Langmuir 1998, 14, 1201-1207
1201
Monte Carlo and Molecular Dynamics Simulations of Electrical Double-Layer Structure in Potassium-Montmorillonite Hydrates Fang-Ru Chou Chang Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York 10964-8000
N. T. Skipper Department of Physics and Astronomy, University College, Gower Street, London WC1E 6BT, United Kingdom
Garrison Sposito* Earth Sciences Division, Lawrence Berkeley National Laboratory, Mail Stop 90/1116, Berkeley, California 94720 Received May 5, 1997. In Final Form: December 10, 1997 Monte Carlo and molecular dynamics simulations of interlayer molecular structure in the one-, two-, and (hypothetical) three-layer hydrates of K-montmorillonite were performed concurrently in order to elucidate counterion speciation and water structure in the electrical double layer of this clay mineral. Calculated layer spacings, interlayer water potential energies, and counterion mobilities were in agreement with available experimental data. In the one-layer hydrate, both outer-sphere and inner-sphere surface complexes of K+ were observed, the latter always near sites of tetrahedral charge substitution, with the counterion species exchanging readily on the simulation time scale (up to 200 ps). In the two- and threelayer hydrates, the surface complexes persisted, but an incipient diffuse layer of counterions also was observed, with all three types of surface species engaging in sluggish exchange. Water molecules in the one-layer hydrate resided at the interlayer midplane, whereas in the two-layer hydrate they lay in two planes between outer- and inner-sphere K+ surface complexes, as well as at the midplane. Hydrogen bonds in the one-layer hydrate were longer and more bent than in bulk liquid water. For all three hydrates, water and cation interlayer mobilities remained below those observed in bulk solution, principally because of the restricted geometry and the retarding effect of clay layer surface charge. Most of our results can be understood in terms of the weak solvation of the counterions by water molecules, which permits significant competition between K+ and water protons for negatively charged sites in the clay mineral layer.
Introduction As a counterion adsorbed on 2:1 layer type clay minerals, notably montmorillonite, K+ may form especially stable inner-sphere complexes with the ditrigonal cavities in the siloxane surfaces of these minerals.1 Weak solvation of K+ by water molecules, necessary to facilitate strong innersphere surface complex formation, is suggested by the IR spectra of thermally dehydrated K-montmorillonite2 as well as by enthalpy of immersion data for outgassed K-montmorillonite.3 Dielectric relaxation data4 for water molecules adsorbed in the monolayer hydrate of Kmontmorillonite indicate that interfacial water dipolar reorientation takes place on the same time scale as it does in bulk liquid water, implying similar rotational hindrance to water molecules from K+ solvation and hydrogen bonding. Solid-state 39K NMR spectra of hydrated Kmontmorillonite5 give clear evidence of a facile desolvation of the counterion to form inner-sphere surface complexes * Corresponding author. E-mail:
[email protected]. Telephone: 510-643-8297. Fax: 510-643-2940. (1) Sposito, G. The Surface Chemistry of Soils; Oxford University Press: New York, 1984; pp 15, 20. (2) Russell, J. D.; Farmer, V. C. Clay Miner. Bull. 1964, 5, 443. (3) Be´rend, I.; Cases, J.-M.; Franc¸ ois, M.; Uriot, J.-P.; Michot, L.; Masion, A.; Thomas, F. Clays Clay Miner. 1995, 43, 324. (4) Mamy, J. Ann. Agron. 1968, 19, 175. (5) Lambert, J.-F.; Prost, R.; Smith, M. E. Clays Clay Miner. 1992, 40, 253.
