Diffusion of Water in a Synthetic Clay with Tetrahedral Charges by

9818

J. Phys. Chem. C 2007, 111, 9818-9831

Diffusion of Water in a Synthetic Clay with Tetrahedral Charges by Combined Neutron Time-of-Flight Measurements and Molecular Dynamics Simulations Laurent J. Michot,*,† Alfred Delville,*,‡ Bernard Humbert,§ Marie Plazanet,| and Pierre Levitz⊥ Laboratoire “EnVironnement et Mine´ ralurgie”, Nancy-UniVersite´ -CNRS UMR 7569, 15, AVenue du Charmois, BP40, 54501 VandoeuVre Cedex, France, Centre de Recherche sur la Matie` re DiVise´ e, CNRS-UniVersite´ d’Orle´ ans, UMR 6619, 1B, Rue de la Fe´ rollerie, 45071 Orle´ ans Cedex 2, France, Laboratoire de Chimie Physique et Microbiologie pour l’EnVironnement, Nancy UniVersite´ -CNRS UMR 7564, 405 route de VandœuVre, 54600 Villers-les-Nancy, France, Institut Laue-LangeVin, B.P. 156 38042, Grenoble Cedex, France, Laboratoire de Physique de la Matie` re Condense´ e UMR 7643, CNRS-Ecole Polytechnique Ecole Polytechnique, 91128 Palaiseau Cedex, France ReceiVed: December 30, 2006; In Final Form: May 4, 2007

The dynamics of water molecules confined in the interlayer space of a synthetic Na saponite clay with a tetrahedral layer charge of 0.7 per half unit cell were studied by combining time-of-flight quasi-elastic neutron experiments (QENS) and molecular dynamics simulation along the water adsorption isotherms. In the monolayer regime, three different adsorbed amounts corresponding to increasing fillings of the interlayer space were investigated whereas two situations (adsorption and desorption) were investigated in the bilayer region. In a first step, molecular dynamics were used to reexamine some of the approximations classically used in the analysis of water motion by QENS (i.e., separation between rotational and translational diffusion, preferred orientation of molecules, and contribution to the elastic incoherent structure factor). A careful analysis of experimental data obtained at two wavelengths and for two orientations of the clay platelets and validated by simulations yielded rotational and translational movements of water molecules in the clay interlayer. Two rotational movements at two different time scales are revealed. The faster one is rather independent of the adsorbed water amount whereas the slower one assigned to the rotation of hydrated cations is significantly slowed down in the monolayer regime, especially upon completion of the first water layer. Translational movements are limited in the longitudinal direction and are significantly slower than in bulk water in the radial direction, even in the bilayer regime.

Introduction Swelling clay minerals are lamellar silicates formed with two tetrahedral sheets (silica) sandwiching an octahedral sheet (dioctahedral aluminum hydroxide or trioctahedral magnesium hydroxide). The chemical composition of the sheets includes isomorphic substitutions by less charged cations. This generates a net negative layer charge compensated by interlayer exchangeable cations whose valence and hydration properties control both swelling and colloidal behavior. Swelling clay materials are then well-adapted materials for studying the structure and dynamics of water molecules in confined bidimensional spaces.1 Furthermore, because of their widespread occurrence, swelling clay minerals play a major role in the environment (soil stability, geocycling, water reserves, etc.) and are also extensively used in industry (waste management, paints, drilling fluids, etc.). In particular, they are increasingly utilized in the design of disposal facilities for hazardous wastes where their main role is to inhibit the migration of contaminants from the waste to the surrounding * Corresponding authors: E-mail: (L.J.M.) [email protected]; (A.D.) [email protected]. † Nancy-Universite ´ -CNRS UMR 7569. ‡ CNRS-Universite ´ d’Orleáns. § Nancy Universite ´ -CNRS UMR 7564. | Institut Laue-Langevin. Present address: European Laboratory for NonLinear Spectroscopy, University of Florence, Polo Scientifico, Via Nello Carrara 1, I-50019 Sesto-Fiorentino, Italy. ⊥ CNRS-Ecole Polytechnique Ecole Polytechnique.

environment. Such a concept is used worldwide in high-level nuclear waste repositories (e.g., ref 2) where a compacted claybased barrier is placed around the canisters containing vitrified radioactive waste. Nuclear reactions in the waste generate temperature and therefore humidity gradients in the surrounding clay barrier that sealing properties can then evolve with time. At the lowest spatial scale (i.e., the clay layer), it is then of prime importance to properly determine the dynamical properties of water molecules in the interlayer space for a wide range of water activity. Quasi-elastic neutron-scattering (QENS) techniques 3-13 and microscopic simulations11-17 are well adapted to study dynamics at the nanometric scale for time windows shorter than 1ns and have then been applied to study water dynamics in clay minerals. Most experimental work has focused on natural clays with octahedral charge deficit (i.e., montmorillonite and hectorite and on vermiculite), which allows working with large crystals. However, because of the important heterogeneity of natural clay samples, the interpretation of the results and comparisons between them can be sometimes difficult. For instance, the existence of interstratified states of various layer hydrates in natural montmorillonite18-21 makes the analysis rather difficult. In addition, the complexity of the layer structure of natural clay samples can be a drawback for molecular simulations as it is difficult to choose a perfectly representative layer structure. For these reasons, the use of synthetic clay samples appears as a

10.1021/jp0690446 CCC: $37.00 © 2007 American Chemical Society Published on Web 06/13/2007

Diffusion of Water in Synthetic Clay by TOF and MD

J. Phys. Chem. C, Vol. 111, No. 27, 2007 9819 TABLE 1: d-Spacing and Status of Water Molecules for the Investigated Relative Pressures water relative pressure

d-spacing

status of water molecules26

0.15 0.30 0.43 0.84

12.30 Å 12.36 Å 12.43 Å 15.07 Å

0.61des

15.05 Å

isolated hydrated cations development of a H-bond network. strongly ordered H-bond network. Bilayer liquidlike water molecules more structured than the bulk same as above

TABLE 2: Structural Parameters of the Various Clay/ Water Interfaces fraction d001 of clay d001 of clay fraction monohydrate of clay dihydrate water relative of clay (Å) dihydrate (Å) pressure monohydrate 0.12 0.23 0.33 0.67 0.85

Figure 1. (A) Structure of saponite. (B) Water adsorption-desorption isotherm obtained at 303 K on the synthetic saponite sample Na1.4(Si6.6,Al1.4)(Mg6)O20(OH)4. The filled circles correspond to the points studied by TOF QENS, and the open circles correspond to the desorption isotherm obtained by GCMC.

fruitful alternative for a proper understanding of the physical chemistry of clay mineral.22 In that context, we recently used a seriesofsyntheticsaponitesofgeneralformula(Si8-xAlx)Mg6O20(OH)4Nax with 0.70 e x e 2.0 whose surface properties,23 crystal chemistry24 and hydration behavior,25,26 were characterized in detail. Such knowledge provides a sound basis for studying in detail the dynamics of adsorbed water molecules for various water contents. In the present paper, we will focus on one synthetic saponite sample with a layer charge x of 1.4 per unit cell and investigate water dynamics along the water adsorption isotherm by combining time-of-flight (TOF) quasi-elastic neutron measurements and molecular dynamics (MD) simulations. Materials and Methods The synthetic saponite samples with a general structural formula of Nax(Si8-x,Alx)(Mg6)O20(OH)4, with 0.7 e x e 2.0 were prepared by Jean-Louis Robert at ISTO (Orleáns, France) by hydrothermal treatment of hydrolyzed gels prepared by coprecipitation of Na, Mg, Al, and Si hydroxides at pH ) 14, according to a slightly modified version of the gelling method of Hamilton and Henderson.27 The detailed synthesis procedure was described previously.25-26 The sample used in the present study has a layer charge of 1.4 per unit cell, and its structural formula is then Na1.4(Si6.6,Al1.4)(Mg6)O20(OH)4 (Figure 1A). The evolution of water structure with water content in the sample was investigated previously by following along water adsorption and desorption: (i) the adsorbed amount by gravimetric and near-infrared (NIR) techniques; (ii) the arrangement of water molecules in the interlayer by X-ray and neutron diffraction

