Thermodynamic Modeling of Multicomponent LiquidâLiquid Equilibria

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Thermodynamics, Transport, and Fluid Mechanics

Thermodynamic Modeling of Multicomponent Liquid-Liquid Equilibria in Ionic Liquid Systems with PC-SAFT Equation of State Kamil Paduszy#ski Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00175 • Publication Date (Web): 27 Mar 2018 Downloaded from http://pubs.acs.org on March 28, 2018

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Industrial & Engineering Chemistry Research

Thermodynamic Modeling of Multicomponent Liquid-Liquid Equilibria in Ionic Liquid Systems with PC-SAFT Equation of State Kamil Paduszyński∗ Department of Physical Chemistry, Faculty of Chemistry Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland E-mail: [email protected]

Phone: +48 (22) 234 56 40

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Abstract This work is a continuation and extension of previously published study showing that the perturbed-chain statistical associating fluid theory (PC-SAFT) is an efficient and robust approach for calculating thermodynamic properties of the mixtures containing ionic liquids (ILs) [J. Phys. Chem. B 2012, 116, 5002–5018]. The modeling strategy presented in the original paper was based on application of infinite dilution activity coefficients of molecular solutes in ILs (γ ∞ ) to calculate binary corrections for the PC-SAFT combining rules. In this work, the idea is further investigated, in particular extended to a broader spectrum of pure fluids (the model parameterization is provided for almost 100 ILs) and evaluated based on a large compilation of liquid-liquid equilibrium (LLE) data, including more than 400 distinct and diverse ternary systems and a number of higher systems. Three PC-SAFT modeling strategies are proposed and systematically reviewed in order to elucidate an effect of γ ∞ data on the quality of LLE predictions. Experimental versus predicted impact of ILs’ cation and anion on LLE for different kinds of binary subsystems of molecular compounds is also highlighted and discussed. Finally, the results obtained with the PC-SAFT are confronted with the calculations carried out with conductor-like screening model for real solvents (COSMO-RS), often perceived or referred to as the state-of-the-art predictive tool of modern thermodynamics of liquid solutions.

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Introduction Since the beginning of the current century, ionic liquids (ILs) have attracted a remarkable amount of attention from research groups and communities concerned with different areas of fundamental and applied sciences. 1,2 From the point of view of categorization of chemical compounds, ILs are nothing else but organic salts, in particular only these consisted of organic cations based primarily on quaternarized amines. Asymmetry in size, shape and conformational flexibility of the ions composing ILs usually result in a significant reduction of net lattice energy, hence much lower melting point compared to “conventional” salts known from inorganic chemistry. 3–5 As being molten salts, ILs do not evaporate, thus have extremely low vapor pressure at relatively high temperatures. Besides, compared to molecular organic compounds, ILs have been shown to disclose much wider liquid range due to enhanced thermal stability. These features minimize an impact of ILs-based lab-scale and industrial processes on the environment, therefore ILs have been widely recognized as potential replacements for volatile organic solvents, in consequence as the solvents of “green” chemistry. 6 Other important characteristic of ILs is a great diversity of their chemical structures due to a number of degrees of freedom available when designing an IL for a given purpose. To my best knowledge, the number of 1:1 ILs that could be formed taking into account only the ions described in the literature can be currently estimated to be of the order of 250 thousands (stated based on in-house databases of diverse physical and thermodynamic properties of pure ILs 7,8 ). A consequence of this is “tuneability” of physical, chemical and thermodynamic properties of ILs by a proper selection of cation core, anion and size/shape/functionalization of the side chains attached to the ions. First of all, this applies to mutual solubility/miscibility of ILs in/with different solvents. This is particularly important as different ILs have been shown to be capable of dissolving a variety of materials, mainly due to the presence of charged moieties in the liquid phase, thus a broader spectrum of forces they can interact with other molecules. In a great majority of solutions, ILs form two phase systems when mixed with molecular compounds, at the same time being capable of selective dissolution of compounds belonging to one chemical family. That is why 3



