Lattice-gas model of a charge regulated planar surface

In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye–Huckel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the nearest-neighbor interactions for representing non-electrostatic forces between adsorbed ions. The Frumkin–Fowler–Guggenheim isotherm obtained from the mean-field analysis accurately reproduces the simulation data points.