Density Fluctuations in an Electrolyte from Generalized Debye-Hückel Theory

Near-critical thermodynamics in the hard-sphere (1, 1) electrolyte is well described, at a classical level, by Debye-H\"uckel (DH) theory with (+,-) ion pairing and dipolar-pair-ionic-fluid coupling. But DH-based theories do not address density fluctuations. Here density correlations are obtained by functional differentiation of DH theory generalized to nonuniform densities of various species. The correlation length ξ diverges universally at low density ρ as (Tρ)^-1/4 (correcting the generalized mean-spherical approximation). When ρ0ex0ex=0ex0exρc one has ξξ₀⁺/t1/2 as t≡(T-Tc)/Tc→0+, where the amplitudes ξ₀⁺ compare informatively with experimental data.