Jack D Evans

François-Xavier Coudert
email: fx.coudert@chimie-paristech.fr

Macroscopic Simulation of Deformation in Soft Microporous Composites

Soft microporous materials exhibit properties, such as gated adsorption and breathing, which are highly desirable for many applications. These properties are largely studied for single crystals, however, many potential applications expect to construct structured or composite systems, examples of which include monoliths and mixed-matrix membranes. Herein, we use finite element methods to predict the macroscopic mechanical response of composite microporous materials. This implementation connects the microscopic treatment of crystalline structures to the response of a macroscopic sample. Our simulations reveal the bulk modulus of an embedded adsorbent within a composite is affected by the thickness and properties of the encapsulating layer. Subsequently, we employ this methodology to examine mixed-matrix membranes and materials of negative linear compressibility. This application of finite element methods allows for unprecedented insight into the mechanical properties of real-world systems and supports the development of composites containing mechanically anomalous porous materials.

Soft microporous materials have demonstrated excellent potential for use in separation, drug delivery and sensing applications. [START_REF] Horike | Soft Porous Crystals[END_REF][START_REF] Thallapally | Flexible (Breathing) Interpenetrated Metal-Organic Frameworks for CO 2 Separation Applications[END_REF][START_REF] Horcajada | Flexible Porous Metal-Organic Frameworks for a Controlled Drug Delivery[END_REF][START_REF] Férey | Large Breathing Effects in Three-dimensional Porous Hybrid Matter: Facts, Analyses, Rules and Consequences[END_REF] Particularly, stimuli-responsive materials can exhibit curious and counter-intuitive properties which have garnered significant experimental and theoretical investigation. [START_REF] Coudert | Responsive Metal-Organic Frameworks and Framework Materials: Under Pressure, Taking the Heat, in the Spotlight, with Friends[END_REF] One such phenomenon is that of adsorption-induced deformation, [START_REF] Neimark | Stress-Based Model for the Breathing of Metal-Organic Frameworks[END_REF] where the adsorption of guest species exerts stress on the porous system causing a deformation (or strain) of the microporous structure. This phenomenon can result, for the specific cases of very soft or highly asymmetric frameworks, in eye-catching experimental observations such as gated adsorption, breathing and negative gas adsorption. [START_REF] Cheng | Tuning of Gate Opening of an Elastic Layered Structure MOF in CO 2 Sorption with a Trace of Alcohol Molecules[END_REF][START_REF] Serre | An Explanation for the Very Large Breathing Effect of a Metal-Organic Framework during CO 2 Adsorption[END_REF][START_REF] Krause | A Pressure-Amplifying Framework Material with Negative Gas Adsorption Transitions[END_REF] Understanding the response of porous materials under physical or chemical stimulation requires a good understanding of the mechanical behavior of the host material itself. The atomistic mechanisms behind these phenomena can be examined in detail using simulation methods at the microscopic scale. [START_REF] Evans | Computational Chemistry Methods for Nanoporous Materials[END_REF] Notably, high accuracy density functional theory (DFT) methods have proven useful in probing this mechanical behavior of microporous materials, in and outside their elastic regime, by correlating atomistic stresses and strains in the fully periodic (and perfect) crystal structure -as illustrated in Figure 1. These methods have been used to uncover the mechanical properties of many crystalline materials resulting in valuable insight into negative linear compressibility, [START_REF] Qiao | Negative Linear Compressibility in Organic Mineral Ammonium Oxalate Monohydrate with Hydrogen Bonding Wine-Rack Motifs[END_REF] auxeticity, [START_REF] Siddorn | A Systematic Typology for Negative Poisson's Ratio Materials and the Prediction of Complete Auxeticity in Pure Silica Zeolite JST[END_REF] and chiral induction. [START_REF] Evans | Microscopic Mechanism of Chiral Induction in a Metal-Organic Framework[END_REF] However, these conventional methods are limited to single crystals of pure phase materials. On the other hand, practical applications of porous crystals are often used within composite materials, such as mixed-matrix membranes (MMMs) [START_REF] Zhu | Metal-Organic Framework Composites[END_REF][START_REF] Bae | A High-Performance Gas-Separation Membrane Containing Submicrometer-Sized Metal-Organic Framework Crystals[END_REF] or thin films anchored on a support. [START_REF] Bradshaw | Metal-Organic Framework Growth at Functional Interfaces: Thin Films and Composites for Diverse Applications[END_REF][START_REF] Bétard | Metal-Organic Framework Thin Films: From Fundamentals to Applications[END_REF] Herein, we describe the application of finite element methods (FEM) [START_REF] Zienkiewicz | The Finite Element Method: Solid Mechanics[END_REF] to examine the macroscopic mechanics of crystalline and nanocomposite materials, Figure 1. FEM are powerful numerical techniques for the resolution of boundary value problems for partial differential equations, which subdivide a large complex problem into small parts that are simpler to solve. In this study, we use it to perform structural mechanics analyses, i.e. solving for deformation and stresses in structures such as an entire single crystal and composites. This results in unprecedented insight into the properties of composite materials, beyond the previous approaches focusing on the periodic lattice or the unit cell. In addition to a fundamental advance, this approach is relevant for practical applications whereby encapsulation has been shown to attenuate deformation [START_REF] Perez | Amine-functionalized (Al) MIL-53/ VTEC TM Mixed-Matrix Membranes for H2/CO2 Mixture Separations at High Pressure and High Temperature[END_REF][20][START_REF] Zornoza | Functionalized Flexible MOFs as Fillers in Mixed Matrix Membranes for Highly Selective Separation of CO 2 from CH 4 at Elevated Pressures[END_REF] and thus diminish the often highly-desired flexible response. Importantly, this property could be potentially leveraged to tune the transition pressure of gated adsorption, Figure 1b, [START_REF] Coudert | Adsorption Deformation of Microporous Composites[END_REF] for energyefficient separations. [START_REF] Mason | Methane Storage in Flexible Metal-Organic Frameworks with Intrinsic Thermal Management[END_REF] In general, the description of a material's volumetric response to adsorption-induced stress can be simply described, in the linear regime, by Hooke's law: where 𝜖 is volumetric strain, 𝜎 A is adsorption stress and 𝐾 A is the bulk modulus of the adsorbing material.

𝜖 = 𝜎 A 𝐾 A (1)
This relation is accurate for the behavior of flexible crystals in the absence of an encapsulating phase.

However, the analytical expression for volumetric strain is more complex for a composite system, and would have to depend on the properties of all phases present, the nature of their interface, as well as the geometry of the composite. Recently, Neimark and coworkers developed analytical models, using well-established laws of elasticity, to quantify how an encapsulating matrix results in an attenuation of the adsorption-induced stress and thus deformation. [START_REF] Coudert | Adsorption Deformation of Microporous Composites[END_REF] This was achieved for a simple spherical model of a single particle, surrounded by an external medium -itself spherical or infinite -to give expressions for three specific cases, which are displayed in Figure 2. Here, we summarize the results obtained by this earlier work, and which will serve as a point of comparison for our numerical investigation.

Figure 2: (a) The model system used by Neimark and coworkers to represent a composite material. [START_REF] Coudert | Adsorption Deformation of Microporous Composites[END_REF] (b) Three cases for which analytic descriptions have been reported: case 1, an unconfined adsorbent; case 2, an adsorbent surrounded by a finite encapsulating shell; case 3, an adsorbent in an infinite matrix.

The soft porous crystal alone, i.e. an unconfined adsorbent under no external pressure (case 1), is well described by Hooke's law, Equation 1. This is the standard volumetric response of any material to external stress, whether that is an external mechanical stress or a stress exerted "from inside" and due to adsorption.

For a spherical adsorbent surrounded by another material (case 2) this standard response is decreased by the confinement, and its expression is given by:

𝜖 = 𝜎 A 𝐾 A ( 1 - 1 1 + 𝐾 A ( 𝑔 3𝐾 + 1-𝑔 4𝐺 ) ) (2)
where 𝐾 and 𝐺 are the bulk and shear moduli of the surrounding material, and 𝑔 = 𝑅 3 (𝑅+ℎ) 3 characterizes the volumetric ratio of the adsorbent and surrounding matrix.

There exists a special instance of case 2 where the adsorbent is surrounded by a non-deformable outer container. Physically, this represents a composite where the surrounding material is much stiffer. This results in different boundary conditions and a different expression for the expected deformation, which is then given by:

𝜖 = 𝜎 A 𝐾 A ( 1 1 + 𝑔𝐾 𝐾A + 4𝐺(1+𝑔) 3𝐾A ) (3)
Finally, another case is that of a spherical adsorbent in an infinite elastic matrix (case 3), which is a simple model corresponding to industrially relevant MMMs -it is equivalent to a MMM with a low concentration of soft crystal particles. In this case the volumetric strain was found to be reduced by a constant factor:

𝜖 = 𝜎 A 𝐾 A ( 1 1 + 4𝐺 𝐾A ) (4)
While composite microporous materials have been investigated with respect to adsorption and gas separation, [START_REF] Keskin | Selecting Metal Organic Frameworks as Enabling Materials in Mixed Matrix Membranes for High Efficiency Natural Gas Purification[END_REF][START_REF] Singh | Rigorous Calculations of Permeation in Mixed-Matrix Membranes: Evaluation of Interfacial Equilibrium Effects and Permeability-based Models[END_REF] the above analytical expressions, developed by Neimark and coworkers, give fundamental insight into their expected mechanical properties. These expressions, however, feature some approximations and are limited to spherical isotropic models and there is thus a need for numerical simulation methods to describe the response of anisotropic crystals, more complex systems and realistic nanostructured composites. In this study, we first investigate the mechanical response of similar simple spherical systems using our FEM approach. Subsequently, we apply this method to physically relevant and more complex models of MMMs and a nanocomposite containing a crystal exhibiting negative linear compressibility (NLC).

