  We investigate the modification of gas phase ion polarizabilities upon
solvation in polar solvents and ionic liquids. To this aim, we develop a
classical electrostatic theory of charged liquids composed of solvent molecules
modeled as finite size dipoles, and embedding polarizable ions that consist of
Drude oscillators. In qualitative agreement with ab-initio calculations of
polar solvents and ionic liquids, the hydration energy of a polarizable ion in
both type of dielectric liquid is shown to favor the expansion of its
electronic cloud. Namely, the ion carrying no dipole moment in the gas phase
acquires a dipole moment in the liquid environment, but its electron cloud also
reaches an enhanced rigidity. We find that the overall effect is an increase of
the gas phase polarizability upon hydration. In the specific case of ionic
liquids, it is shown that this hydration process is driven by a collective
solvation mechanism where the dipole moment of a polarizable ion induced by its
interaction with surrounding ions self-consistently adds to the polarization of
the liquid, thereby amplifying the dielectric permittivity of the medium in a
substantial way. We propose this self-consistent hydration as the underlying
mechanism behind the high dielectric permittivities of ionic liquids composed
of small charges with negligible gas phase dipole moment. Hydration being a
correlation effect, the emerging picture indicates that electrostatic
correlations cannot be neglected in polarizable liquids.
