Dependence of the dielectric constant of electrolyte solutions on ionic concentration: A microfield approach

Abstract

We present a microfield approach for studying the dependence of the orientational polarization of the water in aqueous electrolyte solutions upon the salt concentration and temperature. The model takes into account the orientation of the solvent dipoles due to the electric field created by ions, and the effect of thermal fluctuations. The model predicts a dielectric functional dependence of the form $\ensuremath{\varepsilon}(c)={\ensuremath{\varepsilon}}_{w}\ensuremath{-}\ensuremath{\beta}L(3\ensuremath{\alpha}c/\ensuremath{\beta}),\phantom{\rule{1em}{0ex}}\ensuremath{\beta}={\ensuremath{\varepsilon}}_{w}\ensuremath{-}{\ensuremath{\varepsilon}}_{\mathrm{ms}}$, where $L$ is the Langevin function, $c$ is the salt concentration, ${\ensuremath{\varepsilon}}_{w}$ is the dielectric of pure water, ${\ensuremath{\varepsilon}}_{\mathrm{ms}}$ is the dielectric of the electrolyte solution at the molten salt limit, and $\ensuremath{\alpha}$ is the total excess polarization of the ions. The functional form gives a remarkably accurate description of the dielectric constant for a variety of salts and a wide range of concentrations.