1.0 0.90 0.74 0.07 0

12.23 12.31 12.35 12.80

0 0.09 0.26 0.93 1.0

14.86 14.88 14.97 15.00

under controlled water pressure; and (iii) the molecular structure and interaction of adsorbed water molecules by NIR and Raman spectroscopy under controlled water pressure. Experimental details can be found in refs 25-26. QENS experiments were performed at Institut Laue-Langevin (ILL) in Grenoble, France using the disk chopper TOF spectrometer IN5. To carry out a detailed analysis of both translational and rotational components in the spectra, experiments were performed using two different wavelengths of the incident neutrons (i.e., 5 and 10 Å). For the first incident wavelength, the accessible wavevector range is 0.47 Å-1 e q e 2.2 Å-1 with an energy resolution of 115 µeV, whereas for an incident wavelength of 10 Å, the accessible wavevector range is 0.23 Å-1 e q e 1.1 Å-1 with an energy resolution of 15 µeV. The sample containers were made of two parallel aluminum plates with a gap of around 1 mm. Oriented films of saponite were deposited by drying dispersed suspensions with a final sample weight of around 0.3 g. The films were first dried in a vacuum oven at 110 °C to achieve a well-defined initial state. They were then equilibrated during at least 15 h in a glove box at 298 K at various water vapor relative pressures imposed through the use of saturated salt solutions. Most samples were prepared along the water adsorption isotherm using relative pressures of 0.15, 0.30, 0.43, and 0.84. One sample was prepared in desorption by first equilibrating it at a water relative pressure of 0.98 before its equilibration at a pressure of 0.61. Figure 1B presents the water adsorption isotherm obtained on the synthetic saponite sample at 303 K with the investigated relative pressures being marked as filled circles. The interlayer distance corresponding to such hydration states and the main status of water molecules deduced from vibrational spectroscopy experiments are reported in Table 1. Inelastic neutron-scattering spectra were recorded using two different orientations of the sample holder to analyze movements parallel and perpendicular to the clay layers. Because of the large incoherent scattering cross section of hydrogen, the signal is dominated by the self-diffusion of water molecules. All the spectra were measured at 303 K, and data collection lasted for 6-10 h depending on the resolution and sample. The spectra were corrected for sample holder contribution. Detector efficiencies, energy resolution, and normalization were measured with standard vanadium. Quasi-elastic spectra were fitted using the program QENSFIT available in the Lamp package from the ILL.

9820 J. Phys. Chem. C, Vol. 111, No. 27, 2007

Michot et al.

Figure 2. Mean square displacement of the confined water molecules in the radial and longitudinal direction. (A) Pure monohydrated saponite. (B) Pure bihydrated saponite. (C) Saponite with an adsorbed water amount of 6.5 mmoles/g.

Figure 3. (A) Velocity correlation function evaluated for confined water molecules (adsorbed water amount 6.5 mmoles/g). (B) Average water mobility resulting from the integration of Figure 3A (eq 2).

Figure 5. Schematic representation of the geometry used in the TOF experiments. Top: “parallel” geometry in which the main component of the momentum transfer (Q ) ki - kf) is parallel to the layers (radial direction). Bottom: “perpendicular” geometry (longitudinal direction).

Figure 4. (A) ISF evaluated for qF ) qz ) 0.5 Å-1 (adsorbed water amount 6.5 mmoles/g). (B) ISF evaluated for qF ) qz ) 1.5 Å-1 (adsorbed water amount 6.5 mmoles/g).

Molecular Modeling. A. Description of the Clay/Water Interface. The clay/water interaction is described by the classical clay force field,28 exploiting atomic charges evaluated from ab initio quantum calculations. The water/water and ion/water interactions are described in the framework of the simple SPC model of rigid water molecules.29 The clay/water dispersion forces are restricted to the oxygen atoms of the clay network and are identified with the oxygen/oxygen dispersion force of the water molecules derived from the simple point charge (SPC) model. More information is available in the literature.28 Ewald summation30 is used in addition to the three-dimensional minimum image convention to evaluate the electrostatic energy of the clay/water interface. To ensure the convergence of the electrostatic energy,31 2196 replicas of the simulation cell are used to evaluate the summation in the reciprocal space and the damping parameter in the direct space is set to 0.19 Å-1, leading to an accuracy better than 0.002.31 The clay/water interface results from the stacking of three clay layers, each composed from 24 unit cells. The atomic coordinates of the ideal Si8Mg6O20(OH)4 unit cell modeling the Saponite clay are identified with those of phlogopite.32 The tetrahedral substitution sites were generated randomly in each clay layer by using a selection rule (i.e., two aluminum atoms

cannot be present in the same ditrigonal cavity and are fully compensated by interlamellar sodium counterions). Thirty-four such solvated cations are thus distributed within each clay interlayer. The population of the various clay hydrates and their interlamellar separation result from a previous analysis of highresolution X-ray diffraction measurements33 performed at various water partial pressure along the desorption branch of the isotherm (see Figure 1). Five hydration states of the clay particles were investigated for water partial pressures of 0.12, 0.23, 0.33, 0.67, and 0.85. Table 2 summarizes the population of the various clay hydrates considered in such a procedure together with their interlamellar separation. B. Grand Canonical Monte Carlo Simulations. The initial equilibrium state of the various clay hydrates was determined by grand canonical Monte Carlo (GCMC) simulations34-35 to determine the amount of confined water molecules along the desorption branch of the isotherm. GCMC simulations are composed of 3000 blocks, each with 10 000 elementary steps. For each step, one of the clay interlayers is selected randomly, and with an equal probability we (i) remove a water molecule or (ii) add a water molecule in a random configuration or (iii) move a randomly chosen cation or water molecule. This is repeated until the average number of confined water molecules remain constant for one ensemble of GCMC simulations (i.e., the 3 × 107 elementary steps). Obviously, a few ensembles, at least 10, are needed to satisfy such a thermalization condition. This procedure was already successfully used to analyze the thermodynamical properties of water molecules confined between clay particles.26,36-38 As seen from Figure 1B, the


J. Phys. Chem. C, Vol. 111, No. 27, 2007 9821

Figure 8. (A) Time variation of the Legendre polynomials obtained from MD simulations. (B) Relative importance of the weighting factors of eq 6 as a function of the scattering wave number

Figure 6. (A) Radial component of the ISF evaluated for qF ) 0.5 Å-1 (adsorbed water amount 6.5 mmoles/g). (B) Radial component of the ISF evaluated for qF ) 1.5 Å-1 (adsorbed water amount 6.5 mmoles/ g). (C) Longitudinal component of the ISF evaluated for qz ) 0.5 Å-1 (adsorbed water amount 6.5 mmoles/g). (D) Longitudinal component of the ISF evaluated for qz ) 1.5 Å-1 (adsorbed water amount 6.5 mmoles/g). Figure 9. Comparison between the direct (eq 5b) and approximate (eq 6) derivations of the contribution of the water rotation to the ISF.

