Simple theory for oscillatory charge profile in ionic liquids near a charged wall

The mesoscopic field theory for ionic systems [A. Ciach and G. Stell, J. Mol. Liq. 87, 255 (2000)] is extended to the system with charged boundaries. A very simple expression for the excess grand potential functional of the charge density is developed. The size of hard-cores of ions is taken into account in the expression for the internal energy. The functional is suitable for a description of a distribution of ions in ionic liquids and ionic liquid mixtures with neutral components near a weakly charged wall. The Euler-Lagrange equation is obtained, and solved for a flat confining surface. An exponentially damped oscillatory charge density profile is obtained. The electrostatic potential for the restricted primitive model agrees with the simulation results on a semiquantitative level.