Hybrid Improved Grey Wolf Support Vector Regression Algorithm for Modeling Solubilities of APIs in Pure Ionic Liquids: σ-Profile Descriptors.

The objective of this study was to model the solubility of active pharmaceutical ingredients (APIs) in different ionic liquids (ILs) based on the σ-moments of cations, anions, and APIs that were used as molecular descriptors calculated using the σ-profiles of three categories of descriptors based on conductor-like screening model for real solvents. The database of 83 API-ILs systems composed of 14 APIs, 12 cations, and 7 anions (25 ILs combinations) was collected as 850 data points at different temperature ranges. A hybrid Improved Grey Wolf Support vector regression, abbreviated as I-GWO-SVR(r), algorithm was selected as the learning method. Based on a comprehensive comparison with 11 different models, various statistical factors, and graphical analyses, including an external validation test, analysis of variance (ANOVA), and sensitivity analysis, the capability and validity of the proposed approach have been assessed and verified. The overall study confirmed that the proposed new model provided the best results in terms of predicting the solubility of APIs in ILs.

Extensive Evaluation of the Conductor-like Screening Model for Real Solvents Method in Predicting Liquid-Liquid Equilibria in Ternary Systems of Ionic Liquids with Molecular Compounds.

A conductor-like screening model for real solvents (COSMO-RS) is nowadays one of the most popular and commonly applied tools for the estimation of thermodynamic properties of complex fluids. The goal of this work is to provide a comprehensive review and analysis of the performance of this approach in calculating liquid-liquid equilibrium (LLE) phase diagrams in ternary systems composed of ionic liquid and two molecular compounds belonging to diverse families of chemicals (alkanes, aromatics, S/N-compounds, alcohols, ketones, ethers, carboxylic acid, esters, and water). The predictions are presented for extensive experimental database, including 930 LLE data sets and more than 9000 data points (LLE tie lines) reported for 779 unique ternary mixtures. An impact of the type of molecular binary subsystem on the accuracy of predictions is demonstrated and discussed on the basis of representative examples. The model's capability of capturing qualitative trends in the LLE distribution ratio and selectivity is also checked for a number of structural effects. Comparative analysis of two levels of quantum chemical theory (BP-TZVP-COSMO vs BP-TZVPD-FINE) for the input molecular data for COSMO-RS is presented. Finally, some general recommendations for the applicability of the model are indicated based on the analysis of the global performance as well as on the results obtained for systems relevant from the point of view of important separation problems.

Effect of Side Chain Functional Group on Interactions in Ionic Liquid Systems: Insights from Infinite Dilution Thermodynamic Data.

Measurements of infinite dilution activity coefficients of 48 molecular solutes (including alkanes, alkenes, alkynes, aromatics, ethers, alcohols, water, ketones, pyridine, thiophene, acetonitrile, and 1-nitropropane) in two ionic liquids (ILs), namely, 1-(2-hydroxyethyl)-3-methylimidazolium dicyanamide and 1-(2-chloroethyl)-3-methylimidazolium dicyanamide, are reported in the temperature range from T = 308.15 to 358.15 K. Comparative analysis of an effect of OH/Cl substitution of terminal carbon in side chains of imidazolium cations is presented and discussed in terms of different types of intermolecular forces acting between ILs and solutes. The new data also are confronted to those published previously for a "plain" counterpart of the studied ILs, namely, 1-ethyl-3-methylimidazolium dicyanamide. Infinite dilution capacity and selectivity of the studied ILs are presented to evaluate them as separating agents in extraction of aromatics from alkanes and sulfur compounds from alkanes. Three modeling approaches, namely, linear solvation energy relationship (LSER), regular solution theory, and conductor-like screening model for real solvents (COSMO-RS), are tested for their capabilities of capturing the substitution effects detected experimentally.

Extraction of 2-Phenylethanol (PEA) from Aqueous Solution Using Ionic Liquids: Synthesis, Phase Equilibrium Investigation, Selectivity in Separation, and Thermodynamic Models.

