Hydration and Mobility of Interlayer Ions of (Nax, Cay)-Montmorillonite

Article pubs.acs.org/JPCC

Hydration and Mobility of Interlayer Ions of (Nax, Cay)‑Montmorillonite: A Molecular Dynamics Study Lihu Zhang, Xiancai Lu,* Xiandong Liu, Jinhong Zhou, and Huiqun Zhou State Key Laboratory for Ore Deposits Research, School of Earth Sciences and Engineering, Nanjing University, Nanjing Jiangsu 210023, People’s Republic of China S Supporting Information *

ABSTRACT: In most of natural montmorillonites, Na+ and Ca2+ ions commonly coexist in the interlayer space as compensation ions. Molecular dynamics simulations have been performed to investigate the swelling properties, hydration behaviors, and mobility of the interlayer species of (Nax, Cay)-montmorillonites with different water contents. Nine montmorillonites with different Na+/Ca2+ ratio were selected as model clay frameworks, and the content of interlayer water was set within a range from 0 to 486 mgwater/gclay. The results show that the montmorillonites with coexisting of Na+ and Ca2+ present slightly different swelling curves, hydration energies, and immersion energies from Na- or Camontmorillonite. The double-layered hydrates are the thermodynamically stable states for all montmorillonites in the regime of crystalline swelling. A total of 170 mgwater/gclay is found as the threshold water content for the complexing modes of interlayer Ca2+ and Na+ ions switching from inner-sphere complexes to outer-sphere ones. The self-confusion coefficient of interlayer species obviously reveals the confining effects of clay surfaces. In all montmorillonites, the mobility of Na+ is always much greater than that of Ca2+ due to their different hydration shells. According to the water residence time in typical Na+ and Ca2+ hydration complexes, Ca2+ hydration complexes is pronounced more stable than those of Na+, and in montmorillonites with high Ca2+/Na+ ratio, the inhibitory effects of Ca2+ hydration complexes on the mobility of Na+ is clearly revealed. montmorillonites as compensation ions,20 it is of importance to understand the microscopic interlayer structure, mobility of the interlayer species, and the thermodynamical stability of their hydrates, as well as swelling behaviors of (Nax, Cay)montmorillonites. Computer simulation has been proved as a promising technique to investigate the microstructures and dynamics of interlayer species of montmorillonite.21−27 Molecular dynamic (MD) simulations have revealed that Na-smectite tends to hydrate to high water content and continuously swell, whereas the single-layer hydrate with encaged complexes is energetically the most stable state for K-smectite.5,28 Na+ prefers to interact with water molecules and meanwhile bind to only one clay surface oxygen atom at low water contents.29 The microscopic structures and swelling behaviors of Ca-montmorillonite have been studied by using Monte Carlo methods and found that interlayer waters present as integral layers.30−32 An ab initio molecular dynamics (AIMD) study about the hydration of Li+, Na+, and K+ in montmorillonites reveals that Na+ ions bind to the surface of tetrahedral-substituted montmorillonite, whereas they prefer to be fully hydrated in the interlayer of octahedralsubstituted montmorillonite.33 Another study of Na+/Mg2+/ Ca2+/Sr2+/Ba2+-exchanged montmorillonite employing DFT

1. INTRODUCTION As one of the most common clay minerals, montmorillonite is composed of layers made up of one octahedral sheet sandwiched between two tetrahedral sheets. Isomorphic substitutions of ions in octahedral sheets (e.g., Mg2+ for Al3+) and tetrahedral sheets (e.g., Al3+ for Si4+) make montmorillonite sheets negatively charged, which are compensated by alkali and alkaline earth ions in the interlayer space, such as Na+ and Ca2+ ions.1,2 The exchangeable counterions and charged montmorillonite layer surfaces can interact strongly with water and other polar solvents,3−10 which makes montmorillonite easily undergo hydrating and swelling.11,12 The swelling process usually undergoes two regimes: crystalline swelling and osmotic swelling.13,14 The crystalline swelling occurs in discrete steps and forms integer-layer or mixtures of integer-layer hydrates. Interlayer water molecules in this regime range between zero and approximately four water layers.3−10,15 Under certain conditions, osmotic swelling involving much more hydration occurs and leads to further expansion.14,16 Montmorillonite is widely used as adsorbents in various environmental applications and engineered barrier materials.17,18 For example, in nuclear waste disposal, high-radioactive nuclide waste such as Cs+ can be captured into the interlayer by cation exchange, which qualifies montmorillonite as an effective barrier material.19 The mobility of the interlayer and surface binding ions is crucial for the performance of waste retention. Because Na + and Ca 2+ commonly coexist in natural © 2014 American Chemical Society

