Animated molecular dynamics simulations of hydrated caesium-smectite interlayers
© The Royal Society of Chemistry and the Division of Geochemistry of the American Chemical Society 2002
Received: 22 May 2002
Accepted: 11 September 2002
Published: 24 September 2002
Computer animation of center of mass coordinates obtained from 800 ps molecular dynamics simulations of Cs-smectite hydrates (1/3 and 2/3 water monolayers) provided information concerning the structure and dynamics of the interlayer region that could not be obtained through traditional simulation analysis methods. Cs+ formed inner sphere complexes with the mineral surface, and could be seen to jump from one attracting location near a layer charge site to the next, while water molecules were observed to migrate from the hydration shell of one ion to that of another. Neighboring ions maintained a partial hydration shell by sharing water molecules, such that a single water molecule hydrated two ions simultaneously for hundreds of picoseconds. Cs-montmorillonite hydrates featured the largest extent of this sharing interaction, because interlayer ions were able to inhabit positions near surface cavities as well as at their edges, close to oxygen triads. The greater positional freedom of Cs+ within the montmorillonite interlayer, a result of structural hydroxyl orientation and low tetrahedral charge, promoted the optimization of distances between cations and water molecules required for water sharing. Preference of Cs+ for locations near oxygen triads was observed within interlayer beidellite and hectorite. Water molecules also could be seen to interact directly with the mineral surface, entering its surface cavities to approach attracting charge sites and structural hydroxyls. With increasing water content, water molecules exhibited increased frequency and duration of both cavity habitation and water sharing interactions. Competition between Cs+ and water molecules for surface sites was evident. These important cooperative and competitive features of interlayer molecular behavior were uniquely revealed by animation of an otherwise highly complex simulation output.
The high bioavailability and long halflives of radioactive isotopes of Cs make them a significant environmental hazard. [1–3] To isolate this hazard, nuclear waste containment facilities may be separated from host bedrock by compacted bentonite liners, shown in laboratory experiments to slow the diffusion of Cs+.[1, 2, 4–7] The smectite minerals making up these liners are 2 : 1 layer type clay minerals. Each layer consists of an alumina (dioctahedral) or magnesia (trioctahedral) sheet sandwiched between two silica tetrahedral sheets. The arrangement of silica tetrahedra in sheets results in the creation of a network of six-oxygen rings, at the center of each a distorted hexagonal cavity, across the surface of the mineral. Isomorphic substitution of Mg for Al, or Li for Mg, results in negative octahedral charge sites, while substitution of Al for Si creates negative tetrahedral charge sites. These charge sites are balanced by cations in the interlayer which attract waters of hydration to this region, causing the clay mineral to swell. Although Cs-smectite hydrates have been studied for many years, little detailed information about the mechanisms involved in Cs+ adsorption, hydration, and diffusion has been adduced from experimental findings. Molecular simulation thus has proven to be a useful adjunct to experimental work concerning the smectite interlayer. [10–15]
A number of XRD studies show that the layer spacing of Cs-smectites remains in the range 11.9–12.5 Å after exposure to water vapor at any relative humidity,[9, 16–20] or even after immersion in an aqueous solution. Water vapor adsorption isotherms [16–20] indicate increasing hydration of Cs-smectite with increasing relative humidity, but Calvet and Prost argued that most of the water adsorbed resides in micropores, not in the interlayer region. Indeed, measurements of the micropore volume in homoionic montmorillonites have established the extensive microporosity of Cs-smectites. Calvet and Prost suggested that the 12.4 Å layer spacing in Cs-smectite was achieved and stabilized after the adsorption of only about 1.2–1.4 H2O per unit cell of the clay mineral, well below the nominal monolayer water content of 4 H2O per unit cell observed for smectites containing the strongly hydrating Li+ cation.[17, 19] Our recent Monte Carlo (MC) simulations of model Cs-smectite hydrates at low water contents confirmed this speculation, showing that the 12.4 Å hydrate of Cs-smectite likely contains no more than 2.7 H2O per unit cell (about 2/3 monolayer).
