet. To balance this charge, 0.5 Na cations per unit cell are required. The montmorillonite model constructed here has the same chemical formula. The initial dimensions of the simulated unit cell are 5.28 Å × 9.14 Å. The initial thickness of one clay layer is 6.56 Å. The model simulated consists of two clay layers, each containing four unit cells in the X direction and two unit cells in the Y direction. The resulting overall dimensions of each clay layer are 21.12 Å × 18.28 Å × 6.56 Å. In this work, the initial interlayer spacing of 9.44 Å was used for Na-Mt[2] and 12.44 Å for Na-Mt[3] as compared to 3.44 and 6.44 Å for dry Na-Mt and Na-Mt[1], respectively. The coordinates for the first unit cell are the same that were used in the previous study.14,15 The coordinates are based on those given by Skipper et al.17 The charge of each atom is given by Teppen et al.13 The model of hydrated Na-Mt[2] and Na-Mt[3] included two and three monolayers of interlayer water, respectively. Two monolayers are equivalent to a water content of 0.2 g of water/g of clay or a moisture content of 20%. In the case of the model constructed, that is equal to 64 water molecules. Three monolayers are equivalent to a water content of 0.3 g of water/g of clay or a moisture content of 30%. In the case of the model constructed, that is equal to 96 water molecules. Minimization and MD simulations (17) Skipper, N. T.; Sposito, G.; Chang, F.-R. Monte Carlo Simulations of interlayer molecular structure in swelling clay minerals. 1. Methodology. Clays Clay Miner. 1995, 43 (3), 285-293.

and VMD,20 for interactive studies, were used for the simulations described here. Simulations were run on 128 3-GHz Xeon processor parallel computer system at North Dakota State University. Simulations took three to 4 h on the 128processor system. In the model studied, since there are two separate clay layers not connected, a stepwise minimization procedure was followed. Each layer was minimized individually, keeping the other fixed, followed by minimization of the model as a whole. This method helps to avoid attaining a metastable state and thus reaches the lowest energy state possible. Individual layers were minimized for 7000 iterations, whereas for the whole model 16 000 iterations were used. Minimization was completed several times using varying numbers of iterations. The potential energy was plotted and the number of iterations where no further decrease in potential energy occurred was selected. No constraints were used during minimization. The conjugate gradient algorithm was applied for minimization. The temperature was raised to 300 K followed by increasing the pressure to 1 atm. The temperature was raised gradually. To control the temperature, Langevin dynamics was used. The Nose´-Hoover Langevin piston method21,22 was used to raise the pressure to 1 atm. NAMD uses the Verlet algorithm for the integration of the MD equations. All simulations done as part of this work used a step size of 0.5 fs (10-15 s) to accommodate all possible internal interactions. All simulations were run for a total time of 200 ps (10-12 s) or 400 000 steps. Convergence of the total potential energy was reached after 200 000-250 000 steps. Data collected over the last 20 ps (40 000 steps) of the simulation were averaged to determine the position of the atoms. Periodic boundary conditions are applied with a simulation cell of dimensions 27 Å × 27 Å × 32 Å for Na-Mt[2] and 27 Å × 27 Å × 38 Å for Na-Mt[3], the larger cell being necessary for the increased interlayer spacing. The cutoff distance for van der Waals interactions was 9.5 Å. Particle mesh Ewald was used in the computation of electrostatic interaction between atom pairs. The clay segments were free to move in the z-direction only.

Results and Discussion For Na-Mt[2], forces were applied to the surface oxygen atoms as illustrated in Figure 3 including 0, 10, 25, 50, 75, 100, 150, 200, and 250 pN (10-12 N). Given the surface area of the clay layers and the number of oxygen atoms to which force has been applied, the equivalent stress on the surface of each clay layer was 0, 0.10, 0.26, 0.52, 0.78, 1.04, 1.55, 2.07, and 2.59 GPa. For Na-Mt[3], two additional values of force were used, 110 and 125 pN. (18) Kale´, L.; Skeel, R.; Bhandarkar, M.; Brunner, R.; Gursoy, A.; Krawetz, N.; Phillips, J.; Shinozaki, A.; Varadarajan, K.; Schulten, K. NAMD2: Greater scalability for parallel molecular dynamics. J. Comput. Phys. 1999, 151, 283-312. http://www.ks.uiuc.edu/Research/namd/. (19) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926-935. (20) Humphrey, W.; Dalke, A.; Schulten, K. VMDsVisual Molecular Dynamics. J. Mol. Graph. 1996, 14 (1), 33-38. http://www.ks.uiuc.edu/ Research/vmd/ (21) Feller, S. E.; Zhang, Y.; Pastor, R. W.; Brooks, B. R. Constant pressure molecular dynamics simulation: The Langevin piston method. J. Chem. Phys. 1995, 103 (11), 4613-4621. (22) Martyna, G. J.; Tobias, D. J.; Klein, M. L. Constant pressure molecular dynamics algorithms. J. Chem. Phys. 1994, 101 (5), 41774187.

