Molecular simulations of water adsorption in porous materials
often
converge slowly due to sampling bottlenecks that follow from hydrogen
bonding and, in many cases, the formation of water clusters. These
effects may be exacerbated in metal–organic framework (MOF)
adsorbents, due to the presence of pore spaces (cages) that promote
the formation of discrete-size clusters and hydrophobic effects (if
present), among other reasons. In Grand Canonical Monte Carlo (MC)
simulations, these sampling challenges are typically manifested by
low MC acceptance ratios, a tendency for the simulation to become
stuck in a particular loading state (i.e., macrostates), and the persistence of specific clusters for long periods of the
simulation. We present simulation strategies to address these sampling
challenges, by applying flat-histogram MC (FHMC) methods and specialized
MC move types to simulations of water adsorption. FHMC, in both Transition-matrix
and Wang–Landau forms, drives the simulation to sample relevant
macrostates by incorporating weights that are self-consistently adjusted
throughout the simulation and generate the macrostate probability
distribution (MPD). Specialized MC moves, based on aggregation-volume
bias and configurational bias methods, separately address low acceptance
ratios for basic MC trial moves and specifically target water molecules
in clusters; in turn, the specialized MC moves improve the efficiency
of generating new configurations which is ultimately reflected in
improved statistics collected by FHMC. The combined strategies are
applied to study the adsorption of water in CuBTC and ZIF-8 at 300
K, through examination of the MPD and the adsorption isotherm generated
by histogram reweighting. A key result is the appearance of nontrivial
oscillations in the MPD, which we show to be associated with water
clusters in the adsorption system. Additionally, we show that the
probabilities of certain clusters become similar in value near the
boundaries of the isotherm hysteresis loop, indicating a strong connection
between cluster formation/destruction and the thermodynamic limits
of stability. For a hydrophobic MOF, the FHMC results show that the
phase transition from low density to high density is suppressed to
water pressure far above the bulk-fluid saturation pressure; this
is consistent with results presented elsewhere. We also compare our
FHMC simulation isotherm to one measured by a different technique
but with ostensibly the same molecular interactions and comment on
observed differences and the need for follow-up work. The simulation
strategies presented here can be applied to the simulation of water
in other MOFs using heuristic guidelines laid out in our text, which
should facilitate the more consistent and efficient simulation of
water adsorption in porous materials in future applications.