Role of Cations in Adsorption of Supercritical Carbon Dioxide at

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Role of Cations in Adsorption of Supercritical Carbon Dioxide at Smectite Mineral-Water Interfaces: Molecular Dynamics and Adaptive Biasing Force Simulation Studies Mohan Maruthi Sena, and Marimuthu Krishnan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08594 • Publication Date (Web): 25 Dec 2018 Downloaded from http://pubs.acs.org on December 25, 2018

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The Journal of Physical Chemistry

Role of Cations in Adsorption of Supercritical Carbon Dioxide at Smectite Mineral-Water Interfaces: Molecular Dynamics and Adaptive Biasing Force Simulation Studies Mohan Maruthi Sena and M.Krishnan∗ Center for Computational Natural Sciences and Bioinformatics (CCNSB), International Institute of Information Technology-Hyderabad (IIIT-H), Gachibowli-500032 E-mail: [email protected] Phone: 040-66531447 Abstract The microscopic understanding of uptake and retention of supercritical carbon dioxide by expandable layered aluminosilicate minerals is of central importance for largescale geological sequestration of CO2 . At the molecular scale, the interlayer chargebalancing cations (CBCs) play a crucial role in CO2 adsorption by these cost-effective and environmentally-friendly materials. This Article investigates the influence of CBCs on the structure, dynamics and energetics of CO2 -H2 O mixtures nanoconfined in four different montmorillonites with different CBCs (Cs+ , K+ , Na+ and Ca2+ ) using molecular dynamics and enhanced sampling simulations. The results reveal that both CO2 and H2 O coexist in a single layer at the center of the interlayer, CO2 molecules orient parallel to the basal surface and form two-dimensional percolation paths that facilitate

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their lateral diffusion, and that the near-neighbor CO2 molecules preferentially adopt a distorted slipped-parallel geometry in all these systems. The calculated activation barriers for CO2 and H2 O to diffuse away from the first coordination shells of cations show that Cs+ -CO2 and Ca2+ -H2 O affinities are relatively higher than those for the other cations. The residence times in the cation coordination shells, relative orientations, and diffusion constants of intercalates are also quantified. The presented results can be useful for rational design of engineered layered minerals with improved CO2 retention capacity.

Introduction Expandable layered aluminosilicate minerals are promising candidates for use as cost-effective and environmentally-friendly adsorbents for a variety of environmental pollutants including nuclear wastes, heavy metals, toxic metal ions, and CO2 . 1–10 The natural abundance, nanoporosity, large surface area, and tunable charge density of these materials are some of their key attributes that are considered to be crucial for large-scale applications in agriculture, medicine, and environmental science 1–3,5–8,10–18 . Moreover, the rate of uptake of pollutants, affinity for specific contaminants, and the adsorption capacity of these minerals can be improved by means of suitable chemical modifications including functionalization, substitution, and intercalation of chemical species into their interlayer galleries. 19–24 The interlayer spacings of expandable smectite minerals (for example, montmorillonite and hectorite) increase upon intercalation of simple and complex molecules into their interlayer galleries. 25–29 The size, charge, affinity for clay surface, hydration/solvation energy, and concentration (which depends on the nature and number of isomorphic substitutions on the clay surface) of the charge-balancing cations (CBCs) that are adsorbed into the interlayer space critically control the intercalation and swelling of these layered materials. Moreover, the surface and interfacial chemistry of these expandable clay minerals can be 2


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tailored for specific applications by exchanging the interlayer cations with other alkali, alkaline metal cations, and other organic molecular cations (such as cetyltrimethylammonium bromide (CTAB), and cetyltrimethylammonium chloride). 9,30–32 The intercalation of scCO2 into smectite clay minerals has received increasing attention in recent years due to its implications in large-scale geological sequestration of CO2 . When the compressed CO2 is injected into the natural geological formations such as saline aquifers and depleted oil reservoirs located deep beneath the earth’s surface, it comes in contact with cap rocks that seal these reservoirs. Since the smectite clay minerals are one of the key constituents of the cap rocks, the CO2 retention capacity and adsorption/desorption energetics of these minerals are likely to depend critically on the nature of molecular interactions among CO2 , H2 O, cations, and clay surfaces. Thus, the molecular-level understanding of the structure, dynamics, interactions, and interfacial energetics of CO2 -H2 O binary mixtures confined in clay interlayers is of paramount importance to ensure a leak-proof, long-term geological storage of CO2 . 4,28,33–47 The microscopic investigation of the structure, dynamics, and energetics of the clayconfined intercalates remains experimentally challenging and nontrivial. Despite the ordered structure of the T-O-T framework, the relative positions and orientations of intercalates and cations vary with time, thus giving rise to static and dynamic disorder in the interlayer. Consequently, X-ray diffraction (XRD) fails to provide the atomic positions and dynamics of the interlayer species in these systems. However, XRD is commonly used to measure the interlayer spacing or d-spacing between the clay layers; 48–50 the variation of the d-spacing with intercalate concentration provides insights into the swelling behavior of clay minerals. Using 1

H, 2 H,

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C, alkali and alkaline earth elements, and transition metals as spin probes, NMR

characterizes the dynamics of intercalates, ions, and clay layers. 51–56 However, it is nontrivial to associate the observed NMR signals with unique dynamical processes. Moreover, the presence of paramagnetic iron impurities in clay minerals introduces additional complications into NMR signal interpretation. Neutron scattering studies including time-of-flight,

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neutron spin echo (NSE) and quasi-elastic neutron scattering studies have been limited to the investigation of water dynamics as the hydrogen atoms predominantly scatter the neutrons due to their large incoherent scattering cross-sections. 57–63 However, the presence of structural and dynamical heterogeneity in clay samples makes the direct interpretation of experimental results rather difficult and hence the neutron scattering studies generally rely on simple models to interpret the experimental data. The quartz crystal microbalance (QCM) experiments are used to determine the amount of intercalates in clay interlayers. 45 In addition to QCM, the hydration-dependent variation of the IR-derived integrated absorbance of the asymmetric CO stretching band of the interlayer CO2 molecules has also been used to quantify the amount of CO2 in the interlayer of Na-MMT at 50 0 C and 90 bar. 45 A common limitation of almost all of these experimental techniques is that they fail to distinguish the intercalates present on the exterior of the clay from those located in the interlayer galleries. While the effects of H2 O on the swelling behavior and the physiochemical properties of smectite clay minerals have been studied extensively, relatively little is known about the interlayer structure, cation-CO2 -H2 O-basal surface interaction energetics, and intercalate dynamics in CO2 -containing smectite clay hydrates. For instance, it is known that in the absence of CO2 , the CBCs are hydrated fully or partially by the interlayer water molecules and that the size, charge, and hydration energy of the cations critically influence the amount of H2 O molecules intercalated into clay interlayers and the degree of swelling of clay. 64–69 Furthermore, earlier experimental and simulation studies have shown that Na+ - and Ca2+ MMT can expand to form two layers of water (2WL) or more in the interlayer at higher hydration levels, while Cs+ -MMT cannot expand beyond a single water layer (1WL). 68,70–74 Following the experimental demonstration that CO2 can be incorporated into clay interlayers, the molecular-level structural and dynamical details of clay-confined CO2 are just beginning to emerge, but much remains to be understood about the nature of interactions between CO2 and CBCs, and the effects of pressure and temperature on CO2 uptake by clay minerals. 43,45,75–79 In situ high-pressure and high-temperature X-ray diffraction, infrared

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(IR), and NMR studies have shown that CO2 enters the interlayers of smectite clays under subsurface CO2 storage reservoir conditions. 28,43,45,75–80 The uptake of scCO2 by clays was observed to depend on the interlayer water content; 43–45,80,81 for instance, the intercalation of scCO2 was absent in dry Na-MMT, 43–45,80,81 and CO2 intercalation is favorable at monolayer (1WL) and sub-monolayer water coverages, while CO2 uptake is minimal or null at higher hydration levels. 28,75,77,78 Using XRD, Giesting et al. compared the swelling behavior of K-MMT and Ca-MMT and observed that K-MMT swelled faster than Ca-MMT. 78 The amount of CO2 adsorbed by Na-MMT and Ca-MMT measured at 50◦ C and at various pressures using QCM revealed that CO2 uptake is maximum at 90 bar (0.45 mmol of CO2 per gm of clay in Na-MMT) at submonolayer coverage. 80 A recent experimental study by Bowers et al. on the role of interlayer cations in CO2 adsorption by smectite minerals concluded that cations with smaller radii and larger hydration energies exhibit poor affinity for CO2 , but prefer to be hydrated by water. 82 Scheaf et al. demonstrated that scCO2 is readily adsorbed 47 into Cs+ - and NH+ 4 -montmorillonite.

The computational methods including molecular dynamics (MD), Monte Carlo (MC), and enhanced sampling simulations continue to play a vital role in elucidating the structure, dynamics, and energetics of various clay-confined intercalates. 50,60,83–94,94–96 The grand canonical Monte Carlo (GCMC) simulations carried out by Botan et al. demonstrated that the number of CO2 intercalated into the interlayer of Na-MMT decreases with increasing hydration and that the presence of CO2 influences the diffusion of other species in the interlayers. 97 Using a refined force field for CO2 developed by Cygan et al., 90 Krishnan et al. examined the structural arrangements, dynamics and interactions of CO2 confined in Na-MMT and Na-MMT-CO2 -polyethylene glycol (PEG) composites. 98 Myshakin et al. performed MD simulation of Na-MMT at various concentrations of H2 O/CO2 and concluded that swelling of clay upon CO2 intercalation depends on the initial H2 O content in the clay interlayers. 99 A density functional theory (DFT)-based MD study of hydrated Ca-MMT exposed to scCO2 and CO2 -SO2 mixtures observed the intercalation of CO2 at sub-monolayer

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coverage and a partial displacement of H2 O by CO2 from the Ca2+ coordination shell. 100 In our earlier study, we probed the structure, dynamics and energetics of CO2 /H2 O molecules in the interlayer of Na-MMT at monolayer coverage and observed the Na+ ions to exist in two different types of environments; one in which a cation was surrounded by four water molecules and in the other the cation was coordinated by three water molecules and one CO2 molecule. 92,93,98 Rao et al. investigated the effect of layer charge on H2 O/CO2 adsorption in Na-MMT and concluded that a higher surface charge and RH decrease the CO2 adsorption capacity and it has no effect on the diffusion of intercalates. 66 Loganathan et al. performed grand canonical molecular dynamics (GCMD) simulations of H2 O/CO2 confined in hectorite with different charge balancing cations (Li+ , Na+ , K+ , Rb+ , Cs+ , Mg2+ , Ca2+ , Sr2+ , and Ba2+ ) and showed that cations with larger ionic radii and lower solvation energies favor CO2 intercalation into the interlayer galleries. 101,102 Another MD study examined the permeability of CO2 /H2 O in Na-MMT and showed that the diffusion of the intercalates increases with increase in water concentration. 103 Kadoura et al. performed GCMC/MD simulations on Ca- and Mg-MMT at various RH and demonstrated poor affinity of CO2 for these cations, and consequently, the diffusion coefficient of CO2 was independent of the charge balancing cations in the interlayers. 94 Marami et al. performed MD and multiphase GCMC simulations to characterize the free energy of swelling of Na-MMT and Na-beidellite (Na-BEI) in the presence of H2 O/CO2 . Their results revealed that Na-MMT could expand to two-layers, while Na-BEI could not expand beyond one-water layer (1WL), and that the diffusion of intercalates were significantly retarded in clay confinement than their diffusion in bulk phases. 81 The present article investigates the role of cations in the structure, dynamics and energetics of CO2 /H2 O nanoconfined in MMT using molecular dynamics and enhanced sampling simulations. In particular, using different types of cations that differ in ionic size, charge, and hydration energy, the cation-intercalate coordination geometry, the mechanism and energetics of diffusion of H2 O and CO2 around cations in the clay interlayers are examined.

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Simulation Details The general chemical formula of the MMT models investigated here is given by Mx (Al3.5 M g0.5 )[Si7.75 Al0.25 ]O20 (OH4 ), where the label M (M = Cs+ , K+ , Na+ , Ca2+ ) denotes the alkali cation of interest, x=0.75 for Cs-, Na- and K-MMT, and x=0.375 for Ca-MMT. The simulated fullyflexible MMT models consisted of 128 crystallographic unit cells (8a x 8b x 2c) with two tetrahedral-octahedral-tetrahedral (T-O-T) layers, which are negatively charged due to the substitution of Mg2+ for Al3+ in the octahedral sheets and of Al3+ for Si4+ in the tetrahedral sheets. Each T-O-T layer consisted of 48 substitutions (8 substitutions of Si4+ by Al3+ in each tetrahedral layer and 32 substitutions of Al3+ by Mg2+ in each octahedral layer). The substitution sites in each layer are chosen randomly, but are separated from each other by at least one non-substituted site. The substitution sites, the number of substitutions, and the net negative charge on the clay surfaces are the same across all models investigated. The numbers of CBCs per interlayer space in the model systems are: 48 Cs+ in Cs-MMT, 48 K+ in K-MMT, 48 Na+ in Na-MMT, and 24 Ca2+ in Ca-MMT. In the initial structure, the CBCs are placed 2 ˚ A above the centers of the hexagonal (Si, Al)-O rings of the basal surface. The intercalated systems were prepared by suitably expanding the dry MMT and then randomly placing suitable numbers of H2 O and CO2 molecules in the interlayer galleries using PACKMOL. 104 The numbers of H2 O and CO2 molecules (4 H2 O/cation and 1.33 CO2 /cation) are taken from the the previous MD studies of Myshakin et al. that demonstrated the formation of a stable monolayer hydration state with a d-spacing of ∼ 12 ˚ A at these concentrations. 99 The intercalate concentrations used in our study are higher than those used in the study of Rao et al. (3.8 H2 O/cation and 0.6 CO2 /cation) 95 and of Kadoura et al. (3.73 H2 O/cation and 0.8 CO2 /cation). 94 Classical MD simulations were performed using the CLAYFF 85 force field for the host clay, the SPC model 105 for water and the refined CO2 parameters taken from an earlier study. 90 The MD simulations were carried out in NPT ensemble at a temperature of 323 K and a pressure of 90 bar 28,43–45,75,76,80 using the Langevin thermostat and barostat 106 with a damp7



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ing coefficient of 5 ps−1 using NAMD 2.9. 107 The periodic boundary conditions consistent with the symmetry of the unit cell were applied. The nonbonded interactions were truncated at 10 ˚ A and smoothed between 8 ˚ A and 10 ˚ A. The electrostatic interactions were calculated using the particle mesh Ewald (PME) 108 method with a real space cutoff of 10 ˚ A. The re˚3 grids using sixth-degree B ciprocal space interactions were calculated on 42 x 72 x 27 A splines. The equations of motion were integrated with a time step of 1 fs. The systems were subjected to energy minimization followed by 10 ns equilibration and 20 ns production runs. VMD 109 was used to visualize the interlayer structures and MD trajectories. The atomic density profiles, atomic projections onto the clay basal surface, mean square displacement and diffusion constants of intercalates around the charge balancing cations were calculated from the MD trajectories.

Adaptive Biasing Force Method The adaptive biasing force (ABF) method was used to determine the free energies associated with the diffusion of intercalates into and out of cation coordination shells. 110–113 The ABF calculations with the cation-water and cation-CO2 distances (denoted by rW and rC , respectively) as the reaction coordinates were performed using the collective variable module implemented in NAMD 2.9. 107 The reaction coordinates rW and rC describe the diffusion of H2 O and CO2 , respectively, from the cation coordination shell. The potential of mean force, F(ψ), as a function of the chosen reaction coordinate ψ (here, ψ = rW or rC ) is calculated from the following equation, ∂F (ψ) = ∂ψ

*

∂U (r) ∂ln|J| − kB T ∂ψ ∂ψ

+ = −hf iψ

(1)

ψ

where, U(r) is the potential energy of the system, J is the Jacobian related with the transformation of Cartesian coordinates to the generalized coordinates, T is the temperature, kB is the Boltzmann constant, and hf iψ is the average force determined at a given value of ψ. 8


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The angular brackets denote the statistical averages. The reaction coordinate ψ is divided into windows of equal size dψ. The average force hf iψ is computed in each bin during the course of the simulation and an exactly equal biasing force is added to the dynamic simulations to generate uniform sampling along the chosen reaction coordinate. The accelerated simulations were run for 200 ns for each reaction coordinate with forces accumulated in bins of width 0.1 ˚ A using NPT ensemble at 323 K and 90 bar pressure.

Results and discussion Atomic Z-Density Profiles: The computed atomic density profiles perpendicular to the clay surface for all the systems studied here are shown in Figure 1. The narrow atomic density peaks for the atoms in the T-O-T layers indicate the stability of the MMT structure during the entire simulation time. The computed values of the interlayer thickness are 6.04 ˚ A, 6.19 ˚ A, 6.0 ˚ A, and 5.48 ˚ A for Cs-, K-, Na-, and Ca-MMT, respectively, while the corresponding basal d-spacings are 12.5 ˚ A, 12.6 ˚ A, 12.5 ˚ A, and 12.0 ˚ A. In the absence of intercalates, the calculated values of interlayer thickness are 4.20 ˚ A, 3.5 ˚ A, 3.0 ˚ A, and 2.94 ˚ A for the dry Cs-MMT, K-MMT, Na-MMT, and Ca-MMT, respectively 93,98 and the corresponding values of d-spacings are 10.7 ˚ A, 10.0 ˚ A, 9.4 ˚ A, and 9.36 ˚ A, respectively. A comparison of dry and intercalated systems reveals that the interlayer thickness is increased by 1.84 ˚ A, 3.04 ˚ A, 3.0 ˚ A, and 2.54 ˚ A for Cs-MMT, K-MMT, Na-MMT, and Ca-MMT, respectively, upon intercalation of H2 O and CO2 . Similarly, the d-spacing also increased by 1.8 ˚ A, 2.6 ˚ A, 3.1 ˚ A, and 2.64 ˚ A for Cs-MMT, K-MMT, NaMMT, and Ca-MMT, respectively. The calculated values of intercalate-induced interlayer expansion are in reasonable agreement with previous experimental

4,28,43,45,75–77,114–116

and

simulation studies. 63,90,91,93,97,99,117,118 The nature of distribution of cations in the interlayers differ significantly among the

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systems under consideration. The z-density profiles for Cs+ ions in Cs-MMT and K+ ions in K-MMT exhibit two peaks at z = ±0.77 ˚ A, and z = ±1.28 ˚ A, respectively. The distribution for Na+ ions in Na-MMT exhibits intense peaks at z = ±0.95 ˚ A, representing near-surface Na+ , and shoulders at z = ±0.55 ˚ A, representing Na+ displaced from the basal surface toward the center of the interlayer. The distributions for all monovalent cations are almost symmetric about the mid-plane of the interlayer indicating that the cations are equally shared by the two basal surfaces bordering the interlayer space. However, the Ca2+ ions in Ca-MMT exhibit more than two peaks at z = ±1.7 ˚ A and z = ±0.72 ˚ A. The peaks at z = ±1.7 ˚ A are due to surface-bound cations, while the other peaks at z = ±0.72 ˚ A are due to the cations desorbed and migrated from the surface to the center of the interlayer to get hydrated by the water molecules. The results show that the number of hydrated Ca2+ ions is relatively higher than that of the surface-bound ions. In order to estimate the mean distance between the two layers of the surface-bound cations, we calculated the separation between the corresponding peaks in the cation density distribution and the corresponding values are 1.5 ˚ A and 2.5 ˚ A for Cs+ and K+ , respectively. The calculated distances between the near-surface Ca2+ layers in Ca-MMT and near-surface Na+ layers in Na-MMT are 3.5 ˚ Aand 1.9 ˚ A, respectively, while the corresponding distances between the far-surface cation layers are 1.47 ˚ A, and 1.1 ˚ A. The separation between the peaks corresponding to the surface-bound cations and the basal oxygens of the nearest basal surface provides a measure of the mean distance between the basal surface and the surface-bound cations. The calculated mean cation-surface distances are 2.25 ˚ A, 1.8 ˚ A, and 1.02 ˚ A for Cs+ , K+ , and Ca2+ , respectively. The visual inspection of MD trajectories reveals that most Ca2+ ions in Ca-MMT are surrounded by H2 O molecules, but a small fraction of Ca2+ ions remain bound to the surface during the entire course of the simulation. Although Ca2+ possesses a higher hydration energy than other cations, a comparison of the distance between the surface-bound cation layer and the nearest basal surface shows that the surface-bound Ca2+ ions are relatively closer to basal

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surface than other cations considered. This observation is indicative of the fact that the cation-surface interactions are relatively stronger for Ca2+ than for the other cations. The nonzero cation density at the center (i.e., at z = 0) of interlayer suggests that the cations are able to diffuse between the two basal surfaces of the interlayer. The absence of cation diffusion in dry Na-MMT and Na-MMT-CO2 observed in earlier studies 98 underscores the essential role of water in the transport of cations in clay interlayers. The peaks at z = 0 in the atomic density profiles of the oxygen atoms (Ow ) of H2 O and the oxygen (Oc ) and carbon (Cc ) atoms of CO2 indicate that both water and CO2 coexist in a single layer at the center of interlayer. Since the atomic density profiles of both Oc and Cc of CO2 are peaked at z = 0, it can be concluded that CO2 molecules lie flat on the basal surface. The distributions of oxygen atoms (Ow ) of water molecules in

Figure 1: Atomic z-density profiles for a) Cs-MMT, b) K-MMT, c) Ca-MMT, and d) NaMMT. Here, z = 0 denotes the center of the interlayer. Cs-MMT and Ca-MMT exhibit a single peak around z = 0 indicating the formation of a single layer of water at the center of interlayer (Figure 1). The distribution Ow in Cs11



MMT is relatively broader than that in other systems indicating a relatively higher degree of disorder in the z positions of Ow in the monolayer at the center of the interlayer of CsMMT. To quantify the degree of disorder in water positions, we calculated the full width at half maximum (FWHM) of the atomic density distributions of water oxygens by fitting them with normalized Gaussian functions. The higher the FWHM, the higher the degree of disorder in water arrangement in the interlayer. The FWHM values for Cs-MMT and Ca-MMT are 1.69 ˚ A and 0.63 ˚ A, respectively, which reaffirms that H2 O molecules are more disordered in Cs-MMT than other systems due to weaker interactions between Cs+ and H2 O molecules. Similarly, we estimated the values of FWHM for carbon atoms of CO2 to be 0.73 ˚ A, 0.75 ˚ A, and 0.44 ˚ A in Cs-MMT, K-MMT, and Ca-MMT, respectively. The FWHM for carbon atoms of CO2 molecules in K-MMT is slightly higher than that in Cs-and Ca-MMT indicating a slightly higher degree of packing disorder of CO2 molecules in K-MMT. Unlike other systems, the calculated distribution of Ow in K-MMT (Figure 1 (b)) exhibits two peaks at around z = 0. The observed split in the water distribution is due to the formation of a partial split of a single layer of water molecules, which are sandwiched between layers of surface-bound cations on either side, and a few cations desorbed from the surface are located between the water layers in K-MMT.

Interlayer Structure of Intercalates and Cations The structural arrangement of clay-confined intercalates and cations parallel to the basal surface provides insights into critical interactions among intercalated species and the basal surfaces. Figure 2 shows the lateral arrangement of the intercalates and cations at different instants of time during the course of the simulation. These snapshots reveal that the molecular axes of almost all CO2 molecules are oriented parallel to the basal surface, that most CO2 molecules have at least one near-neighbor CO2 molecule, and that the water molecules prefer to cluster around the cations in the clay interlayer. The interactions between the neighboring

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Figure 2: Snapshots showing the structural arrangement of intercalated molecules on one of the basal surfaces of 1) Cs-MMT, 2) K-MMT, and 3) Ca-MMT; a, b, c, and d indicate the intercalates arrangements at 3 ns, 6 ns, 9 ns, and 12 ns respectively. Cs+ (brown), K+ (tan) and Ca2+ (magenta); H2 O (red/white), CO2 (green); pairs of near-neighbor CO2 molecules in distorted slipped-parallel (black-circle) and T-shape (yellow circle) arrangements are shown. A few representative percolation paths formed by clusters of CO2 molecules are shown in blue color. 13



CO2 molecules favor their clustering in the interlayer, which in turn leads to the formation of percolation paths (Figure 2) for their facile lateral diffusion parallel to the basal surface. These percolation paths are dynamic in nature in that they break and reform at different locations at different instants of time depending upon the positions of cations and other intercalates. A careful examination of relative orientations of near-neighbor CO2 molecules reveals that most pairs of near-neighbor CO2 molecules prefer a distorted slipped parallel geometry and some adopt T-shaped geometry in the interlayer galleries of the model systems investigated here. The snapshots showing the arrangement of near-neighbor CO2 molecules in distorted slipped-parallel and T-shape geometries in various systems are presented in Figure S7. Similar CO2 -CO2 coordination geometries have been observed in previous experimental and theoretical studies on CO2 in bulk and in the confinement of the interlayer galleries of Na-MMT. 93,98,119–123

Planar Atomic Density Distributions The planar atomic density distributions provide detailed atomistic insights into the three dimensional distribution of intercalates around interlayer cations and on the basal surface. The calculated planar atomic density distributions for all systems considered in this study are shown in Figure 3. In all the systems considered, the cations are found in two distinct environments; one at the center of hexagonal ring (referred here as site-I) and the other at the point of intersection of three (Si, Al)-O hexagonal rings (referred here as site-II). The cations at site-I are observed to be highly localized (shown in green color in Figure 3) near the basal surface, while the remaining cations desorb and diffuse away from the basal surface and reach the ditrigonal cavities at the point of intersection of the three (Si, Al)-O hexagonal rings. The locations of site-II cations on a given basal surface actually correspond to the centers of hexagonal rings of the other surface of the interlayer. The dynamic exchange of cations between site-I and site-II was observed during the course of simulation. However,

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Figure 3: Probability density maps of cations (a-c) and intercalates (d-f) on one of the basal surfaces of (a, d) Cs-MMT, (b, e) K-MMT, and (c, f) Ca-MMT (green: site-I cations; magenta and white: site-II cations; blue: carbon of CO2 ; red: oxygen of H2 O). the rate of site-I → site-II hopping of cations was slightly greater than that for site-II → site-I transitions. The observed difference in rates of transitions between these cation sites can be attributed to strong interactions between the cations and the basal oxygen atoms, which are slightly weaker at site-II compared to those at site-I. The degree of fluctuations of Cs+ ions both at site-I and site-II of Cs-MMT is relatively less compared to the fluctuations of other cations in other systems, which can be attributed to the difference in sizes of these ions. The higher ionic radius of Cs+ optimizes its van der Waals contacts with the basal oxygens at site-I and site-II resulting in its localization at these sites. On contrary, owing to their smaller sizes, K+ , Na+ and Ca2+ ions do not fit

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perfectly at site-I and site-II and they continually fluctuate between different neighboring basal oxygens surrounding site-I and site-II. Figure 3 shows the distributions of intercalates around cations on the basal surfaces of the model systems studied. The circular patterns of water density around site-I cations are due to site hopping of the coordinated water molecules to dynamically change the H-bonds with different basal oxygens of hexagonal rings of the basal surface. The site-II cations desorbed from the surface interact with both H2 O and CO2 . In Cs-MMT, the Cs+ ions at site-I are surrounded by four H2 O molecules (type-I), while site-II cations are surrounded by either 2 H2 O and 2 CO2 molecules or by 1 H2 O and 3 CO2 molecules (type-II). Examination of the coordination geometry of type-I cations reveals that three of four water molecules coordinated to a cation are located almost directly above the basal oxygens (OB ) at the intersection of three (Si, Al)-O hexagonal rings of the basal surface. Each of these three coordinated water molecules are oriented such that one of its hydrogen atoms are pointed towards the corresponding basal oxygen underneath of it so as to establish a H-bond with the basal surface. The fourth coordinated water molecule is located above the center of the Cs+ -containing hexagonal ring and is stabilized by cation-water interactions and water-water H-bonds with other coordinated water molecules as observed in Na-MMT. 93 A similar cation-intercalate coordination geometry was observed for both type-I and typeII cations in other model systems studied (Figure 3). The type-II cations are surrounded by 3 H2 O and 1 CO2 molecules in K-MMT indicating a relatively weaker interaction of K+ with CO2 compared to the Cs+ -CO2 interactions. Although both site-I and site-II are occupied by K+ ions in K-MMT, the probability for the cation to be located at site-I is relatively less compared to that of site-II. The K+ ions diffuse/hop along the edges of hexagonal rings to move between different site-II sites on the basal surface. Although both site-I and site-II cations are also observed in Ca-MMT, Ca2+ ions are solvated only by H2 O molecules and CO2 molecules could never enter the first coordination shells of Ca2+ ions during the course of the simulation, which is indicative of weaker Ca2+ -

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CO2 interactions in Ca-MMT.

Orientation of Carbon Dioxide In order to further characterize the relative orientations of near-neighbor CO2 pairs, we calculated the distribution of the angle, χ, between the long-axes of pairs of nearest-neighbor CO2 molecules. The value of χ would be 90◦ for a pair oriented perpendicular to each other, while χ=0◦ or 180◦ when they are parallel to each other. Figure 4 shows the distribution of χ (P(χ)) for all the systems considered in the present study. In general, the calculated P(χ) are symmetric about χ=90◦ and exhibit two broad peaks at 27◦ and 155◦ . If CO2 molecules are randomly oriented in the interlayer, P(χ) would be a uniform distribution such that all values of χ would be equally likely. The presence of peaks in the calculated P(χ) suggests that the clay-confined CO2 molecules are not randomly oriented, but certain relative orientations are preferred by pairs of nearest-neighbor CO2 molecules. The peaks observed at χ < 30◦ and χ > 150◦ reaffirm that the distorted slipped-parallel orientation is most preferred by the pairs of near-neighbor CO2 molecules. The non-zero minimum at χ=90◦ in the distribution indicates that the T-shaped geometry is relatively less probable than the distorted slippedparallel geometry for CO2 pairs in the interlayer galleries of smectite clays. A few cation-sensitive variations in P(χ) merit further attention. The value of P(χ) at χ=90◦ is relatively higher and the distribution is relatively broader in Ca-MMT than in other systems. In fact, P(χ) is much closer to a uniform distribution for Ca-MMT than for other systems, which suggests that the degree of disorder in the orientations of CO2 molecules is high in Ca-MMT than in other systems. The higher orientational disorder of CO2 in Ca-MMT can be attributed to its weaker affinity for Ca2+ ions. Unlike in other systems, P(χ) for Cs-MMT shows shoulders at around χ=60◦ and χ=120◦ , which are indicative of additional orientational order of near-neighbor CO2 molecules in Cs-MMT. Visual inspection of MD trajectories reveals that at least one of CO2 molecules in each pair contributing to

17



Figure 4: Distribution of angle χ between two near-neighbor CO2 molecules in Cs-MMT (blue), K-MMT (red), Ca-MMT (blue), and Na-MMT (green). the shoulders is coordinated to Cs+ ions in Cs-MMT (Figure S4 - SI). Unlike the distorted slipped-parallel and T-shaped geometries that are primarily due to CO2 -CO2 interactions, the orientational ordering corresponding to the shoulders observed in P(χ) is primarily due to Cs+ -CO2 interactions.

Orientation of Interlayer Water Molecules The orientations of clay-confined water molecules critically control the nature and stability of water-water and water-mineral H-bonding networks in the interlayer, which in turn influence the relative orientations, dynamics and energetics of cations and other intercalates in the system. To understand the effects of charge balancing cations on the orientation of H2 O molecules in the interlayer, we calculate four different angles θ, φ, ψ, and η for individual water molecules; here, θ is the angle between the basal surface normal (SN), which in our case is the z-axis, and the dipole vector of the water molecule, φ is the angle between SN and a O-H bond vector of the H2 O molecule, ψ is the angle between SN and the normal to the molecular plane of the water molecule, and η is the angle between the projection vector of the water bisector on the XY-plane and the X-axis. Figure 5(a) shows the distribution of θ, P(θ), for all the systems studied. For K-MMT,

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Figure 5: Distributions of the (a) angle between SN and the dipole vector of H2 O for different systems considered, (b) angle between SN and O-H vector of H2 O molecule, (c) angle between the normal to the molecular plane of a water molecules and SN, (d) angle (η) between SN and XY component of the bisector vector of H2 O molecule. P(θ) is bimodal in nature and it is symmetric about θ = 90◦ with two peaks at 62◦ and 118◦ that are separated by a minimum at 90◦ . Each peak is due to water molecules associated with the surface-bound cations in the interlayer. Given that θ = 90◦ for a water molecule whose dipole vector is oriented parallel to the basal surface, ±28◦ deviations of the peak positions from 90◦ indicate that the dipole vectors of majority of water molecules are titled at an angle of ± 28◦ with respect to the basal surface of K-MMT. The shoulders observed at θ < 30◦ and θ > 150◦ are due to the near-surface water molecules located at the centers of the hexagonal rings of the basal surface and interact directly with the surface. Both hydrogen atoms of these water molecules are pointed towards the surface in such a way that the water dipole vectors are oriented almost parallel or anti-parallel to the basal surface normal (Figure S5 - Supporting Information), while their oxygen atoms can interact with cations or other far-surface water molecules. In fact, these near-surface water molecules contribute to the non-Gaussian tails in the z-density distributions of Ow shown in Figure 1 (Figure S5 - Supporting Information). 19



The water molecules in Cs-MMT and Na-MMT also exhibit a bimodal distribution of θ. The peaks are observed at θ=72.4◦ and θ=109.4◦ for Cs-MMT and at θ=68◦ and θ=113.7◦ for Na-MMT. The calculated deviations of these peaks from 90o are ±18◦ for Cs-MMT and ±22◦ for Na-MMT, which are relatively less compared to those in K-MMT, suggesting that the angles of tilt of the dipole vectors of the water molecules with respect to the basal surface are less in Cs-MMT and Na-MMT than in K-MMT. Here again, the broad shoulders observed at θ < 30◦ and θ > 154◦ are due to a significant number of near-surface H2 O molecules whose dipole vectors are oriented towards the basal surface. The variation in the depths of the minima at 90◦ suggests that the probability for the water molecules to lie flat on the basal surface is less in K-MMT than the other systems investigated here. Unlike Cs-MMT, Na-MMT and K-MMT, the distribution of θ for Ca-MMT shows a broad peak at 90o indicating that a majority of the water molecules in Ca-MMT prefer to have their dipole vectors oriented parallel to the basal surface. The degree of tilt of the water dipoles with respect to the basal surface is likely to be lower if the cation-water interaction is stronger than the surface-H2 O interactions. The calculated mean values of θ are 89.2◦ ±35◦ , 90.1◦ ±37◦ , 89.8◦ ±34◦ and 88.7◦ ±26.7◦ for Cs-, K-, Na-, and Ca-MMT, respectively. The distributions of φ shown in Figure 5 (b) are, in general, symmetric about 90◦ for all the systems studied. P(φ) for K-MMT has three peaks; a broad peak at φ ∼ 90◦ , and two other peaks at φ ∼ 22.7◦ and φ ∼ 159.8◦ . The broad peak at φ ∼ 90◦ is due to the water molecules with their O-H vectors oriented parallel to the basal surface to optimize the Hbond interactions with other neighboring H2 O molecules and the cation-water interactions. The peaks at φ ∼ 22.7◦ and φ ∼ 159.8◦ are due to water molecules whose O-H vectors point towards (downwards or upwards) the basal surface to establish H-bonds with the basal oxygen atoms. For Cs-MMT, P(φ) exhibits peaks at ∼27◦ , ∼65◦ , ∼117◦ , and ∼155◦ . The peaks at φ ∼ 65◦ and φ ∼ 117◦ separated by a minimum at φ ∼ 90◦ suggest that the O-H vectors of a significant number of water molecules are tilted by 25-27◦ with respect to the basal surface. This could be due to the fact that the Cs+ -basal surface interactions are

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relatively stronger than Cs+ -water interactions in Cs-MMT, which results in orientational changes in O-H bond of water molecules to optimize Cs+ -water and water-basal surface interactions. The peaks at φ ∼ 65◦ and φ ∼ 117◦ separated by a minimum at φ ∼ 90◦ suggest that the O-H vectors of a significant number of water molecules are tilted by 25-27◦ with respect to the basal surface in order to optimize Cs+ -water and water-basal surface interactions in Cs-MMT. The observed tilt of O-H vectors of water molecules with respect to the basal surface also indicates that the Cs+ -basal surface interactions are relatively stronger than Cs+ -water interactions in Cs-MMT. For Ca-MMT, a bimodal P(φ) is observed with peaks at φ ∼ 47◦ and φ ∼ 135◦ that are separated by a minimum at φ ∼ 90◦ . Given that the most probable value of θ in Ca-MMT is 90◦ , that the water dipole vector bisects that H-O-H angle, and that the O-H vectors make an angle of 47◦ or 135◦ with the SN, it is inferred that the molecular planes of water molecules are not parallel to the basal surface, but are tilted by some degree. P(ψ) for all systems considered are shown in Figure 5c. ψ = 0o or 180o for H2 O molecules lying flat on the basal surface, while deviations from these values would correspond to situations in which water molecules are tilted with respect to the basal surface. In all the systems considered, the angle ψ has an intense peak at ψ ∼ 90o indicating that the molecular planes of a majority of water molecules are almost perpendicular to the basal surfaces in all the systems studied. This orientation is preferred by water molecules to optimize the hydrogen bonds with the basal surface. The shoulders at ψ < 30o and ψ > 150o are due to some H2 O molecules oriented parallel to the surface. P(η) for all systems considered are shown in Figure 5d. The angle η provides information about the preferential orientation of each H2 O molecule on the clay surface. P(η) for CsMMT, K-MMT, and Na-MMT resemble a uniform distribution suggesting that all values of η are equally likely and that there is no preferential lateral orientation for H2 O molecules in these systems. However, in Ca-MMT, P(η) shows peaks at η ∼49◦ and ∼143◦ suggesting that H2 O molecules have preferred orientations on the clay surface of Ca-MMT. The observed

21



differences in the orientation of interlayer water molecules showcase the essential role of charge balancing cations in balancing the interplay between intercalate-surface, intercalateintercalate, and cation-intercalate-surface interactions in the interlayer galleries of smectite clays.