Layer spacing and molar potential energy of water (MC simulation)15 and self-diffusion coefficients for interlayer water (MD simulation) in Cs-smectite hydrates
MC steps a
Potential energy of water/kJ mol-1 b
Self-diffusion coefficient, Dw/10-9 m2 s-1 c
1/3 water monolayer
12.37 ± 0.08
-47.43 ± 3.53
0.229 ± 0.001
4 × 106
12.31 ± 0.10
-42.98 ± 4.58
0.342 ± 0.002
12.46 ± 0.09
-32.33 ± 4.04
2/3 water monolayer
3.0 × 106
12.41 ± 0.07
-46.56 ± 2.00
0.685 ± 0.006
3.5 × 106
12.68 ± 0.10
-36.66 ± 2.12
1.168 ± 0.006
Bulk liquid water f
-35.4 ± 0.231
The MC simulations were followed by molecular dynamics (MD) simulations. These latter results were analyzed for average properties, such as interlayer water self-diffusion coefficients, as well as for individual molecular properties, such as plots of xyz coordinates sampled by specific Cs+ ions or by water molecules. These traditional simulation outputs were not able to characterize the full complexity of interactions among cations, water molecules, and mineral surface sites. To continue analysis of the MD results, we constructed animations of molecular motions in the five Cs-smectite hydrate systems to examine the effects of charge site and hydration state on the behavior of interlayer species. Stereo-viewing and animated motion have been shown to increase comprehension of three dimensional structures. Because humans understand and navigate through a dynamic, three dimensional world, depiction of MD animations as a collection of spheres in three dimensional space that change position over time is a familiar metaphor that is intuitive to most viewers. Other more traditional forms of presentation, such as a display of the entire path of a molecule over time, can result in a "tangled mess" that is not easy to interpret. Animations thus can be helpful in understanding the complex three dimensional relationships between interacting molecules over time.
Model Cs-smectite hydrates
Hectorite: Cs0.75 [Si8](Mg5.25Li0.75)O20(OH)4
Beidellite: Cs0.75 [Si7.25Al0.75](Al4)O20(OH)4
Montmorillonite: Cs0.75 [Si7.75Al0.25](Al3.5Mg0.5)O20(OH)4
Hectorite is a trioctahedral 2:1 clay mineral, whereas mont-morillonite and beidellite are dioctahedral. Moreover, hectorite shows charge substitution exclusively in the octahedral sheet, whereas beidellite contains only tetrahedral charge substitution. Montmorillonite has both types of charge substitution, with twice as much octahedral as tetrahedral layer charge. Our simulation cell contains eight unit cells, and has lateral (ab) dimensions 21.12 × 18.28 Å. The layer spacing is determined for each simulation system individually during MC equilibration.
Interactions between the interlayer species, and between them and atoms in the clay layers, are represented para-metrically by a MCY-type potential function:
where U is the potential energy of the system, i and j are sites on atoms within the simulation cell, r ij is the distance between sites i and j, q represents atom charge, and A, B, C, and D are van der Waals interaction parameters. We used this form of potential function because it has led to accurate modeling of experimentally accessible quantities such as layer spacing and interlayer species configuration and mobility. [10–15] In addition, the MCY potential function for the water–water interaction is optimized on dimer structures and, therefore, does not enforce the tetrahedral configuration of bulk water as strongly as do other, more empirically-based water–water potential functions. This fact may explain its enhanced ability to model water molecules in the especially constrained geometry of the clay interlayer region.[10, 11, 13] Van der Waals parameters for the Cs–O interaction were obtained through conversion of Lennard-Jones (LJ) (6–12) potential function parameters taken from Smith and Dang, described previously. The MCY Cs–O interaction parameters were: A = 51.0 kJ mol-1, B = 1.0850 Å-1, C = 3.72 × 106 kJ mol-1, D = 4.2758 Å-1. Van der Waals interactions for Cs–H, Cs–Al, and Cs–Si atom pairs were assumed to be negligible.
