Article pubs.acs.org/JPCC
Anisotropy of Water Dynamics in Clays: Insights from Molecular Simulations for Experimental QENS Analysis V. Marry,*,†,‡ E. Dubois,†,‡ N. Malikova,§ J. Breu,∥ and W. Haussler⊥ †
UPMC Univ Paris 06, UMR 7195, PECSA, F-75005 Paris, France CNRS, UMR 7195, PECSA, F-75005 Paris, France § LLB (CEA - CNRS), CEA Saclay, 91191 Gif-sur-Yvette, France ∥ Lehrstuhl für Anorganische Chemie I, Universität Bayreuth, D-95440 Bayreuth, Germany ⊥ Heinz Maier-Leibnitz Zentrum (MLZ), D-85748 Garching, Germany ‡
S Supporting Information *
ABSTRACT: We measure H2O dynamics in a well-defined synthetic hectorite clay by the neutron spin echo technique, in the temperature range from 240 to 347 K. The interlayer spaces of this anisotropic material contain two layers of confined water, corresponding to the so-called bihydrated state. We analyze the experimental data in light of parallel molecular dynamics simulations. Simulations demonstrate that H2O diffusion in the direction perpendicular to the clay layers is not negligible and has to be taken into account in the experimental data analysis. A diffusive model with only two fitting parameters D⊥ and D∥ is well adapted for such analysis. A clear physical meaning for the two fitting parameters exists, in view of the geometry of the system. Experimentally, the diffusion coefficients parallel to the clay layers D∥ were estimated to be slowed down by a factor of 5 compared to bulk water. Further, the activation energy of the diffusion process is higher than in bulk water especially toward the lower temperatures within the range studied (20.3 kJ/mol above 300 K increasing to 28.4 kJ/ mol below 300 K). Simulations suggest that this is connected to the presence of the cations (1 cation per every 8 water molecules) rather than to the formation of hydrogen bonds between H2O molecules and the clay layers. However, improvements of microscopic force fields are necessary to achieve a full quantitative interpretation of the experimental water diffusion coefficients. We suggest the importance of polarizability in such endeavors.
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INTRODUCTION Water dynamics in (charged) confining media is of importance in many areas, including chemistry (heterogeneous catalysis), soil science (permeability and transport in clays), or biology/ biotechnology (encapsulation). Among the large variety of geometries and surfaces, we focus here on a single confining system and geometry: low-hydrated charged clays presenting a quasi-planar confinement for water and ions. Clays are widely studied due to their omnipresence in soils and many technological applications, one of which is the underground storage of radioactive waste, e.g., ref 1. The synthetic fluorohectorite clay used here is a homogeneous model system, well-characterized in the past,2 which enables us to study confined water structured as two layers between the adjacent planar clay surfaces, in the so-called interlayer. We compare the observed H2O motion to the reference of bulk water, and we do so in a range of temperatures, which allows us to determine the related activation energies. In extension to our previous approach, where we considered a pure two-dimensional (2D) motion in the interlayer,2,3 here we investigate H2O translational dynamics both in the plane of the clay surfaces and © 2013 American Chemical Society
perpendicular to them, as the presence of two H2O layers allows some mobility in this direction. This we suggested already in ref 4. On the contrary, in the case of a single H2O layer, we consider the pure 2D motion as the appropriate model.5 The dynamics of water and ions in clays has been studied in the past years both by experimental6−14 and simulation techniques.15−19 Our approach distinguishes itself in the close combination of both of these, which is becoming more represented in the clay science community, both for dynamic and structural properties.9,20 More precisely, here we associate quasi-elastic neutron scattering experiments (the neutron spin echo technique - NSE) with molecular dynamics (MD) simulations, which both give access to molecular motion on the picosecond to nanosecond time scale. Contrary to the more widely used time-of-flight (TOF) neutron scattering technique, NSE gives access to the intermediate scattering function in the Received: April 15, 2013 Revised: June 26, 2013 Published: June 28, 2013 15106
dx.doi.org/10.1021/jp403501h | J. Phys. Chem. C 2013, 117, 15106−15115
The Journal of Physical Chemistry C
Article
