Andrey G Kiselev

Kalinichev

Prof E Yu

Abdenacer Gorbaty

Idrissi

Mikhail G Kiselev

Andrey G Kalinichev

Introduction to the special issue of the Journal of Molecular Liquids "Supercritical fluids. Theory and applications" dedicated to

whether they are published or not. The documents may come

Introduction to the special issue of the Journal of Molecular Liquids "Supercritical fluids. Theory and applications" dedicated to Prof. Yu. E. Gorbaty

Professor Yuri E. Gorbaty was born 30 July 1932 in the city Grozny, in the Soviet Union. He has graduated from the Mendeleev Institute of Chemical Technology, Moscow, in 1955. He has got his Candidate of Sciences (Ph.D.) degree in 1963 for his work on "Non-equilibrium crystallization of the three-component melts", and later in 1988 he was awarded a Doctor of Sciences degree for the work "The effect of temperature and pressure on the nearest ordering in liquid and supercritical water". Between these two dates and then later in his scientific career Yuri E. Gorbaty has become one of the leading experts in the field of experimental studies of the structure and properties of fluids, especially aqueous fluids at high temperatures and pressures, by methods of IR and Raman spectroscopy and by X-ray diffraction.

The uniqueness of his approach to the studies of hydrothermal solutions was in the simultaneous application of several complementary methods to investigate the same object under the same set of thermodynamic conditions. He has devoted a lot of efforts to develop a range of very original and sophisticated experimental optical and X-ray diffraction cells that could reliably withstand extreme conditions of hydrothermal experiments, while still allowing optical and X-ray access to the fluid sample inside through very cleverly designed and carefully sealed windows [START_REF] Babashov | Cuvette for ir spectroscopy of highly absorbing fluids at high pressures and temperatures, Instrum[END_REF][START_REF] Gorbatyi | A simple setup for changing the polarization of laser-radiation[END_REF][START_REF] Gorbatyi | A high-temperature high-pressure-cell for Raman-spectroscopy[END_REF][START_REF] Gorbaty | High-pressure, high-temperature 2-chamber cell with changeable path lengths for accurate measurements of absorption-coefficient[END_REF][START_REF] Gorbaty | Reliable high-pressure seal for multiple applications[END_REF][START_REF] Gorbaty | Soldered high-pressure high-temperature sapphire window[END_REF][START_REF] Gorbaty | High-pressure X-ray cell for studying the structure of fluids with the energy-dispersive technique[END_REF][START_REF] Gorbaty | High-pressure high-temperature Raman cell for corrosive liquids[END_REF][START_REF] Gorbaty | Experimental technique for quantitative IR studies of highly absorbing substances at high temperatures and pressures[END_REF][START_REF] Gorbaty | High-temperature and high-pressure cell for kinetic measurements of supercritical fluids reactions with the use of ultraviolet-visible spectroscopy[END_REF]. Particularly interesting and effective is the IR cell, the thickness of the absorbing layer in which can vary within a range of 0-1.5 mm directly during the experiment at high temperatures (up to 550 °C) and pressures (up to 1500 bars) with an accuracy of ± 0.5 μm [START_REF] Gorbaty | High-pressure, high-temperature 2-chamber cell with changeable path lengths for accurate measurements of absorption-coefficient[END_REF]. In the cell for Raman spectroscopy with internal vessels, the fluid sample only contacts with sapphire and gold, which avoids any interaction of the metal walls of the high-pressure cell with highly corrosive supercritical solutions [START_REF] Gorbaty | High-pressure high-temperature Raman spectroscopy of liquid and supercritical fluids[END_REF]. Cells for energy dispersive X-ray diffractometry, UV spectroscopy and many other devices were also created for conducting physical experiments at high temperatures and pressures [START_REF] Gorbaty | High-pressure X-ray cell for studying the structure of fluids with the energy-dispersive technique[END_REF][START_REF] Gorbaty | High-temperature and high-pressure cell for kinetic measurements of supercritical fluids reactions with the use of ultraviolet-visible spectroscopy[END_REF].

The most valuable data were obtained by measuring the intensity of X-ray scattering from water up to t = 550 °C and P = 1000 bar and up to 8000 bar at room temperature and for the first time extracting experimental information about molecular pair correlation functions of water under these extreme conditions [14][START_REF] Gorbatyi | X-ray-diffraction studies of the structure of liquid and supercritical water at high-temperatures and pressures. 2. The molecular density radial-distribution functions and the paired correlation-functions[END_REF][16][START_REF] Gorbaty | The pair-correlation functions of water at a pressure of 1000 bar in the temperature-range 25-500[END_REF][START_REF] Gorbaty | Effect of pressure on the short-range molecular ordering in liquid water[END_REF][START_REF] Gorbaty | An X-ray study of the effect of pressure on the structure of liquid water[END_REF][START_REF] Okhulkov | X-ray-scattering in liquid water at pressures of up to 7.7 kbar -test of a fluctuation model[END_REF]. These data were complemented by the results of studies using infrared absorption spectroscopy and Raman scattering [START_REF] Bondarenko | Infrared-spectra ν 3 of HDO under high-pressure and temperature[END_REF][START_REF] Bondarenko | Effect of temperature and pressure on vibration-rotation spectra of water supercritical phase[END_REF][START_REF] Bondarenko | Analysis of contour of ν 2 + ν 3 absorption-band in spectra of liquid D 2 O at temperatures from 20 to 350 °C[END_REF][START_REF] Bondarenko | Molecular Rotational and Vibrational Spectra of Deuterated Water at Pressures Up to 500 bar and Temperature Up to 550[END_REF][START_REF] Bondarenko | An infrared study of water-vapor in the temperature-range 573-723-K -dimerization enthalpy and absorption intensities for monomer and dimer[END_REF][START_REF] Bondarenko | In situ Raman spectroscopic study of sulfur-saturated water at 1000 bar between 200 and 500 °C[END_REF][START_REF] Gorbaty | Experimental technique for quantitative IR studies of highly absorbing substances at high temperatures and pressures[END_REF][START_REF] Gorbaty | The effect of pressure on hydrogen bonding in water: IR study of ν(OD) HDO at pressures of up to 1500 bar[END_REF].

Yu.E. Gorbaty proposed a new approach to the description of the structure of liquid and supercritical water, based on the percolation theory. It was shown that the liquid and supercritical states differ qualitatively depending on the existence or absence of an infinite cluster of hydrogen-bonded molecules [START_REF] Gorbaty | The physical state of supercritical fluids[END_REF][START_REF] Gorbaty | The structural features of liquid and supercritical water[END_REF]. The percolation threshold for a three-dimensional network of hydrogen bonds in water is reached in the region of the critical isotherm. Below the percolation threshold, only clusters of finite size can exist in the supercritical region. This explains many interesting and still misunderstood phenomena that occur during the transition of a liquid to the supercritical state. One of the brilliant findings of Prof. Gorbaty together with his colleagues was the experimentally proven idea of universality of hydrogen bonding behavior of alcohols under supercritical conditions [START_REF] Barlow | An IR study of hydrogen bonding in liquid and supercritical alcohols[END_REF]. Until his last days, he was always full of new ideas, and was always ready to share them with his colleagues.

Bibliography of Yuri Gorbaty's publications in chronological order


A G Kalinichev
email: kalinich@subatech.in2p3.fr

N Loganathan

B F Ngouana Wakou

Z Chen

Interaction of ions with hydrated clay surfaces: Computational molecular modeling for nuclear waste disposal applications

Keywords: mineral-water interfaces, clay, molecular dynamics simulations, nuclear waste disposal

The Callovo-Oxfordian clay formation (COx) is the potential host rock for long term nuclear waste repository in France. The clayey component of COx consists mostly of illite, smectite and interstratified illite/smectite (I/S) clay minerals. We performed a series of molecular dynamics (MD) computer simulations in order to quantify the molecular scale mechanisms responsible for the adsorption and transport of ions at the hydrated surfaces of illite, smectite, and I/S clays. New structural models of illite, smectite, and I/S allowed us to identify several structurally different adsorption sites at the basal surfaces of all three clay substrates. Adsorption free energy profiles above each individual adsorption site on each clay surface for a wide range of metal cations were then calculated and the metal sorption properties for the three clay surfaces are compared in terms of the preferable sorption sites and their surface distributions, most stable adsorption distances, and free energies of adsorption. The resulting equilibrium constants for surface adsorption and ion exchange were calculated and found in general agreement with available literature data. The observed discrepancies between the exchange energies obtained in the current MD simulations and the values obtained through the interpretation of recent X-ray reflectivity measurements can be attributed to the differences in the description of the exchange reaction equilibria between the experimental conditions and the simplified conditions of our simulations.

