  Modulating ion transport through nanoporous membranes is critical to many
important chemical and biological separation processes. The corresponding
transport timescales, however, are often too long to capture accurately using
conventional molecular dynamics (\textsc{Md}). Recently, path sampling
techniques such as forward-flux sampling (\textsc{Ffs}) have emerged as
attractive alternatives for efficiently and accurately estimating arbitrarily
long ionic passage times. Here, we use non-equilibrium \textsc{Md} and
\textsc{Ffs} to explore how the kinetics and mechanism of pressure-driven
chloride transport through a nanoporous graphitic membrane are affected by its
lateral dimensions. We not only find ionic passage times and free energy
barriers to decrease dramatically upon increasing the membrane surface area,
but also observe an abrupt and discontinuous change in the locus of the
transition state. These strong finite size effects arise due to the cumulative
effect of the periodic images of the leading ion entering the pore on the
distribution of the induced excess charge at the membrane surface in the feed.
By assuming that the feed is an ideal conductor, we analytically derive a
finite size correction term that can be computed from the information obtained
from a single simulation and successfully use it to obtain corrected free
energy profiles with no dependence on system size. We then estimate ionic
passage times in the thermodynamic limit by assuming an Eyring-type dependence
of rates on barriers with a size-independent prefactor. This approach
constitutes a universal framework for removing finite size artifacts in
molecular simulations of ion transport through nanoporous membranes and
biological channel proteins.