Received: August 20, 2014 Revised: November 16, 2014 Published: December 5, 2014 29811

dx.doi.org/10.1021/jp508427c | J. Phys. Chem. C 2014, 118, 29811−29821

The Journal of Physical Chemistry C

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calculation disclosed that smaller cations (e.g., Mg2+ and Ca2+) preferentially locate close to tetrahedral oxygen atoms of the ditrigonal holes, while larger ones (e.g., Sr2+ and Ba2+) locate relatively symmetrically above and below the ditrigonal holes.34 To our knowledge, previous simulations commonly focused on the montmorillonites with only one specific interlayer ion and rarely paid attention to montmorillonites simultaneously with two- or multiple types of ions existing in the interlayer space. However, the latter situation is actually much more common in nature. By employing MD simulations, this study aims to investigate the hydration behavior of (Nax, Cay)montmorillonite and the mobility of the interlayer Na+ and Ca2+, as well as the stability of their hydrates.

2.2. Simulation Details. All MD simulations were undertaken by using the DLPOLY_2.20 package.41 Interatomic potentials for the clay and interlayer ions were obtained from the CLAYFF force field developed by Cygan et al.42 Each atom in CLAYFF force field has an assigned partial charge derived from DFT calculations, and the flexible simple-point-charge (SPC) water model43 is incorporated to describe water and hydroxyl groups. Since this approach treats most interatomic interactions as unbounded, its high performance has been proved broadly in geochemical and material simulations.28,40,42,44−50 The potential energy was evaluated with a 9.0 Å cutoff (for dry montmorillonites) and a 10.0 Å cutoff (for hydrated montmorillonites) for the short-range van der Waals interaction, and the Ewald summation for the Coulombic interaction was calculated with a precision of 1.0 × 10−6. In order to disclose the swelling behaviors of (Na, Ca)montmorillonites, we performed 21 NσT hoover (1 atm, 298 K) simulations for each model, with 21 kinds of water contents increasing from 0 to 486 mgwater/gclay. In the initial states, ions and water molecules were randomly placed in the interlayer regions. For reference, a water number of N = 640 in each interlayer region corresponds to a gravimetric water content of 486 mgwater/gclay. The simulations were performed in two stages. In the first stage, a 3.0 ns calculation was performed for equilibrium followed by a 1.0 ns calculation for production to study the swelling behaviors. In the second stage, in order to study the microscopic structure and dynamical behaviors of interlayer species, several representative water contents of approximately 48−267, 365, and 486 mgwater/gclay were selected to perform 5 ns NVT (298 K) simulations. The time-step was 1.0 fs for all calculations with an interval of 0.1 ps to accumulate statistics data, and the interval for recording the trajectories is 0.5 ps. 2.3. Simulation Analyses. The basal spacing value (b) was obtained by averaging the box volume during the production stage of NσT simulation:

2. METHODOLOGY 2.1. Montmorillonite Models. Arizona-type montmorillonite, which only bears octahedral charges, was selected as the model clay framework (unit-cell formula: (Nax, Ca(1−x)/2)[Si8][Al3Mg]O20(OH)4, 0.0 ≤ x ≤ 1.0).35−37 The ion-exchange capabilities (CEC) of them are all about 135 mequiv/100 g. A total of nine montmorillonite models with different Na+/Ca2+ ratios were investigated, namely, (Na0.0000, Ca0.5000)-, (Na0.1250, Ca0.4375)-, (Na0.2500, Ca0.3750)-, (Na0.3750, Ca0.3125)-, (Na0.5000, Ca0.2500)-, (Na0.6250, Ca0.1875)-, (Na0.7500, Ca0.1250)-, (Na0.8750, Ca0.0625)-, and (Na1.0000, Ca0.0000)-montmorillonite, respectively. The Mg−Al isomorphic substitutions in octahedral hydroxide sheets obey Loewenstein’s rule,38 that is, two substitution sites cannot be adjacent. The simulation cell consists of two clay sheets of 32 unit cells each: 8 in the x-dimension and 4 in the ydimension, so each simulation box contains two interlayer spaces and 32 isomorphic substitution sites. For instance, 12 Na+ and 10 Ca2+ were placed in each interlayer region of (Na0.3750, Ca0.3125)-montmorillonite (Figure 1). A broad water

b = ⟨V ⟩/(2 × S)

(1)