Introduction

Safe and sustainable geological nuclear waste disposal poses major scientific challenges to the efforts to minimize the environmental footprint of nuclear energy for extremely long periods. [START_REF] Grambow | Geological disposal of nuclear waste: From laboratory data to the safety analysis[END_REF][START_REF] Sellin | The use of clay as an engineered barrier in radioactive-waste management[END_REF] To that purpose, safety assessment models must account for radionuclides behavior over time-and distance-scales spanning many orders of magnitude in space and time. Complementary to substantial experimental work in this field, [START_REF] Grambow | Nuclear waste disposal: Laboratory simulation of repository properties[END_REF] significant efforts are made to develop numerical models that would allow to understand the interactions of radionuclides with natural and engineered barriers (consisting mostly of clay and cementitious materials) and to predict their behavior in the geosphere on various scales from the molecular-level adsorption and transport in clay nanopores to the larger scale geochemical mobility in macroscopically heterogeneous systems. [START_REF] Rotenberg | Multiscale modelling of transport in clays from the molecular to the sample scale[END_REF] Computational molecular modeling can be especially effective in providing fundamental molecular level information on the energetics, structure, and dynamics of ions and water molecules in clay nanopores. [START_REF] Cygan | Molecular models and simulations of layered materials[END_REF] We used molecular dynamics (MD) computer simulations in order to quantify the molecular scale mechanisms responsible for the adsorption and transport of hydrated cations at the basal surfaces of illite, smectite, and interstratified illite/smectite clays and to clarify current macroscopic thermodynamic, geochemical and transport models. The MD simulations with the CLAYFF force field [START_REF] Cygan | Molecular models of hydroxide, oxyhydroxide, and clay phases and the development of a general force field[END_REF] were performed for a number of monovalent (Li + , Na + , K + , Rb + , Cs + ) and divalent (Mg 2+ , Ca 2+ , Sr 2+ , Ba 2+ , Ni 2+ , UO2 2+ ) cations, but our primary focus [START_REF] Loganathan | Quantifying mechanisms of site-specific ion exchange at an inhomogeneously charged surface: Case of Cs + /K + on hydrated muscovite mica[END_REF][START_REF] Wakou | Structural arrangements of isomorphic substitutions in smectites: Molecular simulation of the swelling properties, interlayer structure, and dynamics of hydrated Cs-montmorillonite[END_REF][START_REF] Loganathan | Structure, energetics, and dynamics of Cs + and H2O in hectorite: Molecular dynamics simulations with an unconstrained substrate surface[END_REF][START_REF] Chen | Molecular dynamics simulation of Cs + adsorption on the basal surface of interstratified illite-smectite: Structure, surface hydration and ion exchange[END_REF] is on the behavior of Cs + as one of the most important radionuclide in radioactive waste [START_REF] Grambow | Nuclear waste disposal: Laboratory simulation of repository properties[END_REF][START_REF] Chen | Key factors to understand in-situ behavior of Cs in Callovo-Oxfordian clay-rock (France)[END_REF] which can also be unintentionally introduced in the environment in case of nuclear accidents. [START_REF] Yoshida | Land-surface contamination by radionuclides from the Fukushima Daiichi nuclear power plant accident[END_REF]

Models and methods

All three clay minerals studied belong to the so-called 2:1 clay family and represent layered structures made of several stacking T-O-T units in which one sheet of Al-cations (O) octahedrally coordinated by oxygens and hydroxyls is sandwiched between two sheets of tetrahedrally coordinated Si-cations (T). Isomorphic substitutions (typically, Mg for Al in the octahedral sheets and/or Al for Si in the tetrahedral sheets) give rise to a negative clay layer charge that is compensated by the presence of cations in the interlayer space and on the surface of clay particles.

The newly developed models allowed us to identify several structurally different energetically favorable adsorption sites at the basal surfaces of all three clay substrates. MD simulation results are quantitatively analyzed in terms of the adsorption free energy profiles above each individual adsorption site on each clay surface for each individual cation. For the most highly charged case of muscovite (illite) the tetragonal sheets of the model consisted of hexagonal (ditrigonal) rings of either Si4Al2 or Si5Al composition in equal proportions randomly distributed within the structure and yielding 3 different types of adsorption sites for the charge compensating cations: H2a -two Al tetrahedra are symmetrically places across each other in the hexagonal ring and separated by the presence two Si tetrahedra in the same ring; H2b -two Al tetrahedra asymmetrically separated in the ring by one and three Si tetrahedra from each side, making them in closer proximity to each other than in the symmetric case; H1 -a hexagonal ring containing only one Al substitution. [START_REF] Loganathan | Quantifying mechanisms of site-specific ion exchange at an inhomogeneously charged surface: Case of Cs + /K + on hydrated muscovite mica[END_REF] On the smectitic surfaces of montmorillonite and I/S (both having much lower structural charge than illite) five such types of sites can be identified: H1 as above in muscovite, H0 -a "normal" hexagonal ring without substitution; T1 -above a tetrahedrally substituted Al; type T0 -a "normal" tetrahedral Si site without a substitution next to it; and T0a -a "normal" tetrahedral Si site adjacent to a tetrahedrally substituted Al. [START_REF] Wakou | Structural arrangements of isomorphic substitutions in smectites: Molecular simulation of the swelling properties, interlayer structure, and dynamics of hydrated Cs-montmorillonite[END_REF] It is worth noting that the tetrahedral sites T1, T0, and T0a are also present on the illite surface, but they are not analyzed here because all MD simulations have demonstrated that due to the high illitic surface charge and high concentration of the charge-balancing cations these sites remain unoccupied and do not participate in adsorption processes. The molecular model of the interstratified I/S particles 10 was based on the concept of so-called fundamental particles, [START_REF] Ufer | Rietveld refinement of disordered illite-smectite mixed-layer structures by a recursive algorithm. II: Powder-pattern refinement and quantitative phase analysis[END_REF] which implies that the mixed-layer I/S particles are divided at the interlayer smectitic spaces, therefore the I/S surface sites are similar to the sites of montmorillonite smectite.

The adsorption free energy profiles of ions as function of their distance from the clay surface at thermodynamic equilibrium were determined using potential of mean force (PMF) calculations with the umbrella sampling algorithm, which are discussed in detail elsewhere. [START_REF] Loganathan | Quantifying mechanisms of site-specific ion exchange at an inhomogeneously charged surface: Case of Cs + /K + on hydrated muscovite mica[END_REF] The calculations were performed separately for each individual surface site defined above in order to provide quantitative information on their site-specific adsorption strength and to determine the ion exchange mechanisms on the surface.

Results and discussion

On the surface of muscovite mica (our model of illite), K + ions are naturally present as part of the muscovite composition, and can be exchanged for Cs + from the interfacial aqueous solution. Our MD simulations show that irrespective of the surface site, inner-sphere adsorption represents the most stable surface complex for both K + and Cs + (Fig. 1). Such an adsorption structure is dictated primarily by the high structural charge and strong electrostatic attraction of the cations, which presents a very high energy barrier for the formation of outer-sphere surface complexes or for a complete desorption. Also, regardless of the cationic nature, the strength of the stable adsorption sites is ordered in a sequence of H2a > H2b > H1, which should be attributed to the nature of interaction potentials used in the simulation. In the CLAYFF parameterization, tetrahedrally coordinated Al atoms bear a partial positive charge that is ~30% lower compared to the tetrahedrally coordinated Si atoms. [START_REF] Cygan | Molecular models of hydroxide, oxyhydroxide, and clay phases and the development of a general force field[END_REF] In addition, the bridging oxygen atoms coordinating substituted Al tetrahedra are ~11% more negative than ordinary bridging oxygens around Si tetrahedra. Due to these relatively minor local charge inhomogeneities the short range cation-surface electrostatic interactions are significantly affected and lead to individual site-specific differences in the adsorption strength. Fig. 1. Adsorption free energy profiles of K + and Cs + ( in kJ/mol) as functions of their distance from the surface for 3 different adsorption sites on the muscovite basal surface. [START_REF] Loganathan | Quantifying mechanisms of site-specific ion exchange at an inhomogeneously charged surface: Case of Cs + /K + on hydrated muscovite mica[END_REF] The adsorption sites H2a, H2b, and H1 are defined in the text.

The overall thermodynamic equilibrium of the Cs + /K + ion exchange reaction can be represented by the equation Cs + (aq) + K + -X ⇌ Cs + -X + K + (aq), where X indicates a specific surface adsorption site, and the differences of the hydration free energies of Cs + and K + in bulk aqueous solution are also taken into account. Since muscovite surface contains, on average, 1/6 of sites H2a, 1/3 of sites H2b, and 1/2 of sites H1, the total energy for the Cs + /K + equilibrium exchange reactions is the weighted sum of the exchanges at all three sites. The final thermodynamic parameters of this exchange reaction are estimated to be ∆GCs+/K+ = -4.6 kJ/mol and and Kex = 0.7, in reasonable agreement with the experimentally deduced energetics. [START_REF] Lee | Changes in adsorption free energy and speciation during competitive adsorption between monovalent cations at the muscovite (001)-water interface[END_REF] The discrepancies can be attributed to the differences in the description of exchange reaction equilibria between the experimental conditions and the simplified conditions of our simulations. [START_REF] Loganathan | Quantifying mechanisms of site-specific ion exchange at an inhomogeneously charged surface: Case of Cs + /K + on hydrated muscovite mica[END_REF] For the adsorption of Cs + and Na + on the smectitic surface of I/S clay, [START_REF] Chen | Molecular dynamics simulation of Cs + adsorption on the basal surface of interstratified illite-smectite: Structure, surface hydration and ion exchange[END_REF] our simulations show that: (i) Cs + is improbable to be sorbed on the tetrahedral sites (T1 and T0); (ii) Cs + on such sites is easily exchangeable by Na + existing in the system; (iii) Cs + and Na + can be present together on the I/S basal surface (at different adsorption sites); (iv) Cs + /Na + cation exchange observed in experimental studies [START_REF] Chen | Key factors to understand in-situ behavior of Cs in Callovo-Oxfordian clay-rock (France)[END_REF] should correspond to the Cs + /Na + cation exchange reaction on sites H1 and H0 only (Fig. 2), with sites H0 being strongly predominant, due to the low structural charge and low concentration of H1 sites on the surface of I/S particles. The free energy of the exchange reaction is estimated to be ∆GCs+/Na+ = -2.73 kJ/mol. Fig. 2. Adsorption free energy profiles of Cs + and Na + ( in kJ/mol) as functions of their distance from the surface of I/S clay and the mechanism of their exchange on the hexagonal adsorption site. [START_REF] Chen | Molecular dynamics simulation of Cs + adsorption on the basal surface of interstratified illite-smectite: Structure, surface hydration and ion exchange[END_REF]

Acknowledgements

This work was supported by the industrial chair "Storage and Management of Radioactive Waste" at the Ecole des Mines de Nantes, funded by ANDRA, Areva, and EDF. Generous allocations of supercomputing resources made available within the Distributed European Computing Initiative (projects DECI-07-NUWCLAY and DECI-11-COMPCLAY by the PRACE-2IP receiving funding from the European Community's FP7/ 2007-2013 under grant agreement RI-283493) and at the GENCI supercomputing facilities in France (projects x2012096921, x2013096921, and x2014096921) are also most gratefully acknowledged.


