François-Xavier Coudert

Aurélie U Ortiz

Volker Haigis

David Bousquet

Alain H Fuchs

Anthony Ballandras

Guy Weber

Igor Bezverkhyy

Nicolas Geoffroy

Jean-Pierre Bellat

Guillaume Ortiz

Gérald Chaplais

Joël Patarin

Anne Boutin
email: anne.boutin@ens.fr

Water Adsorption in Flexible Gallium-Based MIL-53 Metal-Organic Framework

Keywords: metal-organic frameworks, adsorption, water, structural transitions, thermodynamics, nanoporous materials

Understanding the adsorption of water in metal-organic frameworks (MOF), and particularly in soft porous crystals, is a crucial prerequisite before considering MOFs for industrial applications. We report here a joint experimental and theoretical study on the behavior of a gallium-based breathing MOF, Ga-MIL-53, upon water adsorption. By looking at the energetics and thermodynamics of Ga-MIL-53, we demonstrate why it behaves differently from its sibling Al-MIL-53, showing a different phase at room temperature (a non-porous phase) and the presence of a hydrated narrow-pore structure at gas saturation pressure. Moreover, we present a complete water vapor pressure vs. temperature phase diagram of Ga-MIL-53 upon water adsorption.

INTRODUCTION

Soft Porous Crystals (SPC) are a fascinating subclass of Metal-Organic Frameworks (MOFs) that exhibit structural transformations of large amplitude triggered by external stimuli such as temperature variations, mechanical pressure or adsorption of guest molecules (in gas or liquid phase). [START_REF] Horike | Soft Porous Crystals[END_REF] The changes in the framework of SPCs in response to the external constraint are reversible and maintain the crystalline character of the solid. A growing number of SPC structures have been synthesized and reported in the literature, and although none of them have yet been directly used at the industrial scale, [START_REF] Czaja | Industrial Applications of Metal-Organic Frameworks[END_REF] they have been proposed for a large range of potential practical applications. In addition to the general application of MOFs, flexible frameworks are expected to present an intrinsic interest due to their large-scale stimuli-responsive transformations, [START_REF] Bureekaew | Chemistry and Application of Flexible Porous Coordination Polymers[END_REF] which could leverage novel nano-biotechnologies, such as sensing for detecting traces of organic molecules, [START_REF] Férey | Hybrid porous solids: past, present, future[END_REF] slow release of drugs for long-release single-injection therapies, [START_REF] Horcajada | Flexible Porous Metal-Organic Frameworks for a Controlled Drug Delivery[END_REF] and specific gas separations. [START_REF] Thallapally | Flexible (Breathing) Interpenetrated Metal-Organic Frameworks for CO 2 Separation Applications[END_REF][START_REF] Remy | Modeling the Effect of Structural Changes during Dynamic Separation Processes on MOFs[END_REF] While the existing Soft Porous Crystals display a large gamut of flexibility mechanisms, [START_REF] Coudert | Thermodynamic Methods and Models to Study Flexible Metal-Organic Frameworks[END_REF] one of the most studied systems in this subclass is the family of MIL-53 materials, in which the adsorption of increasing amounts of guest molecules (carbon dioxide, xenon, alkanes, water, etc.) may induce a double structural transition with volume changes of up to 40%, a phenomenon called "breathing". Various aspects of gas and liquid adsorption in these materials have been studied extensively in the literature: structure, energetics, thermodynamics, dynamics and transport properties. However, despite the critical role that water is known to play in phase stability and gas separation properties in MOFs in general, only a few studies have dealt with the impact of water on the MIL-53 frameworks and their properties. Most dealt with the chromium-based Cr-MIL-53. [START_REF] Serre | Very Large Breathing Effect in the First Nanoporous Chromium(III)-Based Solids: MIL-53 or CrIII(OH).{O2C-C6H4-CO2}.{HO2C-C6H4-CO2H}x[END_REF] In 2010, Bourrelly [START_REF] Bourrelly | Explanation of the Adsorption of Polar Vapors in the Highly Flexible Metal Organic Framework MIL-53(Cr)[END_REF] and Devautour-Vinot [START_REF] Devautour-Vinot | Water and Ethanol Desorption in the Flexible Metal Organic Frameworks, MIL-53 (Cr, Fe), Investigated by Complex Impedance Spectrocopy and Density Functional Theory Calculations[END_REF] published experimental studies of adsorption and desorption of water, among other polar vapors, along with quantum chemistry calculations of the preferential arrangements of the molecules within the pores. A later experimental study of Cr-MIL-53 immersed in liquid water used high resolution powder X-ray diffraction to solve the structure of the pores of both the large-pore (lp) and narrow-pore (np) phases, fully filled with water. [START_REF] Guillou | Rapid and Reversible Formation of a Crystalline Hydrate of a Metal-Organic Framework Containing a Tube of Hydrogen-Bonded Water[END_REF] Molecular simulations were further used to characterize the structure, diffusion and adsorption thermodynamics of water in the lp and np phases of Cr-MIL-53. [START_REF] Salles | Molecular Insight into the Adsorption and Diffusion of Water in the Versatile Hydrophilic/Hydrophobic Flexible MIL-53(Cr) MOF[END_REF][START_REF] Haigis | Structure and Dynamics of the Hydrated Metal-Organic Framework MIL-53(Cr) by First-Principles Molecular Dynamics[END_REF][START_REF] Paesani | Water in Metal-Organic Frameworks: Structure and Diffusion of H 2 O in MIL-53(Cr) from Quantum Simulations[END_REF] A similar molecular simulation approach was also used with success to the understand CO 2 -driven pore opening of Sc-MIL-53. [START_REF] Chen | Elucidating the Breathing of the Metal-Organic Framework MIL-53(Sc) with ab Initio Molecular Dynamics Simulations and in Situ X-ray Powder Diffraction Experiments[END_REF] In the present work, we focus on water adsorption in gallium-based Ga-MIL-53. [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF][START_REF] Chaplais | IM-19: A New Flexible Microporous Gallium Based-MOF Framework with Pressure-and Temperature-Dependent Openings[END_REF] While Ga-MIL-53 is isostructural to Cr-MIL-53 and Al-MIL-53, which both have quite similar behavior, the gallium-based material presents specific features, which we detail below. The behavior of guest-free Ga-MIL-53 as a function of temperature was recently characterized by a combination of in situ Xray diffraction, in situ Fourier transform infrared spectroscopy, differential scanning calorimetry, and heat capacity measurements and Density Functional Theory (DFT) calculations. [START_REF] Boutin | Temperature-Induced Structural Transitions in the Gallium-Based MIL-53 Metal-Organic Framework[END_REF] In particular, it has been shown that, as many materials of the MIL-53 family, Ga-MIL-53 presents two different phases in absence of adsorbates: a narrow-pore phase and a large-pore phase. The lp form is always favored at high temperature for all known MIL-53 materials. However, contrary to Al-and Cr-MIL-53, the np form is thermodynamically more stable at ambient temperature for Ga-MIL-53. In addition, while the empty np form of Ga-MIL-53 behaves like a nonporous material, an intermediate narrow-pore-like hydrated structure was evidenced: this is a swollen variant of the np phase, where the flexible framework has expanded to accommodate water molecules. The exact conditions of stability of this hydrated np phase have not yet been elucidated to date.

In this work, we present a synergistic experimental and theoretical study aimed at providing a coherent picture of water adsorption in Ga-MIL-53, and the thermodynamic behavior of this material in the presence of adsorbed water molecules. This study addresses the following important questions: first, what is the fundamental nature of the difference between Ga-MIL-53 and Al-MIL-53 (or Cr-MIL-53), that accounts for the change in stable phase at room temperature (lp for Al and Cr, np for Ga)? Secondly, what is the nature of the "swollen" narrow-pore phase of Ga-MIL-53, and why is this np to hydrated np transition not observed in Al-MIL-53 or Cr-MIL-53? Thirdly, what is the full temperature-pressure phase diagram of Ga-MIL-53 upon water adsorption? To answer these questions, we report thermogravimetric adsorption measurements, with in situ X-ray diffraction and infrared spectroscopy. By supplementing the experimental data obtained with quantum chemistry calculations and first-principles molecular dynamics, we are able to propose a full thermodynamic model, based on the osmotic thermodynamic ensemble, for the adsorption of water in Ga-MIL-53 as a function of temperature and pressure.

EXPERIMENTAL DETAILS

Thermogravimetry

Adsorption-desorption isotherms of water on Ga-MIL-53 are measured between 273 and 373 K with a homemade McBain thermobalance, using the ultra high vacuum technology. The vapor pressure was ranging from 10 -5 up to 30 hPa. The sample weight was about 15 mg. Before each adsorption the sample was outgassed at 298 or 473 K under vacuum (10 -6 hPa) overnight. Adsorption-desorption isobars are determined using the same thermobalance under a constant saturated vapor pressure of 1 and 8 hPa in the range of temperature 270-473 K. Adsorption experiments are performed step by step by varying the pressure or the temperature by small increments once the equilibrium of mass is reached and maintained over at least one hour. The experimental error estimated on the adsorbed amount is about 10 -3 g.g -1 . This corresponds to around 0.02 water molecule per mole of adsorbent. The accuracy on the pressure data is 1 % and the temperature is measured with a precision of 1 K.

In situ X-Ray Diffraction

The in situ XRD patterns were recorded using Cu Kα radiation on a D8 Advance Bruker apparatus equipped with a Vantec linear detector. To control the sample environment a MRI TC-Radiation chamber was used. An Easidew humidity analyzer from Michell Instruments was used to measure the partial pressure of water in the chamber. The XRD patterns of Ga-MIL-53 under controlled humidity were recorded using the following procedure. First, the sample was placed in the chamber and outgassed at 298 K for 3 h under secondary vacuum (residual pressure lower than 10 -3 hPa). Then, the chamber was filled with nitrogen to ca. 100 kPa and small amounts of ambient air were admitted to the chamber in order to obtain different values of water partial pressure up to 2 hPa. At each pressure value the sample was equilibrated with the atmosphere for ca. 2 h before recording the XRD pattern. The cell parameters of Ga-MIL-53 phases were obtained through the full profile fitting of the patterns using TOPAS software. [START_REF]TOPAS V4.2: General Profile and Structure Analysis Software for Powder Diffraction Data[END_REF]

In situ Infrared Spectroscopy

In situ FTIR absorption measurements were performed in an optical cell specially built to study the interaction of a gas on a nanoporous material. [START_REF] Boutin | Temperature-Induced Structural Transitions in the Gallium-Based MIL-53 Metal-Organic Framework[END_REF][START_REF] Ballandras | Evidence of Structural Phase Transitions in Silicalite-1 by Infrared Spectroscopy[END_REF] The experimental set-up is able to operate over a wide range of controlled pressure from 10 -4 to 1000 hPa at room temperature. The FTIR spectrometer was a Bruker Equinox 55 instrument equipped with a Globar source, a DTGS detector and a KBr beamsplitter. All spectra were recorded at a resolution of 2 cm -1 by coadding 40 scans in transmission mode. Every one spectrum was referenced to a background spectrum recorded in the same conditions without sample. The procedure used for adsorption measurements consists first in the activation of a small amount of powdered sample deposited in between two KBr pellets at room temperature under dynamic vacuum. Then, adsorption measurements were performed at the equilibrium, by increasing then decreasing water vapor pressure step by step, to describe the adsorption-desorption isotherm at 298 K. The amounts of water adsorbed at the equilibrium were determined from the corresponding isotherm determined by gravimetric measurements. Each spectrum of the powdered sample was recorded under equilibrium conditions at constant pressure from P = 0 hPa (activated sample free of water) to about 30 hPa, close to the saturated vapor pressure of water, and reversely, at 298 K.

