The Dielectric Constant of Ionic Solutions: A Field-Theory Approach

TL;DR

This paper develops a field-theory model to predict how the dielectric constant of ionic solutions decreases with salt concentration, providing analytical insights and fitting experimental data across various salts.

Contribution

It introduces a novel field-theoretical approach to analytically predict the dielectric decrement in ionic solutions, incorporating ion size and hydration effects.

Findings

Analytical expression for dielectric decrement as a function of ionic strength

Qualitative description of hydration shell characterized by a single length scale

Good fit to experimental data across different salts with one fit parameter

Abstract

We study the variation of the dielectric response of a dielectric liquid (e.g. water) when a salt is added to the solution. Employing field-theoretical methods we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. We predict analytically the dielectric decrement which depends on the ionic strength in a complex way. Furthermore, a qualitative description of the hydration shell is found and is characterized by a single length scale. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles.