Lattice models of ionic systems

A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye–Hückel theory with ion-pairing and dipole–ion solvation, specific calculations being performed for three-dimensional lattices. As for continuum electrolytes, low-density results for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices indicate the existence of gas–liquid phase separation. The predicted critical densities have values comparable to those of continuum ionic systems, while the critical temperatures are 60%–70% higher. However, when the possibility of sublattice ordering as well as Debye screening is taken into account systematically, order–disorder transitions and a tricritical point are found on sc and bcc lattices, and gas–liquid coexistence is suppressed. Our results agree with recent Monte Carlo simulations of lattice electrolytes.