Here ⟨V⟩ represents the statistically averaged volume, and S is the basal surface area. Since entropy contribution only plays a minor role in the swelling free energy,51−55 it was not taken into account in this study. Only energy contribution was analyzed to understand swelling behaviors of the clays, in which both immersion energy and hydration energy5,51 were investigated specifically. The immersion energy is defined as Q = ⟨U (N )⟩ − ⟨U (N 0)⟩ − (N − N 0)Ubulk

(2)

Here ⟨U(N)⟩ is the average energy of hydrated montmorillonite, and ⟨U(N0)⟩ is the average energy of a referential hydration state (here, the state with the highest water content, 486 mgwater/gclay, was selected). Ubulk is the mean interaction potential of the bulk flexible SPC water. In this study, Ubulk = −42.07 kJ/mol, which is similar to that of SPC/E water (−41.4 kJ/mol).51 The immersion energy Q is the energy released when montmorillonite with water content N transform into the referenced montmorillonite with water content N0 by adsorbing water from bulk water. The hydration energy is defined as

Figure 1. Snapshot of (Na0.3750, Ca0.3125)-montmorillonite at water content of 243 mgwater/gclay: Na+ = violet, Ca2+ = blue, O = red, H = white, Si = gray, Al = fade pink, Mg = green.

content ranging from 0 to 486 mgwater/g has been considered. All the water molecules were inserted into the interlayer space randomly. It should be noted that the water content mentioned in this paper only refers the content of interlayer water. The basal surface area was 41.44 × 35.92 Å2 and the thickness of a clay platelet was about 6.56 Å (Figure 1). It has been proved the current model was large enough to avoid finite size effects.37,39,40 The periodic boundary condition was imposed on three dimensions in all simulations.

ΔU = (⟨U (N )⟩ − ⟨U (0)⟩)/N

(3)

Here ⟨U(0)⟩ is the average potential energy of dry montmorillonite. All energy values in eqs 2 and 3 were 29812



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Figure 2. Density profiles of water (upper), Ca2+ (middle) and Na+ (lower) in the interlayer spaces of all nine montmorillonites. The origin and terminal of the abscissa axis corresponds to the lower and upper surfaces of the interlayer regions, respectively.

obtained from the production stage of NσT simulations, with a sampling interval of 0.1 ps. The atomic density profiles in z-direction (perpendicular to the clay sheets) were acquired by averaging over the trajectories from NVT simulations to characterize the spatial distribution of interlayer species. Taking the plane defined by average bottom tetrahedral basal oxygen positions in Figure 1 as the origin (z = 0), the atomic density reads ρ(z) = ⟨N (z − Δz /2, z + Δz /2)⟩/(Δz × S)

1 N

1 dNA − B 4πρB r 2 dr

i=1

(6)

ri (t) is the Here N is the number of atoms of interest and ⇀ center-of-mass position of the ith one at time t; d is the diffusion dimension, that is, d = 3 for the total coefficient. The left-hand side of eq 6 is usually termed as mean squared displacement (MSD). The basal spacing curve illustrates the swelling manner of (Na, Ca)-montmorillonites during the crystalline swelling range, which can be clearly demonstrated by z-density profile. The immersion energy curve thermodynamically reveals all possible stable hydrated states of montmorillonites. And the hydration energy curve indicates the potential for further hydration and also reflects the hydration ability of Na+ and Ca2+. The RDF and CN curves clearly illuminate the changes of hydrated structures of interlayer ions at different water contents. The mobility of interlayer ions as well as the stability of their hydrated structures can be visually illustrated by the overlapped snapshots and quantitatively interpreted by MSD curves, self-diffusion coefficients.

(4)

Here ⟨N(z − Δz/2, z + Δz/2)⟩ is the average number of atoms locating in the height interval of (z − Δz/2, z + Δz/2), and Δz is 0.02 Å here. The hydration behavior of interlayer species was indicated by the radial distribution function (RDF) and coordination number (CN), both of which were derived from the production stage of NVT simulation with sampling interval of 0.1 ps. The RDF for species B around A is calculated according to Allen and Tildesley.56 GA − B(r ) =

N

ri (t ) − ⇀ ri (0)2 |⟩ = 2dDt ∑ ⟨|⇀

3. RESULTS AND DISCUSSIONS 3.1. Density Profiles of Interlayer Species. The changes in interlayer microstructures can be revealed by the density profiles of interlayer species along z-direction of the nine montmorillonites at different water contents (Figure 2). The results show that, as (Na, Ca)-montmorillonite swells from dry state to highly hydrated states, water in the interlayer will form integer-layer arrangements. At low water content (97 mgwater/ gclay), water molecules present as monolayer in the middle plane of interlayer region for all montmorillonites (Figure 2A1), and Ca2+ ions mainly presents as monopeak, accompanied by small peaks around the main peak (Figure 2A-2), which illustrates that some Ca2+ ions are very close to the clay surface,

