  A field theoretic variational approach is introduced to study ion penetration
into water-filled cylindrical nanopores in equilibrium with a bulk reservoir.
It is shown that (i) an ion located in a neutral pore undergoes two opposing
mechanisms: the deformation of its surrounding ionic cloud of opposite charge,
with respect to the reservoir, which increases the surface tension and tends to
exclude ions form the pore, and (ii) the attractive contribution to the ion
self-energy of the repulsive image forces associated with the dielectric jump
between the solvent and the pore wall, which becomes more and more screened
when ions enter the pore. For pore radii around 1 nm and bulk concentrations
lower than 0.2 mol/L, this mechanism leads to a first-order phase transition,
similar to capillary "evaporation", from an ionic-penetration state to an
ionic-exclusion state. The discontinuous phase transition survives within the
biological concentration range (~ 0.15 mol/L) for small enough membrane
dielectric permittivities (< 5). In the case of a weakly charged pore,
counterion penetration exhibits a non-monotonic behaviour and is characterized
by two regimes: at low reservoir concentration or small pore radii, coions are
excluded and the energy barrier for counterions is reduced but image forces
remain strong enough, so that the counterion partition coefficient in the pore
decreases with increasing reservoir concentration up to a characteristic value;
for larger reservoir concentrations, image forces are screened and the
partition coefficient of counterions increases with the reservoir electrolyte
concentration.
