Research Update: Mechanical properties of metal-organic frameworks – Influence of structure and chemical bonding Open Access

Metal-organic frameworks (MOFs) are a young class of extended solids, which are constructed via coordination association between inorganic metal ions (or clusters) and organic linkers.^1–5 Due to their promising applications in carbon capture,⁶ gas separation,⁷ catalysis,^8,9 sensing,¹⁰ etc., the area of MOF research has become one of the fastest growing fields in materials science over the past 15 years. In light of the imminence of their applications,¹¹ mechanical properties, which are critical to the industrial manufacturing and processing, have to be taken into account. The first work in the area was reported by Allendorf and co-workers in 2007,¹² and more extensive and systematic work has been carried out since then by the Cheetham group and other researchers.^13–35 In 2011, Tan and Cheetham published a comprehensive review paper introducing the fundamental mechanical properties of MOFs and their intrinsic structure–property relationships.³⁶ 

In general, MOFs exhibit more complex mechanical properties compared with traditional inorganic materials, such as zeolites and perovskites. The variable chemical interactions within MOFs, ranging from strong coordination bonds to weaker dispersion forces and hydrogen bonding interactions, may result in significant structural flexibility in response to temperature, hydrostatic pressure, or uniaxial stress.^22,24,37,38 Some MOFs undergo reversible or irreversible amorphization when exposed to mechanical stress,³⁹ while others exhibit drastic pressure-induced phase transitions, associated with striking bond rearrangements.^40,41 Furthermore, the structural anisotropy of many MOFs often gives rise to large mechanical anisotropy and, correspondingly, unique mechanics. For instance, some MOFs have been reported to exhibit negative linear compressibility (NLC)^42–44 and massive positive or negative thermal expansion (PTE and NTE).^45–48 Considering that MOF research is mainly dominated by synthetic chemists, a general introduction to the intrinsic links between chemistry and mechanics is of particular interest, as it will bridge the gap between chemistry and mechanical engineering. In this mini-review, we will discuss the mechanical properties of MOFs from the viewpoint of structure and chemical bonding by presenting a number of prototypical examples to demonstrate the strong connection between chemistry and mechanical behavior.

Before focusing on how chemistry influences the mechanics of MOFs, we briefly discuss two other general factors. First, the supramolecular mechanics of MOFs can be described and understood by analysis of their framework topology, which characterizes the motif of connectivity within a network; this is analogous to a scaffold in mechanical engineering.⁴⁹ For the mechanical properties, this is of major importance. As an approximation, MOFs can be described by simple structural models composed of vertices connected by edges. Naturally, the connectivity of a framework, i.e., the number of edges connecting one vertex with others, determines the general mechanical properties of the framework. Similar to classical mechanics used in civil engineering, higher connectivity often results in higher stiffness and hardness. This has been demonstrated by density functional theory (DFT) calculations on a variety of prototypic cubic MOFs possessing different topologies with distinct connectivity (coordination number) of their secondary building units (SBUs).⁵⁰ HKUST-1 (four connected square planar SBU), ZIF-8 (four connected tetrahedral SBU), and MOF-5 (six connected tetrahedral SBU) exhibit significantly lower Young’s, bulk and shear moduli than UiO-66 (twelve connected octahedral SBU).

The second factor that determines the mechanical behavior of MOFs is the framework geometry.⁵¹ For a given topology, the geometry of the connections between nodes and links often depends on the nature of the individual building units. For example, a 2D 4⁴ topology can either have a square-shaped (isotropic) or a rhomb-shaped (anisotropic) geometry, which could result in significantly different mechanical behavior in response to stress. This has been well demonstrated by Ortiz et al.via a computational investigation of the full elastic tensors of two geometrical isomers of the framework [Zn₂(bdc)₂(dabco)]_n (DMOF = dabco-MOF; bdc = 1, 4-benzenedicarboxylate, dabco = 1, 4-diazabicyclo[2.2.2]octane). DMOF has a winerack-like structure based on [Zn₂(bdc)₂]_n layers with 4⁴ topology, which are pillared by dabco ligands to form a 3D porous framework.⁵² This porous material can feature a square-shaped (DMOF_square) or a rhomb-shaped geometry (DMOF_rhomb) depending on adsorbed guest molecules, while the topology (i.e., the connectivity of the building units) of the network is preserved (Fig. 1 top).⁵³ DFT calculations reveal marked mechanical differences between these two isomers (Fig. 1 bottom). DMOF_square has a more isotropic nature, displaying positive linear compressibility (PLC) with similar magnitude along all three crystallographic directions (β_x = 23 TPa⁻¹, β_y = 12 TPa⁻¹, β_z = 12 TPa⁻¹). In contrast, the distorted DMOF_rhomb features extreme PLC and NLC (β_x = − 623TPa⁻¹, β_y = 23 TPa⁻¹, β_z = 1158 TPa⁻¹) coupled with negative Poisson’s ratio. The drastic differences obviously result from geometric effects: DMOF_rhomb can undergo a facile hinge motion upon compression, whereas DMOF_square only favors isotropic compression due to geometric frustration. Other geometric factors (linker lengths, bond angles, etc.) can influence the framework mechanics in the similar way.