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Figure 4. Comparison of stress-interlayer spacing plots for four water contents.

Figure 5. Relative deformation of the interlayer and clay layers for Na-Mt[2].

From the previous study,14 as stress applied to the clay surfaces was increased, the interlayer distance decreased almost linearly. As increasing stress is applied, the layer thickness is relatively unchanged. In the hydrated case the water layer remained nearly rigid while most of the deformation comes from the Si-water interaction zone. In Figure 4, the relationship between interlayer spacing and applied stress for the interlayer with zero, one, two, and three monolayers of water obtained from the simulations is presented. Unlike the linear response observed between interlayer spacing and stress for dry and one monolayer of water, with increased hydration, the response is nonlinear. In the following sections, the results from the simulations with two and three water layers are described in detail. Simulations with Two Monolayers of Water (NaMt[2]). The deformation of the interlayer relative to the deformation of the clay layers with increasing stress for hydrated Na-montmorillonite with two monolayers of interlayer water is shown in Figure 5. As seen, the clay layers remain nearly rigid while the largest portion of the deformation occurs in the interlayer. The average interlayer spacing and basal spacing for 0 GPa applied stress for hydrated Na-Mt[2] were found to be 8.81 and 15.55 Å respectively. Basal spacing is the distance from the top of one clay layer to the top of the next clay layer. The compression of the interlayer and interlayer water is shown in Figures 6 and 7 for Na-Mt[2]. As with all stress-displacement and stress-strain figures in this paper, a curve has been added to show the trend of the simulation data. The data shows slight variation from this line. This variability is inherent to NAMD, specifically the Langevin dynamics component, not the actual material response. From 0 to 0.52 GPa the interlayer space decreases from approximately 9 to 7 Å. In this range of applied stress, the thickness of the interlayer water decreases from 4.5 to 3.4 Å and is compressed to a single layer of water. The silica-water interaction zone also

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Figure 6. Stress versus interlayer spacing for Na-Mt[2].

Figure 7. Stress versus interlayer water thickness for NaMt[2].

Figure 8. Stress versus interlayer strain for Na-Mt[2].

undergoes compression from 5 Å to approximately 3.75 Å. In the range of 0.52-2.59 GPa, the interlayer decreases from 7 to 6.25 Å. The water thickness continues to be compressed at the same rate as before from 3.4 to 3 Å under stress of 0.52-1.04 GPa. From 1.04 to 2.59 GPa the thickness of the single water layer remains relatively constant at approximately 3 Å. From 0.52 to 2.59 GPa, the silica-water interaction zone thickness remains relatively constant at 3.5 Å. The thickness of the interlayer water was measured in the central region of the model. The interlayer was compressed to roughly the starting dimensions of the interlayer in the previous work studying Na-Mt[1].15 Figures 8 and 9 show the stress-strain relationship for the Na-Mt[2] interlayer and interlayer water. Interlayer strain of approximately 0.2 is observed for a stress of 0-0.52 GPa. Strain in this region appears linear. In this range, the strain in the interlayer water is approximately 0.22. For the same stress value, the silica-water interaction zone experiences a strain of about 0.17. At 0.52-2.59 GPa applied stress, the interlayer strain increases almost linearly to approximately 0.29. Strain in the single water layer increases to approximately 0.38. An attempt is made to evaluate the modulus of the interlayer, water, and the silica-water interaction zone.

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Figure 9. Stress versus strain in the interlayer water for NaMt[2].

As seen in Figures 8 and 9, the responses are nonlinear. Separate linear fits were made to the data in the ranges of 0-0.52 GPa and 0.52-2.56 GPa. For each range of stress, the stress-strain relationship can be written as

σv ) cv*v*

Figure 10. Snapshot showing two water layers compressed to a single layer taken after application of 2.59 GPa stress.

