Understanding Gate Adsorption of CO2 on Elastic Layer-Structured Metal-Organic Framework-11

Metal-organic frameworks (MOFs) with a flexible framework show an adsorption-induced structural transition called gate adsorption. The gate adsorption leads to a steep rise in the adsorption isotherm at a threshold gas pressure depending on a gas molecule, and thus the flexible MOFs are promising for the development of new gas storage and separation processes. Understanding of the gate adsorption behavior is crucial to control gate adsorption pressure for these applications by tailored synthesis of flexible MOFs. We have therefore focused on elastic layer-structured metal-organic framework-11 ([Cu(4,4'-bipyridine)₂(BF₄)₂]_n)¹, which shows a typical gate adsorption behavior of CO₂, and determined precise structures of ELM-11 before and after the CO₂gate adsorption (closed and open state) by in situ synchrotron X-ray powder diffraction (XRPD) measurements. The determination of the both structures is essential to model the gate adsorption behavior with the aid of molecular simulations and free energy analysis.

The gate adsorption should occur at the pressure when the osmotic free energy change between the closed and open state, ΔΩ_os, becomes zero.² The osmotic free energy change is represented as a sum of the Helmholtz free energy change required to deform the host framework (ΔF_host), PΔV term (P is pressure and ΔV is volume change of host), and the grand potential of guest that is obtained from the integration of a fictitious adsorption isotherm of the guest on the open host framework, N_open, as a function of chemical potential of the guest. The thermodynamic relation of ΔF_host is then expressed as: ΔF_host = ΔU_host – TΔS_host, where ΔU_host and ΔS_host are differences in the internal energy and entropy between the closed and open structures.

The closed structure of ELM-11 at 273 K and the open structure of ELM-11 encapsulating CO₂ at 195–298 K were determined by our new structural refinement method^3,4 using the in situ synchrotron XRPD data. We obtained N_open at 195–298 K by grand canonical Monte Carlo (GCMC) simulations using the open framework structures from XRPD. We determined ΔF_host such that the ΔΩ_os value became zero at the experimental gate pressure, and found that there was a linear correlation between ΔF_host and temperature. The least-squares fitting of ΔF_host = ΔU_host – TΔS_host to the obtained ΔF_host values provided ΔU_host = 30.6 kJ/mol and ΔS_host = 65.9 J/Kmol. We then confirmed that the ΔU_host value obtained from the free energy analysis coincided with the value from DFT-D calculations using the closed and open structures (31.2 kJ/mol), which demonstrates that the gate adsorption behavior can be adequately described by the thermodynamic model proposed by Coudert et al.²

References:

1) A. Kondo et al., Nano Lett. 6,2581 (2006).

2) F.-X. Coudert et al., J. Am. Chem. Soc. 130,14295 (2008).

3) H. Tanaka et al., J. Phys. Chem. C 119,11533 (2015).

4) S. Hiraide et al., Dalton Trans. 45,4193 (2016).