This study assessed the effect of ionic liquids (ILs) on extraction of 2-phenylethanol (PEA) from aqueous phase. It consists the synthesis of four new ILs, their physicochemical properties, and experimental solubility measurements in water as well as liquid-liquid phase equilibrium in ternary systems. ILs are an important new media for imaging and sensing applications because of their solvation property, thermal stability, and negligible vapor pressure. However, complex procedures and nonmiscibility with water are often required in PEA extraction. Herein, a facile and general strategy using four ILs as extraction media including the synthesis of new bis(fluorosulfonyl)imide-based ILs, 1-hexyl-methylmorpholinium bis(fluorosulfonyl)imide, [HMMOR][FSI], N-octylisoquinolinium bis(fluorosulfonyl)imide, [OiQuin][FSI], 1-butyl-1-methylpyrrolidinium bis(fluorosulfonyl)imide, [BMPYR][FSI], and N-triethyl-N-octylammonium bis(fluorosulfonyl)imide, [N2228][FSI], were investigated. The thermal properties, density, viscosity, and surface tension of new ILs were measured. Calorimetric measurements (DSC) were used to determine the melting point and the enthalpy of melting as well as the glass transition temperature and heat capacity at glass transition of the ILs. The phase equilibrium in binary systems (IL + PEA, or water) and in ternary systems {IL (1) + PEA (2) + water (3)} at temperature T = 308.15 K and ambient pressure are reported. All systems present liquid-liquid equilibrium with the upper critical solution temperature (UCST). All ILs revealed complete miscibility with PEA. In all ternary systems immiscibility gap was observed, which classified measured systems as Treybal's type II. The two partially miscible binaries (IL + water) and (PEA + water) exist in these systems. The discussion contains the specific selectivity and the solute distribution ratio of separation for the used ILs. The commonly used NRTL model was used for the correlation of the experimental binary and ternary systems with acceptable root-mean-square deviation. The prediction of binary and ternary compositions was provided with acceptable deviations using COSMO RS. The data of ternary LLE show the possible use of [HMMOR][FSI] as a good entrainer for the separation of PEA from water using solvent extraction.

An overview of the performance of the COSMO-RS approach in predicting the activity coefficients of molecular solutes in ionic liquids and derived properties at infinite dilution.

This paper reports a comprehensive evaluation of the conductor-like screening model for real solvents (COSMO-RS) in predicting infinite dilution activity coefficients (γ∞) of molecular solutes in ionic liquids (ILs). In particular, comparative analysis of two quantum chemical levels of calculations used in the COSMO part of COSMO-RS, namely, TZVP-COSMO and TZVPD-FINE, is presented and discussed. The final assessment of the model performance is established based on a comparison of its predictions with the experimental data pool consisting of 41 868 data points extracted form 182 references, covering 233 ILs (including salts belonging to 12 different cationic families) and 150 molecular solutes (including a great variety of non-polar, polar and self-associating organic compounds and water) combined with 8554 distinct binary systems. The impact of the chemical family of both IL and molecular solute on the accuracy of the COSMO-RS predictions is analyzed in terms of both quantitative and qualitative measures. Relevant thermodynamic properties derived from γ∞, namely, infinite dilution partial excess enthalpy of mixing and infinite dilution selectivity are considered and their values obtained from experimental and COSMO-RS predicted γ∞ data are confronted. Finally, the impact of the molecular conformation of cations/anions/solutes on the quality of predictions is demonstrated based on some representative systems.

Thermodynamic Study of Molecular Interactions in Eutectic Mixtures Containing Camphene.

Terpenes are an abundant and diverse class of chemicals having numerous applications in different areas of chemistry. Therefore, a detailed knowledge of physical and thermodynamic properties of terpenes and their mixtures with other compounds is highly desired. This paper reports both a thermodynamic study on solid-liquid equilibrium (SLE) phase diagrams in binary systems formed by (±)-camphene (a representative terpene) and one of the following solvents: n-decane, n-dodecane, 1-decanol, 1-dodecanol, phenylmethanol, 2-phenylethanol, 2-cyclohexylethanol. The observed trends in the measured SLE data are discussed in terms of structure (alkyl chain length, aromacity) of the solvent and molecular interactions. Modeling of the considered SLE phase diagrams with three well-established thermodynamic models, namely, modified UNIFAC (Dortmund), perturbed-chain statistical associating fluid theory (PC-SAFT) and conductor-like screening model for real solvents (COSMO-RS), is presented. A comparative analysis of their performance is given in terms of average absolute deviations between predicted and experimental SLE temperature.