(1)

where σv, cv*, and v* are the applied stress, modulus, and strain along the swelling axis. For calculation of interlayer modulus, the superscript * in eq 1 is replaced by i. Similarly for calculation of the modulus of interlayer water and silica-water interaction zone, the * is replaced by w and sw respectively. For the region of stress from 0 to 0.52 GPa, the interlayer water has two layers. The interlayer modulus, cvi, in this region is 2.49 GPa. The modulus of the interlayer water, cvw, in this same region is 1.59 GPa. The modulus of the silica-water interaction zone, cvsw, is 1.83 GPa. At a stress of 0.52 GPa, the water has transitioned to a single layer. From 0.52 to 2.59 GPa the interlayer modulus is 19.86 GPa. The modulus of the interlayer water (now a single layer) and the silica-water interaction zone are 14.13 and 57.49 GPa, respectively. The interlayer modulus for dry montmorillonite was found in a previous work14 to be 29.51 GPa. The interlayer modulus under dry conditions is due to the nonbonded forces between the two clay layers. Visual inspection was made of the model after each MD simulation. After running MD without the application of force several times, the sodium ions are observed to be located in different positions within the water layers and between the water layers, suggesting random location. The water is oriented with one O-H bond approximately parallel to the clay surface and the other O-H bond pointed toward the clay surface roughly perpendicularly. After the application of 0.52 GPa, the two water layers have collapsed into a single layer. Most water molecules are seen to have one O-H bond directed toward the clay surface and the other parallel to the surface. A few of the water molecules have both water hydrogens toward the surface. In general, the orientation of the water molecules appears more random than before the application of stress. Increasing the stress further to 2.59 GPa did not appreciably change the randomness of orientation, although the thickness of the interlayer water had decreased noticeably, as seen in Figure 10. In the previous work a single water layer was simulated14 and water molecules had one hydrogen pointing toward each clay surface. Simulations with Three Monolayers of Water (NaMt[3]). The deformation of the interlayer relative to the deformation of the clay layers with increasing stress for hydrated Na-montmorillonite with three monolayers of water is shown in Figure 11. The clay layers remain nearly rigid as the interlayer deforms.

Figure 11. Relative deformation of the interlayer and clay layers for Na-Mt[3].

Figure 12. Stress versus interlayer spacing for Na-Mt[3].

Figure 13. Stress versus interlayer water thickness for NaMt[3].

The average interlayer spacing and basal spacing for 0 GPa applied stress for hydrated Na-Mt[3] were found to be 11.17 and 17.90 Å, respectively. In Figures 12-14 the deformation of the interlayer, interlayer water, and silica-water interaction zone are shown for Na-Mt[3]. In the range of 0-0.78 GPa the interlayer spacing decreases

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Figure 14. Stress versus silica-water interaction zone thickness for Na-Mt[3]. Figure 17. Snapshot taken after application of 1.14 GPa.

Figure 15. Stress versus interlayer strain for Na-Mt[3].

Figure 16. Stress versus interlayer water strain for Na-Mt[3].

from 11.2 to 10.6 Å. In this range of applied stress, the interlayer water remains in three distinct layers of relatively constant thickness of approximately 6.25 Å. The silica-water interaction zone decreases from 4.9 to 4.2 Å. From 0.78 to 1.14 GPa, the interlayer is compressed to 8.7 Å. At 1.04 GPa the water remains in three layers, though noticeably compressed to 5.8 Å. At 1.14 GPa the water is seen in two distinct layers with a thickness of 4.5 Å. Between 1.04 and 1.14 GPa, a sudden decrease in interlayer spacing and water layer thickness is seen. As seen in Figure 14 (points circled), in this range of stress, the silica-water interaction zone remains at a fairly constant thickness of about 4.2 Å. This is the transition from three to two water layers. From 1.14 to 2.56 GPa, the interlayer spacing decreases to 8.1 Å. In this range of stress, the water is found to be in two layers, becoming more compressed with increased stress from 4.5 to 4.1 Å. The silica-water interaction zone thickness decreases from 4.2 to 4.0 Å. The interlayer has been compressed beyond the starting dimensions of Na-Mt[2]. Figures 15 and 16 give the stress-strain relationships for the interlayer and interlayer water for Na-Mt[3]. For a stress of 0-0.78 GPa, the interlayer undergoes a strain of approximately 0.06. Strain in this region is nearly linear. In this range the strain in the interlayer water is