THEORETICAL AND CALCULATION DETAILS

Quantum Chemical Calculations

We performed quantum chemical calculations on the Ga-MIL-53 and Al-MIL-53 materials in the density functional theory approach with periodic unit cell, full use of the crystalline symmetry elements, and localized basis sets as implemented in the CRYSTAL09 code. [START_REF] Dovesi | CRYSTAL: a Computational Tool for the Ab Initio Study of the Electronic Properties of Crystals[END_REF] We used the B3LYP hybrid exchange-correlation functional [START_REF] Becke | Density-Functional Thermochemistry. III. The Role of Exact Exchange[END_REF][START_REF] Lee | Development of the Colle-Salvetti Correlation-Energy Formula Into a Functional of the Electron Density[END_REF] with empirical correction for the dispersive interactions following the so-called "D2" scheme of Grimme. [START_REF] Grimme | Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction[END_REF] All electron basis sets were used for all atoms involved: 6-311G(d,p) for H, C and O, 32 8-511G* for Al, [START_REF] Catti | Quantum-Mechanical Calculation of the Solid-State Equilibrium MgO+α-Al2O3⇄MgAl2O4 (Spinel) Versus Pressure[END_REF] and 86-4111d41G for Ga. [START_REF] Pandey | Ab-Initio Study of High-Pressure Phase-Transition in GaN[END_REF] We first performed optimization of the atomic positions and unit cell parameters of each structure, from the experimental crystallographic structures. We then performed harmonic frequency calculations at the Γ point on the optimized geometry; frequencies are obtained by diagonalizing the mass-weighted Hessian matrix obtained by numerical differentiation of the analytic energy gradient. [START_REF] Pascale | The Calculation of the Vibration Frequencies of Crystalline Compounds and its Implementation in the CRYSTAL Code[END_REF][START_REF] Zicovich-Wilson | The Calculation of the Vibration Frequencies of Alpha-Quartz: the Effect of Hamiltonian and Basis Set[END_REF] The frequencies obtained were then used to calculate the zero-point energy of each configuration, as well as the vibrational entropy in the harmonic approximation and low-temperature limit.

Density Functional Theory-Based Molecular Dynamics (DFT-MD)

In order to shed light on the structural response of Ga-MIL-53 to small amounts of adsorbed water, we performed first-principles molecular dynamics simulations. The code package CP2K with its DFT module Quickstep was used to obtain the equilibrium structure of the material at three different water loadings, with zero, one and four water molecules per unit cell and simulation box (i.e. 0, 0.25 and 1.0 water molecules per Ga, respectively). Since a good description of dispersion interactions is essential for obtaining the correct structure of Ga-MIL-53, we used the Van der Waals density functional proposed by Dion et al. [START_REF] Dion | Van der Waals Density Functional for General Geometries[END_REF] The interactions between valence electrons and ion cores were described by GTH pseudopotentials. [START_REF] Goedecker | Separable Dual-Space Gaussian Pseudopotentials[END_REF] The structural flexibility of Ga-MIL-53 was taken into account by running the simulations in the NσT ensemble, i.e. all lattice parameters and angles were completely free to find the optimal structure. The calculation of the stress tensor σ required the use of rather tight computational settings: we used a TZV2P basis set for all elements except for Ga (DZVP-MOLOPT basis set) and a plane-wave cutoff of 600 Ry. Smaller basis sets and/or cutoffs were found to yield unconverged stresses. All three systems were equilibrated for at least 3.5 ps and then simulated between 7.5 and 11 ps. This time was sufficient to relax the unit cell of the material, given the barostat chosen and the relatively small nature of the deformations studied. The time step for the integration of the equations of motion was 0.5 fs, and the temperature of 300 K was controlled by a CSVR thermostat [START_REF] Bussi | Canonical Sampling Through Velocity Rescaling[END_REF] with a time constant of 0.1 ps. A barostat with a time constant of 2 ps was used in order to impose a pressure of 1 bar.

Thermodynamic Model Based on the Osmotic Ensemble

A thermodynamic model developed in the group, [START_REF] Boutin | Breathing Transitions in MIL-53(Al) Metal-Organic Framework Upon Xenon Adsorption[END_REF] based on the osmotic ensemble, has been used in order to understand the coupling between water adsorption and structural changes in the host framework. The free energy of the empty host was assumed to present two minima's corresponding to both the open form and the "nonporous" narrow form of the solid. Adsorption isotherms in each structure of the solid were assumed to follow Langmuir isotherms, and were fitted using thermogravimetry adsorption isotherms. The corresponding Henry constants fulfill certain conditions described in more details in reference 34. The evolution of the maximum loading as a function of the unit cell volume however was defined to take into account the ability of the "nonporous" np form of the material to slightly deform and accommodate a few water molecules. The structure that is thermodynamically stable, depending on the water pressure and the system temperature, is thus determined, and the phase diagram of the material in the osmotic ensemble is obtained.

RESULTS AND DISCUSSION

Relative Stability of Narrow-Pore and Large-Pore Forms: Origin of the Differences Between Al-MIL-53 and Ga-MIL-53

In this section, we investigate the equilibrium between the large-pore (lp) and narrow-pore (np) forms of the material Ga-MIL-53, and the microscopic origins of its difference with the closely related Al-MIL-53 material. Indeed, for both materials, it was shown that variations of temperature in the evacuated material (with no solvent or adsorbate in its pores) can trigger the lp-np structural transition. For both materials, the narrow pore form is the more thermodynamically stable at low temperature, while the large pore form is favored in the limit of high temperatures. At intermediate temperatures, the transition happens with coexistence of the two phases and a large hysteresis loop upon heating-cooling cycles. This was first demonstrated in Al-MIL-53, in which neutron powder diffraction and inelastic neutron scattering techniques showed that the transition took place in the 150-325 K range. [START_REF] Liu | Reversible Structural Transition in MIL-53 with Large Temperature Hysteresis[END_REF] Thermodynamic models based on adsorption measurements of Xe, CO 2 and CH 4 in Al-MIL-53 later allowed some of us to estimate the transition temperature at the thermodynamic equilibrium, T 0 , to be approximately 200 K. [START_REF] Boutin | Breathing Transitions in MIL-53(Al) Metal-Organic Framework Upon Xenon Adsorption[END_REF][START_REF] Boutin | The Behavior of Flexible MIL-53(Al) upon CH 4 and CO 2 Adsorption[END_REF] This temperature corresponds to the point where both empty Al-MIL-53 phases are equally stable, i.e. have the same free energy; it dictates the lp/np equilibrium in the absence of adsorbate. The knowledge of T 0 is important for the understanding of the breathing phenomenon, and is key parameter to build phase diagrams in the presence of adsorbates.

For Ga-MIL-53, while an equilibrium transition temperature T 0 has not yet been established, we have shown in recently reported XRD measurements upon heating that the transition took place in the 450-520 K, [START_REF] Boutin | Temperature-Induced Structural Transitions in the Gallium-Based MIL-53 Metal-Organic Framework[END_REF] which is markedly higher than for Al-MIL-53. In particular, it is striking to observe that the most stable phase of evacuated Al-MIL-53 at room temperature is the large-pore phase, while for Ga-MIL-53 it is a narrow-pore one. In this section, we investigate why T 0 (Ga-MIL-53) is greater than T 0 (Al-MIL-53) using quantum chemistry calculations of the empty host frameworks.

We started by performing an energy minimization of both dehydrated frameworks, followed by a calculation of harmonic vibration frequencies, zero-point energy and vibrational contribution to entropy of each phase. The results obtained are presented in Table 1, in the form of differences in energy and entropy between the lp and np structures for each material. The total energy (E tot ) is the sum of its electronic DFT component (E el ), dispersion correction (E disp ), zero-point energy (E 0 ), the latter being very small. These results confirm in both Al-MIL-53 and Ga-MIL-53 what was demonstrated by Walker et al. [START_REF] Walker | Flexibility in a Metal-Organic Framework Material Controlled by Weak Dispersion Forces: The Bistability of MIL-53(Al)[END_REF] for Al-MIL-53: (i) the narrow-pore form is energetically favored, in line with experimental observations that it is the most stable form at low temperature; (ii) this stabilization is due to dispersive interactions, in a similar fashion to what was observed in σ-bonded dimers of large acenes. [START_REF] Ehrlich | Dispersion-Driven Conformational Isomerism in σ-Bonded Dimers of Larger Acenes[END_REF] Also, it is clear in both cases that the entropy contributions of the framework vibrations favor the large-pore phase, accounting for its higher stability at high temperature.

We now compare the two materials against one another, term by term. First, the contribution of vibrational entropy in Al-and Ga-MIL-53 is similar (36.9 and 33.8 J.mol -1 .K -1 ). This difference, however small, tends to decrease the entropic stabilization of the Ga-MIL-53 large-pore form with temperature, thus moving its lp/np equilibrium temperature T 0 higher than Al-MIL-53. Secondly, we have the energetic term, which is the dominant factor: the narrow-pore form of Ga-MIL-53 is more stabilized than in Al, compared to their respective large-pore forms (∆E tot of 35.7 vs. 39.6 kJ/mol). This extra energetic stabilization (∆∆E ~ 4 kJ/mol) explains, again, why the lp/np equilibrium temperature T 0 is higher for Ga-MIL-53 than Al-MIL-53: it requires a higher temperature to overcome the larger energy difference between the two phases. 1. Energy and entropy differences between the large-pore and narrow-pore forms of Al-MIL-53 and Ga-MIL-53, obtained by quantum chemistry calculations.

