Co-Oriented Fluid Functional Equation for Electrostatic interactions (COFFEE) for Mixtures: Molecular Orientations

The thermodynamic properties of mixtures are often challenging to predict with equations of state (EOS) especially when the components in a mixture differ considerably with respect to the degree or nature of their polar properties. One reason for this is that polar interactions and H-bonds, despite being intrinsically linked through the electrostatic character of the interactions, are often considered by means of separate contributions to the free energy in the most commonly utilized framework for formulating modern EOS, i.e., perturbation theory. Furthermore, classic perturbation theories do not typically consider the changes in fluid structure such as preferential orientations between polar particles that occur as a result of polar interactions. Instead, expressions for the free energy of polar interactions are usually developed around the structure of a reference fluid, i.e., the hard sphere fluid. As a consequence, the dipolar contribution is independent of other contributions beyond the reference, i.e., it is also independent of the H-bonding contribution. To address these challenges, the Co-Oriented Fluid Functional Equation for Electrostatic interactions (COFFEE) was developed. By expansion of the free energy around the structure of the target fluid rather than the reference, preferential orientations between neighboring particles are considered directly with the orientation distribution function (ODF). By additionally allowing for the description of decentral dipoles, a configuration typical of H-bonding species, polar and H-bonding interactions may be linked in a natural way. COFFEE was parametrized on the ODF and vapor liquid equilibria (VLE) of the Stockmayer (ST) fluid and reproduces both the ODF and VLE of ST fluids quantitatively. COFFEE also shows improvements in the description of the VLE of hydrogen chloride over literature models. In this contribution, the extension of COFFEE for the description of ODF in mixtures is presented. This extension also allows for the optional calculation of local concentrations in the near field. First, the correction function of the near field expression is simplified and refitted to new high quality ODF data for pure ST fluids to make the extension to mixtures straightforward. A large database from molecular simulations for the ODF and local concentrations in binary mixtures containing Lennard-Jones (LJ), ST and shifted ST (sST, the dipole is shifted away from the dispersive center) fluids is established for a large temperature range and different compositions to test the quality of the predictions from COFFEE. It is found that COFFEE predicts the ODF in mixtures with similar accuracy as for pure fluids with especially good agreement between simulations and theory for the vapor phase and for nonpolar-polar mixtures. In liquid polar-polar cases, molecular displacement phenomena occur, which currently can not be reproduced with COFFEE as this would necessitate the consideration of multiparticle effects. Predictions for local concentrations agree qualitatively with simulation data in most cases but show quantitative deviations, which may be improved by incorporating the effect of dipolar interactions on the radial distribution function. Thus, the effects of fluid structure in mixtures, especially with regard to orientation, can now be described accurately and considered directly in an EOS.