Marek Szczerba

Artur Kuligiewicz

Arkadiusz Derkowski

Vassilis Gionis

Georgios D Chryssikos

Andrey G Kalinichev

Structure and dynamics of water-smectite interfaces: Hydrogen bonding and the origin of the sharp O-Dw/O-Hw infrared band from molecular simulations

Keywords: clay-water interface, adsorbed water, smectite, molecular dynamics, infrared spectroscopy

Experimental studies have shown that a sharp high-frequency IR band at ~3615 cm -1 (in H2O form) and at ~2685 cm -1 (in D2O form) is a common feature for all smectites, and its position correlates with layer charge. In order to explain the molecular origin of this band in terms of total layer charge, charge localization, as well as nature of interlayer cations influencing the position and intensity of this peak, a series of classical MD simulations were performed for several smectite models. The smectite layers were described using a modified CLAYFF force field, where the intramolecular vibrations of H2O were more accurately described by the Toukan-Rahman potential. The power spectra of molecular vibrations of hydrogens were calculated for selected sub-sets of interlayer H2O to quantitatively analyze their contribution to the observed spectral features. The statistics of hydrogen bonds in the smectite interlayers were also analyzed to support the spectral calculations.

The simulation results demonstrated clearly that only the H2O molecules in close proximity with the smectite surface are responsible for the observed sharp vibrational band.

Other hypotheses on the possible origins of this band were carefully considered and eventually rejected. Two orientations of H2O molecules donating one or two H-bonds to the basal oxygens of the smectite surface (monodentate and bidentate orientations, respectively) are observed. In both orientations these H-bonds are quite weak, pointing to a generally hydrophobic character of the smectite surface. Both orientations were found to contribute to the high-frequency band, but the monodentate orientation provides the predominant contribution because surface H2O molecules in this orientation are much more abundant. In good agreement with experiment, only a small difference in the peak position was observed between smectites with different charge localization. The effect of the total layer charge, i.e. the red-shift for higher charge smectites, was also confirmed. This shift arises from the decrease of the H-bonding distances of H2O in monodentate and bidentate orientation.

INTRODUCTION

Fourier transform infrared spectroscopy (FTIR) is one of the most commonly used techniques for studying clay minerals. However, unambiguous assignment of the vibrational bands originating from the stretching modes of adsorbed molecular H2O (O-Hw) and structural OH (O-Hs) in the clay materials is not always feasible. This is especially true for swelling clay minerals like smectites, which have large water sorption capacities (e.g., [START_REF] Cases | Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite. 3. The Mg 2+ , Ca 2+ , Sr 2+ and Ba 2+ exchanged forms[END_REF][START_REF] Sato | Effects of layer charge, charge location, and energy change on expansion properties of dioctahedral smectites[END_REF] and may contain significant amounts of adsorbed water under air-dry conditions even upon prolonged drying (e.g., [START_REF] Środoń | Surface area and layer charge of smectite from CEC and EGME/H2O retention measurements[END_REF]. Kuligiewicz et al. (2015a) have recently presented new evidence that the sharp highfrequency bands observed at ~3610-3640 cm -1 involve a significant contribution from weakly hydrogen-bonded O-Hw of adsorbed H2O molecules. These observations were in agreement with earlier spectroscopic measurements [START_REF] Russell | Infrared spectroscopic study of the dehydration of montmorillonite and saponite[END_REF]Farmer and Russell, 1971;[START_REF] Suquet | Etude par la spectroscopie infrarouge de l' eau adsorbée par la saponite-calcium[END_REF][START_REF] Sposito | Structure of water adsorbed on smectites[END_REF][START_REF] Cariati | Water molecules and hydroxyl groups in montmorillonites as studied by near infrared spectroscopy[END_REF][START_REF] Cariati | Polarization of water molecules in phyllosilicates in relation to exchange cations as studied by near infrared spectroscopy[END_REF][START_REF] Sposito | Infrared spectroscopic study of adsorbed water on reduced-charge Na/Li-montmorillonites[END_REF], and opened the possibility for obtaining layer charge diagnostics based on the vibrational signature of H2O in smectite (Kuligiewicz et al., 2015b).

Early computational molecular modeling studies of clays [START_REF] Skipper | The structure of interlayer water in vermiculite[END_REF][START_REF] Chang | Computer simulation of interlayer molecular structure in sodium montmorillonite hydrates[END_REF][START_REF] Boek | Monte Carlo molecular modeling studies of hydrated Li-, Na-, and K-smectites: Understanding the role of potassium as a clay swelling inhibitor[END_REF][START_REF] Greathouse | Monte Carlo and molecular dynamics studies of interlayer structure in Li(H2O)3-smectites[END_REF][START_REF] Sposito | Surface geochemistry of clay minerals[END_REF] suggested the existence of H-bonds between water and siloxane surfaces. This H-bonding implies a specific spatial arrangement of the surface H2O molecules with respect to oxygen atoms of the basal plane. These MD calculations confirmed the model of [START_REF] Prost | Interactions between adsorbed water molecules and the structure of clay minerals: Hydration mechanism of smectites[END_REF] with one O-Hw bond of the H2O molecule directed towards the clay surface, donating an H-bond to the basal oxygen atom.

The existence of such interfacial H-bonding with one O-Hw bond oriented towards the clay surface was later confirmed by simulations of smectites and muscovite (e.g. Wang et al., 2005b[START_REF] Wang | Asymmetric hydrogen bonding and orientational ordering of water at hydrophobic and hydrophilic surfaces: A comparison of water/vapor, water/talc, and water/mica interfaces[END_REF][START_REF] Marry | Structure and dynamics of water at a clay surface from molecular dynamics simulation[END_REF][START_REF] Marry | Anisotropy of water dynamics in clays: Insights from molecular simulations for experimental QENS analysis[END_REF][START_REF] Morrow | Structure, energetics, and dynamics of smectite clay interlayer hydration: molecular dynamics and metadynamics investigation of Na-hectorite[END_REF][START_REF] Ngouana Wakou | Structural arrangements of isomorphic substitutions in smectites: Molecular simulation of the swelling properties, interlayer structure, and dynamics of hydrated Cs-montmorillonite revisited with new clay models[END_REF][START_REF] Greathouse | Molecular simulation of structure and diffusion at smectite-water interfaces: Using expanded clay interlayers as model nanopores[END_REF][START_REF] Teich-Mcgoldrick | Swelling properties of montmorillonite and beidellite clay minerals from molecular simulation: Comparison of temperature, interlayer cation, and charge location effects[END_REF][START_REF] Zaunbrecher | Molecular models of cesium and rubidium adsorption on weathered micaceous minerals[END_REF], Loganathan et al., 2016a, 2016b), using more sophisticated force fields, specifically optimized for clay mineral studies, such as CLAYFF (Cygan et al., 2004). The existence of an additional type of interfacial H2O located above the ditrigonal cavities of smecites and with both O-Hw bonds directed towards the basal surface was also reported for 2:1 sheet silicates of high total layer charge (Wang et al., 2005b[START_REF] Wang | Asymmetric hydrogen bonding and orientational ordering of water at hydrophobic and hydrophilic surfaces: A comparison of water/vapor, water/talc, and water/mica interfaces[END_REF]. Ab-initio calculations showed that these Hbonds are relatively short-lived and weaker than typical H2O•••H2O in liquid water [START_REF] Boek | Ab initio molecular dynamics study of the hydration of a sodium smectite clay[END_REF].

In addition, [START_REF] Suzuki | Study of vibrational spectra of interlayer water in sodium beidellite by molecular dynamics simulations[END_REF] calculated the theoretical FTIR spectra of water adsorbed on Na-beidellite with total layer charge of 0.33 per half unit cell (phuc). Based on their modeling, the O-Hw bonds pointing towards the surface of beidellite contribute to a vibrational band at ~3500 cm -1 , whereas the O-Hw H-bonded to other H2O molecules produce a band at ~3365 cm -1 . The relative intensity of the ~3365 to the ~3500 cm -1 bands increased with increasing water content, and for 7 H2O molecules phuc the band at ~3500 cm -1 was no longer detectable.

The experimental and theoretical evidence of the hydrophobic character of the siloxane surface of uncharged clays has been broadly discussed in the literature (e.g., Michot et al., 1994, Bridgeman and[START_REF] Bridgeman | A Monte Carlo study of water at an uncharged clay surface[END_REF][START_REF] Arab | Structure and dynamics of the interlayer water in an uncharged 2 : 1 clay[END_REF][START_REF] Tunega | Ab initio molecular dynamics study of a monomolecular water layer on octahedral and tetrahedral kaolinite surfaces[END_REF][START_REF] Wang | Molecular modeling of the 10angstrom phase at subduction zone conditions[END_REF]2005a;[START_REF] Churakov | Ab initio study of sorption on pyrophyllite: Structure and acidity of the layer organization of water and ions in synthetic Na-smectite with tetrahedral layer charge. Part 2. Toward a precise coupling between molecular simulations and diffraction data[END_REF][START_REF] Rotenberg | Molecular explanation for why talc surfaces can be both hydrophilic and hydrophobic[END_REF][START_REF] Šolc | Wettability of kaolinite (001) surfaces -Molecular dynamic study[END_REF].However, for the siloxane surface of charged clays, like smectites, the picture is not as clear. Based on aromatic hydrocarbon adsorption experiments, [START_REF] Jaynes | Hydrophobicity of siloxane surfaces in smectites as revealed by aromatic hydrocarbon adsorption from water[END_REF] have classified this surface as mostly hydrophobic. On the other hand, [START_REF] Sobolev | Water-clay surface interaction: A neutron scattering study[END_REF] have used neutron scattering technique to determine that the surfaces of smectite clays with tetrahedral substitutions are hydrophilic. The importance of the specific structural charge location within a clay layer for the existence of hydrophobic and hydrophilic patches on its surface has also been determined in Monte Carlo computer simulations [START_REF] Sposito | Surface geochemistry of clay minerals[END_REF]. The relative weakness of the Hbonds donated by the interlayer water molecules to the clay basal surface, compared to the typical strength of the H2O•••H2O bonds in bulk liquid water can be considered as a molecular-scale indication of relative hydrophobicity of the smectite siloxane surface.

The present study is aimed at advancing the aforementioned discussion by adding new spectroscopic arguments. Vibrational spectra of interfacial water molecules in several smectites are calculated and carefully analyzed here on the basis of molecular dynamics simulations in order to identify, interpret and quantify the variability of the position of the sharp H2O vibrational band as a function of total clay layer charge, layer charge localization, and nature of the interlayer cations, as recently observed experimentally (Kuligiewicz et al., 2015a).

METHODOLOGY

Smectite structures and MD simulations

In order to explore systematically the effects of smectite composition, type of the interlayer cations and water content on the structure of interlayer H2O, a series of MD simulations were performed on four models of dioctahedral smectites with a total layer charge of 0.3 or 0.5 phuc and octahedral (montmorillonitic) or tetrahedral (beidellitic) charge localization:

Beid03: M + 0.3(Al2.0)(Si3.7Al0.3)O10(OH)2; Beid05: M + 0.5(Al2.0)(Si3.5Al0.5)O10(OH)2;

Mtm03: M + 0.3(Al1.7 Mg0.3)(Si4.0)O10(OH)2; Mtm05: M + 0.5(Al1.5 Mg0.5)(Si4.0)O10(OH)2 .

The interlayer water content (2.5, 5.0 and 7.5 H2O phuc) and the type of the interlayer cation (Na + , Cs + , and Ca 2+ ) for selected water contents were used as additional variables.

The structural models of the smectites were built on the basis of the pyrophyllite crystal structure [START_REF] Lee | Single crystal X-ray refinement of pyrophyllite-1Tc[END_REF], with isomorphic substitutions introduced at specific atomic sites. The Mg/Al ordering in the octahedral sheets was set by maximizing the distance between Mg atoms, following the work of [START_REF] Ortega-Castro | Density functional theory and Monte Carlo study of octahedral cation ordering of Al/Fe/Mg cations in dioctahedral 2:1 phyllosilicates[END_REF]. The Al/Si ordering in the tetrahedral sheet was random but following the Löwenstein rule, i.e. excluding Al-O-Al linkages [START_REF] Löwenstein | The distribution of aluminum in the tetrahedral of silicates and aluminates[END_REF]. The simulation supercell was 8×4×2 unit cells in the a, b, and c crystallographic directions, respectively (~41.6 Å × 36.1 Å × Z Å; the value of Z varied in the ~12.5-19.0 Å range depending mainly on the amount of water in the interlayer space). The edge surfaces were not considered.

The atoms of the smectite structure were not fixed -i.e. they were allowed to move around their crystallographically determined positions according to the modeling force field used. Only one cation in one octahedral sheet was kept frozen in its position in order to keep 2:1 layers in place during the entire simulation span. Partial atomic charges and other interatomic interaction parameters of smectite layers were described using the CLAYFF force field (Cygan et al., 2004) with structural OH groups modified by introducing a more accurate Morse potential [START_REF] Greathouse | Implementation of a Morse potential to model hydroxyl behavior in phyllosilicates[END_REF]. Ewald summation was used to calculate the long range corrections to the electrostatic interactions and the cutoff distance was set at 10.0 Å.

Non-electrostatic Lennard-Jones parameters of the interatomic interactions involving bridging oxygen atoms were modified after Ferrage et al. (2011) in order to improve the description of the interlayer water structure of hydrated smectites. The necessity of this modification was justified based on comparisons of experimental and calculated XRD and neutron diffraction data (Ferrage et al., 2011). However, unlike the original suggestion of Ferrage et al. (2011), only the parameters of surface oxygen atoms were modified in our work, because initial test simulations showed that the modification for all bridging oxygen atoms leads to a substantial and unrealistic deformation of the clay octahedral sheet if the cell volume is not constrained in the simulations at constant pressure, i.e., in the NPT statistical ensemble (see Supplementary materials). Additionally, the Lennard-Jones parameters of tetrahedral Si and tetrahedral Al in the clay structure were also modified to compensate for the increased size of the surface bridging oxygen atoms by applying the usual arithmetic mixing rules for the parameters of interatomic interactions (Table 1).

=== Table 1 ===

For a more accurate description of the vibrational properties of water molecules, the parameters of intramolecular interactions for H2O were taken from the work of [START_REF] Toukan | Molecular-dynamics study of atomic motions in water[END_REF] using the implementation proposed by [START_REF] Praprotnik | Temperature dependence of water vibrational spectrum: A molecular dynamics simulation study[END_REF]. This allowed a more accurate description of the anharmonicity of the Ow-Hw stretching vibrations in the calculated IR spectra in comparison to the simple harmonic vibrational terms of the original CLAYFF parameterization (Cygan et al., 2004).

NPT-ensemble MD simulations at constant pressure (P = 1 bar) and temperature (T = 300 K) were performed for 2.0 ns with the time step of 1 fs, preceded by one temperature annealing cycle from 400 K to 300 K of 0.1 ns. This long equilibration run was followed by a short 10 ps data analysis run when atomic positions and velocities were recorded every 2 fs.

Standard periodic boundary conditions were applied (e.g., [START_REF] Allen | Computer Simulation of Liquids[END_REF]) and all simulations were performed using the LAMMPS molecular modeling program [START_REF] Plimpton | Fast parallel algorithms for short-range molecular dynamics[END_REF].

Simulation analysis

The MD-simulated structural data were used to calculate the distributions of angles formed by the dipole axis of interfacial H2O molecules with respect to a vector normal to the 2:1 surfaces (angle α) as a function of the distance z of Ow from the plane of the basal bridging oxygens (Ob). The direction of the H2O dipole was defined as a vector from the oxygen atom Ow to the central point between the two hydrogen atoms Hw of the same molecule. As the HOH angle was allowed to vary in the flexible H2O molecular model used, this methodology introduces some small additional spread of the calculated angles.

Additionally, the distributions of angles between a given OH bonds of H2O and a vector normal to the 2:1 surfaces were calculated as a function of the distance z from the Ob plane (angle β). The position of the plane of basal oxygen atoms was determined by the maximum of the atomic density distribution for these atoms, similarly to the previous studies (Wang et al., 2005b[START_REF] Wang | Asymmetric hydrogen bonding and orientational ordering of water at hydrophobic and hydrophilic surfaces: A comparison of water/vapor, water/talc, and water/mica interfaces[END_REF][START_REF] Loganathan | On the hydrogen bonding structure at the aqueous interface of ammonium-substituted mica: A molecular dynamics simulation[END_REF]Szczerba et al., 2014, Ngouana Wakou andKalinichev, 2014;[START_REF] Greathouse | Molecular simulation of structure and diffusion at smectite-water interfaces: Using expanded clay interlayers as model nanopores[END_REF][START_REF] Teich-Mcgoldrick | Swelling properties of montmorillonite and beidellite clay minerals from molecular simulation: Comparison of temperature, interlayer cation, and charge location effects[END_REF]Loganathan et al., 2016aLoganathan et al., , 2016b)). All these properties were calculated by averaging over the last 1 ns of the equilibrium MD simulation runs.

Calculation of power spectra

MD-simulated atomic trajectories can be used to calculate so-called power spectra (PS) of atomic vibrations that contain an entire distribution of the power (density of states) of all atomic motions in the simulated system in a function of vibrations frequency. With certain restrictions, these power spectra can be compared to the experimental vibrational spectra (e.g., [START_REF] Allen | Computer Simulation of Liquids[END_REF][START_REF] Kleinhesselink | The evaluation of power spectra in molecular dynamics simulations of anharmonic solids and surfaces[END_REF]. The power spectra are obtained as Fourier transformations of the so-called velocity autocorrelation function (VACF), which, in turn, can be directly calculated from the MD-simulated dynamic trajectories of the atoms in the modeled system. The frequency of H2O stretching vibration is usually well captured by the VACF of the water hydrogen atoms (e.g., [START_REF] Kalinichev | Molecular simulations of liquid and supercritical water: Thermodynamics, structure, and hydrogen bonding[END_REF].

In the present work, normalized VACF based on the last 10 ps period of every MD simulation run were calculated for selected hydrogen atoms with a moving window of 1 ps from the equilibrium part of the MD trajectory recorded every 2 fs:

            VACF VACF , 1 sel.atoms , 1 sel.atoms ) ( VACF n n f f f n n f t f f v v v v t     ; (2)
where nis the total number of windows, nVACFis the number of windows used in a particular calculation of VACF. The first sum in nominator and denominator corresponds to averaging over total number of windows minus the number of VACF windows. The second sum is calculated over all hydrogen atoms of water molecules, or their selected subset based on the distance of the respective H2O from the clay surface and the angle of H2O dipole orientation (or angle between one of OH groups of H2O and a vector normal to the 2:1 surface). The scalar products of instantaneous atomic velocities and their subsequent Fourier transformation into vibrational power spectra were calculated according to standard VACF and PS definitions (e.g., [START_REF] Allen | Computer Simulation of Liquids[END_REF][START_REF] Kleinhesselink | The evaluation of power spectra in molecular dynamics simulations of anharmonic solids and surfaces[END_REF]. For every VACF window, the determination of a H2O molecule as belonging to a selected position/orientation population was checked at the beginning and at the end of the VACF window. The chosen short duration of the analysis run (10 ps) is, nevertheless, long enough in respect to a typical H-bonding lifetime (0.8-0.9 ps; [START_REF] Kumar | Hydrogen bonding definitions and dynamics in liquid water[END_REF], but still short enough not to allow H2O to change significantly their positions in the interlayer with respect to the clay surface. At the same time, the relatively short time of the individual VACF window (1 ps) is comparable with a typical H-bonding lifetime, but still allows to probe the stretching dynamics of the selected O-Hw bonds (e.g., [START_REF] Kalinichev | Molecular simulations of liquid and supercritical water: Thermodynamics, structure, and hydrogen bonding[END_REF]. The choice of both characteristic calculation times ensured that the H-bonding situation of each H2O molecule was included in a certain selected angle/position subset for VACF calculation.

In order to calculate the power spectra of H2O vibrations, a cosine Fourier transform of VACF for the water hydrogen atoms was performed as:

) cos( ) ( VACF ) ( PS VACF 1 VACF          t n t n t (3)
The statistical noise was preliminarily reduced by applying a filtering function:

) / exp( ) ( VACF ) ( VACF  t t t    (4)
where τ was set to 0.25 ps.

Due to the normalization of VACF, the intensity of the calculated power spectra can, therefore, be considered as proportional to the total number of H2O molecules selected for each calculation.

RESULTS AND DISCUSSION

Characteristic features of MD simulations

The composition and adsorbed water content of all simulated clay models are presented in Table 2 along with the resulting basal spacings. The 2W model for Cs-smectite is purely hypothetical and does not correspond to any experimental or natural conditions (e.g., Ngouana Wakou and Kalinichev, 2014).

=== Table 2 ===

The values of the calculated basal spacings closely match those obtained by modelling the experimental diffractograms: d001_1W = 11.6-12.9 Å, d001_2W = 14.9-15.7 Å and d001_3W = 18-19 Å (e.g., Dazas et al., 2015). The data show clearly that for the same water content and interlayer cation (Na + ) the basal spacing d001 decreases with increasing layer charge (e.g.

15.95 Å for Mtm03Na_2W and 15.37 Å for Mtm05Na_2W). This trend is in agreement with literature data (e.g., [START_REF] Sato | Effects of layer charge, charge location, and energy change on expansion properties of dioctahedral smectites[END_REF], Ferrage et al., 2005[START_REF] Kumar | Hydrogen bonding definitions and dynamics in liquid water[END_REF], whereas some variation is related also to the layer charge location. Substantial differences in basal spacings were also observed as a result of the replacement of interlayer cations from Na + or Ca 2+ to Cs + (e.g., 15.37 Å for Mtm05Na_2W, 15.38 Å for Mtm05Ca_2W and 16.14 Å for Mtm05Cs_2W).

These differences were caused mainly by the increased size of the cation and by differences in hydration energies.

In agreement with other recent simulations (e.g. Wang et al., 2005b[START_REF] Wang | Asymmetric hydrogen bonding and orientational ordering of water at hydrophobic and hydrophilic surfaces: A comparison of water/vapor, water/talc, and water/mica interfaces[END_REF][START_REF] Morrow | Structure, energetics, and dynamics of smectite clay interlayer hydration: molecular dynamics and metadynamics investigation of Na-hectorite[END_REF][START_REF] Ngouana Wakou | Structural arrangements of isomorphic substitutions in smectites: Molecular simulation of the swelling properties, interlayer structure, and dynamics of hydrated Cs-montmorillonite revisited with new clay models[END_REF][START_REF] Greathouse | Molecular simulation of structure and diffusion at smectite-water interfaces: Using expanded clay interlayers as model nanopores[END_REF][START_REF] Teich-Mcgoldrick | Swelling properties of montmorillonite and beidellite clay minerals from molecular simulation: Comparison of temperature, interlayer cation, and charge location effects[END_REF][START_REF] Zaunbrecher | Molecular models of cesium and rubidium adsorption on weathered micaceous minerals[END_REF]Loganathan et al., 2016aLoganathan et al., , 2016b)), a typical snapshot of the interlayer structure (Figure 1) illustrated that H2O molecules close to the siloxane surface tend to be specifically oriented. Within a distance of < 3.5 Å between Ow and the siloxane surface two such preferred orientations could be distinguished. The population closer to the surface corresponds to H2O with both O-Hw bonds pointing towards the surface (bidentate), whereas a more distant and more pronounced population is due to the H2O pointing only one of their O-Hw bonds towards the surface and the second one towards the bulk of the interlayer (monodentate). In order to quantify these differences, these two populations were investigated as a function of smectite charge, type of the interlayer cations, and degree of hydration.

=== Figure 1 ===

Position of the cations in the interlayer space

The distribution of interlayer cations for different smectites (blue solid lines in Figures 2 and3) exhibited a clear dependence on the amount and location of layer charge, as well as on the type of the cation. In the case of 1W sodium smectites, two separate maxima were visible, each corresponding to inner-sphere coordination of H2O to the surface. For 2W sodium structures, a strong tendency to form a third maximum corresponding to fully hydrated cations (outer sphere) in the middle of the interlayer was observed. The ratio between the central and wing (inner sphere) cation distributions depended on the charge location, whereas changes in total charge had similar effect on both of these maxima. This result is in agreement with other recent simulations and is supported by calculated XRD data (Dazas et al., 2015;[START_REF] Teich-Mcgoldrick | Swelling properties of montmorillonite and beidellite clay minerals from molecular simulation: Comparison of temperature, interlayer cation, and charge location effects[END_REF]. In the case of 3W structures, outer-sphere sodium ions formed two maxima close to the interlayer center instead of one as in 2W. The data for the Mtm03Na_3W structure were very similar to the results presented by Dazas et al.

(2014). With increasing tetrahedral charge a tendency to form higher amount of inner-sphere complexes with the siloxane surface was observed.

The effect of changing interlayer cation from Na + to Ca 2+ was investigated for the models with 2W hydration. Comparison of smectites in Ca 2+ form (Figure 3) with those in Na + form (Figure 2) indicated that, despite the two-fold increase in the cation hydration enthalpy, the only effect was the vanishing of the (already weak) population of cations in the vicinity of the surface. The only exception was Beid05Ca_2W, for which some remaining contribution of ions forming inner-sphere complexes was observed.

=== Figure 2 === === Figure 3 === Oppositely, the lowest hydration enthalpy Cs + ions had a tendency to remain close to the surface (Figure 3), which is in excellent agreement with other recent Cs + -smectite simulations (Ngouana Wakou and Kalinichev, 2014;Teich-McGoldrich et al., 2015;[START_REF] Zaunbrecher | Molecular models of cesium and rubidium adsorption on weathered micaceous minerals[END_REF]Loganathan et al., 2016a). The distribution of Cs + in the interlayer was substantially different from those of Na + and Ca 2+ , which were generally quite similar to each other (compare Figures 2 and3).

H2O orientation

The and3).

The presence of monodentate H2O was ubiquitous. This sub-population was abundantly visible for all smectites, all cations and all hydration levels. A noticeable dependence of the location of the distribution maxima was however observed: higher average H2O dipole vector angles were observed for low charge smectites, lower hydration levels, and for Cs + as interlayer cation.

The bidentate H2O population was far less abundant. It could be detected only in high charge smectites and was practically absent in their low charge analogs. Layer charge increasing beyond 0.5 phuc is therefore expected increase further the amount of bidentate molecules, predicting its high contribution at charges approaching 1 phuc (mica, vermiculite), which was indeed reported by Wang et al. (2005b[START_REF] Wang | Asymmetric hydrogen bonding and orientational ordering of water at hydrophobic and hydrophilic surfaces: A comparison of water/vapor, water/talc, and water/mica interfaces[END_REF] and [START_REF] Loganathan | On the hydrogen bonding structure at the aqueous interface of ammonium-substituted mica: A molecular dynamics simulation[END_REF] on muscovite. Further, in all smectites studied, a dependence of the bidentate H2O population on hydration level was observed: for a given smectite, the relative number of bidentate H2O decreases upon drying.

The H2O orientation also depends on the type of the interlayer cation. As the majority of Cs + cations are located close to smectite surface, a noticeable decrease of bidentate H2O population in Cs + -smectites in comparison to their Na + -and Ca 2+ -analogs was observed. This effect was, however, small compared to the dependence of the bidentate population on layer charge. A noticeable decrease of the maximum amplitude corresponding to monodentate population was additionally observed for the Cs + form. This decrease was accompanied by the transfer of H2O to the middle of the interlayer.

