Asymmetric primitive-model electrolytes: Debye-Hückel theory, criticality, and energy bounds

Debye-Hückel (DH) theory is extended to treat two-component size- and charge-asymmetric primitive models, focusing primarily on the 1:1 additive hard-sphere electrolyte with, say, negative ion diameters (Formula presented) larger than the positive ion diameters (Formula presented) The treatment highlights the crucial importance of the charge-unbalanced “border zones” around each ion into which other ions of only one species may penetrate. Extensions of the DH approach that describe the border zones in a physically reasonable way are exact at high T and low density ρ and, furthermore, are also in substantial agreement with recent simulation predictions for trends in the critical parameters, (Formula presented) and (Formula presented) with increasing size asymmetry. Conversely, the simplest linear asymmetric DH description, which fails to account for physically expected behavior in the border zones at low T, can violate a new lower bound on the energy (which applies generally to models asymmetric in both charge and size). Other theories, including those based on the mean spherical approximation, predict trends in the critical parameters quite opposite to those established by the simulations.