Hidratación de montmorillonita de calcio en condiciones de cuenca: una simulación molecular Monte Carlo

Raúl Monsalvo¹, Liberto de Pablo^{2 ,}*, and M. Lourdes Chávez¹

¹ Facultad de Química, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Interior, Del. Coyoacán, 04510 México, D. F., México.

² Instituto de Geología, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior, Del. Coyoacán, 04510 México, D. F., México. * liberto@servidor.unam.mx

Manuscript received: May 10, 2005 ]]> Corrected manuscript received: October 4, 2005
Manuscript accepted: November 18, 2005

ABSTRACT

Monte Carlo simulations in NP_zzT and µVT ensembles of the hydration of Wyoming–type Ca–montmorillonite have shown the interlayer configurations. Ca–montmorillonite may hydrate to one–, two– and three–layer hydrates of d₀₀₁ spacing 11.83, 13.73, and 15.60 Å at 353 K and 625 bar. At lower temperatures and pressures the spacing increases. Grand canonical simulations show that the one–layer Ca–montmorillonite hydrate of d₀₀₁ spacing 12.11 Å is stable at 353 K, 300 bar, –7.21 kcal/mo potential, at a 2.0 km depth of normally compacted sediments. Two– and three–layer hydrates do not form. At 353 K, 625 bar, –5.58 kcal/mol potential, the one–layer hydrate is nearly stable. In the clay interlayer, the water molecules are clustered on the midplane, with their protons pointing towards the siloxane surfaces on both sides and on the midplane. The Ca²⁺ cations are solvated in outer–sphere coordination, separated 2.77 Å from the water molecules. In sedimentary basins under normal geotherms, one–layer Ca–montmorillonite is the single hydrate stable at 2 km depth; under over–compacted sediments at 2.7 km depth it becomes unstable.

Key words: montmorillonite, Ca–montmorillonite, hydration, simulation, Monte Carlo, stability.

RESUMEN

Simulaciones Monte Carlo en conjuntos NP_zzT y µVT de la hidratación de Ca–montmorillonita tipo Wyoming muestran la configuración interlaminar. Ca–montmorillonita puede formar hidratos de una, dos y tres capas, con espaciamiento d₀₀₁ de 11.83, 13.73,y 15.60 Å respectivamente a 353 Ky 625 bar. A temperaturas menores el espaciamiento es mayor. Simulaciones en conjuntos µVT indican la formación del hidrato de una capa, estable a 333 K, 300 bar, potencial –7.21 kcal/mol, espaciamiento d₀₀₁ 12.11 Å. No se forman los hidratos de dos y tres capas. A 353 K, 625 bar, potencial de –5.58 kcal/mol, el hidrato de una capa no es estable. En el espacio interlaminar, las moléculas de agua se agrupan en el plano intermedio alternativamente orientadas con los protones hacia las superficies de siloxano a ambos lados y en el plano intermedio. Los cationes Ca²⁺ están totalmente solvatados, fuera del plano intermedio, a distancia de 2.77Å de las moléculas de agua. En sedimentos bajo condiciones normales el monohidrato de Ca–montmorillonita es estable a 2 km de profundidad, mientras que bajo sedimentos sobre–compactados a 2.7 km de profundidad se vuelve inestable.

Palabras clave: montmorillonita, Ca–montmorillonita, hidratación, simulación, Monte Carlo, estabilidad.

INTRODUCTION

The adsorption of fluids and chemical species by expandable clay minerals is important to digenetic, metamorphic, petrologic, and geochemical processes (Huggett and Shaw, 1993), soil physics, properties and behavior of soils (Aylmore and Quirk, 1967), stability, retention and transport of contaminants (Cotter–Howells and Patterson, 2000), waste management (Rutherford et al, 1980) and, in oil exploration and recovery, to borehole stability (Hall et al, 1986; Hall, 1993), adsorption of stabilizing additives and polymers, overpressure and migration of hydrocarbons (Hall, 1993).

The hydration and dehydration of the minerals result in adsorption or separation of fluids and chemical species that affect contamination, rock strength, pore pressure, swelling, and the overall stability of clay systems. The interactions between the clays and fluids are of particular interest to the retention of nutrients and the adsorption, accumulation, decomposition, release, transport, and ultimate fate of contaminants in soils, to soil mechanics, and in petroleum–rich basins to the recovery of oil and gas and the quality of the reservoir.

