Anomalous strain-dependent thermal conductivity in the metal-organic framework HKUST-1

Metal-organic frameworks (MOFs) have often been used for gas storage owing to their high surface areas and nanoscale pores, where they are packed in the tank. The concomitant exothermicity and endothermicity during the gas storage process strongly affect their storage capacity. Understanding the thermal transport in MOFs under mechanical strain is critical to maximizing the gas uptake capacity of MOFs. Here, we systematically investigate the thermal transport in a typical MOF (i.e., HKUST-1 or equivalently MOF-199) considering the external mechanical strain using molecular dynamics simulations. We find that the thermal conductivity of HKUST-1 decreases with compressive strain and increases with tensile strain, which is contradictory to the classical Liebfried and Schl\"omann theory, i.e., the thermal conductivity of crystals should increase with applied compression. Our spectral analysis further shows that the abnormal strain-dependent thermal conductivity can be well explained by the phonon-gas theory. We find that the relaxation time of vibrations in HKUST-1 decreases when compressive strain is applied. This is because the anharmonicity of compressed HKUST-1 increases compared with that of pristine HKUST-1. The anharmonicity of HKUST-1 decreases when tensile strain is applied, and thus, the corresponding vibrational relaxation time increases. Meanwhile, the vibrational group velocity decreases or increases for compressed or tensile HKUST-1, respectively. This is due to the compression- or stretch-induced shift of vibrational branches caused by the structural softening and hardening. Therefore, the thermal conductivity of HKUST-1 decreases with compressive strain even though the volumetric heat capacity of compressed HKUST-1 increases. The thermal conductivity of HKUST-1 increases with tensile strain, though the corresponding volumetric heat capacity decreases. Here, we provide a fundamental understanding of the thermal transport mechanisms in MOFs considering mechanical strain, which offers guidance for the thermal management design in these corresponding gas storage applications.