Extensive Evaluation of the Conductor-like Screening Model for Real

Article Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

pubs.acs.org/JPCB

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 Kamil Paduszyński* Department of Physical Chemistry, Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland S Supporting Information *

ABSTRACT: 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.

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INTRODUCTION Since many years, ionic liquids (ILs) have been considered as very promising separating agents in various liquid−liquid extractions. In particular, the industrially relevant IL-assisted separation problems most intensively studied thus far are aromatic from aliphatic hydrocarbons,1 organic sulfur compounds (e.g., thiophene, or benzothiophene) from gasolines and oils,2−4 and alcohols from water (e.g., extraction of butanol or 2-phenylethanol from fermentation broth).5−7 Liquid−liquid extraction with ILs was also proposed as an alternative method to separate some common azeotropes, like alkanes/alcohols, alcohols/ethers, and alcohols/water.8 Furthermore, separations of diverse biocompounds (including small biomass-derived organic compounds like terpenes/terpenoids, lipids, proteins, amino acids, nucleic acids, and pharmaceuticals) with ILs has recently emerged as a “hot topic” in the fields of applied physical chemistry and thermodynamics.9 A vast interest of both academic communities and industries in ILs is mainly because of a number of peculiar characteristics disclosed by these chemicals compared with “conventional” molecular solvents. The most advantageous properties of ILs are their extremely low vapor pressures at ambient conditions (thus virtually immeasurable normal boiling point) and good thermal stability over a wide range of temperaturethat is why ILs are commonly referred to as “green” chemicals.10,11 However, the © XXXX American Chemical Society

key feature of ILs that makes them particularly interesting from the standpoint of separation problems is their capacity to form heterogeneous systems and selectively dissolve different kinds of materials, ranging from inorganic or organic gases12 to complex biological polymeric matrices like lignin or lignocellulose.13 Liquid−liquid equilibrium (LLE) data for multicomponent mixtures of ILs with molecular solvents are the most relevant information for evaluating ILs as potential extractants. In fact, that is the fundamental reason justifying a vast amount of experimental effort which have been put into measuring and reporting LLE phase diagrams in recent years. In particular, as can be seen from the recent update of ILThermo database maintained by National Institute of Standard and Technology, United States,14 the most comprehensively explored systems are ternary mixtures composed of a tested IL and two molecular solutes representing a “case study” for a separation problem under study (e.g., toluene/n-heptane or thiophene/nheptane representing broader “aromatic from aliphatic” separation and extractive desulfurization, respectively). On the other hand, only a few data sets on systems higher than ternary Received: December 8, 2017 Revised: February 9, 2018 Published: March 13, 2018 A

DOI: 10.1021/acs.jpcb.7b12115 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

selectivity, or capacity, or solubility parameter) were exhaustively utilized in screening for ILs to be applied as media in a number of separation problems; a detailed review of this field can be found in my previous paper.25 LLE phase diagrams predicted by using the COSMO-RS method was presented many times as well, whereas the most comprehensive overview of the accuracy of the model as well as its capability of capturing different effects of the IL/solute chemical structure on the observed phase diagrams was given in 2012 for binary and ternary systems by Ferreira et al.26,27 Afterward, COSMORS was intensively studied in predicting LLE in various ternary systems, mainly {IL + aromatic hydrocarbon + linear/cyclic alkane},28−36 {IL + organic S-compound + hydrocarbon},37−42 {IL + organic N-compound + hydrocarbon},43−47 and {IL + alcohol + water}.5,6,48 Since the review papers of Ferreira and co-workers,26,27 the number of ILs and systems investigated from the point of view of LLE has significantly increasedin 2012, the predictions were made for approximately 180 distinct systems,27 whereas the current state-of-the-art of experimental LLE data comprises more than 750 ternary mixtures and more than 900 data sets (detailed presentation of the database is given in the following section). Considering the still growing popularity of the COSMO-RS method, I decided to provide a comprehensive evaluation of this model by using substantially extended experimental database and variety of chemical structures of ILs’ constituting ions as well as molecular solutes and molecular binary subsystems. The remaining of the paper is organized as follows. First, the ternary LLE database and fundamentals of the COSMO-RS method are presented. The database is summarized in terms of numbers of ILs/systems regarding diverse separations (represented by pairs of molecular components belonging to different chemical families). Then, the results of calculations using COSMO-RS are compared with experimental data, taking into account both global analysis of accuracy of the model as well as its capabilities of predicting an effect of the molecular structure of solutes on the observed phase behavior. A novelty of this work, compared with the reference paper,27 is that an impact of the level of quantum chemical COSMO calculations (used as an input for further LLE predictions) is analyzed and discussed, in an analogous fashion as done previously.25

can be found in the open literaturehowever, they are not stored in the ILThermo database.14 Because of a huge structural diversity of ILs (in terms of the chemical structures of the cation and anion as well as branching, cyclization, and functionalization of their side chains), systematic experimental investigation and verification of a least of a part of all of them will never be possible. In fact, there is around 170 ILs for which ternary LLE data have been published since 2003, whereas the number of 1:1 ILs composed only of ions described and characterized in the literature is of the order of 150 000.15 Alternatively, chemical thermodynamics can be employed to model the properties of IL-based systems, for instance, chemical potentials necessary in flash calculations. Nowadays, the spectrum of tools allowing for computing the phase diagrams of complex systems is very broad. First of all, it comprises molecular-based models having well-defined physical foundations as well as taking into account various effects of the molecular structure and interactions on the predicted phase behavior. This is essentially important for ILs, for which the “classical” models such as local composition activity coefficient equations or cubic equations of state (EoS) are usually not capable of reproducing the thermodynamic data for the systems of such a complexity. Among the molecular-based approaches, the statistical associating fluid theory (SAFT)16 and its variants seem to be the most promising methods for reliable and effective calculation of physical and thermodynamic properties of ILs and their mixtures with molecular solvents.17−19 SAFTbased methodology, however, suffers from its parameterization procedure, which requires experimental data regarding pure fluids forming the mixture under considerations, or even the mixture itself. In the case of the systems involving ILs, availability of these data is usually limited, which significantly affects the applicability and predictive capacity of the model. Furthermore, the results on SAFT modeling of ILs reported so far were often obtained on the basis of physically incorrect and sometimes unclear molecular scheme, for example, treating IL as formed by ion pairs irrespective of the concentration and other solutes present in the mixture.17−19 Nevertheless, different versions of SAFT have been shown as effective models in representing the phase equilibria and other properties of ILs and their mixtures, mostly binary though, whereas all the mentioned drawbacks were recognized and accepted as a form of compromise between simplicity of the molecular model and robustness/computational cost of modeling.18 Disadvantages in practical issues related to the application of SAFT-based models can be eliminated by adopting the approach known as conductor-like screening model for real solvents (COSMO-RS),20−22 commonly perceived as the stateof-the-art tool for thermodynamic modeling of liquid solutions. In contrast to SAFT, COSMO-RS does involve a number of global, (i.e., universal) parameters but does not require any model- and system-specific adjustable parameters to be fitted to experimental data on a system of interest. Instead, COSMO-RS calculation is carried out based on conductor screening charge densities of molecules resulting from quantum chemical calculations, thus it can be applied to represent any kind of system in a purely predictive fashion. Since the very first communication reported in 2002,23 significant amount of attention has been devoted to the evaluation of COSMO-RS in predicting diverse thermodynamic data for the systems with ILs.24−27 In particular, infinite dilution activity coefficients of molecular solutes in ILs (and some derived properties, e.g.,