Firstly, in order to both validate the FEM approach and probe the validity of the analytic expressions derived by Neimark et al., a series of simulations were performed for simple spherical models displayed in Figure 3a. The structural models are comprised of a spherical adsorbent particle with a radius of 0.4 µm and a surrounding shell of a height between 0 µm (no matrix) and 10 µm (much larger than the adsorbent's radius). The adsorbent and surrounding matrix were simulated with the properties defined in Table 1.

These parameters were chosen to represent the mechanical properties of frequently studied systems, [START_REF] Sorribas | Ordered Mesoporous Silica-(ZIF-8) Core-Shell Spheres[END_REF][START_REF] Falcaro | MOF Positioning Technology and Device Fabrication[END_REF] in particular, ZIF-8 [START_REF] Park | Exceptional Chemical and Thermal Stability of Zeolitic Imidazolate Frameworks[END_REF] and mesoporous silica (adsorbent and matrix 1, respectively). Notably, we do not consider the porosity explicitly by these simulations instead we consider the soft and unique elastic properties which are exhibited by these materials.

Figure 3b illustrates the volumetric strain observed for an adsorption stress applied to the adsorbent material, in a way similar to a classical mechanical stress-strain curve. For an unconfined adsorbent under adsorption stress, we observe the expected response corresponding to Hooke's law, Equation 1. The composite models, however, show reduced strain owing to the encapsulating sphere constructed of stiffer material (matrix 1) with a bulk modulus 8.33 GPa, greater than that of the adsorbent (3.3 GPa). The extent of reduction is observable for a shell of thickness 0.01 µm, i.e. 2% of the radius of adsorbent. The magnitude of this effect reaches a maximum for a width of 1.0 µm, with larger widths showing no greater reduction in strain. Strains computed by FEM simulation were compared to that expected from the analytical models reported previously. We compare the strain elucidated for the maximum attenuation achieved, for a width of 10 µm, in Figure 3b. The models for a flexible sphere and an infinite matrix, Equation 2and Equation 4significantly overstate the reduction observed for the composite material. However, we find a good agreement for Equation 3 corresponding to the case where the external boundary of the matrix is fixed. The source of the discrepancy is likely to result from the simplified boundary conditions chosen during construction of the analytical expressions.

This FEM study has highlighted that the maximum attenuation achieved by the construction of a composite can be described by Equation 3. We find this is accurate for composites comprised of either softer or harder materials, such as matrix 2 and matrix 3. We can thus define for the nanocomposite system an effective bulk modulus (𝐾 eff ) of the adsorbent from the linear stress-strain behavior. Figure 3c demonstrates the evolution of 𝐾 eff for an increasing width of encapsulating material. Notably, we find that even an extremely soft material, such as matrix 2 -softer than the adsorbent itself -yields an increase in effective bulk modulus of the adsorbent from 2.89 GPa to 3.47 GPa. This significant increase would, in practical applications, influence the flexible adsorption properties of the adsorbent and thus its performance. In particular, this demonstrates the advantageous mechanical stability observed for composites containing soft adsorbents. [START_REF] O'neill | Macro-/microporous MOF Composite Beads[END_REF] Ultimately, the results from these numerical FEM simulations parallel the result of the analytical model -the addition of an encapsulating material can be used to tune the mechanical response of an adsorbent.

We find that Equation 3shows good agreement to the strain resulting from adsorption stress in a spherical composite material. Furthermore, the numerical simulations reveal shortcomings of the analytical models for other cases. Subsequently, we have applied this FEM approach to provide insight into two complex and experimentally relevant systems.

Nanocomposite membrane systems, such as MMMs, are desirable for application as they combine the processability of polymers with the gas separation properties of crystalline frameworks producing desirable nanostructured membrane materials. Separation methods employing membranes are more energy efficient than conventional separations [START_REF] Sholl | Seven Chemical Separations to Change the World[END_REF] and the use of flexible adsorbent materials has the potential to significantly improve the energy efficiency of gas separations. [START_REF] Mason | Methane Storage in Flexible Metal-Organic Frameworks with Intrinsic Thermal Management[END_REF] As demonstrated for simple spherical models the formation of a composite has implications for the mechanical properties of the adsorbent and unsurprisingly we expect this to be observed in MMMs. [START_REF] Zornoza | Functionalized Flexible MOFs as Fillers in Mixed Matrix Membranes for Highly Selective Separation of CO 2 from CH 4 at Elevated Pressures[END_REF] To investigate this effect, we produced models of MMMs -illustrated in Figure 4a -where a number of adsorbent particles of fixed radius (10 µm or 20 µm) are randomly dispersed throughout the volume of the encapsulating polymer. The material's properties for the adsorbent are identical to that of the simple spherical model, while for the membrane we use the mechanical properties of "matrix 1". Subsequently, the number of adsorbent particles was varied to result in models with increasing volumetric fraction (or loading). Because the systems were generated with a random dispersion of adsorbent particles for each set of parameters 10 unique simulations were completed at each loading to obtain a representative average. The importance of this methodology is demonstrated for membranes of a low volumetric fraction where the small sample size resulted in large variances.

From the simulation of the stress-strain curves in each case, we computed the effective bulk modulus of the adsorbent for a given volumetric fraction of particles in the composite system displayed in Figure 4b.

Adsorbents of radius 10 µm, despite showing large variance at a low volumetric fraction, exhibit an average effective bulk modulus similar to that expected for a sphere surrounded by a much larger material, described by Equation 3. However, dispersed within membranes with greater volumetric fraction this effect of the surrounding matrix is diminished. Adsorbents at a volumetric fraction of 10.5% have an effective bulk modulus of 7.04 GPa reduced more than 10% from 7.95 GPa observed at 0.03%. This trend is reproduced for larger sized adsorbents although the effective bulk modulus in these cases is noticeably reduced.

The simulations presented here demonstrate the effect that dispersing adsorbents within a matrix can have on the mechanical properties. The large variance observed at low volume fractions suggests than the action for this effect is related to the position of adsorbent within the matrix. To investigate this further, simulations of an individual adsorbent positioned at points centered at various positions through the 400 µm × 400 µm face of the membrane model were conducted. Figure 4c depicts the evolution of the effective bulk modulus of the adsorbent as a function of its 𝑧 coordinate within the membrane. When placed on the surface of the matrix the adsorbent, as expected, shows no change in bulk modulus. Within the surface of the matrix, the effect of the surrounding material is sudden with the adsorbent displaying stiffer mechanical properties even when not completely encapsulated. Furthermore, the amount of surrounding material is observed to have a considerable result on the bulk modulus. Adsorbents positioned barely within the matrix show a softer response than those placed in the center of the membrane structure. This is demonstrated clearly for the larger adsorbent, with a diameter of 40% the width of the matrix, here the bulk modulus is unable to be strengthened to the same extent as the smaller adsorbent. Ultimately, the edge effects illustrated in Figure 4c manifest the volume fraction trend observed in the MMM models. At high concentration of particles there are more positioned at the edges of the structure resulting in a decreased effect of encapsulation. We have thus shown the effect that concentration of adsorbents and position within an MMM has on their mechanical properties. This has highlighted the changes that encapsulation within a different material can have on the bulk modulus which has a significant impact on flexible adsorption processes such as breathing.

Importantly, this approach can be readily applied to predict the flexibility of experimental systems. For example, Gascon and coworkers described an MMM combining flexible NH 2 -MIL-53(Al) and polysulfone. [START_REF] Zornoza | Functionalized Flexible MOFs as Fillers in Mixed Matrix Membranes for Highly Selective Separation of CO 2 from CH 4 at Elevated Pressures[END_REF] The effective bulk modulus of NH 2 -MIL-53(Al) within this system, for a volume fraction of 21%, is predicted to have an average bulk modulus (Reuss averaging scheme 31 ) of 5.85 GPa, almost 17% stiffer than that observed for the bare material. This increased stiffness results in a shift of the breathing phenomena to higher pressures as observed by the experimental study, Figure 4d.

This numerical FEM simulation approach can also be readily extended to anisotropic composite systems, whose behavior is too complex for analytical resolution alone. To illustrate this feature we investigate here composite materials constructed from MIL-53(Al), 32 a soft porous material which displays NLC: [START_REF] Serra-Crespo | Experimental Evidence of Negative Linear Compressibility in the MIL-53 Metal-Organic Framework Family[END_REF] when external isotropic pressure is applied, while the overall volume of the system will decrease, some of its dimensions will increase. Notably, NLC has potential applications in pressure sensors, artificial muscles and actuators. [START_REF] Cairns | Negative Linear Compressibility[END_REF] Previously, DFT investigations have elucidated the NLC response of MIL-53(Al) [START_REF] Ortiz | Anisotropic Elastic Properties of Flexible Metal-Organic Frameworks: How Soft are Soft Porous Crystals?[END_REF] and these results have been used here to simulate the macroscopic consequence of these properties on a particle equivalent to the size of a single crystal. [START_REF] Serra-Crespo | Experimental Evidence of Negative Linear Compressibility in the MIL-53 Metal-Organic Framework Family[END_REF] Simulations employing FEM accurately extend the atomistic NLC phenomenon to single crystal dimensions as demonstrated in Figure 5. Upon application of hydrostatic pressure to a cube structure with the mechanical properties of MIL-53(Al) there is the expected the reduction in volume while, owing to NLC, the width in the 𝑥-axis increases.

