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

TL;DR

This paper investigates how ionic correlations and solvent excluded volume jointly influence the dielectric constant of ionic solutions, providing a comprehensive model that aligns well with experimental data across various conditions.

Contribution

It introduces a combined theoretical framework incorporating both Coulombic correlations and ion size effects to explain dielectric behavior in ionic solutions.

Findings

Both correlations and excluded volume are essential to accurately model dielectric constant.

The model successfully fits experimental data across different salts and temperatures.

Dielectric constant decreases with ionic strength due to reduced solvent volume and correlation effects.

Abstract

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.