Monte Carlo and molecular dynamics simulations
Allen and Tildesley have outlined the general principles of MC and MD simulations of liquids. Chang et al.[10, 11] and Greathouse and Sposito have developed simulation methodologies customized for exploration of the interlayer region of 2:1 clay mineral hydrates. Detailed description of MC calculations performed to establish the equilibrated Cs-smectite hydrate structures has been provided previously. The program MONTE was used to run MC (NσT ensemble) simulations on a variety of Cs-smectite hydrates at 300 K and 100 kPa normal stress (σ). Monte Carlo calculations began with a simulation cell that had a 14 Å layer spacing and contained 6 Cs+ in the midplane of the inter-layer along with several randomly placed water molecules. Three-dimensional periodic boundary conditions were applied. Simulation started with an optimization developed by Chang et al.,[10, 11] consisting of 20,000 MC steps in which only water molecules were allowed to move, followed by another 20,000 steps in which water molecules could move and interlayer spacing could vary. After this optimization, all molecules were allowed to move in any direction, provided that the clay layer only moved about once for every five interlayer molecule movements. Information about total potential energy and layer spacing was collected every 500 steps. Systems were considered MC-equilibrated when convergence profiles of total potential energy and layer spacing provided minimum average values. The standard deviation of the average layer spacing was further required to be consistent with the precision of available experimental data on layer spacing.
The program MOLDY was used to perform MD (NVE ensemble) simulations of the Cs-smectite hydrates which had converged under MC simulation. Monte Carlo-equilibrated configurations in which the layer spacing was held constant were used as initial coordinates for the MD calculations. With the rigid clay layers fixed in position, initial velocities were assigned randomly to interlayer molecules following a Maxwell–Boltzmann distribution. In order to stabilize the temperature at 300 K, the simulations began with 20 ps of temperature scaling using a 0.5 fs time step. Temperature scaling was performed for each molecular species individually, with rotational and translational kinetic energies scaled separately. After initial scaling, the MD simulations proceeded for 800 ps.
Molecular center-of-mass coordinates collected at 0.1 ps intervals during the simulations were used as the input data for our animations. We used a custom animation tool to create a series of JPEG images, one for each set of coordinates, based on the center-of-mass information. The custom animation tool, created by the Lawrence Berkeley National Laboratory/National Energy Research Scientific Computing Center (LBNL/NERSC) Visualization Group in collaboration with the authors, runs on Windows or Unix/Linux platforms, and is based on OpenRM Scene Graph, an Open Source, cross-platform scene graph library. These images were then converted to MPEG-1 format using the Media-Convert tool and executed on a visualization server located in the Visualization Laboratory at LBNL.
Results and discussion
Molecular dynamics simulation and subsequent animation revealed complex and fascinating interactions between Cs+ ions, water molecules, and the charged clay surface. Short animations of twenty to fifty picoseconds (~ 1–2 MB) illustrating features relevant to the discussion below may be obtained from the links provided.
Animations allow us to see changes in the structure of hydrating water molecules around interlayer Cs+ over time. Water molecules move from one Cs+ to another, but are rarely far from an interlayer ion (Plate 1). This behavior leaves small regions of the smectite surface empty in the 1/3 monolayer simulations. Despite the weak coulomb field of Cs+ and its large size, these ions are able to organize water molecules into partial hydration shells (water molecules within a radial distance of < 5 Å from the cation, as shown by our MC radial distribution function calculations). The number of water molecules within each shell varies substantially with time for each cation. The exchange behavior seen among Cs+ waters of hydration contrasts with the results of MD calculations of similarly low water content Li-smectites, in which waters of hydration remained near the same ion for as long as 200 ps. The difference may be attributed to the smaller radius of the Li+ ions, which results in stronger electrostatic attraction for water molecules, as well as to the shorter timespan of the Li-smectite simulations, which may not have been long enough to capture water exchange processes.
