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

Jack D Evans
email: jack.evans@tu-dresden.de

Nanoscale Metamaterials: Meta-MOFs and Framework Materials with Anomalous Behavior

Keywords: metal-organic frameworks, framework materials, metamaterials, adsorption, mechanical properties, thermal expansion

As the number of framework materials known and characterized in the literature grows, it becomes apparent that they can carry properties rarely encountered in more conventional, dense inorganic materials. Among these materials with unusual physical or chemical properties are the ubiquitous metal-organic frameworks, covalent organic frameworks, dense coordination polymers, and molecular frameworks. Many can respond to stimulation by displaying structural responses and changes in properties that range from counter-intuitive to thermodynamically forbidden. In that, they share large similarities with metamaterials, which are engineered to generate properties not found in "normal" materials. We review here the surprising behavior of these meta-MOFs and other framework materials that display properties "beyond" (μετά) the boundaries of common crystalline materials.

Introduction

Metamaterials are materials with outstanding properties defined by a periodic lattice arrangement, which by the specific combination of composition and geometric distribution are greater than a simple sum of their parts [START_REF] Kadic | Metamaterials beyond electromagnetism[END_REF][START_REF] Bertoldi | Flexible mechanical metamaterials[END_REF]. The precise lattice structure of metamaterials can be engineered to influence incident electromagnetic and vibrational waves, either by absorbing, enhancing or bending waves, in order to produce phenomena rarely exhibited by natural materials. For example, several photonic crystals can produce a negative refractive index [START_REF] Smith | Metamaterials and negative refractive index[END_REF] and a zinc blende-like macroscopic network can generate a negative effective bulk modulus [START_REF] Ding | Metamaterial with simultaneously negative bulk modulus and mass density[END_REF]. These interesting phenomena have enabled researchers to design entirely novel devices, which at first seem to belong to the world of fantasy literature, including invisibility and unfeelability cloaks [5,[START_REF] Rowling | The Tale of the Three Brothers[END_REF][START_REF] Bückmann | An elastomechanical unfeelability cloak made of pentamode metamaterials[END_REF].

Metamaterials challenge state-of-the-art manufacturing as features of these complex lattice structures are ideally smaller than the wavelength of corresponding incident waves, whether they are electromagnetic or elastic [START_REF] Shalaev | Optical negative-index metamaterials[END_REF][START_REF] Greaves | Poisson's ratio and modern materials[END_REF]. Despite the complexity of fabricating these materials several elegant examples have been realized. For example, a two-dimensional lattice of concentric cylinders featuring split-ring resonators was fabricated on the millimetre scale, Figure 1a. This structure was demonstrated to act as a invisibility cloak for microwaves, however, the invisibility was imperfect due to material absorption and other approximations [START_REF] Schurig | Metamaterial electromagnetic cloak at microwave frequencies[END_REF]. Advanced three-dimensional laser lithography has also enabled the production of once hypothetical mechanical metamaterials [START_REF] Soukoulis | Past achievements and future challenges in the development of three-dimensional photonic metamaterials[END_REF]. This technology was used to construct a diamondoid structure displayed in Figure 1b with connections as small as 0.55 µm which is expected to have a ratio of bulk modulus to shear modulus of 10000 [START_REF] Kadic | On the practicability of pentamode mechanical metamaterials[END_REF]. Materials with extremely large bulk modulus and low shear modulus are special mechanical metamaterials; solids that also act as fluids [START_REF] Milton | Which elasticity tensors are realizable?[END_REF].

Similar to these optical and mechanical metamaterials, many coordination frameworks and metal-organic frameworks (MOFs) are reported to exhibit exotic physical properties that are rarely observed in nature [START_REF] Coudert | Responsive metal-organic frameworks and framework materials: Under pressure, taking the heat, in the spotlight with friends[END_REF]. Here we will outline the behavior and applications of seminal examples of metamaterial MOFs (meta-MOFs), from the Greek μετά, which means "beyond". Interestingly, many of the structural features observed in mechanical metamaterials are also found in meta-MOFs, such as bending and buckling building units and dynamic topological arrangements (Figure 2). We define meta-MOFs as crystalline framework materials which exhibit unusual behavior not found, or rarely observed, in conventional crystalline materials (e.g., dense oxides). This behavior, as with metamaterials, is attributed to the specific arrangement of the material's nanoscale building blocks into a periodic framework.

The unique properties exhibited by meta-MOFs include similar mechanical properties to that observed in flexible mechanical metamaterials [START_REF] Bertoldi | Flexible mechanical metamaterials[END_REF], as well as anomalous thermal properties. In general the displacement and response of con- ventional metamaterials is macroscopic, however, the properties of meta-MOFs occur at the microscopic molecular scale, where the "building blocks" of the lattice range in size from a single cation to a molecule. The nanoscale structure of meta-MOFs therefore allows access to behavior, such as negative thermal expansion, which is difficult to engineer in micro or macro architectures [START_REF] Wang | Lightweight mechanical metamaterials with tunable negative thermal expansion[END_REF]. Moreover, the nanoporous (or mesoporous) structure of many meta-MOFs opens a rather unique approach of guest adsorption for the generation of deformation and stresses within a framework. Importantly, this growing research area leverages important concepts of mechanics and thermodynamics, including fundamental theories of elasticity and adsorption [START_REF] Evans | Computational chemistry methods for nanoporous materials[END_REF].

In this review we will highlight seminal examples of meta-MOFs which display extraordinary thermal, mechanical and adsorption properties. Subsequently, we will briefly cover potential applications, where these materials can permit exceptional energy absorption and state-of-the-art gas storage.

Physical properties: thermal and mechanical anomalous behavior

We first describe here framework materials that respond in an unusual manner to external physical stimuli. While traditional metamaterials are often described for their response to light and other electromagnetic waves (such as negative index of refraction materials), the most notable anomalous behavior of framework materials, to date, is in response to external constraints of temperature and pressure.

Negative thermal expansion

The first class of meta-MOFs display negative thermal expansion (NTE), i.e., whose volume shrink upon an increase in temperature: (∂V/∂T ) P < 0. This is in contrast to the thermal behavior of most "normal" dense materials, which expand upon heating, and so negative thermal expansion is often called an "unusual" or a "rare" physical property, "limited to certain types of structures" [17]. Likely the most familiar example, taken from undergraduate thermodynamics textbooks, is that of liquid water between 0 and 4°C -and also hexagonal ice! This phenomenon occurs more readily, however, in solids of various types. Including tetrahedrally bonded crystals at low temperature (such as Si and Ge), β-quartz, some ceramics and zeolites with framework structures and inorganic glasses. For a review of these different families of NTE materials, we direct the reader to Refs. 17, 18, and 19. NTE materials are actively sought after, with a particular focus on materials that feature NTE with a particularly large amplitude, in an isotropic manner, or for a wide temperature range. The gold standard NTE material is zirconium tungstate, ZrW 2 O 8 , [START_REF] Mary | Negative thermal expansion from 0.3 to 1050 Kelvin in ZrW 2 O 8[END_REF] a cubic oxide that displays isotropic negative expansion from 0.3 to 1050 K. For ZrW 2 O 8 , the volumetric coefficient of thermal expansion,

α V = 1 V ∂V ∂T P is -7.2 × 10 -6 K -1
, which is quite high.

Beyond the beauty and rarity of this phenomenon, negative thermal expansion is desirable for specific applications. In fact, the negative expansion coefficient is not directly sought after for its sign in itself but because it can be used, in combination with a positive thermal expansion material, in order to produce a composite material with controllable thermal expansion. In particular, such composites are a way to produce zero thermal expansion (ZTE) materials, whose volume is unchanged upon heating or cooling. Single-phase ZTE materials are extremely rare, but are desirable in the design of high-precision instruments and devices. They can also be used for medical applications, for bio-implants and as teeth fillingswhere the mismatch in thermal expansion between tooth and restorative material can create local stress and lead to failure [START_REF] Versluis | Thermal expansion coefficient of dental composites measured with strain gauges[END_REF].

It is an interesting fact that negative thermal expansion appears to occur at a somewhat higher rate in framework materials. This is true, in particular, of several families of zeolites, [START_REF] Attfield | Exceptional negative thermal expansion in AlPO 4 -17[END_REF][START_REF] Attfield | Strong negative thermal expansion in siliceous faujasite[END_REF] such as chabazite, ITQ-4 [START_REF] Woodcock | Negative thermal expansion in the siliceous zeolites chabazite and ITQ-4: A neutron powder diffraction study[END_REF], ITQ-1, ITQ-3, SSZ-23 [START_REF] Woodcock | Strong negative thermal expansion in the siliceous zeolites ITQ-1, ITQ-3 and SSZ-23[END_REF], Mg-doped AlPO 4 -17 [START_REF] Lightfoot | The widespread occurrence of negative thermal expansion in zeolites[END_REF] and hydrated HZSM-5 [START_REF] Marinkovic | Negative thermal expansion in hydrated HZSM-5 orthorhombic zeolite[END_REF]. This feature was originally predicted by lattice dynamic calculations [START_REF] Tschaufeser | Thermal expansion behavior of zeolites and AlPO 4 s[END_REF], before later experimental confirmation. It was rationalized by the occurrence of transverse vibrations of the bridging oxygen atoms between two rigid polyhedrons, or cooperative motions of linked quasi-rigid polyhedral units (so-called "rigid-unit modes"). Furthermore, it appears from several recent reports that other framework materials, and in particular metal-organic frameworks, also readily display negative thermal expansion. This was reported in the archetypal MOF-5, with a linear thermal-expansion coefficient of -16 × 10 -6 K -1 from 4 to 600 K [START_REF] Dubbeldam | Exceptional negative thermal expansion in isoreticular metal-organic frameworks[END_REF][START_REF] Han | Metal-organic frameworks provide large negative thermal expansion behavior[END_REF][START_REF] Zhou | Origin of the exceptional negative thermal expansion in metal-organic framework-5 Zn 4 O(1,4-benzenedicarboxylate) 3[END_REF]. It later surfaced that several other MOFs display that same behavior, [START_REF] Wu | Negative thermal expansion in the metal-organic framework material Cu 3 (1,3,5-benzenetricarboxylate) 2[END_REF][START_REF] Henke | Massive anisotropic thermal expansion and thermo-responsive breathing in metal-organic frameworks modulated by linker functionalization[END_REF][START_REF] Queen | Site-specific CO 2 adsorption and zero thermal expansion in an anisotropic pore network[END_REF] as well as covalent organic frameworks [START_REF] Zhao | Negative thermal expansion in covalent organic framework COF-102[END_REF]. In other cases, the thermal expansion is overall positive, but present as a highly anisotropic response of the material to temperature changes, as for HMOF-1 [START_REF] Devries | Nanoscale lattice fence" in a metal-organic framework: Interplay between hinged topology and highly anisotropic thermal response[END_REF].

