Density Fluctuations in an Electrolyte from Generalized Debye-Hueckel Theory

TL;DR

This paper extends Debye-Hueckel theory to include density fluctuations in electrolytes, revealing a universal divergence of correlation length near criticality and providing results consistent with experimental data.

Contribution

It generalizes Debye-Hueckel theory to non-uniform densities, enabling analysis of density correlations and fluctuations in electrolytes near critical points.

Findings

Correlation length diverges as (T ho)^{-1/4} at low density

At critical density, correlation length scales as t^{-1/2} near T_c

Results align with experimental measurements of electrolyte behavior

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 $\xi$ diverges universally at low density $\rho$ as $(T\rho)^{-1/4}$ (correcting GMSA theory). When $\rho=\rho_c$ one has $\xi\approx\xi_0^+/t^{1/2}$ as $t\equiv(T-T_c)/T_c\to 0+$ where the amplitudes $\xi_0^+$ compare informatively with experimental data.