Bostick et al. recently have interpreted LIII-edge EXAFS spectra of Cs-montmorillonite to suggest the presence of two types of Cs+–surface complex, distinguished by average Cs–O distances of 3.2 and 4.25 Å, respectively. They consider the complex with the shorter Cs–O distance to be an outer sphere complex, fully hydrated and therefore separated from mineral surfaces by water molecules, while the complex with the longer Cs–O distance is thought to be an inner sphere complex, partially dehydrated and directly associated with a mineral surface. Their analysis suggests that in a fully-saturated Cs-montmorillonite, the majority of cations exist as outer sphere complexes directly coordinated by 2–3 water molecules. Our simulations do not support a model of the interlayer which includes outer sphere Cs+ complexes. The cations modeled here have formed inner sphere complexes with the clay mineral surface and are surrounded by at least six oxygen atoms, yet have average Cs–O distances of around 3 Å, similar to the distance Bostick et al. assign to an outer sphere complex. The large size of Cs+ is inconsistent with the large energy of hydration needed to maintain an outer sphere complex near a charged mineral surface, as in the case of Li-montmorillonite.
A highly variable Cs coordination environment caused by sample preparation may account for the discrepancies between our results and EXAFS interpretations. While simulations can focus specifically on the interlayer environment, spectroscopic analysis of Cs-smectites inevitably averages signals from Cs+ in the interlayer, adsorbed to edge sites, and present in micropores. Careful sample preparation after Cs+ saturation, involving a drying step designed to encapsulate the ion between surface cavities in the interlayer, followed by a LiCl rinsing step to remove less tightly bound ions,[36, 37] would result in a sample containing primarily inner sphere Cs+ complexes residing in the interlayer of the smectite. A sample produced with this method would have a far less variable Cs+ coordination environment, and could be useful as an end member describing inner sphere coordination for linear combination fitting of EXAFS spectra. Reinterpretation of the Bostick et al. data using this approach may result in a view of interlayer structure similar to that provided by our simulation.
As was suggested for the EXAFS study mentioned above, a reinterpretation of existing NMR data on Cs-smectites [38–41]also may be in order. These data, which informed the EXAFS analysis, also suggest that outer sphere Cs+ complexes exist in the interlayer region. [38–41] This conclusion, not supported by molecular modeling, does not consider the possibility of two Cs+ bound by one or more shared water molecules.
Though the structural hydroxyls of beidellite are oriented at a shallow angle relative to the surface, which reduces electrostatic repulsion, the tetrahedral charge sites present in the mineral are located directly beneath some of the oxygen triads at the surface, making them attractive locations for interlayer cations (Fig. 4). Molecular modeling of Li-beidellite resulted in Li+ positioned directly over oxygen triads. In contrast, cations within Cs-montmorillonite interlayers can inhabit surface cavities as well as positions near oxygen triads. Only the simulations of montmorillonite contain both structural hydroxyl groups with shallow orientations relative to the surface, and a small proportion of tetrahedral charge, conditions which allow Cs+ to occupy positions within or near six-oxygen cavities and close to oxygen triads (Fig. 4). Although Li+ ions within montmorillonite also displayed greater variation in position than their counterparts in hectorite and beidellite, they did not enter surface cavities, because these ions existed either as inner sphere surface complexes near oxygen triads, tightly bound to substitution sites, or as fully hydrated outer sphere complexes too large to enter a cavity. The difference in solvation of Cs+ and Li+, a result of their contrasting ionic radii, thus modifies the electrostatic effect of the different smectite minerals.
It is possible that the ability to inhabit sites near oxygen triads as well as near or within six-oxygen cavities (Fig. 3), promotes the optimized geometry required for water sharing interactions to develop and perpetuate within the Cs-montmorillonite interlayer over the timescale of our MD simulations. While Cs+ within beidellite does not show this flexibility, the cations show another type of spatial variation, in that they are segregated into two layers along the z axis (Fig. 3), one containing ions attracted to charge sites in the upper mineral layer, the other containing ions attracted to charge sites in the lower mineral layer. Although limited to positions close to oxygen triads, this vertical separation of cations may enhance the potential for sharing water molecules. In contrast, the charge of hectorite is located solely in the octahedral sheet, which compels Cs+ ions to remain in stable, midplane positions near oxygen triads (Fig. 3), possibly inhibiting the formation of sharing configurations.
