Mean field effects in a lattice gas model of ionic space charge

Abstract

Lattice gas models of the diffuse space charge layer in liquids and in ionic solids with Schottky or Frenkel disorder are considered with and without mean-field charge-interaction corrections. Even without explicit interaction corrections, the lattice gas model, by taking some account of charge carrier size in the liquid case and the actual lattice structure of the material in the case of single crystal solids, predicts a saturation in local charge density at high potentials, unlike the physically less realistic conventional Gouy-Chapman ideal gas, or independent particle model. Both unmodified and modified mean field corrections to the lattice gas basis are discussed and Coulombic interaction terms are considered in detail. The Monte-Carlo results obtained by other workers show that, as expected, the actual mean-field interaction terms required for fitting must be much smaller than those predicted by the unscreened Coulombic interaction. It is suggested that the mean field approach of Gurevich and Kharkats, who introduce an attractive mean field interaction between charges of like sign, is unlikely to be applicable over the entire space charge region of solid electrolyte systems and thus may not provide an explanation for the conductivity instability observed in α-AgSbS 2. Some possible future directions of investigation for lattice gas models are also briefly discussed.