(55g) Co-Oriented Fluid Functional Equation for Electrostatic Interactions (COFFEE) for Mixtures: Phase Behavior and Fluid Structure in Mixtures of Differently Polar Fluids

In chemical engineering, the vapor-liquid equilibrium (VLE) is one of the most fundamental characteristics of any given fluid mixture. Apart from being of intrinsic interest, the knowledge of the VLE is also essential for the successful design and operation of separation equipment. For mixtures however, experimental data are often scarce because experiments are time-consuming and expensive. Therefore, it is desirable to have reliable tools that can predict VLE of mixtures without the need for experimental mixture data. Hence, many thermodynamic models and theories are specifically geared towards predicting VLE of mixtures using only pure component data. However, theoretical predictions of the phase behavior of fluid mixtures are often challenging, particularly when the components differ significantly with respect to their polar properties. Conventional theories may yield unsatisfactory results when trying to describe mixtures of polar and nonpolar fluids. Furthermore, with the classic perturbation theory approach, polar and H-bonding interactions are typically considered as distinct contributions to the free energy despite being linked phenomena. That is, H-bonding only occurs in the presence of electrostatic interactions. Electrostatic interactions however, do not always coincide with H-bonding [1]. As has been demonstrated by Langenbach et al. [2], H-bonding behavior can be induced by off-center dipoles, i.e. dipoles that are shifted away from the center of the dispersive interactions of a given molecule. In molecular simulation, this can be easily achieved, by simply placing the site for electrostatic interactions at a small distance from the site for dispersive interactions. Generally, molecular simulation data for basic model fluids and mixtures thereof are often used for the development and assessment of new theoretical approaches to VLE prediction, as they make it possible to isolate the contributions of different types of molecular interactions to the overall fluid behavior.

Using molecular simulation data of polar model fluids, the new perturbation theory Co-Oriented Fluid Functional Equation for Electrostatic interactions (COFFEE) [3] aims at the simultaneous description of dipolar and H-bonding interactions. COFFEE differs from classic perturbation theories in that it separates the polar contribution to the free energy into a near field and a far field contribution, the former describing intermolecular interactions between direct neighbors and the latter particles at greater distances. The far field contribution is formulated as in classic perturbation theories. Within the near field however, the polar interactions are described while directly considering the preferential orientations between molecules that result from the polarity. These preferential orientations are captured by the orientation distribution function (ODF), which may be used to describe mutual orientations for molecules with central and off-center dipoles alike. For this purpose, COFFEE’s near field parameters were fitted to reproduce ODF from molecular dynamics simulations. The direct incorporation of the orientational structure is a unique feature of COFFEE that also allows for the prediction of thermophysical properties that depend on intermolecular orientation such as the relative permittivity [4, 5].

COFFEE has thus far been limited to the description of pure fluids. In this contribution, the recent extension of COFFEE to mixtures is presented. This new extension includes both the near field and the far field contributions and thus enables the prediction of both the ODF and VLE in mixtures of model fluids ranging from completely nonpolar to strongly polar while also considering off-center dipoles. As the nonpolar component, the Lennard Jones (LJ) fluid is chosen, while varying the energy parameter to generate LJ fluids with different volatilities. The polar components are modeled by the Stockmayer (ST) fluid, which consists of a LJ center with a superimposed point dipole, and by the shifted Stockmayer (sST) fluid, for which the point dipole is shifted away from the dispersive center. Several different dipole moments are considered for both the ST and the sST fluid. Binary mixtures of these components are investigated for a wide range of temperatures and across the whole range of compositions. For this purpose, a large base of molecular simulation data is established, including both ODF and VLE data. The VLE were calculated using the molecular simulation tool ms2 [6] and subsequently, ODF were calculated in the single-phase regions using the molecular dynamics software ls1 mardyn [7].

This large data base is then used to extend COFFEE to mixtures and assess the predictive ability of the theory. In a first step, the near field contribution is extended based on the original expression in a way that allows for the prediction of the ODF in mixtures without fitting mixture parameters. It is found that this approach leads to a satisfactory prediction of the ODF in mixtures with particularly accurate results in gas phases and for any binary mixtures containing one polar and one nonpolar component. For the prediction of VLE, good agreement between simulation and theory is found for a broad range of mixtures while keeping computational demand reasonably low. Figure 1 shows a VLE envelope and an ODF for a mixture of a LJ and a ST fluid as calculated by molecular simulation and with COFFEE. To characterize mutual orientations between two ST particles, three angles are required. φ₁ and φ₂ are the angles between the dipole vectors of the particles and the axis that connects the centers of mass of the particles. γ₁₂ is the rotation angle around this axis. The ODF is illustrated in terms of isosurfaces that show mutual orientations that occur with the same probability. Orientations that occur with an average probability are shown as a green surface. The red surface represents mutual orientations that occur with a 40% higher frequency than those on the green surface and on the blue surface, orientations occur at a 40% lower frequency.

In this contribution, an excerpt of the molecular simulation results for ODF and VLE and the respective predictions from COFFEE are shown for a variety of mixtures containing ST and LJ fluids. The theory is critically assessed and compared to alternative approaches.

References

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