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MODELING Experimental LLE Database. For the purpose of versatile and broad COSMO-RS model evaluation, ternary LLE data compilation was prepared on the basis of the experimental works reported in 236 papers published since 2003 to date. A detailed overview of the database, including abbreviations and names of cations, anions, and solutes as well as a full list of references, is provided in the Supporting Information (PDF file, Tables S1−S3). Overall, 9237 tie lines divided into 930 data sets for 779 unique ternary systems were stored in the final database. The difference between the data set and the system is that the data set is identified in terms of the components (i.e., IL + two molecular compounds), temperature at which LLE data were measured, and the data source. Pressure was usually not strictly specified but rather stated as “ambient” or “atmospheric”, so that one can assume p = 0.1 MPa for all systems. On the other hand, the system is defined only by the components it consists of. In particular, for 103 systems, more than a single data set was available, differing either in temperature or in the reference. To be more specific, for 100 B


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Figure 1. Summary of the experimental ternary LLE data compilation used in the COSMO-RS model evaluation. (a) Percentages of ILs belonging to different cationic families (total number of ILs is 173). (b) Percentages of data sets consisting of ILs belonging to different cationic families regardless of molecular solutes (total number of data sets is 930). (c) Scatter plot presenting the types of data sets, classified with respect to chemical family of molecular solutes. Key: circles, number of data sets n ≥ 100; squares, 50 ≤ n < 100; triangles, 10 ≤ n < 50; diamonds, n < 10. Key: Im, imidazolium; Py, pyridinium; Quin, (iso)quinolinium; Pyr, pyrrolidinium; Pip, piperidinium; Mo, morpholinium; N, ammonium; P, phosphonium.

studied from the point of view of LLE are: bis[(trifluoromethyl)sulfonyl]imide [NTf2] (59 ILs), tetrafluoroborate [BF4] (16 ILs), dicyanamide [N(CN)2] (14 ILs), and thiocyanate [SCN] (11 ILs). For the remaining anions, the number of ILs with LLE data available is below 10. This even applies to such common anions like hexafluorophosphate [PF6], trifluoromethylsulfonate [OTf], tris(pentafluoroethyl)trifluorophosphate [FAP], tetracyanoborate [B(CN4)], tricyanomethanide [C(CN3)], carboxylates [CnCOO] (where n = 1, 3, 5, 9), alkylsulfates [CnSO4] (where n = 1, 2, 8), dialkylphosphates [(CnO)2PO2] (where n = 1, 2, 4), and halides [X] (where X = Cl, Br). In particular, for a significant part of anions (12 out of 32), the LLE data for only a single IL can be extracted from the literature. Molecular solutes (in total, 71 unique compounds) forming considered ternary mixtures with ILs were classified into the following chemical families (the names of compounds given in parentheses are followed by the number of data sets/systems involving them): alkanes (n-pentane3/3; n-hexane163/ 148; n-heptane249/216; n-octane54/45; 2,2,4-trimethylpentane9/9; n-nonane22/19; n-decane20/15; n-undecane6/6; n-dodecane71/49; n-tetradecane9/4; n-hexadecane41/37; and n-heptadecane3/1), cycloalkanes (cyclohexane80/74; methylcyclohexane19/15; and cyclooctane12/12), alkenes (1-hexene18/18; 1-heptene2/2; cyclohexene19/19; and limonene8/5), aromatics (benzene152/116; toluene148/119; ethylbenzene44/41; oxylene8/8; m-xylene13/12; p-xylene33/30; n-propylbenzene24/10; cumene2/1; n-butylbenzene9/4; and styrene9/7), S-compounds (thiophene95/88; benzothiophene20/20; dibenzothiophene11/9; 4-methyldibenzothiophene4/2; 4,6-dimethyldibenzothiophene4/2; and 1hexanethiol13/11), N-compounds (pyridine39/39; 3methylpyridine1/1; pyrrole4/4; indoline4/4; quinoline4/4; and 1-methylimidazole1/1), alcohols (methanol29/24; ethanol86/74; 1-propanol13/9; 2-propanol22/16; 1-butanol29/24; 1-pentanol3/3; 2-pentanol2/2; 1-phenylethanol4/4; 2-phenylethanol16/16; and linalool8/5), ketones (acetone3/1 and butanone 6/6), ethers (tert-butylmethyl ether6/6; tert-butylethyl ether5/5; tert-amylmethyl ether4/4; tert-amylethyl ether2/2; di-iso-propyl ether9/5; and tetrahydrofuran 2/2), acids (acetic acid10/10; propionic acid4/4; and butyric acid2/2), esters (methyl acetate3/1; ethyl acetate16/14; butyl acetate3/3; 2-pentyl butyrate2/2;

