Correlation lengths in electrolytes : Exact results and sensible approximations

Abstract
Reliably understanding the phase behavior of basic models for ionic systems is still an important task for theory and one that has experimental relevance, particularly for the critical neighborhood of liquid electrolytes [1, 2]. To that end, exact calculations [3-5] of the charge and density correlations lengths (including the Lebowitz length) for hard-sphere electrolytes of general valences, Z_σ, and diameters, a_στ , have been undertaken using Meeron's diagrammatic analysis [J. Chem. Phys. 28 (1958) 630-643] and the hyper-netted chain graphical resummation. A variety of "universal" types of divergent behavior and leading nonuniversal corrections are found when the overall ionic density approaches zero. The approximate "generalized Debye-Hückel" theories [6-8], which yield charge and density correlation functions for the restricted primitive model (σ τ ± a_στ), may be tested and prove exact as regards the universal behavior at low densities. The critical region, however, still poses profound problems (see, e.g., [9]).¹