Dependence of the dielectric constant of electrolyte solutions on ionic concentration

We study the dependence of the static dielectric constant of aqueous electrolyte solutions upon the concentration of salt in the solution and temperature. The model takes into account the orientation of the solvent dipoles due to the electric field created by ions, the ionic response to an applied field, and the effect of thermal fluctuations. The analysis suggests that the formation of ion pairs by a small fraction of disassociated ions can have a significant effect on the static dielectric constant. The model predicts the dielectric has the functional dependence ε(c) = εw − βL(3αc/β) where L is the Langevin function, c is the salt concentration, εw is the dielectric of the pure water, α is the total excess polarization of the ions and β is the relative difference between the water dipole moment and the effective dipole moment of ion pairs as weighted by the density of ion pairs and their structural rigidity. The functional form gives an extremely accurate prediction of the dielectric constant for a variety of salts and a wide range of concentrations by fitting only the parameter β.