Cation-Intercalate Interaction Energy

Figure 6: Distributions of a) cation-H2 O b) cation-CO2 interaction energies. The cation-intercalate interaction energies (i.e., a sum of the van der Waals and electrostatic energies) of individual cations were calculated from MD trajectories to quantify the 22


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solvation energies of the interlayer cations. Figure 6 shows the distributions of the cationintercalate interaction energies of different types of interlayer cations studied here. The calculated cation-H2 O interaction energies are at least an order of magnitude greater than those for cation-CO2 interactions, which suggests that the cations have relatively higher affinity for water than for CO2 . The distributions of Cs+ -H2 O, K+ -H2 O, and Na+ -H2 O interaction energies are peaked at -34.4 kcal/mol, -45.8 kcal/mol, and -72.8 kcal/mol, respectively, while that of Ca2+ -H2 O interaction energy has an intense peak at around -165.9 kcal/mol and has additional peaks at ∼ -211 kcal/mol, -120.8 kcal/mol, -78.8 kcal/mol and -35.1 kcal/mol. The multiple peaks for Ca2+ -H2 O molecules indicate heterogeneity in the environments of Ca2+ ions in Ca-MMT. The Ca2+ ions solvated by four water molecules (i.e., with a complete solvation shell) contribute to the intense peak in the interaction energy distribution, while partially hydrated Ca2+ ions contribute to the other peaks in the distribution (Figure 6 (a)). The peak at -211 kcal/mol is due to the Ca2+ ion surrounding by five H2 O molecules. The observed differences in the distribution of cation-H2 O interaction energy are indicative of higher affinity of H2 O for Ca2+ ions than for other cations. The calculated mean cation-H2 O interaction energies of Cs+ , K+ , Na+ and Ca2+ are -35.7±17.5 kcal/mol, -45.8±17.8 kcal/mol, -74.1±17 kcal/mol, and -161.5±39 kcal/mol, respectively. The order of cation-water affinity determined in this study is in agreement with previous experimental and MD studies. 82,102,124 The distributions of cation-CO2 interaction energy are shown in Figure 9(b). The calculated cation-CO2 interaction energies are at least an order of magnitude less than cationwater interaction energies indicating that the cations interact to a lesser extent with CO2 than with H2 O in all the systems considered. The distribution of cation-CO2 interaction energy is peaked at -1.9 kcal/mol, -2.0 kcal/mol, -2.02 kcal/mol, and -2.48 kcal/mol for CsMMT, K-MMT, Na-MMT, and Ca-MMT, respectively. Although the peak positions in all four systems are approximately equal, the difference in intensity in the tail part (-13.3 < E < -10.7 kcal/mol) suggests that a significant fraction of CO2 molecules interact strongly with

23



Cs+ in Cs-MMT. The calculated mean cation-CO2 energies are -4.1±2.8 kcal/mol, -3.9±2.7 kcal/mol, -3.4±2.4 kcal/mol, and -2.6±18 kcal/mol for Cs-MMT, K-MMT, Na-MMT, and Ca-MMT, respectively.

Potential of Mean Force of Intercalates

Figure 7: Potential of mean force (PMF) profiles (GX (rw ) and GX (rc )) as a function of the distance between the a) cation and oxygen atom of H2 O (rw ), and b) cation and oxygen atom of CO2 (rc ).

The PMF profiles as a function of cation-water (rw ) and cation-CO2 (rc ) distances calculated from ABF simulations are shown in Figure 7(a) and 7(b), respectively, for different systems studied. The calculated PMF profiles provide energetic insights into the molecular factors governing cation-CO2 and cation-H2 O affinities, the solvation structure of the cations, and the activation energy for the exchange of H2 O and CO2 between the first two 24


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coordination shells of the cations in clay confinement. GCs (rw ) shows a first minimum at rw ∼3.01 ˚ A, an energy barrier at rw ∼4.2 ˚ A and a second minimum at rw ∼5.5 ˚ A. The favorable cation-water interactions, H2 O-H2 O and water-basal oxygen H-bonding interactions contribute significantly to the stabilization of H2 O in the first coordination shell of the cation. The second minimum at rw ∼ 5.5 ˚ A is ∼1.3 kcal/mol less stable than the first minimum. A water molecule with rw > 6.5 ˚ A is located in water-rich regions and stabilized by H-bonding with surrounding water molecules and the basal oxygens (OB ). The calculated activation barrier (denoted by Gw 1→2 ) for the exchange of H2 O from the first coordination to the second coordination shell of Cs+ is ∼2.1 kcal/mol, whereas the energy cost (denoted by Gw 2→3 ) for H2 O to displace out of the second coordination shell into higher coordination shells is ∼0.5 kcal/mol. GCs (rc ), which quantifies the cation-CO2 affinity, exhibits a first energy minimum at rc ∼3.19 ˚ A and a second minimum at rc ∼5.2 ˚ A. An activation barrier, which quantifies the activation energy (denoted by Gc1→2 ) required for a CO2 molecule to move out of the first coordination shell of Cs+ , of 1.7 kcal/mol is located between the first two coordination shells at rc ∼4.4 ˚ A. G(rc ) saturates at rc > 8.6 ˚ A, and the saturation value is ∼ 1.2 kcal/mol, which is 2 times higher than that for CO2 in Na-MMT. 93 A comparison of GCs (rw ) and GCs (rc ) reveals that the width of the first energy well is greater and G1→2 is smaller (by ∼0.5 kcal/mol) for CO2 than those for H2 O. These differences indicate that CO2 is relatively less restricted in the first coordination shell of Cs+ than H2 O. GCs (rc ) calculated for CO2 in the hydrated Cs-MMT differs significantly from GN a (rc ) of Na-MMT. 93 Unlike Cs-MMT, there is no well-defined first minimum in GN a (rc ) of Na-MMT indicating that the affinity of CO2 for Cs+ is a factor of ∼3 higher than that for Na+ . Also, the calculated Gc1→2 is ∼0.5 kcal/mol less in Na-MMT than that in Cs-MMT. The stronger interaction of CO2 with Cs+ than Na+ -CO2 interaction can be attributed to the larger atomic size of Cs+ ion. An important consequence of the higher affinity of CO2 for Cs+ is that the Cs-MMT is likely to retain the intercalated CO2 for a longer period of time than Na-MMT.

