Prediction of Binary and Ternary Diagrams Using the Statistical Associating Fluid Theory (SAFT) Equation of State

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.

Density functional theory for the prediction of interfacial properties of molecular fluids within the SAFT-γ coarse-grained approach

Recently, we have proposed the SAFT-VR Mie MF DFT approach [Algaba et al., Phys. Chem. Chem. Phys., 2019, 21, 11937–11948] to investigate systems that exhibit fluid–fluid interfaces. This formalism is based on the combination of the Statistical Associating Fluid Theory for attractive potentials of variable range using Mie intermolecular potential (SAFT-VR Mie) and a Density Functional Theory (DFT) treatment of the free energy. A mean-field approach is used to evaluate the attractive term, neglecting the pair correlations associated to attractions. This theory has been combined with reported SAFT-γ Coarse-Grained (CG) Mie force fields to provide an excellent description of the vapor–liquid interface of carbon dioxide and water pure fluids. The present work is a natural and necessary extension of this previous study. We assess the adequacy of the proposed methodology for dealing with inhomogeneous fluid systems of large complex molecules, in particular carbon tetrafluoride and sulfur hexafluoride greenhouse gases, the refrigerant 2,3,3,3-tetrafluoro-1-propene, and the long-chain n-decane and n-eicosane hydrocarbons. The obvious diversity of these fluids, their chemical and industrial interest, and the fact of that SAFT-γ CG Mie force fields have been reported for them justify such choice. With the aim of testing the theory, we perform Molecular Dynamics simulations in the canonical ensemble using the direct coexistence technique for the same models. We focus both on bulk, such as coexistence diagrams and vapor pressure curves, as well as interfacial properties, including surface tension. The comparison of the theoretical predictions with the computational results as well as with experimental data taken from the literature demonstrates the reliability and generalization of this method for dealing simultaneously with vapor–liquid equilibrium and interfacial phenomena. Hence, it appears as a potential tool for the interface analysis, with the main advantage over molecular simulation of low computational cost, and solving the experimental difficulties in accurately measuring the surface tension of certain systems.

Comparison of the vapour–liquid surface tensions for substances studied in this work as obtained from SAFT-VR Mie DFT and experiments.

Predicting the Thermodynamics of Ionic Liquids: What to Expect from PC-SAFT and COSMO-RS?

Two popular thermodynamic modeling frameworks, namely, the PC-SAFT equation of state and the COSMO-RS model, are benchmarked for their performance in predicting the thermodynamic properties of pure ionic liquids (ILs) and the solubility of CO₂ in ILs. The ultimate goal is to provide an illustration of what to expect from these frameworks when applied to ILs in a purely predictive way with established parametrization approaches, since the literature generally lacks their mutual comparisons. Two different modeling approaches with respect to the description of the molecular structure of ILs are tested within both models: a cation-anion pair as (i) a single electroneutral supermolecule and (ii) a pair of separately modeled counterions (ion-based approach). In general, we illustrate that special attention should be paid when estimating unknown thermodynamic data of ILs even with these two progressive thermodynamic frameworks. For both PC-SAFT and COSMO-RS, the supermolecule approach generally yields better results for the vapor pressure and the vaporization enthalpy of pure ILs, while the ion-based approach is found to be more suitable for the solubility of CO₂. In spite of some shortcomings, COSMO-RS with the supermolecule approach shows the best overall predictive capabilities for the studied properties. The ion-based strategy within both models has significant limitations in the case of the vaporization properties of ILs. In COSMO-RS, these limitations can, to a certain extent, be surpassed by additional quantum mechanical calculations of the ion pairing in the gas phase, while the ion-based PC-SAFT approach still needs a sophisticated improvement to be developed. As an initiating point, we explore one possible and simple route considering a high degree of cross associations between the counterions in the gas phase.

Equation of state and Helmholtz energy functional for fused heterosegmented hard chains

Modern equations of state for real nonspherical molecules are often based on Wertheim's first-order thermodynamic perturbation theory (TPT1). A major drawback of TPT1 is that it assumes tangentially bonded spheres. In this work, we develop a Helmholtz energy functional for systems comprising hard heterosegmented chains with arbitrary bond lengths. This is achieved by using hard-sphere fragments (i.e., hard spheres with spherical caps removed at the intersection to their neighbors) as monomers as opposed to full hard spheres. The model is written as a Helmholtz energy functional for inhomogeneous systems and the equation of state for a homogeneous system is determined as a special case. We thereby obtain an equation of state that can be used as a reference to develop statistical associating fluid theory models that more accurately describe the thermodynamic properties of nonspherical molecules. The model is validated against molecular simulation results of bulk pressures and density profiles in slit pores. For the bulk pressures, we show that the equation of state is in excellent agreement with results from molecular simulation for dimers, trimers, and chains of up to 20 segments. The density profiles of individual segments of the chains are regarded in slit pores. Some deviations of the theory from results of molecular simulations are observed for strongly fused chains. Overall, however, good agreement is found for inhomogeneous systems.