Figure 7. Evolution with q2 of the full width at half-height of the Lorentzian function used to model the quasi-elastic signal (λ ) 5 Å) in the longitudinal direction.

agreement between experimental and numerical data is excellent for water partial pressures below 0.5. Above that value, the GCMC simulations slightly underestimate the amount of confined water molecules. Note nevertheless that a large fraction of the water molecules adsorbed at partial pressures larger than 0.6 are condensed within the porosity between clay aggregates. They are not confined between the elementary clay sheets and consequently not described by GCMC simulations. As a consequence, the results of these GCMC simulations are in satisfactory agreement with the experimental data, validating the use of the clay force field28 to describe the hydration of the saponite clay without any reparametrization of the clay/water interaction. Furthermore, the various water statuses described in Table 1 are well reproduced by GCMC simulations.

C. Molecular Dynamics Simulations. After thermalization of the GCMC simulations, one final configuration was selected and a Verlet algorithm35 was used to determine the trajectories of the water molecules and the sodium counterions confined in the three clay layers (see above). During these MD simulations, the vibrations of the clay network and water molecules were neglected. In an initial step for determining a thermalized set of initial velocities, a short MD simulation (10-20 ps) was carried out with initial velocities chosen randomly with Maxwell’s distribution. We then evaluated the decorrelation of velocities through a first set of relatively short MD simulations (around 40-50 ps). The quaternion procedure was used to describe water rotation in the framework of a generalized Verlet algorithm.35,39-40 A Berendsen thermostat41 was applied to each component of the translational and rotational kinetic energy of the water molecules. An elementary time step of 1 fs was used to integrate the trajectories of the water molecules and 0.1 fs for that of the sodium counterions. The average temperature was stabilized at 298 ( 5 K during 0.5 ns. The mobility of the diffusing water molecules along any direction (noted R) may be first determined by the asymptotic behavior of the mean-square displacement averaged over the three clay interlayers

DR ) lim τf∞

1

3 Nwat(l)

∑∑ i)1

3 l)1

(xi,R(0) - xi,R(τ))2 (1) 2Nwat(l)τ

where Nwat(l) is the total number of water molecules confined in the interlayer labeled l. Figure 2A,B illustrate these displacements for monohydrated and bihydrated saponite interlayers in both the radial (perpendicular to the clay director (i.e., parallel to the clay layers)) and longitudinal (parallel to the clay director (i.e., perpendicular to the clay layers)) directions, whereas Figure


Michot et al.

Figure 10. Quasi-elastic neutron scattering spectra measured in the radial direction for a wavelength of 5 Å. (A) Saponite with an adsorbed amount of 6.4 mml/g and (B) saponite with an adsorbed amount of 13 mmol/g. The thin continuous line corresponds to the resolution function, the dotted lines to the Lorentzian used, the lines with symbols correspond to experimental spectra, and the thick line is the best fit through the data.

2C takes into account the data of Table 2 to yield the result for a sample with an adsorbed amount of 6.5 mmol/g. Because of the confinement of water molecules, the longitudinal displacement is strongly limited, canceling the apparent mobility determined from the asymptotic slope (eq 1). As already shown,13,38,42 the integration of the velocity autocorrelation function is an alternative procedure

DR ) lim

∫τ 〈VbR (0)VbR (τ)〉dτ

τf∞ 0

(2)

Note that, for unlimited diffusion, the Green-Kubo relationship43 ensures the equivalence of both procedures. As shown in Figure 3, the average water motion appears isotropic for diffusion times less than 0.1 ps. That limit corresponds to the average delay before the first collision between the water molecule and surrounding atoms (clay atoms, sodium cations, and other water molecules). During that ballistic regime, the mobility of the water molecules is isotropic. The same conclusion may be derived from the variation of the mean square displacement for very short times (not shown). An evaluation of the apparent mobility of water molecules during that ballistic regime can be obtained by multiplying the average of the modulus of the water velocity by the average diffusion length. This diffusion length is again the product of the average water velocity multiplied by the maximum diffusion time in the ballistic regime (i.e., 0.1 ps). By using the most probable value of the modulus of the water velocity at 298 K (Vm ) x(2kT/Mwater)), an average water mobility of 2.8 × 10-8 m2/s is derived (i.e., ten times higher than the diffusion coefficient in bulk water). Such a difference is not surprising because the mobility in the ballistic regime is equivalent to the free diffusion in dilute gas (as in the Knudsen regime); it is not reduced by the intermolecular friction resulting from the collisions with the surrounding water. As shown in Figure 2, the mean square displacement of the water molecule during that fast diffusion regime does not exceed 0.1 Å2 along each direction. While the velocity autocorrelation function averages to zero after a diffusion time of 0.5 ps (Figure 3A), the mean square displacement does not reach its asymptotic regime before 40

ps (Figure 2). As a consequence, three diffusion regimes may be identified: (1) a fast ballistic diffusion regime, at times shorter than 0.1 ps; (2) an asymptotic diffusion regime, at times larger than 40 ps; (3) an intermediate diffusion regime, necessary to lose the memory of the initial velocities and average the friction forces between colliding water molecules and their surroundings. Finally, the integration of the velocity autocorrelation function in the radial direction (Figure 3B) leads to a water mobility in agreement with the asymptotic slope of the mean square displacement (Figure 2). However, because of the slow mobility of the water molecules in that diffusing regime, the statistical noise is high (50%), strongly limiting the applicability of that procedure. In the longitudinal direction, the result is worse: the mobility is two times smaller with a statistical error of 200%! QENS Modeling. To simulate the S(Q,ω) of the confined water molecules as measured by QENS, scattering vectors are generated with modulus varying between 0.5 and 1.5 Å-1. To differentiate between the neutron scattering in the radial and longitudinal directions, a set of scattering vectors is generated along each of these directions. For each value of the modulus of the radial-scattering vectors, 100 scattering vectors are generated with a uniform angular distribution, leading to cylindrically averaged scattering properties of the clay/water interface. Three sets of intermediate scattering functions (ISF) are thus generated by exploiting the water trajectories obtained from MD simulations. They correspond to the radial, longitudinal, and total scattering properties of the confined water molecules

bR,t) ) FS(q

1 6

∑

Nwat(l) 2 3 l)11/Nwat(l)

∑ ∑ exp(iqbR(rbl,i,nh(0) i)1 nh)1 b r l,i,nh(t))) (3)

where rl,i,nh describes the position of the proton labeled nh and pertaining to the water molecule labeled i of the clay interface labeled l. The index R describes the three sets of diffusing vectors (radial, longitudinal, and total). As shown in Figure 4, the total scattering of the water molecule may be described with



Figure 12. Evolution of the EISF for the various samples investigated in the radial direction at a wavelength λ ) 5 Å.

Figure 11. Evolution with q2 of the full width at half-height of the Lorentzian functions used to model QENS spectra (λ ) 5 Å) in the radial direction. (A) Translational component. (B) Rotational + translational component.