in preference to diffuse-layer or outer-sphere surface complex species. Evidence for inner-sphere surface complexation in the adsorption mechanism of K+ counterions on montmorillonite comes also from observations of much lower swelling pressures (at a given interlayer separation)6 and of much less Cl exclusion7 in K-montmorillonite aqueous suspensions, as compared to suspensions containing Li- or Na-montmorillonite. Aqueous suspensions of swollen K-montmorillonite in electrolyte solutions do not typically exhibit more than two layers of water molecules intercalated between the clay layers, by contrast with three or more intercalated water layers observed for Li- and Na-montmorillonites under the same conditions.8,9 Newman10 and, more recently, Be´rend et al.3 have compared the hydration properties of homoionic montmorillonites bearing monovalent counterions. Be´rend et al.3 confirmed the existence of one- and two-layer hydrates of K-montmorillonite in their water vapor adsorption and desorption studies. The two-layer hydrate was not stable (6) Lubetkin, S. D.; Middleton, S. R.; Ottewill, R. H. Philos. Trans. R. Soc. London 1984, A311, 353. (7) Edwards, D. G.; Posner, A. M.; Quirk, J. P. Trans. Faraday Soc. 1965, 61, 2816. (8) Posner, A. M.; Quirk, J. P. J. Colloid Sci. 1964, 19, 798. (9) Cebula, D. J.; Thomas, R. K.; White, J. W. J. Chem. Soc., Faraday Trans. 1 1980, 76, 314. (10) Newman, A. C. D. In Chemistry of Clays and Clay Minerals; Newman, A. C. D., Ed.; Wiley: New York, 1987; p 235.
S0743-7463(97)00472-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 02/10/1998
1202 Langmuir, Vol. 14, No. 5, 1998
at water activities below 0.3, whereas the one-layer hydrate gradually disappeared (desorption process) or appeared (adsorption process) at water activities near 0.2. The enthalpy of immersion of degassed K-montmorillonite was found to be less than half that for degassed Li- or Na-montmorillonite.3 These characteristics could reflect the persistence of inner-sphere surface complexes of K+ after hydration of the clay mineral. 5 However, Nishimura et al.,11 using atomic force microscopy, were not able to detect these complexes on the siloxane surface of Kmuscovite that was reexposed to liquid water after heating at 300 °C, whereas they did observe them on the siloxane surface of Li-muscovite treated similarly. A comparable result was reported by Russell and Farmer,2 who used IR spectroscopy to monitor the movement of counterions into the ditrigonal cavities of the siloxane surface of thermally dehydrated (350-550 °C) montmorillonite. A spectral signature for the descent of Li+ into the cavities was observed, but not for K+ under the same experimental conditions. These controversial issues may be clarified by insights provided from simulations of interlayer molecular structure in the low-order hydrates of K-montmorillonite. As is well-known for aqueous solutions of potassium salts,12-15 comparison of molecular simulation results with available experimental data not only tests the potential functions (and phase-space sampling strategies) incorporated into the simulations but also can suggest experiments that will resolve thorny issues such as the degree of innersphere surface complexation of counterions under given clay hydration conditions.16-18 Boek et al.19 recently applied Monte Carlo simulation to examine the role of K+ counterions as inhibitors of interlayer swelling in montmorillonite-water systems. Their simulations utilized the TIP4P potential function21 to model water-water and water-cation interactions. They predicted that, upon initial hydration of K-montmorillonite, the counterions would move from ditrigonal cavities in the siloxane surface to the midplane of the interlayer region, thus forming outer-sphere surface complexes. However, as the water content increased to approach that required to establish a second full monolayer of adsorbed water, some counterions were predicted to leave the midplane and form innersphere surface complexes, and these complexes increased in importance with increasing water content, up to three monolayers of adsorbed water. Thus, the Monte Carlo simulations of Boek et al.19 predicted that K+ counterions would desolvate to form inner-sphere surface complexes as the water content is increased above one monolayer. This behavior was in sharp contrast to that predicted for Li+ and Na+ counterions, which instead were seen to shift from outer-sphere surface complexes to diffuse-layer (11) Nishimura, S.; Biggs, S.; Scales, P. J.; Helay, T. W.; Tsunematsu, K.; Tateyama, T. Langmuir 1994, 10, 4554. (12) Ohtaki, H.; Radnai, T. Chem. Rev. 1993, 93, 1157. (13) Lybrand, T. P.; Kollman, P. A. J. Chem. Phys. 1985, 83, 2923. (14) Bounds, D. G. Mol. Phys. 1985, 54, 1334. (15) Bopp, P. Molecular dynamics simulations of aqueous ionic solutions. In The Physics and Chemistry of Aqueous Ionic Solutions; Bellissent-Funel, M.-C., Neilson, G. W., Eds.; D. Reidel: Boston, MA, 1987; p 217. (16) Skipper, N. T.; Sposito, G.; Chang, F.-R. C. Clays Clay Miner. 1995, 43, 294. (17) Chang, F.-R. C.; Skipper, N. T.; Sposito, G. Langmuir 1995, 11, 2734. (18) Chang, F.-R. C.; Skipper, N. T.; Sposito, G. Langmuir 1997, 13, 2074. (19) Boek, E. S.; Coveney, P. V.; Skipper, N. T. J. Am. Chem. Soc. 1995, 117, 12608. (20) Skipper, N. T.; Chang, F.-R. C.; Sposito, G. Clays Clay Miner. 1995, 43, 285. (21) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926.
