(174e) Understanding Gate Adsorption of CO2 on Elastic Layer-Structured Metal-Organic Framework-11
The gate adsorption should occur at the pressure when the osmotic free energy change between the closed and open state, Î?Î©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 (Î?Fhost), PÎ?V term (P is pressure andÂ Î?V 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 ofÂ Î?Fhostis then expressed as:Â Î?Fhost = Î?Uhost â?? TÎ?Shost, where Î?Uhost and Î?Shost 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 195â??298 K were determined by our new structural refinement method3,4 using the in situ synchrotron XRPD data. We obtained Nopen at 195â??298 K by grand canonical Monte Carlo (GCMC) simulations using the open framework structures from XRPD. We determined Î?Fhost such that theÂ Î?Î©os value became zero at the experimental gate pressure, and found that there was a linear correlation between Î?Fhost and temperature. The least-squares fitting of Î?Fhost = Î?UhostÂ â?? TÎ?Shost to the obtained Î?Fhost values provided Î?Uhost = 30.6 kJ/mol and Î?Shost = 65.9 J/Kmol. We then confirmed that the Î?Uhost 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).