Vibrational spectra of H2O in the smectite interlayer Kuligiewicz et al. (2015aKuligiewicz et al. ( , 2015b) ) found that the sharp high-frequency IR band originating from adsorbed water at ~3615 cm -1 (in H2O form) and ~2685 cm -1 (in D2O form) is a common feature for all hydrated smectites. Its intensity depended very little on the degree of clay hydration over a broad range of relative humidity, and its frequency exhibited a weak but systematic decrease (red-shift) upon increasing the total layer charge, with no measurable dependence on charge location. For a given layer charge, the dependence of the peak position on the field strength of the interlayer cation for high hydration enthalpy cations (Na + , Ca 2+ , Mg 2+ ) was negligible and only low hydration cations (Cs + , K + ) could be distinguished. These trends were opposite to what was observed for the main O-Hw (O-Dw) stretching envelopes, located at ~3400 cm -1 (~2500 cm -1 ). The latter envelopes were known to exhibit a strong dependence of their intensity on hydration level and their position on interlayer cation, but were relatively unaffected by the smectite layer charge or charge localization (e.g., [START_REF] Xu | Infrared study of water sorption on Na-, Li-, Ca-and Mg-exchanged (SWy-1 and SAz-1) montmorillonite[END_REF][START_REF] Madejová | FTIR analyses of water in MX-80 bentonite compacted from high salinary salt solution systems[END_REF], Kuligiewicz et al., 2015a, 2015b).

Thus, the sharp high-frequency IR band observed in water vapor-saturated smectites was attributed to a mechanism that must be common to all smectites at high hydration levels, regardless of interlayer cation. In addition, the high-frequency band must account for Hbonding interactions that are considerably weaker than those encountered in bulk H2O or aqueous solutions of common salts, and its exact position ought to show a measurable dependence on the total charge of the 2:1 layer (Kuligiewicz et al., 2015a(Kuligiewicz et al., , 2015b)).

In order to provide a quantitative explanation for the aforementioned experimental phenomenology, the power spectra for hydrogen atoms of interlayer H2O molecules were calculated for different smectites and compared to the spectrum of pure bulk water, the latter calculated with the same molecular model (Figure 4).

=== Figure 4 ===

The results showed that water in smectites exhibits a considerable increase of its spectral density at higher frequencies (~3600-3800 cm -1 ) in respect to bulk water spectrum.

The simulated spectrum of bulk water, however, shows some excessive high-frequency spectral density around 3730 cm -1 , which is not observed experimentally, and indicates some limitations of the present model. Nevertheless, the shape of the power spectrum of bulk water agrees perfectly well with the spectrum obtained earlier by the same methodology [START_REF] Tay | Hydrogen bond structure and vibrational spectrum of water at a passivated metal nanoparticle[END_REF]) and still represents one of the most accurate models describing the dynamics of Ow-Hw stretching vibrations in water (e.g., [START_REF] Kalinichev | Molecular simulations of liquid and supercritical water: Thermodynamics, structure, and hydrogen bonding[END_REF][START_REF] Guillot | A reappraisal of what we have learnt during three decades of computer simulations on water[END_REF]. Additionally, the calculated results do not show the low-frequency band at ~3250 cm -1 , which has been found in experimental data thus is consistent with an assignment of this band to Fermi resonance (Efimov and Naberukhin, 2002;[START_REF] Sovago | Hydrogen bonding strength of interfacial water determined with surface sum-frequency generation[END_REF].

Power spectra were also calculated for four different smectites with varying content of adsorbed water: Beid03Na, Beid05Na, Mtm03Na and Mtm05Na (Figure 5). The results

showed that with increasing number of H2O molecules in the smectite interlayer the relative intensity of the lower-frequency peak at ~3500 cm -1 increased. This was in qualitative agreement with the experimental observations of Kuligiewicz et al. (2015a), who reported that the higher-frequency peak is nearly fixed and the intensity of the lower-frequency peak is greatly varying with water content. In the present study, the peak intensity at ~3750 cm -1 was found to depend on hydration, but this can be to some extent related to the limitations of the specific H2O molecular models used.

=== Figure 5 ===

In order to further analyze the influence of different factors on the higher-frequency band, its positions was determined by fitting procedures. The low-frequency band was fitted with a mixed Gauss-Lorentz function (percentage of Lorentz function was optimized), while the higher-frequency one with a simple Gauss function. Additionally, a small combination band at ~ 4000 cm -1 was fitted with another Gaussian (Figure 6).

=== Figure 6 ===

Increasing smectite total layer charge was found to induce a noticeable red-shift of the high-frequency peak, in remarkable agreement with experiment data (Kuligiewicz et al., 2015b). This shift was observed in Na + montmorillonites and beidellites at any hydration level (Figure 7a) and also in the 2W forms for any cation (Figure 7b). Only one exception was found: Mtm05Na_3W exhibited higher frequency of the sharp peak than Mtm03Na_3W. In contrary to the experimental observations (Kuligiewicz et al., 2015a), the position of the high-frequency peak was found to depend on charge location and water content.

=== Figure 7 ===

In addition, the MD results showed a substantial difference in peak position between the Na + and Ca 2+ forms of smectites (Figure 7b), which are not visible experimentally (Figure 7c, Kuligiewicz et al., 2015a). Also the peak positions of the Cs + forms exhibited trends in relation to Na + and Ca 2+ forms that are different in MD than in experiment.

These discrepancies between the experimental trends and the outcome of MD simulations can be related to the approximations involved in the latter, primarily in certain features of the CLAYFF model (Cygan et al., 2004). The Lennard-Jones parameters of Ferrage et al. (2011) should be more accurately optimized, the hexagonal cavity in the tetrahedral sheet ought to have lower ditrigonal symmetry. A better description of the structure would affect the distribution and orientation of H2O. The model for H2O may also have limitations and the power spectra have excessive high-frequency spectral density at 3728 cm -1 . Finally, uncertainties introduced by the fitting procedure can be observed (Figure 6). In spite of all these limitations, the overall picture is relatively consistent: All the studied smectites exhibit a stretching band at lower frequencies and this band shift to lower energy upon increasing layer charge (Figure 7ab).

Molecular origin of the sharp O-Dw/O-Hw band

Calculations of the power spectra of specific sub-sets of interlayer water hydrogen atoms were performed in order to explain in more detail which part of the surface H2O population is responsible for the sharp high-frequency vibrational band observed in the experimental spectra (Kuligiewicz et al., 2015a). Each subset was defined by a common range of distances from the surface, z, and H2O dipole orientation angle, α (Figure 1). A H2O molecule belongs to a certain sub-set if it is found within the same (z, α) range in both the first and the last time-window of the VACF calculation. The results for three representative smectites (Mtm03Na_2W, Beid03Na_2W and Mtm05Ca_2W) are presented in Figure 8.

Spectral intensities were scaled by the number of H2O molecules identified in each subset in order to compare the contribution of each subset to the total spectrum.

=== Figure 8 === This analysis demonstrates that H2O molecules at the center of the interlayer are not responsible for producing the sharp spectral feature. The latter originates instead from the overlapping contributions of both monodentate and bidentate orientations of surface H2O. The contribution of the monodentate orientation is, however, much stronger because of the higher number of H2O molecules populating this sub-set. If present, bidentate H2O gives a very small, although non-negligible, contribution to the power spectrum at frequencies that are on average higher than those of the monodentate population. bond donated to the surface (e.g., [START_REF] Kalinichev | Molecular simulations of liquid and supercritical water: Thermodynamics, structure, and hydrogen bonding[END_REF][START_REF] Kumar | Hydrogen bonding definitions and dynamics in liquid water[END_REF]. Therefore, in order to obtain deeper insight into the studied problem, the distribution of the shortest Ow-Hw•••Ob distances in the monodentate and bidentate sub-sets were calculated (Figure 8, right column).

The results showed a relatively broad distribution of the distances, with the maximum for monodentate H2O at ~1.9 Å for Beid03_Na and Mtm05Ca_2W, and ~2.0 Å for Mtm03Na_2W. For comparison, in bulk liquid water the maximum of the shortest Ow-Hw•••Ow distance is at ~1.8 Å (e.g., [START_REF] Kalinichev | Molecular simulations of liquid and supercritical water: Thermodynamics, structure, and hydrogen bonding[END_REF][START_REF] Kumar | Hydrogen bonding definitions and dynamics in liquid water[END_REF]. The weighted average of the calculated Ow-Hw Mtm05Ca_2W the contribution of weak H-bonds due to H2O molecules in monodentate orientation was noticeably smaller. This explains the higher frequency and intensity of the high-frequency monodentate peak in the vibrational spectrum of this smectite. In the case of bidentate population, one of the O-Hw•••Ob distances had a maximum also at ~1.9-2.0 Å, resulting in an H-bond of a comparable strength, while the second one was significantly longer and, respectively, weaker. This analysis suggests that upon increasing total layer charge the H-bond distances of the bidentate sub-set are decreasing and causing the red-shift of the calculated power spectrum.

Due to its ubiquitous presence and relative abundance, the population of monodentate surface H2O is mainly responsible for the presence of the sharp high-frequency OH stretching feature observed in the experiments (Kuligiewicz et al., 2015a). This is in very good agreement with earlier experimental data (e.g., [START_REF] Russell | Infrared spectroscopic study of the dehydration of montmorillonite and saponite[END_REF]Farmer and Russell 1971;[START_REF] Prost | Interactions between adsorbed water molecules and the structure of clay minerals: Hydration mechanism of smectites[END_REF][START_REF] Suquet | Etude par la spectroscopie infrarouge de l' eau adsorbée par la saponite-calcium[END_REF][START_REF] Sposito | Structure of water adsorbed on smectites[END_REF][START_REF] Sposito | Infrared spectroscopic study of adsorbed water on reduced-charge Na/Li-montmorillonites[END_REF] which linked the high frequency band to H2O at the surface of the interlayer, pointing one of their O-Hw bonds towards the siloxane surface. In certain cases the bidentate sub-population may provide a non-negligible contribution as observed for higher charged smectites, e.g., for

Mtm05_Ca_2W.