systems, the temperature-dependent LLE data were identified, whereas in the case of 21 systems, more than a single scientific paper reporting the LLE data was found. In particular, ternary LLE data were measured and reported for 177 unique ILs, whereas the numbers of distinct cations and anions composing the ILs are, respectively, 82 and 32. Therefore, the ILs with the experimental LLE data available pose only a small fraction (≈5%) of all possible cation−anion combinations. This can be perceived as another solid argument justifying the importance of developing new and testing the existing thermodynamic models for phase equilibria prediction. A brief summary of the data compilation is shown in Figure 1. Diversity of ILs that can be found in the database is presented in Figure 1a in terms of the type (chemical family) of the cation core. As can be easily noticed, imidazolium- and pyridinium-based ILs comprise more than a half of the entire pool of ILs (83 and 32 distinct structures, respectively), whereas other families like (iso)quinolinium, pyrrolidinium, piperidinium, ammonium, and phosphonium contribute in less than 10%; it is worth mentioning that unquestionable “predominance” of imidazolium ILs is also observed for other physical and thermodynamic properties of pure fluids and mixtures.15,19,25 Furthermore, it is not surprising at all that the ILs based on 1-(n-alkyl)-3-methylimidazolium cations [CnC1Im] (where CnCH3(CH2)n−1 with n = 1, ..., 6, 8, 10, 12) are the ones most broadly studied from the point of view of ternary LLE (in total, 62 unique ILs). In the case of the “classical” [C2C1Im] and [C4C1Im] cations, ternary LLE data were measured for 17 different ILs (per each). On the other hand, for more than a half of the cations (51 out of 82), single ILs based on them can be found in the database. To some extent, this confirms the fact that the LLE behavior of ILs is still an unexplored field. Figure 1b presents percentages of the data sets regarding the systems composed of ILs belonging to different cationic families. Again, the ILs with an imidazolium core have turned out to be the most extensively studied ones (65% of all data sets). For some cationic families distinguished in Figure 1b, only a few data sets were availablethis applies to (iso)quinolinium ILs (only 5 ILs and 6 data sets) and the ILs labeled as “others” (only 2 ILsthe first was sulfonium-based and the second was based on a bicyclic quaternary ammonium cation). Therefore, a special care should be taken when interpreting the results of COSMO-RS model evaluation presented in this paper for those ILs. Among 32 anions constituting the ILs under consideration, those most widely C


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segment of that surface is characterized by the screening charge density (SCD or σ) playing the role of the key descriptor of the mixture under consideration. Thermodynamics of the system (i.e., the “RS” part of the model) does not require spatial distribution of SCD but rather its histogram (probability distribution) p(σ), the so-called σ-profile. Given the σ-profiles for each component i of the mixture (with the mole fraction xi), the following equation is employed to compute its chemical potential μi

vinyl propionate4/4; and vinyl butyrate2/2), water (water107/74), and others (dimethyl carbonate4/2 and trichloromethane4/2). As seen, for a great majority of solutes, only a few data sets and systems were reported in the literature so far. On the other hand, n-heptane, benzene, nhexane, toluene, water, thiophene, and ethanol can be referred to as “top six” molecular compounds, with respect of the amount of ternary LLE data accessible from the database. Such a significant interest in these particular solutes is due to the potential applications of ILs in the processes of dearomatization and desulfurization of fuels and oils as well as extractive separation of azeotropic mixtures involving aqueous and alcoholic solutions. Diversity of binary subsystems of molecular compounds is presented in Figure 1c in the form of a scatter plot. A more detailed summary of the number of ILs, data sets, systems, binary subsystems, and tie lines corresponding to each kind of binary subsystem is presented in further text; alternatively, this piece of information can be retrieved from the Supporting Information (Table S3, or XLS file). As seen from Figure 1c, the most extensively studied systems were ternary mixtures {IL + aromatic hydrocarbons + alkane} (329 data sets, 251 systems, 87 ILs, 37 binary subsystems, and 3159 tie lines) and {IL + Scompound + alkane} (136 data sets, 121 systems, 65 ILs, 15 binary subsystems, and 1330 tie lines). Other systems like {IL + alcohol + alkane} related to the extractive separation of azeotropic mixtures (87 data sets, 85 systems, 39 ILs, 13 binary subsystems, and 784 tie lines), {IL + aromatic hydrocarbon + cycloalkane} also related to the dearomatization of fuels and oils (76 data sets, 66 systems, 31 ILs, 10 binary subsystems, and 736 tie lines), {IL + alcohol + water} related, for example, to ethanol/butanol recovery from aqueous solutions (70 data sets, 48 systems, 35 ILs, 5 binary subsystems, and 826 tie lines), or {IL + N-compound + alkane} related to the denitrification of fuels and oils (43 data sets, 43 systems, 22 ILs, 9 binary subsystems, and 383 tie lines) have also attracted a significant amount of attention. Experimental LLE data for other types of systems are not so abundant. In particular, the amount of data for the systems {IL + alkene + alkane} (16 data sets, 16 systems, 16 ILs, 1 binary subsystem, and 248 tie lines) tends to systematically grow in the recent years.

μi = μicomb +

∫ pi (σ )μs(σ ) dσ + RT ln xi

(1)

where superscript “comb” refers to modified Staverman− Guggenheim contribution due to differences in the size and shape of the molecules (combinatorial term), whereas μs(σ) denotes the chemical potential of a surface segment with the SCD of σ, described by the normalized distribution function ps(σ) = ∑ixipi(σ) and obtained from the following integral equation ⎡a ⎤ RT ⎧ ln⎨ ps (σ ′) exp⎢ eff (μs (σ ′) − E(σ , σ ′))⎥ ⎣ ⎦ aeff ⎩ RT ⎫ dσ ′⎬ ⎭ (2)

μs (σ ) = −

∫

In eq 2, aeff stands for the effective size of the surface segment (universal COSMO-RS parameter), whereas E(σ,σ′) denotes the interaction energy between segments of SCD σ and σ′ due to electrostatic “misfit” and hydrogen bonding; detailed expressions can be found elsewhere.22 Despite the fact that COSMO-RS is often referred to as “entirely” predictive, one should keep in mind that there are some parameters involved in the model (e.g., aeff) that, in fact, are universal and transferable, nevertheless they were fitted to experimental data.21 Finally, it should be emphasized that in IL-based systems both cation and anion of IL are treated as independent components. This is for sure the most important benefit from using the COSMO-RS compared with the EoS-based models, which are typically based on a more complicated and not really physically correct molecular picture. In fact, handling the database of ion-specific σ-profiles results in greater universality compared with the IL-specific EoS parameters, which are in general not unique and have values strongly dependent on the experimental data used to fit them. On the other hand, the drawback of COSMO-RS is that it describes incompressible fluids only. Therefore, the model does not represent pure-fluid properties and thermodynamic properties at elevated pressure in the way the EoS-based models do. Computational Details. All COSMO-RS calculations summarized in this work were performed using the COSMOtherm program (version C3.0 release 17.05), purchased from COSMOlogic GmbH & Co. KG (Leverkusen, Germany), with C30 1701 parameterization50therefore, the performed COSMO-RS evaluation will additionally check the performance of this software. The COSMO-files (i.e., the files containing the SCDs, thus σ-profiles) for a great majority of cations, anions, and molecular solutes were taken directly from the databases provided by the software supplier. In the case of a number of missing ions and solutes, the COSMO-files were created following the same protocol as described previously.25 First, a 2D structure was prepared in MarvinSketch chemical drawing software (ChemAxon Ltd.).51 Then, a 3D structure with explicit hydrogen atoms was initialized using the built-in