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Although the higher CO2 affinity and retention capacity of Cs-MMT than Na-MMT may suggest that Cs-MMT-rich deep geological repositories could be potential sites for long-term storage of CO2 , the lower relative natural abundance of Cs+ stresses the need to investigate CO2 adsorption in other clay minerals containing naturally abundant alkali metal cations including Na-MMT. 125,126 The calculated PMF profiles GCa (rw ) and GCa (rc ) are used to characterize the Ca2+ H2 O and Ca2+ -CO2 affinities, respectively, in Ca-MMT. GCa (rw ) exhibits a first minimum at rw ∼2.38 ˚ A, a second minimum at rw ∼4.4 ˚ A, and the first energy barrier of 7.2 kcal/mol at ∼3.4 ˚ A. The depth of the first minimum and the height of the first activation barrier are significantly higher than those for other cations investigated in the present study, which indicates that Ca2+ has the highest affinity (at least a factor of three greater than that for other ions) for water in the interlayer of hydrated MMT. The energy penalty for a water molecule to move out of the first coordination shell of Ca2+ is at least ∼3 times greater than that for other cations. On contrary, Ca2+ exhibits lowest affinity for interlayer CO2 molecules than other cations. The absence of the first minimum in GCa (rc ) (Figure 7b) for rc < 4 ˚ A demonstrates weak interactions between CO2 and Ca2+ ions in Ca-MMT. Instead of a globlal energy minimum, only a minor dip is observed in GCa (rc ) at rc ∼ 3.0 ˚ A. The coordination state corresponding to this hump is at least ∼3 kcal/mol less stable than the most stable minimum observed at rc ∼ 5.2 ˚ A, which corresponds to the second coordination shell of Ca2+ . For K-MMT, GK (rw ) shows a first minimum at rw ∼ 2.8 ˚ A, a energy barrier at rw ∼4.2 ˚ A and a second minimum at rw ∼ 5.06 ˚ A. The free energy of the second minimum is 1.4 kcal/mol higher than that of the first minimum and Gw 1→2 =1.76 kcal/mol. GK (rc ) shows a first minimum at ∼ 2.97 ˚ A, a barrier at ∼ 4.1 ˚ A, and second minimum at ∼ 5.18 ˚ A. The activation energy for a CO2 molecule to move out of the first coordination shell (∆G1→2 ) is 1.3 kcal/mol. The presence of non-negligible activation barriers in G(rc ) at lower cation-CO2 distances (rc < 4 ˚ A) for all cations, except Ca2+ , indicates a higher affinity of CO2 towards

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these cations in smectite clay interlayers. At the hydration of 4 H2 O per cation considered in the present study, the observed order of cation-CO2 affinity is Cs+ > K+ > Na+ > Ca2+ . However, it is to be noted that the cation-CO2 affinity and the amount of CO2 intercalated are sensitive to the hydration level of the clay. For instance, interlayer expansion occurs on exposure of mono- and sub-monohydrated montmorillonites to anhydrous CO2 , while the interlayer spacing may increase or decrease upon intercalation of CO2 at higher hydration levels. 28,44,80 The experimental QCM studies have also demonstrated that higher amounts of CO2 (1-2 CO2 per unit cell with 4-6 mmol/g of clay) is adsorbed by Ca-MMT than into Na-MMT at 2.6 H2 O/cation and that the amount of CO2 adsorbed by Ca-MMT decreases with increase in the interlayer water content. 80 The observed order of affinity of interlayer cations for H2 O is Ca2+ > Na+ > Cs+ > K+ . A similar order of cation-water affinity was observed in recent experimental NMR studies on other smectite clay minerals at various hydration levels. 82

Mean Square Displacement The MD-derived mean square displacements (MSD) (hr2 (t)i) of cations, H2 O, and CO2 are shown in Figure 8 and their time averages obtained from MD trajectory (i.e., hh r2 ii R t=tmax 2 1 hr (t)idt; here, tmin = 5 ns and tmax = 10 ns) are presented in Table = (tmax −t t=tmin min ) 1. A cation with a higher affinity for intercalates is likely to have a lower hhr2 ii and a lower diffusion coefficient than those that interact weakly with intercalates. Similarly, the intercalates that interact strongly with the cations and the basal surfaces are likely to be less diffusive than those that interact weakly with them. The cation-intercalate, cationclay, and cation-cation, intercalate-intercalate, intercalate-clay, and clay-clay interactions are the crucial interactions that govern the degree of diffusion of cations and intercalates in clay confinement. Since the composition and dimensions of clay are the same in all model systems investigated here, the observed changes in MSD of CO2 and H2 O are primarily due

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Figure 8: Mean square displacment of a) H2 O, b) CO2 , and c) cations

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to cation-intercalate and intercalate-intercalate interactions. The calculated values of hhr2 ii (see Table 1) for CO2 and H2 O differ among different systems in the following order Ca2+ > K+ > Na+ > Cs+ and K+ > Cs+ > Na+ > Ca2+ , respectively. The observed cation-sensitive variation of hhr2 ii for CO2 indicates that the clay-confined CO2 is relatively more diffusive in Ca-MMT than in K-MMT, Na-MMT, and Cs-MMT and that CO2 possesses relatively higher affinity for Cs+ than other cations. The observed order of the time-averaged MSD of CO2 is in accordance with the order of activation barrier for CO2 to displace out of the first coordination shell of the cation reported in the previous section. The lower value of hhr2 ii for H2 O in Ca-MMT can be attributed to relatively higher activation barrier (∼ 2 times higher) for H2 O to displace out of Ca2+ coordination shell than for K+ and Cs+ ions. The two-dimensional diffusion coefficients of H2 O, CO2 , and cations calculated from the long-time slope of MSD are provided in Table 1. The two-dimensional diffusion coefficients H2 O CO2 (Dxy , Dxy , DIxy ) quantify the degree of diffusion of intercalates and cations in the lateral

plane (i.e., the xy plane) parallel to the clay basal surface. In general, the calculated twodimensional diffusion coefficients of water and carbon dioxide molecules are greater than their three-dimensional counterparts, which is indicative of higher lateral diffusion of intercalates 2 in these systems. DCO in Ca-MMT is factors of two and five greater than that in K-MMT xy

and Cs-MMT, respectively, which reaffirms that the lateral diffusion of CO2 is relatively high in Ca-MMT than in other systems. A comparison of the two-dimensional diffusion coefficients of H2 O and CO2 also reaffirms that water is relatively more diffusive than CO2 in K-MMT and Cs-MMT, whereas a reverse trend is seen in Ca-MMT. In fact, in the presence of CO2 , the water molecules are more restricted in Ca-MMT, while the water diffusion is highest in K-MMT. However, an earlier study showed that, in the absence of CO2 , the water diffusion is highest in Cs-MMT. 127 The higher diffusivity of CO2 in Ca-MMT can be attributed to its weaker affinity for Ca2+ ions. The diffusion coefficients of cations are relatively lower than those of intercalates due to stronger water-cation and cation-surface

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interactions. The calculated diffusion coefficients of intercalates and cations are in reasonable agreement with experimental values obtained using QENS and neutron spin echo experiments on smectites 103,128 and earlier MD simulations. 94,99 Table 1: Diffusion Coefficients of Intercalates and Cations Diffusion Coefficient (10−5 cm2 /sec) DH2O xy DCO2 xy DIxy hh r2 ii (˚ A)2 hh r2 iiH2O xy CO2 hh r2 iixy 2 hh r iiIxy hh r2 iiI

(D)

Ca-MMT

K-MMT

Cs-MMT

Na-MMT

0.0068 0.37 0.0018 28.97 ± 4.03 1233.7±218 3.89 ± 1.04 3.99 ± 1.05

0.29 0.13 0.01 938.85 ± 172 442.7 ± 80.9 39.21 ± 7.18 40.3 ± 7.2

0.14 0.045 0.009 454.5 ± 85 171.5 ± 27 31.6 ± 5.44 20.5 ± 3.5

0.126 0.107 0.015 381 ± 74.9 304 ± 51.6 52.3 ± 9.19 53.1 ± 9.2

Time Correlation Function To further investigate the mobility and retention of intercalates, we examined the residence times of CO2 and H2 O in the coordination shells of interlayer cations using an approach similar to the one proposed by Chandler and co-workers to characterize the hydrogen-bond lifetime in liquids. 129 In this approach, a time-dependent population operator, h(t), is defined for each cation-intercalate pair such that h(t) = 1 when the chosen intercalate is coordinated to the chosen cation at time t, and h(t) = 0 otherwise. An intercalate is considered to be coordinated to a given cation only if it is within 5 ˚ A from that cation. From MD-derived time series of h(t), the time correlation function, C(t), can be calculated for individual cation-intercalate pairs using the following equation

h(0)h(t) C(t) =

h(0)h(0) where

denotes a statistical average over different time origins. 30


(2)