TABLE 3: Dynamical Parameters Deduced from the Analysis of the QENS Spectra in the Radial Direction for a Wavelength λ ) 5 Å relative pressure

adsorbed amount (mmol/g)

bulk water 0.15 0.30 0.43 0.84 0.61des

5.1 5.9 6.4 13.0 12.0

Dtrans (m2 s-1)

τ0 (ps)

L(Å)

τrot (ps)

0.8 ( 0.2 1.3 ( 0.2 1.2 ( 0.2 1.4 ( 0.2

1.5 2.4 ( 0.5 2.2 ( 0.5 2.2 ( 0.5 1.8 ( 0.5 1.7 ( 0.5

2.3 × 10-9 (2.2 ( 1) × 10-10 7.4 ( 5 (3.9 ( 1) × 10-10 11.4 ( 5 (5.8 ( 1) × 10-10 6.1 ( 5 (6.6 ( 1) × 10-10 7.7 ( 5

a fair accuracy (deviation less than 10%) as the product of the radial and longitudinal scatterings because of the relative independence of the radial and longitudinal water motions. The largest deviation is observed for the largest q. By contrast, the ISF evaluated for the smallest q exhibits the highest anisotropy of water mobility. In all cases, the various ISF are described by the sum of two exponentials, with a sharp separation between a fast decrease, occurring on a time scale of 0.1 ps, and a slow decrease, with a time varying between 10 and 100 ps as a function of the scattering length. The fast decrease is easily identified with the previous ballistic diffusion regime, while the slow decrease overlaps the intermediate and asymptotic diffusion regimes (see

Figure 13. Evolution with q2 of the full width at half-height of the narrow Lorentzian function used to model the quasi-elastic signal (λ ) 10 Å) in the longitudinal direction.

above). Because of the fast decay occurring in the ballistic regime, its contribution to the dynamic structure factor is too broad to become experimentally detected. Its broadening is 1 order of magnitude larger than that reported from the analysis of the experimental QENS signal. It is thus quantified by a leastsquared fitting procedure and is removed from the numerical results before any comparison with the experimental data. Results and Discussion Because of the intrinsic geometry of the TOF experiment (Figure 5), data obtained in the “parallel” or “perpendicular” geometry are in fact not oriented in the same way for the whole investigated Q-range. As a first test of the validity of our approach, we then performed a projection of the raw data to measure true S(Q,ω)par and S(Q,ω)perp signals; for each (ω,2θ) point, the Q vector was projected over the two axes parallel and perpendicular to the sample (45 and 135° from the axis of the beam). I(Q,ω)*Qperp/Q gives the intensity projected over Qperp, same for Qpar. To select S(ω,Qpar) at Qperp fixed (or within Qperp + δQperp), only the values of S(Q,ω) having Qperp within the given limits are considered.


Michot et al. and S(Q,ω)perp can be used in a first approximation to yield information about motions parallel and perpendicular to the clay layers (i.e., in the radial and longitudinal directions, respectively). All the experimental data obtained for both resolutions were fitted by using a combination of Lorentzian functions convoluted with the instrumental resolution and assuming that Sinc(Q,ω) can be expressed as a convolution of three terms44 rot Sinc(Q,ω) ) e-1/3Q 〈u 〉 Strans inc (Q,ω) X Sinc(Q,ω) 2

2

(4)

each of which corresponds to a different kind of proton motion.44-45 The exponential term is the Debye-Waller factor, which represents vibrations in the quasi-elastic region; the term is the mean square displacement. The second and third terms are the translational and rotational incoherent dynamic structure factor, respectively. In the case of strongly associated liquids such as water, the assumption of independent translational and rotational movements could be highly debated.46-47 We then used molecular dynamics simulations to check the validity of such an assumption in the case of the clay sample used. In addition to the total radial and longitudinal components of the ISF (eq 3), we have thus also evaluated their contributions resulting from the translation of the center of mass of the water molecule and its rotation48

1

3

Nwat(l)

1

∑

(q bR,t) ) Ftrans S

3 l)1 Nwat(l)

∑ i)1

exp(iq bR(R BC,l,i(0) B RC,l,i(t))) (5a)

bR,t) Frot S (q Figure 14. (A) GCMC configuration of interlayer water (adsorbed amount 6.5 mmol/g). (B) Radial distribution function of water molecules around the sodium ion. (C) Persistence time of water molecules close to the sodium cation.

Figure 15. Comparison between the rotational time constants deduced from MD simulations and QENS measurements in the longitudinal direction.

The quasi-elastic signals thus obtained were then compared with the apparent S(Q,ω)par and S(Q,ω)perp. Only marginal differences could be observed for low Q values in the parallel geometry whereas slightly more significant variations are obtained for low Q values in the perpendicular geometry. It then appears that although not fully rigorous, apparent S(Q,ω)par

)

1

3

∑

1

6 l)1 Nwat(l)

Nwat(l) 2

∑ ∑ exp(iqbR(rbl,i,nh(0) i)1 nh)1 r l,i,nh(t) + B RC,l,i(t))) (5b) B RC,l,i(0) - b

where RC,l,i describes the center of mass of the water molecule. As shown in Figure 6, the approximation of independent rotation and translation appears fully justified, the deviation observed being always smaller than 5% for the radial and longitudinal components of the ISF. Fast Water Motions. Figure 7 presents the evolution as a function of Q2 of the width of the Lorentzian function used to fit quasi-elastic spectra in the longitudinal direction. Under such experimental conditions, the sample causes a shade in some detectors, which have then to be discarded, explaining the lack of points between 0.77 and 1.48 Å. No systematic evolution with Q can be observed, which suggests that only rotational movements occur in the longitudinal direction for the investigated time window. This agrees with the simulation results displayed in Figure 6C,D, which shows that the main contribution to the decrease of the longitudinal component of the ISF results from the rotation of the confined water molecules. Classically, the contribution of the rotation of liquids is treated on the basis of an expansion based on the spherical Bessel functions jl46 ∞

FRot bR,t) ) S (q

(2l + 1)jl2(|q bR||r bCH|)Pl[u bCH(0) * b u CH(t)] ∑ l)0

(6)

where b uCH(t) is the unit vector of b rCH(t), which describes the vector joining the center of mass of the water molecule and a



Figure 16. Quasi-elastic neutron-scattering spectra measured in the radial direction for a wavelength of 10Å. (A) Saponite with an adsorbed amount of 6.4 mml/g and (B) saponite with an adsorbed amount of 12 mmol/g. The thin continuous line corresponds to the resolution function, the dotted lines to the Lorentzian used, the lines with symbols correspond to experimental spectra, and the thick line is the best fit thorough the data.

TABLE 4: Rotational Correlation Times Deduced from the Analysis of the QENS Spectra in the Longitudinal Direction for a Wavelength λ ) 10 Å relative pressure adsorbed amount (mmol/g) τrot (ps)

0.15 5.1

0.30 5.9

0.43 6.4

0.84 13.0

0.61D 12.0

29 ( 5

29 ( 5

44 ( 5

22 ( 5

22 ( 5

TABLE 5: Diffusion Coefficient Extracted from the Attenuation of the ISF Induced by the Longitudinal Motion of the Water Molecules Obtained from MD Simulations relative adsorbed pressure amount (des) (mmol/g) 0.12 0.23 0.33 0.67 0.85

4.9 5.9 6.4 11 11.3

Dtrans (m2 s-1)

Drot (ps-1)

τrot (ps)

(4.0 ( 1.0) × 10-11 (1.2 ( 0.3) × 10-10 (3.0 ( 0.6) × 10-10

(2.0 ( 1.0) × 10-2 (1.0 ( 0.5) × 10-2 (2.0 ( 1.0) × 10-2 (4.0 ( 2.0) × 10-2 (3.0 ( 2.0) × 10-2

