Transport in one-dimensional Coulomb gases: From ion channels to nanopores

We consider a class of systems where, due to the large mismatch of dielectric constants, the Coulomb interaction is approximately one-dimensional. Examples include ion channels in lipid membranes and water filled nanopores in silicon films. Charge transport across such systems possesses the activation behavior associated with the large electrostatic self-energy of a charge placed inside the channel. We show here that the activation barrier exhibits non-trivial dependence on the salt concentration in the surrounding water solution and on the length and radius of the channel.