separations of liquid mixtures employing ILs-based extraction or extractive/azeotropic distillation have been one of the most intensively studied applications of ILs in chemical industry since many years. 9 In particular, a vast amount of attention has been devoted to experimental studies on vapor-liquid equilibrium (VLE), liquid-liquid equilibrium (LLE) and solid-liquid equilibrium (SLE) phase diagrams of ILs-based systems relevant from the point of view of separation problems important from the standpoint of petrochemical industries, namely, e.g. aromatic from aliphatic hydrocarbons, 10 alkenes from alkanes 11 and sulfur and nitrogen organic compounds from alkanes (to be further applied in extractive desulfurization/denitrification of fuels produced from crude oil). 12–14 Recently, ILs-based separation processes of biologically active compounds (e.g. drugs, lipids, proteins, nucleic acids, and so on) have been marked as an urgent scientific activity. 15 Due to the mentioned diversity of ILs and their tailorable properties, predictive models allowing to compute phase equilibria (as well as other important thermodynamic data) seem to be very interesting and attractive tools for time and cost efficient search for ILs that meet some predefined criteria, e.g. these regarding separation problem of interest. Thus far, many contributions on application of different thermodynamic models to predict (or at least reproduce) experimentally obtained phase diagrams have been published in open literature. To be more specific, simple excess Gibss energy correlative models (like Wilson equation, NRTL, or UNIQUAC), UNIFAC group contribution method, classical cubic equations of state, modern molecular-based equations of state coupled with association theories, hybrid models combining statistical thermodynamics and quantum chemistry are the most exhaustively investigated computational approaches used to model the mixtures containing ILs. 16 In particular, statistical associating fluid theory (SAFT) 17–21 and conductor-like screening model for real solvents (COSMO-RS) 22–24 have gained attention of many researchers dealing with phase equilibria and separations involving ILs. Based on a huge number of papers on applying these models in describing and explaining thermodynamic behavior in diverse systems (not only these with ILs), one can surely label them as the currently “leading” methodologies in molecular thermodynamics of fluids. In the case of the SAFT approach, 17,18 various variants of the original theory have been 4


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studied in recent years, but only the perturbed-chain SAFT (PC-SAFT) developed by Gross and Sadowski 19,20 and soft-SAFT proposed by Blas and Vega 21 have been treated systematically for different families of ILs as well as for different physical and thermodynamic properties of pure ILs and their mixtures with diverse molecular compounds. In the case of ILs’ solutions, solubility of various gases (mainly CO2 ) has been the most comprehensively studied property, starting from the pioneering papers in the field published by Economou and co-workers 25,26 and Andreu and Vega. 27,28 Later on, collaborative works of the groups of Vega and Coutinho, 27–36 the papers of Mutelet et al. 37,38 as well as relevant contributions on electrolyte PC-SAFT (ePC-SAFT) given by Held and co-workers 39–42 have been reported. The topic seems to be still in interest for chemical industry, what is confirmed by very recent research activity of other groups. 43–45 Since 2011, applications of the PC-SAFT model in representing other relevant thermodynamic properties like VLE/LLE/SLE phase diagrams as well excess enthalpy of mixing (hE ) have been intensively studied by Paduszyński et al. 46–59 and other leading thermodynamic research groups working in the field physical chemistry of ILs. 60–73 However, it should be stressed that a great majority of contributions was concerned with thermodynamic properties of binary systems {IL + molecular solvent}. In fact, the PC-SAFT equation of state has been shown to be capable of predicting both phase equilibrium and hE data of ILs mixed with non-polar, polar and self-associating solutes with a very good accuracy, when infinite dilution data are involved in fitting binary interaction parameters. 56 On the other hand, only a few papers on SAFT calculations in ternary systems with ILs were published so far, 30,40,60,70,74 in general with promising results obtained. This work summarizes the results of the study on the performance of the PC-SAFT model, when applied to predict LLE phase equilibrium diagrams in ternary and higher mixtures consisting of a single IL and two or more molecular solutes belonging to different families of chemical compounds. Such study was considered to be of great importance mainly because of: (1) very promising results on the performance of the PC-SAFT equation of state in predicting thermodynamic behavior of binary systems containing ILs reported previously; 56 (2) the lack of systematic and comprehensive analysis of the PC-SAFT model in representing ternary and higher ILs-based 5