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COSMO-RS METHOD Molecular Model. Within the COSMO-RS framework,20−22 a real mixture is represented by an ensemble of surface segments, characterized mainly by their polarization charge densities and interacting via local pairwise potentials, whereas the macroscopic properties of the system (like chemical potentials and activity coefficients required in LLE calculations) are obtained by treating the ensemble with the formalism of statistical thermodynamics. The polarization charge densities on the surface of a given molecular system are computed using the rigorous methods of quantum chemistry. This is generally perceived as the major advantage of COSMO-RS over other thermodynamic models (e.g., EoSbased ones), as the only input required to run the calculation is the elemental composition and topology of molecules forming the system, further transformed into optimized geometry. In the particular case of the COSMO-RS approach, the COSMO49 originally proposed and developed by Klamt and Schüürmann is adopted. This approach is one of the continuum solvation models, which provides a discrete surface (cavity) around a molecule embedded in a perfect conductor. Each D


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Table 1. Summary of LLE Database and the COSMO-RS Model Evaluation Expressed in Terms of RMSE between Predicted and Experimental LLE Mole Fractionsa number of binary subsystem alkane

cycloalkane

alkene aromatic

N-compound alcohol

ketone ether acid overall

cycloalkane alkene aromatic S-compound N-compound alcohol acid ester water alkene aromatic S-compound N-compound ketone aromatic alcohol aromatic S-compound N-compound water ester ketone ether ester water other water water water

RMSE (TZVP-COSMO)

RMSE (TZVPD-FINE)

data sets

systems

ILs

binaries

tie lines

total

extract

raffinate

Nstableb

total

extract

raffinate

Nstableb

10 16 329 136 43 87 6 14 9 16 76 3 4 2 3 12 9 8 5 3 1 4 16 15 70 8 3 12 10 930

10 16 251 121 43 85 6 14 6 16 66 3 4 2 3 9 7 8 5 1 1 4 16 11 48 4 1 8 10 779

10 16 87 65 22 39 6 12 6 16 31 2 1 2 2 7 7 8 5 1 1 2 8 11 35 3 1 3 10 177

1 1 37 15 9 13 2 4 1 1 10 2 4 1 3 3 1 1 1 1 1 2 7 4 5 3 1 4 1 139

94 248 3159 1330 383 784 29 102 69 233 736 31 40 21 29 131 143 85 36 23 19 31 172 156 826 89 23 100 115 9237

0.03 0.01 0.07 0.08 0.09 0.11 0.22 0.10 0.11 0.01 0.06 0.05 0.04 0.03 0.03 0.14 0.16 0.06 0.08 0.27 0.29 0.15 0.08 0.21 0.11 0.09 0.03 0.23 0.08 0.09

0.04 0.01 0.09 0.08 0.05 0.09 0.11 0.09 0.13 0.02 0.07 0.06 0.05 0.03 0.04 0.16 0.23 0.06 0.09 0.27 0.36 0.16 0.08 0.22 0.11 0.09 0.04 0.17 0.09 0.10

0.01 0.00 0.04 0.08 0.11 0.14 0.29 0.10 0.10 0.00 0.04 0.05 0.04 0.04 0.01 0.12 0.02 0.05 0.06 0.27 0.20 0.13 0.07 0.19 0.10 0.09 0.01 0.27 0.06 0.08

0 0 103 177 6 20 5 14 21 0 23 10 0 0 0 33 0 49 13 16 6 16 22 114 40 89 0 2 21 800

0.02 0.02 0.09 0.10 0.09 0.12 0.23 0.11 0.19 0.02 0.08 0.08 0.10 0.09 0.02 0.14 0.12 0.09 0.11 0.70 0.36 0.15 0.06 0.22 0.13 0.09 0.06 0.28 0.08 0.11

0.03 0.02 0.11 0.12 0.10 0.13 0.13 0.12 0.22 0.02 0.10 0.10 0.11 0.09 0.03 0.19 0.17 0.12 0.15 0.61 0.36 0.15 0.07 0.22 0.16 0.09 0.09 0.29 0.11 0.13

0.01 0.00 0.05 0.07 0.09 0.11 0.30 0.09 0.15 0.00 0.05 0.04 0.09 0.09 0.02 0.05 0.02 0.01 0.02 0.77 0.36 0.16 0.05 0.21 0.10 0.09 0.01 0.28 0.03 0.09

0 0 26 70 30 52 4 12 17 0 19 5 2 0 0 0 0 7 0 2 19 20 1 129 28 89 0 12 9 553

a

RMSE defined in eq 3. bThe number of data points with thermodynamically stable liquid phase, that is, these for which the COSMO-RS does not predict LLE.

fine 3D cleaning method implemented in MarvinSketch. This approximate geometry was finally treated as a starting guess of the optimum conformation in further quantum chemical optimization carried out by using the Turbomole suite (version 7.0),52 coupled with COSMOconf utility (version 4.0) allowing to find the best set of other relevant conformations representing the molecule under considerationfurther details on implemented algorithms can be found in the COSMOconf documentation freely available from the website of COSMOlogic company.50 Following my previous study on the COSMO-RS model,25 an effect of the quantum chemical input of the COSMO-RS model of the predicted phase diagrams is verified in this work by using COSMO-files obtained at two levels of density functional theory (DFT) calculations, namely, BP-TZVPCOSMO and BP-TZVPD-FINE. Both levels utilize the same Becke−Perdew (BP) functional53,54 for DFT calculations. Thus, they will be henceforth referred to as TZVP-COSMO and TZVPD-FINE, to make the notation more concise. TZVPCOSMO employs a triple-ζ valence polarized basis set (TZVP)55 with standard COSMO cavity calculation.49 In turn, TZVPD-FINE uses a larger TZVPD basis set (TZVP with diffuse functions), a novel hydrogen bond interaction term and a novel type of molecular surface cavity construction (a fine grid marching tetrahedron cavity, FINE), which creates σ

surfaces whose segments are more uniform and evenly distributed compared with the standard COSMO cavity.50 It is worth mentioning that COSMO-RS developers claim that the BP-TZVPD-FINE level is considered to be the “best quality” calculation method currently available, although being subject to ongoing revision and improvement. It was observed in the course of this study that this novel method is much more expensive in terms of the computational time compared with “traditional” TZVP-COSMO, particularly in the case of systems with associating fluids. All computations presented in this paper were performed on a desktop PC with a x64-based Intel Core i7-4710HQ 2.50 GHz CPU (4 cores and 8 threads), 16.0 GB of RAM, and 64bit Microsoft Windows 10 Pro OS (version 1703). The data on p(σ) versus σ are given for all cations/anion/solutes in the Supporting Information (XLS file). All COSMOtherm input/ output files are available on email request.

