Monte Carlo Molecular Simulation of the Hydration of K

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Monte Carlo Molecular Simulation of the Hydration of K-Montmorillonite at 353 K and 625 bar M. de Lourdes Cha´vez Facultad de Quı´mica, Universidad Nacional Auto´ noma de Me´ xico, 04510 Me´ xico, D. F., Me´ xico

Liberto de Pablo* Instituto de Geologıá, Universidad Nacional Auto´ noma de Me´ xico, 04510 Me´ xico, D. F., Me´ xico

Juan J. de Pablo Department of Chemical Engineering, University of WisconsinsMadison, Madison, Wisconsin 53706 Received March 12, 2004. In Final Form: July 12, 2004 Monte Carlo molecular simulations of the hydration of K-saturated Wyoming-type montmorillonite at constant stress in the NPzzT ensemble and at constant chemical potential in the grand canonical µVT ensemble, under basin-like conditions of 353 K and 625 bar, show a strong tendency of the K+ ions to adhere to the siloxane surface, forming predominant inner-sphere complexes with tetrahedral oxygen atoms and adsorbed water molecules. Simulations in the grand canonical ensemble predict that none of the K-montmorillonite hydrates, the one-, two-, and three-layer hydrates, are stable in this environment of high depth, temperature, and pressure. The most nearly stable configuration corresponds to the one-layer hydrate, characterized by a d001 spacing of 12.75 Å, the adsorbed water being 60 molecules/layer or 180.83 mg of H2O/g of clay, an internal energy of -22.73 kcal/mol, an interlayer density of 0.365 g/mL, and a pressure tensor, Pzz, of 1999.9 bar. The interlayer structure consists of two close layers of water molecules 0.50 Å from the midplane, with broad shoulders on the sides, the protons oriented toward the midplane and the siloxane surfaces, and the K+ ions close to the clay surfaces and on the interlayer midplane.

Introduction The adsorption and release of water and chemical species by expandable clay minerals are important for digenetic, metamorphic, petrologic, and geochemical processes. Such processes are relevant to ecology, soil mechanics, agronomy, petroleum migration, exploration, and recovery. The hydration and dehydration of these expandable minerals result in swelling and instability, adsorption, and the release of fluids and chemical species that affect contamination, rock strength, and pore pressure, contributing to overpressure and subsurface fluid migration. The interactions of clay minerals with pore fluids and brines are of particular interest to the adsorption and release of contaminants and nutrients in soils, and in petroleum-rich basins, to the recovery of oil, bore stability, and the quality of the reservoir. Sodium, calcium, and potassium are among the main constituents of pore fluids and brines. Their interactions with expandable 2:1 clay minerals are important, largely as a result of their ability to swell in humid environments into one-, two-, and three-layer water complexes and to develop macroscopic swollen colloidal suspensions when immersed in water.1-3 This behavior is well-known from experimental1-11 and simulation studies12-30 under the * Corresponding author. Phone: 52 555 6224284, ext. 132. Fax: 52 555 6224317. E-mail: [email protected]. (1) Pezerat, H.; Mering, J. C. R. Acad. Sci. Paris 265 (Serie D) 1967, 265, 529. (2) Suquet, H.; de la Calle, C.; Pezerat, H. Clays Clay Miner. 1975, 23, 1. (3) Brindley, G. W.; Brown, G. Crystal Structures of Clay Minerals and their X-ray Identification; Mineralogical Society: London, 1980. (4) Glaeser, R.; Mering, J. C. R. Acad. Sci., Paris 1968, 46, 436. (5) Posner, A. M.; Quirk, J. P. J. Colloid Sci. 1964, 19, 798.

ambient surface conditions of 300 K and 1 bar but is less known at the higher depths, pressures, and temperatures31-40 encountered in sedimentary basins. In the (6) Keren, R.; Shainberg, I. Clays Clay Miner. 1975, 23, 193; 1979, 27, 145. (7) de la Calle, C.; Suquet, H. Rev. Mineral. 1988, 19, 455. (8) Slade, P. G.; Quirk, J. P.; Norrish, K. Clays Clay Miner. 1991, 39, 234. (9) Cases, J. M.; Berend, L.; Besson, G.; Francois, M.; Uriot, J. P.; Thomas, F.; Poirier, J. E. Langmuir 1992, 8, 2730. (10) Sato, T.; Watanabe, T.; Osuka, R. Clays Clay Miner. 1992, 40, 103. (11) Yamada, H.; Nakazawa, H.; Hashizume, H.; Shimomura, S.; Watanabe, T. Clays Clay Miner. 1994, 42, 77. (12) Delville, A. Langmuir 1991, 7, 547; 1992, 8, 1796. (13) Refson, K.; Skipper, N. T.; McConnell, J. D. C. In Geochemistry of Clay-Pore Interactions; Manning, D. A. C., Hall, P. L., Hughes, C. R., Eds.; Chapman and Hall: London, 1993; p 62. (14) Bleam, W. F. Rev. Geophys. 1993, 31, 51. (15) Chang, F. R. C.; Skipper, N. T.; Sposito, G. Langmuir 1995, 11, 2734. (16) Boek, E. S.; Coveney, P. V.; Skipper, N. T. Langmuir 1995, 11, 4629. (17) Skipper, N. T.; Chang, F. R. C.; Sposito, G. Clays Clay Miner. 1995, 43, 285. (18) Skipper, N. T.; Sposito, G.; Chang, F. R. C. Clays Clay Miner. 1995, 43, 294. (19) Boek, E. S.; Coveney, P. V.; Skipper, N. T. J. Am. Chem. Soc. 1995, 117, 12608. (20) Laird, D. A.; Shang, C.; Thompson, M. L. J. Clay Interface Sci. 1995, 171, 240. (21) Karaborni, S.; Smit, B.; Heidug, W.; Urai, J.; van Oort, E. Science 1996, 271, 1102. (22) Laird, D. A. Clays Clay Miner. 1996, 44, 553. (23) Cases, M.; Berend, I.; Franç ois, M.; Uriot, J. P.; Michot, L. J.; Thomas, F. Clays Clay Miner. 1997, 45, 8. (24) Bray, H. J.; Redfern, S. A. T.; Clark, S. M. Mineral. Mag. 1998, 62, 647. (25) Bray, H. J.; Redfern, S. A. T. Phys. Chem. Miner. 1999, 26, 591. (26) Sposito, G.; Park, S. H.; Sutton, R. Clays Clay Miner. 1999, 47, 192.

10.1021/la049349g CCC: $27.50 © 2004 American Chemical Society Published on Web 10/27/2004

Hydration of K-Montmorillonite at 353 K and 625 bar

present study, the stability and swelling of K-saturated Wyoming-type montmorillonite is investigated by Monte Carlo simulations at constant stress in the NPzzT ensemble and at constant chemical potential in the grand canonical µVT ensemble, under the reservoir conditions of a temperature of 353 K and a pressure of 625 bar which are common to sedimentary basins and specifically to petroleum-rich basins. Experimental Section The hydration of K-saturated montmorillonite is studied by Monte Carlo simulation in the NPzzT and µVT ensembles,41 at a temperature of 353 K and a pressure of 625 bar. These conditions are common to sedimentary basins and petroleum-rich reservoirs, where they are equivalent to depths of 5.84, 4.16, and 2 km in terms, respectively, of the hydrostatic, lithostatic, and thermal gradients. By referring to the geotherms known for the Tertiary sedimentary basin in the U.S. Gulf Coast,42,43 it is evident that a temperature of 353 K corresponds to pressures from 500 to 800 bar or a pressure of 625 bar implies temperatures in the range from 323 to 353 K. The simulations employ the model and approach described by Cha´vez-Paéz et al.29 The clay considered in this work is the K-saturated Wyoming-type montmorillonite of unit cell (Si7.75Al0.25)(Al3.50Mg0.50)O20(OH)4K0.75‚nH2O and a charge of 0.75, 33% of which is in the tetrahedral sheet. Eight unit cells form the simulation cell, measuring 21.12 Å in the x-dimension, 18.28 Å in the y-dimension, and 6.56 Å in the z-dimension. The positions and charges of the atoms are those of pyrophyllite,17 with the substitution of octahedral Al3+ in positions (-3.52, -3.05, 0), (7.04, -3.05, 0), (-3.52, 6.09, 0), and (7.04, 6.09, 0) by Mg2+ and tetrahedral Si4+ in positions (2.64, 1.52, 2.73) and (0.88, 1.52, -2.73) by Al3+, as indicated by Cha´vez-Paéz et al.29 The water-counterion and clay-counterion interactions are simulated using the TIP4P model of waterwater interaction,44 with potential parameters taken from Boek et al.19 and Bounds45 (Table 1).

Results and Discussion NPzzT Simulations. The adsorption of 32 water molecules per layer of K-montmorillonite (96 mg of H20/g of clay) under the basin conditions of 353 K and 625 bar results in the formation of the monolayer hydrate with a d001 spacing of 11.61 Å, as listed in Table 2. The density (27) Young, D. A.; Smith, D. E. J. Phys. Chem. B 2000, 104, 9163. (28) Bray, H. J.; Redfern, S. A. T. Mineral. Mag. 2000, 64, 337. (29) Cha´vez-Paéz, M.; Workum, K.; de Pablo, L.; de Pablo, J. J. J. Chem. Phys. 2001, 114, 1405. (30) Cha´vez-Paéz, M.; de Pablo, L.; de Pablo, J. J. J. Chem. Phys. 2001, 114, 10948. (31) Koster van Groos, A. F.; Guggenheim, S. Am. Mineral. 1984, 69, 872. (32) Colten, V. A. Clays Clay Miner. 1986, 34, 385. (33) Koster von Groos, A. F.; Guggenheim, S. Am. Mineral. 1987, 72, 292. (34) Koster van Groos, A. F.; Guggenheim, S. Am. Mineral. 1987, 72, 1170. (35) Huang, W. L.; Bassett, W. A.; Wu, T. C. Am. Mineral. 1994, 79, 683. (36) Wu, T. C.; Bassett, W. A.; Huang, H. L.; Guggenheim, S.; Koster van Groos, A. F. Am. Mineral. 1997, 82, 69. (37) de Siqueira, A. V. C.; Skipper, N. T.; Coveney, P. V.; Boek, E. S. Mol. Phys. 1997, 92, 1. (38) Siqueira, A. V. C.; Lobban, C.; Skipper, N. T.; Williams, G. D.; Soper, A. K.; Done, R.; Dreyer, J.; Humphreys, R. J.; Bones. J. A. R. J. Phys.: Condens. Matter 1999, 11, 9179. (39) Anderson, M. A.; Trouw, F. R.; Tam, C. N. Clays Clay Miner. 1999, 47, 28. (40) Leote de Carvalho, R. J. F.; Skipper, N. T. J. Chem. Phys. 2001, 114, 3727. (41) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: London, 1986; p 385. (42) Burst, J. F. Am. Assoc. Pet. Geol. Bull. 1969, 53, 73. (43) Hower, J. E.; Hower, M. E.; Perry, E. A. Geol. Soc. Am. Bull. 1976, 87, 725. (44) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (45) Bounds, D. G. Mol. Phys. 1985, 54, 1335.

Langmuir, Vol. 20, No. 24, 2004 10765 Table 1. Interaction Parameters for the K-Montmorillonite-Water System19,45

O-O O-K K-H K-Si K-Al

A (kcal/mol)

B (Å-1)

0 538.84 57.47 0.19 0.19

0 333.9 341.28 74.9 74.9

C D E (kcal Å4/mol) (kcal Å6/mol) (kcal Å12/mol) 0 438.0 0 0 0

610.0 638.0 0 0 0

600 000 0 0 0 0

Table 2. Monte Carlo Simulation of Hydrated K-Montmorillonite, NPzzT Ensemble temperature (K) pressure (bar) clay layers K (atoms/cell) water (molecules/cell) water (mg of H2O/g of clay) spacing (Å) density (g/mL) internal energy (kcal/mol) Lennard-Jones energy (kcal/mol) Coulomb energy (kcal/mol) rKO first coordination shell (Å) gKO(r) coordination probability O2-, distance to midplane (Å)

353 625 2 6 32 96 11.61 0.213 -27.963 -32.272 4.254 2.575 12.239 -0.887 -0.062 0.112 0.812

