  A simple lattice model of a solid electrolyte presented as a xy-slab geometry
system of mobile cations on a background of energetic landscape of the host
system and a compensating field of uniformly distributed anions is studied. The
system is confined in the z-direction between two oppositely charged walls,
which are in parallel to xy-plane. Besides the long-range Coulomb interactions
appearing in the system, the short-range attractive potential between cations
is considered in our study. We propose the mean field description of this model
and extend it by taking into account correlation effects at short distances.
Using the free energy minimization at each of z-coordinates, the corresponding
set of non-linear equations for the chemical potential is derived. The set of
equations was solved numerically with respect to the charge density
distribution in order to calculate the cations distribution profile and the
electrostatic potential in the system along z-direction under different
conditions. An asymmetry of charge distribution profile with respect to the
midplane of the system is observed. The effects of the short-range interactions
and pair correlations on the charge and electric field distributions are
demonstrated.
