Nonlinear dielectric decrement of electrolyte solutions: An effective medium approach

The dielectric constant of an electrolyte solution, which determines electrostatic interactions between colloids and interfaces, depends nonlinearly on the salinity and also on the type of salt. The linear decrement at dilute solutions is due to the reduced polarizability in the hydration shell around an ion. However, the full hydration volume cannot explain the experimental solubility, which indicates the hydration volume should decrease at high salinity. Volume reduction of the hydration shell is supposed to weaken dielectric decrement and thus should be relevant to the nonlinear decrement.

According to the effective medium theory for the permittivity of heterogeneous media, we derive an equation which relates the dielectric constant with the dielectric cavities created by the hydrated cations and anions, and the effect of partial dehydration at high salinity is taken into account.

Analysis of experiments on monovalent electrolytes suggests that weakened dielectric decrement at high salinity originates primarily from the partial dehydration. Furthermore, the onset volume fraction of the partial dehydration is found to be salt-specific, and is correlated with the solvation free energy. Our results suggest that while the reduced polarizability of the hydration shell determines the linear dielectric decrement at low salinity, ion-specific tendency of dehydration is responsible for nonlinear dielectric decrement at high salinity.