rehydration at RH = 85% (relative humidity). The water uptake is 7.4 H2O molecules per cation, with the initial water amount being less than 1 H2O molecules per cation.23 Neutron Spin Echo Experiments. Neutron spin echo (NSE) experiments are performed on the RESEDA spectrometer (FRMII, Münich, Germany) for six temperatures between 240 and 347 K. The sample is placed in a flat aluminum cell with an indium seal. The thickness is 2 mm, with an equivalent water thickness of 0.25 mm. With the combination of NSE and NRSE (neutron resonant spin echo), correlation times between 1 ps and 1 ns are reached.24,25 We use two configurations of incident neutron wavelength (λ): λ = 4.6 Å for the shortest correlation times and λ = 5.3 Å for the rest. The wavevectors are chosen as small as possible in the range 0.3 Å−1 < Q < 0.9 Å −1, while avoiding Bragg peaks so that the incoherent scattering contribution dominates. The signal of an empty cell is measured and subtracted from the signal of the sample, and the resolution is measured on a graphite sample. At the end, the incoherent intermediate scattering function Sinc(Q, t) is obtained. While temperature is varied, we checked that the sample remains in the bilayer state by neutron diffraction (incident neutron wavelength of 2.425 Å, G4.1 diffractometer, LLB, CEA Saclay, France). Nevertheless, the diffraction peak reflecting the bilayer interlayer spacing shifts slightly with temperature. This corresponds to an almost linear variation of the interlayer spacing from 15.42 to 15.58 Å, when the temperature is increased from 240 to 347 K. Simulations. In molecular simulations, molecules (clay and mobile species) are described at the atomic scale and moved according to Newton’s equations of motion. For that purpose, the interactions between the atoms of the system must be calculated. The interaction between two atoms is usually described as the sum of an electrostatic interaction, a van der Waals attraction, and an interatomic repulsion. The two last interactions are often taken into account by a Lennard-Jones potential. The general interaction between two atoms is then given by
time-domain and the comparison with MD data is more direct. Also, in general, the NSE technique allows measurements spanning longer correlation times than the TOF technique, into the nanosecond regime.21 The input of MD in our study is double. On one hand, the simulations allow several parameters to be isolated which cannot be obtained experimentally and, where appropriate, reinsert them into the fitting of the experimental data. Indeed, the use of unoriented powder clay samples in our experiments (the case of most studies on dynamics in confinement) gives rise to a signal averaged along all the directions with respect to the confinement and is difficult to analyze in detail unless some parameters are determined independently, here from MD. On the other hand, thanks to the detailed analysis of the simulated data, we were able to separate different contributions in diffusion mechanisms and then to study the conditions of validity of the models used in the analysis of the experimental results. : The detailed interplay between experimental analysis and simulations is depicted in Figure 1. It will be commented in several sections of the paper.
Figure 1. Molecular simulations as useful tools to analyze experimental data: (1) Direct calculation of dynamical quantities from simulations (e.g., mean square displacement or MSD method) allows one to suggest constraints or even decrease the number of fitting parameters in the models necessary in experimental analysis. (2) By comparing dynamical quantities obtained from simulations directly (MSD method) and indirectly (via modeling of the simulation-based S(Q, t)), the limits of validity of the model can be determined.
Vij =
⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij + 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ 4πε0rij r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠ qiqj
(1)
where qi and qj are the partial charges carried by the atoms and εij and σij are the Lennard-Jones parameters obtained from the corresponding atomic parameters using the Lorentz−Berthelot rules. All of these parameters depend on the force field chosen to describe the system. In the present study, we choose the flexible clayFF force field, slightly adapted to our synthetic clay, because it is shown to give transport properties of water close to experiment.5,18 The TIP4P/2005 model for H2O molecules is preferred to the SPC/E model we have used until now. Indeed, TIP4P/2005 is one of the best models to reproduce the phase diagram of water and it gives more accurate values of water diffusion coefficients over a wider range of temperatures, as will be shown in the next section. In our case, this point is important, since it will enable a more direct comparison with experimental values. Although TIP4P is not the original water model used in the clayFF force field, the use of this model with clayFF gives similar results to SPC and SPC/E models.26 The parameters for sodium cations are from Smith and Dang,27 originally used with clayFF.
