Estimation of Montmorillonite Swelling Pressure: A Molecular

Article pubs.acs.org/JPCC

Estimation of Montmorillonite Swelling Pressure: A Molecular Dynamics Approach Linlin Sun,† Janne T. Hirvi,† Timothy Schatz,‡ Seppo Kasa,§ and Tapani A. Pakkanen*,† †

Department of Chemistry, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland B+Tech Oy, FI-00420 Laulukuja 4, Helsinki, Finland § Posiva Oy, FI-27160 Olkiluoto, Eurajoki, Finland

Downloaded by UNIV OF NEBRASKA-LINCOLN on August 28, 2015 | http://pubs.acs.org Publication Date (Web): August 18, 2015 | doi: 10.1021/acs.jpcc.5b04972

‡

ABSTRACT: The swelling pressure of montmorillonite is an important factor in designing the bentonite buffer for geo-disposal of nuclear waste. A method to predict the swelling pressure of montmorillonite based on molecular dynamic simulations has been presented. A model structure of a Na-montmorillonite clay was put into contact with pure water, sodium chloride, and calcium chloride solutions. By imitating the experimental determination of the swelling pressure of bentonite clay, a spring sensor was designed to probe the swelling pressure. The modeled swelling pressure and its sensitivity to the dry density of clay were found to be in agreement with experimental data. The model provides an atomic level computational approach for the prediction of swelling pressure of bentonite clay in the context of geo-disposal of nuclear waste.

1. INTRODUCTION Swelling ability is one of the most important technical properties of bentonite clay when it is hydrated by the inflow of water.1 During swelling, the clay structure can absorb a large amount of water, affecting the movement of aqueous solutions and the transportation of chemical elements.2 Because of these properties, bentonite clays are favored as suitable barrier materials in the disposal of spent fuel nuclear waste.3,4 In underground repositories, the bentonite clay is expected to swell when in contact with water and fill the voids between the waste container and the wall rock providing sufficient sealing of the repository.5 The swelling is restricted by the surrounding wall rock. It gives rise to macroscopic swelling pressure, which acts uniformly on the surroundings.6 The development of swelling pressure is a key function of the barrier material, because it must be high enough to ensure good sealing performance5 but low enough to maintain the stability of the wall rock.7 Therefore, understanding the swelling process and the associated dynamics of swelling pressure is critical for evaluating the feasibility and optimizing the performance of bentonite clay for geo-disposal of nuclear waste.5,8,9 Swelling pressure has been studied intensively with experimental methods.10−15 Many studies have reported a wide range of swelling pressures from less than 1 MPa to about 60 MPa,5,11,12,16,17 depending on the experimental conditions. It is well-established that there is a strong, positive dependence of the swelling pressure of bentonites with density. Additionally, relative losses in swelling pressure for these materials with increasing solution salinity can also be expected. A number of models have been developed to investigate swelling mechanisms and to predict the swelling pressure of bentonite clay.6,9,18−20 The models fall into three main categories, namely, empirical and semiempirical models, diffuse double-layer models, and thermodynamic models. The models have been © 2015 American Chemical Society

used to predict the swelling characteristics of several types of bentonite clays. For instance, Low’s semiempirical model19,21 presents a simple way to relate swelling pressure to clay interlamellar distance. However, the model has been of limited use in actual applications because several empirical parameters are clay-specific and are hard to parametrize.6 Unlike Low’s model, the double-layer model and thermodynamic models are based on theoretical descriptions. The double-layer model is mainly focused on the distribution of ions between charged surfaces.9,16 However, the model performance is poor in cases of high clay densities, and the model is of limited use in concentrated salt solutions. Although the thermodynamic models are able to reasonably predict measured swelling pressure even at brine conditions,6,18,20 they hardly describe the effect of clay structure and lack mechanistic explanations of the swelling processes.6 The physicochemical nature of bentonite material is very complex. For example, the swelling mechanisms governing the regimes of crystalline and macroscopic swelling are significantly different.22 Moreover, these swelling processes and the dynamics of swelling pressure are regulated by multiple factors. The composition of the bentonite mineral,23−28 the interlayer cation species, total layer charge, substitution type, substitution distributions, and environmental conditions29−32 such as underground salt solutions, temperature, and pressure are important parameters in the swelling process. The experimental methods and the current modeling techniques do not provide atomic level understanding of the joint effect of changes in the compositional and environmental variables on the swelling pressure. Received: May 29, 2015 Revised: August 10, 2015 Published: August 11, 2015 19863

