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

## TL;DR

This paper studies how methane gas interacts with a metal-organic framework, revealing how metastable states and energy barriers affect adsorption behavior.

## Contribution

The study presents the first quantitative mapping of methane adsorption free-energy profiles in IRMOF-8 using TMMC simulations.

## Key findings

- Methane adsorption in IRMOF-8 shows metastable states and free-energy barriers leading to hysteresis.
- TMMC simulations reveal cooperative rearrangements in the adsorbed phase due to competing interactions.
- The study links free-energy minima to a three-state structural rearrangement of methane in the framework.

## Abstract

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.