Clay minerals of the smectite type are common. In soils and sediments usually occur Na–, Ca–, and Mg–montmorillonite or their combinations. In clay deposits, in Mexico are found Ca–, Na–, and Mg–montmorillonite in the underclays of the Mexican Basin, subjected to hydration–dehydration, contaminants, and occasional multiplying seismic effects; in Durango the dominant specie is Na–montmorillonite, low–calcic and high–swelling, whereas in other localities, namely Tlaxcala and Guerrero, predominate Ca– and Mg–montmorillonite.

In industrial processes, smectites are normally used in their protonic form or with different adsorbed metallic and organic species to impart distinct properties. Their characteristics and behavior vary, usually associated with their silicic framework and surface properties; structural replacements modify the structural framework to change the surface properties and ultimate behavior of the clay. Reactions on the clay surface define their properties. Na–and Ca–montmorillonite are the most abundant on which other chemical species, fluids, metallic and organic ions or molecules build.

Smectites are relatively stable but prone to transform and modify their properties. Their fine particle size and disordered structure are not easily amenable to some analytical techniques but they are characterized by proper mineralogical procedures. Their surface properties are highly sensitive to the surrounding environment and more complex to characterize, essentially on account of their in situ behavior. As in many geochemical and mineralogical processes, i.e., mineral deposition from hydrothermal fluids or mineral stability at high temperatures, pressures or depths under brines and oil fluids, require complex interpretations and explanations, often distinct from those available from experimental data or extrapolated from different environments and conditions.

In the present paper is discussed the behavior of Ca–montmorillonite under surface and low–depth environments, as determined from molecular simulations. Reactions on the clay surface are fundamental to establish interrelations with parent minerals and understanding related processes. Molecular simulations allow characterization of the clay interlamellar space at the atomic and molecular levels, identifying fundamental properties, reaction mechanisms, thermodynamics, and kinetics of reactions, mimicking in situ conditions not easily reproduced experimentally or where direct observation is not simple.

Ca–montmorillonite is a 2:1 expandable clay mineral that swells upon contact with water. Experimental studies (Posner and Quirk, 1964; Pezerat and Mering, 1967; Keren and Shainberg, 1975; Suquet et al., 1975; McEwan and Wilson, 1980; Slade et al, 1991; Sato et al, 1992; Cases et al, 1997; Bray et al, 1998; Bray and Redfern, 1999, 2000) have shown that at the ambient conditions of 300 K and 1 bar the anhydrous phase of d₀₀₁ spacing 9.55 – 9.96 Å hydrates to 11.19 – 12.45 Å one–layer hydrate, 15.00 – 15.50 Å two–layer hydrate, and 18.0 –19.1 Å three–layer hydrate. Monte Carlo simulations (Chávez–Páez et al, 2001a) have shown that in the same ambient environment of 300 K and 1 bar are formed stable 9.82 Å, 12.20, 14.70, and 18.4–19.0 Å anhydrous, one–, two–, and three–layer hydrates. However, the characteristics and stability of Ca–montmorillonite at conditions other than atmospheric have been scarcely described (Stone and Rowland, 1955; Koster von Groos and Guggenheim, 1987, 1989; Khitarov and Pugin, 1996; Siqueira et al, 1997, 1999; Wu et al, 1997; de Pablo et al, 2005).

Parent Na–montmorillonite has been shown from simulation studies to form the stable monolayer hydrate at 353 K and 625 bar whereas K–montmorillonite does not (de Pablo et al., 2004; Chavez et al., 2004; de Pablo et al., 2005). The condition of 353 K and 625 bar is particularly significant. It prevails at a 2.7 km depth of over–compacted sediments, where clay minerals may transform by adsorbing or releasing components or from reaction with circulating brines, oil and gas flows.

The characteristics and behavior of Ca–montmorillonite at low depths have not been described. In the present study, the stability and swelling of Wyoming–type Ca–montmorillonite are investigated by Monte Carlo simulations at constant stress in the isobaric–isothermal NP_zzT ensemble and at constant chemical potential in the grand canonical µT ensemble, at the basin conditions of 333–353 K and 300–625 bar.

METHODOLOGY

The hydration of Ca–saturated montmorillonite is studied by Monte Carlo simulation in the NP_zzT and µVT ensembles (Allen and Tildesley, 1987), at environments of 333 K and 300 bar existing at 2 km depth in normally compacted sediments, and of 353 K and 625 barprevailing at 2.7 km depth of over–compacted sediments (geotherms at the Gulf of Mexico, geothermal gradient of 30 °C/km, geostatic gradient 150 bar/km, Hower et al, 1976).

