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-Hückel (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 $\xi$ diverges universally at low density $\rho$ as $(T\rho {)}^{-1/4\mathrm{}}$ (correcting the generalized mean-spherical approximation). When $\rho ={\rho }_c$ one has $\xi \simeq {\xi }_0^{+}{/t}^{1/2}$ as $t\equiv \left({T-T}_c\right){/T}_c\to 0+$, where the amplitudes ${\xi }_0^{+}$ compare informatively with experimental data.