Transition Matrix Monte Carlo Analysis of Methane Adsorption in IRMOF-8

Metal-Organic Frameworks (MOFs) are highly porous crystalline materials formed by metal ions/clusters coordinated to linkers comprised of various organic molecules. These nanoporous materials are studied for their wide variety of applications, such as gas storage, gas capture, catalysis, etc. We performed a combination of Grand Canonical Monte Carlo (GCMC) and Transition-Matrix Monte Carlo (TMMC) simulations of methane in IRMOF-8 at subcritical conditions. For each temperature there is a pressure at which the methane uptake jumps sharply between low- and high-density regimes. GCMC shows significant hysteresis between adsorption and desorption isotherms, and significant (often slow) fluctuations of the density are observed. In the TMMC method, simulations are performed in the canonical ensemble with "ghost swaps" that allow the estimation of probabilities of transitions to different numbers of particles. This permits the determination free energy as function of the methane uptake; the global minimum of which determines the thermodynamic equilibrium condition. At various pressures close to the transition we observe the existence of one or more additional local minima and activation barriers resulting in emergence of metastable states which explain the adsorption hysteresis of GCMC and the existence of large, often slow, fluctuations.