approximately 0.02. The silica-water interaction zone undergoes a strain of about 0.14. From 0.78 to 1.14 GPa applied stress, the interlayer strain increases drastically to approximately 0.21. Strain in the water also drastically increases to about 0.3. This significant increase in strain corresponds to the transition from three water layers to two water layers. Strain in the silica-water interaction zone increases slightly to 0.16. As the stress is increased to 2.59 GPa, the strain in the interlayer increases to about 0.27. In this range of stress, the strain in the water increases to 0.35. In the silica-water interaction zone, the strain increases at the same rate as before to 0.2. In the region of stress from 0 up to 1.04 GPa, the interlayer water is in three layers. From 0 to 0.78 the interlayer modulus, cvi, is 14.73 GPa. The modulus of the interlayer water, cvw, itself in this same region is 32.48 GPa. The modulus of the silica-water interaction zone, cvsw, is 6.05 GPa. From 0.78 to 1.14 GPa stress, the interlayer modulus is 2.84 GPa. The moduli of the water and silica-water interaction zone are 1.26 and 22.94 GPa, respectively. At a stress of 1.14 GPa, the interlayer water has transitioned into two distinct layers. From 1.14 to 2.59 GPa the interlayer modulus is 25.26 GPa. The modulus of the interlayer water (now two layers) is 21.55 GPa. The silica-water interaction zone modulus is 22.94 GPa, the same as for the previous range of stress. As with Na-Mt[2], the Na cations are seen in different positions after running MD several times with zero applied stress. As the applied stress is increased, the Na cations move about the interlayer with one generally found in the top and bottom water layers and the remaining two found somewhere in between. Water molecules in layers one and three are oriented with one or both of the hydrogens pointing toward the clay surface. The waters in the middle layer two are found to be randomly oriented. At the stress of 1.14 GPa (Figure 17), the three water layers have been compressed into two. In general, the Na ions are found near the midplane, somewhere between the two water layers. The water molecules are much more disoriented, with no particular preferred orientation. As the stress is increased, the water layers are compressed and move closer to one another. At the higher stresses, as seen in Figure 18 for 2.59 GPa, the Na cations are generally divided evenly between the two water layers, two in the top layer and two in the bottom layer. Results of increased interlayer spacing for varying levels of hydration are presented in Table 1. The increased spacings are with respect to the dry condition and corresponding stress level. As one water layer is added to the interlayer, under 0 GPa applied stress, the interlayer swells by 47%. Throughout the range of stress applied, the expansion is fairly constant. When two water layers

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Table 1. Increase in Interlayer Spacing with the Addition of Water stress (GPa) force per surface atom (pN)

0 0

0.10 10

0.26 25

0.52 50

0.78 75

1.04 100

1.55 150

2.07 200

2.59 250

increase in spacing (Å) % increase in spacing

1.93 47

Addition of One Water Layer to Dry Na-Mt 1.93 1.91 1.92 1.87 47 47 48 47

1.86 47

1.83 47

1.84 48

1.76 46

increase in spacing (Å) % increase in spacing

4.69 114

Addition of Two Water Layers to Dry Na-Mt 4.64 3.66 3.08 2.82 113 90 76 71

2.72 69

2.62 67

2.54 66

2.46 65

increase in spacing (Å) % increase in spacing

7.05 171

Addition of Three Water Layers to Dry Na-Mt 7.04 6.94 6.78 6.58 6.09 171 170 168 165 154

4.63 119

4.45 116

4.30 113

Table 2. Comparison of Basal Spacing, d (Å), without the Application of External Stress, between Four Monte Carlo Studies, Three Experimental Determinations, and the Current MD Study for Various Numbers of Water Layers, nl, Water Molecules, nm, and Water Content, n (mg/g of clay) d (Å) nl

