Guillaume Fraux

Anne Boutin

Alain H Fuchs

Franccois-Xavier Coudert
email: fx.coudert@chimieparistech.psl.eu

We report here the properties of LiCl aqueous solutions at various concentrations confined inside the pores of the ZIF-8 metal-organic framework, based on classical molecular dynamics simulations. This system has been proposed for applications in the storage or dissipation of mechanical energy, using the liquid-phase intrusion of concentrated electrolytes in the hydrophobic framework. We describe the structure of the liquids and the influence of confinement, their dynamics, the mechanical properties of ZIF-8 and the impact of liquid intrusion on them. We show that the presence of the electrolyte has a moderate impact on the ZIF-8 framework, while the presence of the ZIF-8 matrix strongly influences the behavior of the confined aqueous solution, affecting the overall properties of the system. We also computed the free energy profile for the entry of water molecules and ions into the nanopores, showing a difference between anions and cations.

Introduction

Nanoporous crystalline materials such as zeolites, metal-organic frameworks (MOF), carbon nanotubes and inorganic open frameworks enjoy a wide range of applications, ranging from catalysis, fluid separation and purification, to gas capture and detection of dangerous molecules. The fundamental basis for most of these applications is the material's capability to adsorb large quantities of molecules inside its nanometer-sized pores, due to its large specific surface area. [START_REF] Rouquerol | Adsorption by powders and porous solids: principles, methodology and applications[END_REF] In this context, hydrophobic nanoporous materials offer the advantage that the uptake of water from the gas phase -e.g., humidity in the air -is very small. [START_REF] Wu | Enhancing the stability of metal-organic frameworks in humid air by incorporating water repellent functional groups[END_REF][START_REF] Ghosh | Modeling Water and Ammonia Adsorption in Hydrophobic Metal-Organic Frameworks: Single Components and Mixtures[END_REF][START_REF] Wang | Applications of water stable metal-organic frameworks[END_REF] Given that water is often strongly adsorbed and competes with other molecules for adsorption sites, hydrophobic molecular sieves can offer higher separation properties. [START_REF] Flanigen | a new hydrophobic crystalline silica molecular sieve[END_REF][START_REF] Giaya | Liquid and vapor phase adsorption of chlorinated volatile organic compounds on hydrophobic molecular sieves[END_REF] One of the novel applications that has been proposed for hydrophobic nanoporous materials is related to mechanical energy storage or dissipation through water intrusion. [START_REF] Eroshenko | Energetics: A New Field of Applications for Hydrophobic Zeolites[END_REF]8 In a hydrophobic porous material, the pressure at which external water will enter the pore space is greater than the vapor pressure of water. That is, adsorption happens only in the liquid phase -and this high-pressure adsorption is called intrusion. [START_REF] Fraux | Forced intrusion of water and aqueous solutions in microporous materials: from fundamental thermodynamics to energy storage devices[END_REF] This phenomenon has been extensively studied in inorganic nanoporous materials, such as zeolites, [START_REF] Saada | High-Pressure Water Intrusion Investigation of Pure Silica RUB-41 and S-SOD Zeolite Materials[END_REF][START_REF] Desbiens | Water Condensation in Hydrophobic Nanopores[END_REF][START_REF] Humplik | Effect of Hydrophilic Defects on Water Transport in MFI Zeolites[END_REF][START_REF] Humplik | Framework water capacity and infiltration pressure of MFI zeolites[END_REF] and more recently evidenced in hydrophobic metal-organic frameworks. [START_REF] Ortiz | Energetic performances of the metal-organic framework ZIF-8 obtained using high pressure water intrusionextrusion experiments[END_REF][START_REF] Grosu | Stability of zeolitic imidazolate frameworks: effect of forced water intrusion and framework flexibility dynamics[END_REF][START_REF] Michelin-Jamois | Giant Osmotic Pressure in the Forced Wetting of Hydrophobic Nanopores[END_REF] Depending on the nature of the nanoporous material and the strength of the host-guest interactions, intrusion curves can have different shapes and be classified as either as a molecular spring, a shock adsorber, or a bumper. This classification depends on the level of hysteresis during an intrusion-extrusion cycle. For more details, we refer the interested reader to a review we recently wrote. [START_REF] Fraux | Forced intrusion of water and aqueous solutions in microporous materials: from fundamental thermodynamics to energy storage devices[END_REF] A very sought-after property related to the intrusion of water in hydrophobic frameworks is the ability to tune the intrusion pressure and the amount of hysteresis present. This can be achieved by chemical modifications of the structure of the host material, [START_REF] Ortiz | What makes zeolitic imidazolate frameworks hydrophobic or hydrophilic? The impact of geometry and functionalization on water adsorption[END_REF] or by changing the nature of the liquid -namely, by adding ions to the water. [START_REF] Ortiz | Versatile Energetic Behavior of ZIF-8 upon High Pressure Intrusion-Extrusion of Aqueous Electrolyte Solutions[END_REF] Depending on the size of the ions and porous channels, in some cases only water can enter the nanopores while ions stay in the bulk liquid. The change in the intrusion pressure is then directly related to additional osmotic pressure the fluid has to overcome to enter the structure. [START_REF] Michelin-Jamois | Giant Osmotic Pressure in the Forced Wetting of Hydrophobic Nanopores[END_REF] But in other cases, the addition of ions has a more complex impact on both the intrusion pressure and the shape of intrusion curves. For example, in the pure-silica analogue of the β zeolite, [START_REF] Camblor | Spontaneous nucleation and growth of pure silica zeolite-β free of connectivity defects[END_REF] increasing the electrolyte concentration from 5 mol/L to 10 mol/L only shifts the intrusion pressure, but increasing it again to 15 mol/L changes the overall behavior from a shock-absorber to a spring. [START_REF] Ryzhikov | Drastic change of the intrusion-extrusion behavior of electrolyte solutions in pure silica * BEA-type zeolite[END_REF] Such changes indicate that the interaction between the electrolyte fluid and the host structure is not merely reduced to a simple effect of size-based exclusion. At the same time, in situ X-ray diffraction measurements performed during intrusion-extrusion cycles showed that MgCl 2 ions can enter a pure-silica ferrierite during intrusion. [START_REF] Arletti | Intrusion-extrusion experiments of MgCl2 aqueous solution in pure silica ferrierite: Evidence of the nature of intruded liquid by in situ high pressure synchrotron X-ray powder diffraction[END_REF] All this evidence points to a more complex effect than pure osmotic pressure when using an electrolyte fluid for intrusion.

Moreover, we know that adsorption of water in the gas phase can induce large structural changes in nanoporous materials. [START_REF] Lee | First Structural Investigation of a Super-Hydrated Zeolite[END_REF][START_REF] Seoung | Super-Hydrated Zeolites: Pressure-Induced Hydration in Natrolites[END_REF] This is particular true of soft porous crystals, [START_REF] Horike | Soft porous crystals[END_REF] such as flexible MOFs, [START_REF] Schneemann | Flexible metal-organic frameworks[END_REF] exhibiting dynamic frameworks that are able to respond to external stimuli. This has been studied, by both experimental and computational means, on the MIL-53 family of "breathing" frameworks: the presence of water influences the structure of MIL-53(Cr), [START_REF] Haigis | Investigation of structure and dynamics of the hydrated metal-organic framework MIL-53(Cr) using first-principles molecular dynamics[END_REF] and is responsible for the occurrence of numerous structural transitions in MIL-53(Ga), as a function of both water vapor pressure and temperature. [START_REF] Boutin | Temperature-Induced Structural Transitions in the Gallium-Based MIL-53 Metal-Organic Framework[END_REF][START_REF] Coudert | Water Adsorption in Flexible Gallium-Based MIL-53 Metal-Organic Framework[END_REF] Relatively little is known, in contrast, on the impact of liquid water -and aqueous solution -intrusion on the structure of flexible MOFs.

Here, we are interested in the study of the high-pressure electrolyte intrusion in ZIF-8. ZIF-8 is a nanoporous material part of the Zeolitic Imidazolate Frameworks (ZIF) family. These MOF are built from imidazolate anions as their organic linker (mim = 2methylimidazolate in the case of ZIF-8) and a divalent metal cation (here, Zn 2+ ). The frameworks of ZIFs are four-connected, meaning that the ZIFs adopt zeolitic topologies, with the metal center replacing the tetrahedral silicon atom and the linker replacing the oxygen topology. In this topology, large quasi-spherical pores corresponding to the sodalite cages are connected by windows formed by 6 and 4 zinc atoms (see Figure 1). In ZIF-8, the 4 members windows are too small for any molecules to go through, and all of the connectivity of the pore space happens though the 6 members windows. ZIF-8 is hydrophobic, [START_REF] Ortiz | What makes zeolitic imidazolate frameworks hydrophobic or hydrophilic? The impact of geometry and functionalization on water adsorption[END_REF] and presents interesting behavior upon intrusion. While osmotic pressure effects do not depend on the chemical nature of the ions, ZIF-8 shows changes from one energetic behavior to another when the ion nature changes while keeping concentration constant. [START_REF] Ortiz | Versatile Energetic Behavior of ZIF-8 upon High Pressure Intrusion-Extrusion of Aqueous Electrolyte Solutions[END_REF] ZIF-8 behavior can also be tuned chemically, by modifying the nature of the linkers, for example changing the 2-methylimidazolate to a 2-chloroimidazolate increases the intrusion pressure. [START_REF] Mortada | Energetic Performances of ZIF-8 Derivatives: Impact of the Substitution (Me, Cl, or Br) on Imidazolate Linker[END_REF] However, the exact mechanism and behavior at the molecular level upon intrusion of electrolytes in ZIF-8 are still unknown. In this work, we used classical molecular simulations to study the structure, dynamics and energetic implications of confining water and aqueous solutions of LiCl in ZIF-8. Using these simulations, we were able to explore different aspects of the {water, ZIF-8} and {electrolyte, ZIF-8} systems. We describe below the structure of the liquids and the influence of confinement, their dynamics, the mechanical properties of ZIF-8 and the impact of liquid intrusion on them. We conclude by a series of considerations on the energetics of intrusion, and results on the thermodynamics and the free energy of entry of ions in ZIF-8.