(5)

Here ρB is the number density of atoms B; dNA−B is the average number of atom B around a central atom A between the distance of r and r + dr. The coordination number of quasicrystal, liquid, and other disordered systems cannot be precisely defined; however, it can be shown by the RDF. The first coordination number of B around A can be obtained from the integral of the RDF profile from the position starting r = 0, where RDF is approximately zero to the position where the first minimum locates after the first peak. The self-diffusion coefficients (D) of the interlayer species are calculated according to the Einstein relation,56,57 29813



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Table 1. Comparison of Simulated and Experimentally Measured Values of Basal Spacing Na-montmorillonite interlayer water layers 0 1 2 3 4 a

sim. (Å)

sim. (Å)

9.4 12.3 15.2 18.4 21.6

Ca-montmorillonite exp. (Å)

a

10.0 12.0a 15.2a

12.2−12.6b 15.0−15.5b 18.1−19.0b

sim. (Å) 9.4 11.9 15.2 18.2 21.4

sim. (Å) c

9.5 11.9−12.2c 13.5−15.0c 17.9−18.c0

exp. (Å) 9.1−10.3d 11.2−12.4d 15.0−15.5d 18.0−19.1d

Ref 39. bRefs 59−61. cRefs 31 and 39. dRefs 60−72.

while most Ca2+ ions keep staying in the middle plane of interlayer region. The distribution of Na+ ions shows two peaks for most montmorillonites except for (Na1.0000, Ca0.0000)montmorillonite (Figure 2A-3), which means that Na+ ions tend to get close to the montmorillonite surfaces at low water content. As water content increases to 146 mgwater/gclay, a closely arranged double-layer water (Figure 2B-1) as well as both Na+ and Ca2+ ions (Figure 2B-2,-3) can be observed in all montmorillonites. Only a few Ca2+ ions drop into the clay surface, as exhibited by small peaks beside the main peaks (Figure 2B-2), which can be attributed to the stronger electrostatic interaction between Ca2+ and the charged clay sheets. But as the water content increases to 243 mgwater/gclay, Ca2+ and Na+ ions are arranged into a perfect monolayer (Figure 2C-2,-3) sandwiched by the two separated water layers (Figure 2C-1). At much higher water content (365 and 486 mgwater/gclay), triple-layer (Figure 2D-1) and quadruple-layer (Figure 2E-1) arrangements of water emerge successively. Such integral-layer arrangements of water during the stage of crystalline swelling of Ca- and Na-montmorillonite have also been observed in MC simulations.30,31,39 The density profiles of Na+ (Figure 2D-3,E3) and Ca2+ (Figure 2D-2,E-2) present two peaks, both are close to their neighbor clay sheet. However, the layers of Na+ or Ca2+ are separated away from the clay surfaces by the water layers. The distance from Ca2+/Na+ layer to the clay surfaces is greater than 4.0 Å and that from water layers to clay surfaces is about 2.5 Å. Therefore, both Na+ and Ca2+ are fully hydrated to outer-sphere hydration complexes rather than adsorbing onto the clay surfaces via inner complexing, thus, facilitating the swelling of montmorillonite and consequent formation of highhydrated states. This preference is against the case for K+28 and Cs+37,58 preferring to be encaged into the six-membered rings of clay surfaces even at high water content. 3.2. Swelling Behaviors. The calculated basal spacings of Na- and Ca-montmorillonite at different water contents exactly agree with reported values from both simulations and experiments (Table 1). Derived swelling curves of nine montmorillonites (Figure 3) demonstrate the discrete steps swelling behaviors. A plateau at water contents from 24 to 121 mgwater/gclay can be recognized for all montmorillonites. At these low water contents, water molecules are arranged as a monolayer in water density profiles (Figure 2A-1). Another plateau, which is not as obvious as the first one but still can be distinguished, appears at the water contents from 170 to 267 mgwater/gclay. This plateau corresponds to the bilayer water distribution (Figure 2C-1). At the water contents above 267 mgwater/gclay, the basal spacing of all nine montmorillonites just increases linearly without any identified stepwise manner. Such results are in well agreement with XRD measurements.73 Thermodynamically, the immersion energy curves reveal that all possible stable hydrated states of montmorillonite, such as

