  The dielectric constant of ionic solutions is known to reduce with increasing
ionic concentrations. However, the origin of this effect has not been
thoroughly explored. In this paper we study two such possible sources:
long-range Coulombic correlations and solvent excluded volume. Correlations
originate from fluctuations of the electrostatic potential beyond the
mean-field Poisson-Boltzmann theory, evaluated by employing a field-theoretical
loop expansion of the free energy. The solvent excluded-volume, on the other
hand, stems from the finite ion size, accounted for via a lattice-gas model. We
show that both correlations and excluded volume are required in order to
capture the important features of the dielectric behavior. For highly polar
solvents, such as water, the dielectric constant is given by the product of the
solvent volume fraction and a concentration-dependent susceptibility per volume
fraction. The available solvent volume decreases as function of ionic strength
due the increasing volume fraction of ions. A similar decrease occurs for the
susceptibility due to correlations between the ions and solvent, reducing the
dielectric response even further. Our predictions for the dielectric constant
fit well with experiments for a wide range of concentrations for different
salts in different temperatures, using a single fit parameter related to the
ion size.