Computational methods

We ran classical molecular dynamics (MD) simulations and umbrella sampling simulations using the LAMMPS 30 code. The umbrella sampling simulations additionally used the colvars 31 module for collective variables. We used a combination of different force fields for the component of the system: a rigid SPC/E 32 for water, for its ability to describe the dynamics of liquid water and the solvation of ions; a flexible force-field adapted from AMBER by Zheng et al. [START_REF] Zheng | Force Field for Molecular Dynamics Computations in Flexible ZIF-8 Framework[END_REF] for the description of the ZIF-8 framework; and a combination of electrostatic and Lennard-Jones potentials for the ions, reproduced in supplementary information Table S1. [START_REF] Chowdhuri | Hydration structure and diffusion of ions in supercooled water: Ion size effects[END_REF] We used Lorentz-Berthelot mixing rules for cross-terms in Lennard-Jones potential, and Ewald summation to account efficiently for electrostatic interactions.

We used a cutoff of 8.5 A for both the Lennard-Jones potential and the separation between real space and Fourier space in the Ewald summation.

After an initial energy minimization, we carried all simulations in the isothermal-isobaric (N, P, T ) ensemble with a timestep of 1 fs, using a Nosé-Hoover thermostat with a time constant of 1 ps and a Nosé-Hoover barostat with a time constant of 10 ps. We allowed the barostat to make arbitrary changes to unit cell lengths and tilt factors (fully flexible anisotropic cell), while imposing an isotropic pressure to the system. Unless specified otherwise, we ran all simulations in the (N, P, T ) ensemble for 10 ns, and only used the last 4 ns for analysis.

We used three different types of systems in this study. First, bulk liquids at different LiCl concentration: 0 mol/L (pure water), 1 mol/L, 5 mol/L, 10 mol/L, 15 mol/L and 20 mol/Lthe experimental solubility of LiCl in water at 25 °C is 19.87 mol/L. Then we simulated a 3 × 3 × 3 supercell of ZIF-8, with liquid confined inside the pores, at the same concentrations as the bulk liquid. Finally, we used a 2 × 2 × 3 ZIF-8 supercell containing pure water together with a 34 A cubic reservoir of water on top (this system featuring an explicit ZIF-8/liquid interface) for the umbrella sampling simulations.

We generated the initial configuration using the packmol software, [START_REF] Martínez | A package for building initial configurations for molecular dynamics simulations[END_REF] randomly placing the desired number of particles in the system. We started with bulk electrolyte in a 32 A cubic box containing 750 water molecules for the pure water, and added ions for the different LiCl concentrations. For the liquids confined in ZIF-8, we needed to know how many molecules would fit in the ZIF-8 pores. For that, we ran a constant pressure simulation with a reservoir of pure water outside an empty 2 × 2 × 3 ZIF-8 supercell at 0.5 GPa. We ran the simulation for 10 ns and counted 75 water molecules in one unit cell. We then ran simulations of the bulk liquid at varying concentration at the constant pressure of 0 GPa, and recorded the corresponding particles density. Using the density of pure water, we mapped the 75 molecules per unit cell to an accessible porous volume of 2.286 nm 3 , or 46% of the unit cell. From this volume and the density of the bulk liquids, we could now compute the number of molecule to put in the 3 × 3 × 3 supercell for each concentration. The resulting system was a cubic box of 51 A, containing roughly 13 000 atoms.

For analysis, we used the chemfiles library and its cfiles command-line interface (available online at https://github.com/chemfiles/cfiles). Representative input files for the simulations are available online in the data repository at https://github.com/fxcoudert/ citable-data.

Results and discussion

Structure of the liquid

From the point of view of the liquid, the principal effect of intrusion is the confinement of the fluid to a pore space of nanometric dimensions, i.e. the nanoporous material acts as a host matrix -although a flexible one. Here, we look at the effects of this confinement on the liquid structure, as a function of the electrolyte concentration. In order to characterize the structure of the liquid and the solvation of ions confined in ZIF-8, we computed radial distribution function for each pair of atom types in the system. They are presented in supplementary information Figures S1 andS2. Integrating the radial distribution function until the first minimum gives the number of neighbors in the first solvation shell of each atom.

The evolution of this number of neighbors as a function of LiCl concentration is presented in Figure 2, for both the bulk liquid and the confined liquid. The first thing we can see here is that, for all species (Li, Cl and water), the number of neighboring water molecules -i.e., the solvation -decreases as the LiCl concentration increases. At 0 mol/L and 1 mol/L, there are more than enough water molecules with respect to the ions (roughly 55 water molecule per ion at 1 mol/L) so that they can be in their ideal In the bulk liquid, the loss of neighbors is linear with the concentration, as all the molecules in the system are able to adapt to find the state of largest possible solvation. In the confined liquid however, the molecules are geometrically constrained by the presence of the ZIF-8 framework, which manifests as an excluded volume, and thus are not able to adapt as well to the increase in LiCl concentration, making the number of neighbors drop faster. We also note a slight increase in the number of chlorine neighbors of lithium ions at intermediate concentration, compared to the bulk: the effect of confinement, by diminishing the solvation of the ions, favors the occurrence of anion-cation pairs. The number of lithium neighbors for chlorine ions is the same as the number of chlorine neighbors for lithium ions.

Going from bulk liquid to confined liquid also changes the number of neighbors for water and Cl ions, even at 1 mol/L. In addition to preventing a full reorganization of the water molecules when the concentration increases, the presence of the framework also affects the structure of the solvation shells. Molecules close to the framework can only have neighbors from the liquid on one side -an excluded volume effect. However, the framework also has an effect at longer range, the available space in the pores dictating the arrangement of molecules. Instead of being widely distributed, the molecules are restricted to specific preferential locations, due to host-guest interactions. This effect is particularly visible on Figure 3, and is stronger on Cl/water pairs than water/water or Li/water, as the Cl has a larger radius and binds to the hydrogen atoms in water, making its solvation sphere both bigger and "softer".

We also present in Figure 3 the density profile of atoms in the confined liquid, represented in the xy plane, averaged over z and the 3 × 3 × 3 supercell. To account for cell deformation during the (N, P, T ) simulations, we used fractional coordinates to represent the positions of atoms.

Here we clearly see the long distance structuration of water inside the ZIF-8 pores. At low concentration (1 mol/L), the water molecules occupy very well-defined sites, in particular inside the windows between two neighboring cages. As the concentration increases, this organization is perturbed by the ions inserted in the water molecules' network -however this effect is relatively small, and the water distribution is not greatly affected. The same can be observed in the distribution of chlorine ions, with a well defined, high symmetry distribution at low concentration, but as the concentration increases the distribution of ions becomes more and more distributed over the whole pore space. Concerning lithium ions, they present a looser arrangement inside the pores, and are distributed relatively evenly, yet present a preferential occupation next to the water molecules in the 6-member windows (in the diagonal in Figure 3).

These results can be explained by both the difference in kinetic radius 36 for water molecules (2.65 A), chlorine ions (3.2 A) and lithium ions (2.1 A), as well as the strong attraction between water oxygen atoms and lithium (see the radial distribution functions in Figure S2). The difference in size allows lithium ions to fit in smaller spaces, and an even distribution of ions will increase the total entropy of the system. At the same time, chlorine ions and water molecules are more polarizables than lithium, and as such will have stronger interactions with the aromatic linkers, making it preferable for them to take the highly organized arrangement we observe.

Dynamics under confinement

We used two different indicators to quantify the dynamics of water molecules confined in ZIF-8 and the impact of LiCl concentration and pressure on these dynamics. The first one is based on the lifetime of hydrogen bonds between water molecules. Following Luzar and Chandler, [START_REF] Luzar | Hydrogen-bond kinetics in liquid water[END_REF] we characterize the presence of a hydrogen bond between two water molecules as two oxygen atoms separated by less than 3.5 A, with an oxygen-oxygen-hydrogen ( OOH)

angle less than 30°. We then computed the time autocorrelation function of the hydrogen bond existence functions H(t) -set to 1 if the bond exists at time t, 0 if is does not existsas:

C hbonds (t) = H(t 0 ) • H(t 0 + t) t 0
The decay of this autocorrelation function, presented in Figure 4, is characteristic of the dynamics of the hydrogen bond network and the lifetime of individual hydrogen bonds.

This geometric definition of hydrogen bonds has a minor inconvenient: small fluctuations of the atomic positions, near the cut-off values, can be mistaken for hydrogen bond forming and breaking. To overcome this issue, we also computed the time autocorrelation of the orientation vector u(t) of water molecules:

C rot (t) = P 2 (u(t 0 ) • u(t 0 + t)) t 0 ,
where P 2 (x) is the second order Legendre polynomial P 2 (x) = 1 2 (3x 2 -1). [START_REF] Fogarty | Reorientational Dynamics of Water Confined in Zeolites[END_REF] The results for rotational correlation are presented in supporting information Figure S9 and Table S3.

Because water is a strongly associated liquid, breaking a hydrogen bond is predominantly correlated to rotational jumps, both autocorrelations behave in very similar ways, and we focus here the discussion on hydrogen bonds decays. We then fitted all the autocorrelation functions with bi-exponential functions:

f (t) = A 1 e -t/τ 1 + A 2 e -t/τ 2 ,
where τ 1 and τ 2 are the two time scales of decay, and A 1 and A 2 are their relative weights. The resulting fit parameters are presented in supporting information Table S2. The corresponding data is presented in Figure 5 at the pressure of 0 GPa. We found that the pressure only have a negligible influence on both the lifetimes and the weights of these lifetimes. Similar curves for all pressures are presented in supplementary information Figures S7 andS8. In the bulk liquid, the shortest lifetime is almost constant as the concentration increases, but the weight of this fast process (A 1 ) decreases. This suggests that this fastest lifetime is associated with hydrogen bonds between water molecules surrounded only by other water molecules. As more and more ions are added in the system, water molecules are less likely to be surrounded only by other water molecules -as is indicated by the results we presented in section 3.1. We also note that this lifetime is smaller in the confined liquid than it is in the bulk phase, which has already been shown for water at interfaces: Fogarty et al. [START_REF] Fogarty | Reorientational Dynamics of Water Confined in Zeolites[END_REF] showed that it is linked to the librational motions of the OH bonds, and the dynamics of these "dangling" OH groups at interfaces is faster than bulk. [START_REF] Scatena | Water at Hydrophobic Surfaces: Weak Hydrogen Bonding and Strong Orientation Effects[END_REF] On the other hand, the second lifetime, associated to the slowest process, increases with concentration, as well as the corresponding weight (A 2 ). This points to hydrogen bonds between water molecules bounded to ions.

