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.