  The recent measurement of a very low dielectric constant, $\epsilon$, of
water confined in nanometric slit pores leads us to reconsider the physical
basis of ion partitioning into nanopores. For confined ions in chemical
equilibrium with a bulk of dielectric constant $\epsilon_b>\epsilon$, three
physical mechanisms, at the origin of ion exclusion in nanopores, are expected
to be modified due to this dielectric mismatch: dielectric exclusion at the
water-pore interface (with membrane dielectric constant,
$\epsilon_m<\epsilon$), the solvation energy related to the difference in
Debye-H\"uckel screening parameters in the pore, $\kappa$, and in the bulk
$\kappa_b$, and the classical Born solvation self-energy proportional to
$\epsilon^{-1}-\epsilon_b^{-1}$. Our goal is to clarify the interplay between
these three mechanisms and investigate the role played by the Born contribution
in ionic liquid-vapor (LV) phase separation in confined geometries. We first
compute analytically the potential of mean force (PMF) of an ion of radius
$R_i$ located at the center of a nanometric spherical pore of radius $R$.
Computing the variational grand potential for a solution of confined ions, we
then deduce the partition coefficients of ions in the pore. Phase diagrams of
the LV transition are established for various parameter values and we show that
a signature of this phase transition can be detected by monitoring the total
osmotic pressure. For charged nanopores, these exclusion effects compete with
the electrostatic attraction that imposes the entry of counterions into the
pore to enforce electro-neutrality. This study will therefore help in
deciphering the respective roles of the Born self-energy and dielectric
mismatch in experiments and simulations of ionic transport through nanopores.