Cs+ are not the only interlayer species attracted to specific sites within the clay mineral surface. Water molecules in Cs-hectorite with 1/3 water monolayer (Plate 1) frequently dip into the six-oxygen cavities, but rarely remain for more than a hundred picoseconds. The negative dipole of this interlayer species is attracted to the structural hydroxyl group of hectorite which rests at the bottom of each cavity (Fig. 4), creating a population of water molecules with their dipole moments pointing away from the mineral surface. Such a water orientation was found in MC simulations of Cs-hectorite. However, because the charges are small the interaction is not very strong. As a result, water molecules visit the cavities for tens of picoseconds or less. Simulations of Li-hectorite with low water content featured water molecules which inhabited cavities for the entire length of the 200 ps MD calculation, likely due to entrapment caused by the substantially smaller layer spacing of the mineral.
In Cs-montmorillonite with 1/3 water monolayer, we see relatively little water entry into surface cavities (Plate 2). Because montmorillonite contains 1/3 as much tetrahedral charge as beidellite, and its hydroxyl groups are oriented at a low angle with respect to the clay surface, the surface does not strongly attract either the positive or the negative dipoles of water molecules. The observation that Cs+ within montmorillonite can enter six-oxygen cavities, unlike Cs+ within hectorite and beidellite, requires that cations out-compete water molecules for these locations. However, our MC results indicate that a portion of the water molecules within montmorillonite have a similar orientation to the fraction of water molecules in beidellite that are attracted to the mineral surface. Like Li-beidellite, Li-montmorillonite MD calculations did not show water molecules within six-oxygen cavities. This system also featured a larger layer spacing relative to Li-hectorite, allowing for more complete solvation of the strongly hydrating ions.
Animations of 800 ps MD simulations have provided new information concerning the structure and dynamics of the hydrated Cs-smectite interlayer region. A comparison of the five animations presented here reveals the behavior of interlayer species as modified by water content and charge site location. Cs-smectite systems feature ions as inner sphere complexes, hovering near charge sites and occasionally using jump diffusional movements to relocate. Higher water contents encourage more rapid movement in the interlayer for both Cs+ and the water molecules which solvate them. Different mineral charge patterns and structural hydroxyl group orientations create interlayer dynamics with different propensities for water molecule sharing between two Cs+. A low orientation angle for structural hydroxyl groups relative to the mineral surface, combined with a reduced amount of tetrahedral charge, as in montmorillonite, permits interlayer cations to occupy positions above and within six-oxygen cavities frequently. This may allow ions a greater flexibility in placement, and therefore increased ability to enter into water-sharing arrangements. Tetrahedrally charged clays like beidellite provide a different form of flexibility in ion position, due to the separation of ions into two layers along the z axis. This segregation may encourage formation of water sharing arrangements as well. The combination of the octahedral charge and the perpendicular orientation of hydroxyl groups relative to the hectorite surface results in Cs+ being held in stable, midplane locations above oxygen triads on the clay surface, hindering cations from entering into water sharing arrangements. The water sharing phenomenon predicted by our animations reaches an extreme state in the Cs-montmorillonite, 2/3 water monolayer hydrate, in which four Cs+ are held together throughout the 800 ps simulation period in an extended complex of ions and shared water molecules. Our animations also document the attraction between water molecules and the clay mineral surface, which increases with higher water content. Animation reveals competition between water molecules and Cs+ for sites on the mineral surface. Thus, animation of MD data has provided substantial information not available from traditional simulation methods.
Our research was supported in part by the Director, Office of Energy Research, Office of Basic Energy Sciences, Geosciences Division, of the U. S. Department of Energy under Contract No. DE-AC03-76SF00098. The National Energy Research Scientific Computing Center provided generous allocations of CPU time on its Cray J90 and T3E supercomputers. The first author expresses gratitude to the Clay Minerals Society for a grant supporting the purchase of a personal computer for use with her research, to Wes Bethel of the LBNL/NERSC Visualization Group for creating the customized RM Scene Graph program and for valuable discussions on visualization, and to Cristina Siegerist of the same group for help with the MediaConvert tool. Thanks also to the two anonymous reviewers who made valuable suggestions for the manuscript, and to reviewers John Apps and Satish Myneni of LBNL.
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