nm

n

Chang et al.9

0 1 2 3

0 32 64 96

0 100 200 300

12.08 15.28 18.77

Boek et al.23

Chavez et al.24

Skipper et al.25

Fu et al.26

Mooney et al.27

Cases et al.28

current study

10.17 12.32 14.96 17.07

14.86 -

9.90 11.90 14.20 -

9.80 12.60 15.40 -

9.80 12.40 15.20 -

9.55 12.49 15.55 18.10

10.80 12.76 15.55 17.90

are added, the interlayer space increases to 114% under stress of 0 GPa. However, when stress is increased to 2.59 GPa, the interlayer swelling reduces to 65%. With three water layers, the swelling is 171% under zero stress. The interlayer swelling reduces to 113% under 2.59 GPa stress. Data from the previous study14 showing cvi ) 29.51 GPa for dry Na-Mt and cvi ) 30.62 GPa for hydrated Na-Mt[1] are shown in Figure 19. From the previous discussion, both Na-Mt[2] and Na-Mt[3] show a soft response before reaching a region of the stress-strain plot with slope similar to that of dry Na-Mt and hydrated Na-Mt[1]. In this region cvi values for Na-Mt[2] and Na-Mt[3] are 19.86 and 25.26 GPa, respectively. Comparison to Established Results. A comparison is made with experimental results and the results of

previous Monte Carlo studies of the basal spacing of NaMt from the literature9,23-28 in Table 2. Basal spacing is sensitive to the layer charge, location of the charge deficiency, and the number of cations necessary to balance the charge. Chang et al.,9 Boek et al.,23 Chavez et al.,24 and Skipper et al.25 found the basal spacing of Namontmorillonite with 0.72 layer charge using Monte Carlo simulations without application of external stress. In these simulations there were substitutions of Mg for Al in the octahedral sheet and Si for Al in the tetrahedra sheet. The charge deficiency coming from the octahedral sheet was 33.33%. The montmorillonite used for XRD by Fu et al.,26 Mooney et al.,27 and Cases et al.28 had layer charges of 0.75, 0.64, and 0.74, respectively. For the clay used by Cases et al.,28 76% of the charge deficiency is due to substitutions in the octahedral sheet. The clay simulated in the current study had layer charge of 0.5, all of which originates from isomorphous substitution in the octahedral layer. Evaluation of Density of Interlayer Water. The density of interlayer water is evaluated for the three levels of hydration, one, two, and three monolayers with varying external stress. The density of interlayer water can be found from

F)

nmm ∆V

(2)

Figure 18. Snapshot taken after application of 2.59 GPa.

where F is the density of water, nm is the number of interlayer water molecules, m is the mass of one water

Figure 19. Comparison of stress-interlayer strain plots for four water contents.

(23) Boek, E. S.; Coveney, P. V.; Skipper, N. T. Monte Carlo molecular modeling studies of hydrated Li-, Na-, and K-smectites: Understanding the role of potassium as a clay swelling inhibitor. J. Am. Chem. Soc. 1995, 117 (50), 12608-12617. (24) Chavez-Paez, M.; Van Workum, K.; de Pablo, L.; de Pablo, J. J. Monte Carlo simulations of Wyoming sodium montmorillonite hydrates. J. Chem. Phys. 2001, 114 (3), 1405-1413. (25) Skipper, N. T.; Refson, K.; McConnell, J. D. C. Monte Carlo simulations of Mg- and Na-smectites. In Geochemistry of clay-pore fluid interactions; Manning, D. A. C., Hall, P. L., Hughes, C. R., Eds.; Chapman and Hall, London, 1993; pp 40-60. (26) Fu, M. H.; Zhang, Z. Z.; Low, P. F. Changes in the properties of a montmorillonite-water system during the adsorption and desorption of water. Hysteresis. Clays Clay Miner. 1990, 38 (5), 485-492. (27) Mooney, R. W.; Keenan, A. G.; Wood, L. A. Adsorption of water vapor by montmorillonite. II. Effect of exchangeable ions and lattice swelling as measured by X-ray diffraction. J. Am. Chem. Soc. 1952, 74 (6), 1371-1374.

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Schmidt et al. Table 3. Comparison of Water Density from Literature, G (g/cm3), without the Application of External Stress between Two Monte Carlo Studies and the Current MD Study for Various Numbers of Water Layers, nl, Water Molecules, nm, and Water Content, n (mg/g of clay) F (g/cm3) nl

nm

n

Chang et al.9

Skipper et al.25

current study

1 2 3

32 64 96

100 200 300

1.10 0.91 0.83

1.23 1.15 a

1.29 1.06 1.06

a

Figure 20. Comparison of stress-water density plots for various numbers of water layers.

