  Selective ion transport is a hallmark of biological ion channel behavior but
is a major challenge to engineer into artificial membranes. Here, we
demonstrate, with all-atom molecular dynamics simulations, that bare graphene
nanopores yield measurable ion selectivity that varies over one to two orders
of magnitude simply by changing the pore radius and number of graphene layers.
Monolayer graphene does not display dehydration-induced selectivity until the
pore radius is small enough to exclude the first hydration layer from inside
the pore. Bi- and tri-layer graphene, though, display such selectivity already
for a pore size that barely encroaches on the first hydration layer, which is
due to the more significant water loss from the second hydration layer.
Measurement of selectivity and activation barriers from both first and second
hydration layer barriers will help elucidate the behavior of biological ion
channels. Moreover, the energy barriers responsible for selectivity -- while
small on the scale of hydration energies -- are already relatively large, i.e.,
many $k_B$. For separation of ions from water, therefore, one can exchange
longer, larger radius pores for shorter, smaller radius pores, giving a
practical method for maintaining exclusion efficiency while enhancing other
properties (e.g., water throughput).