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RESULTS AND DISCUSSION Because of a huge amount of experimental ternary LLE data collected, it is obviously not possible to present and carefully analyze all of the results in this single contribution. However, all experimental and computed tie lines are provided in the Supporting Information (XLS file), so that the reader interested in the results for a specific IL and/or separation problem is E


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The Journal of Physical Chemistry B encouraged to search for detailed data therein. Furthermore, the plots presenting predicted versus experimental LLE phase diagrams for each individual data set are also presented in the Supporting Information (Figures S1−S930). In further text, analysis of accuracy of the predictions of equilibrium compositions (expressed in mole fraction basis) will be presented, including the analyses of “global” robustness of the model as well as the performance observed for each possible type of molecular binary subsystem. A particular emphasis will be put on a comparison between COSMO-RS predictions obtained adopting the σ-profiles computed using two considered levels of theoryTZVP-COSMO and TZVPD-FINE. Then, some general remarks on the performance of the studied computational approach for some representative and industrially relevant systems will be pointed out. Finally, the model’s capabilities of predicting proper qualitative trends of an impact of the cation/anion chemical structure on the LLE will be highlighted and shortly discussed. Root mean square error (RMSE) between calculated and experimental LLE mole fractions, defined as ⎡ N 3 (x′̂ − x′ )2 + (x ̂″ − x ″)2 ⎤1/2 ji ji ij ij ⎥ RMSE = ⎢∑ ∑ ⎢⎣ ⎥⎦ 6N i=1 j=1

Figure 2. Pseudocolor (checkerboard) plot comparing the performance of two levels of calculations used in this work in COSMO-RS modeling of ternary LLE of ILs with different types of molecular binary subsystems. Squares designate “C” and “F” correspond to a better performance of TZVP-COSMO and TZVPD-FINE, respectively. The “better” level is the one with higher percentage of data sets with lower RMSE. Empty squares designate the binary subsystems not found in the database.

(3)

will be employed throughout the discussion as a quantitative measure of robustness of prediction. In eq 3, prime and double prime denote extract (in this case IL-rich phase) and raffinate, respectively, xij is the mole fraction of the j-th component of the i-th tie line with (with the “hat” corresponding to COSMO-RS outcome), and N stands for the number of tie lines. It is important to note that the calculated tie lines were obtained starting from the feed composition defined as midpoints of the experimental tie lines. If the model does not predict the LLE split, then the feed mole fractions are assigned to the equilibrium compositions of both extract and raffinate. RMSE values obtained for each of the 930 data sets can be found in the Supporting Information (Table S3, or XLS file). In further text, some general remarks on the modeling performance are highlighted and discussed.

Nevertheless, a slightly better accuracy of TZVP-COSMO calculations is found finally. This applies as well to the predictions of the LLE composition of the extract and raffinate; in general, the extract phase is captured by the model with a slightly better accuracy. In particular, COSMO-RS combined with TZVP-COSMO resulted in a lower RMSE for 631 out of all 930 data sets. As can be seen in Figure 2, TZVPD-FINE performs better only in the case ternary mixtures involving {cycloalkane + alkane} (5/10 data sets with lower RMSE), {aromatic hydrocarbon + alkene} (2/3 data sets with lower RMSE), {aromatic hydrocarbon + aromatic hydrocarbon} (6/9 data sets with lower RMSE), {N-compound + cycloalkane/ alkane} (25/47 data sets with lower RMSE), {alcohol + ketone/ether} (10/20 data sets with lower RMSE), and {carboxylic acid + alkane} binary subsystems (4/6 data sets with lower RMSE). These findings might be viewed as a somewhat surprising result because TZVPD-FINE is claimed to be the “best quality” calculation method currently offered by COSMO-RS.50 Nevertheless, this should be emphasized that for 800 feed compositions (i.e., ≈9% of the entire database) TZVP-COSMO calculations did not predict the LLE phase split, whereas for TZVPD-FINE, this number is noticeably lower (553 that corresponds to ≈6%). One can speculate that those “mishit” data points might result in a bias toward lower values in RMSE, particularly if they correspond to relatively “short” experimental tie lines (i.e., those with similar compositions of both liquid phases). In such a case, the assumption of setting the composition of the extract and raffinate to be the same and equal to the feed’s composition may indeed result in quite accurate, though unintentional, estimation. Therefore, the results shown in Table 1 and Figure 2 should be treated with special care, especially for the kinds of systems with significant number of data points with liquid phase split not detected by the model. In fact, this applies to particularly important mixtures with {aromatic hydrocarbon + alkane} or {S-compound + alkane} binary subsystems, for

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GENERAL REMARKS All performed COSMO-RS predictions of ternary LLE are recapitulated in Table 1, where the values of RMSE are listed, including distinct values obtained for extract and raffinate. Moreover, RMSEs calculated over the entire database as well as over only the data sets for which the molecular compounds belong to specified chemical families are given along with the information on the size of data pool used to obtain them. The numbers of experimental tie lines for which COSMO-RS did not predict LLE split are also summarized. Apart from that, a brief comparison of TZVP-COSMO and TZVPD-FINE levels is presented in Figure 2, where the levels are classified as better or worse for each type of molecular binary subsystemthe better level is the one which provides more accurate description (i.e., lower RMSE) for more than a half of data sets of a given type. To enable the reader to carry out even deeper statistical analysis of the modeling performance, the distribution of RMSE values obtained for each individual data set is presented in Figure 3. The first thing that should be noticed is that overall RMSE calculated over all 9237 tie lines is roughly the same (≈0.1), irrespective of the theory level used to obtain the σ-profiles. F


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Figure 3. Distribution of RMSE between COSMO-RS predicted and experimental LLE mole fractions, defined in eq 3, obtained for each type of molecular binary subsystem. (a) Alkanes. (b) Cycloalkanes. (c) Alkenes. (d) Aromatic hydrocarbons. (e) S-Compounds. (f) N-Compounds. (g) Alcohols. (h) Ketones. (i) Ethers. (j) Carboxylic acids. (k) Esters. (l) Water. Red and blue boxes designate RMSE obtained from TZVP-COSMO and TZVPD-FINE levels. Markers correspond to outliers. The central mark on each box is the median. The lower and upper edges of the box correspond to the first and the third quartiles, respectively (interquartile range). The whiskers extend to the most extreme data points not considered as outliers (1.5 of the box width).