Possible alternative molecular mechanisms responsible for the sharp O-Dw/O-Hw band

Evidence from MD simulations in support of the experimental data, suggested that the sharp high-frequency band in the IR spectra of hydrated smectite is clearly originating from H2O molecules oriented towards the clay surface. Can there be any other contribution to this sharp IR band? One possibility that would also be linked to surface H2O, could, for example, involve the second O-Hw bond of monodentate H2O, i.e. the one oriented towards the middle of the interlayer, away from the siloxane surface. As the surface H2O molecules have relatively fixed orientations, their O-Hw bonds that are pointing away from the surface might have a decreased number of available H-bond acceptors within a suitable range and orientation around them. Such a lower coordination could, in principle, contribute in part to the observed sharp high-frequency infrared band. To examine this possibility, the subsets representing two separate hydroxyls of the monodentate population in Mtm05Ca_2W and Mtm05Na_2W were investigated (Figure 9).

=== Figure 9 ===

In the case of monodentate H2O, one H-bond is donated to the surface (thick blue rectangle in Figure 9), while the second one is donated to another H2O (dashed orange rectangle in Figure 9). The corresponding power spectra show that only the hydrogens oriented towards the surface contribute to the high-frequency band. The power spectrum of the second hydrogen resembles that of bulk water, with even a slightly higher intensity of the vibrational band at lower frequency ~3500 cm -1 , indicating a relatively strong H-bonding to other interlayer H2O molecules. This is additionally confirmed by comparison of the shortest Ow-Hw•••Ow distances of this sub-population and the corresponding distances in pure water (right column in Figure 9). The two distributions are practically identical.

A second mechanism potentially responsible for the emergence of the high-frequency H2O stretching band could be related to the influence of interlayer cations. The latter could deform the H-bonding structure of H2O molecules around them and possibly induce some Hbond breaking. A clear evidence against this possibility has been provided already in Figure 8:

H2O molecules in the middle of the interlayer (red rectangle) were found not to contribute to the high-frequency band of interest. This is especially obvious in the case of Mtm05Ca_2W, where H2O molecules in the hydration shell of Ca 2+ are oriented around the ions exactly in the center of the interlayer.

Hydrogen bonding in the interlayer space of smectite

The question regarding other possible molecular mechanisms responsible for the sharp high-frequency O-Dw/O-Hw band can be alternatively expressed as follows: Does interlayer water contain a sub-population of H2O molecules for which the O-Hw•••O distance of donated H-bonds is longer than ~2.2 Å (Libovitzky, 1999)? Obviously, the results of this analysis are only valid in comparison to those on pure bulk liquid water, due to the method-artificial nonnegligible contribution of weak H-bonds in the latter (see Figure 8 and9).

To address this question, the numbers of accepted and donated H-bonds were calculated depending on the distance z of the involved H2O molecules from the smectite siloxane surface. In the ordered ice structure, each H2O donates two strong H-bonds to other H2O and also accepts two strong H-bonds from two other H2O molecules. In liquid water, the number of donating and accepting H-bonds formed by each H2O molecule is somewhat lower than in ice due to the molecular disorder, and depends on temperature, density, and other thermodynamic factors. The exact number of H-bonds experienced by a H2O molecule in each situation also depends to some extent on the assumed criterion used in H-bonding calculation (see., e.g., [START_REF] Kalinichev | Molecular simulations of liquid and supercritical water: Thermodynamics, structure, and hydrogen bonding[END_REF][START_REF] Kumar | Hydrogen bonding definitions and dynamics in liquid water[END_REF].

A geometric definition for counting H-bonds (HB) was adopted from the literature [START_REF] Wang | Asymmetric hydrogen bonding and orientational ordering of water at hydrophobic and hydrophilic surfaces: A comparison of water/vapor, water/talc, and water/mica interfaces[END_REF][START_REF] Loganathan | On the hydrogen bonding structure at the aqueous interface of ammonium-substituted mica: A molecular dynamics simulation[END_REF]. According to this definition, an Hbond is assumed to exist if the H•••O distance between the donor and acceptor is below were identified in all cases (thick solid lines in Figure 10). The maximum of their distribution corresponded to the monodentate population, whereas the small shoulder closer to the surface originated from bidentate H2O. Besides donating to the basal surface, both bidentate and monodentate H2O accepted H-bonds from and donated to other H2O in the interlayer (dashed and thin solid lines, respectively in Figure 10). The maxima of the accepted and donated H- For the general case considering all possible H-bonds in the system (Figure 11a), the number of accepted H-bonds per H2O molecule was found relatively constant with small dependence on the smectite charge and the type of the interlayer cation (dashed lines in Figure 11a). The number of H-bonds donated to basal oxygen atoms was around 2.0 per H2O molecule for the bidentate orientation and slightly below 1.0 for the monodentate orientation for all types of simulated smectite systems (thick solid lines in Figure 11a). The number of Hbonds per H2O donated to other H2O was independent of charge and interlayer cation (thin solid line in Figure 11a).

The average number of weak H-bonds calculated according to the modified geometric criterion also did not show substantial dependence on the type of smectite (Figure 11). The weakest H-bonds (0.8-1.0 of donated H-bonds per H2O; thick solid line in Figure 11b) was clearly attributed to the bidentate orientation, but some contribution from the monodentate population, amounting to ~0.3 donated H-bonds per H2O was also observed. For comparison, the average number of weak H-bonds in bulk liquid water, calculated using the same criteria was ~0.17 per molecule. Therefore, only the fraction of weak H-bonds that is in excess of the value of ~0.17 per molecule can be considered as contributing to the sharp high-frequency vibrational band. In agreement with the calculated power spectra, these H-bonds are solely due to the bidentate and monodentate populations in the vicinity of the surface and no contribution from the central part of the interlayer was found.

CONCLUSIONS

(1) Interfacial water molecules in bidentate and monodentate orientation with respect to the siloxane surface are the only species contributing to the experimentally observed sharp high-frequency O-Hw stretching band of smectites (Kuligiewicz et al., 2015a, Kuligiewicz et al., 2015b). The number of interlayer H2O molecules in the monodentate orientation greatly exceeds that in the bidentate orientation and is, thus, the predominant contributor to the highfrequency vibrational band.

(2) In the bidentate orientation each H2O molecule donates two hydrogen bonds to the surface: one relatively strong, and another much weaker, while in the monodentate orientation it donates only one relatively weak H-bond to the surface.

(3) Increasing total layer charge leads to increasing number of bidentate molecules, but also to decreasing of Ow-H•••Ob distances for both monodentate and bidentate populations. Both factors are responsible for the red-shift of the sharp high-frequency band in smectites upon increasing the layer charge.

(4) The experimentally observed low sensitivity of the position of the high-frequency vibrational band on the type of the (Na + or Ca 2+ ) high hydration enthalpy interlayer cation remains unexplained. The differentiation of Cs + from Na + or Ca 2+ may be due to its tendency to displace surface H2O and form inner-sphere complexes with the siloxane surface as suggested by Kuligiewicz et al. (2015a), but further simulation work is needed to account for the experimental data on Cs + smectites.

(5) The presence of the sharp high-frequency vibrational band in experimental and simulated spectra can be considered as a strong evidence of intrinsic hydrophobicity of the smectite siloxane surface within the studied range of layer charge (0.3-0.5 phuc), independent on the specific charge localization in the clay structure.

FIGURE CAPTIONS

Figure 1. A snapshot of part of the MD simulation cell for Mtm05Na_3W. H2O closer to the layer surface is oriented with two O-Hw bonds pointing to the surface (thin green circle), whereas H2O farther from the surfacewith one O-Hw bond oriented towards the surface (thick blue circle). The inset shows the definition of the angle α formed by the H2O dipole vector and the surface normal. Vertical scale showing average distance in z direction relative to the oxygens of the basal plane is shown in angstroms. Figure 2. Dependence of the H2O dipole vector orientation contours (see Figure 1 for the definition of α) on the distance from the basal surface, z, for various hydration levels of different Na + -smectites. The interlayer distribution of the cations is shown by solid lines (blue in the color copy). Dashed lines mark the location of the surface (basal oxygen positions). Figure 3. Dependence of the H2O dipole orientation contours on the distance from the basal surface, z, for 2W hydration level of Ca 2+ and Cs + -smectites. Figure 4. Power spectra for hydrogens of interlayer H2O in smectites with two hydration layers (2W) in the O-Hw stretching range showing the effect of the total layer charge and the cation-dependence: a) Na + form, b) Ca 2+ form, c) Cs + form. Increase of the spectral density at higher frequency is clearly visible in comparison with the spectrum of bulk water. Figure 5. Power spectra for hydrogens of interlayer H2O in the O-Hw stretching range for Na + -beidellites (top) and Na + -montmorillonites (bottom) with different total layer charge and different water contents. The spectra were scaled by their H2O content. Figure 6. Examples of received fitsDeconvolution of power spectra for of pure water and two representative smectites.

  contour maps of the angular distributions of the interlayer H2O dipole vectors with respect to the direction normal to the surface (α angle) plotted in a function of the distance z from the surface (Figure2) enabled the distinction of the two preferred surfaceoriented types of water molecules marked in Figure1. The predominantly bidentate population was located closer to the surface at z ~ 2.0 Å and α ~ 0-30 o , similarly to ideal theoretical values (observed in smectites with charge 0.5). A more distant and more pronounced monodentate population was at distances z ~ 2.8 Å and oriented in a broad range of angles between 30 o and 80 o with a maximum at α ~ 55 o , which matches the ideal theoretical value for one OH vector pointing perpendicularly to the smectite surface (half of the 105 o angle of H2O). For higher hydration levels, a third population of water molecules was observed closer to the middle of the interlayer. The orientational distribution of this population depended significantly on both, the hydration level of the specific smectite and the type of the interlayer cation. The latter dependence is observed clearly when comparing the distribution in Mtm05 for the same hydration levels but different interlayer cations (Figures 2