20 ( 10.0 40 ( 20.0 30 ( 15.0 15 ( 10.0 15 ( 10.0

proton. The reorientation of the water molecules is included in the Legendre polynomials Pl because its argument is the cosine of the angle between the initial and instantaneous directors joining the center. By assuming a monoexponential decrease of Pl[cos(θ(t))], the corresponding contribution from the water rotation to the incoherent dynamic structure factor becomes ∞

SRot (Q,t) ) [

(2l + 1)jl2 (Q|r bCH|)Il]δ(ω) + ∑ l)0 pl(l + 1)Drot

∞

(2l + 1)jl2(Q|r bCH|) ∑ l)0

π((pω)2 + (pl(l + 1)Drot)2)

(7)

where Il ) limtf∞ Pl[cos(θ(t))]. In the case where l ) 1, the halfwidth at half-height of the Lorentzian function used to model the experimental spectra reduces to

Γrot ) 2pDrot )

p dτrot

(8)

where d is the dimensionality of the system investigated and τrot the rotational characteristic time. As discussed by Sears,46 the simplifications implied in the derivation of eq 6 are valid only for isotropic liquids. One may wonder about its validity

Figure 17. Evolution with q2 of the full width at half-height of the Lorentzian functions used to model QENS spectra (λ ) 10 Å) in the radial direction. (A) Translational component. (B) Rotational + translational component.

for describing the reorientation of confined liquids. Furthermore, in the case of water adsorbed on clay minerals, due to the


Michot et al. TABLE 6: Dynamical Parameters Deduced from the Analysis of the QENS Spectra in the Radial Direction for a Wavelength λ ) 10Å adsorbed relative amount pressure (mmol/g) 0.15 0.30 0.43 0.84 0.61des

Figure 18. Comparison between the dynamical parameters deduced from MD simulations and QENS measurements in the radial direction (λ ) 10 Å). (A) Rotation. (B) Translation.

specific interactions between the clay surface and confined water molecules, the directors cannot reorient freely, leading to a splitting of the NMR resonance line as detected by 2H NMR of heavy water in the presence of clays.49-51 We then used MD to check if the data treatment classically applied in QENS experiments can truly be used in the case of our system. Figure 8 displays the time variation of the Legendre polynomials (eq 6) induced by the reorientation of water molecules confined within saponite at a relative humidity equal to 0.33. The time variation of the Legendre polynomials (Figure 8A) is similar to that of the ISF (Figure 6); it is perfectly fitted by a biexponential law with two well-separated time scales. It must also be pointed out that the long time asymptotic value of all the polynomials differ from zero due to the preferential orientation of the confined water molecules, in agreement with NMR experiments.49-51 As a consequence, not only the term l ) 0 but all the other components of eq 6 may contribute significantly to the ISF.46 Figure 8B exhibits the variation of the corresponding factors allowing to quantify the relative importance of the various components of eq 6. For wavenumbers smaller than 1.5 Å-1, only the two first components (with l ) 0 and 1) contribute significantly to the evaluation of the ISF induced by the water rotation, but at wavenumbers larger or equal to 2 Å-1, the contribution from the next component (with l ) 2) cannot be neglected in the analysis. Figure 9 compares the ISF directly evaluated by the analysis of the rotation motion of the confined water molecules (eq 5b) and that evaluated from the summation of the Legendre polynomials (eq 6 with l ) 0-4). Despite the numerous

5.1 5.9 6.4 13.0 12.0

Dtrans (m2 s-1) (8.3 ( 4) × 10-11 (1.2 ( 0.5) × 10-10 (3.5 ( 1) × 10-10 (3.1 ( 1) × 10-10

τ0 (ps)

L (Å)

τrot (ps)

- 41 ( 10 56 ( 15 1.4 ( 0.5 47 ( 10 81 ( 20 1.9 ( 0.5 49 ( 10 64 ( 20 2.4 ( 0.5 19 ( 5 71 ( 20 2.4 ( 0.5 18 ( 5

assumptions used in the derivation of eq 6,46 both approaches yield similar results even if the structural properties of the confined water molecules differ significantly from that of an isotropic liquid. The approximation based on the summation of the Legendre polynomials slightly underestimates the contribution of water rotation to the ISF with a maximum deviation of 5%. As shown above, the use of eq 8 to determine characteristic rotation times appears valid. Through the use of such an approximation and by taking into account a dimensionality of 2, the derived rotation times are around 2.3 ps for all relative pressures corresponding to the monolayer state and around 2ps for the relative pressures corresponding to the bilayer state. This suggests that the rotational movement observed can be assigned to water molecules bound to the interlayer cation. The values thus obtained are of the same order of magnitude as that observed for Li-montmorillonite by Cebula et al.3 Typical fits of the quasi-elastic signals obtained in the radial direction are presented in Figure 10 whereas Figure 11 displays the evolution as a function of Q2 of the width of the Lorentzian functions used in the modeling of the quasi-elastic spectra. Except, for the sample with the lowest adsorbed amount (5.1 mmol/g, P/P0 ) 0.15) that can be satisfactorily fitted with a single Lorentzian function, two Lorentzians are needed to fit the experimental spectra. The narrow signal with a q-dependent width is assigned to a translational movement (Figure 11A) whereas the broad signal is assigned to a convolution of rotation and translation (Figure 11B) and its width is then that of the translational component plus a constant rotational term. According to such a treatment, the widths of the two Lorentzians used to fit the data are linked, and we then constrained the program QENSFIT to obtain fits that fulfill such a relation. This model remains rather primitive and can certainly be criticized, especially considering that for Q values larger than 1 Å-1, as shown in Figure 8B and in various references (e.g., ref 52), higher orders of the Sears expansion should be taken into account. As a consequence, contributions from rotational movements may be underestimated in our analysis, which may tend to slightly broaden the width of the translational Lorentzian. However, as will be shown in the next sections, the rather simple analysis we chose to use captures well most of the dynamical features of confined water with a relatively low number of adjustable parameters. In the case of the sample with the lowest adsorbed amount (5.1 mmol/g) (i.e., when only isolated hydrated cations are present in the interlayer space),26 rotational movements dominate the quasi-elastic spectra, and no attempt was made to experimentally determine a translational component though it may well be present. The characteristic rotation time derived for that sample (τrot ) 2.4 ps) is similar to that deduced from experiments in the longitudinal direction, which suggests that fast rotational movements are similar irrespective of the orientation. A similar conclusion can be obtained for the rotation in



Figure 19. Comparison between the EISF deduced from MD simulations and QENS measurements in the longitudinal direction.

all other samples that exhibit rotational characteristic times very similar to those determined in the longitudinal direction (Table 3). The translational component is best fitted on the basis of the random jump diffusion model, which considers the residence time τ0 for one site in a given network before jumping to another site.5,53 In that framework, Strans inc (Q,ω) can be written as

Strans inc (Q,ω) )

Γtrans(Q) 1 2 π (pω) + Γ (Q)2

(9)

trans

and the halfwidth at half-height of the Lorentzian can be written as

Γ(Q) )

DtransQ2p 1 + DtransQ2τ0

(10)

Dtrans is the translational diffusion coefficient between two sites and the mean jump diffusion length L is defined as L ) x2dDtransτ0 where d is the dimensionality of the space investigated. Whereas the use of the jump-diffusion model appears justified in the case of the bilayer state, where a significant leveling is observed at high q, it is certainly more debatable in the monolayer systems as a simple translational diffusion model could be used as well. A similar conclusion was reached in a recent QENS study on a natural saponite clay carried out at a wavelength of 4 Å.54 The translational coefficients obtained using such a model (Table 3) are lower for the monolayer samples, a significant difference being observed between the sample at a relative pressure of 0.30 where the hydrogen-bond network is not complete and that at a relative pressure of 0.43 that displays a fully H-bonded percolating network.26 In contrast, the difference observed between the samples in the bilayer state in adsorption and in desorption can certainly not be considered as significant as they are only due to small differences in the full width at half-maximum (fwhm) at high q where the uncertainty on the decomposition is rather high.

