Predicting the Dielectric Constant of Real Polar Liquids

Abstract

The calculation of the permittivity of real polar liquids is one of the oldest problems, dating back to the classical works of Debye, Onsager, and Kirkwood. Despite its long history, such a calculation remains challenging. This is due to the many factors that affect permittivity, such as the geometry of the molecules, the distribution of dipole moments within the molecules, and the magnitude and orientation of these moments. Here, we show that the permittivity of many polar liquids admits a universal description. This occurs when short-range correlations in the dipole system are negligible. In this case, permittivity becomes a function of the average dipole interactions, which are described by the effective Debye parameter, yeff, related to the polarizability and dipole moments of the molecules, as well as their concentration. The explicit universal expression for permittivity, εuni(yeff), is obtained from the third-order virial series in particle concentration, in which all terms depending on the short-range coupling parameter are eliminated. The relationship was applied to approximately one hundred polar liquids with the permittivities ε ≤ 30. The main difficulty in the calculations was the values of the dipole moments of the molecules, which are unambiguously determined only in the gas phase. In solution, the magnitude of a molecule’s dipole moment depends on its neighbors. In calculations, we used the values of dipole moments found experimentally, mainly in benzene solutions. Overall, the theoretical and experimental results for permittivity are in good agreement with each other. Furthermore, the dipole moment predictions obtained from the universal dependence εuni and the experimental permittivity values with high accuracy (±0.1 D) approximate the experimental moment values. Finally, the universal dependence εuni is generalized to the case of mixtures of polar liquids under the assumption of additivity of the mixture’s Debye parameter and volume. This generalization provides an accurate lower estimate of the permittivity of a mixture of real polar liquids.