Modeling of a charged dielectric interface: Comparison of the continuum and discrete lattice representations of surface charges

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.