Chang et al. Table 1. Parameters in the MCY-Based Potential Function for K-Water and K-Clay Mineral Interactionsa interacn
B (kJ mol-1)
C (Å-1)
D (kJ mol-1)
E (Å-1)
H-K O-K Si-K Al-K
203.4882 281.2006 0 0
1.633 26 1.009 606 0 0
118 425.3 266 623.4 6 837.669 6 837.669
3.602 19 3.485 559 1.968 77 1.968 77
a
Parameters in the MCY-type potential function20,24 N
U)
N
∑∑ i)1 j>i
[
qiqj rij
]
- Bije-Cijrij + Dije-Eijrij
where the indices i and j indicate charge sites on each of two interacting species, qi is the effective charge on a site, rij is the intermolecular site separation, and Bij, ..., Eij are parameters obtained by fitting either to the results of ab initio calculations or to experimental data. The values of qi for H, O, Al, and Si and the parameter values for water-water and water-clay interactions are given by Skipper et al.20
species (i.e., become more solvated) as water content increased.19 In this paper, we report the first concurrent Monte Carlo and molecular dynamics simulations of the one- and twolayer hydrates of K-montmorillonite, following the methodology of Chang et al.,17,18 which utilizes the MCY potential function22 to model water-water interactions. Skipper et al.20 and Chang et al.18 have examined the comparative effects on Monte Carlo and molecular dynamics simulations of Na- and Li-montmorillonite hydrates that result from using either the MCY or the TIP4P model, but no such comparison is yet available for K-montmorillonite hydrates. The principal objectives of our study were to ascertain electrical double layer structure and interfacial species mobility in K-montmorillonite hydrates and to investigate whether the K+ speciation shift from outer-sphere to inner-sphere surface complexes predicted by Boek et al.19 could be an outcome specifically of their use of the TIP4P model. Simulation Methods Monte Carlo (MC) and molecular dynamics (MD) simulations of electrical double-layer structure were performed for hydrates of K-saturated, Wyoming-type montmorillonite, K0.75[Si7.75Al0.25]Al3.5Mg0.5O20(OH)4. The MC simulations used the code MONTE (isothermal-isostress ensemble), with the specific adaptations to 2:1 layer type clay mineral hydrates as developed by Skipper et al.16,20,24 and Chang et al.17,18 Three-dimensional periodic boundary conditions are imposed, with a real-space cutoff at 9 Å for short-range interactions and use of a three-dimensional Ewald sum method16, 20 to calculate long-range Coulomb interactions beyond the cutoff distance, which is essential to accurate simulations.25,26 Counterion-water and counterion-clay mineral interactions are represented by potential functions having the mathematical form of the MCY potential function22,23 for water-water interactions (Table 1). The accuracy and limitations of the MCY model, as compared to the TIP4P model of waterwater interactions, were evaluated in detail by Skipper et al.20 and Chang et al.18 for Na- and Li-montmorillonite hydrates. They found that layer spacings, interlayer species configurations, and interlayer species mobilities were predicted more accurately by (22) Matsuoka, O.; Clementi, E.; Yoshimine, M. J. Chem. Phys. 1976, 64, 1351. (23) Beveridge, D. L.; Mezei, M.; Mehoorta, P. K.; Harchses, F. T.; Ravi-Shanker, G.; Vasu, T.; Swaminathan, S. In Molecular-Based Study of Fluids; Haile, J. M., Mansoori, G. A., Eds.; American Chemical Society: Washington, DC, 1983; p 297. (24) Skipper, N. T.; Refson, K.; McConnell, J. D. C. J. Chem. Phys. 1991, 94, 7434. (25) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, U.K., 1987; pp 1, 182. (26) Feller, S. E.; Pastor, R. W.; Rojnuckarin, A.; Bogusz, S.; Brooks, B. R. J. Phys. Chem. 1996, 100, 17011.
