Predicting the Relative Static Permittivity: a Group Contribution Method Based on Perturbation Theory

Abstract

The computer-aided design of (bio)chemical processes requires models that predict thermodynamic properties with as little experimental effort as possible. For the important class of electrolyte systems, the relative static permittivity of the solvent is an important thermodynamic property that depends on the temperature, pressure, composition, and molecular structure of the solvent. This work presents a broadly applicable model for the temperature-dependent relative static permittivity of pure and mixed solvents based on perturbation theory, including a group contribution method. For this purpose, we extend our previous model for polar substances to nonpolar substances. The developed model is parametrized for 785 substances, where permittivity and density data are available in the Dortmund Data Bank and the ThermoML database. Subsequently, a group contribution method is developed to predict the permittivity parameters from the molecular structure. With a mean absolute deviation of 0.2 averaged over all 785 substances, the parametrized model accurately correlates the relative static permittivity over a wide range of permittivities and temperatures. Moreover, the group contribution method achieves a mean absolute deviation of 0.6 for the substances in the training set. A leave-one-out cross-validation shows that the group contribution method accurately predicts substances not included in the training set.

Assessment of Approaches towards the Relative Permittivity of Mixtures

“…Given the univariate dependence of the relative permittivity on dipole strength, it comes as little surprise that the perturbation theory by Tani et al and the model by Neumaier et al , showed great success in predicting the relative permittivities of the mixtures. However, both approaches rely on pure-component permittivity data; the Padé approximant for the correlation integral in the theory by Tani et al was fitted to numerical data, while the model by Neumaier et al requires some data on pure-component permittivities to fit the two adjustable parameters.…”

“…Recently, Neumaier et al modeled the correlation integral as I ( y ′ ) = I d d normalΔ 9 17 π 2 = 1 + a 2 ( e − y ′ − 1 ) where the so-called scaled dipole strength y ′ = a 1 y is introduced. , The model has two adjustable pure-component parameters: the parameter a 1 in eq is meant to account for the nonsphericity of real fluids and must be equal to or greater than zero; the parameter a 2 scales the dependence of the correlation integral on the dipole strength. In this work, we individually adjusted the pure-component parameters to reproduce previously published data , for the relative permittivity of the three pure ST fluids with the reduced dipole moments μ* = 1, 1.5, and 2.…”

“…is introduced. 25,26 The model has two adjustable purecomponent parameters: the parameter a 1 in eq 24 is meant to account for the nonsphericity of real fluids and must be equal to or greater than zero; the parameter a 2 scales the dependence of the correlation integral on the dipole strength.…”

“…Recently, another approach was developed by the group of Gross. 25,26 Their approach is based on the same expansion concept and introduces two adjustable parameters: a nonsphericity parameter, which scales the dipole strength, and a parameter that governs the dependence of the correlation integral on that scaled dipole strength. Both parameters are adjusted to experimental pure-component data.…”

“…The simulation results are provided in the Supporting Information. That data set is used to assess the quality of predictions obtained from COFFEE, the perturbation-theory-based approaches by Tani et al, 21 Gordon and Goldman, 22 and Neumaier et al, 25,26 as well as the mixing rules proposed by Looyenga 29 and Oster. 27 ■ METHODS Studied Model Fluids.…”