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

Abstract

Metal–organic frameworks (MOFs) are a family of materials that have high porosity and structural tunability and hold great potential in various applications, many of which require a proper understanding of the thermal transport properties. Molecular dynamics (MD) simulations play an important role in characterizing the thermal transport properties of various materials. However, due to the complexity of the structures, it is difficult to construct accurate empirical interatomic potentials for reliable MD simulations of MOFs. To this end, we develop a set of accurate yet highly efficient machine-learned potentials for three typical MOFs, including MOF-5, HKUST-1, and ZIF-8, using the neuroevolution potential approach as implemented in the GPUMD package, and perform extensive MD simulations to study thermal transport in the three MOFs. Although the lattice thermal conductivity values of the three MOFs are all predicted to be smaller than 1 W/(m K) at room temperature, the phonon mean free paths (MFPs) are found to reach the sub-micrometer scale in the low-frequency region. As a consequence, the apparent thermal conductivity only converges to the diffusive limit for micrometer single crystals, which means that the thermal conductivity is heavily reduced in nanocrystalline MOFs. The sub-micrometer phonon MFPs are also found to be correlated with a moderate temperature dependence of thermal conductivity between those in typical crystalline and amorphous materials. Both the large phonon MFPs and the moderate temperature dependence of thermal conductivity fundamentally change our understanding of thermal transport in MOFs.

Combining the D3 dispersion correction with the neuroevolution machine-learned potential

“…We used the homogeneous non-equilibrium molecular dynamics (HNEMD) method [33] to calculated the thermal conductivity. The MD simulation details are consistent with the previous work [27] and the relevant inputs are given in appendix C. A driving force with a parameter F e = 2 × 10 −4 Å −1 was used to drive the system out of equilibrium, and we have confirmed that it is sufficiently small to keep the system within the linear-response regime. To be consistent with the previous work [27], we have used a supercell with 5 × 5 × 5 conventional cells (53 000 atoms), which was tested to be sufficiently large to eliminate finite-size effects.…”

“…To confirm the correctness of our GPU implementation of D3 in gpumd and to evaluate the effects of cutoffs, we take three MOF materials (MOF-5, ZIF-8, and HKUST-1) as studied before using NEP models [27] and compare the calculated forces to those from vasp (using the IVDW = 12 option). The results are shown in figure 1.…”

“…After confirming the reliability of the combined NEP-D3 approach, we show its usefulness in practical MD simulations. In a previous work [27], some of the present authors have studied heat transport in three typical MOFs (MOF-5, ZIF-8, and HKUST-1) using MD simulations with NEP models. The reference DFT data used for training these NEP models have no dispersion corrections.…”

Unravelling abnormal in-plane stretchability of two-dimensional metal–organic frameworks by machine learning potential molecular dynamics

“…28 To date, only a few MLPs for MOFs have been reported, exclusively for 3D MOFs, including UiO-66, MOF-5, ZIF-8, and MOF-74. 31–35 Herein, systematic phonon spectrum calculations and first-principles MD simulations first revealed that the proposed 2D MOF material does not exhibit any imaginary phonon modes in the whole Brillouin zone and that it can maintain its structural integrity at room temperature as well as in an aqueous solution. Large-scale modelling of the MOF system, i.e.…”

Machine learning interatomic potentials for amorphous zeolitic imidazolate frameworks

“…To overcome its shortcomings, four other works relied on periodic DFT calculations on the primitive cell of the framework to train their NNP. 25,29–31 An option proposed by Vandenhaute et al 29 to solve the high computational cost of running ab initio simulations with large unit cells, was to use a data-efficient NNP (NequIP 32 ) to reduce the number of ab initio calculations. Interestingly, this work also demonstrated that it was possible to simulate a phase transition for MOFs with MLPs, although the transition was non-displacive and did not involve any bond breaking.…”