This relatively common occurrence of NTE in MOF materials has been studied in detail on specific cases, such as MOF-5 [START_REF] Lock | Elucidating negative thermal expansion in MOF-5[END_REF], and it boils down to the nature of the framework building blocks and their interactions. In a simple dense material based on pair interactions, positive thermal expansion arises primarily from the anharmonicity of the pair interaction potential: vibrations make every bond longer on average, which can propagate in three dimensions to give a volume expansion upon heating. In contrast, in framework materials, the nature of the vibration of molecular linkers is quite different: the modes of lowest frequency (and higher amplitude) are associated with vibration of the linkers outside of its metal-linkermetal axis, which shorten the average metal-metal distance (see Figure 3). This local shortening upon heating of the node distances can be propagated to a threedimensional network, depending on the material's topology. This explains the fact that NTE is quite common in framework materials and MOFs. This approach can be formalized, in the quasi-harmonic approximation of thermal expansion, by studying the phonon modes of a crystal and their respective Grüneisen parameters, which characterize their contribution to thermal expansion -with a particular focus on low-frequency modes. This confirms that MOFs can show NTE even in the harmonic regime, because their behavior is dominated soft vibration modes, while for "conventional" dense materials thermal expansion is dominated by the anharmonicity of pair interactions.

Finally, we note that due to their versatile chemistry and their open pore spaces, and using the principles of reticular chemistry, MOFs present one additional advantage in the search for materials with pronounced NTE: their thermal response can be modulated or tuned [START_REF] Collings | Geometric switching of linear to area negative thermal expansion in uniaxial metalorganic frameworks[END_REF]. This can be achieved, for example by the presence of a controlled amount of guest molecules, such as for the framework material cocrystal analogue Zn[Ag(CN) 2 ] 2 • xAgCN, a cocrystal with two weakly interacting crystalline phases [START_REF] Goodwin | Thermal expansion matching via framework flexibility in zinc dicyanometallates[END_REF]. This guest-dependent control of the thermal expansion coefficient was observed for guest molecules inside the nanoporous onedimensional channels of a MOF [START_REF] Grobler | Tunable anisotropic thermal expansion of a porous zinc(II) metal-organic framework[END_REF]. The thermal behavior of a framework material can also be tuned by functionalization, for example by the addition of alkoxy side chains to the organic linker of a MOF [START_REF] Henke | Massive anisotropic thermal expansion and thermo-responsive breathing in metal-organic frameworks modulated by linker functionalization[END_REF]. It was also demonstrated that, for a given chemical composition (metal center and organic linker), the topology of the material can be used to tune the thermal expansion, in both sign and magnitude. Bouëssel du Bourg et al. [START_REF] Bouëssel Du Bourg | Thermal and mechanical stability of zeolitic imidazolate frameworks polymorphs[END_REF] predicted, using molecular simulation, that ZIF materials can exhibit thermal expansion coefficients between -92 × 10 -6 K -1 and +64 × 10 -6 K -1 depending solely on their topology, as depicted on Figure 4.

Recently, it was demonstrated by Cliffe et al. [START_REF] Cliffe | Defectdependent colossal negative thermal expansion in UiO-66(Hf) metalorganic framework[END_REF] that controlled introduction of defects in a MOF can also lead to changes in its thermal properties. Incorporation of correlated vacancy defects within the UiO-66(Hf) framework was shown to produce a thermally-densified hafnium-based framework that exhibits a record-holding isotropic negative thermal expansion, for a MOF, with α V = -97 × 10 -6 K -1 .

Negative linear compressibility

In addition to temperature, the application of mechanical pressure (or in other terms, stress or load) is another physical stimulus that can generate counter-intuitive responses from a framework material. Dissimilar to heating, it is impossible for the material to expand upon isotropic compression, i.e. its compressibility κ = -(1/V)(∂V/∂P) T must be positive, a condition required for mechanical stability. It is possible, however, that a material expands along one or more directions during this volume compression. This phenomenon is called negative linear compressibility (NLC), and it is a rare behavior [START_REF] Cairns | Negative linear compressibility[END_REF]. Even less common is the expansion in two different crystallographic directions (necessarily accompanied by a massive contraction of the third), a phenomenon for which some authors have coined the term negative area compressibility (NAC) [START_REF] Hodgson | Negative area compressibility in silver(I) tricyanomethanide[END_REF][START_REF] Cai | Giant negative area compressibility tunable in a soft porous framework material[END_REF]. Like all materials with anisotropic, tailored mechanical responses, NLC materials can find applications as pressure sensors, nano-actuators (such as artificial muscles) and switches.

There are several microscopic mechanisms by which an NLC may occur in a material, including ferroelasticity (where the NLC is associated with a phase transition), networks that can tilt, or feature helices. Three such examples are depicted in Figure 5. We refer the reader to the excellent review by Cairns et al. in Ref. [START_REF] Cairns | Negative linear compressibility[END_REF] for a detailed description of these mechanisms. We focus here on the occurrence of NLC in framework materials, where the origin of the mechanical response is linked, for the most part, to the topology of the material. The framework acts like a macroscopic truss, where the organic linkers are the rigid struts, and metal centers act as hinges -and flexibility arises from the deformation of the metal coordination environment [START_REF] Ogborn | Supramolecular mechanics in a metal-organic framework[END_REF][START_REF] Cai | Giant negative linear compression positively coupled to massive thermal expansion in a metal-organic framework[END_REF]. The two most common frameworks type that inherently display NLC are the "wine rack" (somewhat common among MOFs) and "honeycomb" networks. Examples of materials of these topologies featuring NLC include: the archetypal MIL-53 [START_REF] Ortiz | Anisotropic elastic properties of flexible metal-organic frameworks: How soft are soft porous crystals?[END_REF], whose breathing transition (see Section 3) is also associated with NLC [START_REF] Serra-Crespo | Experimental evidence of negative linear compressibility in the MIL-53 metal-organic framework family[END_REF]; the distorted wine rack framework in [NH 4 ][Zn(HCOO) 3 ] MOF [START_REF] Li | Negative linear compressibility of a metal-organic framework[END_REF]; the Zn[Au(CN) 2 ] framework with honeycomb structure [START_REF] Cairns | Giant negative linear compressibility in zinc dicyanoaurate[END_REF]; and calcium fumarate trihydrate, a one-dimensional coordination polymer [START_REF] Sun | Mechanical properties of a calcium dietary supplement, calcium fumarate trihydrate[END_REF]. There is also a know MOF with large negative area compressibility, Zn(CH 3 COO) 2 • 2H 2 O, a hydrogen-bonded 2D supramolecular coordination complex [START_REF] Feng | Negative area compressibility of a hydrogen-bonded two-dimensional material[END_REF] where the NAC arises from cooperative intra-layer coordination and hydrogen-bonding interactions, as well as inter-layer van der Waals forces. Furthermore, like the thermal expansion coefficient, compressibility in MOFs can in principle be tuned by modifications of the framework or inclusion of guest molecules, although reports in that area are still rather scarce. Cai et al. [START_REF] Cai | Giant negative area compressibility tunable in a soft porous framework material[END_REF] showed that it was possible to tune the large-scale negative area compressibility in Zn(L) 2 (OH) 2 (L = 4-(1H-naphtho [2,3-d]imidazol-1-yl)benzoate) by exchanging guests adsorbed from hydrostatic fluids.

Other mechanical surprises

The behavior of framework materials under pressure is rich, and their response to mechanical stimuli is extremely varied. Pressure is not a scalar component, like temperature, and can thus be applied in an isotropic or an anisotropic manner; and the response of the crystal can also be anisotropic [START_REF] Marmier | ElAM: A computer program for the analysis and representation of anisotropic elastic properties[END_REF]. Pressure can be applied directly, by techniques such as nanoindentation, or through a pressure-transmitting fluid [START_REF] Mckellar | Structural studies of metal-organic frameworks under high pressure[END_REF]. Moreover, in the case of nanoporous solids, the fluid can be either nonpenetrating, or enter the pores of the material -in which case the response will be complex, due to both the fluid intrusion inside the pores [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] Fraux | Forced intrusion of water and aqueous solutions in microporous materials: from fundamental thermodynamics to energy storage devices[END_REF]] and the mechanical stress on the framework. Nonlinear phenomena such as pressure-induced structural transitions and amorphization are relatively common in MOFs. Examples include the pressure-induced cooperative bond rearrangement in ZIF-zni [START_REF] Spencer | Pressure-induced cooperative bond rearrangement in a zinc imidazolate framework: A high-pressure single-crystal X-ray diffraction study[END_REF], proton transfer in ZAG-4 [START_REF] Gagnon | MOFs under pressure: The reversible compression of a single crystal[END_REF][START_REF] Ortiz | Remarkable pressure responses of metal-organic frameworks: Proton transfer and linker coiling in zinc alkyl gates[END_REF], phase transitions induced by polar fluid intrusion (water, methanol, ethanol) in Zn(CN) 2 [START_REF] Lapidus | Exploiting high pressures to generate porosity, polymorphism, and lattice expansion in the nonporous molecular framework Zn(CN) 2[END_REF] and indentation-induced bond rearrangements of a Er-based MOF [START_REF] Spencer | Pressure-induced bond rearrangement and reversible phase transformation in a metal-organic framework[END_REF].

Even in the linear elastic regime, MOFs have potential to show unusual mechanical behavior. One of these is the manifestation of auxeticity, i.e. the presence of a negative Poisson's ratio [START_REF] Evans | Auxetic materials: Functional materials and structures from lateral thinking![END_REF]. "Normal" materials have a positive Poisson's ratio, meaning that under uniaxial tension, they shrink in the perpendicular directions (think of rubber, which gets thinner as it is stretched). Auxetic materials, on the other hand, expand in one or two of the perpendicular axes (see Figure 6). Auxeticity is present for example in porous foams or artificial macrostructures [START_REF] Hughes | Auxetic frameworks inspired by cubic crystals[END_REF], but is relatively rare in crystalline materials [START_REF] Lethbridge | Elastic anisotropy and extreme Poisson's ratios in single crystals[END_REF][START_REF] Dagdelen | Computational prediction of new auxetic materials[END_REF]. Among the known auxetic framework materials, zeolites have probably been the most studied [START_REF] Grima | Do zeolites have negative Poisson's ratios?[END_REF][START_REF] Grima | Natrolite: A zeolite with negative Poisson's ratios[END_REF]. More recently, several MOF frameworks have also been shown to present auxeticity, including MIL-140 [START_REF] Ryder | Isoreticular zirconium-based metalorganic frameworks: discovering mechanical trends and elastic anomalies controlling chemical structure stability[END_REF], ZIF-3 [START_REF] Ryder | Explaining the mechanical mechanisms of zeolitic metal-organic frameworks: revealing auxeticity and anomalous elasticity[END_REF] and ZIF-4 [START_REF] Tan | Quantum mechanical predictions to elucidate the anisotropic elastic properties of zeolitic imidazolate frameworks: ZIF-4 vs. ZIF-zni[END_REF].

