Lattice models of ionic systems

Abstract

A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye-Hückel theory with ionpairing and dipole-ion solvation, specific calculations being performed for 3D lattices.As for continuum electrolytes, low-density results for sc, bcc and 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. 2

Lattice models of ionic systems with charge asymmetry

“…The second term in the free energy density is the electrostatic contributionf DH = 20 it can be easily shown that…”

“…This process significantly decreases the number of free ions. In charge-symmetric lattice electrolytes in the critical region the number of neutral ion pairs is 2-3 times larger than the number of free ions, 20 and one can expect that for charge-asymmetric ionic systems this ratio should be even larger because of the larger free energy gain for clusters with the increase of the parameter z.…”

“…In 1 : 1 electrolytes it allows one to define clearly an ion pair as two oppositely charged particles sitting on neighboring lattice sites. 20 Similarly, for chargeasymmetric lattice electrolytes we can easily define different cluster configurations. These particles may be viewed as independent chemical species, and the processes of clustering can be considered as a set of chemical reactions between them.…”

“…In recent years, lattice models have also attracted the attention of researchers as a tool for investigating thermodynamics and criticality in Coulomb systems. 1,18,19,20,21,22 A systematic study of electrolytes on lattices, which utilizes the DebyeHückel approach, has been presented recently. 20 In this work the thermodynamics of a ddimensional system of equal numbers of positive and negative ions, i.e., a charge-symmetric lattice RPM, has been investigated.…”

“…1,18,19,20,21,22 A systematic study of electrolytes on lattices, which utilizes the DebyeHückel approach, has been presented recently. 20 In this work the thermodynamics of a ddimensional system of equal numbers of positive and negative ions, i.e., a charge-symmetric lattice RPM, has been investigated. Specific calculations for Coulomb systems on threedimensional lattices, which included ion pairing and ion-dipole interactions, predicted a gasliquid phase separation at low densities.…”