Eliminating the limiting-current phenomenon by geometric field focusing into nanopores and nanoslots

A peculiar and undesirable current-voltage characteristic of nanoporous membranes is that it exhibits a voltage window with a near-constant limiting-current density when bulk ions near one surface of the membrane are depleted. We show both theoretically and experimentally that this interval disappears for an isolated circular nanopore (or narrow nanoslot) because radial field focusing at the pore entrance enhances the depletion effect and drives an ejecting hydrodynamic vortex pair that amplifies ion flux into the nanopore. This vortex pair is distinct from the vortex arrays that appear in front of a wide nanoslot or a nanoporous membrane with small inter-nanopore separation. It hence suggests that an optimal pore radius/separation ratio exists for maximum current density across a membrane.