  Ionic transport in nano- to sub-nano-scale pores is highly dependent on
translocation barriers and potential wells. These features in the free-energy
landscape are primarily the result of ion dehydration and electrostatic
interactions. For pores in atomically thin membranes, such as graphene, other
factors come into play. Ion dynamics both inside and outside the geometric
volume of the pore can be critical in determining the transport properties of
the channel due to several commensurate length scales, such as the effective
membrane thickness, radii of the first and the second hydration layers, pore
radius, and Debye length. In particular, for biomimetic pores, such as the
graphene crown ether we examine here, there are regimes where transport is
highly sensitive to the pore size due to the interplay of dehydration and
interaction with pore charge. Picometer changes in the size, e.g., due to a
minute strain, can lead to a large change in conductance. Outside of these
regimes, the small pore size itself gives a large resistance, even when
electrostatic factors and dehydration compensate each other to give a
relatively flat -- e.g., near barrierless -- free energy landscape. The
permeability, though, can still be large and ions will translocate rapidly
after they arrive within the capture radius of the pore. This, in turn, leads
to diffusion and drift effects dominating the conductance. The current thus
plateaus and becomes effectively independent of pore-free energy
characteristics. Measurement of this effect will give an estimate of the
magnitude of kinetically limiting features, and experimentally constrain the
local electromechanical conditions.