When this NLC particle is encapsulated by even thin layers of a conventional material, matrix 1, the response is attenuated. Figure 6a illustrates the relative width of the 𝑥-axis of the complete composite for increasing pressure. We find that encapsulation by materials greater than the width of the NLC particle results in complete loss of NLC for the composite. However, for composites constructed with a very thin outer layer (0.1 µm in this case) there remains a small NLC response. In all cases, we find that the particle within the composite retains the NLC behavior as displayed in Figure 6b. Furthermore, as the ratio surrounding matrix to particle increases so too does the stiffness, evidenced by the drastic reduction in volumetric deformation.

This increase in stiffness is attributed to the isotropic encapsulating matrix imparting a greater bulk modulus to the material.

This demonstration of FEM to simulate a composite containing an NLC material highlights the capability of this approach to complex anisotropic materials. Thus unlocking the possibility to investigate combinations of other anisotropic materials providing insight into their macroscopic application.

Computational Methods

COMSOL Multiphysics 5.0 36 was used to create and simulate the 3D composite models. These simulations employed the MUMPS solver and the default, "normal" settings for mesh size to result in approximately 10 5 tetrahedra in each system. The mechanical properties of the materials modeled are summarized in Table 1.

To simulate the stress experienced during guest adsorption, an initial stress was applied to the adsorbent particle(s) and the resulting volumetric strain was measured. The effective bulk modulus was obtained by observing this compression within the linear regime, corresponding in our case to strains smaller than 1%.

Models of MMMs were constructed by randomly dispersing adsorbent spheres within a larger membrane structure. The approach used a MATLAB 37 script to randomly disperse spheres at a given concentration and subsequently build the geometry in COMSOL, similar to a methodology used by Singh and coworkers. [START_REF] Singh | Rigorous Calculations of Permeation in Mixed-Matrix Membranes: Evaluation of Interfacial Equilibrium Effects and Permeability-based Models[END_REF] Finally, in the last section, anisotropy was investigated for a cube particle of size 0.4 µm with properties corresponding to the stiffness matrix of MIL-53(Al), Table 2. Composites were constructed from this particle surrounded by a cube with properties of matrix 1 of increasing width. The geometry of this cube and corresponding composites were simulated for applied hydrostatic pressure. Examples of input files can be found in the supporting information and the group's data repository at https://github.com/fxcoudert/ citable-data.

Figure 1 :

 1 Figure 1: (a) Density functional theory (DFT) methods are employed to relate atomistic strains to a periodic lattice and, in the present work, we have used finite element methods (FEM) to extend this description to the macroscopic scale of an entire crystal. (b) A hypothetical description of gated adsorption in an isolated flexible adsorbent (blue) and an adsorbent surrounded by an elastic matrix (red), adsorption is indicated by filled symbols and desorption empty symbols.

Figure 3 :

 3 Figure 3: (a) The simple three-dimensional spherical models investigated: unconfined adsorbent particle (left) and composite system (right). (b) Volumetric strain for an adsorbent with an encapsulating shell of matrix 1 (points) where the width, ℎ, corresponds to the color code and the prediction of the analytical models are compared (lines). (c) Effective bulk modulus of the adsorbent (𝐾 eff ) for composites comprised of the adsorbent with radius 0.4 µm and a shell of width ℎ for matrix 1, matrix 2, or matrix 3 (blue, green, red; respectively).

Figure 4 :

 4 Figure 4: (a) Illustration and dimensions of one realization of the MMM model used in this study. (b) Effective bulk modulus of the adsorbent (𝐾 eff ) for a given volumetric fraction in the membrane. The individual simulations are displayed by points and lines are drawn between the averages for each volumetric fraction. (c) Effective bulk modulus of an individual adsorbent placed at positions along the 𝑧 axis, centered through the 400 µm × 400 µm face of the matrix structure. Black lines illustrate the surface of the matrix and dashed lines correspond to positions where the adsorbent is completely encapsulated. (d) CO 2 adsorption at 308 K of NH 2 -MIL-53(Al) (adsorbent) and an MMM of NH 2 -MIL-53(Al) within polysulfone (asdorbent@MMM) at 25% volume fraction, reported by Gascon and coworkers. 21 (d, inset) Predicted average bulk moduli (𝐾 R ) corresponding to NH 2 -MIL-53(Al) and NH 2 -MIL-53(Al) particles dispersed within polysulfone at 21% volume fraction.

Figure 5 :

 5 Figure 5: (a) Dimensions of the cube particle used to study the macroscopic NLC response by MIL-53(Al). (b) Changes in the volume and individual dimensions of the particle upon application of increasing hydrostatic pressure.

Figure 6 :

 6 Figure 6: (a) Relative width of the 𝑥-axis of the total composite material of MIL-53(Al) and matrix 1, for increasing width of the encapsulating material corresponding to the color code. (b) Width of 𝑥-axis and volume of the NLC material embedded within the composites.

Table 1 :

 1 Material properties of the adsorbent and three encapsulating matrix materials considered in this investigation.

	adsorbent 924.3	2.895	1.110	0.33
	matrix 1	242.0	8.333	3.846	0.30
	matrix 2	242.0	0.8333	0.3846	0.30
	matrix 3	242.0	41.67	19.23	0.30

material

𝜌 / kg.m -3 𝐾 / GPa 𝐺 / GPa 𝜈

Table 2 :

 2 Stiffness matrix (or matrix of second-order elastic constants) of the anisotropic material MIL-53(Al),[START_REF] Loiseau | A Rationale for the Large Breathing of the Porous Aluminum Terephthalate (MIL-53) Upon Hydration[END_REF] with coefficients given in units of GPa. The values of the elastic constants were obtained using the B3LYP exhange-correlation function with empirical correction for dispersive interactions.[START_REF] Ortiz | Anisotropic Elastic Properties of Flexible Metal-Organic Frameworks: How Soft are Soft Porous Crystals?[END_REF]

	⎛	90.85 20.41 54.28	0	0	0	⎞
	⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝	20.41 65.56 12.36 54.28 12.36 33.33 0 0 0 0 0 0	0 0 7.24 0	0 0 0 39.52	0 0 0 0	⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
		0	0	0	0	0	8.27

Acknowledgement

We thank Lydéric Bocquet and Sophie Marbach for fruitful discussions on mechanics of composites and finite element methods. We acknowledge PSL Research University for funding (project DEFORM, grant ANR-10-IDEX-0001-02) and HPC platforms provided by a GENCI grant (x2016087069).

Supporting Information Available

Examples of the COMSOL input files used for the simulation of the spherical composites, MMMs and anisotropic materials in addition to the MATLAB script used to randomly disperse spheres. This material is available free of charge via the Internet at http://pubs.acs.org/.


