Structural Dynamics by NMR in the Solid State: II. The MOMD Perspective of the Dynamic Structure of Metal-Organic...

We describe the application of the microscopic-order-macroscopic-disorder (MOMD) approach, developed for the analysis of dynamic ²H NMR lineshapes in the solid state, to unravel interactions among the constituents of metal-organic frameworks (MOFs) that comprise mobile components. MOMD was applied recently to University of Windsor Dynamic Material (UWDM) MOFs with one mobile crown ether per cavity. In this work, we study UWDM-9-d₄, which comprises a mobile ²H-labeled phenyl-ring residue along with an isotopically unlabeled 24C8 crown ether. We also study UiO-68-d₄, which is structurally similar to UWDM-9-d₄ but lacks the crown ether. The physical picture consists of the NMR probe─the C-D bonds of the phenyl-d₄ rotor─diffusing locally (diffusion tensor ) in the presence of a local ordering potential, u. For UiO-68-d₄, we find it sufficient to expand u in terms of four real Wigner functions, D_0|, overall 2-3 kT in magnitude, with R_∥ relatively fast, and R_⊥ in the (2.8-5.0) × 10² s^-1 range. For UWDM-9-d₄, u requires only two terms 2-3 kT in magnitude and slower rate constants R_∥ and R_⊥. In the more crowded macrocycle-containing UWDM-9-d₄ cavity, phenyl-d₄ dynamics is more isotropic and is described by a simpler ordering potential. This is ascribed to cooperative phenyl-ring/macrocycle motion, which yields a dynamic structure more uniform in character. The experimental ²H spectra used here were analyzed previously with a multi-simple-mode (MSM) approach where several independent simple motional modes are combined. Where possible, similar features have been identified and used to compare the two approaches.