DOI: 10.1021/acs.jpcc.5b04972 J. Phys. Chem. C 2015, 119, 19863−19868

Article

The Journal of Physical Chemistry C

The dimensions of the simulation cell consisting of montmorillonite layers and bulk solutions are 2.06 × 10 × 10 nm3 (Figure 1b,c). Periodic boundary conditions were applied in all three directions. The simulation cell contained 16 montmorillonite unit-cells in the arrangement of 4 × 2 × 2. There were eight sodium interlayer cations and interlayer water. Three solution compositions were used in the modeling, namely, pure water, 0.25 M sodium chloride, and 0.25 M calcium chloride. The simulation cell contained about 6500 water molecules depending on the solution. 2.2. Spring Model. Based on the simulated clay structure, a spring model for probing the swelling pressure in the clay− water system was developed. In this model, the lower montmorillonite layer (Figure 2) is held completely rigid, i.e.,

Mechanistic models based on the forces and dynamics at atomic and molecular levels can provide a cost-effective way to simulate the complex interactions between clay material and the environment and to predict swelling pressures.33 The tool of choice in atomic level modeling of clay is molecular dynamics (MD) as it is a powerful technique for investigating the dynamic behavior of chemical systems. In the present study we aim at modeling and predicting swelling pressure on an atomic level by using MD simulations. The key advance in this regard is the imitation of experimental swelling pressure measurements. The study is also extended to the effects of environmental saline solutions on the swelling pressure.


2. MODELS AND COMPUTATIONAL DETAILS 2.1. Simulation Setup. The simulation setup included a small, model clay structure (Figure 1a) in contact with bulk

Figure 2. Illustration of the spring model. The bottom layer was fixed while the upper layer was allowed to move in the z-direction. The spring force is compensated by a swelling force. Figure 1. Simulation system containing two montmorillonite layers and a surrounding bulk solution. Panel a shows the two montmorillonite layers; panels b and c provide two views of the simulation cell. The d-spacing of the clay shown in the figure is 1.5 nm.

it is restrained in all three coordinate directions, while the upper montmorillonite layer is restrained in only the x- and ydirections. At an initial condition, a mechanical spring at equilibrium was attached to the upper montmorillonite layer. The spring has a force constant and follows Hooke’s law. As swelling expansion occurs, the displacement (in the positive zdirection) of the montmorillonite layer from its original position results in a compression of the spring from its relaxed (equilibrium) position and an increasing (restoring) spring force which serves to restrain the movement of the upper layer. In this process, the change in the spring length is equivalent to the change in the d-spacing of the clay structure. When the swelling reaches an equilibrium state, the force on the spring is assumed to be equal to the force of swelling. As such, the swelling forces and subsequently the swelling pressure can be calculated from the deformation of the spring. Because both clay layers were restrained in x- and y-directions, the deformation of the spring occurs only in the z-direction. To investigate the swelling pressure dependence on dry density, a series of simulations was performed using different spring constants and initial d-spacings. Spring constants ranging from 10 to 150 kJ mol−1 nm−2 and initial d-spacings from 1 to 3 nm were used. With a smaller spring constant, a greater clay swelling is expected. The swelling pressure was then calculated based on the deformation of the spring at equilibrium:

water solution (Figure 1b). The clay structure is composed of two layers of sodium montmorillonite, which is the main component of bentonite clay. The montmorillonite layer itself is an aluminosilicate, consisting of two tetrahedral layers sandwiching an octahedral sheet. Isomorphous replacements with lower-valency metal cations, Mg2+ and Fe2+ substituting Al3+ in the octahedral sheet and, to lesser degree, Al3+ substituting Si4+ in the tetrahedral sheets, give the structure a net negative charge. Here, only the substitution in octahedral sheets is considered. Na+ ions and water molecules filled the interlayer space and compensated the charge of the octahedral sheets. The bulk solutions containing water and ionic species surrounded the clay structure. To model the swelling pressure, the cations and water molecules, regardless of their original locations, were allowed to move and exchange freely between the interlayer and the surroundings in the model system. The chemical formula of the modeled Na-montmorillonite is Na0.5(Si8) (Al3.5Mg0.5)O20(OH)4. Because the swelling process relies primarily on water exchange and movement between the interlayer and the surrounding bulk solutions, the termination of at least one clay surface becomes necessary. Thus, two stacked montmorillonite layers were created with edge termination along the (010) surfaces.34,35 Each layer was continuous in the x-direction through periodic boundary conditions (Figure 1c). Along the y-direction, the clay structure was cut, and the resulting broken bonds at these edge surfaces were saturated by H, OH, and H2O groups.34,36 The terminated clay edges were used to provide the interface for the water and cation exchange between the interlayer and bulk solutions.

