We
computed the transport of methane through 1 nm wide slit-shaped
pores carved out of selected solid substrates using classical molecular
dynamics simulations. The transport mechanism was elucidated via the
implementation of the well-tempered metadynamics algorithm, which
allowed for the quantification and visualization of the free energy
landscape sampled by the guest molecule. Models for silica, magnesium
oxide, alumina, muscovite, and calcite were used as solid substrates.
Slit-shaped pores of width 1 nm were carved out of these materials
and filled with liquid water. Methane was then inserted at low concentration.
The results show that the diffusion of methane through the hydrated
pores is strongly dependent on the solid substrate. While methane
molecules diffuse isotropically along the directions parallel to the
pore surfaces in most of the pores considered, anisotropic diffusion
was observed in the hydrated calcite pore. The differences observed
in the various pores are due to local molecular properties of confined
water, including molecular structure and solvation free energy. The
transport mechanism and the diffusion coefficients are dependent on
the free energy barriers encountered by one methane molecule as it
migrates from one preferential adsorption site to a neighboring one.
It was found that the heterogeneous water distribution in different
hydration layers and the low free energy pathways in the plane parallel
to the pore surfaces yield the anisotropic diffusion of methane molecules
in the hydrated calcite pore. Our observations contribute to an ongoing
debate on the relation between local free energy profiles and diffusion
coefficients and could have important practical consequences in various
applications, ranging from the design of selective membranes for gas
separations to the sustainable deployment of shale gas.