In Silico Calculation of Infinite Dilution Activity Coefficients of Molecular Solutes in Ionic Liquids: Critical Review of Current Methods and New Models Based on Three Machine Learning Algorithms.

The aim of the paper is to address all the disadvantages of currently available models for calculating infinite dilution activity coefficients (γ(∞)) of molecular solutes in ionic liquids (ILs)-a relevant property from the point of view of many applications of ILs, particularly in separations. Three new models are proposed, each of them based on distinct machine learning algorithm: stepwise multiple linear regression (SWMLR), feed-forward artificial neural network (FFANN), and least-squares support vector machine (LSSVM). The models were established based on the most comprehensive γ(∞) data bank reported so far (>34 000 data points for 188 ILs and 128 solutes). Following the paper published previously [J. Chem. Inf. Model 2014, 54, 1311-1324], the ILs were treated in terms of group contributions, whereas the Abraham solvation parameters were used to quantify an impact of solute structure. Temperature is also included in the input data of the models so that they can be utilized to obtain temperature-dependent data and thus related thermodynamic functions. Both internal and external validation techniques were applied to assess the statistical significance and explanatory power of the final correlations. A comparative study of the overall performance of the investigated SWMLR/FFANN/LSSVM approaches is presented in terms of root-mean-square error and average absolute relative deviation between calculated and experimental γ(∞), evaluated for different families of ILs and solutes, as well as between calculated and experimental infinite dilution selectivity for separation problems benzene from n-hexane and thiophene from n-heptane. LSSVM is shown to be a method with the lowest values of both training and generalization errors. It is finally demonstrated that the established models exhibit an improved accuracy compared to the state-of-the-art model, namely, temperature-dependent group contribution linear solvation energy relationship, published in 2011 [J. Chem. Eng. Data 2011, 56, 3598-3606].

Thermodynamic study of binary mixtures of 1-butyl-1-methylpyrrolidinium dicyanamide ionic liquid with molecular solvents: new experimental data and modeling with PC-SAFT equation of state.

This work is concerned with thermodynamic properties of binary mixtures composed of 1-butyl-1-methylpyrrolidinium dicyanamide ionic liquid (IL) and the following molecular solvents: n-heptane, benzene, toluene, ethylbenzene, thiophene, 1-butanol, 1-hexanol, and 1-octanol. This is the very first time when experimental data on liquid-liquid equilibrium (LLE) phase diagrams and excess enthalpies of mixing (H(E)) for these systems are reported. An impact of the molecular solvent structure on LLE and H(E) is discussed. Furthermore, modeling of the properties under study is presented by using perturbed-chain statistical associating fluid theory (PC-SAFT). The equation of state is used in purely predictive and semipredictive mode. The latter one involves temperature-dependent binary corrections to combining rules employed in the PC-SAFT model determined on the basis of infinite dilution activity coefficients. The results shown indicate that such an approach can serve as an interesting modern thermodynamic tool for representation of thermodynamic data for complex ILs-based systems.

Viscosity of ionic liquids: an extensive database and a new group contribution model based on a feed-forward artificial neural network.

A knowledge of various thermophysical (in particular transport) properties of ionic liquids (ILs) is crucial from the point of view of potential applications of these fluids in chemical and related industries. In this work, over 13 000 data points of temperature- and pressure-dependent viscosity of 1484 ILs were retrieved from more than 450 research papers published in the open literature in the last three decades. The data were critically revised and then used to develop and test a new model allowing in silico predictions of the viscosities of ILs on the basis of the chemical structures of their cations and anions. The model employs a two-layer feed-forward artificial neural network (FFANN) strategy to represent the relationship between the viscosity and the input variables: temperature, pressure, and group contributions (GCs). In total, the resulting GC-FFANN model employs 242 GC-type molecular descriptors that are capable of accurately representing the viscosity behavior of ILs composed of 901 distinct ions. The neural network training, validation, and testing processes, involving 90, 5, and 5% of the whole data pool, respectively, gave mean square errors of 0.0334, 0.0595, and 0.0603 log units, corresponding to squared correlation coefficients of 0.986, 0.973, and 0.972 and overall relative deviations at the level of 11.1, 13.8, and 14.7%, respectively. The results calculated in this work were shown be more accurate than those obtained with the best current GC model for viscosity of ILs described in the literature.