Figure 4. Experimental vs COSMO-RS predicted LLE phase diagrams for representative ternary systems with [C2C1Im][NTf2] (IL). (a) {IL + benzene + n-hexane} at T = 298.15 K.56 (b) {IL + thiophene + n-hexane} at T = 298.15 K.57 (c) {IL + thiophene + toluene} at T = 298.15 K.57 (d) {IL + pyridine + n-hexane} at T = 298.15 K.57 (e) {IL + ethanol + n-hexane} at T = 298.15 K.59 (f) {IL + 1-propanol + water} at T = 298.15 K.58 Key: circles, experimental data; squares, COSMO-RS calculations with TZVP-COSMO level; triangles, COSMO-RS calculations with TZVPD-FINE level. G


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IL- and hydrocarbon-rich phase, a wrong type of phase diagram is eventually obtained by TZVP-COSMO-based computations because of the complete miscibility of IL with thiophene revealed by the modelingfurthermore, the opposite sign of the slope of tie lines is predicted. It is noteworthy that equally disappointing findings were reported recently by Wlazło et al.39 for a number of ternary systems with thiophene or benzothiophene. It should be emphasized that the system presented in Figure 4b is not an incidental case selected just to demonstrate the failure of the COSMO-RS modeling. Indeed, the same results emerged for 45 out of 57 data sets with LLE for {S-compounds + alkane} binary subsystems (including 38 data sets with thiophene and 7 systems with benzothiophene). An LLE split of IL and S-compound was predicted by the TZVP-COSMO level only for the remaining 12 data sets involving ILs consisting of strongly hydrophilic anions like [C1COO], [C2SO4], [(C2O)2PO2], [SCN], and [C(CN)3]. In the case of COSMO-RS calculations combined with the TZVPD-FINE level, an incorrect type of phase diagram was predicted only for 16 out of 57 data sets, including 15 data sets with thiophene and a single data set with benzothiophene, whereas the mentioned problems were met also for the ILs based on [NTf2] and [FAP] anions. However, the immiscibility region as well as tie lines endpoints/slope obtained from TZVPD-FINE is reproduced with much better accuracy compared with TZVP-COSMO. The results obtained for the system {[C2C1Im][NTf2] + thiophene + toluene}, see Figure 4c, indicate that the remarks on the COSMO-RS robustness disclosed for the systems with alkanes can be generalized to the systems with aromatic hydrocarbons as well. TZVP-COSMO and TZVPD-FINE levels fail in the case of 5 and 2 data sets, respectively, out of 8 entries available in the database. Summing up, the TZVPD-FINE level seems to be more suitable to be applied in COSMO-RS-assisted design of ILs for extractive desulfurization of fuels and oils, which is, however, not confirmed by RMSE values listed in Table 1. The performance of the COSMO-RS approach in representing the systems with strongly polar (but non-associating) compound is illustrated in Figure 4d, where the computed LLE phase diagram of {[C2C1Im][NTf2] + pyridine + n-hexane} at T = 298.15 K is plotted along with the experimental data.57 In general, the performance of TZVP-COSMO and TZVPDFINE levels are roughly the same, taking into account all {IL + N-compound + aliphatic/aromatic hydrocarbon} systems. Both of them usually reproduce the LLE region and phase diagram type properly, whereas the errors in the computed mole fractions vary from system to system (see Figure 3), so that it is quite difficult do draw some general conclusions. An interesting finding is, however, that the TZVP-COSMO level exhibits a better representation of the IL-rich liquid phase, whereas TZVPD-FINE returns more accurate concentrations in the raffinatesee Table 1 for the respective values of RMSE. Furthermore, it is worth mentioning that the TZVP-COSMO level provides much a better representation of the systems with rarely investigated N-compounds, like pyrrole, indoline, quinoline, and 1-methylimidazole. For most of those systems, TZVPD-FINE did not predict the LLE split for a significant part of feed compositions, in spite of the fact that the neither length nor slope of the properly predicted tie lines indicates such sudden LLE region disappearance. Possibly, this might be fixed by adjusting the parameters of the LLE calculation algorithm implemented in COSMOtherm.50 However, it was not decided to tune the algorithm for each system individually

which TZVPD-FINE handles predicting the existence of LLE much better than TZVP-COSMO. The analysis of distributions shown in Figure 3 suggests that in many cases the spread in the RMSE values is so significant that it cannot be ignored, when estimating the expected modeling accuracy for a new system. Furthermore, the overall values listed in Table 1 are affected by outlying data sets, for which the deviations of predictions from the experimental data are exceptionally high. Of course, high RMSE may follow not only from inadequacies of the model but also from a bad quality of the experimental data. It was checked that if those poorly described data sets are removed from the discussion (152 and 133 database entries for TZVP-COSMO and TZVPD-FINE, respectively), then the overall RMSE values not higher than 0.1 are obtained, regardless of the type of ternary mixturethis can be easily checked by proper filtering of the data given in the Supporting Information (XLS file), where the data sets considered as outliers are also discriminated. Overall RMSEs obtained after exclusion of data sets designated as outliers (for either TZVP-COSMO or TZVPD-FINE) have a little bit lower values, namely, 0.07 and 0.08 for TZVP-COSMO and TZVPDFINE, respectively. In Figure 4, COSMO-RS predicted LLE phase diagrams are shown for six ternary systems with the most intensively studied IL, that is, [C2C1Im][NTf2], along with the experimental data taken from the literature.56−59 The systems were selected in such a way to properly exemplify the diversity of the systems collected in the database as well as to address the issues just raised in the discussion of RMSE data. Figure 4a shows ternary LLE in the system composed of the IL and two nonpolar and nonassociating components, namely, benzene and n-hexane, at T = 298.15 K.56 As seen, only COSMO-RS with the TZVPD-FINE level captures the type of the phase diagram with two miscibility gaps in the binary mixtures of ILs with both hydrocarbons and complete miscibility of the {benzene + n-hexane} subsystem. On the contrary, COSMO-RS coupled with the TZVP-COSMO level does not predict the liquid phase split in the binary mixture of [C2C1Im][NTf2] with benzene. The same was observed for 22 out of 96 ternary data sets for which LLE gap in mixtures {IL + aromatic hydrocarbon} was experimentally detected and reported. Those sets regard the systems with benzene and toluene, whereas liquid phase instability is usually correctly captured for the heavier alkylbenzenes. Such a behavior was not observed in the case of TZVPD-FINE predicted phase diagramsregardless of IL, applying this level of theory always resulted in a qualitatively proper phase behavior. On the basis of this finding, one can strongly recommend to apply this novel variant of COSMO-RS in computing LLE phase diagrams of mixtures involving aliphatic and aromatic hydrocarbons. Nevertheless, it should be emphasized that irrespective of the level of the theory used to compute σ-profiles, the accuracy of prediction of LLE tie lines is not satisfactory. This applies not only to LLE compositions but also to the slope of the tie lines. In general, the quality of predictions tends to deteriorate with an increase of the concentration of aromatic hydrocarbon in the feed. COSMO-RS predicted versus experimental57 LLE phase diagram for the system {[C1C2Im][NTf2] + thiophene + nhexane} at T = 298.15 K is shown in Figure 4b. As can be easily noticed, the model displays the same behavior as in the case of the system {IL + benzene + n-hexane}. Apart from very inaccurate predictions of the equilibrium compositions of the H