molecule, and ∆V is the change in volume of the interlayer from the dehydrated state to the hydrated state. As seen in Figure 20, the single layer of water of Na-Mt[1] has fairly constant density of about 1.29 g/cm3, up to about 0.52 GPa, followed by a small steady increase to 1.4 g/cm3 at 2.59 GPa. As was shown in a previous study,14 this can be explained by the fact that in Na-Mt[1] the single water layer behaves like a relatively rigid layer of constant thickness; hence, very little volume change is seen throughout the range of applied stress. The interlayer water in Na-Mt[2] increases sharply from 1.06 to about 1.8 g/cm3. As stated earlier, in the region of 0-0.42 GPa, the two water layers collapse to form a single water layer. From 0.52 to 1.04 GPa, the water continues to be compressed at the same rate as before. Beyond 1.04 GPa, the density increases at a much slower rate. For Na-Mt[3], the interlayer water density increases slowly from 1.06 g/cm3 to approximately 1.2 g/cm3. Between 1.04 and 1.56 GPa the density increases steeply from 1.2 to 1.6 g/cm3. As previously stated, this is the range in which the three water layers collapse to form two water layers. Beyond this point, the water density increases much more slowly. The phase diagram of water29 for the temperature of 300 K and pressure of 1 GPa shows water to be at the boundary where ice VI and liquid water coexist. Liquid water in this region has a density of 2.2 g/cm3 while that of ice VI is 1.31 g/cm3. At 1 GPa, water in the clay interlayer is seen to have a density of 1.3, 1.8, and 1.2 g/cm3 for one, two, and three layers of water, respectively. The interlayer water appears to be different from bulk water, as indicated by the higher densities. Table 3 shows a comparison of density values calculated from previous Monte Carlo studies. In these studies density was calculated for Na-Mt without the application of external stress. The values presented in the current study appear reasonable compared to these values. The density observed for one monolayer of water is considerably higher than bulk water at 300 K and 1 atm pressure. The densities observed without the application of force are slightly higher than that of bulk water for the two and three layer cases without application of external stress. Conclusions An atomic model for the interlayer of Na-montmorillonite clay has been developed to simulate multiple levels (28) Cases, J. M.; Berend, I.; Besson, G.; Francois, M.; Uriot, J. P.; Thomas, F.; Poirier, J. E. Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite. 1. The sodium-exchanged form. Langmuir 1992, 8 (11), 2730-2739. (29) Chaplin, M. The phase diagram of water. http://www.lsbu.ac.uk/ water/phase.html, accessed 2004.

Not reported.

of hydration. Steered molecular dynamics simulations of the Na-montmorillonite clay interlayer were conducted to quantitatively evaluate the stress deformation response of the interlayer. Upon the application of external stress, the interlayer is compressed. The deformation of the clay layers is minimal compared to the deformation of the interlayer for a stress range of 0-2.59 GPa. The compression of the interlayer is predominantly the result of the compression of water layers and a decrease in the space between the water and clay surface, defined as the silicawater interaction zone. The response of various components of the interlayer with varying hydration and stress is calculated. The moduli of the interlayer, water, and interaction zone under various levels of hydration and stress are found. The stress-deformation response for the dry and single water layer cases could be considered linear. However, with increasing monolayers of water, the response is nonlinear. The deformation of a single water layer in the interlayer with increasing stress is very small. However, when two and three monolayers of water are introduced in the interlayer, abrupt deformation of the water layers is observed between about 0.5 and 1 GPa of applied stress. This results from compression of two water layers into one layer thickness for the first case and three water layers into two water layer thickness in the second case. The orientation of water molecules appeared more random with increased hydration. It appears from the simulations that nonbonded interactions between clay and water result in the more oriented water molecules. However, with increasing external stress, the oriented structure is disturbed. The density of water in the interlayer was found to be significantly higher than that of bulk water at normal temperature and pressure when a single monolayer of water was introduced, possibly as a result of strong nonbonded interactions between the clay sheets and water. The densities of water at normal temperature and pressure when multiple layers of water were introduced were slightly higher than that of bulk water. The density of water in the interlayer increased with an increase in external stress with only a small increase for the one monolayer case and a large increase for the two and three monolayer water cases. The largest increase in density was observed for the two monolayer case, possibly as a result of the combined influence of nonbonded interactions with the clay sheets and external stress. This study provides a detailed quantitative view of the stress-deformation response of the sodium montmorillonite clay interlayer with hydration. Acknowledgment. The hardware and software support for NAMD at NDSU provided by NDSU Center for High Performance Computing and Dr. Gregory Wettstein is acknowledged. LA050615F