In the confined liquid, weights still evolve in the same way with respect to the concentration, which point to them being associated with the same kind of hydrogen bonds. The second lifetime increases in the confined liquid compared to the bulk liquid. This slowdown of water dynamics under confinement is well-known, [START_REF] Fogarty | Reorientational Dynamics of Water Confined in Zeolites[END_REF] and has been observed in many classes of nanoporous materials. A separate way to quantify the dynamics of the confined and bulk liquid is to look at the diffusion of different species in the liquids. The diffusion coefficient D can be extracted from the mean square displacement using the Einstein relation:

( r(t -t 0 ) -r(t 0 )) 2 t 0 = 6Dt
This relation is only valid for long times, and if diffusion indeed occurs in the system. We computed the mean square displacement for water, lithium and chlorine in both the bulk and confined liquid, the corresponding curves are presented in supplementary information Figures S13 and S14. We then extracted the coefficient diffusion from these curves when possible, they are shown as a function of concentration in Figure 6. We could not get diffusion coefficients for the ions in the confined liquid, since they don't cross the windows -as explained in section 3.6.

The diffusion coefficient for pure water (2.6 × 10 -9 m 2 /s) matches previous studies of the same water model. [START_REF] Tazi | Diffusion coefficient and shear viscosity of rigid water models[END_REF] In the bulk liquid, as the ion concentration increases, both the self diffusion of water and the diffusion of the ions slows down dramatically. At 20 mol/L, the diffusion coefficient of water is only 0.072 × 10 -9 m 2 /s, and the coefficient of the ions is 0.012 × 10 -9 m 2 /s. Concerning the confined liquid, we observe the same slow down of the dynamics as usual, the water being one order of magnitude slower when confined compared to the bulk. Then, concentration effects are added, slowing the diffusion even further. Diffusion thus shows the same behavior as the hydrogen bond dynamics, with two independent and additive processes (confinement and ion presence) explaining the global slowdown of the dynamics.

Deformation of the framework

We have studied the property of the confined liquid inside the ZIF-8 framework, and the changes in the structure and dynamics of this liquid as it goes from a bulk to a confined state. It is also interesting to look at the changes the framework undergoes when going from an empty state to an intruded state. Macroscopic changes to the volume are relatively small (less than 4%), and presented in the next sections . In this section we will look at the internal deformations of the framework under intrusion.

Following previous works on the flexibility of ZIF-8, [START_REF] Chaplais | Impacts of the Imidazolate Linker Substitution (CH3, Cl, or Br) on the Structural and Adsorptive Properties of ZIF-8[END_REF][START_REF] Coudert | Molecular Mechanism of Swing Effect in Zeolitic Imidazolate Framework ZIF-8: Continuous Deformation upon Adsorption[END_REF][START_REF] Fairen-Jimenez | Opening the Gate: Framework Flexibility in ZIF-8 Explored by Experiments and Simulations[END_REF] we used the distribution of the Zn-Zn-Zn-CH 3 dihedral angle (also called swing angle) to characterize the deformations of the framework under intrusion. This angle describe the rotation of the methyl-imidazolate linker around the surrounding zincs axis. The distributions for empty and intruded ZIF-8 are presented in Figure 7. The distribution for the empty framework reproduces the already published results: it is a Gaussian distribution, centered around the equilibrium value of 15°, and with fluctuations of the order of 10°. The distributions for ZIF-8 containing the electrolyte liquid does not seems to depend on the electrolyte concentration. Instead they are all centered around 5°, and still have the same order of magnitude for fluctuations. This is to be contrasted with the effect of nitrogen adsorption at 77 K in ZIF-8; [START_REF] Chaplais | Impacts of the Imidazolate Linker Substitution (CH3, Cl, or Br) on the Structural and Adsorptive Properties of ZIF-8[END_REF] where the equilibrium value goes from 10°to 25°as the pores fill up with nitrogen. It is however interesting to note that the presence of ions does not impact the structure more than the presence of pure water does. This is coherent with the results presented in Figure 3, where the water molecules are located inside the 6-member windows. Water molecules take the place of linkers that rotate to accommodate them in the windows. As ions never enter this window, they don't have any effect on the linkers rotation.

Elastic properties

Given its potential applications in mechanical energy storage, one of the most important properties of the ZIF-8/electrolyte system is its mechanical behavior, and notably its stability under high pressure. As an increasing stress is applied to a material, it will first deform in a reversible and linear fashion, in what is called the linear elastic regime. Under higher stress, the material will start to deform in an irreversible way, and finally break. Information on the linear elastic regime and its extent is useful to study the stability of materials under stress, as stiffer materials are generally tougher and able to bear higher stress before failing. This is particularly important for soft nanoporous materials, where the mechanical stability range is lower than in inorganic porous materials such as zeolites, and where pressure-induced amorphization is common at moderate (sub-gigapascal) pressures. [START_REF] Bennett | Reversible pressure-induced amorphization of a zeolitic imidazolate framework (ZIF-4)[END_REF][START_REF] Cao | Amorphization of the prototypical zeolitic imidazolate framework ZIF-8 by ball-milling[END_REF][START_REF] Ortiz | Investigating the Pressure-Induced Amorphization of Zeolitic Imidazolate Framework ZIF-8: Mechanical Instability Due to Shear Mode Softening[END_REF] We probed the mechanical response of the ZIF-8/electrolyte system using direct simulations of the system under explicit hydrostatic stress. We first note that even though we allowed arbitrary changes to the unit cell lengths and tilt factors, all the simulations cells remained orthorhombic. The Figure 8 present the changes in volume as the pressure increases, for all the liquid concentrations. We can see that up to 1 GPa, the deformation remains in the elastic regime, and that the response is almost linear. Moreover, confining an electrolyte in the ZIF-8 structure do not drastically affect the mechanical properties of the system.

From these curves, we extracted the bulk modulus K of the system, defined as

K = -V ∂P ∂V N,T
We evaluated the derivative (∂P/∂V ) in the above formula as the slope of the curves from 0 GPa to 1 GPa. The values of the bulk modulus in various conditions are reported in Table 1.

The value for the empty ZIF-8 is close to the experimental 50 value of 7.8 GPa. The bulk moduli of pure water and 1 mol/L are further away from the experimental values 51 of 2.4 GPa and 2.6 GPa respectively. These differences are likely coming from the force-fields we used, which were not parameterized on mechanical properties of the framework or the liquids.

The trends, however, are interesting to see. Adding water to the pores of ZIF-8 only changes the bulk modulus by a moderate amount (10%), meaning that most of the stiffness comes from the ZIF-8 framework -the stiffer component of the two. However, adding ions to the liquid has a larger effect, both in the bulk state and the confined state, with the bulk modulus increasing by up to 50% at 20 mol/L with respect to the empty framework.

Since we generated the structures in such a way that the volume occupied by the liquid is always the same, the increase in bulk modulus is not be related to changes in the size occupied by the ions relatively to water. Rather, this increase in bulk modulus comes from the stronger interactions between ions and water molecules, compared to interactions between water molecules. The interactions between lithium cations and water molecules are stronger than water-water hydrogen bonds, and will make the liquid less compressible, especially at high concentration where, statistically, all water molecules are bonded to at least one lithium atom. This is further supported by the fact that the bulk modulus increases by the same order of magnitude (≈ 5 GPa) in both the bulk liquid and the confined liquid in ZIF-8.

Thermodynamics of the intrusion

In order to shed light into the energetics and thermodynamics of electrolyte intrusion in ZIF-8, we extracted the potential energy for various sub-components of the total system by taking the average value of the interaction energy of the corresponding sub-components.

The resulting average energies are presented in Table 2; where E total is the total potential energy of the electrolyte confined in ZIF-8; E ZIF is the interaction of ZIF-8 with itself; E LiCl is the interaction of the confined electrolyte with itself; and E ZIF/LiCl is the interaction of the electrolyte with the ZIF-8. E bulk LiCl refers to the total potential energy of the bulk electrolyte with the same number of particles as the confined one. Every quantity is expressed for one unit cell of ZIF-8, plus the confined liquid inside. From these values, we can extract a few thermodynamic quantities of interest, presented in Table 3:

∆E ZIF (c) = E ZIF (c) -E empty ZIF ; ∆E LiCl (c) = E LiCl (c) -E bulk LiCl (c); ∆H intr (c) = E total (c) -E bulk LiCl (c) -E empty ZIF .
Table 2: Average interaction energy in kcal/mol per unit cell for various subsystems. See the text for the definition of each sub-system. For reference, k B T is 0.6 kcal/mol at 300 K. The sign convention is taken so that all of these energies are negative when the confined state is more stable. We can see in Table 3 that the intrusion process has a relatively small impact on the ZIF: the energy difference between the empty and intruded states ∆E ZIF is in the range of tens of kT (at 300 K, kT ≈ 0.6 kcal/mol). The ZIF-8 framework is slightly destabilized (energetically) in presence of the intruded liquid except at 0 mol/L, where it is slightly stabilized. The overall effect is small compared to the two next trends we see. We have already shown that the presence of ions have little to no effect on the ZIF-8 structure in section 3.3.

LiCl E Total E ZIF E LiCl E LiCl/ZIF E bulk
First, the liquid is always more energetically stable in the intruded phase than in the bulk phase (∆E LiCl ). This might seems strange as ZIF-8 is an hydrophobic material, but the values presented only account for energetic contributions, and do not contain entropy.

Figure 3 shows that the entropy of the confined liquid can indeed be expected to be lower than the entropy of the liquid, because of the strong organization of the confined fluid.

As the LiCl concentration increase, the intruded phases becomes more and more stabilized, the ions adding additional rigidity and strong interactions in the pores network.

