Phonon-Focusing and Rattler-Mode Interference in Thermal Conductivity Transitions of the Breathing Metal-Organic Framework MIL-53

The metal-organic–framework (MOF) MIL-53 has a framework geometry with a wine-rack motif that enables it to transition between open and closed structures either under pressure or due to gas sorption. Here we show that in these breathing MOFs the thermal conductivity, an important property for gas sorption performance, also changes between the open and closed-pore conformations. We present a very simple geometric network model of conductivity in these materials that underpins the base trend of the thermal conductivity and test it against equilibrium molecular dynamics thermal conductivity calculations. In addition, a self-consistent-charge density functional tight binding (SCC-DFTB) approach using the DFTB+ software package has been used to compute phonon properties for both the open- and closed-pore MIL-53(Al). While we observe only small changes in the density of states between both configurations, the dispersion relations suggest the emergence of rattling behavior due to the geometric changes in the framework. A phenomenon of considerable technological interest in the phonon transport community is Phonon focusing, which has been proposed to enable materials with ultra-low thermal conductivity. Our work indicates that the anisotropy in the thermal conductivity stems from a phonon focusing effect tempered by scattering from the non-propagating rattler modes.