(609h) Mesocanonical Ensemble Simulations to Model Adsorption Phase Transitions within Nanopores

Monte Carlo simulation of adsorption isotherms is commonly performed in the grand canonical ensemble (GCMC), mimicking the environmental conditions of the isothermal adsorption measurements. In mesoporous and in some microporous materials, the pore filling is associated with phase transitions between vapor-like and liquid-like adsorbate states revealed in vertical steps on the GCMC isotherms. Moreover, in most cases these transitions involve metastable states and occur spontaneously out of equilibrium with the adsorption and desorption isotherms forming a prominent hysteresis loop. Similar hysteretic behaviors are observed in the experiments due to high nucleation barriers insurmountable within the finite simulation or experimental time. The equilibrium transition between the liquidlike and vaporlike states cannot be determined unless we run the GCMC simulations for an infinitely long time. Mesocanonical ensemble (MCE) has been introduced to sample the continuous S-shaped Van-der Waals type trajectory of metastable and thermodynamically unstable states connecting the vapor-like and liquid-like states.^[1,2] This is achieved by considering the equilibrium between the simulated box with a so-called gauge cell, which represent a finite volume reservoir of particles.^[1,2] The limited capacity of the gauge cell restrict the fluctuations and stabilized the adsorbed phase. MCE MC simulation method is known as a gauge cell MC method. In this work, we implemented the gauge cell MCEMC method in the open-source software RASPA. The method is first validated on MCM-41 and then applied to seven MOFs: IRMOF-1, ZIF-412, UiO-66, Cu-BTC, IRMOF-74-V, VII, and IX. We show that the gauge cell MCEMC simulations agree well and are more than 10 times faster than the Widom particle insertion method in NVT ensemble. Adsorption isotherms calculated using other methods such as the grand canonical Monte Carlo (GCMC) and the transition matrix Monte Carlo (TMMC) are also compared. For all MCEMC simulations, we discuss how to determine the equilibrium transition pressure, calculate the true grand canonical isotherm, and the energy barriers separating the vapor and liquid phases. Using examples of ZIF-412 and IRMOF-74-V, we discuss an interesting effect of consecutive swings of the canonical isotherm when the simulation cell contains multiple pores. Our results demonstrate that the gauge cell MCEMC method is an efficient alternative for simulating adsorption phase transitions in nanoporous materials.

1. Neimark, A. V.; Vishnyakov, A., Gauge cell method for simulation studies of phase transitions in confined systems. Physical Review E 2000, 62 (4), 4611-4622.
2. Vishnyakov, A.; Neimark, A. V., Studies of Liquid−Vapor Equilibria, Criticality, and Spinodal Transitions in Nanopores by the Gauge Cell Monte Carlo Simulation Method. The Journal of Physical Chemistry B 2001, 105 (29), 7009-7020.