Figure 12 displays the corresponding elastic incoherent structure factors that are defined experimentally as

EISF )

Ielast(Q) Ielast (Q) + 1inelast(Q)

(11)

The presence of Bragg peaks is noticeable for q-values around 1.5 Å-1. Taking into account the adsorption-desorption isotherm presented in Figures 1, it is possible to define for each sample the relative amount of protons from the structural OH groups of the clay layers. The theoretical values of the elastic incoherent structure factor (EISF) are then around 0.33, 0.30, 0.28, 0.18, and 0.16 for adsorbed amounts of 5.1, 5.9, 6.4, 12, and 13 mmol/g, respectively. It clearly appears that for the time window used to study fast water motions, a significant proportion of the interlayer H atoms are seen immobile in the experiment. It then appears difficult to deduce any information about confinement volumes for the wavelength used. Slow Water Motions. All the data obtained for an incident wavelength of 10 Å were treated by taking into account the fast rotational movements derived from data obtained for an incident wavelength of 5 Å. This means that a Lorentzian with fixed fwhm corresponding to the rotational correlation times displayed in Table 3 was added in all the spectra obtained at 10 Å incident wavelength. Figure 13 presents the evolution as a function of Q2 of the width of the narrow Lorentzian function used to fit quasi-elastic spectra in the longitudinal direction. The corresponding rotation correlation times are reported in Table 4. The values thus obtained are close to those reported in the literature where values around 20-30 ps are often reported.7-8 As the values obtained are much higher than those corresponding to single water molecules (around 1.5 ps3), these movements can be assigned to the collective planar rotation of hydration water molecules (i.e., the rotation of a cluster Na+ ion + water molecules). It also appears that for a relative pressure of 0.43 (i.e., when the interlayer space is filled with a complete monolayer, rotational movements in the longitudinal direction are significantly slowed down. The presence of such clusters can be evidenced from GCMC simulation (Figure 14A). To prove this point more convincingly, we have calculated the radial


Michot et al.

Figure 20. Comparison between the EISF deduced from MD simulations and QENS measurements in the radial direction.

Figure 21. Evaluation of the self-diffusion propagator of confined water in a saponite sample with an adsorbed amount of 6.4 mmol/g for various diffusion times (A) R2 e 1 Å2. (B) R2 e 10 Å2. (C) R2 e 70 Å2.

TABLE 7: Diffusion Coefficients Extracted from the Attenuation of the ISF Induced by the Radial Motion of the Water Molecule relative pressure (des)

adsorbed amount (mmol/g)

mean square displacement (m2s-1)

Dtrans (m2 s-1)

0.12 0.23 0.33 0.67 0.85

4.9 5.9 6.4 11.0 11.3

(4.0 ( 0.4) × 10-11 (1.4 ( 0.2) × 10-10 (1.8 ( 0.3) × 10-10 (7.0 ( 1.0) × 10-10 (8.0 ( 1.0) × 10-10

(5.0 ( 1.0) × 10-11 (2.0 ( 0.4) × 10-10 (2.0 ( 0.4) × 10-10 (7.0 ( 2.0) × 10-10 (6.0 ( 2.0) × 10-10

distribution function for cation/water (Figure 14B) evaluated for the configuration of Figure 14A. The cation water coordination is clearly evidenced with a first neighbor around 5 Å. In addition, we have observed how many water molecules initially present at less than 7 Å from the cation remain at such separation after a given time t. The decorrelation curve (Figure 14C) presents a bimodal distribution with a short time (11ps) for 20% of the water molecules and a very long time (570 ps) for 72%. This justifies the slow rotation interpreted as corresponding to water molecules coordinated to the cation. Indeed the rotational time observed (50 ps) is much slower than the average residence time of these water molecules within the cation solvation layer (600 ps). The experimental values can be directly compared to those derived from the analysis of MD simulations. Table 5 displays the apparent mobility of the water molecules in the longitudinal direction extracted from the exponential fit of the corresponding

τ0 (ps)

Drot (ps-1)

τrot (ps)

84 60 4 1

(3.0 ( 1.0) × 10-2 (4.0 ( 2.0) × 10-3 (5.0 ( 2.0) × 10-3 (1.0 ( 0.5) × 10-2 (5.0 ( 2.0) × 10-3

10 ( 5 60 ( 30 50 ( 30 25 ( 12 50 ( 30

component of the ISF, after subtraction of the fast component (see QENS Modeling Section). The variation of the apparent mobility as a function of the q2 is analyzed on the basis of a constant rotational contribution plus a diffusion component that varies according to eq 10. If no significant curvature is detected on the variation of the apparent mobility, eq 10 is then linearized and the residence time of the mean jump diffusion model cannot be determined. The uncertainty on the rotational mobility is large because this parameter results from the extrapolation of the apparent mobility corresponding to a wave number equal to zero. Figure 15 provides a direct comparison of the rotational time constants deduced from either experiments or molecular dynamics. The results obtained by both approaches are in good agreement with a similar evolution and close values. It appears that for the complete monolayer system, rotational time constants are higher, which reveals that rotational movements in the longitudinal direction are slowed down in agreement with the


Figure 22. Motion of an initially slow water molecule with regard to the clay layer.

determination of a well-connected hydrogen-bond network.26 MD simulations reveal a translational component for high water content. Such a component was not observed in the experimental QENS modeling procedure. It could have been added but, as shown in Figure 6C,D, in the longitudinal direction the contribution of translation to the total signal is rather low. It would then have been rather artificial to extract such a contribution from the experimental data. Figure 16 shows typical fits observed at high resolution. As previously mentioned, the quasi-elastic spectra are fitted using three components: a broad Lorentzian corresponding to the fast rotation deduced from the analysis of low-resolution data and two narrow Lorentzian functions corresponding respectively to slow rotation + translation and translation. The evolution of the width of the Lorentzian functions used for fitting quasi-elastic spectra in the radial direction is displayed in Figure 17. As in the case of the data obtained at a wavelength of 5 Å, for an adsorbed amount of 5.1 mmol/g, no q-dependence is observed revealing that rotational movements dominate the signal. For all the other samples, translation (Figure 17A) and rotation (Figure 17B) are present. This is particularly obvious in the bilayer samples for high-adsorbed amounts. As for lowresolution data, the translational component is best approached by a jump diffusion model, though such an assumption is certainly not fully robust especially for the two samples with lower adsorbed amounts, where the leveling of the width in the higher q-range is not completely obvious. Table 6 presents the obtained results. As in the case of data obtained for an incident wavelength of 5 Å, there is a significant difference in the translational diffusion coefficient for the two samples in the monolayer region with values of 8 × 10-11 and 1.2 × 10-10 m2 s-1 for adsorbed amounts of 5.9 and 6.4 mmol/ g, respectively. Compared to values already obtained for montmorillonite by molecular simulation and neutron spin echo (NSE),11-12 the values thus obtained reveal slower translational movements that can be assigned to the higher charge of saponite compared to montmorillonite as well as to the tetrahedral charge location. In the analysis carried out in the present work, the TOF technique does not appear to underestimate relaxation times as reported in refs 11-12. In our opinion, this discrepancy is because of the fact that by working with oriented samples, we

