Charge and density fluctuations in electrolytes: The Lebowitz and other correlation lengths

Puzzling features in the observed critical behavior of electrolyte solutions have stimulated the development of a generalized Debye-Hückel (GDH) theory which yields approximate but thermodynamically consistent correlation functions. Since understanding charge and density fluctuations proves crucial, we have employed Meeronʹs (1958) analysis supplemented by the HNC graphical resummation (1959) for the unrestricted primitive model (with distinct diameters, e.g., a++, a+−, and a−−) to compute exact low-density expansions, with leading correction terms, for the zeroth, second, and fourth moment charge-charge and density-density correlation lengths, ξZ,1 (T, ), ξN,1 (T, ), etc., and for the Lebowitz length, ξL (T, ). The latter quantifies the area law of charge fluctuations, QΛ2 , in a large domain Λ. All results confirm the predictions of the GDH approximation in leading orders which, thus, currently seems the best basis for studying criticality in ionic systems.