Thermodynamics of polyatomic fluid mixtures—I theory

Viscosity of Ionic Liquids: Theories and Models

Ionic liquids (ILs) offer a wide range of promising applications due to their unique and designable properties compared to conventional solvents. Further development and application of ILs require correlating/predicting their pressure-viscosity-temperature behavior. In this review, we firstly introduce methods for calculation of thermodynamic inputs of viscosity models. Next, we introduce theories, theoretical and semi-empirical models coupling various theories with EoSs or activity coefficient models, and empirical and phenomenological models for viscosity of pure ILs and IL-related mixtures. Our modelling description is followed immediately by model application and performance. Then, we propose simple predictive equations for viscosity of IL-related mixtures and systematically compare performances of the above-mentioned theories and models. In concluding remarks, we recommend robust predictive models for viscosity at atmospheric pressure as well as proper and consistent theories and models for P-η-T behavior. The work that still remains to be done to obtain the desired theories and models for viscosity of ILs and IL-related mixtures is also presented. The present review is structured from pure ILs to IL-related mixtures and aims to summarize and quantitatively discuss the recent advances in theoretical and empirical modelling of viscosity of ILs and IL-related mixtures.

Multipolar SAFT-VR Mie Equation of State: Predictions of Phase Equilibria in Refrigerant Systems with No Binary Interaction Parameter

An extension of the SAFT-VR Mie equation of state is proposed to predict the properties of multipolar fluids. The new model, referred to as multipolar M-SAFT-VR Mie, incorporates the general multipolar term developed by Gubbins and co-workers, which accounts for dipole-dipole, quadrupole-quadrupole, and dipole-quadrupole interactions. A modification of the third order terms in the perturbation theory results in an accurate description of the simulation data for multipolar Lennard-Jones fluids. Both the M-SAFT-VR Mie and polar soft-SAFT models are extended to account for polarizability, and a good agreement is obtained with molecular simulation data. The M-SAFT-VR Mie model is applied to refrigerant systems, and it is found that including both dipole and quadrupole moments in molecular models leads to more accurate results than using only a dipole moment. The new model provides excellent predictions of the vapor-liquid equilibria of zeotropic and azeotropic refrigerant mixtures without the need for binary interaction parameters, making it a valuable tool for formulating low-GWP working fluids.

Quantifying the effect of polar interactions on the behavior of binary mixtures: Phase, interfacial, and excess properties

In this work, polar soft-Statistical Associating Fluid Theory (SAFT) was used in a systematic manner to quantify the influence of polar interactions on the phase equilibria, interfacial, and excess properties of binary mixtures. The theory was first validated with available molecular simulation data and then used to isolate the effect of polar interactions on the thermodynamic behavior of the mixtures by fixing the polar moment of one component while changing the polar moment of the second component from non-polar to either highly dipolar or quadrupolar, examining 15 different binary mixtures. It was determined that the type and magnitude of polar interactions have direct implications on the vapor-liquid equilibria (VLE), resulting in azeotropy for systems of either dipolar or quadrupolar fluids when mixed with non-polar or low polar strength fluids, while increasing the polar strength of one component shifts the VLE to be more ideal. Additionally, excess properties and interfacial properties such as interfacial tension, density profiles, and relative adsorption at the interface were also examined, establishing distinct enrichment in the case of mixtures with highly quadrupolar fluids. Finally, polar soft-SAFT was applied to describe the thermodynamic behavior of binary mixtures of experimental systems exhibiting various intermolecular interactions (non-polar and polar), not only demonstrating high accuracy and robustness through agreement with experimental data but also providing insights into the effect of polarity on the interfacial properties of the studied mixtures. This work proves the value of having an accurate theory for isolating the effect of polarity, especially for the design of ad hoc polar solvents.

Polar soft-SAFT: theory and comparison with molecular simulations and experimental data of pure polar fluids

The consideration of polar interactions is of vital importance for the development of predictive and accurate thermodynamic models for polar fluids, as they govern most of their thermodynamic properties, making them highly non-ideal fluids.

An equation of state for Stockmayer fluids based on a perturbation theory for dipolar hard spheres

We develop a perturbation theory for the difference between the Helmholtz energy of a Stockmayer fluid, i.e., a fluid interacting by a Lennard-Jones plus point-dipole potential, and a Lennard-Jones fluid. We show that the difference can be approximated by the perturbational Helmholtz energy contribution of a dipolar hard-sphere fluid with a suitably chosen effective hard-sphere diameter, relative to a hard-sphere fluid with the same effective diameter. We analyze both a third and fourth order perturbation theory, both written as Padé approximations. Several recipes for calculating the hard-sphere diameter are investigated; we find that the Weeks-Chandler-Andersen diameter is most suitable. Results of the perturbation theory are shown to be in good agreement with reference data for the Helmholtz energy, internal energy, and isochoric heat capacity as obtained from molecular simulations performed in this work and to vapor-liquid equilibrium data from the literature. Theoretical predictions of the proposed model are compared to results from the perturbation theory of Gubbins and Twu [Chem. Eng. Sci. 33, 863 (1978)], which is a theory based on a Lennard-Jones reference fluid. We find the theories are in good agreement. Our approach can easily be applied to van der Waals potentials, other than Lennard-Jones potentials. If a dipolar Mie fluid is considered, the approach merely requires calculation of the effective hard-sphere diameter for a Mie potential. We further note that the approach has a reduction in the variable space of the underlying correlation integrals, i.e., the correlation functions of a hard-sphere fluid depend on density only, whereas the Lennard-Jones reference correlation functions depend on density and temperature.

