  Traditionally, ion-selectivity in nanopores and nanoporous membranes is
understood to be a consequence of Debye overlap, in which the Debye screening
length is comparable to the nanopore radius somewhere along the length of the
nanopore(s). This criterion sets a significant limitation on the size of
ion-selective nanopores, as the Debye length is on the order of 1 - 10 nm for
typical ionic concentrations. However, the analytical results we present here
demonstrate that surface conductance generates a dynamical selectivity in ion
transport, and this selectivity is controlled by so-called Dukhin, rather than
Debye, overlap. The Dukhin length, defined as the ratio of surface to bulk
conductance, reaches values of hundreds of nanometers for typical surface
charge densities and ionic concentrations, suggesting the possibility of
designing large-nanopore (10 - 100 nm), high-conductance membranes exhibiting
significant ion-selectivity. Such membranes would have potentially dramatic
implications for the efficiency of osmotic energy conversion and separation
techniques. Furthermore, we demonstrate that this mechanism of dynamic
selectivity leads ultimately to the rectification of ionic current,
rationalizing previous studies showing that Debye overlap is not a necessary
condition for the occurrence of rectifying behavior in nanopores.