All these materials display auxeticity in a few directions of space, but not all. The occurrence of a negative Poisson's ratio in all directions of space is even rarer: for a tension applied in any direction of space, it requires expansion in all perpendicular directions. This phenomenon, called complete auxeticity, can be introduced by design in macroscopic structures such as the Hoberman sphere (see Figure 7); it is, however, extremely rare in single crystals. Siddorn et al. [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] proposed a classification for auxeticity, and analyzed the experimental elastic constants of 471 crystalline materials. They showed that partial auxeticity is present in 37% of cases. In stark contrast, average auxeticity (negative average of the Poisson's ratio over all directions) is only present in one compound, α-cristobalite. Moreover, no material in the experimental database was found to present complete auxeticity.

The same authors surveyed by molecular simulations two hundred pure silica zeolites, and predicted the first known example of complete auxeticity in the JST zeolite framework (see Figure 7). The characteristic structural motif of tetrahedra featuring four "stars of David", which forms the JST framework, produces this unique property of complete auxeticity. Given the larger number of know MOF structures than zeolites frameworks, it is possible that several of them feature complete auxeticity -although they have not yet been identified.

Adsorption properties: contraction, expansion and metastability

The combination of a porous framework and unique large-scale flexibility, displayed by many MOFs, can produce interesting responsive behaviors. There are many reports of MOFs, which display significant transformations following the adsorption (or desorption) of gases or liquids. This includes both crystal-tocrystal and crystal-to-amorphous transitions between different phases of the material. These adsorption-induced deformations and transitions in MOFs can be explained with respect to their structures and the relative enthalpy and entropy of guest adsorption. We note that adsorption-induced contraction and expansion of microporous materials, in itself, is a generic phenomenon that has been observed in a wide variety of materials, including microporous carbons, zeolites and MOFs [START_REF] Gor | Adsorption-induced deformation of nanoporous materials-a review[END_REF].

The flexibility of meta-MOFs, however, permits structural changes on an unprecedented scale upon adsorption, with many materials displaying volume changes of ∆V/V 40% and higher. These phase transformations occurring under adsorption can also be observed in response to other external forces, such as hydrostatic pressure [START_REF] Beurroies | Using pressure to provoke the structural transition of metalorganic frameworks[END_REF][START_REF] Krause | Adsorption contraction mechanics: Understanding breathing energetics in isoreticular metal-organic frameworks[END_REF]. The nature of the structural transitions observed is varied, and can include gate-opening, swelling and breathing behavior as illustrated in Figure 8. The mechanisms for achieving these transitions can involve either a massive transformation of the underlying lattice structure, or changes of orientation of molecular moieties that surround the pore structure [START_REF] Loiseau | A rationale for the large breathing of the porous aluminum terephthalate (MIL-53) upon hydration[END_REF][START_REF] Simon | Statistical mechanical model of gas adsorption in porous crystals with dynamic moieties[END_REF]. In this section we highlight the behavior of MOFs that can undergo adsorption-induced contraction and expansion.

Adsorption-induced contraction

As described earlier, adsorption-induced contraction is a relatively common phenomenon in porous materials, being the rule rather than the exception [START_REF] Gor | Adsorption-induced deformation of mesoporous solids[END_REF][START_REF] Ravikovitch | Density functional theory model of adsorption deformation[END_REF]. However it occurs on a much larger scale in soft framework materials [START_REF] Horike | Soft porous crystals[END_REF]. This is considered a counter-intuitive property, as macroscopic structures tend to follow the inverse trend: think of inflating a tire, or adding water to a dried sponge. However surprising it may be, at the microscopic scale adsorption can provide significant internal stress to a porous framework, which can lead to either shrinking or expansion of the material. The most common behavior is that of a contraction at low to intermediate loading (due to weakly attracting interactions between the adsorbate and host framework), followed by expansion of the material at high loading. Neimark and coworkers pioneered the concept of adsorption stress and demonstrated a rigorous theoretical description of this phenomenon [START_REF] Ravikovitch | Density functional theory model of adsorption deformation[END_REF]. For some reference the magnitude of this stress, for Xe adsorption in the gas phase, at 180 K on the zeolite CaNaX, is approximately 20 MPa (Figure 9). In very confined spaces, at low temperature or in the liquid phase, this stress has been measured to go up to 1 GPa [START_REF] Long | Pressure enhancement in carbon nanopores: a major confinement effect[END_REF]. While for many materials this only produces strains on the order of 10 -3 to 10 -2 (0.1% to 1% change in volume) soft porous crystals, however, are much softer than conventional porous materials [START_REF] Tan | Exceptionally low shear modulus in a prototypical imidazolebased metal-organic framework[END_REF][START_REF] Ortiz | Anisotropic elastic properties of flexible metal-organic frameworks: How soft are soft porous crystals?[END_REF] thus this relatively small stress can produce greater changes in structure.

Interestingly, it was demonstrated more recently that soft framework materials can also exhibit significant softening in parallel with this adsorption-induced contraction. A theoretical study of methane adsorption in model systems of simple geometries (slit pores and diamond-shaped channels) demonstrated a nonmonotonic change in the elastic constant upon fluid adsorption [START_REF] Mouhat | Softening upon adsorption in microporous materials: A counterintuitive mechanical response[END_REF]. For the slit pore system the contraction of the pore volume at low loading is accompanied by a lowering of the Young's modulus, in the direction perpendicular to the pore walls, producing a softer material. This behavior was also observed in the analogous diamond-shaped pore system. The changes to the elasticity of these systems is much greater than changes to the pore geometry. For an elastic modulus of 10 GPa, representative of many MOFs, the variation of mechanical properties is up to 5 GPa (for the change in C 33 in the slit pore system), which is much larger than contraction in pore size (0.6 Å for a slit pore of 15 Å). This was further exemplified by careful examination of molecular dynamics trajectories of a ZIF with nog topology. For this material, the softest elastic deformation mode, λ min , showed softening by a factor of two at low methane loading. Curiously, this study found a similar material, ZIF-8 with sod topology, does not show such a behavior. The softening of porous materials by adsorption is thus potentially widespread, but not universal: it appears that specific materials such as ZIF-8 are resistant, possibly due to their topology.

Experimentally, the softening of materials upon the application of external pressure can be identified by careful analysis of the pressure dependence of the bulk modulus (K ). A negative K indicates that a framework becomes more compressible with increasing pressure and this is considered anomalous for conventional solids. Indeed, following contraction a material is more dense than the original structure, and denser phases are usually stiffer. Chapman et al. suggested negative K values may, however, be relatively widespread in porous materials, where small volume reduction is not sufficient to result in unfavorably close contact of atoms [START_REF] Chapman | Pressure-induced amorphization and porosity modification in a metal-organic framework[END_REF]. As a result of negative K values, a number of open framework materials can exhibit large changes in volume, outside of the elastic regime, because of a "snowball" effect. This provides a pathway for drastic changes in pore volume either by transitions to other crystalline phases of higher density, or by catastrophic pressure-induced amorphization [START_REF] Bennett | Reversible pressure-induced amorphization of a zeolitic imidazolate framework (ZIF-4)[END_REF].

However, adsorption-induced contraction does not always trigger an isotropic or volumetric response, and can induce more exotic phenomena, such as a chiral transformation in the framework. Zhang et al. reported that a chiral deformation of the achiral MOF-5 could be induced by immersion in N-methyl-2-pyrrolidone (NMP), an achiral solvent [START_REF] Zhang | Synthesis of a chiral crystal form of MOF-5, CMOF-5, by chiral induction[END_REF]. Following this study we conducted molecular simulations identifying the specific adsorption of NMP within the pores of MOF-5, demonstrated in Figure 10, which is responsible for this chiral deformation [START_REF] Evans | Microscopic mechanism of chiral induction in a metal-organic framework[END_REF].

Finally, we note that all the examples discussed above relate to physical adsorption of guest molecules in a porous structure. However in some cases, even small molecules can ingress in formally nonporous dense framework materials. Recently, Goodwin and coworkers described negative hydration expansion (NHE) in zirconium tungstate, Zr 2 W 2 O 8 . Though nonporous, this structure can be reversibly hydrated to Zr 2 W 2 O 8 • H 2 O, transforming to a disordered phase that is 20% more dense [START_REF] Baise | Negative hydration expansion in ZrW 2 O 8 : Microscopic mechanism, spaghetti dynamics, and negative thermal expansion[END_REF]. Examination of the correlated translation, rotation and distortion of ZrO 6 /WO 4 study identified "spaghetti-like" displacements of a W-O-W network which are responsible for NHE in this material. The same modes are also involved in the strong negative thermal expansion of Zr 2 W 2 O 8 .

Adsorption-induced expansion

As described in the previous section, unit cell changes induced by adsorption follow a nonmonotonic behavior, where low guest loading may produce contraction and softening, but at higher loading porous materials often expand, dilating to accommodate the adsorption of more guest molecules [START_REF] Meehan | The expansion of charcoal on sorption of carbon dioxide[END_REF].

Gate opening -In many cases this behavior results in a small, continuous expansion in pore volume at high pressure and loading. However, some materials will show a gate-opening process, where at a given gas pressure the material suddenly adsorbs a greater amount -resulting in a steep step in the gas adsorption isotherm. The prototypical gate-opening process was reported by Kitaura et al. for a porous coordination-polymer comprising of interdigitating two-dimensional sheets [START_REF] Kitaura | Porous coordinationpolymer crystals with gated channels specific for supercritical gases[END_REF]. From N 2 adsorption data at 77 K this interdigitated structure appears nonporous, however in adsorption experiments at 298 K the structure shows an sudden increase in adsorption at a specific guest-dependent pressure, as depicted in Figure 11. This transition corresponds to the transformation of the material from a non-porous phase, with BET surface area of 24 m 2 g -1 , to a porous phase with an estimated surface area of 320 m 2 g -1 . This first-order phase transition is achieved by displacement of the sheets, held together by π-π interactions in the evacuated structure, thus producing a porous structure.

Many other structures have been reported to display this gate-opening adsorption process. The main microscopic framework features which can result in gateopening include lattice displacement, movement of framework features and deformation of the metal node. For example, the two-dimensional layers of ELM-11, similar to the material of Kitaura et al., separate at given guest pressure and temperature producing a microporous system and a gate-opening transition [START_REF] Li | Hydrogen bond-regulated microporous nature of copper complex-assembled microcrystals[END_REF]. This system has been extensively studied to provide insight into responsive adsorption phenomena [START_REF] Kondo | Gas adsorption mechanism and kinetics of an elastic layer-structured metal-organic framework[END_REF][START_REF] Tanaka | Modeling and visualization of CO 2 adsorption on elastic layer-structured metal-organic framework-11: Toward a better understanding of gate adsorption behavior[END_REF][START_REF] Kultaeva | Elucidating the formation and transformation mechanisms of the switchable metal-organic framework ELM-11 by powder and single-crystal EPR study[END_REF].

A family of isostructural materials named DUT-8 (comprised of transition metal paddlewheel units with 1,4-benzenedicarboxylate and 1,4-diazabicyclo[2,2,2]octane ligands) shows significant deformation of the paddlewheel unit which permits a large degree of flexibility [START_REF] Klein | Monitoring adsorption-induced switching by 129 Xe NMR spectroscopy in a new metal-organic framework Ni 2 (2,6-ndc) 2 (dabco)[END_REF][START_REF] Bon | Exceptional adsorptioninduced cluster and network deformation in the flexible metal-organic framework DUT-8(Ni) observed by in situ X-ray diffraction and EXAFS[END_REF]. DUT-8(Ni) exhibits gate-opening adsorption processes where a complete collapse after solvent removal is reversible following the adsorption of gas at a specific pressure and temperature.

