Computation of dielectric constants of solvent mixtures and electrolyte solutions

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Abstract

A general model has been developed for calculating the static dielectric constant of mixed-solvent electrolyte solutions. For mixtures of solvents without electrolyte components, the model is based on an empirical modification of the Kirkwood theory for multicomponent systems. For systems containing electrolytes, the model takes into account the effects of ions and ion pairs and, therefore, it is capable of reproducing the dependence of the dielectric constant on electrolyte concentration. For most solvent mixtures, dielectric constants can be reasonably predicted using only pure solvent properties. In the case of strongly nonideal solvent mixtures, the results can be significantly improved by adjusting a single binary parameter. The model has also been verified for a number of electrolyte solutions in various solvents over wide composition and temperature ranges. In particular, the increase in the dielectric constant due to ion pairing and its decrease due to the presence of ions and their solvation can be accurately represented.

Introduction

The static dielectric constant is of central importance in the thermodynamics of electrolyte solutions. Excess thermodynamic properties of electrolyte solutions arise from various intermolecular interactions, especially those involving charged particles. Quantitative description of the electrostatic properties of the medium in which the charges are immersed is necessary for modeling the charge interactions that contribute to excess properties. Accurate modeling of the dielectric constant and its derivatives with respect to density and composition is important for the representation of chemical and phase equilibria in electrolyte solutions. Correlations of the dielectric constant for the most commonly used solvent, water, have been extensively studied in [1], [2], [3], [4]. Successful models for the dielectric constant of liquid mixtures have also been reported [5], [6], [7], [8], but these studies are limited to nonelectrolyte mixtures. While the concentration dependence of the dielectric constant of ionic systems has been recognized from experimental evidence, few attempts have been made to take this effect into account when modeling electrolyte solutions. At the same time, a substantial body of experimental data has been accumulated in the literature, thus making it possible to study compositional effects for systems with or without ionic components. Experimental data for the dielectric constant of liquid mixtures and electrolyte solutions have been published since the early 1900s. Akhadov [9] has compiled data for binary mixtures published prior to 1980. More data have been reported since then [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21].

This paper describes the development of a model for the representation of the dielectric constant for mixed solvents and electrolyte solutions as a function of temperature, pressure and concentrations of both nonionic and ionic components. The expressions obtained in this work are intended to be used in a comprehensive mixed-solvent electrolyte thermodynamic model, which accounts for not only phase equilibria, but also speciation effects.

The dielectric constant model is developed in two steps. In the first step, a formalism is established for predicting dielectric constants of solvent mixtures. In the second step, a correction for the presence of ions and ion pairs is introduced.

Section snippets

Dielectric constant of solvent mixtures

In this section, we first describe a simple method for predicting the dielectric constant of a fluid mixture using only pure-component data. Then, an extended form is developed that introduces a binary parameter and accounts for any deviations of the experimental dielectric constant from the regularities implied by the simple model.

Based on the Kirkwood theory [22] for a pure fluid, the dielectric constant, ε, is related to intermolecular interactions by(ε−1)(2ε+1)9ε=4πNA3vα+μ2g3kTwhere α is

Effect of electrolyte on the dielectric constant

The dielectric behavior of electrolyte solutions is more complicated in comparison to that of solvent mixtures because of ion solvation and association. Depending on the solvent’s properties and the extent of ion association or dissociation, the values of εs for the electrolyte solution may increase or decrease with rising electrolyte concentration. For example, addition of alkali and alkaline-earth halides to water and methanol results in a decrease in the dielectric constant of the solution

Results and discussion

Using , , , , , and appropriate thermophysical property data for pure components (e.g. εH2O, vi, Tc and Pc for water and organic solvents) [2], [44], dielectric constants of selected binary and ternary mixtures have been predicted and compared with the published experimental results. Table 1 gives results for the prediction of the static dielectric constant for 15 binary and six ternary systems, along with binary parameters in , and the average relative deviations (Δε%) from experimental data

Conclusions

General equations have been developed for calculating the static dielectric constant of mixed-solvent electrolyte solutions. Dielectric constants of solvent mixtures can be reasonably predicted on the basis of only pure solvent properties. The agreement with experimental data can be further improved by adjusting a single, temperature-independent binary parameter. The effects of ions and ion pairs are taken into account using empirical functions obtained by analyzing an extensive set of

Acknowledgements

The authors gratefully acknowledge the financial support of the Department of Energy under the Cooperative Agreement Number DE-FC02-00CH11019.

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