The simulations employ the model and approach described by Chávez–Páez et al. (2001a, 2001b). The clay considered is the Ca–saturated Wyoming–type montmorillonite Of unit cell (Si_7.75Al_0.25)(Al_3.50Mg_0.50)O₂₀(OH)₄Ca_0.375• nH₂O and charge of 0.75, 33% of which is in the tetrahedral sheet. Eight unit cells form the 320–atoms 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 in the unit cell are those of pyrophyllite (Skipper et al., 1995a), with substitution in the simulation cell 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⁺.

The total interaction energy between atoms is defined by Equation 1, which includes the Coulomb attraction–repulsion energy and the Lennard–Jones and van der Waals dispersion energy. Chávez–Páez et al. (2001a) simulated the interaction energy from Equation 2, which combines the model of Skipper et al. (1995a, 1995b) for the clay–water system and the TIP4P water model of Jorgensen et al. (1983). In Equation 2, the first term of the summation represents the Coulomb attraction–repulsion contribution to the total energy of interaction whereas the remaining terms correspond to the Lennard–Jones dispersion contribution, m_i and m_j are the number of sites in molecules i and j, q_ia is the charge at site a of molecule i, q_jb is the charge at site b of molecule j, r_iajb is the distance between atom a in molecule / and atom b in molecule./. The parameters A, B, C, D, E, F, and G are site specific parameters developed for the interaction between calcium and TIP4P water. In the present case the parameters of Bounds (1985) (Table 1) are used.

In constant stress simulation, NP_zzT, the stress P_zz normal to the clay surface, the temperature T, and the number of molecules N are kept constant. The system is allowed to sample the configuration space through molecular displacements and volume fluctuations. Volume fluctuations are allowed only in the direction normal to the clay surface. The acceptance probability of a new configuration n generated from a configuration m by displacing an atom orby changing the volume of the simulation box is given by Equation 3.

U_nm is the difference in energy between the two configurations, V_nm is the difference in volume, and V_n and V_m are the corresponding volumes, β^–1 = k_bT is the inverse temperature, k_b is Boltzmann's constant and T is the absolute temperature.

In the grand canonical ensemble, µVT, chemical potential, volume, and temperature are kept constant. The system samples the configuration space through molecular displacements and concentration fluctuations. However, due to the high densities that water can reach in the clay inter–layer, sampling can be inefficient and a biasing technique has to be implemented to improve sampling. It is achieved by implementing a rotational–bias insertion method, were a water molecule is inserted randomly in the system and the selection of its orientation is biased. Trial insertions are accepted with probability

and deletion of water molecules is accepted with probability

δU_nm is, like U_nm in Equation 3, the energy difference between the two configurations, P_j is the probability of selecting jth orientation from k randomly generated orientations; z =exp (βµ) / Λ³ is the activity, Λ is the thermal length of the molecule, and µ is the chemical potential of bulk water (Allen and Tildesley, 1987; Chávez–Páez et al., 2001a, 2001b).

We simulate the water–calcium interaction applying the TIP4P water model of Jorgensen et al. (1983) and the parameters of Bounds (1985) (Table 1). At 300 K and 333 bar and at 353 K and 625 bar, we prefer the TIP4P model because its influence on the density or the energy does not appear significant, and by doing so our results can be compared with those known previously on Ca–saturated montmorillonite under the surface ambient environment (Boek et al., 1995; Chávez–Páez et al., 2001a). The water–clay and clay–calcium interactions are neglected. The simulations required 2 x 10⁶ Monte Carlo steps for equilibration and, after the equilibration period, simulations proceeded for additional 2 x 10⁶ Monte Carlo steps, until the statistics was satisfactory and smooth calculated functions developed.

RESULTS AND DISCUSSION

NP_zzT simulations

Simulations in the NP_zzT ensemble at constant mass, pressure, and temperature indicate that at the basin conditions of 353 K and 625 bar the adsorption of 32 water molecules per layer of Ca–montmorillonite (98 mg/g of clay) results in the formation of the one–layer hydrate of d₀₀₁ , spacing 11.83 Å (Table 2). The water molecules are clustered on the interlayer midplane, tilted with their hydrogen atoms oriented towards the siloxane surfaces on both sides and to the midplane (Table 2, Figure 1a). The Ca²⁺ ions are on the interlayer midplane solvated in outer–sphere complexes, but some are closer to the clay surface. A distance of 1.624 Å separates the outmost proton layers. The configuration is illustrated in the snapshot of Figure 2a.

