Anisotropic Elastic Properties of Flexible Metal-Organic Frameworks: How Soft are Soft Porous Crystals?

Abstract

We performed ab initio calculations of the elastic constants of five flexible metal-organic frameworks (MOFs): MIL-53(Al), MIL-53(Ga), MIL-47, and the square and lozenge structures of DMOF-1. Tensorial analysis of the elastic constants reveals a highly anisotropic elastic behavior, some deformation directions exhibiting very low Young's modulus and shear modulus. This anisotropy can reach a 400:1 ratio between the most rigid and weakest directions, in stark contrast to the case of nonflexible MOFs such as MOF-5 and ZIF-8. In addition, we show that flexible MOFs can display extremely large negative linear compressibility. These results uncover the microscopic roots of stimuli-induced structural transitions in flexible MOFs, by linking the local elastic behavior of the material and its multistability.

On the Thermodynamics of Framework Breathing: A Free Energy Model for Gas Adsorption in MIL-53

“…The free energy profile of the empty host material would need to be recalculated, as changing a metal influences the flexibility of a material. 55 The interaction profile would also need to be recalculated using another metal at the chromium position. Our methodology can also be applied on structures with MIL-53 topology but longer or functionalized linkers (e.g., MIL-53-NH 2 , 10,28 COMOC family 61 ), on other MOF families (e.g., DMOF-1 42 ), or on adsorption with other gases can be investigated.…”

“…Serra-Crespo et al report a bulk modulus of 10.9 GPa for the NH 2 −MIL-53(In) material. 54 Neimark et al find a bulk modulus equal to 2 GPa for the lp shape and 10 GPa for the np shape of MIL-53(Cr) at a temperature of 300 K. 52 Ortiz et al calculated bulk moduli in the range 1−20 GPa for a range of flexible porous materials at 0 K. 55 Our profile F host at 300 K gives a bulk modulus of 8.7 GPa in the lp shape, which has an acceptable order of magnitude.…”

Molecular Mechanism of Swing Effect in Zeolitic Imidazolate Framework ZIF‐8: Continuous Deformation upon Adsorption

“…[51] The accuracy of this methodology is now well established for the calculation of MOF and ZIF structures, their relative energies, [52] and elastic constants. [53,54] Unit cell parameters obtained for ZIF-8 was 16.86 (vs. 16.99 experimentally), [5] while for SALEM-2 it is 17.01 (experimentally 16.83 ) [35] -although that latter experimental value was determined not for ap ure imidazolate-based SALEM-2 but for am ixedligand ZIF of composition Zn(im) 1.7 (mim) 0.3 .C alculations were repeated with the PBESOL0 exchange-correlation functional, and the conclusions were identical. After full optimization in the crystal's symmetry group, negative frequencies remained corresponding to the free rotation of the ZIF-8 methyl top.…”

Computational characterization and prediction of metal–organic framework properties

“…[143] The detailed analysis of the elastic properties of metal-organic frameworks has, in the last few years, been applied to different properties. In addition to the low elastic moduli of MOFs in general, Ortiz et al [145,146] demonstrated that the existence of high anisotropy in elastic properties, coupled with directions of very small Young's and shear moduli (sub-GPa), is a signature of the flexibility of soft porous crystals, [147] determining their ability to undergo large structural deformations under stimulation (see Figure 13). [148] This has allowed the prediction of flexibility for new structures, such as NOTT-300 and CAU-13 [149] (the latter has since been confirmed experimentally [150]).…”