Looking at Table 1, we see that the extra stabilization of the np phase in Ga-MIL-53 is the sum of two terms whose effect go in different directions: the dominating term is the electronic (DFT) energy (∆∆E el = 12.5 kJ/mol), while the smaller difference in dispersion energy (∆∆E disp = -6.8 kJ/mol) is due to an effect of the overall framework density: the narrow-pore of Al-MIL-53 is denser than that of Ga-MIL-53 (V = 886.9 Å 3 (ref. 35) vs. 895.9 Å 3 (ref. 19)), leading to higher dispersive interactions.

In order to better understand the difference in electronic energy, we performed addition calculations by building molecular clusters of the carboxylate-M(OH) 2 -carboxylate joint, where M is Al or Ga. To create such neutral clusters and maintain the coordination of the metal centers, we substituted F -ions to the missing carboxylate oxygen atoms, and switched the two remaining dicarboxylate linkers to monocarboxylates. This cluster can be seen (for the case of M = Al) on Figure 1. We started with clusters built from the np coordination geometry of Al-and Ga-MIL-53, i.e. a distorted octahedral coordination. We first optimized the positions of only the fluoride, in order to relax the starting cluster. Then, we performed a full relaxation of the system, with all atoms being free to move. During this full relaxation, in the case of both Al-and Ga-MIL-53, we observed the linkers to untwist, moving in a way that the metal center could regain its undistorted octahedral coordination. This relaxation, corresponding to the energetic penalty for the distorted "narrow-pore" conformation of the metal coordination, corresponded to a change in energy of 97.3 kJ/mol for Al, and 87.8 kJ/mol for Ga. From this, we conclude that the energetic penalty for the distortion of the Ga coordination is smaller than it is for Al, because of its more diffuse orbitals.

Thus, the more diffuse orbitals of Ga compared to Al is the reason behind the higher stability of its np phase, and thus the reason why Ga-MIL-53 is in np phase at room temperature (rather than lp for Al-MIL-53). The more diffuse nature of the Ga orbitals also means that its coordination sphere can deform more, thus allowing the benzene linkers to get closer in Ga-MIL-53 than Al-MIL-53. This, in turns, explains why the narrow-pore phase of Ga-MIL-53 lacks porosity, even though its overall framework density is slightly lower than Al-MIL-53.

However satisfying this analysis, we have to note its limitations: the approximation of the solid's entropy using zero-Kelvin vibrational entropy terms, while in qualitative agreement with experimental findings, is not accurate enough for a quantitative "ab initio" calculation of the equilibrium temperatures T 0 . Doing so, one finds T 0 (Al) = 967 K and T 0 (Ga) = 1172 K; though the order is correct, the values are too high overall, showing that vibrational terms underestimate the entropy of the solid phases (as could be expected).

Water adsorption at room temperature

In order to understand the behavior of Ga-MIL-53 in presence of water, we measured the adsorption and desorption isotherms of water on this material at 298 K. We also performed in situ XRD measurements at various water vapor pressures at 298 K, in order to put in parallel the thermodynamics and the structural evolution of Ga-MIL-53 upon water adsorption. Figure 2 presents the adsorption-desorption isotherm (in blue), and the evolution of the unit cell parameter b (corresponding to the smaller diagonal of the diamond-shaped channel) upon adsorption (in red). The sample was outgassed under vacuum at room temperature before the measurements, thus the starting structure is the closed one (hereafter called np_empty) as shown in reference 19. This np_empty structure is the stable one at room temperature (temperature lower than T 0 ). The adsorption-desorption isotherm is found to be fully reversible. It exhibits three distinct regions as the water vapor pressure is increased: (i) an initial rise in the amount of water adsorbed at low pressure (below 0.14 hPa) followed by a plateau region up to around 0.37 hPa corresponding to a loading of 0.05 mol.mol -1 (per mole of Ga(OH)(bdc)); (ii) a continuous increase in the amount adsorbed up to 0.24 mol.mol -1 at 0.76 hPa; and (iii) a vertical step followed by a continuous increase of the amount adsorbed up to 1 mol.mol -1 at 30 hPa (see on the full pressure scale on Fig. S1).

Besides, the evolution of the b cell parameter with the loading also shows three distinct regions (Fig. 2). Below 0.6 hPa, an increase in b from 6.9 to 7.05 Å, which corresponds to a deformation (swelling) of the np_empty phase upon partial hydration. Above 0.8 hPa, we observe a new peak, corresponding to the np_H 2 O phase, in line with our earlier work. [START_REF] Boutin | Temperature-Induced Structural Transitions in the Gallium-Based MIL-53 Metal-Organic Framework[END_REF] The b cell parameter of this phase increases from 7.5 to 7.6 Å in the pressure range of 0.8 to 1.6 hPa. Between these two ranges of pressure there is coexistence of the two phases: np_empty and np_H 2 O. The X-ray diffractograms obtained at pressures of 0, 0.4, 0.8 and 1.5 hPa are presented in Fig. S2.

We thus see that the stepped adsorption isotherm of water vapor in Ga-MIL-53 is linked to a structural transition, with the appearance of a new hydrated phase of the material. This transition was confirmed by FTIR spectroscopy, showing a sudden reversible jump in the ν s (CO 2 -) vibration band location, as shown in Figure 3. Below 0.9 hPa, the position of vibration band does not change with pressure. This behavior accounts for the presence of only one phase (partially hydrated np_empty). Above 2 hPa, this band is shifted by 2 cm -1 consecutive to the structural change of Ga-MIL-53 leading to the np_H 2 O phase.

Density functional theory study of Ga-MIL-53 at low water loading

In order to shed light on the structural response of Ga-MIL-53 to small amounts of adsorbed water, we performed first-principles molecular dynamics simulations at various hydration levels. The resulting structural parameters of Ga-MIL-53 with 0.0, 0.25 and 1.0 water molecules per Ga atom, averaged over the trajectory, are listed in table 2. While the lattice parameters a and c and the angles hardly change upon water adsorption, the parameter b is very sensitive to the amount of adsorbed molecules and increases by more than 15%. Furthermore, the expansion along b takes place already at 0.25 water molecules per Ga, and then increases only slightly upon further adsorption. Our simulation results for the lattice parameter b as a function of water loading are plotted along with the results of X-ray diffraction experiments in Figure 4. The simulation slightly overestimates b, especially at larger loading. This may be explained by the fact that this direction is very soft [START_REF] Ortiz | Anisotropic Elastic Properties of Flexible Metal-Organic Frameworks: How Soft Are Soft Porous Crystals?[END_REF] and hence, b is extremely sensitive to the density functional used in the simulation. But regarding the overall evolution of b, both simulation and experiment indicate that the np_H 2 O phase already appears at about 0.2 water molecules per Ga and then keeps its structure upon further adsorption. The X-ray data show that the np_H 2 O phase coexists with the np_empty phase up to values of 0.6 H 2 O/Ga. This suggests that the filling of Ga-MIL-53 proceeds non-uniformly: as soon as a layer of the material has reached the threshold of 0.2 H 2 O / Ga, it transforms from np_empty to np_H 2 O and will preferentially adsorb further water molecules, whereas the partially hydrated np_empty layers remain inert with water loading less than 0.2 H 2 O / Ga, until further hydration forces them to transform to np_H 2 O, too, layer by layer.

H 2 O / Ga a (Å) b (Å) c (Å) α (°) β (°) γ (°) V (Å

Analytical model at macroscopic level

Given what we have learnt from ab initio molecular simulation (section 3), how can we now interpret the experimental adsorption isotherm and in situ XRD data described in section 2? In this section, we provide a simple model at the macroscopic level to rationalize our findings.

It as been shown by Triguero et al. [START_REF] Triguero | Mechanism of Breathing Transitions in Metal-Organic Frameworks[END_REF] that structural transformations in materials of the MIL-53 family occur via layer-by-layer shear, on the level of the crystal, due to interplay between host framework elasticity and guest molecule adsorption. The structure of all unit cells is thus the same within a given layer. This phenomenon has also been observed in molecular dynamics simulations of Ghoufi et al. [START_REF] Ghoufi | Physics Behind the Guest-Assisted Structural Transitions of a Porous Metal-Organic Framework Material[END_REF] The simple thermodynamic model we propose here to understand water-induced structural transformations in Ga-MIL-53 at the macroscopic level is founded on that basis. Let consider a layer of N unit cells containing n adsorbed water molecules. Each layer can be either in the np_empty phase (which we refer to as np0 in this model, to simplify the notation) or the hydrated np_H 2 O phase (referred to here as np1). Let us call H k i the enthalpy of a layer of N unit cells in phase k (np0 or np1) with i adsorbed molecules, and ∆H ads k the adsorption enthalpy of a water molecule in the pore of a unit cell in structure k. Starting from the empty layer in phase np0 (case A in Fig. 5), the adsorption of n water molecules in this layer can either occur without structural change (case B) or induce a deformation of the porous host (case C). If the host structure remains unchanged, the adsorption leads to a change in enthalpy of:

H np0 n -H np0 0 = n ∆H ads np0 (eq. 1)
corresponding to a gain of n times the adsorption enthalpy in phase np0. On the other hand, if the host framework is deformed, the adsorption of n water molecules involves a change of enthalpy of:

H np1 n -H np0 0 = n ∆H ads np1 + N (H np1 0 -H np0 0 ) (eq. 2)
corresponding to the loss of energy due to structural change (np0 being the stable phase, (H np1 0 -H np0 0 ) > 0) and a gain of n times the adsorption enthalpy in structure np1. In order to determine which one of the two cases (B or C) is energetically the most favorable during adsorption, the enthalpy difference ∆H between case B and C can be calculated using equations 1 and 2 :

∆H = H np0 n -H np1 n = n (∆H ads np0 -∆H ads np1 ) -N (H np1 0 -H np0 0 ) (eq.3)
It is worth mentioning that we do not incorporate entropy differences in this simple model since the np0 and np1 structures are similar and we do not expect any significant changes in entropy between theses two cases.

All unit cell of a layer will thus exhibit a structural change from np0 to np1 if ∆H > 0. This condition can be rewritten as : n / N > (H np1 0 -H np0 0 ) / (∆H ads np0 -∆H ads np1 ) (eq. 4) or n / N > ∆H host / ∆∆H ads Because the adsorption of water in np1 is more favorable than in np0, we have (∆H ads np0 -∆H ads np1 ) > 0. Thus, the equation 4 obtained as a result of the model can be interpreted as follows:

-The larger ∆H host the larger n / N. The structural change from np0 to np1 will take place at larger value of adsorbed quantity; the adsorption enthalpy hardly compensates the unfavorable structural change. This model thus gives us a possible interpretation of the experimental results. As seen in the XRD data, the adsorption of the first few water molecules does not trigger the adsorption-induced transition. The first few molecules adsorbed cannot induce a whole layer transformation because of the energy penalty for the remaining unfilled np1 unit cells. Thus, there is a threshold amount of adsorbed water for the transition to be triggered. This explains why we see a strained (swelled) np0 state at low water loading, in region (ii) of Fig. 2. The adsorption of the first few molecules in the np0 structure create a stress on this very dense (small pore) structure, yielding a positive strain explaining the increase in the b unit cell parameter, seen by XRD.