K-Montmorillonite Hydrates
Langmuir, Vol. 14, No. 5, 1998 1203 Table 2. Initial-State and MC Simulation Parametersa
hydrate dehydrated one-layer two-layer
three-layer
initial layer spacing (Å)
initial K+ distribn
optimizingrun steps
total simulation steps
simulation identifier
10.0 14.0 16.0 16.5 16.5 16.0 19.0 19.0
0:0:6:0:0 0:0:6:0:0 1:0:4:0:1 3:0:0:0:3 3:0:0:0:3 0:0:6:0:0 1:0:4:0:1 1:2:0:2:1
0/0 20 000/20 000 10 000/10 000 20 000/20 000 20 000/20 000 10 000/10 000 100 000/100 000 100 000/100 000
300 000 1 200 000 1 540 000 2 360 000 10 760 000 1 540 000 6 000 000 2 000 000
m1 a1 a1 a2 a3b m1 j1 j2
a Column 2 gives the initial layer spacing, whereas column 3 indicates the initial counterion spatial distribution along the c axis (z direction) in the following format: number at 5 Å from center of a clay mineral layer: number at 8.5 Å from the center of a clay mineral layer: number at interlayer midplane: number at 8.5 Å from center of a clay mineral layer. For example, 1:0:4:0:1 means two K+ are at 5 Å from the center of a clay mineral layer and four are at the interlayer midplane. Column 4 gives the number of steps in each of two consecutive optimizing runs that were designed to provide the most reliable estimates of water molecule configurations, subject to the subsequent movement of clay mineral layers and K+ counterions. b Initially the same as simulation a2, but with a change in the frequency of clay movement relative to interlayer species, from 5 to 50, after 760 000 steps.
the MCY model, probably because of its lesser commitment to reproduce the tetrahedral local structure that dominates in bulk liquid watersan advantage when simulating molecular configurations in constrained geometric environments such as clay mineral interlayers. Our MD simulations utilized the code MOLDY27 (isothermal-isochoric ensemble) as implemented for Na- and Li-montmorillonite by Chang et al.17,18 The MD initial state used is the final output of MC simulations that, in turn, have been conditioned on “optimizing runs”, in which interlayer configurations and layer spacings are tuned to facilitate efficient phase-space sampling. Both the MC and the MD simulations were conducted at 300 K, with 100 kPa normal stress applied to the clay layers in the MC simulations and a fixed MC-equilibrated layer spacing in the MD simulations. Monte Carlo Simulations. The MC simulation cell (Figure 1 in ref 17) comprised two opposing clay mineral layers and eight crystallographic unit cells. The clay interlayer region included 6 K+ counterions and 32, 64, or 96 water molecules, representing the one-, two-, or (hypothetical) three-layer hydrate of Kmontmorillonite.3 The simulation cell is repeated infinitely in all directions via three-dimensional periodic boundary conditions. The K+ counterions were placed initially at the midplane of the simulation cell in both the dehydrated K-montmorillonite and its one-layer hydrate. In simulations of the two- and three-layer hydrates, however, various initial-state configurations were used,18 as listed in Table 2. In the first optimizing run, only water molecules are permitted to move, while the layer spacing and K+ positions remain as indicated in columns 2 and 3 of Table 2. In the second optimizing run, water molecules move and the layer spacing (under 100 kPa normal stress) is permitted to vary. Thereafter, the upper clay mineral layer is allowed to move one step in any direction for approximately every five movements of interlayer water molecules. Outputs of total potential energy, layer spacing, interlayer cation and water atom density profiles, orientations of interlayer water molecules, and radial distribution functions are recorded after every 500 attempted steps. The MC results deemed “best” were those giving the lowest and most stable potential energy and layer spacing, as inferred from typical convergence profiles.16,20,23 A three-layer hydrate of K-montmorillonite has not been observed, experimentally, even in aqueous suspensions.3,8,9 Despite the apparent instability of a three-layer K-montmorillonite hydrate, MC calculations with 96 water molecules per simulation cell were performed in order to explore fully the issue of counterion species distributions among surface complexes and the diffuse layer. Molecular Dynamics Simulations. Equilibrium molecular configurations taken from the MC output, and representing approximately the average features of the “best” simulations, were used as initial states for the MD simulations, which were carried out for a total elapsed time of 205 ps with 0.5 fs time steps. Intermediate configurations were saved every 100 time (27) Refson, K.; Skipper, N. T.; McConnell, J. D. C. In Geochemistry of Clay-Pore Fluid Interactions; Manning, D. C., Hall, P. L., Hughs, C. R., Eds.; Chapman and Hall: London, 1993; p 1.
