Understanding the Anisotropic Elastic Properties of Metal-Organic Frameworks at the Nanoscale: The Instructive Example of MOF-74

Metal-organic frameworks (MOFs) are a particularly intriguing class of self-assembled materials, whose elastic properties crucially impact many of their envisioned applications. Thus, we here present an in-depth, "nanoscale" discussion of these properties for the prototypical class of MOF-74 derivatives. These provide a particular wealth of insights due to their pronounced anisotropy with fundamentally different building blocks connecting the structures parallel and perpendicular to the pore direction. To go beyond solely reporting macroscopic parameters, we trace their values back to atomistic displacements under stress employing state-of-the-art dispersion-corrected density functional theory. Interestingly, all of the studied MOFs exhibit qualitatively different responses to either unidirectional or isotropic stress, which can be ascribed to distinctly different atomic rearrangements for stress parallel or perpendicular to the channel direction. In the former case, one primarily observes a lateral expansion and rotation of the nodes, which can be impeded, e.g., by an exoskeleton formed by an adsorbed water layer. Conversely, for stress perpendicular to the channel, the MOFs comply with a deformation of the hexagonal pores, which causes a significant expansion perpendicular to the stress direction. We also show that the details of these atomistic motions impact the structure-to-property relationships for a variety of MOF-74 variants beyond the expectations based on bonding strengths and the degree of porosity.