Local framework dynamics -While most the examples we have discussed above manipulate changes in density to affect the pore volume, rotational dynamics of the framework can also provide a similar adsorption phenomenon without change in the total unit cell volume. This has been widely reported for materials of the ZIF-8 [START_REF] Fairen-Jimenez | Opening the gate: Framework flexibility in ZIF-8 explored by experiments and simulations[END_REF] family, which features a swing effect of imidizolate sub-units allowing for accommodation of more guest molecules and a relatively small step in the gas adsorption isotherm of N 2 at 77 K as demonstrated in Figure 12 [START_REF] Hobday | Understanding the adsorption process in ZIF-8 using high pressure crystallography and computational modelling[END_REF].

As the deformations and dynamics responsible for these transitions occur on a molecular level, it enables tuning this expansion phenomenon by chemical approaches. The swing effect of ZIF-8 can be altered by modifying chemistry of the imidizolate unit, which has a pendant -CH 3 group that can be replaced by other chemical moieties. Recently, Chaplais and coworkers reported the impact of different imidizolate functionality [START_REF] Chaplais | Impacts of the imidazolate linker substitution (CH 3 , Cl, or Br) on the structural and adsorptive properties of ZIF-8[END_REF]. In their work, it was discovered nitrogen adsorption isotherms for the framework composed of Cl functionality (ZIF-8-Cl) showed similar behavior to the original ZIF-8 (ZIF-8-CH 3 ), however the Brfunctionalized system (ZIF-8-Br) displayed a rigid response during gas adsorption. Molecular simulations of the flexible materials, ZIF-8-CH 3 and ZIF-8-Cl, identified that the rotation of the ligand is influenced by the adsorption of N 2 but remains unchanged for ZIF-8-Br. The reordering of adsorbed nitrogen molecules responsible for the swing effect [START_REF] Ania | Understanding gas-induced structural deformation of ZIF-8[END_REF] is unable to occur ZIF-8-Br as the greater Tuning of gate opening -Changes of ligand composition are also able to tune the gate-opening pressure in a series of pillar-layer MOFs, structurally similar to DUT-8. Henke et al. described how, in these materials, the substitution pattern of the ligand sub-unit and the bulkiness and chemical nature of the substituents profoundly affect the structure and energetics of the collapsed pore phase and thus the responsive gate-opening behavior [START_REF] Henke | Directing the breathing behavior of pillared-layered metal-organic frameworks via a systematic library of functionalized linkers bearing flexible substituents[END_REF]. Similarly, DUT-8 can be produced using a variety of transition metals as inorganic nodes, and the degree of flexibility displayed by DUT-8 is dependent on the composition of the paddlewheel [START_REF] Klein | Structural flexibility and intrinsic dynamics in the M 2 (2,6-ndc) 2 (dabco) (M = Ni, Cu, Co, Zn) metal-organic frameworks[END_REF]. For instance DUT-8(Cu) shows rigid behavior and remains open after solvent evacuation, but DUT-8(Zn) will collapse to a different phase and does not expand upon exposure to gas. We note that the underlying chemistry behind the different responses for different metal paddlewheels, as observed in other framework systems [START_REF] Schneemann | Different breathing mechanisms in flexible pillared-layered metal-organic frameworks: Impact of the metal center[END_REF], is not yet well understood.

Recently, McGuirk et al. reported the affects different metals have on the gateopening behavior of the ZIF-7 framework, a zeolitic imidazolate framework with sodalite (SOD) topology and benzimidazolate ligands [START_REF] Mcguirk | Influence of metal substitution on the pressure-induced phase change in flexible zeolitic imidazolate frameworks[END_REF]. A smaller length (or greater strength) of metal-ligand bonds was observed to be correlated with a shift in gate-opening pressure to higher pressure in these materials. However, considerably longer (or weaker) metal-ligand bonds can produce greater flexibility, permitting the formation of different collapsed pore states which in turn also require greater pressure for gate-opening. It is thus clear that the effect of coordination chemistry on framework flexibility is far from simple, with many questions still open.

Metastable transitions

The expansion and contraction of meta-MOF systems usually occur at stable equilibrium, where the contracted or expanded states correspond to lowest free energy structures. Equilibrium transitions between contracted and expanded phases are responsible for established adsorption processes, as described previously, although some small hysteresis around the transition can be observed [START_REF] Ortiz | Predicting mixture coadsorption in soft porous crystals: Experimental and theoretical study of CO 2 /CH 4 in MIL-53(Al)[END_REF]. These processes can also occur out of equilibrium, where the material is able to remain in long-lived metastable states and this can result in novel adsorption phenomena.

Tanaka et al. observed a unique kinetic gate-opening process in a flexible porous coordination polymer comprising of interdigitated sheets of cadmium with benzophenone-4, 4 -dicarboxylate and 4, 4 -bipyridyl ligands [START_REF] Tanaka | Kinetic gate-opening process in a flexible porous coordination polymer[END_REF]. Gas adsorption isotherms for this material showed a sudden increase of adsorption gate-opening pressures concomitant with a decrease in pressure, as can be seen on Figure 13. This process is interpreted as a delayed onset of the traditional gateopening transition because of the particular kinetic behavior of this material. The authors carefully measured the adsorption kinetics and observed the kinetics for the onset of gate-opening does not follow a simple diffusion limited process. Instead this closed phase is first transformed to an intermediate before an open porous phase and during the formation of this intermediate state gas molecules can only condense on the crystal surface, as the crystal remains nonporous. This is able to explain how intermolecular interactions of the guest molecules govern this process and as such the gate-opening pressures observed are not dictated by diffusion.

The initial report from Tanaka et al. suggests similar kinetically delayed gateopening processes should be observed for other gate-opening materials, when gases lacking strong intermolecular forces are used. In fact three doubly interpenetrated MOFs with wine-rack-like topology have been reported to show a similar kinetic gate-opening process with N 2 adsorption [START_REF] Li | The dynamic response of a flexible indium based metal-organic framework to gas sorption[END_REF][START_REF] Su | Redox-switchable breathing behavior in tetrathiafulvalene-based metal-organic frameworks[END_REF][START_REF] Shi | Guest-induced switchable breathing behavior in a flexible metal-organic framework with pronounced negative gas pressure[END_REF]. We note that careful analysis of adsorption kinetics is required to ensure the pressure step is due a long-lived metastable state and not caused by inadequate equilibration.

Similar to gate-opening materials, where the collapsed pore state can remain metastable leading to a drop in pressure when opened, there are also breathing materials where the more porous state is metastable and a release of gas is generated upon the transition to a less porous state. This behavior has been named negative gas adsorption (NGA) [START_REF] Krause | A pressureamplifying framework material with negative gas adsorption transitions[END_REF]. At the time of writing, only two materials have been reported which display this phenomenon: a synthetic faujasite zeolite and a highly porous MOF.

In 1969, Riekert reported the CO 2 and C 2 H 6 adsorption on a HY zeolite, obtained by calcination of NH 4 Y at 400°C [START_REF] Riekert | Instability of sorption complexes in synthetic faujasites[END_REF]. The isotherms show spontaneous desorption of the gas when a critical amount of adsorbate is present. This was attributed to a change of equilibrium positions of the cations by the adsorbate leading to a significant change in the adsorption properties and thus desorption [START_REF] Smith | Crystal structures with a chabazite framework. part v. interpretation of physicochemical properties in terms of the crystal structure[END_REF]. Cation displacement can result in small changes in adsorption properties, however, pore volume changes can produce a much greater change.

The second, and ground breaking material, is DUT-49 which is a MOF constructed from large tetratopic carbazole ligands and copper paddlewheels [START_REF] Stoeck | A highly porous metal-organic framework, constructed from a cuboctahedral supermolecular buildinangew. chem. int. ed.g block, with exceptionally high methane uptake[END_REF]. This material boasts exception porosity with a BET surface area of 5476 m 2 g -1 and pore volume of 2.91 cm 3 g -1 . Investigation of CH 4 and n-butane adsorption at sub-critical temperatures reveal a drastic breathing transition where there is over a 60% change in pore volume as displayed in Figure 14a [START_REF] Krause | A pressureamplifying framework material with negative gas adsorption transitions[END_REF]. Breathing tran- sitions as illustrated in Figure 8e begin with adsorption induced contraction, to a closed pore phase, which at higher loading is followed by adsorption-induced expansion, back to the original open pore phase. Surprisingly, the initial extremely porous phase of DUT-49 remains metastable during adsorption allowing for the pores of the structure to adsorb a significant amount of gas. At the point of NGA the open pore phase has adsorbed much more than is feasible by the closed pore phase and thus this results in a release of gas molecules producing the isotherm profile illustrated in Figure 14b. Detailed in situ measurements and molecular simulation were able to identify the structure of the two phases present in the NGA transition and calculations of their relative enthalpy of adsorption were used to explain the driving force for the massive change in structure. Pore structures with smaller pore size have a substantially stronger affinity for the adsorption of gas than mesopores, like that found in DUT-49. It was demonstrated than the energy gain from adsorption in the low porosity phase offset the energy penalty of structural deformation. As a result this material appears to disobey a general rule of thermodynamics where, at constant temperature, the absolute amount of the adsorbed phase (n ads ) always increases with increasing pressure (p): dn ads /dp ≥ 0. Following this initial study we have continued to explore the process of NGA. Examination of the structural deformation of the ligand sub-unit of DUT-49, using quantum chemistry methods, highlighted a buckling process as depicted in Figure 15 [START_REF] Evans | Origins of negative gas adsorption[END_REF]. This buckling motif is also observed in traditional macroscopic metamaterials and enables a sudden and drastic change in the structure of the framework at a critical stress [START_REF] Ren | Design and characterisation of a tuneable 3D buckling-induced auxetic metamaterial[END_REF]. Recently, an isoreticular analogue of DUT-49 was reported which is observed to be rigid with no breathing or NGA [START_REF] Krause | Adsorption contraction mechanics: Understanding breathing energetics in isoreticular metal-organic frameworks[END_REF]. The analogue, DUT-48, is constructed with a smaller ligand which leads to a smaller pore size. The absence of structural transition in this material is explained due to the greater stress required to buckle shorter beams and a significantly lower adsorption enthalpy difference because the pore size difference between the open pore and deformed pore phase is much less than for DUT-49.

Potential applications

The unique and exotic responses of meta-MOFs provide access to a number of exciting applications [START_REF] Burtch | Mechanical properties in metal-organic frameworks: Emerging opportunities and challenges for device functionality and technological applications[END_REF]. Traditional mechanical metamaterials have found use in advanced applications such as the deployment of satellite solar panels in space [START_REF] Zhai | Origami-inspired, on-demand deployable and collapsible mechanical metamaterials with tunable stiffness[END_REF]. Many meta-MOFs have similar mechanical properties as metamaterials and thus also similar applications but on a nanoscale.