Water adsorption-desorption isotherms and isobars

In earlier work on Xe, CO 2 and CH 4 adsorption in Al-MIL-53, we have shown that pressuretemperature phase diagrams are very helpful tools to understand, rationalize and predict the interplay between adsorption and structural transitions in flexible metal-organic frameworks. [START_REF] Boutin | Breathing Transitions in MIL-53(Al) Metal-Organic Framework Upon Xenon Adsorption[END_REF][START_REF] Coudert | The osmotic framework adsorbed solution theory: predicting mixture coadsorption in flexible nanoporous materials[END_REF] To this aim, we have measured the adsorption-desorption isotherms of water on Ga-MIL-53 at 273, 298, 323, 348 and 373 K, and isobars at 1 and 8 hPa (Fig. 6). Prior to adsorption the sample was outgassed under vacuum at 473 K. From these experimental data, we were able to construct a water vapor pressure-temperature diagram for the structural transitions, by building on our methodology for the simplest case of xenon, which had no intermediate structure. In this section, we explain how we amended the thermodynamic model of ref. 33 to take into account the specific features of Ga-MIL-53. As in our earlier work on Al-MIL-53, we fitted the experimental isotherms at all temperatures and pressures in order to derive the key parameters of the phase diagram. These parameters include the Henry constants and adsorption enthalpies, which characterize the affinity of the gas for the host, and its dependence on temperature. The parameters obtained from Langmuir fits of the isotherms are described in detail in the SI (Table S1, Figures S3 to S5).

Necessary parameters of the model also include the saturation uptake as a function of volume, i.e. the maximum amount of adsorbate that can fit in a particular geometry of the pore. Contrary to earlier work, where this was assumed to be linear as a function of pore volume, we needed here to adjust the functional form of that function to reproduce the experimental ability of the narrow-pore form of Ga-MIL-53 to accommodate a few water molecules, due to the ability of the framework to deform slightly. Thus, a step at low loading was introduced in the profile of maximum loading (presented in Fig. S6). The volume corresponding to the undeformed np_empty phase is here considered as strictly nonporous, and does not adsorb any molecules. For a slightly higher volume, roughly one water molecule per unit cell in average can fit in the pores. Afterward and for higher porous volume, the maximum loading is assumed to be linear with the volume.

Finally, the last parameter is the equilibrium temperature between the phases np_empty and lp of the empty material. Previous studies have shown the transition from np_empty to lp when heating the sample occurs in the range of 420-520 K. [START_REF] Boutin | Temperature-Induced Structural Transitions in the Gallium-Based MIL-53 Metal-Organic Framework[END_REF] Given the usually large hysteresis of temperatureinduced structural transition, there is a strong uncertainty on this value. Although an equilibrium of 450 K as been chosen in the following, we have shown that this value does not change the features we extract from the model (see Figure S7 the phase diagram obtained if an equilibrium temperature of 350 K is chosen). Once all these parameters were determined, we could use the thermodynamic model to calculate a number of properties of the system. In particular, the adsorption isotherms are obtained after adding in a constant term accounting for surface adsorption, and shown in Figure 7. We can see that the main features are reproduced, and the three domains observed experimentally can clearly be identified. The first one corresponds to the adsorption on the surface of the crystal, the intermediate is consistent with an adsorption in a slightly deformed np_empty structure, which is labeled int, while the vertical step marks the equilibrium pressure between this int form and the np_H 2 O one.

We can also calculate, based on the model, what is the most stable phase depending on the thermodynamic conditions (more specifically the water pressure and the temperature). Figure 8 shows the domains of stability of each phases in the (T,P) ensemble, i.e. the water pressuretemperature phase diagram of Ga-MIL-53. The red lines correspond to the domain (ii) observed experimentally in the adsorption isotherm for several temperatures, and it fits very well with the domain of stability of the slightly deformed structure int. It should be noted that the only two stable forms of the dehydrated material (at P = 0) are the lp phase (at T > T 0 = 450 K) and the np_empty phase (at T < T 0 ). A version of the phase diagram in linear pressure scale is presented in Fig. S8, which makes this fact clearer than the logarithmic scale of Fig. 8.

Finally, the thermodynamic model can also be used to calculate free energy profiles as a function of the volume (or deformation) of the host, which are shown in Fig. S9. One can, in particular, extract the values of the energy barrier for the transition between the np_empty, int, np_H 2 O and lp forms. We observe that the first transition from the np_empty to the int states has a very low barrier, around 0.1 kJ/mol. The same is true for the int-np_H 2 O transition albeit with a slightly higher value of 0.3 kJ/mol. Both of these free energy barriers are thus very low compared to the np-lp barriers in Ga-MIL-53 (7 to 10 kJ/mol), and np-lp barriers of other materials in the MIL-53 family. [START_REF] Bousquet | Adsorption Induced Transitions in Soft Porous Crystals: An Osmotic Potential Approach to Multistability and Intermediate Structures[END_REF] This explains the lack of hysteresis during an adsorption-desorption loop, a striking feature of water adsorption in Ga-MIL-53, since all other adsorption-induced structural transitions in MIL-53 materials reported to date show large hystereses.

CONCLUSION

We have studied the behavior of the breathing Ga-MIL-53 material by a large combination of experimental and theoretical tools: thermogravimetric measurements of adsorption isotherms and isobars, in situ XRD and FTIR spectroscopy, quantum chemical geometry optimizations, firstprinciples molecular dynamics, as well as macroscopic thermodynamic models. We were able to rationalize the differences observed experimentally between Ga-MIL-53 and Al-MIL-53 in terms of the coordination chemistry and molecular orbitals. We showed that water adsorption in Ga-MIL-53 involves an intermediate structure of the material, which we identified experimentally and explained on theoretical bases. Furthermore, we measured water adsorption isotherms at various temperatures and used these experimental results to build a thermodynamic phase diagram of Ga-MIL-53 as a function of temperature and water pressure. The understanding of water-induced structural transitions in this material gained in this study will enable further study into its hydrothermal and mechanical stability in various thermodynamic conditions. This provides an experimental confirmation of the earlier work of Bousquet et al. [START_REF] Bousquet | Adsorption Induced Transitions in Soft Porous Crystals: An Osmotic Potential Approach to Multistability and Intermediate Structures[END_REF] which showed on a theoretical basis that adsorption could give rise to new intermediate structures that are not stable in the absence of adsorbate. This phenomenon has also been hinted at experimentally in Fe-MIL-53, [START_REF] Millange | Effect of the nature of the metal on the breathing steps in MOFs with dynamic frameworks[END_REF] highlighting the crucial influence of the nature of the metal in the MIL-53 family of structures.

Figure 1 .

 1 Figure 1. Molecular cluster built from Al-MIL-53 in the narrow-pore configuration (Al -purple; F -green; O -red; C -gray; H -white).

Figure 2 :

 2 Figure 2: Experimental water adsorption-desorption at 298 K on Ga-MIL-53 (in blue; filled symbols and line: adsorption; empty symbols: desorption) outgassed under vacuum at 298 K (np_empty phase), along with evolution of the unit cell parameter b under adsorption, as measured by in situ XRD (red). Lower panel: view of a 1x2x1 supercell of the Ga-MIL-53 np_empty structure, showing the unit cell parameter b.

Figure 3 :

 3 Figure 3: Dependence of the position of ν s (CO 2 -) vibration band of the terephthalate ligands of Ga-MIL-53 after outgassing under vacuum at 298 K on water adsorption at 298 K (closed symbols: adsorption, open symbols: desorption).

Figure 4 .

 4 Figure 4. Lattice parameter b as a function of water loading, obtained from simulations (blue circles) and X-ray diffraction (red triangles). Lines are a guide for the eyes.

Figure 5 :

 5 Figure 5: Schematic representation of deformation in our simple macroscopic model for water adsorption in Ga-MIL-53.

-

  The larger ∆∆H ads the lower n / N. The adsorption enthalpy compensates easily the energetically unfavorable structural change.

Figure 6 :

 6 Figure 6: Top panel: water adsorption isotherms obtained at 273 (blue), 298 (green), 323 (orange), 348 (pink) and 373 K (red) on Ga-MIL-53. Lower panel: isobars obtained at 1 (blue) and 8 hPa (red) for in Ga-MIL-53.

Figure 7 :

 7 Figure 7: Water adsorption isotherms at 298 K (left) and 323 K (right). Experiments (black) and model (red).

Figure 8 :

 8 Figure 8: Water pressure vs. temperature phase diagram of Ga-MIL-53, indicating the domains of stability of the different structures of the material. Red segments correspond to the experimental transitions (domain (ii) in the nomenclature of section 2).

  ∆ (lp -np) ∆E tot (kJ/mol) ∆E el (kJ/mol) ∆E disp (kJ/mol) ∆E 0 (kJ/mol) ∆S vib (J.mol -1 .K -1 )

	Al-MIL-53	35.7	-65.8	101.3	0.25	36.9
	Ga-MIL-53	39.6	-53.3	94.5	-1.61	33.8
	Table

Table 2 :

 2 Structural parameters of Ga-MIL-53 at different water loadings, obtained from firstprinciples molecular dynamics simulations in the NσT ensemble.

	3 )

ACKNOWLEDGMENTS

The authors acknowledge funding from the Agence Nationale de la Recherche under the project ''SOFT-CRYSTAB'' (ANR-2010-BLAN-0822) and generous allocation of computing time by GENCI (grants i2013086882 and x2013086114).

SUPPORTING INFORMATION AVAILABLE

Water adsorption-desorption isotherm, X-ray diffractograms, details of the thermodynamic model employed. This material is available free of charge via the Internet at http://pubs.acs.org.

Table of Contents


Multidisciplinary project in Kalimantan Timur (Indonesia

Introduction

Island Southeast Asia has been the location of important archaeological discoveries regarding human evolution and recent human population history. Since 2003, a French-Indonesian archaeological research project has been in the karstic area of East Kalimantan (Indonesia) (fig. 1), which has notably led to the discovery of caves with unique rock art paintings, dating back to at least the early Holocene (9900 years BP; [1] [2]). A new multidisciplinary project was initiated in 2010, involving archaeological, anthropobiological and ethno-linguistic approaches, in order to document the past human occupations in this area.

