A Computational and Experimental Approach Linking Disorder, High‐Pressure Behavior, and Mechanical Properties in UiO Frameworks

Abstract Whilst many metal–organic frameworks possess the chemical stability needed to be used as functional materials, they often lack the physical strength required for industrial applications. Herein, we have investigated the mechanical properties of two UiO‐topology Zr‐MOFs, the planar UiO‐67 ([Zr6O4(OH)4(bpdc)6], bpdc: 4,4′‐biphenyl dicarboxylate) and UiO‐abdc ([Zr6O4(OH)4(abdc)6], abdc: 4,4′‐azobenzene dicarboxylate) by single‐crystal nanoindentation, high‐pressure X‐ray diffraction, density functional theory calculations, and first‐principles molecular dynamics. On increasing pressure, both UiO‐67 and UiO‐abdc were found to be incompressible when filled with methanol molecules within a diamond anvil cell. Stabilization in both cases is attributed to dynamical linker disorder. The diazo‐linker of UiO‐abdc possesses local site disorder, which, in conjunction with its longer nature, also decreases the capacity of the framework to compress and stabilizes it against direct compression, compared to UiO‐67, characterized by a large elastic modulus. The use of non‐linear linkers in the synthesis of UiO‐MOFs therefore creates MOFs that have more rigid mechanical properties over a larger pressure range.

Metal-organic frameworks (MOFs) continue to be of exceptional interest to the scientific community because of their guest-specific gas sorption, separation, drug-delivery, and catalytic properties. [1] Whilst significant progress has been made in increasing the chemical stability of MOFs, [2] their "soft" mechanical properties often lead to framework collapse or structural distortion upon application of temperature, shear stress,o rh ydrostatic pressure. [3] This poses as evere problem during sintering and pelletization processes,used to shape MOF powders into industrially useful morphologies. [4] Any structural deformation however also alters the highly selective guest-binding properties of MOFs,w hich therefore means that structural durability is ah ighly desired quality. Routes to such mechanically robust structures have included embedding MOFs into polymer matrices,o rc oating nanoparticles with silica, [5] although both lead to substantial deterioration in guest sorption ability.
While sometimes problematic for applications,s tructural flexibility does however give rise to av ery rich and diverse array of pressure-and temperature-induced mechanical responses in MOFs,w hich may be tuned to individual application needs. [6] Thei mportance of this mechanical behavior motivated us to investigate the link between stimuli-induced mechanical response and chemical structure in the well-known UiO family of Zr-MOFs.
Thei soreticular series of UiO-type MOFs consists of Zr 6 O 4 (OH) 4 nodes,w hich are interconnected by linear or bent dicarboxylate ligands. [7] Thehigh valencyofZr IV and 12fold coordination of the metal cluster are associated with high shear and bulk moduli, which surpass those of other MOFs. [8] In this work, we build upon recent advances in the synthesis of single crystals of UiO frameworks,a nd present ac ombined computational and experimental study of the mechanical behavior of UiO-67 [Zr 6 O 4 (OH) 4 (bpdc) 6 ]( bpdc:4 ,4'biphenyl dicarboxylate) [9] and an azobenzene derivative, UiO-abdc [Zr 6 O 4 (OH) 4 (abdc) 6 ](abdc:4,4'-azobenzene dicarboxylate) [10] (Figure 1). Acombination of single-crystal nanoindentation, high-pressure X-ray diffraction studies,d ensity functional theory (DFT) calculations,a nd first-principles molecular dynamics (MD) simulations were used to show that the dynamic disorder induced in UiO-abdc by the ligand has asignificant impact upon the mechanical behavior of the framework.