Gérald Chaplais
email: gerald.chaplais@uha.fr

Guillaume Fraux

Jean-Louis Paillaud

Claire Marichal

Habiba Nouali

Alain H Fuchs

François-Xavier Coudert

Joël Patarin

Impacts of the Imidazolate Linker

come

Introduction

Zeolitic Imidazolate Frameworks (ZIFs) constitutes a sub-class of Metal-Organic Frameworks (MOFs) and represent an emerging family of microporous materials owing to both their chemical and thermal stabilities as well as textural properties (microporous volume and surface areas) compared to a large number of MOFs. [START_REF] Park | Exceptional Chemical and Thermal Stability of Zeolitic Imidazolate Frameworks[END_REF][START_REF] Canivet | Water Adsorption in MOFs: Fundamentals and Applications[END_REF][START_REF] Chen | Zeolitic Imidazolate Framework Materials: Recent Progress in Synthesis and Applications[END_REF][START_REF] Duan | Water-Resistant Porous Coordination Polymers for Gas Separation[END_REF] ZIFs are mainly built from divalent metal ions (e.g., Zn 2+ , Co 2+ , Cd 2+ , Cu 2+ ) bridged by ditopic imidazolate-type anionic linkers. Each metal cation is most often tetrahedrally linked, through nitrogen atoms, to four imidazolate linkers, thereby leading essentially to extended three-dimensional structures. [START_REF] Park | Exceptional Chemical and Thermal Stability of Zeolitic Imidazolate Frameworks[END_REF][START_REF] Phan | Structure, and Carbon Dioxide Capture Properties of Zeolitic Imidazolate Frameworks[END_REF][START_REF] Tian | Cadmium Imidazolate Frameworks with Polymorphism, High Thermal Stability, and a Large Surface Area[END_REF][START_REF] Pimentel | Zeolitic Imidazolate Frameworks: Next-Generation Materials for Energy-Efficient Gas Separations[END_REF] Thanks to their intrinsic physico-chemical features, a vast field of applications involving ZIFs such as, e.g., gas storage, 5, 8-10 separation, [START_REF] Chen | Zeolitic Imidazolate Framework Materials: Recent Progress in Synthesis and Applications[END_REF][START_REF] Pimentel | Zeolitic Imidazolate Frameworks: Next-Generation Materials for Energy-Efficient Gas Separations[END_REF][START_REF] He | Microporous Metal-Organic Frameworks for Storage and Separation of Small Hydrocarbons[END_REF][START_REF] Herm | Hydrocarbon Separations in Metal-Organic Frameworks[END_REF][START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF][START_REF] Van De Voorde | Adsorptive Separation on Metal-Organic Frameworks in the Liquid Phase[END_REF][START_REF] Adatoz | Opportunities and Challenges of MOF-Based Membranes in Gas Separations[END_REF][START_REF] Bao | Potential of Microporous Metal-Organic Frameworks for Separation of Hydrocarbon Mixtures[END_REF] encapsulation, [START_REF] Chen | Zeolitic Imidazolate Framework Materials: Recent Progress in Synthesis and Applications[END_REF][START_REF] Zhu | Metal-Organic Framework Composites[END_REF] catalysis, [START_REF] Bhattacharjee | Zeolitic Imidazolate Frameworks: Synthesis, Functionalization, and Catalytic/Adsorption Applications[END_REF][START_REF] Dhakshinamoorthy | Metal Organic Frameworks as Heterogeneous Catalysts for the Production of Fine Chemicals[END_REF][START_REF] Huang | Multifunctional Metal-Organic Framework Catalysts: Synergistic Catalysis and Tandem Reactions[END_REF] has been explored. Since few years, we have developed a new type of application, i.e., energetic applications involving such materials from both experimental and modelling approches. [START_REF] Ortiz | Energetic Performances of the Metal-Organic Framework ZIF-8 Obtained Using High Pressure Water Intrusion-Extrusion Experiments[END_REF][START_REF] Ortiz | Versatile Energetic Behavior of ZIF-8 upon High Pressure Intrusion-Extrusion of Aqueous Electrolyte Solutions[END_REF][START_REF] Ortiz | Energetic Performances of "ZIF-71-Aqueous Solution" Systems: A Perfect Shock-Absorber with Water[END_REF][START_REF] Ortiz | What Makes Zeolitic Imidazolate Frameworks Hydrophobic or Hydrophilic? The Impact of Geometry and Functionalization on Water Adsorption[END_REF][START_REF] Khay | Water Intrusion-Extrusion Experiments in ZIF-8: Impacts of the Shape and Particle Size on The Energetic Performances[END_REF][START_REF] Khay | Assessment of the Energetic Performances of Various ZIFs with SOD or RHO Topology Using High Pressure Water Intrusion-Extrusion Experiments[END_REF][START_REF] Mortada | Energetic Performances of ZIF-8 Derivatives: Impact of the Substitution (Me, Cl or Br) on Imidazolate Linker[END_REF][START_REF] Fraux | Forced Intrusion of Water and Aqueous Solutions in Microporous Materials: from Fundamental Thermodynamics to Energy Storage Devices[END_REF] In a recent study, [START_REF] Mortada | Energetic Performances of ZIF-8 Derivatives: Impact of the Substitution (Me, Cl or Br) on Imidazolate Linker[END_REF] some of the authors compared the energetic performance using high pressure intrusion-extrusion experiments of non-wetting liquids (water, KCl and LiCl aqueous solutions) in three SOD ZIF-8 derivatives herein named ZIF-8_CH 3 (commonly known as ZIF-8), ZIF-8_Cl and ZIF-8_Br. The latter are two analogs of ZIF-8_CH 3 with chlorine or bromine atoms bore in position 2 by the linker instead of methyl group. Significant differences in terms of energetic behaviors concerning the nine studied "ZIFs-non-wetting liquids" systems have encouraged us to further analyze the considered materials, especially ZIF-8_Cl and ZIF-8_Br, by examining their crystallographic structures and evaluating their potential flexibility.

These two halogenated hybrids were reported for the first time by Li et al. [START_REF] Li | Zeolitic Imidazolate Frameworks for Kinetic Separation of Propane and Propene[END_REF][START_REF] Li | Zeolitic Imidazolate Frameworks for Kinetic Separation of Propane and Propene[END_REF] for the assessment of their kinetic separation properties of propane/propene. Even if the authors listed the related crystal data and structure refinement parameters and deposited the information in the Cambridge Structural Database, [START_REF] Groom | The Cambridge Structural Database[END_REF] as referenced as AWIWEJ and AWIWIN, actually for only the crude compounds, namely the hybrid matrixes with remaining occluded solvent molecules, no further details about the needed atomic positions were provided from the two sources. Later, solely ZIF-8_Cl (also named ZIF-Cl) was investigated in relation to isostructural ZIFs as part of CO 2 capture/separation by using Density Functional Theory (DFT) calculations [START_REF] Amrouche | Experimental and Computational Study of Functionality Impact on Sodalite-Zeolitic Imidazolate Frameworks for CO 2 Separation[END_REF] and Grand Canonical Monte Carlo (GCMC) simulations, [START_REF] Hu | Effects of Water Vapor and Trace Gas Impurities in Flue Gas on CO 2 Capture in Zeolitic Imidazolate Frameworks: the Significant Role of Functional Groups[END_REF] or to estimate their hydrophobic/hydrophilic nature by combining molecular simulation results with a quantitative structure-property relationship (QSPR). [START_REF] Amrouche | Prediction of Thermodynamic Properties of Adsorbed Gases in Zeolitic Imidazolate Frameworks[END_REF] On another note, one distinctive property of some of the ZIFs lies in the possibility of structural transitions, occurring through rotation (or swing) of the linkers, which highlights the flexibility of these materials. For ZIF-8_CH 3 , this was evidenced by the structural work of Moggach et al., [START_REF] Moggach | The Effect of Pressure on ZIF-8: Increasing Pore Size with Pressure and the Formation of a High-Pressure Phase at 1.47 GPa[END_REF] which have shown that the swing of linkers occurs upon high pressure in diamond anvil cell high-pressure experiments. Fairen-Jimenez et al. evidenced also this peculiar phenomenon through a combined experimental-simulation study based on nitrogen sorption measurements and crystallographic results. [START_REF] Fairen-Jimenez | Opening the Gate: Framework Flexibility in ZIF-8 Explored by Experiments and Simulations[END_REF] They assigned a step observed at low relative pressure in the isotherm to the structural transition. Ania et al. used experimental and simulation studies in order to demonstrate that this reorientation is governed by characteristics (polarizability, molecular size, shape) of the investigated gases (N 2 , Ar, O 2 , CO), and that the stepped adsorption behavior is defined by the guest packing the inside the host. [START_REF] Ania | Understanding Gas-Induced Structural Deformation of ZIF-8[END_REF] Afterwards, several investigations shed the light on the correlation between the crystal size/shape of ZIF-8_CH 3 and the stepped uptake profile noticed at low relative pressure in the nitrogen/argon sorption isotherms, by thereby underlining the possibility to modulate the triggering of the swing of linkers. [START_REF] Zhang | Crystal-Size-Dependent Structural Transitions in Nanoporous Crystals: Adsorption-Induced Transitions in ZIF-8[END_REF][START_REF] Tanaka | Adsorption and Diffusion Phenomena in Crystal Size Engineered ZIF-8 MOF[END_REF][START_REF] Tian | Role of Crystal Size on Swing-Effect and Adsorption Induced Structure Transition of ZIF-8[END_REF][START_REF] Watanabe | Synthesis of Zeolitic Imidazolate Framework-8 Particles of Controlled Sizes, Shapes, and Gate Adsorption Characteristics Using a Central Collision-Type Microreactor[END_REF] Besides, the flexibility of ZIF-8_CH 3 has also been characterized by using 129 Xe NMR spectroscopy. [START_REF] Springuel-Huet | Flexibility of ZIF-8 Materials Studied Using 129 Xe NMR[END_REF] Finally, it was recently shown by a combination of quantum chemistry calculations and first-principles molecular dynamics (MD) simulations that the structural transition featured upon adsorption for ZIF-8_CH 3 is continuous as the function of pore loading, and that thermodynamics of packing effects contribute to explain the experimental stepped adsorption isotherms. [START_REF] Coudert | Molecular Mechanism of Swing Effect in Zeolitic Imidazolate Framework ZIF-8: Continuous Deformation upon Adsorption[END_REF] Consequently, volumetric nitrogen sorption and molecular dynamics (MD) simulations constitute complementary and suitable tools in order to appreciate the flexible/stiff behavior of ZIFs. Herein, we report firstly a full crystallographic study of ZIF-8_Cl and ZIF-8_Br based on a synergetic combination of powder X-ray diffraction and [START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C MAS NMR spectroscopy techniques. In a second part, we discuss in details about the nitrogen sorption isotherms of ZIF-8_Cl and ZIF-8_Br compared to the one of ZIF-8_CH 3 performed at 77 K before commenting the related results providing molecular dynamic simulations.

Experimental Section

Materials

Reagents and solvents. The reagents, zinc nitrate hexahydrate (Zn(NO 3 ) 2 6H 2 O, 99%), 2methylimidazole (Hmim, 97%), 2-chloroimidazole (Hcim-2, 97%), 2-bromoimidazole (Hbim-2, 95%), were provided by Alfa Aesar. The alcoholic solvents such as methanol (MeOH, 99.9%) and ethanol (EtOH, 99.9%) were purchased from Carlo Erba whereas the basic ammonium hydroxide solution (NH 3 , 31.5%) was supplied by Sigma Aldrich.

Homemade deionized water was also used to prepare ZIF-8_CH 3 . All the reagents, base and solvents were used without further purifications.