  Based on the correlation of IR frequency of the O-H stretching band and the length of the H-bond, O-Hw•••O, (Libovitzky, 1999), a peak at ~ 3600 cm -1 may correspond to a O-Hw•••O distance > 2.2 Å (i.e. an Ow...O distance >3.2 Å), and indicates a relatively weak H-

2

  .45 Å and the angle between the O-H and O•••O vectors is below 30 o . A systematic application of this criterion enabled the quantitative visualization of the general H-bonding trends of interlayer H2O molecules for several model smectites (Figure 10). As expected, Hbonds donated to surface Ob atoms from both bidentate and monodentate H2O populations

  bonding distributions corresponded clearly to the expected (e.g.,Ferrage et al., 2011;[START_REF] Ngouana Wakou | Structural arrangements of isomorphic substitutions in smectites: Molecular simulation of the swelling properties, interlayer structure, and dynamics of hydrated Cs-montmorillonite revisited with new clay models[END_REF] twin maxima of the Ow distribution along z, shown previously for all 2W structures (Figures2 and 3). Subtler differences in the fractions of accepting and donating H-bonds depended on the charge and the type of the interlayer cation (Figure10).=== Figure 10 ===The distributions of H-bonds along z (Figure10) provide a general picture of the Hbonding structure in smectite interlayers, but they do not directly indicate the location of particularly weak hydrogen bonds. To address this issue, the distributions of H-bonds on the basis of their strength was also calculated (Figure11). This was achieved by modifying the aforementioned geometric definition of H-bond to probe only the relatively weak interactions having Ow-H•••O distances in the range 2.2-2.7 Å and compare such a subset of the H-bonds distribution to the original definition (Ow-H•••O distance <2.45 Å). In both cases the H-Ow•••O angle was kept < 30 o . The plots in Figure 11 show only the average distributions of Hbonds experienced by each H2O molecule, and therefore do not inform on the absolute contribution of each molecular orientation to the final spectra. === Figure 11 ===

Figure 7 .

 7 Figure1. A snapshot of part of the MD simulation cell for Mtm05Na_3W. H2O closer to the layer surface is oriented with two O-Hw bonds pointing to the surface (thin green circle), whereas H2O farther from the surfacewith one O-Hw bond oriented towards the surface (thick blue circle). The inset shows the definition of the angle α formed by the H2O dipole vector and the surface normal. Vertical scale showing average distance in z direction relative to the oxygens of the basal plane is shown in angstroms. Figure2. Dependence of the H2O dipole vector orientation contours (see Figure1for the definition of α) on the distance from the basal surface, z, for various hydration levels of different Na + -smectites. The interlayer distribution of the cations is shown by solid lines (blue in the color copy). Dashed lines mark the location of the surface (basal oxygen positions). Figure3. Dependence of the H2O dipole orientation contours on the distance from the basal surface, z, for 2W hydration level of Ca 2+ and Cs + -smectites. Figure4. Power spectra for hydrogens of interlayer H2O in smectites with two hydration layers (2W) in the O-Hw stretching range showing the effect of the total layer charge and the cation-dependence: a) Na + form, b) Ca 2+ form, c) Cs + form. Increase of the spectral density at higher frequency is clearly visible in comparison with the spectrum of bulk water. Figure5. Power spectra for hydrogens of interlayer H2O in the O-Hw stretching range for Na+ -beidellites (top) and Na + -montmorillonites (bottom) with different total layer charge and different water contents. The spectra were scaled by their H2O content. Figure6. Examples of received fitsDeconvolution of power spectra for of pure water and two representative smectites. Figure 7. Comparison of fitted frequencies: a) dependence on water content for Na + -smectites in MD; b) dependence on interlayer cation for 2W forms in MD.; c) in comparison to c) results from Kuligiewicz et al. (2015a). To obtain frequencies for H2O, the experimental values for D2O were scaled by factor ofx 1.36. Figure 8. H2O dipole orientation with respect to the surface normal for selected sub-sets of water molecules having their z and α values within the marked ranges (left) and power spectra of O-Hw stretching vibrations calculated for each individual sub-set (center): thin green -bidentate population, thick bluemonodentate population, dashed red -water in the center of interlayer. Right column -the distributions of the shortest H-bonding distances of interfacial H2O molecules with basal oxygens (Ow-Hw•••Ob) in the bidentate and monodentate orientations, compared to distribution of Ow-Hw•••Ow distances in pure water. Figure 9. Orientation of the O-Hw vector of interfacial H2O with respect to the surface normal (β) at various distances, z, from the basal surface of Mtm05Ca_2W and Mtm05Na_2W smectites (left). Calculated power spectra for the sub-sets of H2O molecules (color marked for the selected β and z ranges) are shown in the center. Right: the distributions of the shortest H-bonding distances of monodentate H2O with the basal oxygens (Ow-Hw•••Ob) and/or other oxygen of H2O (Ow-Hw•••Ow), compared to distribution of Ow-Hw•••Ow distances in pure water. Thin green -bidentate population, thick bluewater O-Hw bond oriented towards the surface, dashed orange -O-Hw bond oriented towards the interlayer. Power spectra were scaled by the number of H2O molecules. A bulk water spectrum is also shown for comparison. Figure 10. Distributions of Ow atoms with H-bonds donated and accepted and donated by the interlayer H2O and Ob in the 2W smectite structures studied. Figure 11. Distributions of Ow atoms with H-bonds of various types (normalized per one H2O) for the 2W smectite structures studied. (a) -all H-bonds with Ow-H•••O distances below 2.45 Å. (b) -weak (long) H-bonds with Ow-H•••O distances in the range of 2.2-2.7 Å. In both cases the H-Ow•••O angle is < 30 o .

  •••Ob distributions is, however, a little bit greater than the , but this is much smaller than for smectites. Low charge smectites exhibited a significantly larger contribution of weak H-bonds. For the high charge smectite

maxima: 2.24 Å for Beid03_Na, 2.16 Å for Mtm05Ca_2W, and 2.27 Å for Mtm03Na_2W, comparing to 1.95 Å in bulk water. In bulk water a contribution of H-bond distances > 2.2 Å was observed

Table 1 .

 1 EDF. VG and GDC acknowledge partial support from project KRHPIS 447963 -Polynano (GSRT, TPCI-NHRF). edge sites. Journal of PhysicalChemistry B, 110,[4135][4136][4137][4138][4139][4140][4141][4142][4143][4144][4145][4146] Cygan, R.T., Liang, J.J., and[START_REF] Wang | Molecular modeling of the 10angstrom phase at subduction zone conditions[END_REF] Molecular models of hydroxide, oxyhydroxide, and clay phases and the development of a general force field. Journal Parameters of interatomic interactions used in present MD simulations. The modifications compared to the original CLAYFF parameters (Table1inCygan et al., 2004) are highlighted in bold.

	of Physical Chemistry B, 108, 1255-1266.
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	stretching and bending vibrations in liquid water. Spectrochimica Acta A, 58, 519 -
	524.
	Farmer, V.C. and Russell, J.D. (1971) Interlayer complexes in layer silicates: The structure of
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Ferrage, E.,

Sakharov, B.A., Michot, L.J., Delville, A., Bauer, A., Lanson, B., Grangeon, S., Frapper, G., Jiménez-Ruiz, M., and Cuello, G.J. (2011)

Hydration properties and inter-

Table 2 .

 2 Interlayer cation and water content of the simulated clay models and the resulting basal spacing.

	Model	n(H2O) phuc n(H2O)/n(M + )	H2O wt% normalized to the total mass (smectite + H2O)	H2O wt% normalized to dry mass (smectite)	calculated d001 (Å) *
	Beid03Na_1W	2.5	8.333	10.93	12.28	12.99
	Beid03Na_2W	5	16.667	19.71	24.55	15.94
	Beid03Na_3W	7.5	25.0	26.92	36.83	18.88
	Beid05Na_1W	2.5	5.0	10.82	12.13	12.76
	Beid05Na_2W	5.0	10.0	19.53	24.26	15.38
	Beid05Na_3W	7.5	15.0	26.68	36.39	18.34
	Mtm03Na_1W	2.5	8.333	10.95	12.29	12.86
	Mtm03Na_2W	5.0	16.667	19.73	24.58	15.95
	Mtm03Na_3W	7.5	25.0	26.94	36.88	18.95
	Mtm05Na_1W	2.5	5.0	10.84	12.16	12.58
	Mtm05Na_2W	5.0	10.0	19.56	24.31	15.37
	Mtm05Na_3W	7.5	15.0	26.72	36.47	18.14
	Beid03Ca_2W	5.0	33.334	19.75	24.61	15.82
	Beid05Ca_2W	5.0	20.0	19.59	24.36	15.38
	Mtm03Ca_2W	5.0	33.334	19.77	24.64	15.95
	Mtm05Ca_2W	5.0	20.0	19.62	24.41	15.38
	Beid03Cs_2W	5.0	16.667	18.39	22.53	16.34
	Beid05Cs_2W	5.0	10.0	17.45	21.13	16.13
	Mtm03Cs_2W	5.0	16.667	18.40	22.55	16.41
	Mtm05Cs_2W	5.0	10.0	17.47	21.17	16.14

*)

Standard deviation is ~ ± 0.05 Å.

ACKNOWLEDGMENTS

This work was supported by the project ATLAB (FP7-REGPOT-2011-1 No. 285989) funded by the European Union. MS also acknowledges NCN (grant 2012/05/B/ST10/01948), which provided IGS PAS with a high-performance computing server and also PLGRID infrastructure. AGK acknowledges the support of the industrial chair "Storage and Disposal of Radioactive Waste" at the Ecole des Mines de Nantes, funded by ANDRA, Areva, and