Ion association and electrical conductance minimum in Debye–Hückel-based theories of the hard sphere ionic fluid

We investigate the ion–ion pair association equilibrium in the hard sphere ionic fluid as predicted by several Debye–Hückel-based theories. The degree of dissociation is examined in a pairing theory based on Ebeling’s definition of the association constant, and in extensions of this theory for ion pair–free ion interactions by Fisher and Levin, and ion pair–ion pair interactions by Weiss and Schröer. The effect of an increase of the dielectric constant on the degree of dissociation is studied. In all cases, minima of the density-dependent degree of dissociation along isotherms are found at low ionic density, at least over part of the temperature range. The loci of these minima in the temperature-density plane are calculated. The results are compared with conductivity data. We discuss a possible resemblance of the system’s behavior in a region in which the degree of association changes rapidly with a tricritical scenario, in which a line of second-order insulator–conductor phase transitions intersects the coexistence curve.