  The confinement of an ionic liquid between charged solid surfaces is treated
using an exactly solvable 1D Coulomb gas model. The theory highlights the
importance of two dimensionless parameters: the fugacity of the ionic liquid,
and the electrostatic interaction energy of ions at closest approach relative
to thermal energy, in determining how the disjoining pressure exerted on the
walls depends on the geometrical confinement. Our theory reveals that
thermodynamic fluctuations play a vital role in the "squeezing out" of charged
layers as the confinement is increased. The model shows good qualitative
agreement with previous experimental data, with all parameters independently
estimated without fitting.