The results indicate that, at 353 K and 625 bar, the adsorption of 32, 64, and 96 water molecules places the molecules respectively at 0.012, 0.912–0.987, and 1.787–1.737 Å from the interlayer midplane. The interlayer configuration changes from one–layer when adsorption is between 32 and near 64 water molecules to two–layer when increased to 64 – 96 molecules. The Ca²⁺ ions are essentially in outer–sphere complexes in the water layers, symmetrical to the protons and slightly off the oxygen atoms.

At 333 K and 300 bar, prevailing at 2 km depth, the adsorption of 50 water molecules develops a one–layer hydrate of d₀₀₁ , spacing 12.11 Å, higher than that formed at 353 K and 625 bar. It has water molecules off the interlayer midplane, closer to the clay surface (Table 2). Its snapshot (Figure 2c) illustrates a bulkier interlayer relative to that at 353 K when 32 molecules were adsorbed (Figure 2a).

Our simulated d₀₀₁ spacing of 11.83 and 12.11 Å for the one–layer hydrates at 353 K and 625 bar and at 333 K and 300 bar are within the range of 11.19–12.45 Å known from experimental studies (McEwan and Wilson, 1980; Bray and Redfern, 1999, 2000) and are shorter than the 12.20 Å simulated for Ca–montmorillonite under surface conditions of 300 K and 1 bar (Laird et al., 1995; Laird, 1996; Chávez–Páez et al, 2001a) (Table 3). The simulated 15.60 Å spacing limiting the two–layer hydrate, with 96 adsorbed molecules of water, compares with the experimental 15.0–15.8 Å (Posner and Quirk, 1964; Keren and Shainberg, 1975; Sato et al., 1992; Bray et al., 1998), the 15.0 Å measured at 260–300 K and 48–7075 bar (Wu et al, 1997), and the 14.7 Å (Chávez–Páez et al, 2001a) known from simulations at 300 K and 1 bar. The reported three–layer hydrates of 18.50–19.10 Å spacing (Posner and Quirk, 1964; Suquet et al, 1975; Sato et al, 1992; Wu et al, 1997; Chávez–Páez et al, 2001a) were not simulated in the present work.

The radial distribution functiong(r) shows for the one–layer Ca–montmorillonite hydrate a coordination probability of 10.026 molecules of water per cation, at a Ca–0 separation of 2.775 Å (Table 2, Figures 3a and 3b). Increasing the adsorption to the two–layer hydrate state raises the separation to 2.815 Å and reduces the probability to 7.441. When temperature and pressure are decreased to 333 K and 300 bar, the probability is 7.906 with the r_CaO distance remaining at 2.775 Å. Integration of g(r) as per Equation 6 (Allen and Tildesley, 1987) indicates solvationof the cation by 10 water molecules, which is within the 9–10 range known for the calcium–water system (Bounds, 1985).

The progressive hydration of Ca–montmorillonite increases the d₀₀₁ , spacing and the separation of the water layers from the interlayer midplane (Table 2, Figure 4a). The energy of interaction between atoms increases in the order –24.245, –19.664, and –17.714 kcal/mol as the adsorbed H₂O changes from 32 to 96 molecules (Table 2, Figure 4b).

The Coulomb energy decreases from 1.415 to –6.679 and –10.137 kcal/mol, inverse to the Lennard–Jones energy that increases to –26.369, –13.167, and–7.648 kcal/mol. The total interaction energy is lower for Ca–montmorillonite in the 333 K, 300 bar environment.

Grand canonical µVT simulations

To ascertain the thermodynamic stability of hydrated Ca–montmorillonite, simulations were conducted in the grand canonical µVT constant mass, volume and temperature ensemble. The simulations started by calculating the chemical potentials of bulk water for a system of 216 water molecules (Chávez–Páez et al., 2001a, 2001b) at 353 K and 625 bar and at 333 K and 300 bar. For the former, the simulated chemical potential was of–5.58 kcal/mol and for the latter –7.21 kcal/mol.