Since variations in framework topology or geometry can often be achieved by simple alterations in chemical composition and synthetic conditions, chemical aspects encompass both the above effects and can influence mechanical properties of MOFs in a more comprehensive way. The chemistry of the molecular building units (MBUs) determines the supramolecular structure of a MOF (i.e., topology and geometry), and thus also characterizes the framework mechanics. In 2012, the concept of mechanical building units (XBUs), which allows for the qualitative estimation of a framework’s mechanical response based on the mechanical nature of the individual building blocks, was introduced by Ogborn et al.⁵⁴ Based on strong (covalent or coordinative bonds) and weak chemical interactions (hydrogen bonds, dispersion forces), XBUs can be analyzed and their rigidity and flexibility estimated. Some XBUs are prone to show stronger bending or flexing than others and, hence, the incorporation or exchange of XBUs with different mechanical nature will result in different framework stiffness. In the following paragraphs, we will discuss the critical importance of various chemical effects for MOF mechanics based on four prototypical examples, focusing on the influence of XBUs as well as guest-framework interactions, to give the reader a concise introduction to the intrinsic relationship between framework chemistry and mechanics.

The first example shows how the mechanical properties of winerack frameworks can be influenced significantly via simple building block exchange.⁵⁵ MIL-53 is constructed from one-dimensional M-OH-M pillars (M = Al, Cr, Fe, Ga, In) composed of corner sharing metal-oxo-octahedra, which are interconnected by linear bdc linkers to form a winerack-like framework. Importantly, the framework is very compliant and allows hinging around the metal-carboxylate bonds. Exchanging half of the M-OH-M pillars in MIL-53 with a 1,4,5,8-naphthalenetetracarboxylate results in MIL-122, having the identical network topology as MIL-53 (Fig. 2). In comparison to the flexible four-connected metal-carboxylate unit, the tetracarboxylate is more rigid and does not allow flexing around this network node.⁵⁵ 

Consequently one half of the XBUs of the MIL-122 framework are non-compliant, while the others are the same as in MIL-53. As a consequence of the spatial arrangement of compliant inorganic vertices and non-compliant organic vertices, the overall mechanical nature of MIL-122 differs significantly from MIL-53, resulting in considerably higher and more isotropic Young’s moduli for MIL-122 compared to the highly anisotropic elastic nature of MIL-53.

