Understanding the origins of reversible and hysteretic pathways of adsorption phase transitions in metal-organic frameworks.

Phase behavior of nanoconfined fluids adsorbed in metal-organic frameworks is of paramount importance for the design of advanced materials for energy and gas storage, separations, electrochemical devices, sensors, and drug delivery, as well as for the pore structure characterization. Phase transformations in adsorbed fluids often involve long-lasting metastable states and hysteresis that has been well-documented in gas adsorption-desorption and nonwetting fluid intrusion-extrusion experiments. However, theoretical prediction of the observed nanophase behavior remains a challenging problem. The mesoscopic canonical, or mesocanonical, ensemble (MCE) is devised to study the nanophase behavior under conditions of controlled fluctuations to stabilize metastable and labile states. Here, we implement and apply the MCE Monte Carlo (MCEMC) simulation scheme to predict the origins of reversible and hysteric adsorption phase transitions in a series of practical MOF materials, including IRMOF-1, ZIF-412, UiO-66, Cu-BTC, IRMOF-74-V, VII, and IX. The MCEMC method, called the gauge cell method, allows to produce Van der Waals type isotherms with distinctive swings around the phase transition regions. The constructed isotherms determine the positions of phase equilibrium and spinodals, as well as the nucleation barriers separating metastable states. We demonstrate the unique capabilities of the MCEMC method in quantitative predictions of experimental observations compared with the conventional grand canonical and canonical ensemble simulations. The MCEMC method is implemented in the open-source RASPA and LAMMPS software packages and recommended for studies of adsorption behavior and pore structure characterization of MOFs and other nanoporous materials.