Ricaut, François-Xavier (fx.ricaut@infonie.fr) (1); Oktaviana, Ahdi Agus (2); Ferrié, Jean-Georges (3); Sugiyanto, Bambang (4); Sarel, Josette (5); Plutniak, Sébastien (6); Guerreiro, Antonio (7); Tuniz, Claudio (8) Grenet, Michel (6); Voeltzel, Benedicte (5); Amuranto, Budi (9); Chazine, Jean-Michel (7); Sulistiyanto, Bambang (2)

Results and Discussion

Archaeological excavation. The test-pit conducted in Liang Abu in 2012 revealed a stratigraphic sequence with 14 sedimentary units (fig. 5). The bedrock was reached at approximately 160cm below the surface. Evidence of human presence were observed throughout the stratigraphy, except perhaps for the deepest level (US16). More than 70 kg of archaeological material were discovered and are currently under study. The AMS radiocarbon datings already performed were consistent with the stratigraphy. The layer 2 has been dated at BP (1686-1528 cal BP ;[3]) and 1524±22 BP (1515-1349 cal BP) from charcoals ; the layer 10 at 10222±38 BP (12082-11768 cal BP) from charcoal ; the layer 12 at 12660±58BP (15453-14570 cal BP) from bone.

Material and Methods

The project includes 4 scientific work packages 1 -Archaeology. Two rock shelters were selected for test-pit excavations, both are located 130 km northwest of the shore of the Makassar Strait, near the remote Lebbo' village of Merabu (East Kalimantan, Indonesia): Liang Abu, excavated in 2009-2012 (fig. 2) and Liang Pemalawan, excavation planned from 2013 (fig. 3) 4 -Ethno-archaeology/history/linguistic. The Lebbo' are an isolated autochthonous population and have lived in this inner region for a long time. Ethno-linguistic studies of their oral traditions and cultural practices are on-going to determine their former uses of the caves. Some of their representations could be related to the prehistoric rock art found in nearby caves.

3 -Prehistoric Rock Art. On-going analyses focus on several sites and should determine the pigments used (portable XRF system), the date of the prehistoric rock art (Th/U dating), characteristics of the rock art « population » (forensic approach: sex, height), the link between Lebbo' myths and rock art paintings (fig. 4) and make a correlation between the rock art and the archaeological material.

Genetic analysis using Illumina 700k DNA ship are preliminary (fig. 8) but suggests that the Lebbo' population is homogenous, with a main Austronesian (65%), a Proto-Malay (30%) and a Papuan (5%) component. The level of DNA preservation did not allow genetic information to be retrieved from the human remains.

Pottery.

Pottery is concentrated inside the layer 1 and 2. In total, there were 1102 sherds (94 rims, 86 carination, 922 body) among which 52% are decorated (impressed or incised). The typological analysis identified the presence of 5 shape classes. Interestingly the occurrence of red-slipped (3 sherds) and cord-marked pottery (7 sherds) was documented (fig. 6). Lithic. Lithic material is present through all the stratigraphy with a relative homogeneity. There are more than 2000 artefacts. The raw material used is rather varied (limestone, jasper, andesite, flint, chert). There is any standardisation of products and the knapping is oriented towards the production of flake blanks of varied morphologies and dimensions. Few tools have been uncovered (~1% denticulate, retouch pieces and burin). Preliminary use-wear analysis has shown that some elements may have been use on meat and vegetal matter.

Faunal remains. The faunal remains are very abundant and present throughout the stratigraphy. Analysis is ongoing to determine the taphonomic history of the assemblages. In each level, mammals and reptiles (mainly turtles) are the main taxonomic groups identified, the birds and fishes being rare. Among the mammals, Suids remains are the most abundant. The presence of a bone industry was also documented.

-Anthropobiology.

Analyses was based on morphometric analyses and DNA polymorphisms from ancient human remains and current human populations (Lebbo'). Unrelated individuals were sampled and information collected included languages spoken, current residence, familial birthplace, and a genealogy of four generations to establish regional ancestry. All samples were obtained with informed consent. The study was approved by the appropriate ethical committees. Ethno-linguistic investigation recorded some unique shamanic myths (fig. 7), linguistic data and determined post-marital residence (uxorilocality strategy), in agreement with the higher genetic diversity of the maternal lineages than paternal lineages. An interesting myth is Belian Danyam describing how the 8 wives of a mythic hero put their hands on cave walls to take control of a territory.

Conclusion

This pluridisciplinary project is providing new information on the past human occupations in East Borneo. The ongoing studies of the material and the next excavations should contribute to improving our knowledge of the rich human history in Island Southeast Asia.

Figure 6 .

 6 Figure 6. Red-slipped (A) and cord-marked pottery (B)

Figure 1 .

 1 Figure 1. Location of Liang Abu and other sites in Borneo.

Figure 3 .

 3 Figure 3. Liang Pemalawan Figure 2. Liang Abu

Figure 5 .

 5 Figure 5. Stratigraphic sequence from Liang Abu

Figure 4 .

 4 Figure 4. Rock art in Gua Beloyot Atas, near Liang Abu

Figure 7 .

 7 Figure 7. Pak Lempar (Epic song 2011)


Anne Boutin
email: anne.boutin@ens.fr

David Bousquet

Aurélie U Ortiz

François-Xavier Coudert

Alain H Fuchs

Anthony Ballandras

Guy Weber

Igor Bezverkhyy

Jean-Pierre Bellat

Guillaume Ortiz

Gérald Chaplais

Jean-Louis Paillaud

Claire Marichal

Habiba Nouali

Joël Patarin

Temperature-Induced Structural Transitions in Gallium-Based MIL-53 Metal-Organic Framework

Keywords: metal-organic frameworks, porous materials, structural transitions, densityfunctional theory, in situ X-Ray diffraction, FTIR

We report a structural and thermodynamic investigation of the phase behavior of Ga(OH,F)-MIL53, a gallium-based MOF having the MIL-53 topology containing 0.7 wt% fluorine bonded to the metal. Despite some small structural differences, especially for the hydrated form, the overall physical chemistry behavior of Ga(OH,F)-MIL-53 is very similar to standard fluorine free Ga-MIL-53 material. A combination of in situ X-ray diffraction, in situ Fourier transform infrared spectroscopy, differential scanning calorimetry and heat capacity measurements allowed to establish that Ga(OH,F)-MIL53 under vacuum (i.e. in the empty material) exhibits two stable phases: a nonporous narrow-pore (np) phase favored at low temperature and a large-pore (lp) phase favored at high temperature, accompanied by a huge hysteresis effect. Structure determination of the hydrated material Ga(OH,F)-MIL-53_np_H 2 O obtained after synthesis, activation and rehydration, was also performed. Density functional theory calculations show that it is not a stable structure of Ga(OH,F)-MIL53 in absence of adsorbed water molecules. Instead, this hydrated structure is a swollen variant of the np phase, where the flexible framework has expanded to accommodate water molecules.

Introduction

Within the last fifteen years, the development of a new class of organic-inorganic hybrid compounds called metal-organic frameworks (MOFs) has experienced a large acceleration [START_REF] Horike | Soft Porous Crystals[END_REF][START_REF] Férey | Large Breathing Effects in Three-Dimensional Porous Hybrid Matter: Facts, Analyses, Rules and Consequences[END_REF][START_REF] Kitagawa | Chemistry of Coordination Space of Porous Coordination Polymers[END_REF][START_REF] Férey | Swelling Hybrid Solids[END_REF] . Such solids are synthesized from metal and organic sources and give rise to one-dimensional, two-dimensional or three-dimensional porous structures where the inorganic sub-network is made up of clusters, chains, layers or even three-dimensional networks. The tremendous interest in this family of solids can be related to their extremely large range of crystal structures and host-guest properties, giving them a major potential impact in adsorption/separation technologies for strategic gases (e.g. H 2 , CO 2 and CH 4 ) linked with energy supply and environmental problems. [START_REF] Long | The Pervasive Chemistry of Metal-Organic Frameworks[END_REF][START_REF] Férey | Hybrid Porous Solids: Past, Present, Future[END_REF] The combination of tunable porosity, functionalization of the internal surface together with structural flexibility of the host framework opens the way to an extremely rich host-guest chemistry, putting this class of materials in a unique position. Depending on their characteristics (porosity, structure, nature of the organic linker), many subtypes of MOF's have been defined in the literature as PCP's (Porous Coordination Polymers), MMOF's (Microporous MOF's), ZMOF's (Zeolite-like MOF's), ZIF's (Zeolitic Imidazolate Frameworks), or SPC's (Soft Porous Crystal). This last-mentioned family consists of materials behaving in a remarkable guest-responsive fashion. Soft porous crystals 1 exhibit a variety of large amplitude dynamic behaviors of their frameworks in response to external stimuli of weak intensity (light, electric field, gas exposure…). The change in the framework of SPC's in response to the external constraint is reversible and maintains the crystalline character of the solid. As an example, one may cite the MIL-53 type frameworks [START_REF] Férey | Large Breathing Effects in Three-Dimensional Porous Hybrid Matter: Facts, Analyses, Rules and Consequences[END_REF][START_REF] Millange | Structure Determination and Properties of MIL-53(as) and MIL-53(ht): The First Cr(III) Hybrid Inorganic-Organic Microporous Solids[END_REF][START_REF] Horcajada | Flexible Porous Metal-Organic Frameworks for a Controlled Drug Delivery[END_REF][START_REF] Chaplais | IM-19: A New Flexible Microporous Gallium Based-MOF Framework with Pressure-and Temperature-Dependent Openings[END_REF][START_REF] Coudert | Thermodynamics of Guest-Induced Structural Transitions in Hybrid Organic-Inorganic Frameworks[END_REF][START_REF] Boutin | Breathing Transitions in MIL-53(Al) Metal-Organic Framework Upon Xenon Adsorption[END_REF] which exhibit guest-induced structural phase transitions upon guest adsorption and desorption, called "breathing" transitions. The bistable behavior of this system is controlled by the gas pressure that acts as the external stimulus but temperature, mechanical stress, liquid phase adsorption can also induce structural transitions [START_REF] Liu | Reversible Structural Transition in MIL-53 with Large Temperature Hysteresis[END_REF][START_REF] Beurroies | Using Pressure to Provoke the Structural Transition of Metal-Organic Frameworks[END_REF][START_REF] Maes | Separation of Styrene and Ethylbenzene on Metal-Organic Frameworks: Analogous Structures with Different Adsorption Mechanisms[END_REF] .

