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The dielectric constant of ionic solutions is known to reduce with increasingionic concentrations. However, the origin of this effect has not beenthoroughly explored. In this paper we study two such possible sources:long-range Coulombic correlations and solvent excluded volume. Correlationsoriginate from fluctuations of the electrostatic potential beyond themean-field Poisson-Boltzmann theory, evaluated by employing a field-theoreticalloop expansion of the free energy. The solvent excluded-volume, on the otherhand, stems from the finite ion size, accounted for via a lattice-gas model. Weshow that both correlations and excluded volume are required in order tocapture the important features of the dielectric behavior. For highly polarsolvents, such as water, the dielectric constant is given by the product of thesolvent volume fraction and a concentration-dependent susceptibility per volumefraction. The available solvent volume decreases as function of ionic strengthdue the increasing volume fraction of ions. A similar decrease occurs for thesusceptibility due to correlations between the ions and solvent, reducing thedielectric response even further. Our predictions for the dielectric constantfit well with experiments for a wide range of concentrations for differentsalts in different temperatures, using a single fit parameter related to theion size.

Dielectric Constant of Ionic Solutions: Combined Effects of Correlations and Excluded Volume