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

TL;DR

This study uses ab initio calculations to analyze the highly anisotropic elastic properties of flexible metal-organic frameworks, revealing extreme directional differences in stiffness and large negative linear compressibility, which relate to their structural flexibility.

Contribution

It provides the first detailed tensorial analysis of elastic constants in flexible MOFs, linking microscopic elastic behavior to their multistability and stimuli-induced transitions.

Findings

Elastic anisotropy can reach a 400:1 ratio between directions.

Flexible MOFs exhibit large negative linear compressibility.

Elastic behavior explains structural transitions in flexible MOFs.

Abstract

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.