Simulations in the grand canonical ensemble define the stability of the clay mineral when the chemical potentials in the mineral interlayer and of the bulk supernatant fluid are equal. The thermodynamic stability of the Ca–montmorillonite hydrates is determined from the minima in the swelling free energy as a function of the interlayer separation (Chávez–Páez et al, 2001a, 2001b). The free energy is calculated from Equation 7 where P_zz is the interlayer pressure tensor and (P_zz)^npp is the normal external bulk pressure. The derivative of this expression defines the stable d₀₀₁spacing when the calculated pressure tensor P_zz equals the bulk pressure on the clay. Values of P_zz distinct from the bulk pressure do not represent real solutions and lack any physical meaning; opposite assumptions would lead to collapse or blow the clay structure. A simple graphical solution is a plot depicting the dependence of P_zz on the d₀₀₁ spacing.

Simulations using the TIP4P water model (Jorgensen et al, 1983) show that for d₀₀₁ spacings between 11.5 and 18 Å, the adsorbed water increases from 39.27 to 140.40 molecules per layer or 120.36 to 430.33 mg/g (Table 4, Figure 5a), the total energy changes from –22.871 kcal/mol to –16.383 kcal/mol, the Lennard–Jones energy varies from –22.116 to –3.970 kcal/mol, and the Coulomb energy from –0.601 to –12.538 kcal/mol (Figure 5b). Simulations at 333 K and 300 bar (Table 5, Figure 5c) indicate adsorption of 150.86–316.53 mg water/g, d₀₀₁ spacing of 12.0–16.0 Å, energy of interaction –23.549 — –19.110 kcal/mol, Lennard–Jones energy –18.118 — –11.396, Coulomb energy –5.647 — –7.564 kcal/mol, and pressure tensor from 10654.69 – 2532.54 bar. The Lennard–Jones and Coulomb energies add to the total energy of interaction; the values presented in Tables 2 and 4 do not do exactly add, due to some mishandling of the data outputs.

The variation of the pressure tensor P_zz with the adsorbed water depicts the path shown in Figure 6. At 353 K and 625 bar, the data in Figure 6a show that within the statistical uncertainty associated with Monte Carlo simulations, the one–layer hydrate Ca–montmorillonite approaches stability, without attain it. In the less deep environment of 333 K and 300 bar, the one–layer hydrate is stable (Figure 6b), characterized by a d₀₀₁ spacing of 12.11 Å. Two– and three–layer hydrates do not form.

At 353 K and 625 bar, the nearly stable one–layer Ca–montmorillonite hydrate has a d₀₀₁ spacing of 12.50 Å, formed by the adsorption of 55.21 water molecules (169.22 mg H₂O/g clay), total interaction energy –21.107 kcal/mol, and interlayer density 0.342 g/mL. At 333 K and 300 bar, the stable one–layer hydrate has d₀₀₁ 12.11 Å, adsorbs 54.50 molecules of water, interaction energy –22.803 kcal/mol, Lennard–Jones dispersion –6.345 kcal/mol, Coulomb attraction–repulsion –16.449 kcal/mol, density 0.337 g/mL. The density profiles (Figure 7) show that at 353 K and 625 bar the water molecules cluster in a broad band 0.087 Å off the interlayer midplane, with protons on the midplane and 1.087 Å and 1.137 Å to each side, and the calcium cations off the midplane, solvated in outer–sphere complexes within the water layer. At 333 K and 300 bar, the density profiles indicate that the water molecules are on the interlayer mid–plane, oriented to both siloxane surfaces, with the protons 1.112 and 1.137 Å to both sides, slightly farther apart than at 353 K and 625 bar; the calcium atoms are solvated off the interlayer midplane. Snapshots of both hydrates (Figures 8a and 8b) show a broad layer of water molecules with the cations coordinated in the water layer, away from the siloxane surface.

Our simulations in the NP_zzT ensemble show that Ca–montmorillonite can form one–, two– and three–layer hydrates. Simulations in the (µVT ensemble confirm that in normally compacted sediments at 2.0 km depth, 333 K and 300 bar, one–layer Ca–montmorillonite hydrate is stable but two– and three–layer hydrates do not form. At 353 K and 625 bar, mimicking over–compacted sediments at 2.7 km depth, the one–layer hydrate is nearly stable, not attaining full stability. In this environment, the unstable clay could transform to other minerals, adsorb from or release species to the surrounding environment to develop a stable configuration. The simulations point that Ca–montmorillonite could be stable at 353 K and 625 bar and possibly even under more stringent environments, if sediments were normally compacted or potentials more suitable.

