Density Fluctuations in an Electrolyte from Generalized Debye-Hueckel Theory

Abstract

Near-critical thermodynamics in the hard-sphere (1,1) electrolyte is well described, at a classical level, by Debye-Hueckel (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 {\it non}-uniform densities of various species. The correlation length $ξ$ diverges universally at low density $ρ$ as $(Tρ)^{-1/4}$ (correcting GMSA theory). When $ρ=ρ_c$ one has $ξ\approxξ_0^+/t^{1/2}$ as $t\equiv(T-T_c)/T_c\to 0+$ where the amplitudes $ξ_0^+$ compare informatively with experimental data.