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The function C(t) measures the probability that a tagged cation-intercalate pair is coordinated at time t, given that it was coordinated at time zero. The rate of decay of C(t) quantifies the mean residence time of the intercalate in the cation coordination shell. For instance, C(t) = 1 at all times for an intercalate that remains coordinated to a cation during the entire course of the simulation, while C(t) = 0 at all times for an uncoordinated cationintercalate pair. C(t) decays with time for an intercalate that visits the first coordination shell of the cation less frequently during the course of the simulation and the frequency of visit determines the rate of decay and the long-time value of C(t). The mean C(t), which was calculated by averaging over all cation-intercalate pairs (excluding the uncoordinated pairs), for cation-CO2 and cation-H2 O pairs are shown in Figure 9. For all the systems, C(t) of H2 O (Figure (9a)) decays rapidly to 0.8 at short times (t < 1.25 ps) due to fast librations of cations and intercalates in the interlayer. 129,130 For t > 1.25 ps, C(t) decays monotonically, but the rate of decay and the long-time value of C(t) are different for different systems studied. For instance, C(t) for Ca-MMT decays slowly to a long-time value of ∼ 0.48 at 10 ns, whereas for all other systems C(t) decays rapidly to a long-time value of 0.01. The decay of C(t) is fastest for K-MMT. These observations indicate that the water molecules reside for a longer period of time near Ca2+ , and K+ has the lowest affinity for H2 O than for the other cations studied here. The observed order of residence times of H2 O near cations is in line with the order of activation barriers for the displacement of H2 O from the first coordination shells of cations. For all the systems except Cs-MMT, C(t) of CO2 decays relatively faster than that of H2 O, indicating that these cations have relatively higher affinity for H2 O than for CO2 . However, C(t) of H2 O and of CO2 almost overlap for Cs-MMT, which suggests that Cs+ ions display comparable affinity for H2 O and CO2 (in fact, the affinity of Cs+ for H2 O is slightly greater than that for CO2 ) in Cs-MMT. The decay of C(t) of CO2 is fastest for Ca-MMT, it is the slowest for Cs-MMT, and it is intermediate for K-MMT and Na-MMT. The fastest decay of C(t) in Ca-MMT is indicative of a very weak affinity of CO2 for Ca2+ ,

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while the slowest decay of C(t) in Cs-MMT suggests a higher residence time of CO2 near Cs+ ions. The observed order of residence times of CO2 near cations is also in line with the order of activation barriers for the displacement of CO2 from the first coordination shells of cations.

Figure 9: Time correlation function C(t) for a) H2 O b) CO2

Conclusions The microscopic understanding of the mechanism of uptake and retention of supercritical carbon dioxide by expandable smectite clay minerals is of central importance for largescale geological sequestration of CO2 . The interlayer galleries of these minerals serve as a potential storehouse of CO2 , H2 O and charge-balancing cations. The size, charge, and solvation energies of the interlayer cations are thought to greatly influence the structure, dynamics and energetics of the intercalated CO2 and H2 O molecules. Using Cs-MMT, K32


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MMT, Na-MMT, and Ca-MMT as model systems, the present study has investigated the role of cations in the structure, dynamics and energetics of H2 O/CO2 intercalated into MMT using all-atom molecular dynamics simulation and an enhanced sampling free energy method. 131 In particular, relative positions, orientations, dynamics, and interaction energies of intercalates and cations are quantified using molecular dynamics simulations, while the free energy profiles for intercalates to associate and dissociate with cations are calculated using the adaptive biasing force (ABF) method. The results showed that in the absence of H2 O and CO2 , the cations were localized at the centers of the tetrahedral Si,Al-O hexagonal rings of the basal surface in all the systems investigated. However, the locations and dynamics of cations are significantly altered in the presence of intercalates. The cation-intercalate interactions drive the cations to desorb from the surface and to reach the center of the interlayer to get solvated by intercalates, while a few cations remain bound to the basal surface. The interplay of cation-intercalate and cation-surface interactions critically determine the populations of desorbed and surfacebound cations in the interlayer. In particular, the hydration energy of the cation (i.e., cation-water interaction energy) is a key factor at the molecular level for the desorption of cations from the basal surface; the higher the cation hydration energy, the higher is the degree of the desorption of cations from the surface. Among the systems investigated in the present study, Ca2+ ions in Ca-MMT desorbed more from the basal surface than K+ , Cs+ , and Na+ ions in K-MMT, Cs-MMT, and Na-MMT, respectively. The cations desorbed from the surface were primarily surrounded by water molecules at the center of the interlayer. The calculated water density profiles revealed the formation of a single layer of H2 O molecules at the center of interlayer of Cs-MMT, Na-MMT and CaMMT, while a bimodal water distribution was observed for K-MMT due to the formation of a partial split of a single layer of H2 O molecules sandwiched between the basal surfaces. The water molecules were relatively more disordered in Cs-MMT than in Ca-MMT and KMMT. The molecular planes of a majority of H2 O molecules were oriented perpendicular to

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the clay surface to establish H-bonds with both the basal surface and the neighboring H2 O molecules. The estimated activation barrier for a water molecule to move out of the first coordination shell of Ca2+ was at least ∼3 times greater than that for the other cations. The results showed that cation-water affinity was highest in Ca-MMT, while it was the lowest in Cs-MMT (the observed order of cation-water affinity was Ca2+ > Na+ > Cs+ > K+ ). The residence time of water molecules in the first coordination shell of Ca2+ was relatively higher than that for the other ions. The calculated diffusion constant of water indicated that the H2 O molecules are relatively less diffusive in Ca-MMT than in other systems (the observed order of water diffusivity was K+ > Cs+ > Na+ > Ca2+ ). In all the systems considered in this study, the cations are found to be in two distinct environments, one at the centers of hexagonal rings (site-I) and the other at points of intersection of three adjacent (Si,Al)-O hexagonal rings (site-II). The cations at site-I are surrounded by H2 O molecules and the cations at site-II surrounded by both H2 O and CO2 molecules. The computed orientation angles (θ, φ, ψ and η) show that the H2 O molecules are not oriented parallel to the basal surfaces but are tilted to different degrees with respect to the basal surface. The CO2 molecules lie on a plane parallel to the basal surface at the center of the interlayer. The O-C-O axes of CO2 molecules were oriented parallel to the basal surface. A majority of near-neighbor CO2 pairs preferred a distorted slipped-parallel geometry in all four systems considered. The potential of mean force calculations quantified the activation energy for a CO2 to move out of the first coordination shell of Cs+ to be ∼1.5 kcal/mol, which is relatively higher than that for K+ , Na+ , and Ca2+ ions. At the hydration of 4 H2 O per cation considered in the present study, the observed order of cation-CO2 affinity was Cs+ > K+ > Na+ > Ca2+ . The examination of the cation-sensitive variation of CO2 diffusion indicated that the CO2 molecules were relatively more diffusive in Ca-MMT, while the diffusivity of CO2 was the least in Cs-MMT. In general, the cation-CO2 interaction energies were an order of magnitude less than the cation-water interaction energies suggesting that the interlayer

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cations interact to a lesser extent with CO2 than with H2 O in all the systems considered. In summary, the present study has provided detailed atomistic insights into the role of cations in determining the structure, dynamics, and energetics of H2 O and CO2 intercalated into montmorillonite. We believe that the results of our study are crucial for understanding the molecular basis of CO2 capture and retention by expandable clay minerals and for a rational design of engineered CO2 -philic clay minerals.

Acknowledgement We thank Dr. Andrey G. Kalinchev for providing us with the initial structure of the montmorillonite model and Dr. Moumita Saharay for meaningful discussions.

Supporting Information Available The Supporting Information is available free of charge on the ACS Publications website at DOI: This material is available free of charge via the Internet at http://pubs.acs.org/.

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Role of Cations in Adsorption of Supercritical Carbon Dioxide at

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