353 625 2 6 64 192 13.64 0.363 -22.353 -17.097 -5.526 2.665 6.432 -0.837 0.887

353 625 2 6 96 288 15.83 0.469 -19.518 -10.874 -8.741 2.755 5.152 -1.887 -0.112 1.887

O2- outmost layers separation (Å) H+, distance to midplane (Å) -0.712 0.737

1.724 -1.637 -0.287 0.337 1.662

H+ outmost layers separation (Å) K+, distance to midplane (Å)

3.299 -2.712 -2.137 -0.562 -0.062 0.662 1.987 2.812

3.774 -2.737 -1.512 0.412 1.562 2.762 5.499 -3.837 -3.237 -1.637 1.162 1.762 3.012 3.287 3.912

1.449 -1.812 -0.887 0.837

profiles show that the water molecules are largely clustered on the interlayer midplane, with their hydrogen atoms oriented toward the siloxane surfaces on both sides (Figure 1a); some molecules are closer to the clay surface. The K+ ions are quite near the siloxane surface, coordinated with tetrahedral oxygen atoms and water molecules in inner-sphere complexes, but some are further away from the clay surface, forming outer-sphere complexes with the adsorbed water molecules. None of the K+ ions appear to occupy positions in the ditrigonal cavities. The configuration of Figure 2a illustrates the strong tendency of K+ to adhere to the clay surface. A distance of 1.449 Å separates the outmost proton layers. The adsorption of 64 molecules (192 mg/g) increases the d001 spacing to 13.64 Å, placing the water molecules in two well-defined layers, one to each side of the interlayer midplane, 1.724 Å apart (Table 2, Figure 1b), with weak shoulders on the sides due to some molecules closer to the clay surface. The water protons are distributed over four layers, with the two outmost layers being 3.299 Å apart and the two other ones being closer to the central plane. The K+ ions are (1) directly coordinated in inner-sphere complexes to siloxane tetrahedral oxygen atoms and adsorbed water molecules; (2) with this same coordination but further separated from the clay; and (3) dispersed in the water layers, in outer-sphere coordination with water molecules, cross-linking between the two water layers (Figure 2b). At higher water contents, namely, 96 molecules (288 mg/g), the spacing increases to 15.83 Å. The

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de Lourdes Cha´ vez and de Pablo

Figure 2. Snapshots of K-montmorillonite: (a) monolayer hydrate, with 32 adsorbed water molecules; (b) two-layer hydrate, with 64 water molecules; (c) two-layer hydrate changing toward an incipient three-layer hydrate, with 96 water molecules.

Figure 1. Density profiles of hydrated K-montmorillonite, at 353 K and 625 bar, NPzzT ensemble, with (a) 32, (b) 64, and (c) 96 adsorbed water molecules. Water molecules are in the interlayer midplane, in the two outmost layers, and in three layers, with the K+ ions close to the siloxane surface. Atoms are at the indicated distances from the interlayer midplane. Curves represent water oxygen (bold solid), hydrogen (dashed), and potassium (solid) ions.

water molecules maintain the two-layer configuration, 3.774 Å apart, with the excess water molecules accom-

modating between then and closer to the interlayer midplane (Table 2, Figure 1c). The protons form four layers, two on each side of the oxygen layers, with the outmost protons separated by 5.499 Å. In this state of higher hydration, the K+ ions are displaced toward the clay surfaces. About half of them are coordinated with surface oxygen atoms and water molecules, whereas the other half are in the water layers cross-linking between them. None of the K+ ions occupy positions on the interlayer midplane or in the ditrigonal cavities. Our results show that at 353 K and 625 bar the adsorption of 32, 64, and 96 H2O molecules places the molecules, respectively, in one single layer on the interlayer midplane or in two distinct layers closer to the siloxane surfaces, increasingly separated from the midplane as the adsorbed water rises (Table 2, Figure 1). Water in excess to that required to make the two layers remains in the interlayer midplane. The hydration compares to that at 300 K and 1 bar that places up to 24 water molecules in the interlayer midplane of the monolayer hydrate and from 48 to 56 molecules in the twolayer hydrate and that takes beyond 64 and up to 96 water molecules without forming a third central layer.19 The K+ ions, at 353 K and 625 bar, are coordinated with siloxane tetrahedral oxygen atoms and adsorbed water molecules, and are additionally dispersed in the water layers. A different distribution occurs in the surface environment of 300 K and 1 bar,19 where, at hydration states below 48 water molecules, the K+ ions remain in