The solids of the MIL-53 type family solids are obtained from terephthalic acid (H 2 BDC) and a variety of metals such as Al, Cr, Fe, Ga, V, In, Sc, Mn, … It has been shown that the nature of the metal strongly affects the behavior of the solid [START_REF] Millange | Effect of the Nature of the Metal on the Breathing Steps in MOFs with Dynamic Frameworks[END_REF][START_REF] Mowat | A Novel Structural Form of MIL-53 Observed for the Ccandium Analogue and Its Response to Temperature Variation and CO 2 Adsorption[END_REF][START_REF] Nouar | Tuning the Breathing Behaviour of MIL-53 by Cation Mixing[END_REF] as well as functionality of the linker molecules [START_REF] Devic | Functionalization in Flexible Porous Solids: Effects on the Pore Opening and the Host-Guest Interactions[END_REF][START_REF] Biswas | Partially Fluorinated MIL-47 and Al-MIL-53 Frameworks: Influence of Functionalization on Sorption and Breathing Properties[END_REF][START_REF] Pera-Titus | Quantitative Characterization of Breathing upon Adsorption for a Series of Amino-Functionalized MIL-53[END_REF][START_REF] Lescouet | Homogeneity of Flexible Metal-Organic Frameworks Containing Mixed Linkers[END_REF] .

In 2008, Vougo-Zanda et al. [START_REF] Vougo-Zanda | Tossing and Turning: Guests in the Flexible Frameworks of Metal(III) Dicarboxylates[END_REF] published the syntheses and the structures determined by single crystal X-ray diffraction of two gallium based MOFs having the MIL-53 topology, that is, Ga(OH)(BDC)•0.74H 2 BDC and Ga(OH,F)(BDC)•0.74 H 2 BDC. Since then, several teams published gallium-containing MIL-53 type materials. In particular, Férey's group, pioneer team of the MIL-53 family [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] , and our group with the synthesis of gallium-containing MIL-53, named IM-19 [START_REF] Chaplais | IM-19: A New Flexible Microporous Gallium Based-MOF Framework with Pressure-and Temperature-Dependent Openings[END_REF][START_REF] Chaplais | Nouveau matériau hybride organique-inorganique et son procédé de préparation[END_REF][START_REF] Chaplais | Nouveau matériau hybride organique-inorganique et son procédé de préparation[END_REF] . In the present paper we report a study of the latter material named hereafter Ga(OH,F)-MIL53, which partially contains fluorine in the framework in contrast to the conventional Ga-MIL-53 [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] that is fluorine free and the Al(F)-MIL53 [START_REF] Liu | AlF 1,4-Benzenedicarboxylate: Synthesis and Absorption Properties[END_REF] in which all the OH groups are replaced by fluorine atoms [START_REF] Liu | AlF 1,4-Benzenedicarboxylate: Synthesis and Absorption Properties[END_REF] .

One of the specificities of the gallium based MIL-53, is that upon dehydration a narrow pore (np) structure is observed at room temperature, in contrast to well-studied aluminum or chromium based MIL-53 for which the stable phase of the bare material at room temperature is an open form (large pore, lp). Structure characterization of gallium based MIL-53 has been performed in the presence of H 2 BDC (benzenedicarboxylic acid), DMF (dimethylformamide) or water and without guest molecules. [START_REF] Chaplais | IM-19: A New Flexible Microporous Gallium Based-MOF Framework with Pressure-and Temperature-Dependent Openings[END_REF][START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] Depending on the presence or not of guest molecules, their nature and temperature, an expansion/shrinkage phenomenon is observed. However, some questions still subsist about the thermodynamics of the solid-solid phase transition in the empty material (i.e. under vacuum): its reversibility and its energetics.

In the present paper, we have used a combination of experimental and theoretical tools to shed light onto these issues. We performed a complete study of the solid-solid phase transition in Ga(OH,F)-MIL53 under secondary vacuum in a large temperature range, by using in situ X-Ray Diffraction (XRD), in situ Fourier Transform Infrared Spectroscopy (FTIR), Differential Scanning Calorimetry (DSC) as well as Density Functional Theory (DFT) calculations.

Experimental and theoretical details

Synthesis

All reagents and chemicals were used without any further purification. The metal source, gallium nitrate hydrate Ga(NO 3 ) 3 !xH 2 O (99.99 %), was purchased from Strem Chemicals. The organic linker, H 2 BDC (99 %), was supplied by Fluka. The solvents, DMF (≥ 99 %) and ethanol (EtOH, ≥ 99.8 %), were provided by Sigma-Aldrich and VWR, respectively. Hydrofluoric acid (HF, 40 %) was purchased from Prolabo.

Ga(OH,F)-MIL53_np_H 2 O.

Crude form of Ga(OH,F)-MIL53 (i.e. Ga(OH,F)-MIL53_lp_H 2 BDC) was hydrothermally prepared from a mixture of Ga(NO 3 ) 3 !x H 2 O (8.19 g; 32.02 mmol by assuming x=0), H 2 BDC (10.64 g; 64.04 mmol), HF (1.60 g; 32.02 mmol) in deionized water in 1/2/1/100 molar ratio. The mixture was heated at 493 K for 3 days in a Teflon®-lined stainless steel autoclave. The solid was filtered, washed with hot DMF (for removing the unreacted molecules of H 2 BDC), ethanol and dried at room temperature. White crystals were obtained with a yield of 45 % based on Ga (5.35 g; 14.25 mmol). Then, the asmade material was treated with DMF in a Teflon®-lined stainless steel autoclave at 433 K for 6 days. The solid (i.e. Ga(OH,F)-MIL53_lp_DMF) was recovered by filtration, washed with DMF and dried at room temperature. Finally, Ga(OH,F)-MIL53_np_H 2 O was obtained from Ga(OH,F)-MIL53_lp_DMF after removal of DMF by immersion in EtOH at room temperature during 24 h. After filtration, the white crystals were heated in air at 548 K for 1 day. After cooling down, a white crystalline powder was recovered. The presence of fluoride anion was evidenced by [START_REF] Biswas | Partially Fluorinated MIL-47 and Al-MIL-53 Frameworks: Influence of Functionalization on Sorption and Breathing Properties[END_REF] F NMR spectroscopic analyses in both liquid (after dissolution of the solid) and solid phases, the former characterization technique having enabled in addition the quantification of fluorine in the hydrated solid (Figures S1 andS2). These results combined with the one of thermogravimetric analysis (not shown) converge on the following formula, Ga(OH 0.9 F 0.1 )(BDC)•0.9H 2 O, for Ga(OH,F)-MIL53_np_H 2 O. It is worth noting that elemental analysis performed in the work of ref. 9 did not allow evidencing the traces of fluorine that [START_REF] Biswas | Partially Fluorinated MIL-47 and Al-MIL-53 Frameworks: Influence of Functionalization on Sorption and Breathing Properties[END_REF] F NMR clearly shows here.

Powder XRD and Rietveld refinement

High resolution powder XRD pattern of Ga(OH,F)-MIL53_np_H 2 O was first recorded by collecting the data on a STOE STADI-P diffractometer equipped with a curved monochromator Ge(111) and a linear position sensitive detector, in the 8-90° (2θ) range (step size: 0.01°, time acquisition/step: 150 s) and in the Debye-Scherrer scan mode by using CuKα 1 radiation (λ = 0.15406 nm). The Rietveld refinement was performed with the GSAS package 27 . More details on data collection are given in Supporting Information. The final Rietveld refinement gave excellent reliability factors; the final Rietveld plot is displayed in Figure S3 and crystal as well as Rietveld refinement parameters are listed in Table S1. Atomic parameters are listed in Table S2 and selected bond distances and angles are given in Table 5! S3. Figure S4 displays the asymmetric unit of Ga(OH,F)-MIL53_np_H 2 O. A crystallographic information file (CIF file) of Ga(OH,F)-MIL53_np_H 2 O can be obtained from the Cambridge Crystallographic Data Centre, quoting deposition numbers CCDC 912634.

Besides in situ XRD patterns were recorded using Cu Kα radiation on a D8 Advance Bruker apparatus equipped with a Vantec linear detector. Measurements were performed under vacuum (< 10 -3 hPa) at increasing then decreasing temperatures within the thermal stability temperature range 298-573 K, by using a MRI TC-Radiation chamber.

FTIR

In situ FTIR absorption measurements were performed in an optical cell specially built to study the interaction of a gas on a nanoporous material. This cell is a stainless steel six-way cube equipped with two KBr windows and two view ports for high vacuum, each of them being placed on opposite sides of the cube. The lower part of the cube is closed by means of a fixed solid flange and the upper part is connected to a heat chamber and to both a vacuum line and a gas inlet. The windows are located at a short distance from each other of about 10 mm in order to optimize the signal-to-noise ratio and to allow the exploration of a wide domain of pore filling of the adsorbent. The sample is dispersed between two KBr discs and placed in the sample holder, which can be moved up and down from the heat chamber to the optical cell, by using a magnetic sample transporter. After a thermal treatment under vacuum up to 573 K the sample holder is moved to the optical cell where the spectra are recorded at room temperature over a wide range of controlled pressure from 10 -4 to 10 3 hPa. The FTIR spectrometer was a Bruker Equinox 55 instrument equipped with a globar source, a DTGS detector and a KBr beamsplitter. All spectra were recorded at a resolution of 2 cm -1 by summing 40 scans in transmission mode. Each spectrum was referenced to a background spectrum recorded in the same conditions without sample.

DSC

Calorimetric measurements were carried out by means of a C80 Setaram Tian-Calvet differential calorimeter. The sample mass was around 300 mg. The heat capacity was measured by increasing the sample temperature step by step from 298 to 553 K. Temperature increment was 10 K and the heating rate was 0.5 K.min -1 . The change of enthalpy at the phase transition was measured under vacuum by heating the sample from 298 to 553 K with a heating rate of 0.1 K.min -1 . In all measurements the sample was kept under a dynamic vacuum of 10 -5 hPa. In both cases, blank experiments without sample were performed under the same conditions in order to take into account the thermal deviation of the calorimetric apparatus.