Secondly, we see that the energetic behavior of the whole process (∆H intr ) is more complex: the intrusion process is energetically favorable for low concentrations (≤ 5 mol/L),

and becomes unfavorable at higher LiCl concentrations (≥ 10 mol/L). The interaction between the liquid and ZIF-8 (E LiCl/ZIF in Table 2) makes for the difference between ∆E ZIF + ∆E LiCl and ∆H intr . Even if the process is energetically favorable at low concentrations, intrusion is not spontaneous because of the entropy contribution to the Gibbs free energy, which makes the adsorption overall thermodynamically unfavorable. This balance of effects, computed here from molecular simulations, could be measured experimentally using high-pressure calorimetry, as it has been done for the purely siliceous silicalite-1 zeolite. 52,53

Thermodynamics of ion entry into the nanopores

In the previous sections, we described the behavior of intruded electrolytes in the pores of ZIF-8, using full periodic boundary conditions. Here, we want to investigate the thermodynamics of the process by which species (water molecules and ions) can actually enter the nanopores space, i.e. pass through the windows of the material and its external surface. We have thus modeled an explicit water/ZIF-8 interface, depicted in Figure 9: the system here thus contains both water in the bulk state in a 34 A×34 A×30 A reservoir, and water confined inside ZIF-8. We used the umbrella sampling simulations and the WHAM analysis method [START_REF] Grossfield | the weighted histogram analysis method, version 2[END_REF] to reconstruct the free energy profile of a single species (Li + , Cl -, or H 2 O) entering ZIF-8

Figure 9: Representation of the system used for umbrella sampling simulation to compute the free energy profile of entry of lithium ions in ZIF-8. We used similar systems for the free energy profile of entry of chlorine and water. Water molecules are represented in red, lithium ions in pink and chlorine ion in green. ZIF-8 is represented as a transparent matrix.

along the (111) crystallographic axis. We placed the molecule of interest at 5 A of a window between the bulk and confined water, and the corresponding counter ion on the other side of the ZIF-8 slab (to keep the system neutral yet minimize ion-ion interactions). We ran a total of 121 umbrella sampling simulation for each species, spaced every 0.33 A. Each simulation ran for 500 ps in the (N, V, T ) ensemble, using the last step of the previous simulation as starting point. The resulting free energy profile is presented in Figure 10, together with the average number of neighbors at a given position on the axis (lower panel).

The first conclusion is that there is no free energy barrier for entry of the water molecule: the energy profile is flat and the number of neighbors is constant and around 4. This is coherent with the results already presented on the location of water molecules inside the ZIF-8 windows and on the number of neighbors for water molecules inside ZIF-8. It also confirms that the nature of the liquid-phase intrusion process is not a kinetic limitation of water adsorption, but actually due to thermodynamic hydrophobicity of the framework. For chlorine anions, we observe two barriers on the free energy profile, which correspond to the ZIF-8 windows at 0 and 15 A. These barriers are correlated to a lower number of neighbors for the anion, dropping to a value of 4: there is not enough space inside the window to fit a chlorine ion and 7 water molecules, and the anion has to partially desolvate to pass through The first ZIF-8 windows is at x = 0; the x < 0 area corresponds to bulk water, and the x > 0 area to water-filled ZIF-8. We evaluated the uncertainty on the free energy profile using Monte Carlo bootstrapping, [START_REF] Grossfield | the weighted histogram analysis method, version 2[END_REF] and found it to be at most 0.08 kcal/mol for H 2 O, and 0.3 kcal/mol for Cl -and Li + .

the window -explaining the presence of the free energy barrier. Outside of these barrier, the profile is flat and at the same level as in the bulk liquid, meaning that while the entry of a single chlorine ion is a rare event, at long thermodynamic time scale, Cl ions should be able to enter in ZIF-8. Generally speaking, the Cl ions have a kinetic barrier to entry in the ZIF-8.

The results for Li are more surprising. We see both a high barrier at the first (x = 0 A) and second (x = 15 A) windows; and a free energy difference between outside and inside the pores of roughly 13 kcal/mol. This free energy difference is not only due to the bulk liquid to confined liquid transition, as it is also present in the transition between before and after the second window. At the same time, these barriers and energy differences are not linked to a difference in solvation as in the chlorine case, as the number of neighbors of lithium stays constant and around 4. Indeed, the solvation of Li + by water is much stronger, and its solvation sphere is smaller in size than Cl -. As lithium does not partially desolvate or rearrange to pass the barrier, the whole solvation sphere needs to go though a relatively small window, thus making the barrier higher. This points to a difference in nature between the Li + and Cl -ions, which will have to be probed further, for example by studies on other ions of different size.

From this 13 kcal/mol free energy difference, we can calculate a partition coefficient of K = exp(-∆F/kT ) 4 10 -10 . This very small value means that there is, in practice, exclusion of the Li + ions from the nanopores -at infinite dilution. There may, however, be a collective effect when the concentration of LiCl increases, meaning we would get a very different value for a LiCl solution than for a single, isolated Li + cation.

Conclusion

Liquid intrusion of water and concentrated aqueous solutions in hydrophobic materials have been proposed for applications in mechanical energy storage and dissipation, and recently ZIF frameworks have been highlighted for the high energy density that they can store. However, while the process of intrusion has been well studied in various zeolitic materials over the last 20 years, there is relatively little information available on the behavior -at the microscopic scale -of water and electrolytes in hydrophobic metal-organic frameworks. These systems are difficult to probe experimentally, because liquid intrusion has to occur under high pressure.

Therefore, we have used molecular dynamics simulations to shed some light onto the properties of LiCl aqueous solutions at various concentrations confined inside the pores of the ZIF-8 metal-organic framework. We show that the presence of the electrolyte has a moderate impact on the ZIF-8 framework, while the presence of the ZIF-8 matrix strongly influences the behavior of the confined aqueous solution, affecting the overall properties of the system.

We also computed the free energy profile for the entry of water molecules and ions into the nanopores, showing a difference between anions and cations.

While this work provides an interesting picture of the LiCl electrolytes in ZIF-8, it also opens a few venues for future research. The main one is the impact of the ion size on the properties of the confined liquid. Experiments have been performed with other ions of larger size, including KCl, and there it is not even clear what fraction of the larger cations (K + ) actually can diffuse inside the nanopores. Computational approaches to these systems will be of great help in rationalizing the experimental results and provide a view of the microscopic mechanisms that are behind them.

Another one is to give a deeper look at the free energy barriers for ions passing through the windows of ZIF-8. While the windows are found, in the gas phase, to be very flexible and let diffuse molecules of large diameter (up to butane), we find that the entry of solvated species, such as ions in water, can be linked to a significant free energy barrier. Our free energy simulations of this process will have to be extended to other ions, in order to probe the influence of the size of both the ion and its solvation shell, but also to look at the influence of electrolyte concentration on the free energy profiles. Initial tests in this direction have shown that it should be technically possible, but convergence in such highly constrained systems is very difficult to achieve.

Finally, this work focused on the ZIF-8 framework, perhaps the most archetypal of the ZIF materials. The influence of framework functionalization with various imidazolate derivatives, which has shown to greatly impact adsorption in the gas phase, will surely also manifest itself in the liquid-phase intrusion processes. Relationships between nanoporous structure and intrusion properties have been studied in the past in hydrophobic zeolites, where the impact of structural flexibility does not greatly impact the intrusion behavior -except in cases of chemical reactivity between water and framework. Future work will need to address the question of the impact of the nanoporous host's flexibility on the intrusion-extrusion cycle: questions of both thermodynamics and kinetics are still widely open. In particular, whether one can fine-tune the intrusion of aqueous solutions in hydrophobic materials by control of flexibility is of large interest, since it would add another possible variable (in addition to pore size and solution concentration) to the dimensionality of the problem.

Figure 1 :

 1 Figure 1: (left) schematic representation of the sodalite topology. (right) molecular structure of ZIF-8. The color code is black for carbon, white for hydrogen, blue for nitrogen and green for zinc. 4-members and 6-members windows are delimited by zinc atoms.

Figure 2 :

 2 Figure 2: Number of water neighbors in the first solvation shell in the confined liquid (plain lines) and the bulk liquid (dotted lines) as function of the concentration, at the constant pressure of 0 GPa. The number of chlorine neighbors for lithium ions is also represented.

Figure 3 :

 3 Figure 3: Two-dimensional density profile of oxygen (top), lithium (middle) and chlorine (bottom) atoms in LiCl electrolyte confined in ZIF-8 at 0 GPa as a function of LiCl concentration (left to right). The atoms from the ZIF-8 framework are superimposed, with some linkers omitted for clarity between the four central zinc atoms.

Figure 4 :

 4 Figure 4: Hydrogen bonds existence autocorrelation in bulk (top) and confined (bottom) electrolyte as function of LiCl concentration.

Figure 5 :

 5 Figure 5: Variations of the time constant and weights of the bi-exponential hydrogen bonds autocorrelation decay at 0 GPa in bulk and confined liquid as function of the LiCl concentration.

Figure 7 :

 7 Figure 7: Swing dihedral angle distribution in empty and intruded ZIF-8 at all the LiCl concentrations.

Figure 8 :

 8 Figure 8: Deformation of bulk liquid (A) and ZIF-8 with confined electrolyte (B) as function of the pressure. Lines connect the different simulations using the same concentration.

LiCl Empty -746. 8 -746. 8 0

 88 mol/L -1617 -758.1 -703.1 -155.5 -822.9 1 mol/L -1859 -739.5 -974.0 -145.8 -1080 5 mol/L -2753 -738.3 -1864 -149.7 -1995 10 mol/L -3628 -735.5 -2744 -148.6 -2898 15 mol/L -4295 -732.5 -3416 -146.0 -3581 20 mol/L -4818 -728.4 -3949 -140.9 -4117 ∆E ZIF is the energetic change in ZIF-8 during intrusion; ∆E LiCl is the energetic change in the electrolyte during intrusion; and ∆H intr is the intrusion enthalpy, i.e. the enthalpy change during the ZIF-8 + liquid → liquid ∈ ZIF-8 process.

Figure 10 :

 10 Figure 10: (A) Free energy profile of a single molecule entering ZIF-8 and (B) corresponding number of neighbors in the first solvation shell as function of the position of the molecule along the (111) crystallographic axis. The first ZIF-8 windows is at x = 0; the x < 0 area corresponds to bulk water, and the x > 0 area to water-filled ZIF-8. We evaluated the uncertainty on the free energy profile using Monte Carlo bootstrapping,[START_REF] Grossfield | the weighted histogram analysis method, version 2[END_REF] and found it to be at most 0.08 kcal/mol for H 2 O, and 0.3 kcal/mol for Cl -and Li + .

Table 1 .