Mechanical energy absorption

Auxetic macroscopic lattice materials have found applications as shock absorbers [START_REF] Greaves | Poisson's ratio and modern materials[END_REF] and similarly MOFs have also been investigated for this application [START_REF] Yot | Metal-organic frameworks as potential shock absorbers: the case of the highly flexible MIL-53(Al)[END_REF]. Nanoscale mechanical systems can be classified depending on the reversibility and hysteresis in the response to mechanical force. This includes shock absorbers, (featuring irreversible compression), dampers (compression-decompression with hysteresis) or molecular springs (compression-decompression without hysteresis). Researchers have combined experiment and simulation to explore the mechanical properties MOFs for use in this context [START_REF] Rogge | Reliably modeling the mechanical stability of rigid and flexible metal-organic frameworks[END_REF].

The wine-rack frameworks MIL-53(Al) and MIL-47(V) have both been investigated for this purpose [START_REF] Yot | Metal-organic frameworks as potential shock absorbers: the case of the highly flexible MIL-53(Al)[END_REF][START_REF] Wieme | Exploring the flexibility of MIL-47(V)-type materials using force field molecular dynamics simulations[END_REF]. These materials are isoreticular and constructed from the same ligands however they differ in metal composition of the metal-oxide one-dimensional chain (aluminium for MIL-53(Al) and vandium for MIL-47(V)). The structure of MIL-47(V) is displayed in Figure 16. MIL-53(Al) requires low hydrostatic pressure of approximately 15 MPa to transform to a closed pore phase and will remain in this phase after the applied pressure is decreased to ambient pressure thus producing a shock absorber-type response. MIL-47(V), however, requires greater applied pressure to transform to a closed pore phase (about 100 MPa) and will return to the initial open pore phase when pressure is decreased with hysteresis, resulting in a shock dampener behavior displayed in Figure 16 [START_REF] Yot | Large breathing of the MOF MIL-47(V IV ) under mechanical pressure: a joint experimental-modelling exploration[END_REF].

The force absorbing responses described above can result in the absorption of significant amounts of energy and for reversible processes this can be stored and released. From the pressures and associated volume changes work energies can be derived by W =

V 2 V 1
PdV. Owing to their large volume changes MOFs are able to store significantly more energy than traditional porous materials such as silicates (11 J g -1 ) [START_REF] Tzanis | Influence of the aqueous medium on the energetic performances of silicalite-1[END_REF]. The systems DUT-48 and DUT-49 can absorb 85 and 106 J g -1 , however, this is irreversible [START_REF] Krause | Adsorption contraction mechanics: Understanding breathing energetics in isoreticular metal-organic frameworks[END_REF].

Recently, this concept of mechanical energy storage was demonstrated beyond bulk measurements by hydrostatic intrustion. Miao et al. reported a study of MOF single crystals under uniaxial compression using in situ transmission electron microscopy [START_REF] Miao | Energy storage during compression of metal-organic frameworks[END_REF]. Under high applied pressures, greater than 8 GPa, the energy absorption of zirconium MOFs, UiO-66 and UiO-67, reach up to 4 kJ g -1 . As a comparison the energy released during an explosion of TNT is about 4 kJ g -1 [START_REF] Sochet | Blast effects of external explosions[END_REF].

Adsorbents with intrinsic heat management

The large volume changes that result in impressive mechanical force absorption can also be used in combination with the exceptional adsorption properties of MOFs to provide state-of-the-art gas storage performance.

In 2015, Mason et al. reported the methane storage performance of iron and cobalt MOFs with the ligand 1,4-benzenedipyrazolate (Fe(bdp) and Co(bdp)) [129]. These materials display a wine-rack topology, similar to MIL-47(V), and demonstrate a gate-opening process at high pressure (approximately 25 bar for H 2 at 77 K) [START_REF] Choi | Broadly hysteretic H 2 adsorption in the microporous metal-organic framework Co(1,4-benzenedipyrazolate)[END_REF]. For CH 4 at 25°C, the gate-opening occurs at 16 bar producing the isotherm profile displayed in Figure 17. The stepped isotherm profile provides extraordinary gas uptake and release within a narrow pressure region providing efficient adsorption-desorption cycling. Moreover, the gate-opening process can intrinsically manage the thermal costs associated with storage and release. Exothermic adsorption and endothermic desorption are often neglected when discussing the performance of a material for gas storage. These processes, however, can produce temperature changes of up to 80°C resulting in a substantial deterioration of adsorption capacity [START_REF] Walton | Natural gas storage cycles: Influence of nonisothermal effects and heavy alkanes[END_REF]. Responsive porous materials are able to use the enthalpy change associated with phase transition to offset the cost of adsorption and desorption. Porous materials with weak interactions with CH 4 generally display adsorption enthalpies of -12 kJ mol -1 to -15 kJ mol -1 [START_REF] Mason | Evaluating metal-organic frameworks for natural gas storage[END_REF], however, for Co(bdp), the differential enthalpy of adsorption at the steepest part of the CH 4 isotherm, where it is likely to be the strongest, is considerably lower at -8.4 kJ mol -1 . This decease in the thermal cost of adsorption is due to the endothermic framework expansion partially offsetting the exothermic heat of adsorption.

The remarkable gas storage performance of Fe(bdp) and Co(bdp) has inspired researchers to consider other materials which display gate-opening pressures for this purpose. Hiraide et al. investigated the ELM-11 system for the capture and storage of CO 2 using molecular simulation [START_REF] Hiraide | Intrinsic thermal management capabilities of flexible metal-organic frameworks for carbon dioxide separation and capture[END_REF]. They observed that the flexible ELM-11 structure can produce a thermal offset, at 298 K, of over 41% and also indicate that intrinsic thermal management is also effective for desorption. Furthermore, ELM-11 displays two steps in the isotherm thus it appears systems which exhibit multiple gate-opening steps are also promising candidates for intrinsic heat management adsorbents. The previously discussed ZIF-7 analogs reported by McGuirk et al. were also investigated for this purpose and the heat released from CH 4 adsorption at in ZIF-7 and ZIF-9 was observed to be offset by between 18 and 20% [START_REF] Mcguirk | Influence of metal substitution on the pressure-induced phase change in flexible zeolitic imidazolate frameworks[END_REF]. The above highlight only a few of the possible applications of meta-MOFs and related materials. The unique behavior exhibited by these materials provide boundless opportunity. This is especially true for materials that display changes in phase upon the application of stimuli, which show promise for the development of novel switches.

Summary and perspectives

Throughout this review we have described many notable examples from materials that display unusual mechanical, thermal, and adsorption-driven phenomena. These include properties such as negative compressibility, complete auxetic-ity, negative thermal expansion, gate opening and negative gas adsorption. If one were to look back at the process of discovery of these novel and exotic behaviors in framework materials, one would find that it was in all cases a product of chance. Though there has been a large body of work on the understanding of the microscopic roots of the phenomena, and similarly a significant effort spent on tuning and modification of this behavior, the process of identification of novel meta-MOFs is still wide open. Finding these needles in the haystack, which is the ever growing number of known MOF materials, is an enormous challenge.

Observations show that many of the materials we classify as meta-MOFs share common traits in ligand composition or topology, which provide some guidance to the design of targeted "unusual" responses. Many MOFs which share similar structural features, however, are not reported to exhibit the same bizarre properties. One possible reason behind that fact, often overlooked, is the realization that crystal size has a significant influence on flexibility [START_REF] Sakata | Shape-memory nanopores induced in coordination frameworks by crystal downsizing[END_REF][START_REF] Krause | The effect of crystallite size on pressure amplification in switchable porous solids[END_REF]. Moreover, kinetics of the structural transitions can also affect the response of these materials, with the presence of spatial transient state [START_REF] Kondo | Trapping of a spatial transient state during the framework transformation of a porous coordination polymer[END_REF]. Finally, the presence of defects in the crystalline structure -and the possibility of disorder -can strongly affect the material's response as well [START_REF] Cheetham | Defects and disorder in metal organic frameworks[END_REF]. Nevertheless, these effects of crystal size, kinetics, defects and disorder are currently not well understood and may represent a barrier to the discovery of novel responsive materials and anomalous properties. Yet, they could also provide a unique approach to tuning a material's response.

Going beyond this view from the "eye of the chemist" is necessary to generate more systematic approach to discovery. For more conventional properties, largescale computational screening of databases of real and hypothetical materials have shown to be useful tools, e.g., for the selection of inorganic materials with potential for water splitting applications [START_REF] Davies | Computational screening of all stoichiometric inorganic materials[END_REF], or porous materials with high capacity for specific gases [START_REF] Colón | High-throughput computational screening of metal-organic frameworks[END_REF]. For meta-MOFs, no large-scale screening study has been published so far -however, it is clear from the examples above that computer simulations, in combination with experimental characterization techniques, play a vital role in the our understanding. Current progress towards multiscale modeling will provide unparalleled understanding of these complex systems on a wide range of length and timescales [START_REF] Fraux | Recent advances in the computational chemistry of soft porous crystals[END_REF], and thus be applicable to the design of novel materials or large-scale screening of novel properties for known materials.

Figure 1 :

 1 Figure 1: (a) Two-dimensional structure of a microwave cloak illustrating the structure of the splitring resonator features. This includes a plot showing the material parameters of permeability (µ) and permittivity (ε). (b) Electron micrograph of a mechanical metamaterial with extremely large bulk modulus and low shear modulus fabricated by laser lithography. Reproduced with permission from Refs. 10 and 12

Figure 2 :

 2 Figure 2: Local and framework features that are used in the construction of mechanical metamaterials, and similar motifs which are observed in meta-MOFs.

Figure 3 :

 3 Figure 3: Simple dense materials based on pair interactions display positive thermal expansion due to anharmonicity of the pair interaction potential. Framework materials, however, show very different vibrational modes, which produce a shortening of the distance between nodes.

Figure 4 :

 4 Figure 4: (a) The molecular components of ZIFs which can generate diverse structural topologies. (b) Thermal expansion coefficients of ZIF frameworks with varying topology (LTL, MER, DFT, CAN, nog, SOD, cag, coi, and FAU). Values for some other MOFs are reported for comparison: MOF-5, MOF-C22, and [Ag(en)]NO 3 . Reproduced with permission from Ref. 42 and Ref. 41

Figure 5 :

 5 Figure 5: Framework materials featuring negative linear compressibility. Top to bottom: MIL-53, [NH 4 ][Zn(HCOO) 3 ] and Zn[Au(CN) 2 ]. Reproduced with permission from Refs. 47, 48 and 49

Figure 6 :

 6 Figure 6: Illustration of the sign of a material's Poisson's ratio.

Figure 7 :

 7 Figure 7: (top) Hoberman Twist-O,[74] a variant of the Hoberman sphere, a macroscopic structure with complete auxeticity (loonie for scale). (bottom) JST zeolite framework, featuring complete auxeticity, and its characteristic assembly of four "stars of David" into a tetrahedron. Reproduced with permission from Ref. 75.