Rapid Determination of Interfacial Tensions in Nanopores: Experimental Nanofluidics and Theoretical Models

A rapid and accurate determination of interfacial tensions (IFTs) in nanopores is scientifically and practically significant, while most existing experimental measurements are restricted to the micrometer scale and theoretical calculations are relatively limited. In this study, six series of the IFT measurement tests for the binary CO₂-C₁₀, C₁-C₁₀, and N₂-C₁₀ mixtures are conducted at temperatures ( T) of 25.0 and 53.0 °C in a self-manufactured nanofluidic system. Moreover, a nanoscale-extended equation-of-state model considering the effects of the confinement, intermolecular interactions, and disjoining pressure and a semianalytical correlation are proposed to calculate the IFTs of the three mixtures in bulk phase and nanopores. Third, a new Tolman length formulation is developed for the IFT corrections in nanopores. Overall, the calculated IFTs from the two theoretical methods agree well with the measured results for most cases in nanopores. On the other hand, effects of the pore scale, temperature, pressure, and fluid composition on the IFTs of the three mixtures are effectively validated and specifically investigated. One suggestion comes from this work that the two theoretical methods for calculating the IFTs are better to be applied concurrently to minimize errors. Another important future work is to include more pore surface parameter (e.g., wettability) into the theoretical model.

Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal

The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.

A simulation assessment of the thermodynamics of dense ion-dipole mixtures with polarization

Molecular dynamics (MD) simulations are employed to ascertain the relative importance of various electrostatic interaction contributions, including induction interactions, to the thermodynamics of dense, hot ion-dipole mixtures. In the absence of polarization, we find that an MD-constrained free energy term accounting for the ion-dipole interactions, combined with well tested ionic and dipolar contributions, yields a simple, fairly accurate free energy form that may be a better option for describing the thermodynamics of such mixtures than the mean spherical approximation (MSA). Polarization contributions induced by the presence of permanent dipoles and ions are found to be additive to a good approximation, simplifying the thermodynamic modeling. We suggest simple free energy corrections that account for these two effects, based in part on standard perturbative treatments and partly on comparisons with MD simulation. Even though the proposed approximations likely need further study, they provide a first quantitative assessment of polarization contributions at high densities and temperatures and may serve as a guide for future modeling efforts.

Effective coarse-grained solid–fluid potentials and their application to model adsorption of fluids on heterogeneous surfaces

In the present contribution we emphasise the necessity of using an adequate averaging procedure to obtain effective fluid–surface potentials. A procedure to develop free-energy-averaged fluid–surface potentials retaining the important temperature dependence of the coarse-grained particle-surface interaction is described.

TOWARDS A MOLECULAR THEORY FOR THE VAN DER WAALS–MAXWELL DESCRIPTION OF FLUID PHASE TRANSITIONS

We briefly review developments of theories for phase transitions of molecular fluids and mixtures, from semi-phenomenological approaches providing equations of state with adjustable parameters to first-principles microscopic methods qualitatively correct for a variety of molecular models with realistic interaction potentials. We further present the generalization of the van der Waals–Maxwell description of fluid phase diagrams to account for chemical specificities of polar molecular fluids, such as hydrogen bonding. Our theory uses the reference interaction site model (RISM) integral equation approach complemented with the new closure we have proposed (KH approximation), successful over a wide range of density from gas to liquid. The RISM/KH theory is applied to the known three-site models of water, methanol, and hydrogen fluoride. It qualitatively reproduces their vapor-liquid phase diagrams and the structure in the gas as well as liquid phases, including hydrogen bonding. Furthermore, phase transitions of water and methanol sorbed in nanoporous carbon aerogel are described by means of the replica generalization of the RISM approach we have developed. The changes as compared to the bulk fluids are in agreement with simulations and experiment. The RISM/KH theory is promising for description of phase transitions in various associating fluids, in particular, electrolyte as well as non-electrolyte solutions and ionic liquids.

Prediction of the PC-SAFT associating parameters by molecular simulation

In this work, we propose a new methodology to determine association scheme and association parameters (energy and volume) of a SAFT-type EoS for hydrogen-bonding molecules. This paper focuses on 1-alkanol molecules, but the new methodology can also be applied for any other associating system. The idea is to use molecular simulation technique to determine independently monomer and free hydrogen fractions from which the association scheme can be deduced. The 3B scheme thus appeared to be the most appropriate for 1-alkanols. Once the association scheme is defined, the association strength can be back-calculated from molecular simulation results and used as an independent property for the equation of state parameters regression, in addition of the classical phase properties such as vapor pressure and liquid molar volume. A new set of parameters for 1-alkanol for the PPC-SAFT equation of state has been proposed following this methodology. Results are found in good agreement with experimental data for both phase properties and free hydrogen-bonding sites. Hence, this new methodology makes it possible to optimize parameters allowing an accurate reproduction of pure compounds data and yielding physically significant values for associating energy and associating volume.