Synthesis of ZIF-8_CH 3 . The synthesis protocol of He et al. [START_REF] He | Facile Synthesis of Zeolitic Imidazolate Framework-8 from a Concentrated Aqueous Solution[END_REF] was followed with modifications in terms of quantities (ca. 12 times up-scaling), recovering of material (filtration instead of centrifugation) and activation (soakings in MeOH) processes. Briefly, in a glass bottle, 7.01 g (23.6 mmol) of Zn(NO 3 ) 2 6H 2 O are dissolved under stirring in 39.00 g (2164.3 mmol) of deionized water to form a solution (S 1 ). Meanwhile, in a 250 mL round bottom flask, 3.87 g (47.1 mmol) of Hmim are dissolved under stirring in 40.78 g (754.3 mmol NH 3 ) of aqueous ammonia to get a solution (S 2 ). Afterwards, S 1 is added to S 2 under stirring. The final composition in molar equivalents of the reaction mixture is 1 Zn: 2 Hmim: 32 NH 3 : 164 H 2 O. After a 10 minutes stirring, a white suspension is obtained. A white solid is recovered by filtration and washed abundantly (420 mL) with deionized water per portions in order to lower the filtrate pH at around 7. After drying under air overnight, the white solid is soaked in 100 mL of MeOH for 4 h and recovered by filtration. The activation stage is repeated three times more. After drying under air, 1.79 g of white powder is obtained (yield of 33%). Powder X-ray diffraction (not shown) and thermogravimetric analysis (see Figure S1) evidenced the crystalline purity of the sample and the absence of occluded molecules.

Synthesis of ZIF-8_Cl. The synthesis protocol was adapted from the one provided by Li et al. [START_REF] Li | Zeolitic Imidazolate Frameworks for Kinetic Separation of Propane and Propene[END_REF] by changing the quantities (ca. 11 times up-scaling based on Zn source), the nature of the solvent (EtOH instead of MeOH), the linker on metal source ratio (2.0 instead of 2.6) as well as the composition in molar equivalents, and the heating duration (3 instead of 2 days).

In a 150 mL PTFE-lined stainless-steel autoclave, 1.37 g (4.6 mmol) of Zn(NO 3 ) 2 6H 2 O is dissolved in 74.00 g (1606.3 mmol) under stirring. Afterwards, 0.98 g (9.2 mmol) of Hcim-2 is added, thereby resulting for the reactional mixture the following molar composition in equivalents: 1.0 Zn: 2.0 Hcim-2: 350 EtOH: 6 H 2 O. After a 10 minutes stirring, the suspension is heated at 100°C for 72 h. After cooling down to room temperature, 0.90 g of an ecru powder is obtained (yield of 73%) after filtration, washing with 100 mL of EtOH and drying at 70°C for 3 h. Powder X-ray diffraction (see Figure S2) and thermogravimetric analysis (see Figure S1) proved the crystalline purity of the sample and the absence of occluded molecules.

Synthesis of ZIF-8_Br. The synthesis protocol was also adapted from the one provided by Li et al. [START_REF] Li | Zeolitic Imidazolate Frameworks for Kinetic Separation of Propane and Propene[END_REF] where the quantities were increased (ca. 11 times up-scaling based on Zn source, with 1.36 g (4.6 mmol) of Zn(NO 3 ) 2 6H 2 O) and synthesis stages (molar composition in equivalents of reactional mixture, container type, heating temperature and duration, as well as washing process) were the same ones as previously followed for ZIF-8_Cl except that Hcim-2 was substituted with Hbim-2. 1.24 g of an ecru powder is obtained (yield of 75%).

Powder X-ray diffraction (see Figure S3) and thermogravimetric analysis (see Figure S1) highlighted the crystalline purity of the sample and the absence of occluded molecules.

Characterization Techniques

Powder X-Ray Diffraction. A small amount of ZIF-8_Br and ZIF-8_Cl samples were transferred into glass capillaries (Mark-tube made of special glass, no. 14, outside diameter 0.3 mm, Hilgenberg Gmbh) for powder XRD (PXRD) analysis. Two scans for each sample were collected between 6° and 95° (2θ) on a STOE STADI-P diffractometer in Debye-Scherrer geometry, equipped with a linear position-sensitive detector (PSD, 6° in 2θ) and employing Ge monochromated Cu K α1 radiation (λ = 1.5406 Å) (step 0.01°, 120 s of time acquisition per PSD step (0.1°). The two scans were averaged into a single one for better statistics on the collected data. The resulting powder X-ray diffraction patterns show wellresolved diffraction peaks which confirm a good crystallinity. All diffraction peaks were ticked and indexed with the WinX POW package [START_REF]STOE Powder Diffraction Software Package WinX POW , version 2.20[END_REF] using the Louër algorithm [START_REF] Boultif | Indexing of Powder Diffraction Patterns for Low-Symmetry Lattices by the Successive Dichotomy Method[END_REF] with a cubic unit cell and refined in space group I43m (no. 217) with a = 17.0370(3) Å (FOM(30) = 548.5) and a = 17.0832( 6) Å (FOM(30) = 709.2) for ZIF-8_Cl and ZIF-8_Br, respectively. The Rietveld analysis [START_REF] Rietveld | Profile Refinement Method for Nuclear and Magnetic Structures[END_REF] was performed with the GSAS package [START_REF] Larson | General Structure Analysis System (GSAS)[END_REF] and EXPGUI as an interface. [START_REF] Toby | a Graphical User Interface for GSAS[END_REF] A Lebail refinement [START_REF] Bail | The Ab-Initio Structure Determination of Lithium Antimony Tungstate (LiSbWO 6 ) by X-Ray Powder Diffraction[END_REF] enabled the determination of the background and profile parameters. The empty structure of ZIF-8_CH 3 described in space group I43m and published by Moggach et al. (CCDC 739168 and RefCode TUDKEJ), [START_REF] Moggach | The Effect of Pressure on ZIF-8: Increasing Pore Size with Pressure and the Formation of a High-Pressure Phase at 1.47 GPa[END_REF] where the CH 3 group in position 2 of the linker was here replaced by a Cl or Br atom, was used as the starting model for the Rietveld refinement. After the first stage of the Rietveld analysis, after scale factor determination, Fourier difference maps showed unambiguously for both compounds a splitting of the halogen atomic positions on both sides of the imidazolate plane. This splitting is explained by a tilt of the linker around the axis defined by both nitrogen atoms. Following this observation and to take this disorder into account, a second set of atoms defining a differently oriented linker was introduced with the same shared nitrogen atoms. Each moieties having a specific occupancy factor, the sum of them being constrained to one.

During the Rietveld refinement process, all atoms were refined isotropically and soft restraints (bonds, angles and planes) were added to maintain a proper structure of the imidazolate linker. The final Rietveld refinement gave excellent reliability factors; crystal as well as Rietveld refinement parameters are listed in Tables S1 andS4. Atomic parameters and selected bond distances and angles are listed in Tables S2,S3, S5 and S6.

Crystallographic information files (CIF files) of ZIF-8_Cl and ZIF-8_Br can be obtained from the Cambridge Crystallographic Data Centre, quoting deposition numbers CCDC 1860457 and 1860456, respectively.

13 C MAS NMR Spectroscopy. [START_REF] Park | Exceptional Chemical and Thermal Stability of Zeolitic Imidazolate Frameworks[END_REF] H decoupled [START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C solid-state MAS NMR spectra were recorded on a Bruker AVANCE II 400WB spectrometer (B 0 = 9.4 T) operating at 100.64 MHz for [START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C and 400.18 MHz for 1 H. Samples were packed in a 4 mm cylindrical zirconia rotor and spun at a spinning frequency of 12 kHz. Experiments were performed with a π/4 pulse duration of 2.7 μs and a recycle delay of 60 s. [START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C chemical shifts were referenced to tetramethylsilane (TMS). Decomposition of the NMR spectra to extract the proportion of the corresponding species were performed with the DMfit software. 51

Nitrogen Adsorption-Desorption Measurements. Nitrogen adsorption-desorption isotherms were performed at 77 K using a Micromeritics ASAP 2420 apparatus. Prior to performing the sorption measurements, the samples were outgassed at 473 K for 12 h under secondary vacuum. The Langmuir and Brunauer-Emmett-Teller surface areas, denoted S L and S BET , respectively, were calculated according to the criteria specified in the literature 52- 53 by applying thereby the corresponding models to the 0.0004 ≤ p/p° ≤ 0.0034 range for ZIF-8_CH 3 , in the 0.0003 ≤ p/p° ≤ 0.0047 range for ZIF-8_Cl, and in the 0.0001 ≤ p/p° ≤ 0.0018 range for ZIF-8_Br. The microporous volumes, named V µ , were determined according to the t-plot method (Harkins and Jura model) for a thickness of 6-12 Å for ZIF-8_CH 3 and ZIF-8_Br and 10-16 Å for ZIF-8_Cl. Accessible volumes for the three ZIF-8 derivatives are mapped in Figure S4 and supplementary data are summed up in Table S7.

Scanning Electron Microscopy. The size and the shape of the ZIF-8 derivatives crystals were determined by scanning electron microscopy (SEM) using a Philips XL 30 FEG microscope. The micrographs are supplied in Figure S5.