Figure 3. Basal spacing curves of all nine montmorillonites from molecular dynamics simulations.

the single-, double-, and triple-layer hydrates (Figure 4), are consistent with local or global immersion energy mini-

Figure 4. Simulated immersion energy curves of all nine montmorillonites. A and B correspond to the immersion energy curves of pure Na- and Ca-montmorillonite, respectively.

ma.51,53−55 The energy barriers between these minima can specify the relative stabilities of different hydrated states.28 The immersion energy of Ca-montmorillonite are much greater than that of Na-montmorillonite at a specific water content less than 243 mgwater/gclay, which is qualitatively agreement with experimentally measured immersion heat for dry Na- and Camontmorillonite.63,74,66 The immersion energy of other (Na, Ca)- montmorillonite ranges between the two end members roughly proportionally to the Na/Ca ratio. For montmorillonites with high Na+/Ca2+ ratios, the global minimum clearly occurs at 243 mgwater/gclay, while it shifts to 29814



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approximately 267 mgwater/gclay for those with low Na+/Ca2+. Hence, the full double-layer hydrated state is the most thermodynamically favorable one. The energy barrier appearing at 170 mgwater/gclay between the first local minimum and the global minimum, in a manner, can hinders further hydrating of (Na, Ca)-montmorillonite from one-layer hydrate to doublelayer hydrate (Figure 4). However, the barrier (about 13.7 J/ gclay) for Na-montmorillonite (Figure 4 A) gradually gets obscure as Na+/Ca2+ decreases and eventually disappears for Ca-montmorillonite (Figure 4B), which is closely related to the hydration enthalpy of Ca2+ (−1577 kJ/mol) and Na+ (−406 kJ/mol).75 As the hydration enthalpy of Ca2+ is much greater than that of Na+, the energy barrier for Ca-montmorillonite needs to overcome is smaller than that of Na-montmorillonite. This means the existence of Ca2+ ions may facilitate (Na, Ca)montmorillonite hydrate in the stage of crystalline swelling. For Na-montmorillonite, the energy barrier between the second local minimum at 389 mgwater/gclay and the global minimum at 243 mgwater/gclay is relative small (about 9.4 J/gclay; Figure 4A), thus, Na-montmorillonite can swell to higher hydrated states (e.g., triple-layer hydrate), agreeing well with previous simulations28 and experiments.62,76 Similar preference of high hydrated states of double-layer and triple-layer is also found for Ca-montmorillonite (Figure 4B). Thus, all (Na, Ca)-montmorillonites exhibit great hydrating tendency and swelling potential in the range of crystalline swelling. However, it is worthy to note that the swelling of clays is not an infinite process in nature as there are many other factors influencing the swelling process, such as the realistic complicated edges, environmental humidity, salvation pressures, and so on. There is a forbidden layer spacing called by Ravina and Low77 between crystalline swelling (basal spacing increases from about 10 Å in the dehydrated state up to about 19 Å in three-layer hydrated state) and osmotic swelling (basal spacing increases from about 40 Å). Such forbidden layer spacings between ∼19 and ∼40 Å have not been detected by X-ray diffraction analyses in experimental studies.14,78−80 This means the transition from crystalline swelling to osmotic is not a spontaneous and continuous process, which well agrees with the immersion curves, that is, no driving force of further immersion after global minimum. In our calculation, the hydration energy denotes the energy change of the water as the water enters into the interlayer space from bulk water. Therefore, the hydration energy of interlayer water in all models approaches toward the bulk water energy (−42.07 kJ/mol), while montmorillonite swells to high hydrated state (Figure 5). But even the water content as high as 365 mgwater/gclay, the hydration energies of all montmorillonite models are still much lower than that of bulk flexible SPC water, indicating the potential for further hydration in water-enriched environments. This is well consistent with previous experimental findings that Ca-montmorillonite could continuously swell to the forbidden layer spacing as humidity increased81 and the MD simulation of Na-montmorillonite.28 Furthermore, at each water content, it is observed that the hydration energy decreases as the Na+/Ca2+ ratio decreases because the hydration enthalpy Ca2+ is much greater than that of Na+. Comparing with Na-montmorillonite, the lower hydration energy of water in Ca-montmorillonite makes hydration of Ca-montmorillonite more preferable than that of Na-montmorillonite. However, the changes in hydration energy are generally caused by hydration of interlayer ions and surface confining of clay sheets. At low water contents, the hydration energy change mainly derived by hydration of ions may be not