Renewable feedstocks in green solvents: thermodynamic study on phase diagrams of D-sorbitol and xylitol with dicyanamide based ionic liquids.

Experimental and theoretical studies on thermodynamic properties of three ionic liquids based on dicyanamide anion (namely, 1-butyl-3-methylimidazolium dicyanamide, 1-butyl-1-methylpyrrolidinium dicyanamide, and 1-butyl-1-methylpiperidinium dicyanamide) and their binary mixtures with sugar alcohols (D-sorbitol and xylitol) were conducted in order to assess the applicability of the salts ionic liquids for dissolution of those biomass-related materials. Density and dynamic viscosity (at ambient pressure) of pure ionic liquids are reported in the temperature range from T = 293.15 to 363.15 K. Solid-liquid equilibrium phase diagrams in binary systems {sugar alcohol + ionic liquid} were measured with dynamic method up to the fusion temperature of sugar alcohol. The impact of the chemical structure of both the ionic liquid and sugar alcohol were established and discussed. For the very first time, the experimental solubility data were reproduced and analyzed in terms of equation of state rooted in statistical mechanics. For this purpose, perturbed-chain statistical associating fluid theory (PC-SAFT) was employed. In particular, new molecular schemes for the ionic liquids, D-sorbitol, and xylitol were proposed, and then the pure chemicals were parametrized by using available density and vapor pressure data. The model allowed accurate correlation of pure fluid properties for both ionic liquids and sugar alcohols, when the association term is taken into account. The results of solid-liquid equilibria modeling were also satisfactory. However, one or two adjustable binary corrections to the adopted combining rules were required to be adjusted in order to accurately capture the phase behavior. It was shown that a consistent thermodynamic description of extremely complex systems can be achieved by using relatively simple (but physically grounded) theoretical tools and molecular schemes.

Excess enthalpies of mixing of piperidinium ionic liquids with short-chain alcohols: measurements and PC-SAFT modeling.

This work is a continuation of our systematic study on thermodynamic properties of 1-n-alkyl-1-methylpiperdinium bis[(trifluoromethyl)sulfonyl]imides homologous series of ionic liquids ([CnC1Pip][NTf2]). Excess enthalpies of mixing (H(E)) of four binary systems containing two ionic liquids, namely [C4C1Pip][NTf2] and [C6C1Pip][NTf2], and two short-chain alcohols, namely ethanol and 1-propanol, were measured by isothermal titration calorimetry. Alcohol-to-ionic liquid and ionic liquid-to-alcohol titration experiments were carried out at temperature T = 298.15 K and atmospheric pressure. The experimental data were modeled in terms of perturbed-chain statistical associating fluid theory (PC-SAFT). Wolbach-Sandler combining rules were adopted in order to account for ionic liquid-alcohol cross-association. The model was applied in a conventional manner (i.e., without any binary corrections) as well as in a novel predictive mode developed previously by our group [Paduszynski, K.; Domanska, U. J. Phys. Chem. B 2012, 116, 5002-5018; Domanska et al. J. Phys. Chem. B 2012, 116, 8191-8200]. The latter approach employs temperature-dependent binary correction fitted to experimental limiting activity coefficient of alcohol in ionic liquid.

Perturbed-chain SAFT as a versatile tool for thermodynamic modeling of binary mixtures containing isoquinolinium ionic liquids.