Ps =

Fswelling S

=

Fspring S

=

k × Δz S

(1)

where Ps is the swelling pressure, Fswelling the swelling force, and S the clay surface area. The swelling force was calculated as the product of the spring constant, k, and the average displacement, Δz, from the initial d-spacing. A given d-spacing was converted into a dry density as follows: 19864


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ρ=

mclay Vclay + Vinterlayer

(2)

where ρ is the dry density, mclay the solid mass of the clay structure, Vclay the volume of the clay layers, and Vinterlayer the volume of the interlayer space. 2.3. Molecular Dynamics Simulations. Water molecules and ions were initially randomly distributed in the simulation cell around the centered clay structure. The charge-balancing sodium ions were divided equally between each basal surface. First, energy minimization was performed, followed by an equilibration simulation of 1 ns with the fixed clay structure in the NPT ensemble at 1 bar and 300 K. The Berendsen barostat37 was used for pressure coupling, while temperature was maintained using the velocity rescaling thermostat.38 During the NPT simulations, the charge-balancing sodium ions were observed to move away from clay basal surface and become solvated in the presence of interlayer water. Actual swelling pressure simulations were then performed as a continuation in the NVT ensemble. The last 40 ns of the total simulation time of 50 ns were used for analysis. A timestep of 0.5 fs was employed, and data was collected after every 5 ps. The long-range Coulombic interactions were calculated using particle−mesh Ewald electrostatics (PME).39 The cutoff distance for short-range Coulomb and Lennard-Jones interactions was 9 Å. All simulations were performed using the Gromacs simulation package.40 The interaction forces were modeled by the CLAYFF force field,41 which represents water molecules with the flexible SPC model.42 CLAYFF force field together with SPC water model have been proven to be efficient parametrization for hydrated, multicomponent mineral systems and the interfaces with aqueous solutions.41,43,44 The force field parameters for the OH groups in the octahedral sheet and SPC water models were used to model the terminal OH and H2O groups coordinated to aluminum atoms, respectively. On the other hand, the broken bonds of edge silicon atoms were saturated by dissociation of SPC water molecules to form terminal OH groups. Hence, the overall layer charge was maintained, enabling also dynamic equilibrium of terminal water molecules with the bulk solution.

Figure 3. Unconstrained and constrained swelling of sodium montmorillonite in water. The initial d-spacing of the clay structure was 1.5 nm. The curves are running averages of 50 data points.

progress, two major swelling types were identified: the first swelling type was recognized as a stepwise swelling, and it mostly occurred to clay structures with smaller d-spacings; and the second represented a continuous swelling process, which was observed at larger d-spacings. 3.2. Swelling Pressure of Na-montmorillonite in Pure Water. It is well-known that sodium montmorillonite initially swells stepwise in water.1,45−48 This behavior is due to water layer formation in the interlayer space. In the present simulations, stepwise swelling was observed for clay structures with initially small d-spacings during the course of the swelling process. The goal of the simulations was the determination of the equilibrium swelling against a restraining force; thus, the initial stepwise swelling was not analyzed in further detail. In contrast to the stepwise swelling, the clay structures with larger d-spacings swell in a continuous manner. For each simulation, the swelled d-spacing was averaged and used in the calculation of swelling pressure. The calculated swelling pressure of Na-montmorillonite in pure water is shown in Figure 4. Each point represents an independent simulation using a different combination of initial d-spacing and spring constant. The simulations show that the swelling pressure declines quickly with increasing d-spacings.

3. RESULTS AND DISCUSSION 3.1. Validation of Spring Model. A short simulation was first performed for the pure water−clay system without the spring. The changes in d-spacing during the 10 ns simulation period are shown in Figure 3. In the absence of the spring, the maximum swelling of about 4.5 nm was reached soon after the simulation starts. This result is due to the finite size of the simulation cell. Water molecules were observed to move from the bulk water solution into the interlayer space. When the spring is included, the swelling of the clay structure levels off and is limited to d-spacings dependent on the value of the spring constant. The average d-spacings of the equilibration states decrease from 2.23 to 1.79 nm and further to 1.63 nm when the spring constant is increased from 10 to 50 to 150 kJ mol−1 nm−2. Further increases in the value of the force constant prohibits the movement of the clay layers, and no swelling is observed. The largest considered force constant is 150 kJ mol−1 nm−2, which restrains clay movements but still permits some swelling of the clay layers. In addition to the varying spring constant, the influence of the initial d-spacing was also considered. Based on the swelling

