Structural Dynamics by NMR in the Solid State: The Unified MOMD Perspective Applied to Organic Frameworks with...

The microscopic-order-macroscopic-disorder (MOMD) approach for NMR lineshape analysis has been applied to the University of Windsor Dynamic Materials (UWDM) of types 1, 2, α-3, β-3, and 5, which are metal-organic frameworks (MOFs) comprising mobile mechanically interlocked molecules (MIMs). The mobile MIM components are selectively deuterated crown ether macrocycles - 24C6, 22C6, and B24C6. Their motion is described in MOMD by an effective/collective dynamic mode characterized by a diffusion tensor, , a restricting/ordering potential, u, expanded in the Wigner rotation matrix elements, D_0, , and features of local geometry. Experimental ²H lineshapes are available over 220 K (on average) and in some cases 320 K. They are reproduced with axial , u given by the terms D_0,0² and D_0,|2|², and established local geometry. For UWDM of types 1, β-3, and 5, where the macrocycle resides in a relatively loose space, u is in the 1-3 kT, R_∥ in the (1.0-2.5) × 10⁶ s^-1, and R_⊥ in the (0.4-2.5) × 10⁴ s^-1 range; the deuterium atom is bonded to a carbon atom with tetrahedral coordination character. For UWDM of types 2 and α-3, where the macrocycle resides in a much tighter space, a substantial change in the symmetry of u and the coordination character of the ²H-bonded carbon are detected at higher temperatures. The activation energies for R_∥ and R_⊥ are characteristic of each system. The MOMD model is general; effective/collective dynamic modes are treated. The characteristics of motion, ordering, and geometry are physically well-defined; they differ from case to case in extent and symmetry but not in essence. Physical clarity and consistency provide new insights. A previous interpretation of the same experimental data used models consisting of collections of independent simple motions. These models are specific to each case and temperature. Within their scope, generating consistent physical pictures and comparing cases are difficult; possible collective modes are neglected.