 1 [START_REF] Haigis | Investigation of structure and dynamics of the hydrated metal-organic framework MIL-53(Cr) using first-principles molecular dynamics[END_REF][START_REF] Jeffery | Direct measurement of molecular stiffness and damping in confined water layers[END_REF][START_REF] Romero-Vargas Castrillón | Evolution from Surface-Influenced to Bulk-Like Dynamics in Nanoscopically Confined Water[END_REF][START_REF] Scalfi | Structure and Dynamics of Water Confined in Imogolite Nanotubes[END_REF] It is attributed to the stronger organization of water as well as water molecules finding fewer partners for hydrogen bond exchange. The same arguments also apply to the increase in LiCl concentration, both in the bulk and confined liquid. This is coherent with what we see on the changes on bulk modulus as concentration changes in

	diffusion coefficient (10 -9 m 2 /s)	0.001 0.01 0.1 1 10	0	5	10	15 water Li Cl	20
					concentration (mol/L)

Figure

6

: Diffusion coefficients from mean square distance in bulk liquid (plain lines) and confined liquid (dashed line). No diffusion coefficient was extracted for Li and Cl in confined liquid, since they don't diffuse through ZIF-8 windows.

Table 1 :

 1 Bulk modulus of the bulk electrolyte liquids and of ZIF-8 containing a confined electrolyte liquid.

	Concentration Bulk liquid Liquid ∈ ZIF-8
	0 mol/L	4.3 GPa	11.2 GPa
	1 mol/L	4.4 GPa	13.0 GPa
	5 mol/L	5.0 GPa	13.6 GPa
	10 mol/L	6.1 GPa	14.4 GPa
	15 mol/L	7.2 GPa	15.2 GPa
	20 mol/L	8.4 GPa	15.4 GPa
	Empty ZIF-8		10.5 GPa

Table 3 :

 3 Derived thermodynamic quantities in kcal/mol per unit cell. See the text for the definition of each quantity.

	LiCl	∆E ZIF ∆E LiCl ∆H intr
	0 mol/L -11.3 -120 -47.3
	1 mol/L	7.3	-106 -32.2
	5 mol/L	8.5	-131 -11.2
	10 mol/L	11.3	-154	16.8
	15 mol/L	14.3	-165	32.8
	20 mol/L	18.4	-168	45.8

Acknowledgement

We acknowledge access to high-performance computing platforms provided by GENCI grant A0050807069.

Supporting Information Available

LAMMPS input files and initial configurations of the systems.

TOC Graphic


Remo N Widmer

Giulio I Lampronti

Simone Anzellini

Romain Gaillac

Stefan Farsang

Chao Zhou

Ana M Belenguer

Craig Wilson

Hannah Palmer

Annette K Kleppe

Michael T Wharmby

Xiao Yu

Seth M Cohen

Shane G Telfer

Simon A T Redfern

François-Xavier Coudert

Simon G Macleod

Thomas D Bennett

Pressure Promoted Low-Temperature Melting of Metal-Organic Frameworks

Metal-organic frameworks (MOFs) are microporous materials with huge potential for chemical processes, including retention or separation of guest molecules.

Structural collapse at high-pressure, and transitions to liquid states at high temperature, have recently been observed in this family. Here, we show that the effect of simultaneous high pressure and temperature application on ZIF-62 and ZIF-4 results in complex behaviour, with distinct high-and low-density amorphous phases occurring over different regions of the pressure-temperature phase diagram. In-situ powder X-ray diffraction, Raman spectroscopy and optical microscopy reveal that the stability of the liquid MOF-state expands significantly towards lower temperatures at intermediate, industrially achievable pressures.

Furthermore, the MOF-glass formed by melt quenching the high temperature liquid is shown to demonstrate permanent, accessible porosity. Our results thus imply a novel route to the synthesis of functional MOF glasses at low temperatures, avoiding decomposition upon heating at ambient pressure.

Introduction

The discovery of a growing family of over 60,000 metal-organic framework (MOF) and coordination polymer compounds [START_REF] Moghadam | Development of a Cambridge Structural Database Subset: A Collection of Metal-Organic Frameworks for Past, Present, and Future[END_REF] demonstrates the chemical versatility of these functional microporous materials. Their high surface areas, generated by regular arrays of metal nodes connected by organic ligands, has led to proposed applications in water harvesting 2 , gas storage [START_REF] Mason | Methane storage in flexible metal-organic frameworks with intrinsic thermal management[END_REF][START_REF] Yoon | Selective nitrogen capture by porous hybrid materials containing accessible transition metal ion sites[END_REF] , gas separation 5 and catalysis [START_REF] Mondloch | Destruction of chemical warfare agents using metalorganic frameworks[END_REF] .

Research in this field has focused predominantly on ordered, crystalline MOF materials. However, there is growing recognition of other unusual physical properties in this family of "soft crystals" [START_REF] Horike | Soft porous crystals[END_REF] , with examples including defects [START_REF] Dissegna | Defective Metal-Organic Frameworks[END_REF] , framework flexibility [START_REF] Schneemann | Flexible metal-organic frameworks[END_REF] and disorder 10 extending our appreciation of the impact of MOF materials [START_REF] Slater | Function-led design of new porous materials[END_REF][START_REF] Kitagawa | Future Porous Materials[END_REF] . A rich set of structural responses to external forces has been uncovered [START_REF] Coudert | Responsive Metal-Organic Frameworks and Framework Materials: Under Pressure, Taking the Heat, in the Spotlight, with Friends[END_REF] , including negative gas adsorption [START_REF] Krause | A pressure-amplifying framework material with negative gas adsorption transitions[END_REF] , breathing [START_REF] Carrington | Solvent-switchable continuous-breathing behaviour in a diamondoid metal-organic framework and its influence on CO2 versus CH4 selectivity[END_REF] , and temperature (T)- [START_REF] Longley | Uncovering a reconstructive solidsolid phase transition in a metal-organic framework[END_REF] or pressure (P)-induced phase transitions [START_REF] Lapidus | Exploiting High Pressures to Generate Porosity, Polymorphism, And Lattice Expansion in the Nonporous Molecular Framework Zn(CN)2[END_REF] . However, much still remains to be discovered about MOFs, especially with respect to their dynamic behavior.

Like MOFs, silicates and other minerals also display a wide diversity of interesting physical behaviours, in particular at non-ambient conditions. For example, studies of stability boundaries and properties in P-T-space are well established [START_REF] Hazen | High-temperature and High-pressure Crystal Chemistry[END_REF] . Silica [ SiO 2 ] itself is an archetypical material and shows seven crystalline polymorphs [START_REF] Hurlbut | Manual of Mineralogy[END_REF][START_REF] Dove | Crystal structure of the high-pressure monoclinic phase-II of cristobalite, SiO2[END_REF] , numerous metastable porous phases (all-silica zeolites), two polyamorphs [START_REF] Hemley | Pressure-induced amorphization of crystalline silica[END_REF] , and a complex melting curve at high-P-T conditions. Surprisingly, despite their apparent chemical differences, many MOFs find analogues in the mineral world [START_REF] Natarajan | Metal-organic framework structures -how closely are they related to classical inorganic structures?[END_REF] . For example, certain metal-oxalate MOFs [START_REF] Decurtins | A concept for the synthesis of 3-dimensional homo-and bimetallic oxalatebridged networks [M2 (ox) 3] n. Structural, Moessbauer, and magnetic studies in the field of molecular-based magnets[END_REF][START_REF] Sadakiyo | Control of Crystalline Proton-Conducting Pathways by Water-Induced Transformations of Hydrogen-Bonding Networks in a Metal-Organic Framework[END_REF] were recently shown to be synthetic analogues of two minerals [START_REF] Huskić | Minerals with metalorganic framework structures[END_REF] More similarities between MOFs and minerals are apparent in terms of topological structure. Zeolitic imidazolate frameworks (ZIFs), an important subgroup of MOFs [START_REF] Banerjee | High-throughput synthesis of zeolitic imidazolate frameworks and application to CO2 capture[END_REF] , comprise tetrahedral ZnN 4 units as their main building blocks. This structural motif, interlinked with imidazolate (Im, C 3 H 3 N 2 -) based ligands, forms continuous lowdensity networks. ZIFs can be directly compared to natural zeolites, which form frameworks of interlinked tetrahedral SiO 4 and AlO 4 units. Both, ZIFs [START_REF] Park | Exceptional chemical and thermal stability of zeolitic imidazolate frameworks[END_REF][START_REF] Mckellar | Structural studies of metal-organic frameworks under high pressure[END_REF] and zeolites [START_REF] Cruciani | Zeolites upon heating: Factors governing their thermal stability and structural changes[END_REF][START_REF] Hazen | Zeolite Molecular Sieve 4A: Anomalous Compressibility and Volume Discontinuities at High Pressure[END_REF] retain their microporosity even at relatively high T and P. Even higher T and P ultimately induces phase transitions [START_REF] Su | Bond breakage under pressure in a metal organic framework[END_REF][START_REF] Chapman | Trapping Guests within a Nanoporous Metal-Organic Framework through Pressure-Induced Amorphization[END_REF][START_REF] Zhao | Pressure-induced oversaturation and phase transition in zeolitic imidazolate frameworks with remarkable mechanical stability[END_REF][START_REF] Henke | Pore closure in zeolitic imidazolate frameworks under mechanical pressure[END_REF][START_REF] Bennett | Thermal Amorphization of Zeolitic Imidazolate Frameworks[END_REF] and melting [START_REF] Bennett | Melt-Quenched Glasses of Metal-Organic Frameworks[END_REF] . The formation of glasses from such MOF-liquids [START_REF] Gaillac | Liquid metal-organic frameworks[END_REF] is of special interest due to their nature as a new class of melt-quenched glass material formed of amorphous SiO 2 -like continuous random networks [START_REF] Bennett | Hybrid glasses from strong and fragile metal-organic framework liquids[END_REF] . The formation of MOF glasses via solid state conversion or meltquenching is of great importance due to their inherent MOF-like chemical connectivity and composition. [START_REF] Bennett | Melt-Quenched Glasses of Metal-Organic Frameworks[END_REF][START_REF] Bennett | Hybrid glasses from strong and fragile metal-organic framework liquids[END_REF] The glass formed from one structure, ZIF-62, has been demonstrated to exhibit significant resistance against crystallization [START_REF] Qiao | A metal-organic framework with ultrahigh glass-forming ability[END_REF] , whilst that formed from ZIF-76 has recently been demonstrated to show permanent, accessible porosity [START_REF] Zhou | Metal-Organic Framework Glasses with Permanent Accessible Porosity[END_REF] . Alongside their unique internal structures, MOF glasses and liquids are of great interest since they provide a route to manufacturing complex, monolithic glassy MOF objects from MOF powders by melt-casting [START_REF] Bennett | Melt-Quenched Glasses of Metal-Organic Frameworks[END_REF] and hotpressing [START_REF] Wenqian | Glass Formation of a Coordination Polymer Crystal for Enhanced Proton Conductivity and Material Flexibility[END_REF] .

