Starting from the 13,512 MOFs generated by Gómez-Gualdrón et al.,we selected those MOFs that are composed of the organic ligands and nodes depicted in Figure 1 , resulting in a shortlist of 3,385 MOFs. In Figure 1 , the entire list of the 14 organic ligands and 28 organic or metal-based nodes we used in this study are shown; the selected ligands are classified according to their length, and the nodes are classified according to their coordination number (i.e., the number of organic ligand connections for every metal-based or organic node). From the original database, we deliberately selected non-functionalized linkers in a manner to reflect the effect of linker length with one, two, and three additional carbon-carbon triple bonds (T), phenyl linker chemistry: from simple acetylenedicarboxylic acid and benzene-1,4-dicarboxylic acid, rings (P), or nitrogenated phenyl rings (N, tetrazines). All structures are made up of perfect crystals, i.e., no defects or residual solvent are present. The database used here contains 41 distinct topologies creating a widely diverse set of geometric properties, which enables a thorough exploration of the structure-mechanical stability relations in MOF space ( Figures S1 and S2 ).

(B and C) (B) Organic nodes (ON) and (C) inorganic nodes (M). The numbers are used as identifiers. The purple circles represent connecting points to other building blocks.

High-Throughput Calculations of Mechanical Properties in MOFs: Structure-Stability Relationships

45 Evans J.D.

Coudert F.-X. Predicting the mechanical properties of zeolite frameworks by machine learning. Figure 2 High-Throughput Simulations of Mechanical Properties of MOFs Show full caption Bulk modulus (K) is plotted versus the largest cavity diameter (LCD) for 3,385 MOFs. Selected topologies are highlighted by different colors; all other topologies are shown in light gray. Each point represents a different MOF. Figure 2 shows the correlation between the bulk modulus (K) and the largest cavity diameter (LCD). The LCD is in turn correlated with other structural properties, such as the pore volume, void fraction, surface area, and density. General trends similar to the ones observed here between the bulk modulus and the LCD were also found between the shear modulus and the LCD ( Figure S3 ). All structures with K > 30 GPa have an LCD <30 Å, whereas at LCD values <20 Å, a wide spread of K values (0–140 GPa) can be observed. To shed light on the importance of topology on the mechanical robustness of certain structures, we added another dimension to the K versus LCD representation and highlighted selected topologies for comparison ( Figure 2 ). Even for structures having the same LCD (e.g., see LCD = 10 or 15 Å), a quite large spread of the K values is observed depending on the topology. In other words, certain topologies have higher or lower bulk moduli irrespective of their pore size. For example, pth and spn topologies—highlighted in green and blue and for instance encountered in CMOF-1 and MOF-808—show low K values across all pore sizes, whereas fcu (e.g., UiO-66), reo (e.g., DUT-51), and ftw (e.g., NU-1100) consistently present stiffer structures at similar pore size ranges. While the ith topology, encountered, e.g., in DUT-78, has some of the highest bulk moduli found in MOFs, even comparable with those of zeolites,it is outperformed by many other topologies when considering structures with an LCD >5 Å (e.g., at an LCD of 10 Å fcu MOFs show higher K values than ith MOFs).

Although the large datasets presented in Figure 2 clearly correlate the mechanical properties of MOFs with their LCD and topology, it is thus far not clear how various structural complexities—linker length, volumetric and gravimetric surface area, density, node coordination characteristics, void fraction, pore volume, pore limiting diameter (PLD), LCD, and PLD/LCD ratio—contribute to the mechanical behavior of MOFs and how these structural-mechanical stability relations are correlated with the topology. To obtain insights into these subtle dependencies, we developed an interactive visualization tool to explore the structure-mechanical stability relationships with the key advantage that users can examine how these 12 MOF structural features and, most importantly, topology determine the mechanical properties. With the aim of providing strategies to improve the mechanical stability of MOFs, the web-based tool we developed is capable of presenting the structure-mechanical stability landscape of MOFs considering 15 descriptors along 5 dimensions (see http://aam.ceb.cam.ac.uk/mof-explorer/mechanicalproperties ), allowing the user to filter the data or to zoom in on a specific area of the graphical representations. See Video S1 for more details.

https://www.cell.com/cms/asset/f680900c-69a2-4ca7-9396-19d4e811d70d/mmc3.mp4 Loading ...

