Statistical mechanical model of gas adsorption in porous crystals with dynamic moieties

Abstract

Some nanoporous, crystalline materials possess dynamic constituents, for example, rotatable moieties. These moieties can undergo a conformation change in response to the adsorption of guest molecules, which qualitatively impacts adsorption behavior. We pose and solve a statistical mechanical model of gas adsorption in a porous crystal whose cages share a common ligand that can adopt two distinct rotational conformations. Guest molecules incentivize the ligands to adopt a different rotational configuration than maintained in the empty host. Our model captures inflections, steps, and hysteresis that can arise in the adsorption isotherm as a signature of the rotating ligands. The insights disclosed by our simple model contribute a more intimate understanding of the response and consequence of rotating ligands integrated into porous materials to harness them for gas storage and separations, chemical sensing, drug delivery, catalysis, and nanoscale devices. Particularly, our model reveals design strategies to exploit these moving constituents and engineer improved adsorbents with intrinsic thermal management for pressure-swing adsorption processes.metal-organic frameworks | flexible metal-organic frameworks | statistical mechanics | porous materials | gas storage M etal-organic frameworks (MOFs) are porous, crystalline materials with very large internal surface areas (1). The consequent adsorption properties of MOFs have demonstrated promise toward solving paramount energy problems (2) such as in gas storage (3) and gas separations (4). MOFs are also being explored for chemical sensing (5), drug delivery (6), and catalysis (7). In the synthesis of MOFs, metal nodes or clusters and organic linker molecules self-assemble (8). Owing to their modular and versatile chemistry, tens of thousands of MOFs have been synthesized (9).Some MOFs are dynamic/flexible and respond to gas molecules adsorbing into their pores by exhibiting structural changes while retaining their crystallinity (reviews in refs. 10-14). Reported modes of guest-induced structural changes in MOFs include breathing (15), swelling (16), and subnetwork displacement (17), as well as less dramatic changes, such as the rotation of a ligand (18) or deformation (19). In molecular recognition and enzyme catalysis in biology, a conformation change of the enzyme is often involved in substrate binding (20,21). Responsive, dynamic constituents thus may endow MOFs with enzymelike selectivities (11) for selective gas adsorption, chemical sensing, and catalysis.In the long run, a more intimate understanding of MOFs with moving parts may enable the construction of molecular machines (22). Because of their crystallinity and tunability, MOFs are an ideal scaffold on which to organize machine subunits and tune their response to stimuli. Notably, Zhu et al. (23) used a [2] rotaxane molecular switch as a building block in a MOF to construct a conceptual molecular machine.Several reported MOFs possess dynamic constituents, e.g., bridging ligands that can rotate, while maintaini...

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