systems, except a number of papers published recently; 30,40,60,70,74 (3) still increasing interest in the PC-SAFT as chemical science and engineering tool for applications in modeling ILs and their systems, particularly in separations. In particular, three strategies for the equation-of-state binary interaction parameter determination will be presented and tested. Furthermore, comparison of the PC-SAFT model with the COSMO-RS is provided, using the results reported in my very recent paper. 75 The role of the COSMO-RS model in this comparison can be seen as the reference or state-of-the-art predictive model. Analysis of the PC-SAFT performance will be given in terms of both quantitative and qualitative measures, i.e. deviations of the predicted equilibrium phase compositions and a feasibility of predicting by the models experimentally revealed structural effects on phase diagrams, respectively. The primary goal of the presented analysis is, however, to elucidate an effect of complexity of the molecular model used in the calculations on their accuracy. In other words, I will attempt to answer the following question: Is there actually any advantage of physically sound molecular model and sophisticated computational approach like COSMO-RS over simpler method like PC-SAFT?

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Modeling PC-SAFT Equation of State Fundamentals In the PC-SAFT approach, proposed by Gross and Sadowski 19,20 as an extension of the original theory of Chapman and co-workers, 17,18 real molecules are represented as chains composed of tangentially connected spherical segments interacting via pair-wise square-well potential with “soft repulsion” included. As in the case of the other SAFT variants, thermodynamics of the system is expressed in terms of molar residual Helmholtz free energy, ares = ares (T, ρ, x), dependent on temperature T, number density ρ and composition x = [x 1, . . ., x C ] (where x i denotes mole fraction of component i and C stands for the number of components). Total value of ares is given as a sum of contributions, namely ares ≡ a˜ res = a˜ hc + a˜ disp + a˜ assoc + . . . RT

(1)

due to hard-chain formation (denoted by “hc”; the reference term of the perturbation expansion — the key feature of the PC-SAFT compared to the original SAFT) and different intermolecular forces acting between the segments, like dispersive forces (denoted by “disp”), or association (“assoc”). Ellipsis in eq (1) indicates that some extra terms can be added, e.g. these describing electrostatic interactions between dipolar/quadrupolar molecules or ions. Given a˜ res , all the properties relevant from the point of view of phase equilibrium calculations (like pressure, or chemical potential) can be obtained by means of differentiation, following some fundamental thermodynamic formulas (see the Appendix of reference 19). Details on each term can be found in the original PC-SAFT papers. 19,20 For the purpose of this paper, general remarks on the model’s parameters and their determination are presented only. Within the molecular picture which the PC-SAFT model is based on, each compound (regardless of its chemical family) is described by three parameters: m — the number of segments forming 7



the model chain (or relative length of the chain — this parameter is not required to have an integer value); σ — diameter of the segment forming the chain; u — depth of the square-well potential representing van der Waals dispersive interactions (usually given in temperature units, scaled by the Boltzmann constant k B ). In the case of the components capable of interacting via specific interactions (e.g. hydrogen bonding, or forming Lewis acid-base complexes) the following has to be additionally defined: (1) association scheme, i.e. the types and the numbers of associating sites (A, B, . . . ) mimicking the functional groups acting as donors/acceptors in a specific interaction as well as specification which groups can interact with each other; (2) parameters expressing the energy and geometric effect of each A· · · B interaction, denoted as ε AB /k B and κ AB , respectively. Although many attempts have been done to determine all these parameters by using some independent methods like quantum chemical calculations, 76 or computer simulations, 77 or group contribution models, 78 fitting them to pure-fluid data still remains the most popular approach. In the case of molecular compounds, temperature-dependent saturated liquid density and vapor pressure are the thermodynamic data commonly used to obtain the PC-SAFT parameters to be used in further calculations of other properties, e.g. phase diagrams of mixtures. SAFT Molecular Scheme of ILs In the literature, two main SAFT-based molecular schemes for modeling the systems with ILs can be encountered, namely, the “ion pair” approach usually used with the “classical” SAFT models since 2007, 27,28 and the “electrolyte” approach identified mainly with the ePC-SAFT. 42 The former one assumes that ILs are treated as electrically neutral ion pairs, whereas the electrostatic interactions between the ions are mimicked by strong association. In the case of the latter method, both cation and anion are treated as separate molecules interacting via Coulombic forces described the Debye-Hückel term included in eq (1). Of course, both these methodologies have their pros and cons. In particular, the “electrolyte” approach seems to be more physically sound, but it requires more parameters to be fitted to pure-fluid and binary data. In turn, “ion pair” approach has been established as an acceptable compromise between computational efficiency and the level 8