Table 3. Thermodynamic Properties of K-Montmorillonite Hydrates Obtained by MC Simulation hydrate one-layer two-layer a1 a2 a3 m1 ave three-layer j1tc j1fd j2 ave
∆U (kJ mol-1)a
d (Å)b
-50.6
12.46 ( 0.08
-33.9 -34.3 -34.6 -34.3 -34.0 ( 0.3
16.18 ( 0.12 16.29 ( 0.13 16.83 ( 0.12 15.89 ( 0.12 16.3 ( 0.4
-35.08 -34.39 -33.06 -34 ( 1
19.57 ( 0.16 20.03 ( 0.17 20.55 ( 0.18 20.1 ( 0.5
a Differential potential energy per mole of interlayer water.17 Layer spacing (c axis) and standard deviation. c Averaged from 500 001 to 4 000 000 steps. d Averaged from 500 001 to 6 000 000 steps. e Mean value for all simulations.
b
steps to calculate self-diffusion coefficients (D), interlayer density profiles, and trajectories of the water molecules and K+ counterions. A three-dimensional Einstein relation (in preference to integration of the displacement autocorrelation function25) was used to calculate self-diffusion coefficients:
D)
1 d 〈|r(t)|2〉 6 dt
(1)
where 〈|r(t)|2〉 is the mean-square displacement (averaged over all diffusing species of a chosen type) and t is the simulation elapsed time after the transient free-molecule motions have disappeared (2 < t e 205 ps). A plot of 〈|r(t)|2〉 vs t yields a slope equal to 6D.
Results Thermodynamic Properties. Monte Carlo results are listed in Table 3 for the differential potential energy17 of interlayer water and the layer spacing, under 100 kPa applied pressure, at 300 K in the three K-montmorillonite hydrates. The differential potential energy of interlayer water may be compared with the internal energy of bulk MCY23 water, -36.4 kJ mol-1, and with heat of immersion data for hydrated K-montmorillonite3 (after renormalization by adding the heat of condensation of bulk liquid water, -43.9 kJ mol-1). The value of ∆U for the one-layer hydrate is more negative than the MCY internal energy for bulk water and is in approximate agreement with the renormalized heat of immersion3 for K-montmorillonite measured at a water content of 0.1 kg/kg clay, -45 kJ mol-1. The values of ∆U for the two- and three-layer hydrates are essentially the same as that for bulk MCY
1204 Langmuir, Vol. 14, No. 5, 1998
water, a trend also noted for Li- and Na-montmorillonite hydrates by Chang et al.17,18 The predicted layer spacings in Table 3 are in agreement with the averages of published experimental values, 12.1 ( 0.3 Å and 15.6 ( 0.5 Å, for the one- and two-layer hydrates, respectively, as determined by X-ray or neutron diffraction.28-30 However, the MC layer spacing predicted for dehydrated K-montmorillonite, 11.3 Å, is significantly larger than the experimental value of 10 Å.3,5,29,30 This discrepancy may be a result of not achieving full claylayer registration along the c axis in the MC simulations, such that the K+ counterions in the dry mineral are completely encapsulated in 12-fold coordination by two opposing ditrigonal cavities of the siloxane surfaces.1 Alternatively, maintaining the structural OH groups in the octahedral sheet of the clay mineral in a fixed orientation during the simulations could have hindered entry of K+ into these cavities.1 Perfect registration of the clay layers might be achieved more readily in MC simulations that are initiated at higher pressure and/or lower temperature than in the present study or that permit relaxation of the structural OH, to facilitate K+ capture by opposing ditrigonal cavities. Boek et al.19 predicted a layer spacing of 9.86 ( 0.04 Å for dehydrated Kmontmorillonite using a TIP4P-type potential function to model K+-clay mineral interactions. This result, in better agreement with experiment than ours, is tempered by their subsequent prediction19 of layer spacings for the oneand two-layer hydrates of K-montmorillonite that were significantly smaller (11.8 and 13.7 Å) than the average experimental values given