Besides the exchange of flexible inorganic XBUs for rigid organic ones, a simple variation of the metal centers of a framework can markedly influence the stiffness of the material. Tan et al. studied the elastic properties of a series of four isomorphous formate frameworks [dma][M(HCOO)₃]_n (dma = dimethyl ammonium, M = Mn, Co, Ni, Zn) with the ABX₃-type perovskite architecture in which the A, B, and X sites are occupied by the dma cations, M²⁺, and formate ligands, respectively. The nanoindentation results revealed significant variations in the Young’s modulus (E) depending on the metal center (Fig. 3).⁵⁶ Interestingly, the trend in mechanical stiffness cannot be ascribed to the different ionic radii of the four metal ions. Mn²⁺ and Zn²⁺ feature markedly different ionic radii (0.82 Å for Mn²⁺, 0.75 Å for Zn²⁺) but their Young’s moduli along the (012) direction are nearly identical (E ≈ 19 GPa). The Co (E ≈ 22 GPa) and Ni (E ≈ 25 GPa) perovskite frameworks, however, are significantly stiffer. The authors found that the differences in framework stiffness correlate well with the ligand field stabilization energy (LFSE) of the octahedrally coordinated divalent metal centers. The LFSE of Mn²⁺ (3d⁵) and Zn²⁺ (3d¹⁰) is zero due to the half filled and fully filled 3d electron configurations, while those of Co²⁺ (3d⁷) and Ni²⁺ (3d⁸) are 71.5 and 122.6 kJ mol⁻¹, respectively. Elastic deformation along the (012) direction includes distortions of the formate linker, the M-O-C bridging angle, and the MO₆ octahedra. For the four isostructural frameworks, all of these contributions are expected to be identical, except for the MO₆ octahedra. The high LFSE of Ni²⁺ and Co²⁺ suggests a higher resistance against distortion of the MO₆ octahedra, which thus gives rise to increased framework stiffness. It is quite remarkable that these electronic effects can play a more important role for the mechanical properties of MOF materials than the metal ion radii. Given that many MOF families include a series of isostructural compounds based on different metal centers, it is, in principle, possible to fine tune the mechanical nature of these MOFs by selecting different transition metals with the desired electronic properties.

Many MOFs have pores, which can host a variety of guest molecules (e.g., solvents, gases). Though these guests are not part of the extended framework skeleton, it has been shown that they can affect the mechanical behavior (e.g., compressibility) of the respective MOF quite drastically.^30,32 We have recently demonstrated that this is particularly true for flexible and responsive MOFs, which are able to change their structure reversibly upon adsorption of different guests.⁵⁷ By analogy with the previously discussed [Zn₂(bdc)₂(dabco)]_n framework, [Zn₂(NO₂-bdc)₂(dabco)]_n (NO₂-DMOF; NO₂-bdc = 2-nitro-1,4-benzenedicarboxylate) undergoes distinct changes in network geometry upon exchange of guest molecules (Fig. 4 top). As-prepared NO₂-DMOF hosts N,N-dimethylformamide (DMF), which can be exchanged by immersion of the crystal in other solvents, for example, dimethylsulfoxide (DMSO), mesitylene, or toluene. Therefore, the structure transforms in a single-crystal-to-single-crystal fashion from a rhomb-shaped network (DMF guests) to a tetragonal network featuring bent (DMSO) or straight linkers (mesitylene, toluene). Notice that the guest-triggered structural response of NO₂-DMOF is deemed to rely on weak guest-framework interactions and is mainly restricted to the two-dimensional [Zn₂(NO₂-bdc)₂]_n layers, while the stacking along the dabco axis is unaffected.

Nanoindentation along the dabco-linker plane (shown in cyan in Fig. 4) reveals large changes of the directional Young’s modulus of NO₂-DMOF depending on the adsorbed guest (Fig. 4 bottom). The rhomb-shaped framework, NO₂-DMOF⊃dmf, where the NO₂-bdc linker is tilted by about 6° to the indenter axis, features the lowest Young’s modulus of only 2.1(1) GPa, while the square-shaped tetragonal frameworks NO₂-DMOF⊃mesitylene and NO₂-DMOF⊃toluene, with the NO₂-bdc linker aligned parallel to the indenter axis, have Young’s moduli of 6.1(2) and 6.5(2) GPa, respectively. NO₂-DMOF⊃dmso, having bent linkers and a tetragonal structure, features a modulus of 3.7(2) GPa and lies in between the other two geometries. It is noteworthy that the Young’s modulus along the direction parallel to the dabco axis varies only slightly with the guest content. These results confirm that the adsorption of different guests can alter the stiffness of such flexible MOFs dramatically because their guest-responsive nature gives rise to different network geometries, which hence possess distinct mechanical properties. These large variations of the elastic modulus also suggest significant variations in other mechanical properties (e.g., thermal expansion behavior, compressibility) of these guest-responsive flexible frameworks.