J. Phys. Chem. C, Vol. 111, No. 27, 2007 9829 were able in our analysis to separate rotational from translational movements, which provides a better estimate of the translational dynamics. The two samples in the bilayer domain exhibit similar translational coefficients around 3.5 × 10-10 m2 s-1. It then appears that the translational diffusion of water is at least three times faster in the bilayer region compared to the monolayer domain. Furthermore, the way in which equilibrium is reached (i.e., adsorption or desorption) does not seem to modify the dynamical characteristics of water molecules. There again, the valuesobtainedareslowerthanthoseobtainedformontmorillonite3-7,11-12 where values ranging between 7 × 10-10 and 1 × 10-9 m2 s-1 are classically obtained. This shows the influence of charge density and charge location on the dynamical properties of interlayer water molecules. In comparison to the values obtained by NSE for bilayer Na-vermiculite (1.6-1.8 × 10-10 m2 s-1),9 the values derived here by the TOF technique are only slightly higher, showing that high-charge saponite has a behavior closer to vermiculite than to montmorillonite. Charge location in the clay layer then appears as an important parameter in determining the dynamical properties of adsorbed water molecules. To extend the above discussion, it is useful to compare our experimental results with those derived from MD (Table 7 and Figure 18). The resulting translational mobilities are fully compatible with the radial self-diffusion coefficients obtained from the long-time asymptotical variation of the mean-squared radial displacement (Figure 2). This set of data is in good quantitative agreement with the experimental data though MD predict slightly faster translational movements in the bilayer regime. By contrast with the analysis of the experimental data, our numerical predictions result from the analysis of the ISF based on a single detectable exponential decrease of the ISF. A careful inspection of the numerical data (Figure 4,B) reveals a reduced oscillation of the numerical data around the exponential fit in the intermediate range of diffusion time (between 30 and 100 ps). That reduced feature suggests the existence of a third component, ensuring the transition between the fast and the slow decreasing regimes identified previously (see Section C). This analysis will perhaps provide a supplementary rotation time fitting the intermediate time scale like those reported in Table 3. However, because of the statistical noise and the small gap between the second and third diffusion regime, we refrain to extend our analysis of the numerical data on the basis of three exponentials. Finally, Figures 19 and 20 present for all the samples the EISF measured on the basis of the fitting procedure previously described together with those extracted from the apparent residual ISF in the longitudinal and radial direction, respectively. Both techniques provide a good agreement in both directions especially for the two extreme samples for adsorbed amounts of 5.1 and 12 mmol/g. The quantitative agreement is less satisfactory for adsorbed amounts of 5.9 and 6.4 mmol/g where QENS measurements yield EISF that are significantly lower than those obtained by MD simulation. This discrepancy may be due to the low dimensionality54 of the system that strongly affects the intensity at zero energy transfer. As shown in ref 54, such a problem could have been addressed by carrying out a more systematic study of the evolution of the spectra as a function of energy resolution. In the longitudinal direction (Figure 19), in the cases where a significant proportion of water molecules is investigated, the EISF can be interpreted as indicative of the confinement geometry. In the bilayer regime, the EISF appears constant for q-values >1 Å-1. Such a value would correspond to a distance

9830 J. Phys. Chem. C, Vol. 111, No. 27, 2007 of around 6 Å, which is perfectly coherent with the d-spacing of 15 Å observed in such a case (Table 1). For the samples in the monolayer region, the experimental EISF at high q is affected by the presence of a Bragg peak, and it is then difficult to provide a clear value for the leveling off of the EISF. However, the EISF derived from molecular dynamics simulation does not appear to level even for q ) 1.5 Å-1, which suggests confinement distance lower than 4 Å, in agreement again with the d-spacing of 12.5 Å. In the radial direction (Figure 20), in the monolayer regime for an adsorbed amount of 6.4 mmol/g both the experimental and simulated EISF appear constant for q-values >0.75 Å-1 (i.e., for a distance around 8.5 Å). For the sample in the bilayer region, for an adsorbed amount of 12 mmol/g the leveling off of the EISF appears for q > 0.6 Å-1 (i.e., for a distance around 10.5 Å). In that region, at high q-values the calculated EISF increases as a function of the wave number in contrast with the expected behavior (cf. Figure 4). That discrepancy could result from an incomplete analysis of the ISF that should include an additional exponential component. In all cases, the experimental and simulated EISF do not reach the theoretical limits, which could discredit to some extent the dynamical analysis carried out in this paper. To check for potential problems associated with this feature, we have evaluated for the system with an adsorbed amount of 6.4 mmol/g the self-diffusion propagator of confined water (Figure 21). It exhibits a Gaussian behavior for long times but for all diffusion times, there is a proportion of slower water molecules (slower but not immobile). For various diffusion times (0.02, 0.2, 2, 20, and 200 ps), we have identified the 10% slowest water molecules that influence the start of the propagator. From one diffusion time to another, these water molecules are not the same ones, which clearly shows that no confined water molecules are blocked. This means that the dynamical analysis we carried out remains valid even if for a given time some of the water molecules are not counted in the analysis. In addition, we have evaluated the trajectories of these initially slow water molecules (Figure 22). They are initially located close to the center of the ditrigonal cavity and exhibit jumps with, sometimes, returns to the initial position. This could somehow justify the use of the jump diffusion model in our analysis of the dynamics. The mean displacement of these molecules however appears continuous as it results from an averaging over a large number of molecules. Conclusions and Perspectives In the case of synthetic clay systems, whose properties are well defined in terms of adsorbed water amount and structure, the combination of QENS modeling at two experimental resolutions and for two different orientations and MD simulations can provide a robust analysis of water dynamics. First, it enables us to reexamine and validate some of the approximations classically used in the analysis of water motion (i.e., separation between rotational and translational diffusion, preferred orientation of molecules, and contribution to the EISF). Second, it shows in a convincing way the very strong mobility reduction of confined bidimensional water, compared to bulk water, and allows looking at subtle effects such as the reduction of diffusion coefficients upon completion of the first hydrated layer. Third, it reveals significantly different dynamics in the radial and longitudinal directions, which shows that for lamellar materials such as clay minerals, it is more relevant to work with oriented samples rather than with powdered ones. In view of the importance of swelling clay minerals in the environment and in waste storage applications, the data derived