Figure 5. Simulated hydration energy curves of all nine montmorillonites. The dotted horizontal line corresponds to the bulk energy of flexible SPC water.

the dominant component to the energy change of the whole system. Thus, the water contents corresponding to minima of immersion energy hardly link to the hydration energy curve. 3.3. Hydration of Interlayer Na+ and Ca2+. Interaction between interlayer ions and water/surface of clay sheet were investigated by the calculation of RDF and CN of Ca2+-Ow/Ob (Figure 6) and Na+-Ow/Ob (Figure 7) at some representative water contents. Here, Ob represents the surface oxygen atom of clay sheet and Ow denotes the water oxygen atom, respectively. In all Ca2+-Ow RDFs, the main peak appearing at about 2.43 Å represents the first hydration shell (Figure 6), which agrees well with experimental value (2.46 Å)82 and MC simulations (2.3−2.4 Å).32 Whereas, on the Ca2+-Ob RDFs, the peak at about 2.52 Å representing the first coordination shell only appears in the montmorillonites with water contents less than 170 mgwater/gclay (Figure 6), suggesting that oxygen atom of clay surface contributes to the first coordination sphere of Ca2+ only at low water contents. As for the Na+-Ow RDFs, the first peak locates at about 2.35 Å (Figure 7), which agrees well with previous ab initio MD simulations, such as 2.37,83 2.33,33 and 2.35 Å in liquid water.84 However, the peak at about 2.50 Å in the Na+-Ob RDFs (Figure 7) diminishes as water content increases from 121 to 170 mgwater/gclay and finally disappears at approximately 194 mgwater/gclay. Hence, 170 mgwater/gclay is the threshold water content for the transition of coordination of both Na+ and Ca2+ ions with clay sheet surface from innersphere complex to an outer-sphere one. The CN of the first coordination sphere complexes of Ca2+ and Na+ are calculated through integration of the RDF curves from zero to the first minimum and are listed in Tables S1 and S2 in the Supporting Information (SI). As water content increases from 121 to 194 mgwater/gclay, the number of water molecules in the first coordination sphere of Ca2+ gradually increases from 4.82 to 7.87, while the contribution of Ob correspondingly decreases from about 2.24 to 0 (Figure 6). The same tendency is also found for Na+ ions. The number of coordinated Ow increases from about 3.66 to 5.68 and Ob decreases from 2.06 to 0.10 (Figure 7). At the water contents above 194 mgwater/gclay, both Na+ and Ca2+ only form outersphere hydration complexes, and the coordination number of water is about 8.0 for Ca2+ (Figure 6) and 6.0 for Na+ (Figure 7), and the radius of hydration shell of Na+ and Ca2+ is approximately 2.35 and 2.43 Å, respectively, which agrees well with previous studies on interlayer Ca2+ of montmorillonite at 29815



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Figure 6. Radial distribution functions (black) for Ca2+-Ow/Ob and coordination numbers (blue) of eight montmorillonites containing Ca2+.

Figure 7. Radial distribution functions (black) for Na+-Ow/Ob and coordination number (blue) of eight montmorillonites containing Na+.

high water content32 or Ca2+ in bulk water disclosed by computational simulations.85,86 However, there is a lack of consensus on the coordination number of the first hydration shell of Na+. Ab initio MD simulations indicate values of 4.8,33 5.0,83 6.0,86 and 7.0,87 whereas coordination number ranging from 4.0 to 8.0 has been reported from experiments (e.g., X-ray,

neutron diffraction, and Raman spectroscopy).88,89 According to a recent ab initio calculation,90 the coordination number of Na+ is 4 + 1, that is, an inner subset of four water oxygen atoms and one “loosely” coordinated water locating slightly further. Comparing with the hydration enthalpy of Ca2+ (−1577 kJ/ mol), the much lower hydration enthalpy of Na+ (−406 kJ/ 29816



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Figure 8. Overlapped final 500 ps NVT simulation snapshots of interlayer Na+ (violet ball), Ca2+ (blue ball), and water (red point) of (Na1.0000, Ca0.0000)-, (Na0.3750, Ca0.3125), and (Na0.0000, Ca0.5000)-montmorillonite at different water contents. It can be observed that the overlapped trajectories of Ca2+ and their accompanying coordinated water molecules is much denser than the case of Na+. This means that the coordination sphere around Ca2+ is more stable and the mobility of Ca2+ is lower, while Na+ does not have stable coordination sphere and is continuously moving, especially at high water contents.