Molecular Simulation methods. To probe the relationship between the structure changes and the adsorbed molecules, we used molecular dynamics (MD) simulations. In order to describe fully the flexibility of the frameworks without any assumption, we favored first principles molecular dynamics (FPMD; also called ab initio molecular dynamics) over force field-based MD -as there are currently no force fields available for the various ZIF-8 variants studied here. For each framework (ZIF-8_CH 3 , ZIF-8_Cl, ZIF-8_Br), we ran five simulations corresponding to different number N of nitrogen molecules inside the porous space, going from empty framework (N = 0) to the fully loaded host material. The maximal loading was determined from the experimental isotherms to be close to N = 50 molecules per unit cell for ZIF-8_CH 3 and ZIF-8_Cl and N = 40 molecules per unit cell for ZIF-8_Br. To create the starting configurations, we started from the energy-minimized configuration of the empty frameworks, and randomly placed the selected number of nitrogen molecules in the unit cell. The whole {ZIF, adsorbate} system was then minimized again before starting the molecular dynamics simulations.

We used the Quickstep module [START_REF] Vandevondele | QUICKSTEP: Fast and Accurate Density Functional Calculations Using a Mixed Gaussian and Plane Waves Approach[END_REF] of the CP2K software package (version 2.5.1, available online at http://www.cp2k.org/) for all the simulations, with a PBE exchange-correlation functional [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] with D3 dispersion corrections, [START_REF] Grimme | A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu[END_REF] a double zeta polarizable valence (DZVP) basis set, and an energetic cutoff of 600 Ry. All the systems were simulated with a 1 fs timestep giving a total of 12 to 22 ps of simulation. Temperature was held constant at 77 K with a CVSR thermostat, [START_REF] Bussi | Canonical Sampling Through Velocity Rescaling[END_REF] using a thermostat time constant of 1000 fs. We used the last 5 ps of simulation for analysis, leaving time to the system to equilibrate. Representative input files for the molecular dynamics simulations are available online in the data repository at https://github.com/fxcoudert/citable-data.

Results and Discussion

Structural Characterizations of ZIF-8_Cl and ZIF-8_Br

Structure Description of ZIF-8_Cl and ZIF-8_Br. The structural study from Rietveld analysis reveals a similar disorder for both structures. It is highlighted in Figures 1a and1b representing the asymmetric units of ZIF-8_Cl and ZIF-8_Br and where an occupancy factor of approximatively 50% for the tilted linkers was refined in both cases (see Tables S2 andS5). In Figure 1c, the dihedral angles between the disordered halogenated imidazolate planes is slightly greater for ZIF-8_Cl in comparison with the one observed for ZIF-8_Br (see Figure 1d), the difference being of about 3°. distinctly different linker orientations with small energy differences. [START_REF] Springer | A Zeolitic Imidazolate Framework with Conformational Variety: Conformational Polymorphs Versus Frameworks with Static Conformational Disorder[END_REF] On the other hand, in the same study, they conclude that such disorder cannot exist in SOD-type ZIFs with 2substituted imidazolate linkers. The present study tends to prove the opposite.

For ZIF-8_Br and ZIF-8_Cl, the linker disorder involves also two different dihedral angle between the plane defined by the six zinc atoms of the 6-membered ring of the sodalite cage and the linker plane, [START_REF] Coudert | Molecular Mechanism of Swing Effect in Zeolitic Imidazolate Framework ZIF-8: Continuous Deformation upon Adsorption[END_REF] they are of 3.60(7)° and 11.69(6)° for ZIF-8_Cl and 0.61(7)° and 11.62(6)° for ZIF-8_Br. These values are consistent with the computed distributions in the case of zero adsorbed N 2 molecule even if only one configuration is taken into account for the calculation (see computational study in section 3.2.).

13 C NMR MAS Measurements. [START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C MAS NMR is a powerful tool to probe the local environment of carbon atoms belonging to the framework linkers of ZIFs and gives complementary information to powder XRD results making possible a reliable structure elucidation. Figure 2 displays the 1 H decoupled [START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C MAS NMR spectra of the three samples.

The spectrum of ZIF-8_CH 3 presents three resonances (as expected from the asymmetric unit 36 ) at 13.8 ppm, 124.2 ppm and 151.2 ppm accounting for 26, 48 and 26% of the total signal, respectively. These resonances are assigned to the methyl group, the two protonated aromatic carbon atoms and the quaternary carbon atom of the 2-methylimidazolate (mim) linker in agreement with the literature. [START_REF] Sneddon | Investigation of Zeolitic Imidazolate Frameworks Using 13 C and 15 N Solid-State NMR Spectroscopy[END_REF] For ZIF-8_Cl, two sharp resonances are detected at 140.2 and 135.4 ppm accounting each for 17% of the total signal whereas a broader resonance is observed at 126 ppm corresponding to 66% of the signal. This latter resonance is assigned to the two protonated aromatic carbon atoms of the 2-chloroimidazolate (cim-2) linker. It is interesting to note that the width at mid-height of this resonance is 375 Hz, that is, significantly greater than the one of the corresponding resonance in ZIF-8_CH 3 (160 Hz).

This is in agreement with the coexistence of two disordered linkers that are not resolved on the [START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C MAS NMR spectrum but probably responsible for the observed broadening.

Moreover, the resonance corresponding to the quaternary carbon atom is split in two resonances of equal intensity in agreement with the suggested two different orientations of the cim-2 linker in the structure with a 50% occurrence each. As expected, the substitution of the CH 3 group by a Cl atom shifts the resonance of the carbon atom bearing the substituent toward high field. For ZIF-8_Br, a main component is detected at 127.9 ppm corresponding to the aromatic C-H. Despite a small deshielding of the resonance the broadness is similar to the one observed for ZIF8_Cl. The resonance(s) corresponding to the quaternary carbon atom(s) are not resolved. Nevertheless, additional broad components around 140 ppm and 120 ppm are observed that could account for the quaternary carbon atoms of the two different orientations of the 2-bromoimidazolate (bim-2) linker. Indeed, [START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C resonances corresponding to carbon atoms covalently bonded to quadrupolar nuclei such as 79 Br (I=3/2) can be broadened or split by second-order quadrupolar effects via residual dipolar coupling. [START_REF] Vioglio | Natural Abundance 15 N and 13 C Solid-State NMR Chemical Shifts: High Sensitivity Probes of the Halogen Bond Geometry[END_REF] This effect is expected to be more significant for 79 Br than for [START_REF] Moggach | The Effect of Pressure on ZIF-8: Increasing Pore Size with Pressure and the Formation of a High-Pressure Phase at 1.47 GPa[END_REF] Cl (I=3/2) because the quadrupolar moment of 79 Br is 3.6 times greater than the one of [START_REF] Moggach | The Effect of Pressure on ZIF-8: Increasing Pore Size with Pressure and the Formation of a High-Pressure Phase at 1.47 GPa[END_REF] Cl.

Flexibility or Stiffness of ZIF-8 Derivatives under Nitrogen Adsorption

As already mentioned, the nitrogen sorption measurements especially when they are combined with MD simulations enable to determine the flexible/stiff behavior of ZIF-type materials.

