Assessment of Approaches towards the Relative Permittivity of Mixtures

Relative permittivities of binary mixtures of model fluids, i.e., mixtures of two different Stockmayer fluids or Stockmayer + Lennard-Jones mixtures, are studied comprehensively using molecular dynamics (MD) simulations. The molecular interaction parameters are varied systematically in such a way that the mixtures possess very different types of vapor-liquid equilibrium behavior. The simulation results reveal that in line with findings from previous work on pure components, also for these mixtures the relative permittivity is a univariate function of the dipole strength, which combines the influence of density, inverse temperature, the squared dipole moments of the components, and their mole fractions. Furthermore, the capabilities of the molecular thermodynamics framework COFFEE are extended to describing permittivities in such mixtures predictively. This is achieved by using Kirkwood's equation for the relative permittivity together with the orientational information provided by COFFEE, which is necessary for calculating the Kirkwood factor. A suitable expression for the Kirkwood factor of mixtures is derived in detail. The predictions obtained with COFFEE as well as results from perturbation theories and empirical mixing rules from the literature are assessed systematically by comparison to the MD results. It is found that the perturbation theories developed solely for the purpose of modeling relative permittivities describe the data accurately, while only one of the empirical mixing rules does so as well. The new extension of COFFEE does not match the MD data as accurately; however, the main deficiencies arise from inaccuracies in the pure-component permittivities, while the general mixing characteristics are predicted correctly in all cases. The largest deviations occur at high densities and dipole moments, where it is known that the approximations in COFFEE lead to deviations in the orientation behavior.