mol) is responsible for the much looser hydration shell of Na+ and further causes the much higher mobility than that of Ca2+. 3.4. Mobility of Interlayer Ions and the Stability of Hydration Shells. 3.4.1. Mobility of Interlayer Species. A 500 ps overlapped trajectory of three representative montmorillonites (i.e., (Na1.0000, Ca0.0000)-mont, (Na0.3750, Ca0.3125)-mont, and (Na0.0000, Ca0.5000)-mont) at 6 typical water contents (from monolayer hydrate to bilayer hydrate) are employed to illustrate the mobility and hydration of interlayer Ca2+ and Na+. It can be observed that the coordination sphere around Ca2+ is much more stable and the mobility of Ca2+ is lower, while Na+ does not have a stable coordination sphere and is constantly moving, especially at high water contents (Figure 8). The hydration enthalpy of Ca2+ (−1577 kJ/mol) is much greater than that of Na+ (−406 kJ/mol),75 which leads to a much more stable hydration shell of Ca2+ than that of Na+. Comparing with the hydration energy of water in Namontmorillonite (Figure 5), the much lower one in Camontmorillonite also confirm this. In Na-montmorillonite with high water contents (>170 mgwater/gclay), the interlayer Na+ ion moves in a relatively free way (Figure 8A-1−F-1). But for the Na+ and Ca2+ coexisting montmorillonites, the moving regions of Na+ are apparently constrained by the hydration shells of Ca2+ as well as interlayer spatial confinement91 (Figure 8A-2−F-2). Hence, the mobility of Na+ in (Na, Ca)-montmorillonite is lower than that of pure Na-montmorillonite. At low water content, almost all water molecules are involved in the first and second coordination shell of Ca2+ in Ca-montmorillonites (Figure 8A-3−C-3) and two coordination shell of Ca2+ can join together through sharing their second coordination shell (e.g., Figure 8C-2, D-2, E-2, C-3, D-3). Thus, the mobility of Ca2+ is further inhibited, which further limits the movement of Na+ and water molecules. The mean square displacement (MSD) of interlayer Na+ and Ca2+ of three representative montmorillonits ((Na1.0000,

Ca 0.0000)-mont, (Na0.3750 , Ca 0.3125 )-mont, and (Na0.0000 , Ca0.5000)-mont) fluctuates clearly with water contents (Figure 9). Therefore, the MSD data of Na+ and Ca2+ are sometimes hard to be fitted with eq 6 for obtaining reliable self-diffusion coefficients, especially at low water contents (i.e., 48 and 121 mgwater/gclay). The undetectable macroscopic diffusion of Na+

Figure 9. Mean square displacements of Na+ and Ca2+ of three montmorillonites at different water contents. 29817



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and Ca2+ is due to the strongly confining by clay surfaces, which leads to discontinuous movements. Even so, we still calculated the self-diffusion coefficients of interlayer species of three representative montmorillonites at six water contents for roughly comparing (Figure 10). The results are quantitatively

Figure 11. Ow/Ob residence time in the first hydration shell of Ca2+ (A, C) and Na+ (B, D) in (Na0.3750, Ca0.3125)-montmorillonite at water content of 48 and 243 mgwater/gclay, respectively.

+

(Figure 11A), but only 10 ps for Na+ (Figure 11B). The stability of the hydration shell of Ca2+ is much higher than that of Na+. The interlayer confining effect restricts the mobility of interlayer ions and water, and this could result in the longer residence time and lower exchange frequency. The similar tendency has been disclosed in Na- and Ca-saturated saponite.93 However, in the montmorillonite with very low water content (e.g., 48 mgwater/gclay), Ca2+ and Na+ tend to directly coordinate with oxygen atoms of clay surface and fall into the silicate−oxygen six-membered rings. The residence time of a single water in the coordination complexes of Na+ or Ca2+ is as long as more than 4.5 ns, and Na+ and Ca2+ never escaped from the surface holes during the whole simulation trajectory (Figure 11C,D).