Michot et al. from the present study are clearly relevant, as they provide robust conclusions on water motions in the interlayer spaces for subnanosceond time scale. However, real swelling clay systems are in fact deformable porous media whose structure and organization vary at different spatial scales depending on hydration conditions. A full understanding of the dynamics of such complex assemblies must then encompass the various hierarchical scales present in these materials. The present study yields a precise description of dynamics at the elementary organization, and the information thus obtained can then be used as constraints for exploring upper scales, where other experimental techniques (e.g., NMR relaxometry, or pulsed field gradients NMR) and simulation strategies must be employed. Acknowledgment. The authors would like to thank Dr. Isabelle Bihannic and Dr. John Ramsay for their help in the TOF neutron scattering experiments and Dr. Jean Louis Robert for providing the synthetic saponite sample used in this study. We would also like to thank the three anonymous reviewers of this paper for their constructive comments and judicious suggestions. References and Notes (1) Michot, L. J.; Villie´ras, F.; Franç ois, M.; Bihannic, I.; Pelletier, M.; Cases, J. M. C. R. Geosci. 2002, 334, 611-631. (2) Madsen, F. T. Clay Miner. 1998, 33, 109. (3) Cebula, D. J.; Thomas, R. K.; White, J. W. Clays Clay Miner. 1981, 29, 241. (4) Poinsignon, C.; Estrade-Schwarzckopf, J.; Conard, J.; Dianoux, A. J. Proceedings International Clay Conference Denver, 1985; Schultz, L. G., Van Olphen, H., Mumpton, F. A., Eds.; The Clay Minerals Society: Bloomington, IN, 1987; p 284. (5) Tuck, J. J.; Hall, P.; Hayes, M. H. B.; Ross, D. K.; Poinsignon, C. J. Chem. Soc., Faraday Trans. 1984, 80, 309. (6) Tuck, J. J.; Hall, P.; Hayes, M. H. B.; Ross, D. K.; Hayter, J. K. J. Chem. Soc., Faraday Trans. 1985, 81, 833. (7) Poinsignon, C. Solid State Ionics 1997, 97, 399. (8) Swenson, J.; Bergman, R.; Howells, W. S. J. Chem. Phys. 2000, 113, 2873. (9) Swenson, J.; Bergman, R.; Longeville, S. J. Chem. Phys. 2001, 115, 11299. (10) Mamontov, E. J. Chem. Phys. 2004, 121, 9193. (11) Malikova, N.; Cadene, A.; Marry, V.; Dubois, E.; Turq, P.; Zanotti, J.-M.; Longeville, S. Chem. Phys. 2005, 317, 226. (12) Malikova, N.; Cadene, A.; Marry, V.; Dubois, E.; Turq, P. J. Phys. Chem. B 2006, 110, 3206. (13) Skipper, N. T.; Lock, P. A.; Tililoye, J. O.; Swenson, J.; Mirza, Z. A.; Howells, W. S.; Fernandez-Alonso, F. Chem. Geol. 2006, 230, 182. (14) Chang, F.-R. C.; Skipper, N. T.; Sposito, G. Langmuir 1995, 11, 2734. (15) Marry, V.; Turq, P. J. Phys. Chem. B 2003, 107, 1832. (16) Malikova, N.; Marry, V.; Dufreˆche, J.-F.; Simon, C.; Turq, P.; Giffaut, E. Mol. Phys. 2004, 102, 1965. (17) Malikova, N.; Marry, V.; Dufreˆche, J-F.; Turq, P. Curr. Opin. Colloid Interface Sci. 2004, 9, 124. (18) Berend, I.; Cases, J. M.; Franç ois, M.; Uriot, J. P.; Michot, L. J.; Masion, A.; Thomas, F. Clays Clay Miner. 1995, 43, 324. (19) Cases, J. M.; Berend, I.; Franç ois, M.; Uriot, J. P.; Michot, L. J.; Thomas, F. Clays Clay Miner. 1997, 45, 8. (20) Ferrage, E.; Lanson, B.; Sakharov, B. A.; Drits, V. A. Am. Mineral. 2005, 90, 1358. (21) Ferrage, E.; Lanson, B.; Malikova, N.; Planç on, A.; Sakharov, B. A.; Drits, V. A. Chem. Mater. 2005, 17, 3499. (22) Eypert-Blaison, C.; Michot, L. J.; Humbert, B.; Pelletier, M.; Villie´ras, F.; d’Espinose de la Caillerie, J.-B. J. Phys. Chem. B 2002, 106, 730. (23) Michot, L. J; Villie´ras, F. Clay Miner. 2002, 37, 39. (24) Pelletier, M.; Michot, L. J.; Humbert, B.; Barre`s, O.; d’Espinose de la Caillerie, J.-B.; Robert, J.-L. Am. Mineral. 2003, 88, 1801. (25) Michot, L. J.; Bihannic, I.; Pelletier, M.; Rinnert, E.; Robert, J.-L. Am. Mineral. 2005, 90, 166. (26) Rinnert, E.; Carteret, C.; Humbert, B.; Fragneto-Cusani, G.; Ramsay, J. D. F.; Delville, A.; Robert, J. L.; Bihannic, I.; Pelletier, M.; Michot, J. L. J. Phys. Chem. B 2005, 109, 23745. (27) Hamilton, D. L.; Henderson, C. M. B. Mineral. Mag. 1968, 36, 832.

Diffusion of Water in Synthetic Clay by TOF and MD (28) Cygan, R. T.; Liang, J. J.; Kalinichev, A. G. J. Phys. Chem. B 2004, 18, 1255. (29) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (30) Heyes, D. M. Phys. ReV. B 1994, 49, 755. (31) Hummer, G. Chem. Phys. Lett. 1995, 235, 297. (32) Pabst, A. Am. Mineral. 1955, 40, 967. (33) Ferrage, E. Etude expe´rimentale de l’hydratation des smectites par simulation des raies 00l de diffraction des rayons X. Implications pour l’e´tude d’une perturbation thermique sur la mine´ralogie de l’argilite du site Meuse-Haute Marne. The`se de Doctorat, Universite´ Joseph Fourier, Grenoble, France, 2004. (34) Adams, D. J. Mol. Phys. 1974, 5, 1241. (35) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1994. (36) Delville, A. Langmuir 1991, 7, 547. (37) Delville, A. J. Phys. Chem. 1995, 99, 2033. (38) Porion, P.; Al Mukhtar, M.; Fauge`re, A. M.; Pellenq, R. J. M.; Meyer, S.; Delville, A. J. Phys. Chem. B 2003, 107, 4012. (39) Evans, D. J.; Murad, S. Mol. Phys. 1977, 34, 327. (40) Fincham, D. Mol. Simul. 1992, 8, 165. (41) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684.

J. Phys. Chem. C, Vol. 111, No. 27, 2007 9831 (42) Schoen, M.; Cushman, J. H.; Diestler, D. J.; Rhykerd, C. L. Jr. J. Chem. Phys. 1988, 88, 1394. (43) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; Academic Press: London, 1990. (44) Bee, M. Quasi-Elastic Neutron Scattering; Adam Hilger: Philadelphia, PA, 1988. (45) Beé, M. Chem. Phys. 2003, 292, 121-141. (46) Sears, V. F. Can. J. Phys. 1967, 45, 237. (47) Sears, V. F. Can. J. Phys. 1966, 44, 1279. (48) Harpham, M. R.; Ladanyi, B. M.; Levinger, N. R. J. Phys. Chem. B 2005, 109, 16891. (49) Delville, A.; Grandjean, J.; Laszlo, P. J. Phys. Chem. 1991, 95, 1383. (50) Petit, D.; Korb, J. P.; Delville, A.; Grandjean, J.; Laszlo, P. J. Magn. Reson. 1992, 96, 1992. (51) Woessner, D. E.; Snowden, B. S., Jr. J. Chem. Phys. 1969, 50, 1516. (52) Liu, L.; Faraone, A.; Chen, S.-H. Phys. ReV. E. 2002, 65, 041506. (53) Egelstaff, P. A. An Introduction to the Liquid State; Clarendon: Oxford, 1992. (54) Chakrabarty, D.; Gautam, S.; Mitra, S.; Gil, A.; Vicente, M. A.; Mukhopadhyay, R. Chem. Phys. Lett. 2006, 426, 296. (55) Lechner, R. E. Solid State Ionics 1995, 77, 280.

Diffusion of Water in a Synthetic Clay with Tetrahedral Charges by

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