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of physical fidelity required to obtain reliable descriptions of the thermophysical properties of fluids. 67 In fact, modeling ILs as non-dissociated compounds is less strict in terms of physical detail, but parameterization of ILs using this scheme is much easier as standard and readily available experimental pure-fluid data can be utilized in fitting process. Nevertheless, it is worth mentioning that a special care should be taken when applying the PC-SAFT to ILs in such manner. In fact, some parameterizations are likely to exhibit some numerical pitfalls resulting in unrealistic phase diagrams. 79 There is no doubt that the main controversy with the “ion-pair” approach is that it completely ignores the existence of ions in pure ILs. Furthermore, there are no strict rules on how many donor/acceptor associating sites should be identified to be located at the chains representing the ion pairs. For instance, some authors have applied simple schemes adopted directly from alcohols, like 2B (i.e. one donor and one acceptor site per chain). 43,64,66,70 In my opinion, this is not a good practice of applying the association term to ILs, because the parameters fitted in this manner may result in strongly overestimated vapor pressure of pure ILs. Hence, the key feature of the ILs, i.e. extremely low volatility, may not be captured by the model properly. On the other hand, Mac Dowell et al. 67 supported their selection of the number of sites on the basis of charge and polarity distribution of the ions’ molecules resulting from quantum chemical calculations. Alternative approach, extensively applied in the previous papers of mine and my collaborators, 46–59 is to assign the number both donor and acceptor associating sites to the number of lone pairs located and exposed at the anion, e.g. seven sites for ethylsulfate, 52 five for bistriflamide, 53,56,58,59 four for tetracyanoborate, 49 three for dicyanamide, 48,54 or tricyanomethanide, 50 and so on. First of all, this method allows to get the parameters resulting in reliable predictions of vapor pressure (thus consistent thermodynamics of VLE in the mixtures). 56 It also enables the PC-SAFT model to account for the differences in the ILs based on diverse anions — in fact, the anion’s chemical structure is the key factor influencing physical and thermodynamic properties of ILs. Apart from unquestionable robustness and versatility of “ion pair” approach (as comprehensively demonstrated in reference 56), this was the main reason why I finally decided to follow this strategy of the 9



PC-SAFT model parameterization in this study. Another problem with applying all the SAFT-based models to systems with ILs is the lack of experimental data on their vapor pressure (with a few exceptions), so that density (temperatureand/or pressure-dependent) remains the only property readily available for the parameters’ fitting process; however, some attempts to fit the PC-SAFT parameters to both density and vapor pressure data have been made. 37,54 In general, adjusting all the PC-SAFT parameters to density data only is highly not recommended, because such procedure usually does not allow to get an unique mathematical solution of optimization. This particularly regards the “energetic” PC-SAFT parameters, i.e. u/kB and ε AB /k B , whose values significantly affect the quality of predictions of other thermodynamic properties, e.g. vapor pressure, enthalpy of vaporization. In the literature, different approaches were proposed to circumvent this issues: (1) fitting m, σ and u/kB to density data only while transfering association constants from other compounds, 65 or fixing them as some predefined values; 43,68 (2) fitting all the parameters simultaneously to pure-fluid density and some binary data like VLE and infinite dilution activity coefficients (γ ∞ ); 64,69 (3) fitting all the parameters at the same time to densities and the Hildebrand solubility parameters derived from γ ∞ data treated with regular solution theory. 49,50,57–59 Based on my previous experience with approach no. 3, I decided to apply it in this work as well. In order to reduce the number of adjustable parameters, it was assumed that parameters ε AB /k B and κ AB (sometimes u/k B ) are anion-specific and/or universal within a given homologous series of ILs or their anionic family. All the PC-SAFT parameters presented in this paper were optimized using both in-house and built-in functions/subroutines coded in the MATLAB environment (version 2017a, on academic license from Mathworks, Inc.). The sum of squares of relative deviations between computed and experimental properties (weighted with the numbers of data points for each property) was adopted as objective function minimized following Levenberg-Marquardt algorithm, implemented in lsqnonlin function of the MATLAB Optimization Toolbox. All the computations were performed using a desktop PC with x64-based Intel® CoreTM i7-4710HQ 2.50 GHz CPU (4 cores and 8 threads), 16.0 GB of RAM and 64-bit Microsoft Windows 10 Pro OS (version 1703). 10