In the same way that non-directional guest-framework interactions can influence the mechanical behavior of flexible MOFs, strong and directional hydrogen bonding interactions can also have an impact on MOF mechanics. Li et al. reported that the mechanical properties of a family of structurally similar MOF perovskites, [gua][Mn(HCOO)₃]_n (MOFP-1, gua = guanidinium), and [aze][Mn(HCOO)₃]_n (MOFP-2, aze = azetidinium), are strikingly dependent on the different hydrogen bonding modes between the anionic manganese-formate framework and the organic ammonium cation hosted in the perovskite cavities.⁵⁸ As seen in Fig. 5, MOFP-1 and MOFP-2 have similar pseudocubic unit cells, though they crystallize in different orthorhombic space groups.

Nanoindentation measurements were performed along the three pseudocubic axes of the two frameworks, namely, normal to the (010), (101), and (10-1) planes (Fig. 6). Strikingly, the Young’s moduli of MOFP-1 (E ≈ 24-29 GPa) are about twice as high as those of MOFP-2 (E ≈ 12-13 GPa). As both hybrid perovskites possess the identical anionic [Mn(HCOO)₃]⁻ framework, the substantial mechanical contrast must be attributed to their distinct hydrogen bonding modes. As seen in Fig. 5, each gua⁺ in MOFP-1 is tilted 56.7(4)° to the (101) plane, and cross-links three alternative edges of the pseudo-cubic unit cell via six hydrogen bonds to give strong bridging constraints in three dimensions. In MOFP-2, however, each aze⁺ is oriented normal to the (101) plane and hydrogen-bonded to the two opposite formate ligands within the same (⁠$10 1 ¯$⁠) face by four N–H⋅⋅⋅ O bonds. These four hydrogen bonds add only a few cross-linked constraints to one face of the pseudo-cubic unit cell. As a result of the significantly different hydrogen bonding constraints in these two frameworks, MOFP-1 can resist much larger elastic and plastic deformation, hence giving higher Young’s moduli and hardnesses. DFT calculations, high-pressure, and variable temperature single-crystal X-ray studies support the above conclusions. For instance, the thermal expansion of the weakly hydrogen-bonded framework, MOFP-2, is about five times higher than those of the strongly hydrogen-bonded MOFP-1. In marked contrast to the significant mechanical modulation based on the nature of the A-site cation (only ∼15% size difference between gua and aze) in the MOF perovskites,^59–62 the ∼22% radius difference of the A-site metal ion in perovskite oxides, GdAlO₃, and ScAlO₃, leads to only ∼15% variation of the elastic modulus. This work presents further evidences that the mechanical properties of MOFs can be fine tuned via guest-framework interactions through simple chemical modification.¹⁵ 

Another way to tune and enhance the mechanical properties of MOFs is the preparation of MOF-based composites to exploit the synergistic interactions between them and inorganic nanomaterials. This was demonstrated recently by Kumar et al., who have shown that it is possible to preserve the functionality of the MOFs while enhancing the mechanical properties considerably in MOF− boron nitride (BN) nanocomposites by growing MOF particles on the BN nanosheets.⁶³ This avenue offers exciting possibilities for discovering new materials that combine functionalities of several different constituents.⁶⁴ 

In this mini-review, we have summarized some of the recent advances in MOF mechanics with the purpose of attracting more attention from the broad materials community. As strain is coupled to all physical properties of a material due to its perturbation on the intrinsic structure, the connection between chemistry (including structure) and mechanics is far more apparent than might have been expected. There are many interesting phenomena with respect to MOFs which can only be addressed properly by the combined approach of both chemistry and mechanics, such as mechanoluminescence,⁶⁵ negative compressibility and thermal expansion,²⁶ magnetoelastic coupling,⁶⁶ and framework breathing and gate opening.^67,68 Moreover, the interplay between chemistry and mechanics of MOFs can offer great opportunities to realize optimal MOF performance, namely, combined functionality and processability, targeted for industrial applications. Recent advances in mechanical testing techniques, especially the utilization of nanoindentation techniques that allow for probing mechanical properties of small volume materials,^69,70 and increased computational power needed for precise calculations of such properties, are facilitating major advances in this interdisciplinary field. We hope this mini-review will not only bridge the gap between the materials chemistry and materials engineering sub-communities of the MOF field, but also encourage more MOF chemists to collaborate with materials scientists and engineers to examine their materials from a new perspective.

W.L. acknowledges the Engineering and Physical Sciences Research Council for providing financial support. S.H. thanks the Alexander von Humboldt Foundation for a Feodor Lynen Fellowship.