Our results extend the stability of the one–layer Ca–montmorillonite hydrate to 2.0 km depth and probably higher, upwards from previous investigations limiting its stability to burial depths of 1.5 km, with possible conversion to other minerals in deeper environments (Siqueira et al, 1997). The present simulations did not reach the high temperature and pressure of 513 K and 1200 bar (Siqueira et al, 1999) and above (Wu et al, 1997) experimentally determined for the stability of the 18–19 Å 3–layer hydrate and of 260–310 °C and 48–260 bar along the 0.7 g/mL iso–chore (Wu et al, 1997) and of 453 K and 900 bar (Siqueira et al, 1999) determined for its transformation to the 15 Å two–layer hydrate. Recent data from de Pablo et al (2005) have confirmed that one–layer Ca–montmorillonite is stable down to 8.7 km in normally compacted sediments; two–and possibly three–layer hydrates develop at 6.7 km depth, 473 K and 1000 bar. Na– and K–montmorillonite form in similar environments one– and two–layer hydrates of d₀₀₁ , spacing larger than Ca–montmorillonite.

SUMMARY

Monte Carlo simulations on the hydration of Ca–montmorillonite under basin–like conditions of 353 K and 625 bar and of 333 K and 300 bar reveal interlayer configurations similar to those known at the surface ambient environment of 300 K and 1 bar. At low states of hydration, the water molecules cluster on the interlayer midplane with their protons alternatively oriented towards the siloxane surfaces and on the interlayer midplane. At higher states of adsorption, the water molecules are distributed in two separate layers close to the clay surfaces, with the molecules tilted so their protons point towards the siloxane surfaces and the interlayer midplane. The calcium ions form outer–sphere complexes in the water layers, always positioned off the interlay er midplane.

For the force field considered in this work, within the statistical error of Monte Carlo simulations, Ca–montmorillonite forms a 12.11 Å one–layer hydrate stable at 333 K and 300 bar, at a 2 km depth of normally compacted sediments. Two– and three–layer hydrates do not form. At 353 K and 625 bar, prevailing at 2.7 km depth of over–compacted sediments, the one–layer hydrate only approaches stability without quite reaching it. Under equal conditions of temperature, pressure, and chemical potential our previous simulations indicate that Na–montmorillonite is clearly stable (de Pablo et al., 2004) but K–montmorillonite may not (Chavez et al., 2004). A difference is established with clays under the ambient surface setting of 300 K and 1 bar where two– and three–layer hydrates are formed. The results imply that Ca–montmorillonite as well as Na– and K–montmorillonite may, at depth, loose water to their one–layer hydrates.

ACKNOWLEDGMENTS

REFERENCES

Allen, M.P., Tildesley, D.J., 1987, Computer Simulation of Liquids: London, U.K., Clarendon Press, 404 p.        [ Links ]

Anderson, M.A., Trouw, F.R., Tam, C.N., 1999, Properties of water in calcium– and hexadecyltrimethylammonium–exchanged bentonite: Clays and Clay Minerals, 47, 28–35.         [ Links ]

Aylmore, L.A.G., Quirk, J.P., 1967, The micropore size distribution of clay mineral systems: Journal of Soil Science, 18, 1–17.         [ Links ]

Boek, E.S., Coveney, P.V., Skipper, N.T., 1995, A study of hysteresis in the swelling curves of sodium montmorillonite: Langmuir, 11, 4629–4631.         [ Links ]

Bounds, D.G., 1985, A molecular dynamics study of the structure of water around the ions Li⁺, Na⁺, K⁺, Ca²⁺, Ni²⁺, and Cl^-: Molecular Physics, 54, 1335–1355.        [ Links ]

Bray, H.J., Redfern, S.A.T., 1999, Kinetics of dehydration of Ca–montmorillonite: Physics and Chemistry of Minerals, 26, 591–600.        [ Links ]

Bray, H.J., Redfern, S.A.T., 2000, Influence of counterion species on the dehydroxylation of Ca²⁺–, Mg²⁺–, Na⁺– and K⁺– exchanged Wyoming montmorillonite: Mineralogical Magazine, 64, 337–346.        [ Links ]

Bray, H.J., Redfern, S.A.T., Clark, S.M., 1998, The kinetics of dehydration in Ca–montmorillonite; An in–situ x–ray synchrotron study: Mineralogical Magazine, 62, 647–656.        [ Links ]