Experimental study. The properties of the ZIF-8 derivatives were characterized by nitrogen adsorption-desorption measurements at 77 K. The corresponding isotherms are depicted in Figures 3a-d where the nitrogen sorption capacities are expressed as a function of the relative pressure and either in cm 3 g -1 STP and mmol g -1 (Figures 3a and3b) or in cm 3 cm -3 STP and mmol cm -3 (Figures 3c and3d). Figures 3b and3d group the same plots as Figures 3a and3c, respectively, but provided in the logarithmic instead of linear scale. The textural parameters are recapitulated in Table 1. In more details, ZIF-8_CH 3 isotherm is characterized by a two-stepped uptake starting to p/p° ≈ 0.005 and ending at p/p° ≈ 0.02 as well as by a sharper reverse phenomenon occurring in the 0.075-0.005 p/p° range. This leads to the formation of an hysteresis loop which has been already shown dependent on the crystals size and shape, [START_REF] Zhang | Crystal-Size-Dependent Structural Transitions in Nanoporous Crystals: Adsorption-Induced Transitions in ZIF-8[END_REF][START_REF] Tanaka | Adsorption and Diffusion Phenomena in Crystal Size Engineered ZIF-8 MOF[END_REF][START_REF] Tian | Role of Crystal Size on Swing-Effect and Adsorption Induced Structure Transition of ZIF-8[END_REF][START_REF] Watanabe | Synthesis of Zeolitic Imidazolate Framework-8 Particles of Controlled Sizes, Shapes, and Gate Adsorption Characteristics Using a Central Collision-Type Microreactor[END_REF] the nature of probe molecules and the temperature of sorption measurements. [START_REF] Ania | Understanding Gas-Induced Structural Deformation of ZIF-8[END_REF] It reveals the flexibility of this material due to a structural transition based on the reorientation (swing) of linkers making possible the accommodation of large molecules [START_REF] Peralta | The Separation of Xylene Isomers by ZIF-8: a Demonstration of the Extraordinary Flexibility of the ZIF-8 Framework[END_REF] or more probe molecules as expected in the case of a stiff framework. [START_REF] Fairen-Jimenez | Opening the Gate: Framework Flexibility in ZIF-8 Explored by Experiments and Simulations[END_REF] Indeed, the experimental microporous volume (0.66 cm 3 g -1 ), which is consistent with the literature, [START_REF] Khay | Water Intrusion-Extrusion Experiments in ZIF-8: Impacts of the Shape and Particle Size on The Energetic Performances[END_REF] exceeds of ca. 25% the theoretical value of 0.53 cm 3 g -1 calculated for a stiff structure (see Table S7 and ref. [START_REF] Pérez-Pellitero | Adsorption of CO 2 , CH 4 , and N 2 on Zeolitic Imidazolate Frameworks: Experiments and Simulations[END_REF] ). A reversible uptake, taking place at low relative pressure (p/p° ≈ 0.007), similarly to ZIF-8_CH 3 , is also noticed for ZIF-8_Cl. Nevertheless, this phenomenon is labeled by a single-stepped and very sharp adsorption without hysteresis loop as the adsorption and desorption branches are superimposable. This is presumably due to the larger ZIF-8_Cl crystals which also tend to form agglomerates whose sizes reach several tens of micrometers, without presenting a specific shape (see Figure S4). In contrast, the ZIF-8_CH 3 crystals display a well-defined chamfered cubic shape with a noticeable monodispersed size centered at ca. 600 nm. It is worthy to note that this sudden uptake observed for ZIF-8_Cl enables the nitrogen capacity to increase significantly from 269.3 cm 3 g -1 STP (or 0.42 cm 3 g -1 , 12.0 mmol g -1 , 291.2 cm 3 cm -3 STP, 13.0 mmol cm -3 , 38.7 molecules per unit cell) to 347.9 cm 3 g -1 STP (or 0.54 cm 3 g -1 , 15.5 mmol g -1 , 376.3 cm 3 cm -3 STP, 16.8 mmol cm -3 , 50.0 molecules per unit cell) at p/p° ≈ 0.01. The swing of the cim-2 linkers in the SOD-type ZIF-8_Cl structure, following the example of the one of mim linkers in ZIF-8_CH 3 , explains why the latter surpasses the theoretical values evaluated at 0.47 (see Table S7) or 0.41 cm 3 g -1 . [START_REF] Amrouche | Experimental and Computational Study of Functionality Impact on Sodalite-Zeolitic Imidazolate Frameworks for CO 2 Separation[END_REF] Furthermore, according to our computational study (see below), it is due to a repacking of nitrogen probe molecules inside the porous cages of ZIF-8_Cl as pressure increases, enabling this material to fit more molecules inside the porous cavities. After a plateau between p/p° ≈ 0.01 -0.10, a second adsorption step, also reversible but much less marked than the previous one, is also noted for ZIF-8_Cl. It occurs in the broad relative pressure range from 0.10 to 0.95 and thereby enhances more the nitrogen capacity which totals 382.1 cm 3 g -1 STP (or 0.59 cm 3 g -1 , 17.0 mmol g -1 , 413.2 cm 3 cm -3 STP, 18.4 mmol cm -3 , 54.9 molecules per unit cell) at the highest limit. Such an uptake at relative high pressure was already observed for ZIF-90 (with topology SOD and built from imidazolate-2-carboxyaldehyde) at p/p° ≈ 0.4 but, with a steeper effect. This was assigned to either a slight constriction of the pores due to the presence of the aldehyde functionality on the linker, [START_REF] Morris | Crystals as Molecules: Postsynthesis Covalent Functionalization of Zeolitic Imidazolate Frameworks[END_REF] a constriction in the pores, [START_REF] Thompson | Hybrid Zeolitic Imidazolate Frameworks: Controlling Framework Porosity and Functionality by Mixed-Linker Synthesis[END_REF] or a gate opening phenomenom. [START_REF] Xin | Nanopolyhedrons and Mesoporous Supra-Structures of Zeolitic Imidazolate Framework with High Adsorption Performance[END_REF] For ZIF-8_Cl, it remains still unclear if this second step corresponds to slight modification of packing molecules or surface adsorption. However, our computational study (see below) suggest that it would be assigned to the transition towards an accommodated molecules arrangement more ordered. It is also striking to note from nitrogen isotherms when expressed in cm 3 cm -3 (or in mmol cm -3 ) (see Figures 3c and3d), so by excluding the mass component, a strong similarity (except for the second uptake) for ZIF-8_CH 3 and ZIF-8_Cl both in terms of adsorption capacities and the behavior of the linkers (swing) upon pressure. For ZIF-8_Br, the nitrogen physisorption measurements reveal a classical reversible Type Ia isotherm. [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF] The experimental microporous volume of 0.35 is consistent with the theoretical value of 0.32 cm 3 g -1 (see Table S7). These experimental results, which are confirmed by the computational study (see below), evidence that ZIF-8_Br constitutes a stiff porous material upon nitrogen adsorption and consequently that no reorientation (swing) of bim-2 linkers is observed, presumably because of steric hindrance of Br atom borne in position 2 by the imidazolate. Moreover, the three functionalized ZIF-8 derivatives are also distinguishable by the sorption capacities at very low pressures, below p/p° ≈ 0.005-0.007, so before the "gate opening" pressures observed for ZIF-8_CH 3 and ZIF-8_Cl (see Figures 3b and3d). The strength of interplays between nitrogen probe molecules and host materials frameworks decreases in the order: ZIF-8_Br > ZIF-8_Cl > ZIF-8_CH 3. The latter may be explained by electrostatic interactions or entropic parameters or a combination of both hypotheses. Indeed, even though the nitrogen molecules are commonly used for evaluating the textural properties of porous materials, they displays a quadrupole moment [START_REF] Li | Selective Gas Adsorption and Separation in Metal-Organic Frameworks[END_REF] and may interact preferentially on the internal surface with linkers in the ascending order: mim < cim-2 < bim-2, as all ZIFs are Zn-based materials.

From a point of view concerning the entropy, the stiffness of ZIF-8_Br structure could generate preferentially initial favorable adsorption sites in pore mouth for the 6 membered facets. Finally, Figure 3d, where nitrogen capacities of the ZIF-8 derivatives are expressed in cm 3 cm -3 STP, highlights also a peculiar point resulting from the intersection of the three isotherms. This point takes place at p/p° ≈ 0.005-0.007 and corresponds to an adsorbed nitrogen capacity of ca. 13 mmol cm -3 (ca. 38 molecules per unit cell). Above, from an experimental point of view, we have argued that this point represents the "gate opening" pressure due to the swing of linkers in the cases of ZIF-8_CH 3 and ZIF-8_Cl, thereby enabling more probe molecules to be accommodated. Given the high structural similitude of ZIF-8 counterparts (except the flexibility/stiff characteristic), the slight increase from 13 to 14.5 mmol cm -3 observed for ZIF-8_Br is certainly related to a slight modification packing of nitrogen molecules.

In order to provide insights into the mechanism behind the different behavior of the three frameworks with respect to nitrogen adsorption, a computational study was realized.

Computational Study. The adsorption of nitrogen probe molecules at low temperature in parent compound ZIF-8 (herein named ZIF-8_CH 3 ) has already been studied extensively, both experimentally and by computational methods. Early work demonstrated that the structure of ZIF-8_CH 3 goes through at least two phases during the adsorption: an Ambient-Pressure phase named AP (or ZIF-8 I), and a High-Pressure phase named HP (or ZIF-8 II).

These phases mainly differ by the orientation of the linkers around the 4 and 6-membered windows. [START_REF] Fairen-Jimenez | Opening the Gate: Framework Flexibility in ZIF-8 Explored by Experiments and Simulations[END_REF] A recent, more detailed characterization of the structural evolution upon adsorption showed that the transition from AP to HP is linked to a continuous swing (rotation) of the mim linker, which can be followed as the dihedral angle Zn-Zn-C-CH 3 goes from an equilibrium value of 7° in AP phase to an equilibrium value of 35° in HP phase. [START_REF] Coudert | Molecular Mechanism of Swing Effect in Zeolitic Imidazolate Framework ZIF-8: Continuous Deformation upon Adsorption[END_REF] In this work, the same approach using the Zn-Zn-C-X dihedral angle (where X stands for CH 3 , Cl or Br for ZIF-8_CH 3 , ZIF-8_Cl or ZIF-8_Br, respectively) enabled us to follow the evolution of the three SOD frameworks upon nitrogen adsorption, through first-principles molecular dynamics. The distributions of angles as a function of various nitrogen molecules loadings are shown in Figure 4 for the three ZIFs. For ZIF-8_CH 3 , a gradual increase of the dihedral angle is observed versus the loading while the distribution profile conserves a Gaussian type. These results are consistent with the already published ones for ZIF-8_CH 3 .