Synthetic conditions leading to single-crystals of UiO-type MOFs are rare and typically require the addition of asignificant excess of monocarboxylic acid crystallization modulators. [11] We have found the amino acid l-proline to be ahighly efficient modulator in the synthesis of Zr UiO-MOFs. [12] Addition of 5a nd 1equivalents (with respect to the linker) of l-proline and HCl (a known synthetic promoter [13] )during solvothermal syntheses yielded single crystals of % 50 mm diameter of both UiO-67 and UiO-abdc (Supporting Information, Section SI-1). Both UiO-67 and UiO-abdc crystallize in the cubic space group Fm " 3m (a % 26.85 a nd 29.32 respectively), and contain octahedral cages of diameter 16 (UiO-67) and 19 (UiO-abdc), which share faces with eight smaller tetrahedral pores of diameters 12 ( UiO-67) and 15 ( UiO-abdc). [10] Room temperature single-crystal diffraction data were collected to compare to our high-pressure data at room temperature.For UiO-67, some libration was observed on the bpdc ligand, while much larger ellipsoids and more disorder were apparent in the abdc ligand in UiO-abdc. Phenyl rings in UiO-abdc were modelled over three positions (one halfoccupied, the other quarter-occupied over two positions), while the diazo moiety was modelled over four positions. Both libration and disorder are unsurprising, as the ligands in both cases are bisected by mirror planes,whilst occupational disorder in abdc is ascribed to the lack of ligand mirror symmetry.Whilst the average structure is cubic and isostructural with UiO-67, the local structure of the abdc ligand must break this symmetry ( Figure 1d). Interestingly,t his disorder did not result in any observable diffuse scattering, which has been ap oint of great interest recently. [14] Quantum mechanical simulations were performed on both UiO-67 and UiO-abdc using the crystallographic coordinates as starting models (Supporting Information, Section SI-2). Motion of the six independent linker arms was followed by MD simulations,w hich revealed highly dynamic behavior. Atomic probability density functions (PDFs), analogous to thermal ellipsoid models in crystallographic refinements,w ere derived for the Zr 6 O 4 (OH) 4 core,a nd one of the six linker units in each case ( Figure 2). [15] Theresulting plots clearly demonstrate the extent of ligand movement observed across the horizontal mirror plane during the simulations (Supporting Information, Figure S2). Ab owing angle, q,w as defined for each ligand (the angle that the benzene carboxylate makes with the Zr 4 metal cluster square plane) and an average magnitude defined for both frameworks.W hilst the bpdc ligands in UiO-67 remain approximately planar (hj q ji = 3(2)8 8), the geometric frustration in UiO-abdc is accommodated by am ore significant bowing of the ligands hj q ji = 5(3)8 8 ( Figure 2). Good agreement between bond lengths in the time averaged MD and crystallographic models of both UiO-67 and UiO-abdc (Supporting Information, Table S1) is observed. Thesimulated/experimental overlay image of UiO-67 (Figure 2a)s hows close alignment between the MD time-averaged and crystallographic models. In astark contrast, bowing of the abdc ligand on either side of the horizontal mirror plane is clearly observed in UiO-abdc ( Figure 2b).
To investigate the effect of the higher flexibility and geometric frustration of abdc on the mechanical properties of the UiO framework, high-pressure experiments were performed on both UiO-67 and UiO-abdc by loading suitable single-crystals into modified Merrill-Bassett diamond anvil cells (DACs). [16] In separate experiments,t he MOF crystal was then surrounded by either methanol (MeOH) or fluorinert FC-70 as the hydrostatic medium ( Figure 3). Pore volume and content as afunction of pressure were calculated using the SQUEEZE algorithm within PLATON(Supporting Information, Section SI-4). [17] On increasing pressure using MeOH as ah ydrostatic liquid, both UiO-67 and UiO-abdc expand initially at 0.16 and 0.19 GPa, respectively ( Figure 3). Such behavior has been observed in other compression studies of porous MOFs, where MeOH molecules penetrate into the solid and cause the framework to expand. [18] On increasing pressure further, both frameworks begin to compress,before plateauing at 1.15 and 1.20 GPa in UiO-67 and UiO-abdc,respectively.UiO-67 then remains almost incompressible to 2.4 GPa, while UiOabdc displays similar behavior to 4.8 GPa. Theoverall change in unit cell volume of the solvated UiO-abdc of less than 1.2 % for such al arge pressure regime is highly unusual. Experimental bulk moduli (K)were extracted from the experimental cell volume-pressure relationships using EoS Fit(Supporting Information, Section SI-4). [19] Bulk moduli over as imilar pressure range (0-2 GPa) of 174 GPa and 580 GPa for UiO-67 and UiO-abdc in MeOH were determined from the experimental data, though these numbers cannot be compared to existing literature data owing to the over-solvated state of both frameworks.N evertheless,t he drastic change that inclusion of MeOH in the framework pores has on the compressibility is evident from these values,w ith the more porous MOF with the flexible abdc ligand being much more resilient to direct compression on inclusion of MeOH to much higher pressures than observed for the more rigid UiO-67.
On initial pressurization using FC-70 (a mixture of large perfluorinated hydrocarbons,u sually considered an on-pen-etrating hydrostatic medium) indirect evidence of guest inclusion can be observed due to an increase in compressibility observed in UiO-67. On increasing pressure further, direct compression takes place in both frameworks.U nlike with MeOH, further increases in pressure are not accompanied by ap lateau in cell volume.I nf act, Bragg diffraction is lost from UiO-67 at ar elatively modest pressure of 0.3 GPa, yet UiO-abdc undergoes alarge change in unit cell volume of almost 10 %t o1 .8 GPa, while remaining crystalline.A bove 1.8 GPa, the quality of data resolution for UiO-abdc was severely reduced, such that structural responses to increasing pressure could not be determined. Theflexibility of the ligand in UiO-abdc would, however, appear to impart ag reater degree of resistance to increasing pressure whilst remaining crystalline.
