Understanding Pore Filling Processes and Adsorption/Desorption Hysteresis in Nanoporous Metal–Organic Frameworks: Insights from Grand Canonical Monte Carlo Simulations and Free Energy Calculations

Grand canonical Monte Carlo (GCMC) simulations were used
to investigate
pore filling and hysteresis in nanoporous metal–organic frameworks
(MOFs). Adsorption and desorption isotherms were calculated for argon
at 87 K in 1866 MOFs from the CoRE MOF database and for short n-alkanes in selected MOFs, keeping the adsorbent structure
rigid. Analysis of the molecular configurations showed two different
mechanisms and origins of hysteresis: one involving a transition of
the adsorbate arrangement in the pores similar to a gas-to-liquid
transition associated with a large change in the loading and one more
similar to a liquid-to-solid transition associated with a relatively
small change in the loading. Our GCMC simulations in MOFs with diverse
pore topologies indicate exceptions to an empirical relationship for
the minimum diameter of a cylindrical pore required for hysteresis
as a function of the adsorbate diameter and reduced temperature. The
simulations reveal some structures where isotherms exhibit two steps
in the adsorption branch and only one step in the desorption branch.
Hysteresis loops with different numbers of adsorption and desorption
steps are not common. To better understand why hysteresis is observed
in the GCMC simulations, the concept of the transition probability
for observing a step in the adsorption isotherm at a given pressure
in a GCMC simulation is introduced. We used two different methods
to calculate the transition probabilities and found that these yielded
comparable results. The transition probability provides a measure
of the length of GCMC simulations to yield reliable results.