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