Interestingly, the two other frameworks behave differently. For ZIF-8_Cl, no change is noticed in the distribution profile upon adsorption until the highest value of loading (i.e., N = 50). In this case, the distribution shifts and the profile is no longer Gaussian type. It indicates that some of the linkers do not rotate (swing) even at high loading. This non-zero value of the distribution at φ = 0 contrasts with the case of ZIF-8_CH 3 . Finally, for ZIF-8_Br, no change occurs for the dihedral angle distribution as the loading increases. Although correlated with it, this behavior is not however sufficient to explain the presence of the adsorption step encountered at low relative pressure (p/p° ≈ 0.005-0.007) in the nitrogen isotherms of ZIF-8_CH 3 and ZIF-8_Cl, and its absence in the one of ZIF-8_Br. One hypothesis often formulated for ZIF-8_CH 3 is that the swinging motion leads to an increase of the accessible porous volume in the structure, thereby increasing nitrogen uptake. In order to show that this is not the case, and that the effect is more subtle, we computed the pore size distribution (see Figure 5) and the accessible volume (see Figure 6) from our MD trajectories using Zeo++. [START_REF] Willems | Algorithms and Tools for High-Throughput Geometry-Based Analysis of Crystalline Porous Materials[END_REF] The results presented in Figure 5 highlight that the pore size distribution (PSD) remains constant in all cases as the loading increase and the linkers swing. The three PSDs are similar albeit a shift toward smaller pores is noticeable in the order ZIF-8_CH 3 > ZIF-8_Cl > ZIF-8_Br. This is also reflected in the accessible volume which remains roughly constant as the loading increase and the linkers swing (see Figure 6). The origin of the steep uptake at low relative pressure observed in the nitrogen sorption isotherm of ZIF-8_CH 3 is actually linked to a reordering (repacking) of the nitrogen molecules in the cavity, thereby leading to an increase of adsorbed molecules in the same total pore volume as well as the swing of the linkers aiming to accommodate the new packing. This hypothesis had been already proposed by Ania et al., but the intermediate adsorption regime was then not probed or interpreted. [START_REF] Ania | Understanding Gas-Induced Structural Deformation of ZIF-8[END_REF] In order to visualize this packing, we have projected the positions of all adsorbed nitrogen atoms in the xy plane and created a density map of the adsorbed phase. Figure 7 groups the 2D density maps of the positions of the adsorbed nitrogen atoms in the xy plane both at various loadings and for the three frameworks. For ZIF-8_CH 3 , two different molecular packing are encountered according to the loading.

With 10 or 25 molecules in the unit cell, the density maps show clear delimited positions on a cubic-like arrangement, whereas with 40 and 50 molecules, they show a tetragonal-like arrangement of the molecules. This reordering of the adsorbed nitrogen molecules from a cubic-like phase to a tetragonal-like phase is at the origin of the steep uptake at low relative pressure. For ZIF-8_Cl, the behavior is roughly similar: the molecules first pack in a cubiclike fashion in the cases of 10, 25 and 40 molecules per unit cell, before a reordering toward a tetragonal-like arrangement at 50 molecules per unit cell. This is consistent with the dihedral angles distributions as shown in Figure 4 and evidences that the molecular packing rearrangement happens conjointly with the swing of the linkers. It is interesting to note that some disorder in the tetragonal arrangement remains for a loading of 50 molecules per unit cell as the molecules positions are not as well defined as the one in ZIF-8_CH 3 . Again, this is coherent with the dihedral angles distribution at 50 molecules per unit cell for ZIF-8_Cl which is not of a single Gaussian type, indicating that this disorder can also be found in the framework structure. For ZIF-8_Br, the behavior is different. A same cubic-like arrangement is found at the lower loadings of 8 and 20 molecules per unit cell, whereas the arrangement at the higher loadings of 40 and 50 molecules per cell differ from the tetragonal-like one seen for ZIF-8_CH 3 and ZIF-8_Cl. Indeed, the latter appears as a mix of the cubic and the tetragonal organization as the molecules are mostly distributed on a cube with additional molecules in the [111] channels on the diagonals of the cube. Consequently, because of the absence of a neat reordering of adsorbed nitrogen molecules in ZIF-8_Br, its sorption isotherm does not display the S-shaped adsorption step. Given that the change in functional group, and thus in partial atomic charges, does not significantly impact the strength of the Zn-N coordination bond, we ascribe the origin of this different sorption feature between the three ZIF-8 derivatives to the difference pore size and shape, the pores in ZIF-8_Br being too small to enable a molecular reordering to occur.

Conclusions

Three ZIF-8 derivatives of SOD topology, i.e., ZIF-8_CH 3 (commonly known as ZIF-8), ZIF-8_Cl (also called ZIF-Cl) and ZIF-8_Br, have been prepared from imidazole-type organic

1 .

 1 (9)°15.29(9)°F igure Asymmetric units of (a) ZIF-8_Cl, and (b) ZIF-8_Br (50% of probability ellipsoid). Dihedral angles between the disordered imidazolate linkers of (c) ZIF-8_Cl and (d) ZIF-8_Br. Such a disorder in ZIF of topology SOD exists in SALEM-2 which has been synthesized via a partial Solvent-Assisted Linker Exchange (SALE) of 2-methylimidazolate by imidazolate from the non-disordered ZIF-8_CH 3 . 58 Besides, Springer et al. have recently demonstrated from theory and experiment that Zn-based ZIFs of SOD topology prepared with 4,5dichlorinated imidazolate linkers are subject to different order and/or disorder having

Figure 2 . 1 H

 21 Figure 2. 1 H decoupled 13 C MAS NMR spectra of (a) ZIF-8_CH 3 , (b) ZIF-8_Cl and (c) ZIF-8_Br.

Figure 3 .

 3 Figure 3. Nitrogen adsorption-desorption isotherms measured at 77 K of the ZIF-8 derivatives. Nitrogen uptakes are expressed (a), (b) in cm 3 g -1 STP on the left axis and in mmol g -1 on the right axis, and (c), (d) in cm 3 cm -3 STP on the left axis and in mmol cm -3 on the right axis. Plots are also given with (a), (c), a linear scale and (b), (d) a logarithmic scale of the relative pressure. Spherical and empty symbols correspond to the adsorption and desorption branches, respectively.

Figure 4 .

 4 Figure 4. Distribution of linker swing angle (Zn-Zn-C-X dihedral angle, where X stands for CH 3 , Cl or Br for ZIF-8_CH 3 , ZIF-8_Cl or ZIF-8_Br, respectively) at various values of nitrogen loading in ZIF-8_CH 3 , ZIF-8_Cl and ZIF-8_Br.

Figure 5 .

 5 Figure 5. Pore size distribution (no unit) under increasing loading for the three structures.

Figure 6 .

 6 Figure 6. Porous volume changes in the three isoreticular structures during adsorption.

Figure 7 .

 7 Figure 7. 2D density maps of the adsorbed nitrogen atoms positions in the xy plane at various loadings in ZIF-8_CH 3 (top), ZIF-8_Cl (middle), ZIF-8_Br (bottom). The loading increases from left to right.

sources functionalized in position 2

 2 by a CH 3 group, Cl atom or Br atom, respectively. The first part of this study is devoted to the description of the two structures (desolvated/activated phases) of the halogenated and isoreticular materials enabled by the contributions of powder X-ray diffraction and[START_REF] Qiu | Metal-Organic Framework Membranes: from Synthesis to Separation Application[END_REF] C MAS NMR spectroscopy. These two techniques reveal a disorder (tilt) of the linker in the two investigated structures where the occupancy of the two subsets is about half. In the second part, the behaviors of the three MOFs under nitrogen molecules adsorption are comparatively screened. The experimental nitrogen sorption isotherms indicate that ZIF-8_Cl behaves roughly as ZIF-8_CH 3, that is with a singular, marked and reversible uptake at low relative pressure. Conversely, ZIF-8_Br displays a typical Type Ia isotherm. These results show that ZIF-8_Cl adopts a flexible structure like ZIF-8_CH 3 , where a swing (rotation) of the linker makes the accommodation of 12-14 supplementary molecules per unit cell possible. By contrast, ZIF-8_Br possesses a framework significantly more stiff. Furthermore, molecular dynamic simulations carried out on the three isoreticular structures corroborate these trends by evaluating the Zn-Zn-C-X dihedral angle (where X stands for CH 3 , Cl or Br for ZIF-8_CH 3 , ZIF-8_Cl or ZIF-8_Br, respectively) which evolves as a function of accommodated molecules for ZIF-8_CH 3 and ZIF-8_Cl but remains unchanged for ZIF-8_Br. Importantly, these simulation methods highlight that the structural transition (swing of linker) is triggered by a repacking of nitrogen molecules thereby inducing this "gate opening" or "swing effect". Finally, this study based on both experimental and simulation methods evidences clearly the influence of functional group bore by the linker on the flexible/stiff structural nature of three isoreticular ZIFs of SOD topology. A similar observation, involving ZIF-8_CH 3 , ZIF-90, and ZIF-65, with respective -CH 3 , -CH=O, -NO 2 groups and using highpressure single-crystal X-ray diffraction, density functional theory, and grand canonical Monte Carlo simulations, has been recently published.[START_REF] Hobday | Tuning the Swing Effect by Chemical Functionalization of Zeolitic Imidazolate Frameworks[END_REF]

Table 1 .

 1 Linker and textural parameters of ZIF-8 derivatives: microporous volume (V µ ), corresponding number of nitrogen molecules per unit cell (N µ ), BET (S BET ) and Langmuir (S L ) surface areas.

	ZIF	ZIF-8_CH 3	ZIF-8_Cl	ZIF-8_Br
	Linker	mim	cim-2	bim-2
	V µ (cm 3 g -1 )	0.66	0.57	0.35
	N µ (molecule per unit cell)	52.1	52.5	43.0
	S BET (m 2 g -1 )	1380	1175	863
	S L (m 2 g -1 )	1386	1181	865

Table of Contents (TOC) Image

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Acknowledgments

PXRD Collection, Thermal Analyses (TGA), 13 C MAS NMR Measurements, Nitrogen Sorption Measurements and SEM Micrographs were performed on the technical platforms of IS2M.

Funding

We acknowledge access to the CINES high-performance computing platforms provided by GENCI grant A0030807069.

Associated Content

Supporting Information Available: TG Curves of the Three Studied Materials, Crystallographic data of ZIF-8_Cl and ZIF-8_Br, Assessment of Nitrogen Accessible Volume for ZIF-8 Derivatives, Crystalline Morphologies of ZIF-8 Derivatives. This material is available free of charge via the Internet at http://pubs.acs.org.