Figure 8 :

 8 Figure 8: Illustrations of transitions that are induced by adsorption stresses. (a) Swelling, (b) gateopening by ligand dynamics, (c) lattice deformation, (d) lattice displacement and (e) breathing by lattice deformation.

Figure 9 :

 9 Figure 9: (a) Experimental (points) and calculated (line) adsorption isotherms of xenon on zeolite CaNaX at 180 K. (b) Experimental strain (points, right vertical axis) and calculated solvation pressure or adsorption stress (line, left vertical axis) as a function of the pressure. Reproduced with permission from Ref. 82.

Figure 10 :

 10 Figure 10: (a, b) DFT optimizations for a widely used solvent molecule, dimethylformamide, and (c,d) NMP within the MOF-5 structure. (a,c) Extent of chiral induction on the framework structure. (b,d) The distinct local ordering of guest molecules. Reproduced with permission from Ref. 89.

Figure 11 :Figure 12 :

 1112 Figure 11: (a) Structure of the interdigitating two-dimensional sheets of Cu(dhbc) 2 (4,4 -bpy), with hydrogens removed for clarity; dhbc = 2,5-dihydroxybenzoate, bpy = bipyridine. (b) Nitrogen adsorption isotherms at 298 K where the blue and red dashed lines correspond to Langmuir plots fit in the high and low pressure ranges, respectively. (c) Adsorption isotherms of N 2 , CH 4 , CO 2 and O 2 at 298 K. Adsorption and desorption is displayed by open and filled symbols, respectively. Reproduced with permission from Ref. 93.

Figure 13 :

 13 Figure 13: (a) Adsorption isotherms at 90 K for 1) O 2 adsorption, 2) N 2 and 3) Ar, in Cd(bpndc)(bpy) (where bpndc = benzophenone-4,4 -dicarboxylate, bpy=4,4 -bipyridyl). Adsorption is illustrated by open symbols and desorption by filled symbols. The O 2 adsorption isotherm at low pressure is displayed inset. Pressure versus time graphs from (b) point x to point y of the inset displayed in (a), and (c) from point y to point z. (d) Structural description of the identified kinetic pathway for this gate-opening process. Reproduced with permission from Ref. 110.

Figure 14 :Figure 15 :

 1415 Figure 14: (a) Illustration of the structural transition and phases responsible for NGA in DUT-49. (b) The experimental isotherm of DUT-49 during methane adsorption at 111 K and expected isotherm for a rigid material, calculated by molecular simulation (blue and red, respectively).Reproduced with permission from Ref.[START_REF] Evans | Origins of negative gas adsorption[END_REF].

Figure 16 :

 16 Figure 16: (a) The structural transition exhibited by MIL-47(V), and other wine-rack frameworks. (b) Cumulative volume of intruded mercury for two intrusion/extrusion cycles as a function of the applied pressure as obtained for MIL-47(V). Reproduced with permission from Ref. [125].

Figure 17 :

 17 Figure 17: (a) CH 4 adsorption isotherm for Co(bdp) at 25°C. (b) Expected adsorption behavior for a traditional microporous material (red) and stepped adsorption material (green). Materials with stepped adsorption profiles have greater usable capacities than traditional porous materials for a pressure swing process (between P ads and P des ) as indicated by the arrows. Reproduced with permission from Refs. 129 and 108.

Acknowledgments

We thank Marc-André Delsuc for the gift of the Hoberman Twist-O sphere displayed in Figure 7.


Dr Jingjing Yan

Prof. Dr John C Macdonald

Alex R Maag

Prof. Dr François-Xavier Coudert

Prof. Dr Shawn C Burdette
email: scburdette@wpu.edu

MOF Decomposition and Introduction of Repairable Defects Using a Photodegradable Strut

Keywords: Metal Organic Framework, Photodecomposition, Ligand Exchange Reactions, Density Functional Theory, X-ray Crystallography

Photoswitchable components can modulate the properties of metal organic frameworks (MOFs); however, photolabile building blocks remain underexplored. A new strut NPDAC (2-nitro-1,4phenylenediacetic acid) that undergoes photodecarboxylation has been prepared and incorporated into a MOF using post-synthetic linker exchange (PSLE) from the structural analogue containing PDAC (p-phenylenediacetic acid). Irradiation of NPDAC-MOF leads to MOF decomposition and concomitant formation of amorphous material. In addition to complete linker exchange, MOFs containing a mixture of PDAC and NPDAC can be obtained through partial linker exchange. In NPDAC30-MOF which contains approximately 30% NPDAC, the MOF retains crystallinity after irradiation, but the MOF contains defect sites consistent with loss of decarboxylated NPDAC linkers. The defect sites can be repaired by exposure to additional PDAC or NPDAC linkers at a much faster rate than the initial exchange process. The photoremoval and replacement process may lead to a more general approach to customizable MOF structures.

Introduction

The large void spaces and high surface areas within metalorganic frameworks (MOFs) make them appealing for a wide variety of applications in storage, [1] sequestration [START_REF] Puthiaraj | Postcombustion Carbon Dioxide Capture Materials[END_REF] and separations. [START_REF] Qiu | [END_REF] With the notable exception of recent interest in flexible systems, [4] most MOFs applications take advantage of the rigid structures to achieve the desired properties; however, the scope of possible applications would be expanded if MOFs could be designed to respond to external stimuli. Incorporating azobenzene ligands onto the side chains of struts can create photoresponsive MOFs.

Azobenzene cis←trans photoisomerization provides a technique to block MOF channels; [5] however, azobenzene isomerization is nearly [6,7] or completely [8,9] restricted when the ligand is utilized as a structural support. Moreover, photochromic diarylethene derivatives have been incorporated as MOF struts, and local framework movement can be achieved by diarylethene ring opening and closing, [10][11][12] but the framework change is minimal and the MOF skeleton is retained. Alternatively, photolabile protecting groups on side chains can be removed to control channel access, [13,14] but the extent to which strut photolysis has been explored is limited.

MOFs are susceptible to degradation under acidic conditions, or when exposed to strongly coordinating molecules, due to linker protonation and displacement respectively. Although these and other processes of structural breakdown are impediments in some fields, MOF decomposition can be exploited for molecular release in applications such as drug delivery. [15] Most MOFs designed for drug delivery are engineered to respond to the acidic compartments in the cell cytoplasm or in lysosomes. [16,17] In the absence of pH changes however, the options for triggered release of guest from MOFs are restricted. As with MOF side chains, the most convenient approach to controlled degradation would be light-mediated processes.

Light degradable materials have been studied extensively, [18- 20] but there are limited examples of MOF photodecomposition. While complexes that release metal ions in response to light are relatively common [21,22] including photocaged complexes that release zinc upon decarboxylation, [23] the analogous photochemistry has not been explored extensively in MOFs. Photodecarboxylation in a benzothiadiazole-derived MOF led to detectable structural changes and differences in gas adsorption although the experimental data for the proposed behavior not definitive, [24] and an azobenzene-containing MOF reportedly degrades upon irradiation; [25] however, irradiation only accelerates the basal rate of decomposition. Local and dynamic structural modulation upon irradiation has been reported with MOFs [6] and COFs [7] containing photoswitchable struts; however, direct evidence for the changes are limited. Inspired by our earlier studies on molecule release triggered by photodecarboxylation of a capping on MOF surface, [26] we envisioned incorporating photolabile dicarboxylates as struts to facilitate photodegradation of MOFs. Although benzoic acids typically used in MOF synthesis are quite photostable, we hypothesized that photoactive phenylacetic acids derivatives could be incorporated in MOF structures and provide access to degradable materials. silica (200-400 mesh). TLCs were developed by using mixture of dichloromethane (DCM) and methanol (MeOH). 1 H and 13 C NMR spectra were recorded with a 500 MHz Bruker Biospin NMR instrument. FT-IR spectra were recorded using Bruker Vertex70 Optics FT-IR spectrometer equipped with a Specac Golden Gate attenuated total reflection (ATR) accessory by collecting 256 scans over a scan range from 4000 to 600 cm - 1 at 4 cm -1 resolution. Elemental microanalyses for C, H, and N were performed by Micro Analysis Inc. (Wilmington DE). Thermogravimetric analysis (TGA) measurements were carried out on a TA Instruments Hi-Res TGA 2950 Thermogravimetric Analyzer from room temperature to 800 °C under nitrogen atmosphere at a heating rate of 10 °C/min. LC/MS was carried on a Single Quadruple, Agilent Technologies 1200 series LC system. High resolution mass spectra were obtained at the University of Notre Dame mass spectrometry facility using microTOF instrument operating in positive ionization mode. Melting-point information was obtained using a Hydrothermal Mel-Temp instrument.

2-Nitro-1,4-phenylenediacetic acid (NPDAC, 2)

. Concentrated sulfuric acid (5 mL) and p-phenylenediacetic acid (0.300 g, 1.54 mmol) were combined at 0 °C, and concentrated nitric acid (0.5 mL) was added dropwise to the mixture. After stirring in the dark for 1 h, the reaction mixture was added dropwise to ice (200 g), and the product was extracted into EtOAc (2 × 100 mL). The combined organic layers were washed with saturated NaCl (2 × 100 mL), dried over Na2SO4 and the solvent was removed to yield the product as a light-yellow powder without further purification (0.280 g, 76.1% yield). TLC Rf = 0.41 (silica, 6.5:1, DCM/MeOH). Mp = 246-248 °C. [Zn(PDAC)(4,4'-bipyridyl)•CH3OH]n (PDAC-MOF). PDAC-MOF was prepared at room temperature by modifying the reported solvothermal synthesis. [27] Sodium hydroxide (8.00 mg, 0.200 mmol) was added to a solution of p-phenylenediacetic acid (19.4 mg, 0.100 mmol) and 4,4'bipyridine (15.6 mg, 0.100 mmol) in 1 mL of MeOH/H2O (4:1). The solution was layered with MeOH (5 mL) to induce slow mixing with a third layer of MeOH (1 mL) containing zinc nitrate tetrahydrate (Zn(NO3)2 • 6 H2O 226 mg, 0.100 mmol) for 5 d to yield colorless needles (33. [Zn(NPDAC)(4,4'-bipyridyl)•CH3OH]n (NPDAC-MOF). NPDAC (215 mg, 0.900 mmol) and NaOH (72.0 mg, 1.80 mmol) were dissolved in 10 mL MeOH to prepare a 0.090 M NPDAC sodium salt solution. Crystalline PDAC-MOF (20.0 mg, 45.0 µmol) was immersed in 5 mL MeOH, and 5 mL of NPDAC sodium salt solution (0.090 M) was added. The mixture was kept in dark for 7 d to yield colorless needles suitable for X-ray analysis (16.7 mg, yield 83.2%). FT-IR (neat, cm -1 ) 2918. The ligand composition of the resulting MOF crystals was determined by 1 H NMR after digesting the crystals with D2SO4 in DMSO-d6, which show 100% of the original PDAC was replaced by NPDAC. TGA shows a 16.5% weight loss between 23-46 °C, which may correspond to absorbed solvent. Decomposition occurs at 112 °C. Brunauer-Emmett-Teller shows a surface area of 6.3 m 2 g -1 for N2 molecules. NPDAC30-MOF. PDAC-MOF crystals (20.0 mg, 45.0 µmol) were immersed in 5 mL MeOH, and combined with 1.5 mL of NPDAC sodium salt solution (0.090 M) and 3.5 mL additional MeOH. The mixture was kept in dark for 7 d to induce linker exchange. The ligand composition of the resulting MOF crystals was determined by 1 H NMR after digesting the crystals with D2SO4 in DMSO-d6, which show approximately 30% of the original PDAC was replaced by NPDAC.