26 Wu H.

Yildirim T.

Zhou W. Exceptional mechanical stability of highly porous zirconium metal–organic framework UiO-66 and its important implications. , 44 Rogge S.M.J.

Wieme J.

Vanduyfhuys L.

Vandenbrande S.

Maurin G.

Verstraelen T.

Waroquier M.

Van Speybroeck V. Thermodynamic insight in the high-pressure behavior of UiO-66: effect of linker defects and linker expansion. Figure 3 Structure-Stability Relationships in MOFs Show full caption (A–C) Bulk modulus, K, versus the largest cavity diameter (LCD) for 3,385 MOFs. Colored (A) structures with one, two, and three phenyl rings (selected common MOFs containing phenyl rings are highlighted in the dataset); (B) structures and topologies with maximum coordination numbers (MCN) of 4, 8, and 12; filled black circles represent all other MOFs in (A) and (B). (C) Bulk modulus, K, versus the gravimetric surface area; the color code represents the density of the MOFs. (D–F) Box and whisker plots comparing bulk modulus changes with LCD for different maximum coordination numbers: (D) MCN = 12; (E) MCN = 8; (F) MCN = 4. The markers represent the minimum, first quartile, median, third quartile, and maximum values, respectively. Outliers, identified as 1.5 × the minimum or maximum values, are represented by gray data points. Mean K values for different LCD ranges are shown in red points. Data points are offset laterally for better visualization. The tool is used to explore what makes certain topologies more robust than others and how this is affected by particular choices of key structural features, such as organic linker length and type as well as the coordination environment between inorganic nodes and organic nodes or linkers. Some structures consist of both metal-based and organic nodes that show different coordination numbers; as such, in our analysis, we used the maximum coordination number (MCN) of these two values. To begin, we examined the effect of the linker length—which is generally associated with the void fraction and pore volume—on the bulk modulus. Figure 3 A shows K values versus LCD with structures containing 1 (green), 2 (yellow), and 3 phenyl rings (cyan) highlighted in the dataset. Clearly, frameworks containing one phenyl block, generally associated with narrower porosities and limited pore volumes, confer higher mechanical strength relative to those with longer linkers, e.g., structures with 2 or 3 phenyl rings. Similar trends were observed for structures containing triple bonds and nitrogenated linkers ( Figures S4 and S5 ). To further expand on this finding, we highlighted two well-known series of MOFs belonging to the fcu and pcu topologies: the zirconium-based UiO-66 and zinc-based IRMOF-type materials, respectively. In agreement with the general trend observed for the highlighted structures with an increasing number from 1 to 3 phenyl rings, there is a decrease in the bulk moduli for IRMOF-1, -10, and -16 and more prominently for UiO-66, -67, and -68. This finding suggests that shortening or expanding ligands in certain topologies presents more significant changes in the mechanical properties of MOFs, confirming the earlier theoretical results that focused on the UiO-66 series.

33 Kapustin E.A.

Lee S.

Alshammari A.S.

Yaghi O.M. Molecular retrofitting adapts a metal–organic framework to extreme pressure. 18 Howarth A.J.

Liu Y.

Li P.

Li Z.

Wang T.C.

Hupp J.T.

Farha O. Chemical, thermal and mechanical stabilities of metal–organic frameworks. , 31 Rogge S.M.J.

Waroquier M.