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MATERIALS AND TECHNIQUES Samples. The sample considered here is a well-defined and homogeneous synthetic hectorite clay synthesized at high temperature.22 Its formula is [Na0.4]inter[Mg2.6Li0.4]oct[Si4]tetO10F2 for the half unit cell, which means that the charge is 0.4 e per half unit cell and is compensated by sodium counterions in the interlayer. This charge has been chosen because it is similar to the charge of the natural MX80 montmorillonite, reference clay in France for the studies of the radioactive waste storage. In this system, the structural OH− groups in the layers are replaced by F− atoms; therefore, there are no structural H atoms in the system. Thanks to the homogeneity of the clay, pure states can be obtained with either a monolayer of H2O molecules or a bilayer. The bilayer state investigated here is obtained from the dry clay (dried at 110 °C during 24 h) after 15107
dx.doi.org/10.1021/jp403501h | J. Phys. Chem. C 2013, 117, 15106−15115
The Journal of Physical Chemistry C
Article
Molecular dynamics simulations are performed in the NVT ensemble with the LAMMPS simulation package28 for the temperatures 270, 285, 300, 323, and 347 K, corresponding to the temperatures of the experiments. The clay+H2O simulation boxes contain two clay layers of lateral dimensions 41.92 × 45.47 Å2, corresponding to 80 unit cells of formula [Na0.4][Mg2.6Li0.4]Si4O10F2 per layer. The total number of counterions is then 64. The number of H2O molecules per cation used in the simulations is fixed to 8: it is close to the quantity of water taken by the clay when going from the dry state to the bihydrated state, considering that the dry state can contain some remaining H2O molecules.23 The initial interlayer spacing which fixes the volume V of the box is chosen to fit the corresponding experimental value obtained from the position of the (100) Bragg peak as a function of T. Thus, in the simulations, the interlayer spacings are fixed to 15.46 Å at 270 K, 15.48 Å at 285 K, 15.5 Å at 300 K, 15.54 Å at 323 K, and 15.58 Å at 347 K. For each temperature, we perform four simulations of 5 ns, after a phase of equilibration. All structural and dynamical quantities are averaged over these 20 ns. The error estimates are computed using the block averaging method.29
Figure 3. Experimental Sinc(Q, t) for Q = 0.7 Å−1 (symbols) and their fits with the model of eq 8 with D⊥ = 0.7D∥ (solid lines). For clarity, the experimental data points have been rescaled by the factor A(Q) (see text for details).
Considering that the characteristic time scales for the vibrational, rotational, and translational motion are rather different, these types of motion can be considered as decoupled. The expression of Sinc(Q, t) is then
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RESULTS AND DISCUSSION Principle of Experimental Analysis. Referring back to Figure 1, we note that experiments such as NSE give access to scattering functions. In particular, for the case of clays, via NSE we access the incoherent intermediate scattering function Sinc(Q, t). Examples of such functions can be seen in Figures 2
Sinc(Q, t ) = Svib(Q, t )Srot(Q, t )Strans(Q , t )
where Svib(Q, t) represents intramolecular vibrations of H2O molecules and Srot(Q, t) and Strans(Q, t) their overall rotational and translational motion. In the Svib(Q, t) term, we can also include librations of H2O molecules, corresponding to vibrations of H2O molecules inside a cage formed by surrounding molecules. In NSE experiments at temperatures close to ambient, the internal vibrations of H2O molecules cannot be seen, the corresponding energy transfers being beyond the cutoff energy probed by the NSE spectrometer (a few meV). However, the librations, which are about 10 times lower than intramolecular vibrations, somehow participate to the measured Sinc(Q, t). The time scale of these motions being less than a few picoseconds at these temperatures, Svib(Q, t) can however be considered as having almost reached a constant in the time range of the experiment (1−1100 ps). Let us denote it A(Q). Also, in the low Q range (