Gas sorption. Gas sorption was performed using an ASIQ iQ Quantachrome Instrument by adding degassed of PDAC-MOF, NPDAC-MOF or photolyzed NPDAC30-MOF (30 mg) and increasing the temperature at 2 °C min -1 with 15-min temperature holds at 60, 80, 100 and 120 °C before increasing to 150 °C, where the temperature was maintained for 11 hours. Nitrogen was dosed as the adsorbate into the sample cell cooled with liquid N2 and 50 isothermal P/P0 points ranging from 6 × 10 -6 to 0.95 followed by 15 desorption points between P/P0 of 0.95 to 0.1 were obtained. Each surface area was determined by applying the Brunauer-Emmett-Teller (BET) method to model the adsorption isotherm between P/P0 of 0.15 to 1.

X-ray Crystallography. Structural analysis was carried out in the X-Ray Crystallographic Facility at Worcester Polytechnic Institute. Crystals were glued on tip of a glass fiber or were covered in PARATONE oil on 100 μm MiTeGen polyimide micromounts and were mounted on a Bruker-AXS APEX CCD diffractometer equipped with an LT-II low temperature device. Diffraction data were collected at room temperature using graphite monochromated Mo-Kα radiation (λ = 0.71073 Å) using the omega scan technique. Empirical absorption corrections were applied using the SADABS program. [28] The unit cells and space groups were determined using the SAINT+ program. [28] The structures were solved by direct methods and refined by full matrix least-squares using the SHELXTL program. [29] Refinement was based on F 2 using all reflections. All nonhydrogen atoms were refined anisotropically. Hydrogen atoms on carbon atoms were all located in the difference maps and subsequently placed at idealized positions and given isotropic U values 1.2 times that of the carbon atom to which they were bonded. Hydrogen atoms bonded to oxygen atoms were located and refined with isotropic thermal parameters. Mercury 3.1 software and Diamond Version 3.1d were used to examine the molecular structure. Relevant crystallographic information is summarized in Table 1, and the 50% thermal ellipsoid plots are shown in Figure 1A.

Powder X-ray diffraction. PXRD data were collected on a Bruker-AXS D8-Advance diffractometer using Cu-Kα radiation with X-rays generated at 40 kV and 40 mA. Bulk samples of crystals were placed in a 20 cm × 16 cm × 1 mm well in a glass sample holder, and scanned at RT from 3° to 50° (2θ) in 0.05° steps at a scan rate of 2°/min. Simulated PXRD patterns from single crystal data were compared to PXRD patterns of PDAC-MOF and NPDAC-MOF to confirm the uniformity of the crystalline samples. General Spectroscopic Methods. All aqueous solutions were prepared from Millipore (BiopakTM Ultrafiltration Cartridge) water. All organic solutions were prepared using spectroscopic grade solvents. UV-vis absorption spectra were obtained by taking sample solutions in 1.0 cm quartz cuvette at 23 °C with total volumes kept at 2 mL or 3 mL, and recorded on Thermo Scientific Evolution 300 UV-vis spectrometer with inbuilt Cary winUV software. Photolysis was carried at 23 °C in 1.0 cm quartz cuvette illuminated by 3 W UV LED (Mouser Electronics, 365 nm, 200 mW) powered by a 700 mA LuxDrive FlexBox using a variable DC source set at 12 VDC. Rate of photolysis and photoproducts were analyzed using LC/MS (Single Quadrupole, Agilent Technologies) by monitoring at changes at 277 nm.

Quantum Efficiency and Photoproducts Determination. A 2 mL solution of NPDAC (15 mM) in MeOH (5% H2O) was prepared from a 45 mM stock solution and exposed to a LED UV irradiation for 60, 180, 360, and 600 s. A fresh 2 mL solution was used for each time interval irradiation, and 100 μL of ketoprofen in MeOH (100 mM) was added as internal standard before subjecting samples to LC-MS analysis. The quantum efficiency was calculated following established procedures. [29] The photoproducts were confirmed using HPLC and 1 H NMR analysis. All the samples were eluted using an isocratic mixture of 95:5 CH3CN:H2O containing 0.1% formic acid at a flow rate of 0.3 mL/min. The identity of individual peaks that are labeled from 2-5 in the HPLC traces in Figure 3 were identified by m/z values in the mass spectrum. Bulk photolysis of NPDAC was carried out by dissolving NPDAC (23.9 mg, 0.100 mmol) in 2 mL D2O containing NaOH (8.0 mg, 0.20 mmol). The solution was irradiated with 365 nm light for 35 min. The D2O mixture was analyzed by 1 H NMR spectroscopy, and then extracted successively with 2 mL hexanes and 2 mL DCM, and the combined organic phase was removed. The combined organic-soluble extracts were dissolved in CDCl3 and the 1 H NMR was recorded.

Photolysis of NPDAC-MOF. NPDAC-MOF (5.00 mg, 11.2 µmol) was immersed in MeOH (2 mL), kept in dark for 2 h, and UV-vis absorption spectra was recorded. The mixture was exposed to 365 nm of light for 2 h in total, the first 1 h without stirring and the second hour with stirring. After 10 min of irradiation, the mixture was removed to the dark for 30 min before measuring the absorbance of the supernatant liquid. This process was repeated after total irradiation times of 20, 30, 45 and 60 min (3.5 h elapsed). After irradiation, the solution was filtered through glass wool, and LC-MS analysis was performed on the filtrate using ketoprofen as an internal standard. The sample was eluted using an isocratic mixture of 95:5 CH3CN:H2O containing 0.1% formic acid at a flow rate of 0.3 mL/min, and the absorbance at 277 nm was monitored.

Defects Creation and MOF Repair. NPDAC30-MOF (20 mg) was as immersed in MeOH (2 mL). The mixture was irradiated (365 nm) with stirring for 2 h. The resulting material was isolated, rinsed with MeOH, and divided into two equal portions. The two samples were immersed in 5 mL MeOH containing 135 µmol PDAC or 1.5 mL NPDAC sodium salt solution (0.090 M) combined with 3.5 mL MeOH for 1 d. The materials were isolated and crystallinity was verified by PXRD. The ligand composition of the resulting MOF crystals was determined by 1 H NMR after digesting the crystals with D2SO4 in DMSO-d6.

Computational methods. Quantum chemistry calculations were performed using a density functional theory (DFT) approach on the periodic structures with full accounting for symmetry and all-electron localized basis sets [30,31] using the CRYSTAL14 software. [32] Calculations were performed at the generalized-gradient approximation (GGA) level, with the PBEsol exchange-correlation functional. [33] Long-range dispersion interactions were taken into account using the Grimme "D2" dispersion correction scheme. [34] The k-point mesh was generated using the Monkhorst-Pack method, with a 2 × 2 × 2 supercell. Given the layered nature of the structure, we performed each energy minimization with respect to atomic positions only, with fixed unit cell parameters, and varied the value of the a lattice parameter in an external loop. Representative input files are available online in the data repository at https://github.com/fxcoudert/citable-data..

Results and Discussion

Since multicarboxylates, specifically dicarboxylate struts like 1,4-benzenedicarboxylic acid (BDC), are nearly ubiquitous in MOFs, we envisioned designing a light-reactive dicarboxylate ligand as the photoreactive MOF unit. We recently exploited the photochemistry of meta-nitrophenylacetic acid (m-NPAA) derivatives to design zinc photocages [23] and photocapping groups, [26] so we hypothesized that a similar functional group could be adapted to construct the desired photodegradable strut. Although much less common than BBC, para-phenylenediacetic acid (PDAC) has been used to construct MOFs with [35,36] and without bipyridine groups. [27] In contrast to BDC as well as other related benzoic acids, the methylene spacer between the aryl and carboxylic acid groups means that PDAC is more flexible, and the diacid strut must adopt a non-planar carboxylate-carboxylate arrangement between metal nodes. This structural flexibility likely explains the limited number of MOFs reported using PDAC-like ligands. Selective nitration of PDAC yielded the desired photoactive linker NPDAC in 76% yield, since mono-nitration deactivates the ring to further electrophilic aromatic substitution reactions (Scheme 1). Upon exposure to light, NPDAC decomposes to provide a mixture of photoproducts that includes 4-methyl-2nitrophenylacetic acid (3) with m/z 194.1, 2-nitro-p-xylene (4) with m/z 302.0 as a dimer ion, and 4-methyl-2-nitrobenzaldehyde (5) with m/z 164.0, which was determined by LCMS analysis and verified by NMR. Bulk photolysis of NPDAC in D2O also was monitored by 1 H NMR. After 35 min of irradiation, the 1 H NMR shows a mixture of NPDAC and one major photoproduct, 4methyl-2-nitrophenylacetic acid (3) that is produced by the photodecarboxylation characteristic of m-NPAA compounds. [37,38] Several minor unidentifiable photoproducts also are observable. During the irradiation, the clear yellowish solution became opaque, which indicates the possible formation of hydrophobic photoproducts. After extracting the mixture with hexane and then DCM, two additional photoproducts were recovered. Photoproduct 4 corresponds to a second photodecarboxylation at the ortho position. While decarboxylation ortho-NPAA was anticipated, [37] the exact pathway that leads to the aldehyde 5 remains unclear. Under aerobic conditions however, ortho-and para-nitrotoluene derivatives are susceptible to oxidation, and the photolysis conditions are amenable to radical formation, which could account for the observed photoproduct. [39][40][41][42] Phenylacetic acids also can be converted directly to benzaldehyde derivatives with various reagents, [43][44][45] so the presence of 5 is unremarkable.

A photolysis quantum yield (Φphotolysis) of 33% was calculated by quantifying the disappearance of NPDAC over the course of the reaction using LCMS.

The NPDAC ligand exhibited the desired photodecarboxylation chemistry, but initially we were unable to access a MOF due to apparent decomposition of NPDAC strut during the solvothermal synthesis conditions used to prepare PDAC-MOF. [27,35] In order to avoid thermal decomposition, we examined solvent layering techniques to prepare PDAC-MOF crystals as a facile alternative to high temperature conditions. The PDAC-MOF framework we obtained at room temperature exhibits an identical semi-pillared paddle-wheel (sppw) structure as previously reported, but with an improved R value. [35] Solvent layering techniques however, failed to produce crystalline material when PDAC was replaced with NPDAC.