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Figure 5. Experimental vs COSMO-RS predicted distribution ratio of toluene (β2upper panels) and n-heptane/toluene selectivity (S23lower panels) in the presence of different ILs as a function of feed’s toluene mole fraction x2 (feed composition defined as the midpoint of a tie line). (a) Effect of the cation core: circles, [C4C1Im][NTf2];60 squares, [C4Py][NTf2];61 triangles, [C4C1Pyr][NTf2].62 (b) Effect of cation alkyl side-chain length: circles, [C1C1Im][NTf2];60 squares, [C2C1Im][NTf2];60 triangles, [C3C1Im][NTf2];63 diamonds, [C4C1Im][NTf2];60 crosses, [C6C1Im][NTf2].60 (c) Effect of cation side-chain substituent: circles, [C2C1Im][NTf2];60 squares, [C1vC1Im][NTf2];63 triangles, [C1PhC1Im][NTf2];64 diamonds, [C2OHC1Im][NTf2].65 (d) Effect of anion: circles, [C4C1Im][NTf2];60 squares, [C4C1Im][SCN];66 triangles, [C4C1Im][N(CN)2];67 diamonds, [C4C1Im][C(CN)3].68 Solid and dashed lines designate the COSMO-RS model used with TZVP-COSMO and TZVPD-FINE level of theory, respectively.

can be noticed that the TZVP-COSMO level provides equilibrium mole fractions which are much closer to the experimental data compared with those obtained from TZVPDFINE predictions. In general, applying TZVP-COSMO σprofiles resulted in lower RMSE for a great majority of {IL + alcohol + water} data sets (63 out of 70); this also applies to other aqueous systems (e.g., those with ketones and ethers), see Figures 2 and 3. In fact, this is one of the most unexpected finding of this study because the COSMO-RS with the TZVPD-FINE level incorporates a novel term accounting for hydrogen bonding.50 Therefore, this approach is supposed to display improved thermodynamic property prediction results for compound classes, where the classical COSMO-RS hydrogen bonding term showed weaknesses. Furthermore, it should be also pointed out that for the mixtures containing associating fluids, the COSMO-RS calculation-based TZVPDFINE σ-profiles require much more time to be performedin fact, COSMOtherm run to get several LLE tie lines in a crossassociating mixture may take several hours on a single CPU, whereas in the case of classical TZVP-COSMO, it is usually a matter of a few seconds, at most minutes. This may be perceived as an important obstacle in further applications of TZVPD-FINE in other fields, for example, high-throughput screening for ILs of desired properties.

to demonstrate a fair evaluation of the COSMOtherm suite with its default setup. The quality of the COSMO-RS predictions for the mixtures composed of associating fluids is demonstrated in Figure 4e,f, where both calculated and experimental ternary LLE phase diagrams are plotted for representative systems {[C2C1Im][NTf2] + ethanol + n-hexane} at T = 298.5 K59 and {[C2C1Im][NTf2] + 1-propanol + water} at T = 303.15 K,58 respectively. In the case of the former system, it can be seen that the COSMO-RS model provides reasonable estimates of extract phase mole fractions and very poor predictions of raffinate mole fractions, irrespective of the level of the theory used to obtain σ-profiles of molecules forming the system. Nevertheless, in the case of {IL + alcohol + alkane} mixtures, the final accuracy strongly depends on the IL’s cations and/or anionas can be noticed from Figure 3, those mixtures disclose one of the highest variance of RMSE. For instance, RMSE values for different [NTf2] varies from 0.02 to 0.19 for both TZVP-COSMO and TZVPD-FINE levels. On the other hand, RMSE typically does not exceed 0.10 for the systems with imidazolium alkylsulfates and some dialkylphosphates, irrespective of the level. For 44 out of 87 data sets with {alcohol + alkane} subsystems, the calculations employing the TZVPCOSMO level resulted in lower RMSE. However, higher values of RMSEs obtained for the TZVPD-FINE level may be also attributed to the misleading behavior of the LLE algorithm (the same as in the case of the systems with N-compounds) observed for a greater number of data points compared with TZVP-COSMO. As can be deduced from Table 1, the level of theory also influences the performance of the COSMO-RS approach in modeling the mixtures containing more than one associating component, in particular, the systems with water. Although the phase behavior of the representative {IL + alcohol + water} system presented in Figure 4f is qualitatively correct, it

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IMPACT OF CATION/ANION ON LLE Capability of capturing different effects of the molecular structure on physical and thermodynamic properties is another feature of a modern thermodynamic tool that should be highlighted and evaluated. This is particularly regarding not only the so sophisticated model like COSMO-RS but also so complex systems and properties like ILs and LLE in their ternary mixtures with molecular compounds. In the case of I


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TZVP-COSMO level, for which x̂2″ versus x2″ data are symmetrically distributed along the diagonal. To extend this kind of qualitative analysis to all ILs available for a presumed separation problem, one can use the limiting (x2 → 0) values of β2 and S23 computed at the lowest feed concentrationusually they correspond to the highest distribution ratio and selectivity, thus they will be denoted as βmax and Smax 2 23 . Figure 6 shows the comparison of the orders of

ternary LLE data, it is generally easier to discuss the validity of the predicted structure−property relationships by using the distribution ratio and selectivity, defined as β2 =

S23 =

x 2′ x 2″ β2 β3

(4)