above. This type of underprediction using the TIP4P model also was noted by Skipper et al.20 and Chang et al.18 in their comparative studies of montmorillonite hydrates. Counterion Speciation. Figure 1 shows density profiles along the c axis for K+ as obtained from MD simulations. In the one-layer hydrate (Figure 1a), K+ counterions are distributed mainly near the midplane, but with a transient shoulder population located about 0.5 Å from the midplane. (The cation density profiles in Figure 1, being MD “snapshots”, do not necessarily display the full symmetry expected at equilibrium.) These shoulder species should be K+ ions that have formed inner-sphere surface complexes, which are more easily detected in cumulative MD trajectory plots (Figure 2). Trajectories of individual K+ (labeled 1-6) moving on the siloxane surfaces (XY plane) over 205 ps elapsed time are shown within dashed-line perimeters, with circles drawn in to indicate some of the basal-plane oxygen ions (Figure 2, top). Sites near Al-for-Si isomorphic substitution (tetrahedral charge sites) in either of the opposing clay layers are denoted by filled circles. Correspondences between XY plane and XZ plane counterion trajectories are indicated by vertical dash-dot lines. The K+ counterions appear to be attracted toward the two tetrahedral charge sites (filled circles), but the counterions are not constrained to the small triangular region above these sites. Instead, they hover close to the basal-plane oxygen ions surrounding the charge sites and appear to be forming evanescent inner-sphere surface complexes with ditrigonal cavities (denoted by arrows). The K+ ions in outer-sphere surface complexes appear to exchange readily with the innersphere surface species, on the simulation time scale, and to move around the peripheries of the ditrigonal cavities, sporadically interacting with basal-plane oxygen ions. (28) Posner, A. M.; Quirk, J. P. Proc. R. Soc. London 1964, A278, 35. (29) Brindley, G. W.; Ertem, G. Clays Clay Miner. 1971, 19, 399. (30) Calvet, R. Bull. Soc. Chim. Fr. 1972, 8, 3097.
Chang et al.
Figure 1. Interlayer density profiles along the c axis for K+ counterions, from MD simulations in (a) the one-layer hydrate and (b) the two-layer hydrate, plotted relative to the interlayer midplane taken as the origin.
In the two- and three-layer hydrates, the counterion density profiles (Figure 1b shows the MD “snapshot” for the two-layer hydrate) indicate that the K+ ions form surface complexes that are both inner-sphere (peaks about 2.2-2.4 Å from the midplane) and outer-sphere (peaks about 1.8 Å from the midplane). Transient diffuse-layer species also exist (cation density near the midplane), but there are too few at any time to create large peaks. Cumulative MD trajectory plots for the K+ (Figures 3 and 4) suggest counterion species exchange similar to that observed in the one-layer hydrate. Cumulative trajectory plots for K+ moving in a hypothetical three-layer hydrate (Figure 4, layer spacing of 19.57 Å) suggest a more sluggish exchange between the diffuse-layer, outer-sphere complex and inner-sphere complexed species than occurs in the two-layer hydrate. Interlayer Water Structure. Radial distribution functions (RDF) for K-O, O-O, and O-H are summarized in Figures 5-7. The K-O RDF has a first peak at 2.8 Å in all three hydrates. A broad second peak occurs near 5.4 Å only in the one-layer hydrate. The nearest-neighbor
K-Montmorillonite Hydrates
Figure 2. Cumulative trajectory plots for K+ in the one-layer hydrate (upper view, XY plane; lower view, XZ plane). The trajectories of six individual counterions in a simulation cell are numbered on the dashed perimeters. Inner-sphere surface complexes are indicated by vertical lines ending in arrows near the tetrahedral charge sites (two filled circles).