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Figure 3. Radial distribution function, gKO(r), at 353 K and 625 bar, NPzzT ensemble, with 32 (bold line), 64 (dashed line), and 96 (weak solid line) adsorbed water molecules.

a single layer in the midplane region and, at states from 56 to 96 adsorbed water molecules, they form a cation bilayer close to the siloxane surface without interposed water molecules.19 Previous studies have reported the weak solvation of K+ from Monte Carlo simulations in the NPzzT ensemble,46 from infrared spectrometry studies,47 and from 39K NMR studies.48 Comparison between the interlayer structures of K-, Na-, and Ca-montmorillonite under surface conditions and under reservoir conditions shows that whereas in K-montmorillonite the K+ remains close to the siloxane surface with little disposition to solvate, Na+ and Ca2+ tend to stay away from the surface, in the interlayer midplane, in outer-sphere coordination with water molecules from the two outmost water layers.13,15,19,29,30,49,50 Our simulated d001 spacings of 11.61, 13.64, and 15.83 Å under basin conditions of 353 K and 625 bar compare with those at 300 K and 1 bar of 9.95, 13.30, 15.50, 17.80, and 20.40 Å estimated by the crystalline swelling method,22 with an experimental average of 15.6 Å for the two-layer hydrate,51-53 and with those simulated of 10.12, 11.31, 12.08, and 16.43 Å,54 with an experimental average of 12.46 Å for the monolayer hydrate19 and of 15.526 and 15.89-16.83 Å for the two-layer hydrates.19 The 11.61 Å spacing of the monolayer K-montmorillonite is shorter than the 12.46 Å spacing under surface conditions, and the spacing of the two-layer hydrate extending from 13.64 to 15.83 Å is on the short side of the 15.89-16.83 Å range calculated at the surface environment. The radial distribution function, gKO(r), shows that in the monolayer K-montmorillonite hydrate the coordination probability is 12.24 water molecules per K+, at a K-O separation of 2.57 Å (Table 2, Figure 3). Increasing hydration separates 2.66 Å the K+ from the water molecules and reduces the probability of coordination to (46) Chang, F. R. C.; Skipper, N. T.; Sposito, G. Langmuir 1998, 14, 1201. (47) Russell, J. D.; Farmer, V. C. Clay Miner. Bull. 1964, 5, 443. (48) Lambert, J. F.; Prost, R.; Smith, M. C. Clays Clay Miner. 1992, 40, 253. (49) de Pablo, L.; Cha´vez, M. L.; Sum, A. K.; de Pablo, J. J. J. Chem. Phys. 2004, 120, 939. (50) de Pablo, L.; Cha´vez, M. L.; Sum, A. K.; de Pablo, J. J. Langmuir, submitted for publication, 2004. (51) Posner, A. M.; Quirk, J. P. J. Colloid Sci. 1964, 19, 798. (52) Calvet, R. Bull Soc. Chim. Fr. 1972, 8, 3097. (53) Cebula, D. J.; Thomas, R. K.; White, J. W. J. Chem. Soc., Faraday Trans 1 1980, 76, 314. (54) Berend, I.; Cases, J. M.; Francois, M.; Uriot, J. P.; Michot, L.; Masion, A.; Thomas, F. Clays Clay Miner. 1995, 43, 724.

Figure 4. Hydration of K-montmorillonite, at 353 K and 625 bar, NPzzT ensemble: (a) variation of the basal spacing (O), water H+ outmost layers separation (∆), and water O2- outmost layers separation (0); (b) variation of the internal energy (O), Lennard-Jones contribution (0), and Coulomb contribution (∆).

6.43. In the state of 96 adsorbed water molecules, the coordination decreases to 5.15 and the cation-water separation increases to 2.75 Å. Integration of these functions indicates coordination numbers of 6.0, 5.7, and 5.7, respectively, for the adsortion of 32, 64, and 96 water molecules. They compare with that of 6.3 known from simulations under ambient conditions.26 The K-O distances are on the short side of those of 2.88-3.25 Å when the coordination is 12 and of 2.72-2.91 when it is 6.55 Na-montmorillonite33 and Ca-montmorillonite show a similar reduction in the coordination probability.49,50 The simulated rKO values are larger than the 2.30-2.33 Å separations simulated for Na-montmorillonite49 and shorter than the 2.75 and 2.82 Å separations simulated for Ca-montmorillonite50 under the same reservoir conditions. Ca-montmorillonite is known to have a higher water uptake capacity than Na- and K-montmorillonite.56 The simulated internal energies increase from -27.963 to -22.353 to -19.518 kcal/mol as the adsorbed water changes from 32 to 64 to 96 molecules, respectively (Table 2, Figure 4). The Coulomb contribution to the energy decreases from 4.254 to -5.526 to -8.741 kcal/mol, inverse to the Lennard-Jones contribution that increases from -32.272 to -17.097 to -10.874 kcal/mol. These energies are smaller than those known at 300 K and 1 bar of -14.35 (55) International Tables for X-ray Crystallography; Lonsdale, K., Ed.; Kynoch Press: Birmingham, England, 1962; Vol. III, p 258. (56) Chiou, C. T.; Rutherford, D. W. Clays Clay Miner. 1997, 45, 867.

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Table 3. Monte Carlo Simulation of Hydrated K-Montmorillonite, Grand Canonical µVT Ensemble temperature (K) pressure (bar) clay layers K (atoms/layer) water adsorbed (molecules/layer) water adsorbed (mg/g) spacing (Å) density (g/mL) internal energy (kcal/mol) Lennard-Jones energy (kcal/mol) Coulomb energy (kcal/mol) pressure tensor, Pzz (bar) rKO first coordination shell (Å) gKO(r) coordination probability water O2-, distance to midplane (Å)

353 625 2 6 29.48 88.72 11.0 0.207 -27.085 -31.402 4.352 44869.6

353 625 2 6 51.10 153.78 12.0 0.329 -24.505 -21.524 -3.358 6402.0

353 625 2 6 53.70 161.60 12.1 0.344 -23.907 -19.630 -4.494 4916.9 2.615 7.395

1.087

353 625 2 6 57.71 173.67 12.5 0.357 -23.277 -18.532 -4.786 4902.2

353 625 2 6 60.09 180.83 12.75 0.365 -22.732 -17.045 -5.557 1999.9 2.655 6.473

1.437

353 625 2 6 81.27 244.57 14.0 0.449 -20.301 -12.849 -7.452 5099.7

353 625 2 6 95.39 287.07 15.0 0.492 -19.680 -10.143 -9.635 3909.1 2.705 5.306

353 625 2 6 109.50 329.53 16.0 0.530 -18.666 -7.991 -10.675 4602.3

353 625 2 6 124.49 374.64 17.0 0.569 -17.862 -7.497 -10.353 4283.0

353 625 2 6 135.83 408.77 18.0 0.584 -17.589 -6.874 -10.715 3740.2

2.012

0.062 1.237

0.312 0.387 1.462

O2- outmost layers separation (Å) water H+, distance to midplane (Å)

0 0.837 0.112 0.962

0.699 1.262 0.012 1.312

H+ outmost layers separation (Å) K+, distance to midplane (Å)