Cases, M., Berend, I., Francois, M., Uriot, J.P., Michot, L.J., Thomas, F., 1997, Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite. 3. The Mg²⁺, Ca²⁺, Sr²⁺, and Ba²⁺ exchanged forms: Clays and Clay Minerals, 45, 8–22.        [ Links ]

Chávez–Páez, M., de Pablo, L., de Pablo, J.J., 2001a, Monte Carlo simulations of Ca–montmorillonite hydrates: Journal of Chemical Physics, 114, 10948–10953.        [ Links ]

Chávez–Páez, M., van Workum, K., de Pablo, L., de Pablo, J.J., 2001b, Monte Carlo simulations of sodium montmorillonite hydrates: Journal of Chemical Physics, 114, 1405–1413.        [ Links ]

Chávez, M.L., de Pablo, L., de Pablo, J.J., 2004, Monte Carlo molecular simulation of the hydration of K–montmorillonite at 353 K and 625 bar: Langmuir, 20, 10764–10770.        [ Links ]

Cotter–Howells, J.D., Patterson, E., 2000, Minerals and soil development, in Vaughan, D.J., Wogelius, R.A. (eds.), Environmental Mineralogy: Budapest, Eótvós University Press, 91– 124.        [ Links ]

De Pablo, L., Chávez, M.L., Sum, A.K., de Pablo, J. J., 2004, Monte Carlo molecular simulation of the hydration of Na–montmorillonite at reservoir conditions: Journal of Chemical Physics, 120, 939–946.        [ Links ]

De Pablo, L., Chavez, M.L., de Pablo, J.J., 2005, Stability of Na–, K–, and Ca–montmorillonite at high temperatures and pressures; A Monte Carlo simulation: Langmuir, 21, 10874–10884.        [ Links ]

Glaeser, R., Mering, J., 1968, Domaines d'hydratation homogene des smectites: Comptes Rendus de l'Academie des Sciences (Paris), 267, Serie D, 463–466.        [ Links ]

Hall, P. L., 1993, Mechanism of overpressuring; an overview, in Manning, D.A.C., Hall, P.L., Hughes, C.R. (eds.), Geochemistry of Clay–Pore Interactions: London, U.K.,Chapman and Hall, 265–315.        [ Links ]

Hall, P. L., Astill, D. M., McConnell, J. D. C, 1986, Thermodynamic and structural aspects of the dehydration of smectites in sedimentary rocks, 21, 633–648.        [ Links ]

Hower, J.E., Hower, M.E., Perry, E.A., 1976, Mechanism of burial metamorphism of argrillaceous sediment; 1. Mineralogical and chemical evidence: Geological Society of America Bulletin, 86, 725–737.        [ Links ]

Huggett, J.M., Shaw, H.F., 1993, Diagenesis of Jurassic mudrocks of the North Sea, in Manning, D.A.C., Hall, PL., Hughes, C.R. (eds.), Geochemistry of Clay–Pore Interactions: London, U.K., Chapman and Hall, 107–126.        [ Links ]

Jorgensen, W.L., Chandrasekhar, J., Madura, J.D., Impey, R.W., Klein, M.L., 1983, Comparison of simple potential functions for simulating liquid water: Journal Chemical Physics, 79, 926–935.        [ Links ]

Keren, R., Shainberg, I., 1975, Water vapor isotherms and heat of immersion of Na/Ca–montmorillonite systems–I. Homoionic clay: Clays and Clay Minerals, 23, 193–200.        [ Links ]

Khitarov, N.L., Pugin, V.A., 1996, Behavior of montmorillonite under elevated temperatures and pressures: Geochemistry International, 3, 621–626.        [ Links ]

Koster von Groos, A.F., Guggenheim, S., 1987, Dehydration of a Ca–Mg–exchanged montmorillonite (SWy–1) at elevated pressures: Clays and Clay Minerals, 72, 292–298.        [ Links ]

Koster von Groos, A.F., Guggenheim, S., 1989, Dehydroxilation of a Ca– and Mg–exchanged montmorillonite: American Mineralogist, 74, 627–636.        [ Links ]

Laird, D.A., 1996, Model for the crystalline swelling of 2:1 layer phyllosilicates: Clays and Clay Minerals, 44, 553–559.        [ Links ]