peak is at approximately the same position (2.6-2.9 Å) in the K-O RDF for concentrated aqueous solutions.12,31 The main peak in the O-O RDF (Figure 6) occurs at 2.9 Å in the one-layer hydrate and at 2.8 Å in the two- and three-layer hydrates, as compared to 2.7 Å in the O-O RDF for MCY water. Secondary peaks (non-hydrogenbonded O) also appear in the one-layer hydrate at 4.6 and 5.4 Å; in the two-layer hydrate at 5.3 Å; and in the threelayer hydrate at 4.6 and 5.4 Å for water molecules near the clay mineral surface (s) or 4.9 Å for water molecules near the midplane (m). The sharpness of the first peak in the RDF suggests that water molecules near the midplane (m) in the three-layer hydrate are wellorganized, whereas the breadth of the first peak in the RDF suggests the opposite for water molecules in the one(31) Neilson, G. W.; Enderby, J. W. Adv. Inorg. Chem. 1989, 34, 195.
Langmuir, Vol. 14, No. 5, 1998 1205
Figure 3. Cumulative trajectory plots for K+ in the two-layer hydrate, labeled as in Figure 2.
layer hydrate. The O-H RDF (Figure 7) peaks indicate that hydrogen bonds are stretched significantly in the one-layer hydrate (2.1 Å vs 1.9 Å in bulk water), whereas they more resemble those in the bulk liquid at the midplane (m) in the three-layer hydrate. The next-nearest neighbor O-H distances (3.3-3.4 Å), similar in all three hydrates, indicate hydrogen bonds that are bent somewhat more than in bulk liquid water (O-H distance g3.2 Å).16,23 Interlayer Species Mobilities. The self-diffusion coefficient of water molecules (DW) predicted by MD simulation (Table 4) increases nearly 7-fold between the one- and two-layer hydrates but still remains less than one-third the value for bulk liquid water.32 There appear to be no experimental data with which to check our MD predictions, but measured DW values for the one- and twolayer hydrates of Li- and Na-montmorillonite are in the ranges (0.5-4.0) × 10-10 and (2.5-10.0) × 10-10 m2 s-1, respectively18scomparable to the results in the present study. The self-diffusion coefficient of K+ (DK), on the (32) Sposito, G. J. Chem. Phys. 1981, 74, 6943.
1206 Langmuir, Vol. 14, No. 5, 1998
Chang et al.
Figure 5. Graphs of the K-O radial distribution function (RDF) for the three hydrates.
Figure 4. Trajectory plots for K+ in the three-layer hydrate (d ) 19.6 Å), labeled as in Figure 2.
other hand, varies about 2-fold between the one- and twolayer hydrates and is an order of magnitude smaller than the bulk aqueous solution value, in rough accord with DK inferred from conductivity measurements made on Kmontmorillonite gels at a relatively high water content.33 No experimental DK values are available for lower-order K-montmorillonite hydrates. Discussion and Conclusions The picture that emerges from the present MC and MD simulation results is simpler than what came out of our studies of the low-order hydrates of Li- and Na-montmorillonite.17,18 In the one-layer hydrate, the K+ ions either reside at the interlayer midplane, forming outersphere surface complexes largely with octahedral charge sites, or remain near or in the ditrigonal cavities of the basal planes to form inner-sphere surface complexes. Water molecules in the one-layer hydrate share the (33) Nye, P. H. Adv. Agron. 1979, 31, 225.
Figure 6. Graphs of the O-O RDF for interlayer water molecules in the three hydrates.
midplane with the K+ ions and orient about them as they do in a concentrated aqueous solution.12.31 Hydrogen bonds among the water molecules are stretched relative to those in liquid water (Figure 7). This structure, however, is quite dynamic (Figure 2), since the K+ ions are able to exchange (on a 200 ps time scale) between outer-sphere and inner-sphere surface complexes. Thus, the residence time of K+ in an inner-sphere surface complex is
