Free Energy Landscapes and Metastability in Methane Adsorption within a Representative Metal-Organic Framework

Metal-organic frameworks (MOFs) are promising crystalline materials for gas storage due to their tunable porosity and high surface area. Adsorption in these materials exhibits complex behavior arising from confinement. We investigate methane (CH₄) adsorption in an IRMOF-8 model under subcritical conditions using Grand Canonical Monte Carlo (GCMC) and Transition-Matrix Monte Carlo (TMMC) simulations. The uptake N displays sharp transitions between low- and high-density adsorption states, reflecting underlying metastable configurations separated by free-energy barriers. In GCMC, slow fluctuations and hysteresis complicate equilibrium characterization, while TMMCusing ghost particle insertions/deletions in the canonical ensembleenables direct computation of the free-energy profile Ω-(N), revealing both stable and metastable adsorption states. These metastable states give rise to the hysteresis observed in GCMC. We also show that the uptake transitions correspond to cooperative rearrangements in the adsorbed phase, driven by competing adsorbate-adsorbate and adsorbate-framework interactions. To our knowledge, this is the first quantitative TMMC mapping of Ω-(N) for methane in IRMOF-8 that explicitly links free-energy minima to a three-state structural rearrangement of the confined CH₄ phase. Although the simulations employ a rigid model framework the observed free-energy landscapes and cooperative rearrangements of the adsorbed phase illustrate general features of methane adsorption in nanoporous solids. These results clarify the thermodynamic origin of metastability in confined adsorption and provide a transferable framework for analyzing complex adsorption phenomena in porous materials.