  Two main approaches in particle-based simulations for modeling a charged
surface are using explicit, discrete charges and continuum, uniform charges. It
is well-known that these two approaches could lead to substantially distinct
ionic distributions, whereas a systematic exploration of the origin is still
absent. In this short communication, we calculate the electrostatic force of a
single point charge above a planar substrate characterized by a surface charge
density and dielectric mismatch and compare the differences in the
electrostatic forces produced by discrete and continuum representations of
surface charges. We demonstrate that while the model of uniform surface charges
gives a rather simple picture, the model of discrete surface charges can
exhibit different scenarios, depending on the respective values of ion-surface
distance versus lattice spacing and a self-image interaction parameter.
