Effects of Missing Linker Defects on the Elastic Properties and Mechanical Stability of the Metal–Organic Framework HKUST-1

Abstract

The defects can naturally exist or be artificially designed in metal−organic frameworks (MOFs), which could significantly affect their mechanical properties. In this paper, the elastic properties of HKUST-1 with randomly distributed missing linker defects are investigated by reactive molecular dynamics simulations together with the strain-fluctuation method. Although all elastic constants of HKUST-1 are found to reduce due to the linker missing, the cubic symmetry is retained in the defective HKUST-1, indicating that the simplified Born stability criterion is still applicable in determining its mechanical stability. On the basis of the simplified Born stability criterion together with direct compression simulations, the critical pressure of instability of HKUST-1 with randomly distributed defects is found to almost linearly decrease as the defect concentration grows. The mechanical instability is similarly attributed to the compression mode in both pristine and defective HKUST-1. Moreover, the direct compression simulations indicate an obvious intermediate transition process existing during the structural collapse of the defective HKUST-1, which is absent in its pristine counterpart. Overall, this work is expected to provide a more precise understanding of the mechanical properties of realistic MOFs.

Plastic Avalanches in Metal–Organic Framework Crystals Due to the Dynamic Phase Mixing

“…As shown in Figure b, when the historical maximum strain is smaller than 0.05, the Young’s modulus of HKUST-1 crystals exhibiting an almost pure op structure is around 5.52 GPa, almost independent of the historical maximum strain. The Young’s modulus measured here agrees well with the value of 5.42 GPa predicted from MD simulations on the intrinsic op structure of HKUST-1 . After the yield occurs or the historical maximum strain becomes larger than 0.05, the Young’s modulus of HKUST-1 crystals with the mixed phase is found to grow as the historical maximum strain increases, which ultimately increases to 11.94 GPa at a historical maximum strain of around 0.49.…”

“…We attribute this difference to the different stress distributions in the different HKUST-1 structures considered, as the flexibility of MOFs has been proven to be dependent on their textural properties . In bulk HKUST-1 under compression, the stress uniformly distributes, causing the simultaneous collapse of all nanopores . This also explains the disappearance of serrations from the plastic flow of HKUST-1 micropillars as shown in a recent study, since the stress can similarly distribute uniformly in the column-like micropillar structures.…”

“…(b) Young’s modulus of HKUST-1 crystals previously compressed with various historical maximum strains. Here, results extracted from previous MD calculations and measured from previous and present IITs are also shown for the sake of comparison. (c) Schematic illustration of the composite model comprised of the op and cp phases, representing the HKUST-1 model with phase coexistence.…”

“…To overcome the limitations of DFT calculations, molecular dynamics (MD) simulations were also employed to investigate the mechanical properties and deformations of various MOF crystals. The significant impact of various factors such as temperature and defects on mechanical properties of MOFs has been observed in MD simulations, − while responses of MOFs under various mechanical stimuli including compression, shearing, and shock also have been investigated. − Although MD can simulate the MOF crystals with a larger size, the size of the largest MOF models that can be effectively handled by MD simulations is still much smaller than that in reality. , This size discrepancy may cause some quantitative errors due to the so-called size effect. , Thus, experimental measurements are more direct and reliable in the examination of the mechanical properties of MOFs, among which the nanoindentation test based on the instrumented indentation or atomic force microscopy is the most popular method. , Although various mechanical properties including the Young’s modulus, hardness, and fracture toughness can be captured through nanoindentation, only the local rather than overall mechanical properties of MOFs can be achieved, since a sharp tip is used in the nanoindentation to probe the mechanical properties nearby . The in situ compression technique inside a scanning electron microscope (SEM) or transmission electron microscope can be an alternative for characterizing the overall mechanical responses of powders like MOF crystals, , but the in situ compression study of MOFs is still in its infancy.…”

Sub-Micrometer Phonon Mean Free Paths in Metal–Organic Frameworks Revealed by Machine Learning Molecular Dynamics Simulations

“…To further evaluate the accuracy of the NEP models in MD simulations, we compare the radial distribution functions and angular distribution functions of the three MOFs at 300 K calculated from the NEP models with those obtained from DFT and a few representative existing force fields (see Figure 2). The selected force fields include MOF-FF, 49 UFF4MOF, 46 and ReaxFF, 54 which have been widely used in MD simulation of the thermodynamics of MOF-5, 48 HKUST-1, 55 and ZIF-8. 19 For radial distribution functions, we considered the most important pairs at the metal-linker interfaces: Zn−O in MOF-5, Cu−O in HKUST-1, and Zn−N in ZIF-8.…”