To determine the compressibility of both frameworks without inclusion of the hydrostatic media, the mean atomic position structures obtained from the MD simulations were geometrically optimized by periodic DFT calculations,a nd then used as starting models for simulated hydrostatic compression in 0.2 GPa steps up to 1GPa, thereby simulating direct compression experiments on guest-free frameworks (Supporting Information, Figure S3). Compressions in cell volume of approximately 4.0 %a nd 6.0 %w ere observed at 1GPa, respectively,f or UiO-67 and UiO-abdc. While a2 nd order Birch-Murnaghan equation of state (Supporting Information, Section SI-4) allowed the determination of ab ulk modulus of 16.8 GPa for UiO-abdc;astep in the compression

Angewandte Chemie
Communications curve for UiO-67 in the 0.2-0.4 GPa range prevents us from making as imilar calculation. This hint of as tructural transition could be linked to the loss of crystallinity observed experimentally in the same pressure range.T hese results are similar to previous computational work performed on evacuated MOF-5, which reported 5% compression at 1GPa and abulk modulus of 16.52 GPa. [18] Consistent with the mechanical response of MIL-type frameworks, [20] the largest structural responses to the external pressure is observed for the ]C-O-Zr-Zr angle (f)o ft he carboxylate functional group, which undergoes changes of up to 58 8 during compression of UiO-abdc (Supporting Information, Figure S3).
ForUiO-abdc,the values of bulk moduli calculated from experimental data and calculations are in good agreement, with values of 14.8 GPa and 16.8 GPa, respectively.B ecause the early onset of pressure amorphization for UiO-67 in FC-70 precludes determination of K,a nd that value is similarly inaccessible from DFT under compression calculations,w e turned to DFT calculations in the elastic regime (with infinitesimal strains). From the elastic tensors obtained (Supporting Information, Section SI-7), the Voigt-Reuss bulk moduli calculated for UiO-abdc is 15.2 GPa, in good agreement with the data above despite the very different methodology.T he bulk modulus of UiO-67 is slightly higher, at 17.4 GPa. Thus,t he inclusion of the more flexible azobenzene-based linker logically leads to asofter framework (higher compressibility), though the effect is quantitatively small. In comparison, the effect on the robustness or mechanical stability of the framework is much bigger:asixfold increase in its hydrostatic pressure at which it loses crystallinity.
To look at the response of the material under ad ifferent mechanical stimulation, we probed evacuated single crystals of UiO-67 and UiO-abdc by nanoindentation, to determine their Youngs moduli, E,and hardness, H.Single-crystal X-ray diffraction was performed to establish Miller indices of the crystal facets (Supporting Information, Section SI-5). Using the load-displacement data (Supporting Information, Section SI-6) gained during the indentation, E and H were calculated as afunction of depth. Theaverage values for each sample were calculated as E = 20.02 GPa and H = 1.27 GPa (UiO-67), and E = 13.24 GPa and H = 0.65 GPa (UiO-abdc). Thetrend seen in Youngs moduli is in agreement with values derived from DFT calculations of elastic stiffness tensors, with UiO-abdc again softer than UiO-67 under uniaxial compression (24.1 and 21.5 GPa, respectively).
Thee lastic modulus of UiO-67 is amongst the largest reported by nanoindentation for MOFs,a nd agrees with the low compressibility of the framework. Themagnitude of this rigidity is,h owever,s urprising given the empirical inverse relationship observed between E and framework solvent accessible volume (SAV), which for UiO-67 is only moderately high (65.9 %; Supporting Information, Section SI-8). [21] Indeed, HKUST-1 [Cu 3 (C 9 O 6 H 3 ) 2 ]h as as imilar SAVo f 64.3 %, yet an elastic modulus of just 9.3 GPa. [22] UiO-67 is also markedly stiffer than the prototypical frameworks ZIF Thee lastic modulus of UiO-abdc is substantially lower than that of UiO-67, which is in agreement with its higher SAV(71.8 %). It is interesting to note that this large decrease in rigidity is accompanied by ar elatively small increase in SAV, whereas previous work on ad ifferent family of MOFs noted that changes in SAVofaround 20 %would be required to elicit decreases in mechanical response of as imilar order (ca. 40 %). [23b] This vastly more flexible nature is consistent with our observation of the frustrated, bowed nature of the abdc ligand in UiO-abdc.
In conclusion, the different mechanical behavior of two UiO-type frameworks has been fully characterized by computational and experimental methodologies.Bulk and elastic moduli for both UiO-67 and UiO-abdc demonstrate mechanical robustness. [24] Then ear-zero compressibility of UiO-67 and especially UiO-abdc when over-solvated in MeOH is unique amongst the MOF world, and provides yet another example of the rich physical diversity of these systems,i n addition to their much heralded chemical versatility. E in each case lies above those of other highly porous MOFs,a nd indeed approaches the mechanical response expected of dense hybrid frameworks. [25] Thelarge differences in elasticity with relatively small changes in SAVmay allow fine-tuning of mechanical response in these highly porous systems,t hough the effect of defects upon the properties of such materials remains an issue. [14a, 26] Theu nexpected increase in resistance to pressure and the large decrease in the elastic modulus for UiO-abdc compared to UiO-67 are both ascribed to the presence of the azobenzene linker,w hich bows out of the horizontal plane.S imilarly frustrated, bowed linkers cause significant disorder in other non-UiO MOF structures, [27] and as such may be ag eneral phenomenon that subsequently impacts their mechanical behavior.T hese results are important for those looking to introduce flexibility and/or pressurecoping mechanisms in other hybrid MOF systems.