First principles calculations

Experimental crystallographic structures of the Ga(OH,F)-MIL53 and Ga-MIL53 materials were fully relaxed by optimizing both atomic positions and unit cell parameters. We performed first principles calculations in the density functional theory approach with periodic unit cell, full use of the crystals' symmetry elements and localized basis sets as implemented in the CRYSTAL09 code. [START_REF] Dovesi | CRYSTAL: a Computational Tool for the Ab Initio Study of the Electronic Properties of Crystals[END_REF] We used the B3LYP hybrid exchange-correlation functional [START_REF] Becke | Density-Functional Thermochemistry. III. The Role of Exact Exchange[END_REF][START_REF] Lee | Development of the Colle-Salvetti Correlation-Energy Formula Into a Functional of the Electron Density[END_REF] with empirical correction for the dispersive interactions following the scheme of Grimme. [START_REF] Grimme | Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction[END_REF] All electron basis sets were used for all atoms involved: 6-311G(d,p) for H, C and O, [START_REF] Gatti | Crystal Field Effects on the Topological Properties of the Electron Density in Molecular Crystals: The Case of Urea[END_REF] 8-511G* for Al [START_REF] Catti | Quantum-Mechanical Calculation of the Solid-State Equilibrium MgO+α-Al2O3⇄MgAl2O4 (Spinel) Versus Pressure[END_REF] and 86-4111d41G for Ga. [START_REF] Pandey | Ab-Initio Study of High-Pressure Phase-Transition in GaN[END_REF]

Results and discussion

Structure determinations: crystallography and first-principles calculations

The structure of Ga(OH,F)-MIL53_np_H 2 O is compared with the one of Ga-MIL-53_np_H 2 O, both at room temperature, in Figure!1. Like all the MOFs displaying the MIL-53 topology, it is built from 1D chains of MO 6 (M=Ga here) octahedra sharing OH vertices (running along the c axis) which are linked by terephthalate ligands to generate a 3D framework with rhombus-shaped channel. Moreover, liquid and solid state [START_REF] Biswas | Partially Fluorinated MIL-47 and Al-MIL-53 Frameworks: Influence of Functionalization on Sorption and Breathing Properties[END_REF] F NMR analyses evidence the presence of fluorine in the framework. The amount of fluorine determined by liquid state [START_REF] Biswas | Partially Fluorinated MIL-47 and Al-MIL-53 Frameworks: Influence of Functionalization on Sorption and Breathing Properties[END_REF] F NMR analysis is 0.7 wt % (Figure S1) which corresponds to a F/OH ratio around 1/9, i.e. one amongst ten bridged positions is occupied by one fluorine atom (nine others by OH groups). Besides, it is worth noting that because of, firstly, the small amount of fluorine in the framework and, secondly, the similarity of F and OH scattering factors, the Rietveld refinement of Ga(OH,F)-MIL53_np_H 2 O based on powder XRD pattern has been carried out without explicitly considering the presence of fluorine. The refined unit cell chemical composition taking into account the fluorine amount obtained from chemical analysis of Ga(OH,F)-MIL53_np_H 2 O is Ga(OH 0.9 F 0.1 )(BDC)•0.83 H 2 O (see Table S1). The refined number of water molecules is in good agreement with the one obtained by TG analysis.

Both Ga(OH,F)-MIL53_np_H 2 O and Ga-MIL53_np_H 2 O crystallize in monoclinic system (Table 1). Nevertheless the main difference resides on different space groups, i.e. noncentrosymmetric Cc group for Ga(OH,F)-MIL53_np_H 2 O and centrosymmetric P2 1 /c group for Ga-MIL-53_np_H 2 O with a double unit cell volume. As a result of the lowering of the symmetry, in Ga-MIL53_np_H 2 O, we observe a tripling of the gallium and a doubling of the water crystallographic sites compared with Ga(OH,F)-MIL53_np_H 2 O for which a unique crystallographic site is observed for gallium and water, respectively. Accordingly, two types of rhombus-shaped channels exist for Ga-MIL53_np_H 2 O as depicted in Figure 1b whereas only one type of channels appears for Ga(OH,F)-MIL53_np_H 2 O. This could be expressed by the twist angles between the terephthalate linker's planes. Indeed, for Ga(OH,F)-MIL53_np_H 2 O the angle formed by neighboring aromatic moieties, i.e. the ligands involved in the sharpest angle of the lozenge, is unique and around 35.3°. For Ga-MIL53_np_H 2 O the value of this angle depends on the nature of the channel. For A-type channels, one counts two values, 24.4 and 41.4° whereas for B-type channels the unique value of 31.3° is observed. [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] It is however difficult to rule on the reason of the structural difference between the two materials which can be considered as similar. The presence of fluorine in the framework in Ga(OH,F)-MIL53_np_H 2 O even at 0.7 wt % and the shorter heating duration for the preparation of the crude form of Ga-MIL53 could be underlined. It should also be noticed that the number of water molecules in the structure is slightly lower in the case of Ga(OH,F)-MIL53_np_H 2 O (=0.83, see table S2) than in the case of the hydrated Ga-MIL53 (=1, see ref. 23), possibly linked to the hydrophobic character of fluorinated materials.

We further investigated the nature of the difference between the various structures obtained experimentally by performing first principle energy minimization calculations in the Density Functional Theory formalism. The level of theory used is state-of-the-art for the determination of MOF structures, coupling a hybrid exchange-correlation function and corrections accounting for dispersion interactions. The details of our calculations are reported in ref. 35.

7!

We first characterized the structure of the large pore phase. As no experimental structure has been resolved for an adsorbate-free large pore material (either Ga-MIL-53 or Ga(OH,F)-MIL53), we used as a starting point the experimental crystallographic structure of Ga(OH,F)(BDC)•C 5 H 5 N synthesized by Vougo-Zanda et al. [START_REF] Vougo-Zanda | Tossing and Turning: Guests in the Flexible Frameworks of Metal(III) Dicarboxylates[END_REF] The published structure was edited to remove the guest pyridine molecules contained in its pores and add hydrogen atoms. The structure obtained was of in Imma space group, which is consistent with the indexing of the X-ray diffraction patterns for the empty high-temperature phase of Ga-MIL-53. [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] Energy minimization then yielded a structure in good agreement with the experimental unit cell parameters for MIL-53(Ga)_ht of Volkinger et al. [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] (unit cell volumes of 1452.7 Å 3 vs. 1479.7 Å 3 ; unit cell parameters are given in Table!2).

In a second time, we studied Ga(OH,F)-MIL53_np_empty, a narrow-pore structure with no adsorbed molecule. Using the experimental structure for Ga-MIL-53, published by Volkringer et al., [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] as a starting point, we minimized the atomic positions and unit cell parameters in the C2/c space group. The energy minimization converged to a structure close to the experimental one, with a slight increase in unit cell volume (from 886.3 Å 3 to 899.0 Å 3 ). Details of the unit cell parameters are given in Table! 2. A geometrical analysis of accessible pore volume showed the resulting structure to be non-porous for a probe molecule of the size of water (kinetic diameter of 2.4 Å): the largest sphere that can access the pores has a diameter of 2.2 Å. We confirmed this geometrical analysis with Grand Canonical Monte Carlo simulations of water adsorption. No water molecule was adsorbed in the range of pressure up to P sat = 3.5 kPa, the saturation pressure of water at 300 K.

Finally, we turned our attention to the hydrated narrow-pore phase whose experimental structure was determined by X-ray diffraction, for both the Ga-MIL-53 and Ga(OH,F)-MIL53 materials. Starting from the experimental structure of Ga(OH,F)-MIL53_np_H 2 O (space group Cc), we first relaxed the hydrated structure, leading to a small shrinking of the unit cell (from 973.4 Å 3 to 948.6 Å 3 ). We then removed the water molecules and optimized the empty structure: the material underwent a contraction of larger amplitude, yielding a final structure almost identical to the Ga(OH,F)-MIL53_np_empty structure discussed in the above paragraph (volume of 897.9 Å 3 vs. 899.0 Å 3 ; see Table 2 for all unit cell parameters). As a conclusion, our quantum chemistry calculations reveal that the conformation of the Ga(OH,F)-MIL53_np_H 2 O framework is not a stable structure in the absence of adsorbed water molecules. Instead, removal of water spontaneously leads to the formation of Ga(OH,F)-MIL53_np_empty.

We then performed the same analysis on the hydrated Ga-MIL-53_np material reported by the Férey group. The structure of this latter is slightly different from the Ga(OH,F)-MIL53_np_H 2 O, in that it has been indexed in a double unit cell (and space group P2 1 /c). As discussed above, its super structure is composed of two different channels with two distinct crystallographic sites for water molecules (named sites A and B). Upon removal of water molecules from hydrated Ga-MIL-53_np and energy minimization of the structure, we observed that the structure relaxation proceeds in two clearly separated stages. At first, the aromatic rings of the material rotate from their initial "twisted" position. This leads to more symmetric structure, in which the differentiation between channel types A and B has been lost. During later steps of the energy minimization, the framework then contracts into a nonporous structure, similarly to what was observed for Ga(OH,F)-MIL53_np_H 2 O. The final crystalline structure has, however, a lower unit cell volume (V = 840.7 Å 3 ). We conclude again that Ga(OH,F)-MIL53 and Ga-MIL-53 behave in a similar fashion despite small structural differences which are still to be fully elucidated. The less reasonable structure obtained when starting from Ga-MIL-53 may be attributed to difficulties in the optimization µ 2 -hydroxo group hydrogen bonded to adsorbed water molecules [H 2 O…H-O(Ga) 2 ]. The last three bands, located at 983, 624 and 582 cm -1 , can also be assigned to bands arising from the interaction of water with Ga(OH,F)-MIL53. All other vibrational bands are almost unchanged upon dehydration at room temperature.

Upon heating under vacuum, the infrared spectrum of Ga(OH,F)-MIL53_np_empty undergoes further strong modifications due to the np_empty-lp structural transition. Over the nineteen vibrational bands examined in the range 2000-400 cm -1 , only six are not modified during the phase transition. Ten vibrational bands are blue or red shifted by jump at either 453 or at 499 K, depending on the nature of the vibration (Figure 5). The shifts are at least 5 cm -1 for the band referenced as ν17B and located at 890 cm -1 , and they can reach 19 cm -1 for the ν as (CO 2 -) vibrational mode of the terephthalate ligands that is located at 1546 cm -1 in the np_empty form. As specified by Volkringer et al. [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] for the vibrational band located at around 1020 cm -1 and referenced as 18A in Figure 5, these shifts reflect the opening phenomenon of the Ga(OH,F)-MIL53_np_empty network to give the lp phase. One another band located at 544 cm -1 disappears after heating above 453 K (Figure S7) and two new bands located at 513 and 580 cm -1 , characteristic of the lp phase appear at temperature higher than 499 K (Figure S8).

From this analysis of the location of vibrational bands as a function of the temperature it is clear that the np_empty and lp phases exist as pure phases in the temperature ranges below 453 K and above 499 K, respectively. Between 453 and 499 K, the coexistence of characteristic bands of the two structures indicates the presence of a mixture of the np_empty and lp phases.

The values of the temperature of phase transition determined by in situ FTIR spectroscopy and XRD are in good agreement, as can be seen on the diagram shown in Figure!6. The small discrepancy between the values of the temperature from which the lp phase appears can be attributed to differences of sensitivity of the techniques or to the accuracy on measured values of temperature from one technique to another.

Calorimetric measurements

In order to shed light onto the energetics of the phase transitions observed in Ga(OH,F)-MIL53, we performed calorimetric measurements upon dehydration and heating of the material. The heat absorbed during the dehydration step led to an integral enthalpy of dehydration close to +49 kJ per mole of water desorbed. From this value, close to the standard vaporization enthalpy of water (+44 kJ.mol -1 ), we could conclude that the water is not strongly bound to the surface. Moreover, this integral enthalpy is the sum of two thermal effects: the endothermic desorption of water and the exothermic phase transition from np_H 2 O to np_empty structures. So, the energy of interaction between the water molecules and the channel surface should be greater than 49 kJ.mol -1 .