The separate pressure and temperature dependent studies carried out on ZIFs previously, alongside the investigation of the behavior of the liquid MOF phase at higher pressures, motivated us to attempt to construct the first high P-T phase diagram of any metal-organic framework system. We selected ZIF-62

[Zn(Im) 1.75 (bIm) 0.25 ] (bIm, benzimidazolate, C 7 H 5 N 2 -) due to its known stable liquid state, which occurs between the relatively low melting temperature of ca. 430 °C, and a decomposition temperature of ca. 500 °C36 . The three-dimensional structure (Figure 1a and 1b) crystallizes under solvothermal conditions in the Pbca space group, and adopts a network topology identical to that of the phosphate minerals variscite 42 and strengite [START_REF] Song | New Iron(III) Phosphate Phases: Crystal Structure and Electrochemical and Magnetic Properties[END_REF] , and CaGa 2 O 4 [START_REF] Deiseroth | Über Erdalkalimetalloxogallate. III. Untersuchung des Aufbaus von CaGa2O4[END_REF] . Both the natural phosphates and the synthetic gallate display interesting pressure-induced polymorphism [START_REF] Song | New Iron(III) Phosphate Phases: Crystal Structure and Electrochemical and Magnetic Properties[END_REF][START_REF] Lazić | Rietveld Analysis of a High Pressure Modification of Monocalcium Oxogallate (CaGa2O4)[END_REF] . To map out the P-T phase diagram of ZIF-62, we combined in-situ powder X-ray diffraction (PXRD, Diamond Light Source, beamline I15) and optical microscopy at simultaneous high-P and high-T with ex-situ electron microscopy. We also performed first-principles constant-pressure molecular dynamics simulations in order to provide insight into the pressure dependence at the molecular level.

Results and Discussion

Constructing a P-T phase diagram of ZIF-62

A resistively-heated membrane diamond anvil cell (DAC, Figure 1c

Crystalline to solid-amorphous boundary

At ambient P, the ZIF-62 structure underwent T-induced amorphization at ca. 320°C, which is in good agreement with a previous study [START_REF] Bennett | Melt-Quenched Glasses of Metal-Organic Frameworks[END_REF] . At high-P and ambient-T, the framework underwent amorphization at ca. 5 GPa. In comparison, a topologically identical structure containing only the unsubstituted imidazolate ligand, ZIF-4, undergoes reversible P-induced amorphization at ca. 1 GPa [START_REF] Bennett | Reversible pressure-induced amorphization of a zeolitic imidazolate framework (ZIF-4)[END_REF] . This significant difference in high-P stability at ambient-T between these two ZIFs may be explained by the more sterically hindered benzimidazolate linkers present in ZIF-62 protruding into the pore cavities and offering additional stabilization against framework collapse (Figure 2a). Force-field based molecular dynamics simulations (see methods) of the elastic properties of ZIF-62 and ZIF-4 were performed to highlight this structural stabilization. The results (Supplementary Tables 1 &2), demonstrate higher bulk (4.7

GPa), Young's (8.7 GPa) and shear (3.6 GPa) moduli in ZIF-62, compared to ZIF-4

(2.7 GPa, 5.6 GPa and 2.4 GPa, respectively).

P-and T-induced amorphization in ZIF-62 were found to be distinct in nature. Under pressure, the related ZIF-4 demonstrably undergoes a displacive transition since the material was shown to revert to a crystalline phase upon decompression [START_REF] Bennett | Reversible pressure-induced amorphization of a zeolitic imidazolate framework (ZIF-4)[END_REF] . We have similar evidence for short-range ordering in ZIF-62 from in-situ Raman spectroscopic data. The loss of the characteristic phonon frequencies and the internal modes was found to be fully reversed upon decompression (Supplementary Figure 1). A synchrotron high-pressure PXRD experiment was carried out on ZIF-62, and demonstrated amorphization to occur at 5 GPa. This amorphous phase reverts to the starting crystalline phase upon decompression, and thus is assigned as a displacive transition (Fig. 2a, Supplementary Figure 2). This is consistent with a displacive mechanism of formation. In contrast, thermal amorphization of ZIF-62 is irreversible and is ascribed to a reconstructive phase transition. Diffraction patterns from samples of ZIF-62 amorphized at (i) 7.6 GPa and 25 °C, and (ii) 350 °C under vacuum, show complete loss of all diffraction peaks in each case (Supplementary Figure 3).

Amorphization at simultaneous high-P and -T is therefore expected to share aspects of both processes. Moreover, the changing gradient of the crystalline to solidamorphous transition (Figure 2a) found across P-T-space is indicative of high-P and high-T amorphous phases with different densities. This can be derived from the Δ𝑆 Δ𝑉 term of the Clausius-Clapeyron relation for a boundary with a changing gradient as opposed to having a constant gradient.

We denote the high-P and high-T amorphous phases a HP and a HT , and the corresponding crystalline-amorphous transitions c-a HP and c-a HT , respectively. The difference in slopes of the transitions dominated by either c-a HP or c-a HT in P-T-space implies that ∆𝑉 %&'() < ∆𝑉 %&'(, and consequently, we find that a HP is of higher density than a HT , as anticipated under the influence of pressure. We defined an approximate boundary between a HT and a HP by extrapolating the c-a HP boundary to higher pressures (dashed line in Figure 2a).

Solid-amorphous to liquid boundary

The melting point of ZIF-62 at ambient-P was identified at ca. 430 °C by differential scanning calorimetry (DSC) measurements (Supplementary Figure 4). Melting points at high-P ranging from approximately 2 GPa to 3.5 GPa were determined visually and are shown in Figure 2a. A representative video showing the melting is shown in Supplementary Video 1. Six independent melting points at variable P were fitted linearly with a slope of 𝑑𝑃/𝑑𝑇 = 0.031(4). Achievable P-T conditions in DAC experiments are constrained to lie on isochores dictated by the properties of the pressure-transmitting medium. For this reason, it was not technically feasible to target P-T conditions for intermediate-P and high-T. However, we are able to constrain the upper limit of the melting curve up to approximately 5 GPa by solids that were quenched from high-P-T conditions indicated in Figure 2a by red crosses,

showing no morphological signs of melting (Figure 2c).

The negative slope of the melting curve interpolated from ambient pressure to < 2

GPa (boundary between pale red and yellow in Figure 2a) implies a solid phase with lower density than the liquid phase. At pressures > 2 GPa, we find a melting curve with a positive gradient (boundary between dark red and yellow in Figure 2a), implying the opposite, a solid phase with a higher density than the liquid phase. Both conditions are in accordance with, and support, our model of two distinct amorphous phases a HT and a HP . The intersection of the low-and high-P melting curve with the assumed boundary between a HT and a HP (dashed line in Figure 2a) defines a triple point.

Structural evolution

T-and P-dependent lattice parameters of crystalline ZIF-62 were refined from synchrotron and lab-based X-ray powder diffraction data. Figure 3a MOFs can be made permanently accessible to incoming guest molecules such as CO 2 and CH 4 [START_REF] Zhou | Metal-Organic Framework Glasses with Permanent Accessible Porosity[END_REF] . Gas adsorption isotherms were used to identify and characterise the accessible pores of crystalline ZIF-62 and a g ZIF-62, by quenching from T m at ambient pressure. Crystalline ZIF-62 takes up H 2 at 77 K and CO 2 at 273 K (Supplementary Figure 8). However, at 77 K, diffusion limitations prevent the ingress of N 2 guest molecules [START_REF] Bennett | Melt-Quenched Glasses of Metal-Organic Frameworks[END_REF] . CH 4 measurements were also performed to show that this is not a size exclusion effect (Supplementary Figure 8).

The permanent porosity of a g ZIF-62 was confirmed by recording its uptake of CO 2 at 273 K (Figure 3c, Table 1). This material reversibly adsorbs 20.1 mL(STP)/g at a pressure of one bar, which equates to 3.8 wt%. In contrast to the crystalline material, limited uptake of H 2 at 77 K is observed for a g ZIF-62, which is accompanied by significant hysteresis (Supplementary Figure 9). This hysteresis is ascribed to diffusion limitations at this temperature, on the basis of the reversibility of the H 2 isotherm measured at 195 K and the CO 2 isotherm measured at 273 K. At 77 K, a small component of H 2 cannot be removed in the desorption branch of a g ZIF-62 at very low pressures under practical operating conditions. To confirm that this does not correspond to irreversible chemical modification of a g ZIF-62, the residual gas was removed, by warming the sample to room temperature under vacuum. It thus appears that a g ZIF-62 kinetically traps a small amount of H 2 , as has been observed in some crystalline systems, [START_REF] Yang | Cation-induced kinetic trapping and enhanced hydrogen adsorption in a modulated anionic metal-organic framework[END_REF] where the some of the pore openings and H 2 have similar diameters. With regards to ZIF-4, first principle molecular dynamics calculations combined with neutron total scattering data [START_REF] Gaillac | Liquid metal-organic frameworks[END_REF] and positron annihilation lifetime spectroscopy [START_REF] Thornton | Porosity in metal-organic framework glasses[END_REF] have also shown that both the liquid and the quenched glass retain porous characteristics similar to the crystalline phase. Here, ex-situ Raman spectra of high-P meltquenched ZIF-62 (Supplementary Figure 10) are very similar to those of the crystalline starting material, with all Raman modes associated both with the phonon frequencies (< 300 cm -1 ) and the internal modes of organic linkers (> 300 cm -1 ) observed. The only significant difference between the crystalline and the meltquenched material is the smoothing of the continuum at wavenumbers < 300 cm -1 . A second, high-P-T synchrotron experiment was carried out using ZIF-4 (Supplementary Figure 11). At ambient T, amorphization, recrystallization to the dense ZIF-zni phase and melting were confirmed at ca 250 °C, 320 °C and 580 °C as expected [START_REF] Bennett | Hybrid glasses from strong and fragile metal-organic framework liquids[END_REF] . Application of pressure however resulted in a dramatic lowering of amorphization and recrystallization, to < 200°C and ca. 250°C, and melting was observed at high pressures below the ambient melting point T m . This hints at the transferability in the pressure-induced lower temperature melting phenomenon.

