  In this paper, the authors study the limit of a sharp interface model for the
solvation of charged molecules in an implicit solvent as the number of solute
molecules and the size of the surrounding box tend to infinity. The energy is
given by a combination of local terms accounting for the physical presence of
the molecules in the solvent and a nonlocal electrical energy with or without
an ionic effect. In the presence of an ionic effect, the authors prove a
screening effect in the limit, i.e., the limit is completely localized and
hence electrical long-range interactions of the molecules can be neglected. In
the absence of the ionic effect, the authors show that the behavior of the
energy depends on the scaling of the number of molecules with respect to the
size of the surrounding box. All scaling regimes are identified and
corresponding limit results proved. In regimes with many solute molecules this
limit includes electrical interactions of $H^{-1}$-type between the molecules.
