Emergence of Coupled Rotor Dynamics in Metal-Organic Frameworks via Tuned Steric Interactions

Abstract

The organic components in metal-organic frameworks (MOFs) are unique: they are embedded in a crystalline lattice, yet, as they are separated from each other by tunable free space, a large variety of dynamic behavior can emerge. These rotational dynamics of the organic linkers are especially important due to their influence over properties such as gas adsorption and kinetics of guest release. To fully exploit linker rotation, such as in the form of molecular machines, it is necessary to engineer correlated linker dynamics to achieve their cooperative functional motion. Here, we show that for MIL-53, a topology with closely spaced rotors, the phenylene functionalization allows researchers to tune the rotors' steric environment, shifting linker rotation from completely static to rapid motions at frequencies above 100 MHz. For steric interactions that start to inhibit independent rotor motion, we identify for the first time the emergence of coupled rotation modes in linker dynamics. These findings pave the way for function-specific engineering of gear-like cooperative motion in MOFs.

Chart 1. Schematic of the Energy Profile of a Terephthalate Rotor Linker

Figure 1

Structure of three members of the MIL-53 family viewed along the pore direction. (a) MIL-53(Al) (lp), (b) NO₂-MIL-53(Al) (lp), and (c) NH₂-MIL-53(Al) (np). This topology is characterized by four distinct rows of linkers per unit cell forming rhombic pores. Closest row distances for each MOF are marked in magenta. For compete unit cell parameters, see Table S2.

Figure 2

Effect of linker rotation on the potential energy as studied by DFT. (a) Unit cell of NO₂-MIL-53(Al) with central linker in 0° rotation with respect to (011) plane (pink); hydrogens omitted for clarity. (b) Rotation angle is defined as the angle between benzene ring plane and (011) plane, taking 0° as the conformation with the functional group pointing in the positive [100] direction. The sign of the angle is assigned based on the direction normal of the reference plane. (c) Potential energy profiles for the rotation of one linker in a NH₂-MIL-53(Al) and NO₂-MIL-53(Al) unit cell. The direction of rotation is indicated by the direction of the marker. (d) Example of an unfavorable head-to-head nitro group encounters in adjacent linkers when they are located on the same side of the ring (top) and on different sides (bottom).

Figure 3

Dielectric spectra of the three systems. (a, b) Imaginary part (ε′′) of ε* for NO₂-MIL-53(Al) with respect to temperature (a) and frequency (b). The latter includes the fitted Cole–Cole model as continuous lines. (c, d) Temperature dependence of ε″ for NH₂-MIL-53(Al) (c) and MIL-53(Al) (d).

Figure 4

Solid-state ²H NMR studies of NO₂-MIL-53(Al)-d₃. (a) Experimental (black) and simulated (red) variable-temperature ²H SSNMR spectra of NO₂-MIL-53(Al)-d₃. (b) Spectra are composed of overlapping patterns representing SML (<10³ Hz) and FML (>10⁷–10⁸ Hz) motions, with relative integrated intensities indicated to the right of the simulated spectra. (c) Cartesian frame of reference for the rotation model. (d) Representation of ²H exchange sites and angles used in the model; deuterons are shown in light blue.

Figure 5

Cooperative rotation in NO₂-MIL-53(Al). (a) Rotation angle traces of two neighboring rings in a 2 × 1 × 1 cell MD simulation at 700 K. Correlated motion is observed, with simultaneous angle changes in opposite directions (i, ii, iii), when nitro groups are in proximity (N···N distance ca. 4 Å). (b) Selected snapshots (i–iv) of linker pair conformation during a coupled rotation. As ring A rotates in the positive direction, ring B reaches the space originally occupied by ring A.