Criticality in ionic fluids: Debye-Hückel theory, Bjerrum, and beyond

Abstract

Debye-H\"uckel (DH) theory predicts phase separation in the primitive model electrolyte: hard spheres of diameter a with charges \ifmmode\pm\else\textpm\fi{}q. The coexistence curve (CC) is acceptable with ${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$\ensuremath{\equiv}${\mathit{k}}_{\mathit{B}}$${\mathit{T}}_{\mathit{c}}$a/${\mathit{q}}^{2}$=1/16, which is roughly correct, but the critical density, ${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}^{\mathrm{*}}$\ensuremath{\equiv}${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$${\mathit{a}}^{3}$=1/64\ensuremath{\pi}, is far too low. Allowing for association into ideal dipolar pairs, following Bjerrum, improves ${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}$ and leaves ${\mathit{T}}_{\mathit{c}}$ unchanged but yields an unphysical CC. Extending DH theory to compute the dipole-ionic-fluid coupling yields a mean-field description with sensible CC and (${\mathit{T}}_{\mathit{c}}^{\mathrm{*}}$,${\mathrm{\ensuremath{\rho}}}_{\mathit{c}}^{\mathrm{*}}$) close to Monte Carlo based estimates: (0.057\ifmmode\pm\else\textpm\fi{}${1}_{5}$ , 0.030\ensuremath{\mp}8).