The temperature dependence of the heat capacity of anhydrous Ga(OH,F)-MIL53 is shown in Figure!7 (green circles): it ranges from 50 to 180 J.K -1 .mol -1 . For comparison, the standard heat capacity of gallium oxide Ga 2 O 3 is equal to 83.6 J.K -1 .mol -1 at 323 K [START_REF] Satoh | The Heat Capacities of Some Organic Compounds Containing Nitrogen and the Atomic Heat of Nitrogen[END_REF] and that of terephthalate acid is equal to 199.6 J.K -1 .mol -1 at 298 K [START_REF] Rossini | Selected values of chemical thermodynamics properties[END_REF] . At 450 K, the slope of the Cp-T curve changes, and remains surprisingly constant between 450 and 553 K. Comparing with XRD and FTIR results, this change of slope can be attributed to the appearance of an lp 10! phase. The constancy of Cp above 450 K may be explained by the endothermal np_empty→lp phase transition, which interferes with Cp measurements. This suggests that the np_empty→lp transition occurs gradually from a temperature of about 450 K, and that it is complete at 553 K. The existence of a biphasic domain characterized by DSC is in good agreement with experimental results obtained by in situ XRD and FTIR (Figure !6c).

The heat flux was measured by the calorimeter upon heating Ga(OH,F)-MIL53 from 298 to 553 K under dynamic vacuum (blue curve in Figure !7), and compared to a blank experiment performed without sample (red curve). While the variation of heat flux for the blank experiment is linear with temperature, this is not the case in presence of the sample: an endothermic effect is observed. This means that the enthalpy does not jump at the phase transition, which takes place at around 450 K, but varies continuously upon heating above this temperature.

As it is not possible to measure directly the enthalpy change of the np_empty→lp phase transition, we estimated it in two steps. We thus measured the integral enthalpy of dehydration under vacuum of Ga(OH,F)-MIL53 at room temperature (np_H 2 O→np_empty transition), as well as that of hydration of Ga(OH,F)-MIL53 at room temperature after activation at 553 K (lp→np_H 2 O, lp being metastable at room temperature):

ΔH np_empty → lp = -(ΔH np_H2O → np_empty + ΔH lp → np_H2O )
Results are collected in Table! 3. From this estimation, the integral enthalpy of the phase transition from np_empty to lp is of about 5.5 kJ.mol -1 . This value is only an estimate, because the interaction energy of water with the np_empty phase is certainly different from that observed with the lp phase.

CONCLUSION

In this paper, we used a wide array of experimental techniques over the 300-600 K temperature range in order to study the solid-solid phase transition in Ga(OH,F)-MIL53 under vacuum. Results obtained from in situ X-Ray Diffraction (XRD), in situ Fourier Transform Infrared Spectroscopy (FTIR) and Differential Scanning Calorimetry (DSC) were all found to be in good agreement. We showed that, in addition to the hydrated 300 K structure resulting from the synthesis, Ga(OH,F)-MIL53 exhibits two different phases under vacuum: a nonporous narrow-pore phase (np), thermodynamically favored at lower temperature, and a large-pore phase (lp), favored at high temperature. Experimental measurements (both XRD and FTIR) upon heating and cooling Ga(OH,F)-MIL53 revealed large hystereses of the temperature-induced structural transitions, highlighting the importance of the material's thermal history to its physical and chemical properties. Finally, geometry optimization of the experimental crystallographic structures within the framework of the Density Functional Theory enabled us to conclude that the hydrated phase at low temperature is not a stable structure in the absence of adsorbed water molecules. Instead, the hydrated structure is a swollen variant of the narrow-pore phase, where the framework has expanded to accommodate water molecules. Giving that the behavior of guest-free Ga(OH,F)-MIL53 as a function of temperature has now been established, work is ongoing to assess its behavior in presence of adsorbates, and particularly in presence of water in vapor or liquid state.

Finally, it is now clear that despite some small structural differences, Ga(OH,F)-MIL53 should be considered as displaying a similar physical chemistry behavior to the standard Ga-MIL53, especially with respect to the phase behavior and the breathing phenomenon. It turns out that, just like the other MIL-53 (M) ; M= Cr, Al, Fe, … materials, the empty gallium based MIL-53 material exhibits two, and only two stable phases, something that was not clear up to now.

Ga-MIL-53_lp

MIL-53(Ga)_ht [START_REF] Volkringer | XRD and IR Structural Investigations of a Particular Breathing Effect in the MOF-Type Gallium Terephthalate MIL-53[END_REF] high temperature 1479.7

a = 6 . 9 ( 23 GaTable 2 :Table 3 :Figure 1 :Figure 2 :

 69232312 Figure 1: Structural representations of a) Ga(OH,F)-MIL53_np_H 2 O and b) Ga-MIL-53_np_H 2 O

Figure 3 :

 3 Figure 3: Evolution of the XRD patterns of Ga(OH,F)-MIL53 under vacuum as a function of temperature.

Figure 4 :

 4 Figure 4: Evolution of the XRD pattern of Ga(OH,F)-MIL53 on cooling under vacuum from 573 to 303 K.

Figure 5 :

 5 Figure 5: Variation of the position of the!ν as (CO 2 -)!vibrational modes and the ring stretching!ν(C=C) (referenced as! ν19A) vibrational mode, the! δ(C-H) (referenced as ν18A) 40 in plane vibrational deformation modes and the γ(C-H) (referenced as ν17B) 40 out of plane vibrational deformation modes of the terephthalate ligands of Ga(OH,F)-MIL53 with temperature, under vacuum.

Figure 6 :

 6 Figure 6: Schematic diagram reporting the values of temperature of the phase transition of Ga(OH,F)-MIL53 determined under vacuum by XRD (a), FTIR (b) and DSC (c), (np for np_empty: narrow pore form; lp: large pore form).

Figure 7 :

 7 Figure 7: Heat capacity (green curve) of Ga(OH,F)-MIL53 and heat flow measured by the calorimeter during heating from 298 to 553 K under dynamic vacuum (blue curve: sample experiment with Ga(OH,F)-MIL53; red curve: blank experiment without sample).

Table 1 :

 1 Unit cell parameters of Ga(OH,F)-MIL53_np_H 2 O, MIL-53(Ga)_np_H 2 O, MIL-53(Al)_np_H 2 O

	96751(8)

* double cell

a unit cell parameters refined with the Le Bail method (GSAS 27 , a = 19.77488

(22)

Å, b = 6.

Acknowledgments

The authors gratefully acknowledge Dr. Didier LE NOUEN (LCOB -UHA -EA4566) for carrying out the liquid state NMR experiments.! Funding from the Agence Nationale de la Recherche under project ''SOFTCRYSTAB'' (ANR-2010-BLAN-0822) is acknowledged.

of this complex molecular crystal, starting from a geometry that is more distorted than Ga(OH,F)-MIL53_np_H 2 O (and twice its size). Further theoretical work on this aspect is ongoing.

In situ XRD characterization of phase transitions

The XRD patterns of Ga(OH,F)-MIL53 recorded at 303 K under air and vacuum are compared in Figure 2. It is worth noting that under vacuum, all water molecules are desorbed from the sample at room temperature (see the thermodesorption curve shown in supporting information, Figure S6). Thus, the removal of water molecules from Ga(OH,F)-MIL53_np_H 2 O results in formation of another phase, which has been previously observed and designated phase p1 at T > 353 K under ambient atmosphere. [START_REF] Chaplais | IM-19: A New Flexible Microporous Gallium Based-MOF Framework with Pressure-and Temperature-Dependent Openings[END_REF] The XRD pattern of this phase is the same as that observed for the structure referred to as MIL-53(Ga)_lt in ref. 23 for which the structure was determined to be a narrow pore form of MIL-53. Our XRD data thus allows us to conclude that the stable form of the guest-free Ga(OH,F)-MIL53 at 303 K is a narrow pore form, that we hereafter call Ga(OH,F)-MIL53_np_empty.

Further heating of the solid under vacuum in its thermal stability range (characterized by thermodesorption experiment, see Figure S6) induces a progressive transformation of Ga(OH,F)-MIL53_np_empty into another phase, identical to phase p2 identified under air by Chaplais et al. [START_REF] Chaplais | IM-19: A New Flexible Microporous Gallium Based-MOF Framework with Pressure-and Temperature-Dependent Openings[END_REF] The corresponding diffraction pattern is similar to those of MIL-53(Al)_ht and MIL-53(Cr)_ht, where it was identified as a large pore structure. [START_REF] Loiseau | A Rationale for the Large Breathing of the Porous Aluminum Terephthalate (MIL-53) Upon Hydration[END_REF] This phase is designated here as Ga(OH,F)-MIL53_lp. The np_empty → lp transformation under vacuum occurs in the same temperature range as for the sample heated in air [START_REF] Chaplais | IM-19: A New Flexible Microporous Gallium Based-MOF Framework with Pressure-and Temperature-Dependent Openings[END_REF] : it begins at 423 K and it is complete at 523 K (Figure !3).

To verify the reversibility of the phase transition under vacuum, the sample was cooled down from 573 K (Ga(OH,F)-MIL53_lp) to 303 K. The XRD patterns of the sample were then recorded every 194 min (Figure 4). The cooling to 303 K induces a partial structural transformation of lp into np_empty as can be inferred from the appearance of the characteristic peaks (the most intense being the (110) peak located at 2θ = 13.5°). On further aging at 303 K, the intensity of the peaks of Ga(OH,F)-MIL53_np_empty slightly increases, but after ca. 6 h it remains constant. The structural phase of Ga(OH,F)-MIL53 at 303 K under vacuum appears therefore to be dependent on the thermal history. After water desorption at 303 K, the stable phase is the narrow pore form Ga(OH,F)-MIL53_np_empty. By contrast after heating to 573 K and cooling, the solid consists of a mixture of lp and np_empty structures, with a majority of lp structure. Such a behavior is indicative of a large temperature hysteresis in the structural transition for Ga(OH,F)-MIL53, similar to what has been observed in MIL-53(Al) [START_REF] Liu | Reversible Structural Transition in MIL-53 with Large Temperature Hysteresis[END_REF] .

In situ FTIR characterization of phase transitions

After outgassing under vacuum at room temperature, the infrared spectrum of Ga(OH,F)-MIL53 undergoes modifications in the wavenumber range 4000-400 cm -1 due to the phase transition from np_H 2 O to np_empty during dehydration. This structural transformation induces the disappearance of at least five vibrational bands characteristic of Ga(OH,F)-MIL53_np_H 2 O. The first one, located at 1626 cm -1 , is assigned to the fundamental ν 2 (H 2 O) band of encapsulated water. The second one, at 1123 cm -1 , corresponds to the δ(OH) band of

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