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
, which shows a typical gate adsorption behavior of CO2
, and determined precise structures of ELM-11 before and after the CO2
gate 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, ΔΩos, 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 (ΔFhost), 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, Nopen, as a function of chemical potential of the guest. The thermodynamic relation of ΔFhost is then expressed as: ΔFhost = ΔUhost – TΔShost, where ΔUhost and ΔShost 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 method3,4 using the in situ synchrotron XRPD data. We obtained Nopen at 195–298 K by grand canonical Monte Carlo (GCMC) simulations using the open framework structures from XRPD. We determined ΔFhost such that the ΔΩos value became zero at the experimental gate pressure, and found that there was a linear correlation between ΔFhost and temperature. The least-squares fitting of ΔFhost = ΔUhost – TΔShost to the obtained ΔFhost values provided ΔUhost = 30.6 kJ/mol and ΔShost = 65.9 J/Kmol. We then confirmed that the ΔUhost 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
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).