Origin of the weakly temperature-dependent thermal conductivity in ZIF-4 and ZIF-62

It is known that the temperature-dependent thermal conductivity of conventional crystals follows the classical 1/$T$ trend due to the dominant umklapp phonon-phonon scattering at high enough temperatures. However, the thermal conductivity of many crystalline metal-organic frameworks is very low and shows a weak temperature dependence when all the vibrational modes are occupied. By studying two metal-organic frameworks, i.e., zeolitic imidazolate framework-4 (ZIF-4) and crystal zeolitic imidazolate framework-62 (ZIF-62), we computationally prove that the ultralow thermal conductivity in ZIF-4 and ZIF-62 is resulting from the strong scattering among the vibrations due to the large mass difference between the metal atom and the organic sites and the large diffusion of organic sites. Unlike only propagating vibrational modes, i.e., phonons, existing in the conventional crystalline Si, our mean free path spectrum analysis uncovers that both propagating and nonpropagating anharmonic vibrational modes exist and contribute largely to thermal conductivity in ZIF-4 and ZIF-62. The obtained weak temperature dependence of thermal conductivity is found to stem from the temperature dependencies of those two kinds of vibrations. Our study provides a fundamental understanding of thermal transport in metal-organic frameworks and will guide the design of thermal-related applications, e.g., inflammable gas storage, chemical catalysis, and solar thermal conversion.

Figure 1

Unit cell of ZIF-4 in a front view (a), side view (b), and top view (c). The front view (d), side view (e), and top view (f) of ZIF-62. The perspective view of ZIF-4 (g) and ZIF-62 (h). Big gray atoms are Zn, light blue atoms are N, purple atoms are C atoms, and pink atoms are H atoms. (i) Pore size distribution of ZIF-4 and ZIF-62

Figure 2

The time dependent thermal conductivity of (a) ZIF-4 and (b) ZIF-62 with a 3 × 3 × 3 supercell, and (c) crystalline silicon (cSi) at different temperatures.

Figure 3

The volume vs pressure for (a) ZIF-4 and (b) ZIF-62. The black dots are molecular dynamics (MD) simulations results, and the red lines are the fitting lines.

Figure 4

The temperature-dependent thermal conductivity of crystalline silicon (upper panel), crystal ZIF-4 (middle panel), and ZIF-62 (lower panel) calculated using Green-Kubo equilibrium molecular dynamics (GKEMD) and nonequilibrium molecular dynamics (NEMD). The measurements of ZIF-4 and ZIF-62 are taken from Ref. [47].

Figure 5

The mean free path spectrum of (a) crystal silicon, (b) ZIF-4, and (c) ZIF-62 at different temperatures, and the accumulative thermal conductivity of (d) crystalline silicon, (d) ZIF-4, and (f) ZIF-62 at the corresponding temperatures mentioned above. The dashed lines are eye guidance.

Figure 6

The temperature-dependent thermal conductivity of propagating vibrational modes and nonpropagating vibrational modes of (a) ZIF-4 and (b) ZIF-62. The vibrational density of the state of Zn and N atoms of (c) ZIF-4 and (d) ZIF-62 at various temperatures.

Figure 7

The trajectories of Zn (black) and N (blue) atoms of ZIF-4 at (a) 300 K, (b) 600 K, and ZIF-62 at (c) 300 K and (d) 600 K.