Assessment of Low Global Warming Potential Refrigerants for Drop-In Replacement by Connecting their Molecular Features to Their Performance

The use of hydrofluorocarbons (HFCs) as an alternative for refrigeration units has grown over the past decades as a replacement to chlorofluorocarbons (CFCs), banned by the Montreal's Protocol because of their effect on the depletion of the ozone layer. However, HFCs are known to be greenhouse gases with considerable global warming potential (GWP), thousands of times higher than carbon dioxide. The Kigali Amendment to the Montreal Protocol has promoted an active area of research toward the development of low GWP refrigerants to replace the ones in current use, and it is expected to significantly contribute to the Paris Agreement by avoiding nearly half a degree Celsius of temperature increase by the end of this century. We present here a molecular-based evaluation tool aiming at finding optimal refrigerants with the requirements imposed by current environmental legislations in order to mitigate their impact on climate change. The proposed approach relies on the robust polar soft-SAFT equation of state to predict thermodynamic properties required for their technical evaluation at conditions relevant for cooling applications. Additionally, the thermodynamic model integrated with technical criteria enable the search for compatibility of currently used third generation compounds with more eco-friendly refrigerants as drop-in replacements. The criteria include volumetric cooling capacity, coefficient of performance, and other physicochemical properties with direct impact on the technical performance of the cooling cycle. As such, R1123, R1224yd(Z), R1234ze(E), and R1225ye(Z) demonstrate high aptitude toward replacing R134a, R32, R152a, and R245fa with minimal retrofitting to the existing system. The current modeling platform for the rapid screening of emerging refrigerants offers a guide for future efforts on the design of alternative 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.

Characteristic Curves of the Lennard-Jones Fluid

Equations of state based on intermolecular potentials are often developed about the Lennard-Jones (LJ) potential. Many of such EOS have been proposed in the past. In this work, 20 LJ EOS were examined regarding their performance on Brown's characteristic curves and characteristic state points. Brown's characteristic curves are directly related to the virial coefficients at specific state points, which can be computed exactly from the intermolecular potential. Therefore, also the second and third virial coefficient of the LJ fluid were investigated. This approach allows a comparison of available LJ EOS at extreme conditions. Physically based, empirical, and semi-theoretical LJ EOS were examined. Most investigated LJ EOS exhibit some unphysical artifacts.

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.

Insights into the influence of the molecular structures of fluorinated ionic liquids on their thermophysical properties. A soft-SAFT based approach

Development of predictive models for FILs.

A methodology to parameterize SAFT-type equations of state for solid precursors of deep eutectic solvents: the example of cholinium chloride

Novel methodology for the development of coarse-grained models applicable to DES – a more realistic association scheme and model parameters regression from experimental data.

An accurate density functional theory for the vapor–liquid interface of chain molecules based on the statistical associating fluid theory for potentials of variable range for Mie chainlike fluids

A new Helmholtz free energy density functional is presented to predict the vapor–liquid interface of chainlike molecules.

Vapor Liquid Equilibria of Binary Mixtures of 1-Butyl-3-methylimidazolium Triflate (C4mimTfO) and Molecular Solvents: n-Alkyl Alcohols and Water

Isobaric vapor liquid equilibria (VLE) of binary mixtures of the ionic liquid (IL) 1-butyl-3-methylimidazolium trifluoromethanesulfonate (C₄mimTfO) with either water or short chained n-alkyl alcohols (methanol, ethanol, propan-1-ol, and butan-1-ol) are described in this study. Two different microebulliometers and a classical VLE apparatus were compared and the VLEs were determined in the composition range 0.4 ≤ x(solvent) ≤ 1 at three different pressure levels ( p = 500 mbar, 700 mbar, and 1000 mbar). The experimental data were modeled using the soft-SAFT equation of state, which was able to accurately describe the nonideal behavior of these mixtures. The combined experimental-modeling results obtained contribute to establish the structure-property relationship between the C₄mimTfO and n-alkyl alcohol molecules and to infer about its influence on the phase behavior of these solvents.

Thermophysical Characterization of Ionic Liquids Based on the Perfluorobutanesulfonate Anion: Experimental and Soft-SAFT Modeling Results

Fluorinated ionic liquids (FILs) exhibit complex molecular behavior, where three different nanodomains (polar, hydrogenated nonpolar, and fluorinated nonpolar) have been identified by molecular simulations. Given the high number of possible anion/cation combinations, a theoretical tool able to describe the thermophysical properties of these compounds in a systematic, rapid, and accurate manner is highly desirable. We present here a combined experimental-theoretical methodology to obtain the phase, interface, and transport properties of the 1-alkyl-3-methylimidazolium perfluorobutanesulfonate ([C_n C₁ Im][C₄ F₉ SO₃ ]) family. In addition to providing new experimental data, an extended version of the Statistical Associating Fluid Theory (soft-SAFT) is used to describe the physicochemical behavior of the [C_n C₁ Im][C₄ F₉ SO₃ ] family. A mesoscopic molecular model is built based on the analysis of the chemical structures of these FILs, and supported by quantum chemical calculations to study the charge distribution of the anion, where only the basic physical features are considered. The resulting molecular parameters are related to the molecular weight, providing the basis for thermophysical predictions of similar compounds. The theory is also able to predict the minimum in the surface tension versus the length of the hydrogenated alkyl chain, experimentally found at n=8. The viscosity parameters are also in agreement with the free-volume calculations obtained from experiments.