1.799 1.987 1.112 0.262 0.912 2.037

2.574 2.337 1.412 0.037 1.437

kcal/mol for the state of 32 water molecules, -12.36 for the state of 64 water molecules, and -11.77 for the state of 96 water molecules.19 They are close to those simulated for Ca-montmorillonite of -24.24, -19.66, and -17.71 kcal/mol for the three states of hydration under the reservoir conditions50 and smaller than those of 24.29, 6.60, and 0.56 kcal/mol simulated for Na-montmorillonite.49 The enthalpy of the first dehydration of Kmontmorillonite measured experimentally is 11.01 kcal/ mol, and that of the second dehydration is 13.10 kcal/ mol.33 The enthalpy of dehydroxylation estimated from high-pressure differential thermal analysis (DTA) studies is 62.10 kcal/mol, with the dehydroxylation occurring at 978 K and 1-2 atm and at 1073 K and 40 bar.34 Grand Canonical (µVT) Simulations. The chemical potentials of the mineral interlayer and of the bulk fluid are equal at equilibrium. The thermodynamic stability of the K-montmorillonite hydrates will be determined by the minima in the swelling free energy as a function of the adsorbed water or the interlayer separation.29 The mechanically stable hydrates will be those that have their pressure tensor, Pzz, equal to the bulk pressure or when the curve depicting the variation of Pzz with the d001 spacing intercepts with negative slope the line representing the pressure on the system.29 To ascertain the thermodynamic stability of the hydrated K-montmorillonite complexes under basin conditions, simulations are conducted in the grand canonical ensemble, allowing the water molecules to fluctuate in and out of the interlayer while maintaining constant the number of K+ ions. The grand canonical simulations are started by calculating the chemical potential of bulk water at 353 K and 625 bar. For 216 water molecules,29,30,49,50 the resulting excess chemical potential is -5.58 kcal/mol. Simulations on the hydration of K-montmorillonite using the TIP4P water interaction model44 show that, for d001 spacings varying from 11 to 18 Å, the adsorbed water increases from 29.48 to 135.83 molecules per layer or from 88.72 to 408.77 mg/g (Table 3, Figure 5a). The total energy changes from -27.085 kcal/mol at 11.00 Å to -17.589 kcal/mol at 18 Å, the Lennard-Jones contribution varies from -31.402

353 625 2 6 62.11 186.91 13.0 0.370 -22.622 -16.846 -6.152 3147.4

1.462 0.012 1.487 2.062 2.949 2.362 1.387 1.412 2.412 4.774 3.462 1.312 1.387 3.462

to -6.874 kcal/mol, and the Coulomb contribution varies from 4.352 to -10.715 kcal/mol (Figure 5b).

Figure 5. Hydration of K-montmorillonite, grand canonical µVT ensemble: (a) variation of the d001 spacing; (b) change of the internal energy (O), Lennard-Jones contribution (0), and Coulomb contribution (∆).


Langmuir, Vol. 20, No. 24, 2004 10769

Figure 8. Snapshot of the two-layer K-montmorillonite hydrate, grand canonical µVT ensemble, unstable at 353 K and 625 bar.

Figure 6. Correlation between the pressure tensor, Pzz, and the d001 spacing of hydrated K-montorillonite. The minimum pressure tensor corresponds to an unstable spacing of 12.50 Å or an adsorption of 60 water molecules.

Figure 7. Density profile of the two-layer K-montmorillonite hydrate, at 353 K and 625 bar, grand canonical µVT ensemble.

The correlation between the pressure tensor, Pzz, and the spacing (Table 3) is shown in Figure 6. The system would be mechanically stable when the interlayer pressure tensor, Pzz, equals the 625 bar bulk pressure. Our data indicate that, under the basin conditions of 353 K and 625 bar, the pressure tensor is not equal to the 625 bar bulk pressure. We conclude that K-montmorillonite hydrates are not stable at this basin depth, high-pressure, hightemperature environment. The most nearly stable hydrate is the 12.75 Å monolayer K-montmorillonite hydrate formed by the adsorption of 60 water molecules (180.83 mg of H2O/g clay), with an internal energy of -22.732 kcal/mol, an interlayer density of 0.365 g/mL, and a pressure tensor, Pzz, of 1999.9 bar. Two- and three-layer hydrates, with pressure tensors bigger than the bulk pressure, do not form. We presume that the one-, two-, and three-layer K-montmorillonite hydrates might form and be stable under less stringent environments of lower temperature and pressure, where the potential would possibly be smaller than the -5.58 kcal/mol prevailing at 353 K and 625 bar. Such behavior deviates from the known stability of the corresponding hydrates at the ambient surface environments of 300 K and 1 bar.29,30 The density profile of the nearly stable monolayer K-montmorillonite hydrate (Figure 7) shows the water molecules distributed in two layers 0.699 Å apart, with some molecules in shoulders 1.437 and 1.462 Å from the