This contribution reports a recapitulation of our experimental and modeling study on thermodynamic behavior of binary systems containing N-alkylisoquinolinium ionic liquids (ILs) based on bis(trifluoromethylsulfonyl)imide anion, [CniQuin][NTf2] (n = 4,6,8). In particular, we report isothermal vapor-liquid equilibrium (VLE) phase diagrams and molar excess enthalpies of mixing (H(E)) for binary mixtures of [C8iQuin][NTf2] IL with various organic solutes including benzene, toluene, thiophene, pyridine, and butan-1-ol. The measured VLE data represented simple homozeotropic behavior with either negative or positive deviations from ideality, depending on polarity of the solute, temperature, and mole fraction of IL. In turn, the obtained data on H(E) were negative and positive for the mixtures containing aromatic hydrocarbons or thiophene and butan-1-ol, respectively, in the whole range of IL's concentration. All of the measured and some previously published data regarding phase behavior of [C8iQuin][NTf2] IL were analyzed and successfully described in terms of perturbed-chain statistical associating fluid theory (PC-SAFT). The methodology used in this work was described by us previously. In general, the proposed modeling results in VLE diagrams, which are in excellent agreement with experimental data. In the case of H(E), the results obtained are good as well but not so satisfactory such as those for VLE. Nevertheless, they seem to be very promising if one take into account the simplicity of the utilized molecular model against significant complexity of IL-based systems. Thus, we concluded that PC-SAFT equation of state can be viewed as a powerful and robust tool for modeling of systems involving ILs.

Thermodynamic modeling of ionic liquid systems: development and detailed overview of novel methodology based on the PC-SAFT.

We present the results of an extensive study on a novel approach of modeling ionic liquids (ILs) and their mixtures with molecular compounds, incorporating perturbed-chain statistical associating fluid theory (PC-SAFT). PC-SAFT was used to calculate the thermodynamic properties of different homologous series of ILs based on the bis(trifluormethylsulfonyl)imide anion ([NTf2]). First, pure fluid parameters were obtained for each IL by means of fitting the model predictions to experimental liquid densities over a broad range of temperature and pressure. The reliability and physical significance of the parameters as well as the employed molecular scheme were tested by calculation of density, vapor pressure, and other properties of pure ILs (e.g., critical properties, normal boiling point). Additionally, the surface tension of pure ILs was calculated by coupling the PC-SAFT equation of state with density gradient theory (DGT). All correlated/predicted results were compared with literature experimental or simulation data. Afterward, we attempted to model various thermodynamic properties of some binary systems composed of IL and organic solvent or water. The properties under study were the binary vapor-liquid, liquid-liquid, and solid-liquid equilibria and the excess enthalpies of mixing. To calculate cross-interaction energies we used the standard combining rules of Lorentz-Berthelot, Kleiner-Sadowski, and Wolbach-Sandler. It was shown that incorporation of temperature-dependent binary corrections was required to obtain much more accurate results than in the case of conventional predictions. Binary corrections were adjusted to infinite dilution activity coefficients of a particular solute in a given IL determined experimentally or predicted by means of the modified UNIFAC (Dortmund) group contribution method. We concluded that the latter method allows accurate and reliable calculations of bulk-phase properties in a totally predictive manner.

Solubility of aliphatic hydrocarbons in piperidinium ionic liquids: measurements and modeling in terms of perturbed-chain statistical associating fluid theory and nonrandom hydrogen-bonding theory.

Ionic liquids (ILs) reveal many unique properties which make them very interesting for applications in modern "green" technologies. For that reason, detailed knowledge about correlations between the ions' structure, their combinations, and the bulk properties is of great importance. That knowledge can be accessed by reliable measurements and modeling of systems with ILs in terms of various theoretical approaches. In this paper we report new experimental results on liquid-liquid equilibrium (LLE) measurements of 10 binary systems composed of piperidinium ILs [namely, 1-propyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)imide and 1-butyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)imide] and aliphatic hydrocarbons (n-hexane, n-heptane, n-octane, cyclohexane, and cycloheptane). Moreover, new results on liquid density of pure 1-butyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)imide are presented. Upper critical solution temperature type of phase behavior for all studied systems was observed. Decrease of solubility of n-alkane with an increase of its alkyl chain length and increase of solubility when changing linear into cyclic structure of hydrocarbon were detected. LLE modeling of investigated systems was performed in terms of two modern theories, namely, perturbed-chain statistical associating fluid theory (PC-SAFT) and nonrandom hydrogen-bonding theory (NRHB). Pure fluid parameters of the models were obtained from fitting of experimental liquid density and solubility parameter data at ambient pressure and tested against high pressure densities. Then literature values of activity coefficients of n-alkanes and cycloalkanes at infinitely diluted mixtures with ILs were used to optimize binary interaction parameters of the models. Finally, the LLE phase diagrams were calculated with average absolute relative deviations of 4.1% and 3.4% of the IL mole fraction for PC-SAFT and NRHB, respectively. The PC-SAFT and NRHB models were both able to capture phase behavior in a qualitative manner. Both models predict the order in which solubility of hydrocarbon in the IL increases, including the effects of chain length of n-alkane as well as chain length of alkyl substituent in piperidinium cation. Moreover, predicted solubility of cycloalkanes is also higher than that of respective n-alkanes. Our results suggest that the presented approach of PC-SAFT and NRHB modeling can be successfully applied to cross-associating systems as well. In summary, we have shown that relatively good results can be obtained for such complex systems by using quite simple molecular models and combining rules. To the best of our knowledge, this is the very first paper in which such equation-of-state modeling has been adopted for systems with ILs.