Molecular simulations

In order to give microscopic and thermodynamic insight into the evolution of the ZIF melting processes upon application of pressure, we performed first principles molecular dynamics (FPMD) simulations based on a quantum chemical description of the system at the Density Functional Theory (DFT) level, detailed in the Supplementary Methods. These simulations were performed on both ZIF-4 and ZIF-62, in the 0-5 GPa pressure range at the previously identified computational melting point (for ZIF-4) of 1200 K [START_REF] Gaillac | Liquid metal-organic frameworks[END_REF] . Given the limited timescale attainable through FPMD simulations, these simulations probe the melting behavior of the crystalline phase near the experimental crystalline to high-T-amorphous and high-T-amorphous to liquid phase transitions.

Analysis of the FPMD simulations suggests that the mechanism behind the melting of the ZIFs is not significantly affected by pressure. On the other hand, the application of pressure in the GPa range affects both the dynamics and thermodynamics of the systems. Figure 4a depicts the potential of mean force (PMF)

for the zinc-nitrogen coordination, calculated from the free FPMD simulations of ZIF-62 at various pressures. There is a clear decrease in the free energy barrier upon increasing pressure from 0.1 GPa to 5 GPa, associated with the rupture of the coordination bond (Table 2, Supplementary Table 5). This can be linked to the softening of the Im-Zn-Im angle upon pressurization, which was previously shown to be the driving force of the pressure-induced amorphization of ZIF-8 and ZIF-4 at room temperature [START_REF] Du Bourg | Thermal and mechanical stability of zeolitic imidazolate frameworks polymorphs[END_REF][START_REF] Ortiz | Investigating the Pressure-Induced Amorphization of Zeolitic Imidazolate Framework ZIF-8: Mechanical Instability Due to Shear Mode Softening[END_REF] . Confirmation of this behaviour is also found in the dynamics of the Zn-N coordination bonds, for which the average time between Zn-N cleavage events during the FPMD is shown in Figure 4b. This softening of the porous framework's coordination upon pressurization means that melting becomes thermodynamically easier upon application of pressure, explaining the observed negative slope of the ZIF-62 melting curve in P-T-space. Simulations were also carried out using the published structural model for ZIF-4, finding similar results (Supplementary Figure 12) and reinforcing the idea that the pressure-induced lowering of the melting point can be extended to other ZIFs -similarly to the pressure-induced amorphization mechanism [START_REF] Ortiz | Investigating the Pressure-Induced Amorphization of Zeolitic Imidazolate Framework ZIF-8: Mechanical Instability Due to Shear Mode Softening[END_REF] .

This is a very counter-intuitive behaviour, since for most solids application of pressure inhibits melting. This raises the possibility that the liquid-solid phase relations of amorphous ZIFs share similarities with those of other disordered framework materials such as H 2 O ice.

Negative melting curves have also been inferred from separate ambient T, and ambient P experiments on inorganic zeolites [START_REF] Greaves | Zeolite collapse and polyamorphism[END_REF] , though importantly these deal with collapse of the crystalline state to amorphous solid states, and not to macroscale liquids, as in this study.

There is a large difference in chemistry between ZIFs and zeolites, and specifically the weaker Zn-N bonding compared to Si-O interactions [START_REF] Meneau | Probing the dynamics of instability in zeolitic materials[END_REF] . This facilitates melting to a liquid at accessible temperatures and allows us to perform the high-P-T experiments required to confirm the negative melting behaviour in these materials.

In contrast, the Zn-N bond is stronger than the interactions present in organic ionic liquids [START_REF] Armand | Ionicliquid materials for the electrochemical challenges of the future[END_REF] , and results not only in higher melting points of ZIFs, but also in a different mechanism of melting. For example, whilst melting in examples of ionic liquids has been shown to result in the complete conformational freedom of component species [START_REF] Lima | Unraveling the Stepwise Melting of an Ionic Liquid[END_REF] , and molten salt structures such as ZnCl 2 have been shown to retain tetrahedral, or octahedral coordination [START_REF] Mcgreevy | The Structure of Molten Salts[END_REF] , the melting of a ZIF does not result in fully undercoordinated Zn 2+ centres or Zn(Im) 4 fragments [START_REF] Gaillac | Liquid metal-organic frameworks[END_REF] , but in a strongly associated liquid -once again, similar to liquid water.

Conclusion

The P-T phase diagram of the metal-organic frameworks ZIF-4 and ZIF-62 have been created by combining in-situ X-ray diffraction and optical microscopy with thermodynamic considerations. Importantly, we show how the stability field of the liquid phase extends substantially towards lower temperatures at increasing hydrostatic pressure. Aside from the fundamental interest in negative Clapeyron slope melting behaviour displayed here, reducing the melting temperature is an important objective in developing new MOF glasses. We have also demonstrated the permanent accessible porosity of a g ZIF-62, which will encourage others to research porous glasses, as compounds decompose at temperatures below their potential melting temperatures [START_REF] Gaillac | Liquid metal-organic frameworks[END_REF] . The possibility to synthesize liquid MOF states via highpressure thermal melting opens a route to synthesis of a very wide range of amorphous MOFs. The pressures regime required for lowering the melting temperatures is achievable through industrially viable processes such as hotpressing and specialised autoclaves.

The exploration of P-T-space here also provides essential information on the stability of individual phases and the nature of transformations between those phases. The density contrast delineated between high-P and high-T amorphous MOF phases confirms distinct amorphization mechanisms and infers the existence of point of coexistence between these two amorphous phases and the crystalline state. For example, pressure-or temperature-induced transitions have been found in non-ZIF metal-organic frameworks such as PCN-250 56 and [NH4][Zn(HCOO) 3 ] 57 . This already hints at the possibility for rich phase diagrams of the MOF family, even at relatively low temperatures and pressures.

Finally, the study of MOFs under simultaneous high-T and -P ultimately links polymer chemistry with mineralogy. Tools which are used for non-ambient studies in mineral sciences have been adapted for the MOF field, providing a compelling new perspective on MOFs and drawing parallels between their rich phase transition behavior, and that of classical inorganic solids such as SiO 2 .

was used as pressure transmitting medium. Data were collected at a wavelength of λ = 0.4246 Å using a MAR345 detector. Diffraction images were integrated using the DAWN software suite [START_REF] Filik | Processing two-dimensional X-ray diffraction and small-angle scattering data in DAWN 2[END_REF] . Internal pressures were calculated from the unit cell volume of NaCl using equation-of-state parameters from literature [START_REF] Dorogokupets | Equations of state of MgO, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales[END_REF] . A K-type thermocouple with an accuracy of < 0.4 % was glued close to one of the diamonds to provide temperature measurements. Before each heating ramp, the DAC-internal P was raised to a target value by inflating the membrane. This membrane pressure was kept constant throughout the individual runs. T was raised continuously at an average rate of 0.5 °C/min for run 1 and 1 °C/min for run 2, resulting in simultaneous increase of T and P. Diffraction patterns were collected in approximately 10 °C temperature increments.

Melting points of ZIF-62 at high-P were determined visually from lab-based, externally heated DAC experiments in silicone oil as pressure transmitting medium (Supplementary Figures 20 &21). Optical images of the recovered ZIF-4 samples are in Supplementary Figure 22. The temperature was measured using a K-type thermocouple glued to one of the diamonds. P was determined from the shift of the fluorescence peaks of ruby [START_REF] Dewaele | Compression curves of transition metals in the Mbar range: Experiments and projector augmentedwave calculations[END_REF] corrected for the T-induced shift [START_REF] Rekhi | Temperature-induced ruby fluorescence shifts up to a pressure of 15 GPa in an externally heated diamond anvil cell[END_REF] . T was increased continuously at approximately 5 °C/min, while initial membrane pressure was kept constant. The lowest possible pressure at a certain temperature is dictated by the isochoric path followed through T increase. Therefore, it was not possible to access pressures below 2 GPa between 300 °C and 350 °C. After reaching maximum T and P conditions, the external heater was switched off resulting in an approximate cooling rate of 2.5 K/min. P was released after reaching room T. The gaskets containing samples were transferred to SEM stubs, kept under vacuum for 48h to evaporate silicone oil residues, and carbon coated for subsequent SEM imaging. Back-scattered electron images were acquired on a FEI Qemscan Quanta650F operated at 10 kV at a working distance of 10 mm.

Rietveld refinement of experimental diffraction patterns was performed using TOPAS-Academic v6 [START_REF] Coelho | TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C plus[END_REF] based on a ZIF-62 and ZIF-4 structure model from literature [START_REF] Banerjee | High-throughput synthesis of zeolitic imidazolate frameworks and application to CO2 capture[END_REF] . Synchrotron based powder XRD data was fitted sequentially using experimental peak shapes from LaB 6 reference measurements. An experimental, fixed background profile measured from an empty DAC in the vacuum vessel was fitted together with 5 th order Chebychev polynomial. 8 th order spherical harmonics were applied to intensities for preferred orientation correction. Lattice parameters, scale factors, and lorentzian strain was refined individually for all measurements.

Numeric fit results are presented in the supporting information.

Lab-based, variable-temperature PXRD data sets were fitted parametrically. An internal silicon standard allowed for refining individual sample displacements using fixed, temperature dependent standard lattice parameters for Si at each temperature. Subsequently, ZIF-62 and ZIF-4 were fitted using fixed, previously refined, specimen displacements.

Gas adsorption isotherms were measured by a volumetric method using ultra-high purity gases. Prior to analysis, the samples were degassed under a dynamic vacuum at 10 -6 Torr for 10-20 hours at 130-250 °C. Accurate sample masses were calculated using degassed samples after sample tubes were backfilled with nitrogen.

  , stepanovite [NaMgFe(C 2 O 4 ) 3 •8-9H 2 O] and zhemchuzhnikovite [NaMg(Fe 0.4 Al 0.6 )(C 2 O 4 ) 3 •8-9H 2 O].

Figure 1 .