=

x 2′/x 2″ x3′/x3″

(5)

instead of equilibrium mole fractions. In eq 4, “2” and “3” denote molecular compounds, in particular, the solutes going to be separated in the process of liquid−liquid extraction. In further text, the performance of the COSMO-RS method in predicting an effect of chemical structure on LLE is discussed for two pairs of molecular solutes representing the separation of aromatics and S-compounds from fuels and oilsobviously, only representative systems had to be chosen for the needs of this short paper, whereas more detailed analyses can be carried by using the data provided in the Supporting Information (XLS file). Figure 5 presents β2 and S23 of separation “toluene (2) from n-heptane (3)” computed for a number of ILs differing in a single element of the chemical structure. An effect of the cation core on β2 and S23 is depicted in Figure 5a, on the basis of LLE data for ternary systems with [NTf2]-based ILs with [C4C1Im], [C4C1Pyr] (1-butyl-1-methylpyrrolidinium), and [C4Py] (1butylpyridinium) cations.60−62 As seen, neither the TZVPCOSMO nor TZVPD-FINE level is capable of reproducing the correct variation of thiophene distribution ratio, namely, [C4C1Im] ≈ [C4C1Pyr] < [C4Py]. In the case of selectivity, only the TZVP-COSMO level provides qualitatively correct predictions. An effect of the cation alkyl chain length on β2 and S23 is shown in Figure 5b on the basis of the LLE data reported in the literature for [CnC1Im][NTf2] homologous series of ILs (n = 1, 2, 3, 4, 6).60,63 It is easily seen that both levels correctly reproduce the variation of β2 and S23 with n. However, TZVPCOSMO performs much better compared with TZVPD-FINE, especially in the case of S23. The experimentally revealed and predicted impact of the substitution of the cation alkyl side chain by vinyl/phenyl/hydroxyl groups do not converge, as depicted in Figure 5c. However, experiments indicate that both β2 and S23 are of the same order of magnitude, regardless of the type of cation’s functionalization,63−65 so that such delicate variation has to be extremely difficult to capture. Furthermore, some of the data are subject to significant scattering, so that one should treat this evaluation with care. Finally, the predicted trend in both β2 and S23 is demonstrated in Figure 5d for [C4C1Im] cation-based ILs with four anions and compared with the experimental evidence.60,66−68 The model provides qualitatively correct variation of β2 as a function of the anion, namely, [NTf2] > [C(CN)3] > [N(CN)2] > [SCN], regardless of the theory level used to obtain σ-profiles. An interesting remark that is worth to be made after the analysis presented {IL + toluene + n-heptane} mixtures is that the TZVPD-FINE level produces underestimated values of both β2 and S23. On the basis of more detailed insights into the obtained results, it can be explained by a tendency of TZVPD-FINE to overestimate x″2 this can be easily checked using the data collected in the Supporting Information (XLS file). In the case of all binary subsystems {aromatic hydrocarbon + alkane}, x̂2″ > x2″ for almost 90% of tie lines. This is indeed in contrast with the

Figure 6. Experimental vs COSMO-RS predicted variation in maximum distribution ratio of (βmax 2 ; upper panel) and maximum selectivity (Smax 23 ; lower panel) with chemical structure of IL. (a) {Toluene (2) + n-heptane (3)}. (b) {Thiophene (2) + n-heptane (3)}. Key: solid lines, experimental data; circles, COSMO-RS calculations with TZVP-COSMO level; squares, COSMO-RS calculations with TZVPD-FINE level. Dashed lines serve as guide for the eye.

ILs obtained from experimental and COSMO-RS predicted LLE data, obtained for “toluene (2) from n-heptane (3)” (Figure 6a) and “thiophene (2) from n-heptane” (Figure 6a) the computed data were permuted according to the increasing or Smax experimental values of βmax 2 23 . From a general point of view, the results suggest that ordering the COSMO-RS predicted results to select the IL with the desired distribution ratio or selectivity can result in misleading findingsindeed, the trends predicted by the model fluctuate very strongly along the trend obtained from the LLE measurements. It is also worth to be noted from Figure 6 that there are many inconsistencies in the trends predicted by COSMO-RS, depending on which the level of theory is considered.

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CONCLUSIONS A detailed and extensive evaluation of the COSMO-RS method (implemented in COSMOtherm suite) in predicting ternary LLE phase diagrams in IL systems was carried out on the basis of a large experimental data collection. First of all, it was shown based on many examples that the performance of the model is strongly dependent on the type of both IL (including cationic family and anion) and molecular binary subsystem (depending on the chemical nature of the constituting solutes, such as J



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aromaticity, polarity, and/or association). A significant part of the study was devoted to highlight an effect of the level of the theory used in obtaining σ-profiles and treating intermolecular interactions of thermodynamic model. Both TZVP-COSMO and TZVPD-FINE yielded roughly the same global values of RMSE. However, the more common TZVP-COSMO level displayed some serious problems in representing LLE in the systems relevant from the point of view of interesting separation problems. Thus, for the LLE calculations involving aromatics and organic S-compounds applying this level with a special care is recommended. Nevertheless, it was shown that the novel, more advanced, TZVPD-FINE level requires further revisions and improvements as well, particularly when the main goal is the calculation of the thermodynamic properties of complex liquid mixtures with cross-association. Besides, some effort should be put into optimization of the COSMOtherm code to reduce the computational cost of LLE calculations as much as possible. I am firmly convinced that the results presented in this contribution may have a significant impact on the scope and range of applications of the COSMO-RS method in chemical engineering. Despite somewhat disappointing model’s capability of capturing basic structural effects, the presented evaluation will possibly make the design of IL-based products and IL-assisted processes easier. To be more specific, the provided review of the modeling accuracy and robustness will accelerate some new applications of the COSMO-RS approach in research and development of novel extractants based on ILs. In fact, the presented study on an impact of theory level as well as statistics of the errors between the predicted and experimental LLE tie lines can guide the engineers in deciding whether they should consider COSMO-RS as a tool for solving the problems requiring phase equilibrium data as well as in estimating the reliability of computed data.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b12115. List of cations of ILs; list of anions of ILs; ternary LLE database and COSMO-RS calculations summary; and experimental versus predicted LLE phase diagrams (PDF) Microsoft Excel spreadsheet containing full lists of cation/anions/solutes (including their IUPAC names and abbreviations), references to experimental LLE data, σ-profiles, and all the experimental and COSMO-RScomputed LLE tie lines (ZIP)

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +48 (22) 234 56 40. ORCID

Kamil Paduszyński: 0000-0003-2489-6983 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS Funding for this research was provided by the National Science Centre, Poland, UMO-2016/23/B/ST5/00145. K


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Extensive Evaluation of the Conductor-like Screening Model for Real

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