Figure 4. Simulated swelling pressure of Na-montmorillonite in pure water. The symbols represent simulations with different initial dspacings and spring constants. 19865


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The Journal of Physical Chemistry C Variation of the spring constants in more compact clay systems generated a spread of equilibrium d-spacings larger than that for those systems in which the clay was less compact. For the clay layers with very long separation, the simulated swelling will be limited because of the finite size of the simulation cell. By adjusting the initial d-spacing and spring constant, it is possible to simulate a wide range of swelling pressures as a function of d-spacing with high computational efficiency. There is some scatter in the simulated pressure values due to the fluctuations in the equilibrium distances in the simulations, as seen in Figure 3. This is related to the slight variations in the equilibrium structures comprising thousands of molecules. However, the overall trend is clear, and a curve can be reliably fitted to the calculated pressures. 3.3. Swelling Pressure of Na-montmorillonite in Salt Solutions. Simulated sodium montmorillonite swelling pressures in water, sodium chloride, and calcium chloride solutions as a function of clay dry density are shown in Figure 5. In general, the swelling pressures increase exponentially. The

tial relationship to the dry density. In the middle region of clay dry densities, the simulated swelling pressures were notably higher than the experimental values. In our simulation system, the clay flakes are perfectly packed and oriented, whereas the montmorillonite structures found in nature are more complex, containing both swelling and nonswelling compositions.13 The nonswelling clay components, such as other mineral impurities and the water in macropores, are not considered in the swelling pressure simulation. The primary reason for the swelling is, however, the penetration of water into the interlayer space, and the simulation results can be considered as upper limits for the swelling pressure. Overall, the rather small and simple molecular dynamics model reproduces surprisingly well the montmorillonite swelling trends in water and salt solutions.

Figure 5. Comparison of the simulated and experimental swelling pressures.14,49

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4. CONCLUSIONS A new computational approach for quantifying montmorillonite swelling pressure has been presented. The key idea in the method is the use of a restraining force to probe the swelling of a model clay structure in different solutions. The molecular dynamics simulations demonstrate that experimentally determined general swelling trends of sodium montmorillonite in pure water can be reproduced with good accuracy. The simulations were also extended to clay structures in salt solutions. Swelling pressures showed a marked decrease as the bulk solution changed from water to sodium chloride and calcium chloride solutions. The simulation results are again in line with experimental findings. Overall, this work provides a computational approach for the prediction of sodium montmorillonite swelling pressure in various solutions. The approach can be extended to other clay systems and is expected to be useful in the prediction and comparison of the swelling pressure of bentonite buffer in geologic nuclear waste disposal over a range of potential candidate materials and variations in the montmorillonite mineral.

pressures in the salt solutions are lower than that in pure water. This can be rationalized by the differences of the cation concentrations in different environments. Water moves to dilute the high salt concentration in the interlayer space. The larger the concentration difference, the higher the swelling pressure. The tendency of swelling is thus stronger in the case of pure water, resulting in larger swelling pressures. Compared to the swelling pressure in the sodium chloride solution, the swelling pressure in the calcium chloride solution was significantly lower. An explanation for the different swelling behavior can be traced to an exchange of Na+ for Ca2+ in the calcium chloride solutions. By inspecting the dynamic process of simulations, we found that the interlayer sodium ions are gradually exchanged for the calcium ions originating from the bulk solution. At the equilibrium state, the dominant cations in the interlayer region are thus calcium ions. Such an ion exchange process is also supported by experimental observations.50,51 By transforming from Na-montmorillonite to Camontmorillonite, the potential to swell macroscopically is largely reduced, as reflected in the lower swelling pressures. The simulated swelling pressures are compared to experimental results14,49 in Figure 5. For the three investigated systems, the fitted curves show exponentially increasing swelling pressure as dry density increases. The swelling pressures obtained from experiments show a similar exponen-

AUTHOR INFORMATION

Corresponding Author

*E-mail: tapani.pakkanen@uef.fi. Phone: +358 405028982. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Financial support provided by the Finnish Funding Agency for Technology and Innovation TEKES and the European Union/ European Regional Development Fund (ERDF) for the “Sliding Surfaces” project and Posiva Oy are gratefully acknowledged. The computations were made possible by use of the Finnish Grid Infrastructure resources.

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Estimation of Montmorillonite Swelling Pressure: A Molecular

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