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

We performed ab initio calculations of the elastic constants of five flexible metal-organic frameworks: MIL-53(Al), MIL-53(Ga), MIL-47 and the square and lozenge structures of DMOF-1. Tensorial analysis of the elastic constants reveal 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 with the case of non-flexible MOFs such as MOF-5 and ZIF-8. In addition, we show that flexible MOFs can display extremely large negative linear compressibility (NLC). 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.