Limiting activity coefficients and gas-liquid partition coefficients of various solutes in piperidinium ionic liquids: measurements and LSER calculations.

This paper is a continuation of our systematic investigations on piperidinium ionic liquids and presents new data on activity coefficients at infinite dilution for 43 solutes: linear and branched alkanes, cycloalkanes, alkenes, alkynes, benzene, alkylbenzenes, alcohols, water, thiophene, tetrahyrdofuran (THF), methyl tert-butyl ether (MTBE), linear ethers, acetone, and linear ketones in the ionic liquid 1-butyl-1-methyl-piperidinium bis(trifluoromethylsulfonyl)imide, [BMPIP][NTf2]. The data were determined by gas-liquid chromatography (GLC) at temperatures from 308.15 to 358.15 K. These values were compared to those previously published for the bis-(trifluoromethylsulfonyl)imide-based ionic liquids. The partial molar excess enthalpies ΔH1(E,∞) and entropies ΔS1(E,∞) at infinite dilution were calculated from the experimental γ13(∞) values obtained over the temperature range. The values of the selectivities for different separation problems were calculated from γ13(∞) and compared to literature values for N-methyl-2-pyrrolidinone (NMP), sulfolane, and additional ionic liquids. Experimental limiting activity coefficients were used to calculate gas-IL partition coefficients of solutes, K(L). The modeling with specific linear solvation energy relationship (LSER) equations was performed for data obtained in this work and those reported earlier for 1-butyl-1-methylpiperidinium thiocyanate, [BMPIP][SCN].

Phase equilibria study in binary systems (tetra-n-butylphosphonium tosylate ionic liquid + 1-alcohol, or benzene, or n-alkylbenzene).

Ambient pressure (solid + liquid) equilibria (SLE) and (liquid + liquid) equilibria (LLE) of binary systems--ionic liquid (IL) tetra- n-butylphosphonium p-toluenesulfonate + 1-alcohol (1-butanol, 1-hexanol, 1-octanol, 1-decanol, or 1-dodecanol), benzene, or n-alkylbenzene (toluene, ethylbenzene, n-propylbenzene)-have been determined by using dynamic method in a broad range of mole fractions and temperatures from 250 to 335 K. For binaries containing alcohol, simple eutectic diagrams were observed with complete miscibility in the liquid phase. Only in the case of system [IL + n-propylbenzene] was mutual immiscibility with an upper critical solution temperature (UCST) with low solubility of the IL in the alcohol and high solubility of the alcohol in the IL detected. The basic thermal properties of pure IL, i.e., melting and glass-transition temperatures as well as enthalpy of melting, have been measured with differential scanning microcalorimetry technique (DSC). Well-known UNIQUAC, Wilson, NRTL, NRTL1, and NRTL2 equations have been fitted to obtain experimental data sets. For the system containing immiscibility gap [IL + n-propylbenzene], parameters of the equations have been derived only from SLE data. As a measure of goodness of correlations, root-mean square deviations of temperature have been used. These experimental results were compared to the previously measured binary systems with tetra- n-butylphosphonium methanesulfonate. Changing anion from methanesulfonate to p-toluenesulfonate decreases solubilities in systems with alcohols and increases the solubilities in binary systems with benzene and alkylbenzenes.