Owing to the failure of direct synthetic methods, we explored post-synthetic linker exchange (PSLE) as a different strategy to prepare a photodegradable MOF. PSLE has been applied successfully to prepare MOFs that resist de novo syntheses, [46][47][48] and as a strategy to prevent framework interpenetration. [49,50] When MOFs are introduced into a concentrated solution of the new ligand with similar shape and coordination requirements to existing structural components, small energy differences between the two different linker analogues in the heterogeneous reaction create dynamic equilibrium necessary for interconversion. Exposure of PDAC-MOF to a ten-fold excess of NPDAC with respect to PDAC resulted in the isolation colorless needles of NPDAC-MOF after 7 days (Scheme 2A). Given the unusual structure requirements of PDAC/NPDAC struts, we would not anticipate the PSLE process would result in well-defined materials when used in conjunction with other common MOF structural motifs. Single crystal X-ray analysis revealed nearly identical cell parameters for PDAC-MOF and NPDAC-MOF. Like PDAC-MOF, the framework of NPDAC-MOF adopts a sppw structure (Figure 1A). Unlike typical pillared-paddle wheel structures, the two carboxylates are not in the same plane, forming a tilted paddle wheel with one NPDAC ligand facing up and the other facing down. An extended three-dimensional structure is shown in Figure 1B, with yellow octahedra representing Zn 2+ atoms ligated by four oxygen and two nitrogen atoms. The nitro group on each dicarboxylate ligand is disordered in the X-ray structure; however, the digested 1 H NMR and LCMS experiments indicate the complete replacement of PDAC by NPDAC. The X-ray structure also reveals MeOH guest molecules contained within the NPDAC channels, which are quite narrow.

To understand how the linker exchange could take place in a PDAC-MOF that has limited space for diffusion into the coordination network, we performed quantum chemistry calculations on this structure. Upon removal of the encapsulated solvent molecules, we calculated the response of the resulting P-1 layered structure to strain along the crystallographic a axis, which is perpendicular to its layers. The resulting energy profile is shown in Figure 2, and it clearly demonstrates the very "soft" nature of the PDAC-MOF along the a axis. Large variations of unit cell size are possible, up to 14% upon presence or absence of solvent molecules, with moderate energetic cost. Moreover, the smaller curvature of the energy profile at large a values, shows that the elastic modulus of the material in this region is smallfrom a fit of that part of the curve, we can estimate a Young's modulus of 0.8 GPa, comparable to highly flexible framework materials. [51,52] This flexibility explains how linkers can easily A B diffuse in, through, and out of the MOF during the post-synthetic linker exchange process, even though based on purely geometric considerations of the experimental structure, diffusion of PDAC and NPDAC is expected to be very slow. This presence of "swollen" solvated phases in soft porous crystals, where diffusion is enhanced, has been demonstrated in several other materials in the past. [53,54] Figure 2. Variation of energy ∆E as a function of strain applied along the a axis of a PDAC-MOF, from DFT calculations. The strain is calculated with reference to the experimental PDAC-MOF cell parameters, and the lowest-energy structure (at strain -14%) is taken as energy reference.

The NPDAC-MOF obtained by PSLE appears to be stable indefinitely in the absence of light when stored in MeOH. Upon exposure to UV light however, several photoproducts were detectable by UV-vis spectroscopy and LCMS (Figure 3). The increase in absorbance centered at 240 nm corresponds to 4,4'bipyridine, which is consistent with fragmentation of the paddle wheel sheets and release of the pillars. Like NPDAC ligand, three new peaks appear in the LC trace, corresponding to same three products of photodecarboxylation in addition to the 4,4'-bipyridine peak. Irradiation of PDAC-MOF under identical conditions reveals no evidence of decomposition. The photoreaction also can be monitored by PXRD. Initially, the NPDAC-MOF powder pattern simulated from using the single crystal data shows good agreement with predicted reflections. After 1 h of irradiation the disappearance of Bragg diffraction at 2θ between 7-13° and 15-25°, along with the broadening of diffraction peaks, suggests decreasing crystallinity and increasing amorphization. All the Bragg diffraction peaks disappear after 2 h of irradiation, and two broad diffraction peaks at 2θ = 5-10° and 15-30° appear, which indicates of complete phase change from crystalline to amorphous.

A light-digestible MOF has many possible intriguing applications such as a delivery vehicle for chemical reagents or therapeutic agents. Although the channels in NPDAC-MOF are relatively narrow, we have evidence that the material is flexible, so this may not necessarily preclude inclusion of medium-sized molecules. The necessity of using a NPAA group to achieve the photodecarboxylation currently limits the library of available MOF structures that can be rapidly accessed. Further development of our photodegradable MOF strategy will require exploring heretofore unknown structures prepared from new synthetic struts containing NPAA functional groups. Although we hope to expand the library of photodegradable MOF structures by developing a general design strategy for successfully using these flexible struts in the future, we sought to use the current model systems to explore the potential to semi-rationally modify the contents and properties of an assembled MOF. The original PSLE conditions used to prepare NPDAC-MOF suggested no incomplete strut replacement; however, reducing the excess of NPDAC in the PSLE reaction yields mixed PDAC/NPDAC MOFs. Specifically, by employing a 3-fold excess of NPDAC instead of a 10-fold excess, the digested 1 H NMR suggested approximately 30% of PDAC in PDAC-MOF had been replaced by NPDAC (NPDAC30-MOF). We hypothesized that if a PDAC-MOF contained a sub-stoichiometic amount of a photodecomposable ligand, the reactive strut could be removed while retaining a stable or semi-stabile MOF structure. Furthermore, we would be able to observe evidence of vacancies with analytical techniques such as gas adsorption.

After extended irradiation of NPDAC30-MOF, no amorphous material was detected by PXRD; however, NMR analysis revealed the NPDAC content decreased from 30% to 16% after acid digestion. Currently, there does not appear to be a suitable analytical technique to map the NPDAC substitution pattern, or subsequent vacancies introduced within NPDAC30-MOF by photolysis. We suspect NPDAC groups nearer to the surface of the MOF are more efficiently removed since refracted light can be absorbed by bipyridine and PDAC groups within the lattice, thereby reducing the amount of light penetrating deep into the crystalline material capable of photolyzing internal NPDAC groups. The photolysis of NPDAC30-MOF resulted in a significant changes in the MOF surface area as measured by N2 adsorption using the BET method. NPDAC-MOF and PDAC-MOF exhibit nearly identical surface areas of 6.3 and 6.6 m 2 /g, respectively. After photolysis however, the surface area of NPDAC-30 measured 99 m 2 /g, an increase consistent with defects created within the MOF by strut photolysis and loss. Although photolysis of NPDAC30-MOF creates more surface area, the absolute value is over an order of magnitude smaller than that measured in many familiar MOFs.

The ability to create defects in MOF structures is of increasing interest, [55] and there are a few examples of filling such vacancies by introducing additional struts. [56,57] To further explore the properties of the vacancies created in NPDAC30-MOF, an irradiated sample was divided into two equivalent portions, which were then immersed in solutions containing either 3-fold excess PDAC or NPDAC for 1 d. The digested 1 H NMR shows the NPDAC content in the first portion is 32% and in the second portion is 13%. These experiments suggest that a photolyzed NPDAC30-MOF can be efficiently reconstituted under facile conditions since the amount of NPDAC present after immersion is identical to that found in the original NPDAC30-MOF sample within experimental error (32% vs 30%). The decreased NPDAC (13% vs 30%) and increased PDAC content after reconstituting the irradiated NPDAC30-MOF with PDAC further supports the reconstitution model (Scheme 2B). The NPDAC percentage in both portions of the reconstitution experiment corresponds to the theoretical content if all the defect sites were filled by one of the two ligands. Since the reconstitution process is significantly faster than the original PSLE synthesis, we hypothesize that the MOF structural flexibility provides ready access to the vacancies created by photoysis. Although the filling of open sites should be faster, we cannot yet rule out the possibility of substitution reactions at intact sites.

Conclusions

Utilizing a photolabile ligand as MOF strut can make a framework undergo full or partial decomposition upon irradiation. A NPAA derivative has been incorporated into MOF as a backbone linker via PLSE method. The photo-induced decarboxylation of the NPDAC-MOF represents a novel way of degrading a MOF, which provides an innovative approach to formulating photoresponsive porous materials with potential applications ranging from molecular release to drug delivery. When photoactive linker is mixed with non-photolabile linker via partial PLSE, the MOF structure can be retained after irradiation, but with the introduction of multiple vacancies, offering a new method to create defects in MOFs. Defect repair can be achieved by treatment with replacement ligands, the scope of which is an interesting area for developing customizable MOF contents. The use of carboxylate struts capable of undergoing photodecarboxylation may lead to a general approach introducing MOF defects for a variety of new applications, and will be the subject of further investigations.

Scheme 1 .

 1 Scheme 1. Synthesis and photolysis of 2, showing the three major photoproducts, 4-methyl-2-nitrophenylacetic acid (3), 2-nitro-p-xylene (4) and 4methyl-2-nitrobenzaldehyde (5).

Figure 1 .

 1 Figure 1. Thermal ellipsoid representation of NPDAC-MOF showing sppw structure with 50% thermal ellipsoids and labels for heteroatoms. Hydrogen atoms and MeOH are omitted for clarity. 1B. Two-dimensional layer showing the crystal packing, with bright yellow octahedral showing Zn 2+ atoms are coordinated by four oxygen atoms and two nitrogen atoms.

Figure 3 .

 3 Figure 3. HPLC traces for the photolysis of NPDAC-MOF after 1 h (red) and NPDAC (2) after 10 min (black). Ketoprofen was used as internal standard (S) with 4-methyl-2-nitrophenylacetic acid (3), 2-nitro-p-xylene (4) and 4-methyl-2nitrobenzaldehyde (5) photoproducts, and liberated 4,4'-dipyridine (6). Upper inset photo shows the color changes in the crystalline material from light yellow to dark yellow over the course of the irradiation. Lower inset shows the changes in the UV-Vis spectrum of NPDAC-MOF after irradiating period of 1 h, which indicates the presence of soluble nitro-phenyl species.

Table 1 .

 1 Crystal data and structure refinements for NPDAC-MOF

	Compound	NPDAC-MOF
	Formula	C42H38N4.25 O10.5Zn2
	Formula weight (g mol -1 )	901.01
	Crystal size	0.55 × 0.15 × 0.08
	Crystal system	Triclinic
	Color	Colorless
	Space group	P-1
	a/Å	9.620(6)
	b/Å	10.724(7)
	c/Å	11.122(7)
	α/°	116.790(15)
	β/°	105.111(16)
	γ/°	95.384(16)
	Volume/Å 3	958.6(11)
	Z	1
	Temp, K	296 (2)
	ρcalcg/cm 3	1.561
	Radiation	Mo Kα (λ = 0.71073Å)
	2θ range for data collection/°	4.36 to 45.02
	Index ranges	-10≤h≤10, -11≤k≤11, -12≤l≤12
	Reflections collected	17759
	Independent reflections	2588
	Observed reflections	2255
	R	0.036
	wR2	0.1242

Acknowledgements

This work was supported by the National Science Foundation grant CHE-0955361, the American Chemical Society Petroleum Research Fund grant 53977-ND3 and Worcester Polytechnic Institute. Access to high-performance computing platforms was provided by GENCI grant A0050807069.