2+

Figure 10. Self-diffusion coefficients of Na (red), Ca (blue), and water (black) of (Na1.0000, Ca0.0000)-, (Na0.3750, Ca0.3125), and (Na0.0000, Ca0.5000)-montmorillonite at different water contents.

consistent with the recently reported self-diffusion coefficients of Na+ in clay nanopores.92 The diffusion coefficients of all interlayer species at high water content are significantly higher than those at low water contents. However, even at the highest water content (486 mgwater/gclay), the diffusion coefficient of interlayer water (i.e., about 1.20 × 10−9 m2 s−1) is still much lower than the case of bulk water (about 2.30 × 10−9 m2 s−1), which is controlled by layer charge of clay sheet and geometrical confinement.93 The electrostatic interaction between water molecules and cations/clay sheets is a crucial factor retarding the diffusion of interlayer water. More specifically, as Ca2+ content in montmorillonites increases, the diffusion of interlayer Na+ and water are both suppressed despite of water content due to poor diffusing pathway (Figure 10), which can be attributed to the blocking effects of larger hydration shell of Ca2+. 3.4.2. Water Residence Time in the First Hydration Shell of Na+ and Ca2+. The stability of the hydration complexes of Na+ and Ca2+ is evaluated by calculating the water residence time in the first hydration shell of (Na0.3750, Ca0.3125)-montmorillonite at 243 mgwater/gclay, which was extracted from the trajectory of 5 ns NVT simulation. At first, we positioned the trajectory at 2.5 ns and randomly selected one Na+ ion and one Ca2+ ion and labeled the water molecules in their first hydration shell. Then, we tracked the changes in distance between the labeled water molecules and selected Na+/Ca2+ ion during the whole 5.0 ns NVT simulation. It is found that the residence time of water molecules in the first hydration shell of Ca2+ (Ow2, Ow3, Ow4, Ow7, and Ow8 in Figure 11A) can exceed over 200 ps, while only 50 ps for that of Na+ (Ow3 in Figure 11B). Actually, as some water molecules escape from the hydration shell, other water molecules join in to maintain the 8- and 6-coordinated hydration shell of Ca2+ and Na+, respectively. The residence time of water in the hydration shell of interlayer Ca2+ is much longer than that in bulk condition (about 40 ps for Ca2+ hydration shell94). The water exchange between hydration shell and other interlayer water can be as long as 100 ps for Ca2+

4. CONCLUSIONS Based on comprehensive MD simulations of nine (Na, Ca)montmorillonites, the hydration and swelling, mobility of interlayer species, and interlayer structures have been well disclosed. From the analysis of basal spacings and density profiles, montmorillonite with different Na+/Ca2+ ratios present very similar stepwise swelling patterns and tend to form layered structures in interlayer regions. The immersion energy provides a thermodynamic understanding of clay swelling and demonstrates the discrete step swelling behavior of (Na, Ca)montmorillonite, and reveals that double-layer hydrate state is the most thermodynamically stable state for all montmorillonites regardless of the Na+/Ca2+ ratios. The hydration energies of all montmorillonite models are still much lower than that of bulk flexible SPC water, indicating the potential for further hydration in water-enriched environments. Both Na+ and Ca2+ tend to form inner-sphere complexes at low water content and outer-sphere complexes at high water content. The coordination number of water in the first hydration shell of Na+ and Ca2+ of all montmorillonites gradually increases as water content increases, while the contribution of basal oxygen atoms presents an opposite tendency. The transition from inner-sphere complexes to outersphere complexes occurs approximately at the water content of 170 mgwater/gclay and corresponds to the swelling process of (Na, Ca)-montmorillonite from monolayer hydrated state to 29818



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bilayer hydrated state. In the outer-sphere complexes, the residence times of coordinated water in the hydrate shell of Ca2+ and Na+ are longer than that in their hydration complexes in bulk solution, and the water exchange between the hydrate complexes of Na+ and other free interlayer water is much more frequent. This also can be reflected by the hydration energy: comparing with Na-montmorillonite, the much lower hydration energy in Ca-montmorillonite at each water content indicates a much more stable hydration structure of Ca2+. The mobility of interlayer species is dramatically influenced by the confining effect of clay surface, especially at low water content. The self-diffusion coefficient of Ca2+ is lower than that of Na+ due to the much more stable and larger hydration shell of Ca2+. It is clear that the movement of Na+ is spatially constrained by the hydration complexes of Ca2+ and exhibits relatively low mobility

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ASSOCIATED CONTENT

S Supporting Information *

The coordination number (CN) of the first coordination sphere complexes of Ca2+ and Na+. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 86-25-89681065. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the National Science Foundation of Jiangsu Province (BK2010008), the China National Basic Research Program (973) of China (No. 2012CB214803), and the National Science Foundation of China (Nos. 41222015, 41103029, and 41425009). We also acknowledge the High Performance Computing Center of Nanjing University for the calculations carried out on IBM Blade cluster.

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REFERENCES

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Hydration and Mobility of Interlayer Ions of (Nax, Cay)-Montmorillonite

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