 1 Figure 1. Crystal structure of ZIF-62 and experimental set-up a, Representative slice of the ZIF-62 structure (N = light blue, C = white, ZnN 4 tetrahedra = pink) perpendicular to the a-axis revealing the main connectivity of 8-and 4-membered-rings. For clarity, only the range of fractional coordinates from 0.2 to 0.8 along a is shown, and H atoms are omitted. b, Characteristic building unit of ZIFs with four crystallographic independent linkers, including one benzimidazole for imidazole substitution, coordinating tetrahedral Zn 2+ cations. Approximate bridging angles are indicated, and are similar to those of SiO 4 networks of minerals. c, Schematic drawing of the membrane driven diamond anvil cell (Betsa, France) used for lab-based high-P experiments. A ring-shaped membrane is inflated by gas-pressure, driving the opposing diamond anvils against each other. A gasket with a 200 µm hole containing the sample material and a ruby sphere and the pressure transmitting medium is shown in the close-up view. d, Water cooled vacuum vessel with Kapton windows and part of the X-ray collimator assembly containing an externally resistive-heated, membrane-driven DAC for simultaneous high-P-T powder X-ray diffraction experiments at a synchrotron light source. The direction of beam is indicated by a red arrow.

  and 1d) was used to investigate the phase stability of ZIF-62 in a P-T range from ambient pressure to 8 GPa and from ambient temperature to 450 °C, respectively. A crystalline sample of evacuated ZIF-62 (see methods) was loaded in the DAC together with high purity silicone oil as a non-penetrating pressure transmitting medium. In-situ characterization of the P-T evolution of crystalline ZIF-62 was performed with three separate synchrotron-and one lab-based X-ray diffraction experiment. The amorphization of ZIF-62 was tracked by observing the loss of diffraction peaks. Lab-based optical microscopy was performed to visually determine melting points. The resulting stability fields of crystalline, solid-amorphous, and liquid ZIF-62 are shown in Figure 2a. Solid-state amorphization and melt-formation were differentiated by morphological observations of quenched and recovered material (Figure 2b-d).

Figure 2 .

 2 Figure 2. Experimentally derived P-T phase diagram for ZIF-62a, The stability field of crystalline ZIF-62 is shown in blue, tracing phase analysis from PXRD (blue squares). Two distinct amorphous phases with high and low densities relative to each other are shown in dark red (high-pressure) and light red (high-temperature), respectively. This distinction is based on changing slopes of both crystalline-amorphous and solid-liquid phase-boundaries. The phase boundary between the two amorphous phases is tentatively indicated with a dashed black line.The phase-field for liquid ZIF-62 is shown in yellow, defined by melting points (black diamonds) observed optically at high-pressure and using DSC at ambient pressure. Crosses indicate highpressure/high-temperature conditions from which the samples were quenched for morphological analysis. b, c, and d, Scanning-electron microscopic images of the three main phases of ZIF-62, in false colors corresponding to the stability fields. Crystalline, as-synthesized, ZIF-62 (blue), highpressure amorphous (red), quenched from 440 °C, 5 GPa and high-pressure molten (yellow), quenched from 420 °C, 3.4 GPa.

  displays the unit cell volume of ZIF-62 in P-T-space. Pure T-and P-dependent unit cell dimensions are shown in Figure 3 and Supplementary Figure 5, respectively. Experimentally derived bulk moduli and linear thermal expansion coefficients are given in treatment. Conversely, we have recently demonstrated that glasses derived from

Figure 3 .

 3 Figure 3. Structural evolution of ZIF-62 in P-T-space a, Unit cell volume of crystalline ZIF-62 as a function of P and T from Rietveld refinements. A graphically interpolated surface is included as a guide to the eye. b, Thermal expansion under vacuum, indiscernible on the scale of hydrostatic compression, plotted as relative and normalized change. Strong anisotropic expansion is apparent from the individual crystallographic axes. A volume collapse precedes complete amorphization above 270 °C. c, CO 2 gas adsorption isotherm for the ambient pressure melt-quenched ZIF-62 glass. Filled symbols represent adsorption, open symbols represent desorption.

3 P

 3 re ss ur e /G P a T e m p e ra tu re /°C

Figure 4 .

 4 Figure 4. Potential of mean force for the Zn-N distance, and dynamics of Zn-N cleavages. a. Potential of mean force for the Zn-N distance, obtained from first-principles molecular dynamics of ZIF-62 at pressures between 0.1 GPa and 5 GPa, at a temperature of 1,200 K. The values of the free energy barrier ∆G ≠ corresponding to the breaking of the Zn-N coordination bond (visible as vertical arrows) are given in Table2.b. Average time between events of cleavage of a given Zn-N bond, averaged from the firstprinciples MD trajectories, as a function of pressure applied.

Table 1 .

 1 Gas uptakes measured by adsorption isotherms and compared with calculated values.Uptakes are given in units of mL(STP)/g at a pressure of one bar.

	Gas (Kinetic Diameter / Å)	H2 (2.9)	CO2 (3.3)	O2 (3.46)	N2 (3.64)
	Temperature / K	77	273	273	77
	ZIF-62	130	39	-	0
	agZIF-62	9.3	20.1	1.5	0

Table 2 . Evolution of the Zn-N coordination free energy barrier with pressure, for ZIF-62

 2

	Pressure (GPa)	0.5	1.0	2.0	4.0	5.0
	∆G	≠ (kJ/mol)	50	45	45	37	34

Acknowledgements R.N.W. acknowledges support of the EPSRC in the form of a DTG Graduate Studentship. R.N.W. and A.M.B thank Prof. Chris Hunter and his group, at the Department of Chemistry (University of Cambridge), for the use of their HPLC facilities. T.D.B. thanks the Royal Society for a University Research Fellowship and for their support (UF150021). C.Z. acknowledges the financial support of the Elite Research Travel Scholarship from the Danish Ministry of Higher Education and Science. We thank Diamond Light Source for access to beamline I15 (EE16133 and EE19046-1). This work benefitted from the financial support of ANRT (these CIFRE 2015/0268) and access to HPC platforms provided by a GENCI grant (A0030807069). Gas sorption on the a g ZIF-62 was supported by a grant from the National Science Foundation, Division of Chemistry under award number CHE-1661655. Laurine Friche, Nisansala Bandata and Omid T. Qasvini (Massey Unviersity) are thanked for technical assistance, alongside Dr. Brian R. Pimentel (UCSD). British Crown Owned Copyright 2018/AWE. Published with permission of the Controller of Her Britannic Majesty's Stationary Office. F.-X.C. designed, performed, and analysed the molecular simulations. All Authors participated in discussing the data. R.N.W. and T.D.B. wrote the manuscript with input from all authors.

Data Availability

The data that support the findings of this study are available from the corresponding author on request.

Supplementary Tables 3 &4. Following quasi-linear thermal volume expansion upon heating from ambient-T up to 270 °C, a significant volume collapse is observed between 270 °C and complete amorphization at 320 °C. Thermal expansion here is, however, not negative, as shown in Figure 3b -consistent with previous computational work indicating positive thermal expansion for ZIFs of cag topology [START_REF] Du Bourg | Thermal and mechanical stability of zeolitic imidazolate frameworks polymorphs[END_REF] . This collapse of the unit cell volume coincides with a decrease in diffraction intensity and is due to progressive collapse to a higher density phase. Upon hydrostatic compression at ambient temperature, the c-axis is the least compressible direction.

Under vacuum, thermal expansion is net-zero along the c-axis, slightly negative along the a-axis, and strongly positive along the b-axis. This extreme anisotropic behavior can be understood from the topology of the rings formed by interconnected Zn sites. A network of 8-membered rings extends perpendicular to a with bIm linkers protruding along the major-axes of their elliptical shape. This direction is dominantly parallel to b. Shearing of the rings perpendicular to the bIm linkers by expansion along c is therefore sterically blocked. A network of 6-membered rings extending predominantly perpendicular to b is of a more isotropic and rigid geometry, resulting in a subtler response along a and c compared to b (Supplementary Figure 6). In comparison, structurally identical but unsubstituted ZIF-4 shows no hindrance by bulky benzimidazole linkers and indeed strongly contracts along c while also expanding along b (Supplementary Figure 6 &7).

The structure of melt-quenched ZIF-62, hereby referred to as a g ZIF-62, has previously been investigated by X-ray total scattering [START_REF] Bennett | Melt-Quenched Glasses of Metal-Organic Frameworks[END_REF] . It was found that the Zn-N association is virtually identical between crystalline precursor and melt-quenched glass. Permanently porous glasses are rare. Where they do exist, the porosity in these materials is typically generated by post-synthetic chemical or physical Methods ZIF-62 and ZIF-4 were prepared and desolvated according to a procedure adapted from the literature [START_REF] Gustafsson | Crystal formation and size control of zeolitic imidazolate frameworks with mixed imidazolate linkers[END_REF] . Specifically, ZIF-62 and ZIF-4 were synthesized by a solvothermal method in which 1.515 g Zn(NO 3 ) 2 • 6H 2 O (8 mmol), 7.35 g imidazole (108 mmol), and 1.418 g benzimidazole (12 mmol) (ZIF-62), and 1.2 g Zn(NO 3 ) 2 • 6H 2 O (4.03 mmol), and 0.9 g imidazole (13.2 mmol) (ZIF-4) were dissolved in 75 ml of dimethylformamide (DMF) and transferred into a 100 ml glass jar. The jars were sealed tightly and heated to 130 °C for 48 h in an oven. The filtered off, assynthesized ZIFs were soaked in dichloromethane for solvent exchange during 24 hours and subsequently desolvated in a vacuum oven at 0.01 mbar and 140 °C. A sample of a g ZIF-62 was prepared by heating ZIF-62 under argon in a tube furnace to 430 °C, and cooling naturally.

The resulting compositions are Zn(Im) 1.76 (bIm) 0.24 for ZIF-62, and Zn(Im) 2 for ZIF-4 as determined by high-performance liquid chromatography (HPLC) (Supplementary Methods, Supplementary Figure 13). The XRD patterns and Raman spectra of the starting materials are shown in Supplementary Figure 14. Ambient pressure variable temperature powder X-ray diffraction data were collected under vacuum on a Bruker D8 Advance diffractometer equipped with a MRI radiation-heating stage. Pure silicon powder was mixed with ZIF-62 and ZIF-4 and used as an internal standard for sample displacement corrections.

Additional information

Supplementary Information is available in the online version of the paper.

Correspondence and requests for materials should be addressed to T.D.B.

Competing interests

The authors declare no competing financial interests.