interlayer midplane, closer to the siloxane surfaces. The water protons are on the interlayer midplane and to both sides. The K+ ions take positions (1) close to the clay surface, coordinated in inner-sphere complexes with tetrahedral oxygen atoms and water molecules; (2) farther from the surface, coordinated with water molecules in outer-sphere complexes; and (3) in the interlayer midplane. This interlayer configuration appears intermediate between the monolayer hydrate and an incipient two-layer hydrate. The simulated d001 spacing of 12.75 Å is larger than the 12.46 Å spacing simulated under surface conditions.19 A snapshot of the interlayer configuration is shown in Figure 8. K-montmorillonite shows characteristics at 353 K and 625 bar intermediate between Na-montmorillonite that forms the 12.72 Å 1,2-layer hydrate49 and Ca-montmorillonite that does not develop stable hydrates.50 The behavior of K-montmorillonite at high temperatures and pressures has not been much documented, but some correlations could be expected. It is known from anvil and synchrotron studies that Ca-montmorillonite, at pressures between the liquid-vapor water boundary and ∼10 kbar, transforms from the 19 Å hydrate to the 15 Å hydrate over the temperature range 533-623 K; along the 1.053 g/mL isochore, the transformation occurs at 573-623 K, and along the 0.7 g/mL isochore, it takes place at 533583 K.57 Na-montmorillonite changes from the three- to two-layer hydrate along the 0.8 g/mL isochore at 603658 K and 1468-2309 bar and from the two- to one-layer hydrate at 758-773 K and 4400-4450 bar.58 We would expect somehow parallel transformations in K-montmorillonite. However, when grand canonical simulations were attempted at these high temperatures and pressures, near or above the critical point of water of 647.15 K, 221.3 bar, and a density of 0.323 g/mL,59 unreliable chemical potentials and unsuitable simulations developed41,60 which prevented us from confirming these data. We find our grand canonical simulations more comparable to those of Na-montmorillonite in the NPzzT ensemble using the TIP4P water model, that showed that, at a 3 km depth, equivalent to 450 bar, the adsorption of 32, 64, and 96 H2O molecules develops densities of 1.09-1.0 g/mL and energies of -30.33 to -11.22 kcal/mol, and, at 6 km, equivalent to 900 bar and 457 K, densities of 1.08-0.95 g/mL and energies of -100.07 to -48.48 kcal/mol.37,61 Such behavior sustains observations assessing that, under high (57) Wu, T. C.; Bassett, W. A.; Huang, W. L.; Guggenheim, S.; Koster van Groos, A. F. Am. Mineral. 1997, 82, 69. (58) Huang, W. L.; Bassett, W. A.; Wu, T. C. Am. Mineral. 1994, 79, 683. (59) Perry, R. H. In Perry’s Chemical Engineers Handbook; Perry, R. H., Green, D. W., Maloney, J. O., Eds.; McGraw-Hill: New York, 1973; pp 3-112. (60) Widom, B. J. Phys. Chem. 1982, 86, 869. (61) de Siqueira, A. V. C.; Skipper, N. T. Mol. Phys. 1997, 92, 1.

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pressures, water may be squeezed out from the clay pores, making hydrated smectite enthalpically stable only up to a 1.5 km depth, below which it transforms to other minerals such as illite.37,61 Conclusions Monte Carlo molecular simulations in the NPzzT and µVT ensembles of the hydration of K-montmorillonite under basin-like conditions of 353 K and 625 bar have shown the strong tendency of K+ ions to adhere to the siloxane surface, forming inner-sphere complexes with tetrahedral oxygen atoms and adsorbed water molecules. As the hydration progresses from 32 to 96 water molecules, the K+ ions move from predominant inner- to outer- to inner-sphere complexes which appear to be the most stable interlayer structure. Simulations in the grand canonical ensemble indicate that none of the hydrates, the one-,


two-, and three-layer hydrates, are stable at 353 K and 625 bar. The most nearly stable configuration corresponds to the one-layer hydrate with a d001 spacing of 12.75 Å, the adsorbed water being 60 molecules/layer (180.83 mg of H2O/g clay), an internal energy of -22.73 kcal/mol, an interlayer density of 0.365 g/mL, and a pressure tensor, Pzz, of 1999.9 bar. It is presumed that the K-montmorillonite hydrates would only be stable under less stringent environments of depth, temperature, and pressure. The probability of coordination of water molecules around K+ ions decreases with solvation, freeing water to the bulk. Acknowledgment. This work was supported by DGAPA, Grant No. IN106502, and by the Instituto Mexicano del Petro´leo. LA049349G

Monte Carlo Molecular Simulation of the Hydration of K

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