Van Speybroeck V. Reliably modeling the mechanical stability of rigid and flexible metal–organic frameworks. 2/g and densities of 0.5–1 g/cm3 (light blue and green points) can relatively confer high mechanical strength while maintaining good adsorptive characteristics, a combination that makes them more appealing for energy applications. Open structures with low densities and very high surface areas (>7,000 m2/g) show extremely low mechanical strength and are therefore of only limited relevance for industrial applications. Figure 3 B shows how the K values correlate with the MCN of the MOF. Structures with an MCN of 12 dominate the high bulk modulus space, whereas structures with an MCN of 8 and 4 have lower bulk moduli. This shows how resistance to mechanical forces is highly influenced by the number of node connections. Physically, topologies with low-coordinated nodes (e.g., bor, pth, pts, and tbo; Figure 3 ) have bond angles that can potentially flex with relative ease, allowing the frameworks to accommodate stress and deform under pressure and shear ( Figure S3 ), whereas highly coordinated topologies (e.g., ith, fcu, and ftw; Figure 3 ) are less flexible, and thus changes in bond angles and lengths are associated with higher energy costs. This observation was recently exploited to stabilize MOFs via retrofitting.It is noteworthy that high-K MOFs—characterized by structures with high coordination numbers—are dominated by materials with zirconium cuboctahedral nodes (e.g., M13 in Figure 1 A) such as those present in the UiO-66 family. In addition to the high coordination number of the nodes, zirconium-based MOFs have been previously reported to render superior mechanical stability due to the strong oxophylic character of zirconium, leading to strong zirconium-oxygen bonds. Figure S6 shows that variations between bulk moduli exist among topologies containing the same MCN. For example, for MCN = 12, fcu presents higher bulk moduli over ftw and ith topologies for MOFs with 10 Å < LCD <20 Å. For the same range of LCD values, reo and csq for MCN = 8 and pto for MCN = 4 show higher bulk moduli compared with other topologies. The web-based visualization tool can also be used to determine the mechanical properties in terms of other specific structural properties such as the surface area of the MOFs. The latter is a key factor in determining the potential of these materials for energy applications for which their gas adsorption capacity is a central quantity. Figure 3 C shows that although dense structures with very low surface areas (purple points) close to zero are mechanically very robust, they probably would exhibit limited adsorption capacities. MOFs with surface areas of 1,000–3,000 m/g and densities of 0.5–1 g/cm(light blue and green points) can relatively confer high mechanical strength while maintaining good adsorptive characteristics, a combination that makes them more appealing for energy applications. Open structures with low densities and very high surface areas (>7,000 m/g) show extremely low mechanical strength and are therefore of only limited relevance for industrial applications.

26 Wu H.

Yildirim T.

Zhou W. Exceptional mechanical stability of highly porous zirconium metal–organic framework UiO-66 and its important implications. , 44 Rogge S.M.J.

Wieme J.

Vanduyfhuys L.

Vandenbrande S.

Maurin G.

Verstraelen T.

Waroquier M.

Van Speybroeck V. Thermodynamic insight in the high-pressure behavior of UiO-66: effect of linker defects and linker expansion. To quantitatively analyze whether the linker length or the coordination number and topology is a more important descriptor in determining the mechanical stability, we compared the K values for structures with MCN 12, 8, and 4 with respect to their LCD ( Figures 3 D–3F). The absolute values and the variation of the bulk moduli for each MCN at different pore sizes are remarkable. For 5 Å < LCD <10 Å, average K values are 40, 25, and 15 GPa for MCNs amounting to 12, 8, and 4, respectively. For MCN = 12, there is a considerably steeper decrease in bulk modulus as the pore size increases compared with MCN = 8 and MCN = 4. For the lowest MCN of 4, the bulk modulus decreases only slightly as the pore size increases. These trends indicate that the expansion of the organic linkers induces more drastic changes in mechanical stability decay for network topologies with high coordination numbers. such as ith, fcu, and ftw, explaining why these effects have been predominantly observed in the UiO-66 series exhibiting the fcu topology.Furthermore, structures consisting of only triple-bond linkers (e.g., L1/L4/L8 in Figure 1 B) tend to have slightly higher bulk moduli than those with only phenyl rings, while variations exist within the dataset ( Figure S7 A). When linkers containing both phenyl ring and triple-bond blocks are considered, our high-throughput calculations do not show any appreciable differences between different positions of, e.g., phenyl rings in the linker and the mechanical properties of MOFs ( Figure S7 B). This point is fully addressed later in this work, where molecular dynamics calculations based on accurate ab initio-based force fields are performed for selected materials.