Laird, D.A., Shang, C., Thompson, M.L., 1995, Hysteresis in crystalline swelling of smectites: Journal Colloid Interface Science, 171, 240–245.        [ Links ]

McEwan, D.M.C., Wilson, M.J., 1980, Interlayer and intercalation complexes of clay minerals, in Brindley, G.W., Brown, G. (eds.), Crystal Structures of Clay Minerals and their X–Ray Identification: London, U. K., Mineralogical Society, 197–248.        [ Links ]

Pezerat, H., Mering, J., 1967, Recherches sur la position des cations exchangeable et de l'eau dans les montmorillonite: Comptes Rendus de l'Académie des Sciences (Paris), Serie D, 265, 529–532.        [ Links ]

Posner, A.M., Quirk, J.P., 1964, Changes in basal spacing of montmorillonite in electrode solution: Journal of Colloidal Science, 19, 798–812.        [ Links ]

Rutherford, D.W., Chiou, C.T., Eberl, D.D., 1980, Effects of exchanged cation on the microporosity of montmorillonite: Clays and Clay Minerals, 45, 534–543.        [ Links ]

Sato, T., Watanabe, T., Osuka, R., 1992, Effect of layer charge, charge location, and energy change on expansion properties of dioctahedral montmorillonites: Clays and Clay Minerals, 40, 103–113.        [ Links ]

Siqueira, A.V.C. de, Skipper, N.T., Coveney, P.V., Boek, E.S., 1997, Computer simulation evidence for enthalpy driven dehydration of smectite clays at elevated pressures and temperatures: Molecular Physics, 92, 1–6.        [ Links ]

Siqueira, A.V. de, Lobban, C., Skipper, N.T., Williams, G.D., Soper, A.K., Done, E., Dreyer, J.W., Humpreys, R.J.O., Bones, J.A.R., 1999, The structure of pore fluids in swelling clays at elevated pressures and temperatures: Journal of Physical Condensed Matter, 11, 9179–9188.        [ Links ]

Skipper, N.T., Sposito, G., Chang, F.R.C., 1995a, Monte Carlo simulation of interlayer molecular structure in swelling clay minerals. 2. Mondayer hydrates: Clays and Clay Minerals, 43, 294–303.        [ Links ]

Skipper, N.T., Chang, F.R.C., Sposito, G., 1995b, Monte Carlo simulation of interlayer molecular structure in swelling clay minerals. 1. Methodology: Clays and Clay Minerals, 43, 285–293.        [ Links ]

Slade, P.G., Quirk, J.P., Norrish, K., 1991, Crystalline swelling of smectite samples in concentrated NaCl solutions in relation to layer charge: Clays and Clay Minerals, 39, 234–238.        [ Links ]

Stone, R.L., Rowland, R.A., 1955, DTA of kaolinite and montmorillonite under H₂O vapor pressure up to six atmospheres, in Third National Clay Conference of the Clay Minerals Society: Houston, Texas, National Academy of Sciences and National Research Council, 39, 103–116.        [ Links ]

Suquet, H., de la Calle, C., Pezerat, H., 1975, Swelling and structural properties of saponite: Clay and Clay Minerals, 23, 1–9.        [ Links ]

Wu, T.C., Bassett, W.A., Huang, H.L., Guggenheim, S., Koster van Groos, A.F., 1997, Montmorillonite under high H₂O pressures: Stability of hydrated phases, dehydration hysteresis, and the effect of interlayer cations: American Mineralogist, 82, 69–78.        [ Links ] ]]> 1987 404 1999 47 28-35 1967 18 1-17 1995 11 4629-4631 1985 54 1335-1355 1999 26 591-600 2000 64 337-346 1998 62 647-656 1997 45 8-22 2001 a 114 10948-10953 2001 b 114 1405-1413 2004 20 10764-10770 2000 91- 124 2004 120 939-946 2005 21 10874-10884 1968 267 Serie D, 463-466 1993 265-315 1986 21 633-648 1976 86 725-737 1993 107-126 1983 79 926-935 1975 23 193-200 1996 3 621-626 1987 72 292-298 1989 74 627-636 1996 44 553-559 1995 171 240-245 1980 197-248 1967 265 529-532 1964 19 798-812 1980 45 534-543 1992 40 103-113 1997 92 1-6 1999 11 9179-9188 1995 a 43 294-303 1995 b 43 285-293 1991 39 234-238 1955 Houston Texas 103-116 1975 23 1-9 1997 82 69-78