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Modeling Strategies for Mixtures Extension of the PC-SAFT equation of state to mixtures requires some new parameters accounting for the molecular interactions between alike segments, let us say these representing components denoted by i and j. In general, three distinct types of such i- j cross-interactions (and the following PC-SAFT parameters corresponding to them) may be encountered in any mixture: (1) crossdispersive interactions between alike segments — expressed in terms of parameters ui j /k B and σi j ; (2) “induced” association between component i which is not self-associating fluid itself, but has in its chemical structure a group Ai enabling it to interact via specific interactions with associating sites B j of self-associating fluid j — accounted for by the parameters ε Ai B j /k B and κ Ai B j ; (3) cross-association between the sites of two self-associating fluids, in particular between donor groups of component i (Ai ) and acceptor groups of component j (B j ) as well as acceptor groups of component i (Bi ) and donor groups of component j (A j ) — represented by the parameters ε Ai B j /k B , κ Ai B j and ε A j Bi /k B , κ A j Bi , respectively. In particular, cross-dispersion has to be taken into account irrespective of a chemical nature of compounds forming the mixture, because dispersion term of eq (1) is an “intrinsic” element of the SAFT. Induced association is considered in this work for the mixtures of ILs with polar compounds with carbonyl group C−O, i.e. acetone, or butanone, and ethyl acetate, as well as the mixtures of these solutes with alcohols or water. Finally, cross-association is accounted for in the case of the mixtures of ILs, alcohols, water and pyridine (modeling strongly polar chemicals like pyridine as self-associating component has been shown to be physically sound and effective in representing thermodynamic data of the systems of ILs 50,57 ). The simplest approach to obtain these cross-interaction parameters is to use so-called combining rules expressing them in terms of pure-fluid parameters. The following rules of Lorentz-Berthelot (LB), Kleiner-Sadowski (KS) 80 and Wolbach-Sandler (WS) 81 are usually used in the PC-SAFT calculations to represent cross-dispersion, induced association and cross-association, respectively: √ ui j = ui u j 1 − kiLB j

(2a)

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σi j =

σi + σ j 1 − liLB j 2

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(2b)

εA j B j 1 − kiKS j 2 ! √ 2 σi σ j 3 Aj Bj 1 − liKS =κ j σi + σ j

ε Ai B j =

(2c)

κ Ai B j

(2d)

ε Ai B i + ε A j B j 1 − kiWS j 2 !3 √ p 2 σ σ i j 1 − liWS = κ Ai B i κ A j B j j σi + σ j

ε Ai B j = ε A j B i =

(2e)

κ Ai B j = κ A j B i

(2f)

The coefficients kiXj and liXj (where X stands for LB, KS, or WS) are the binary corrections for the energetic and geometric PC-SAFT parameters, respectively. They describe how much do the actual values of cross-terms on left-hand side of eq (2) deviate from the values estimated using the right-hand side given that kiXj = liXj = 0. In the conventional equation-of-state modeling, the binary corrections are obtained from experimental binary data of interest by means of fitting. Such an approach results in vanishing of the predictive capabilities of the model, unless a distinct method for calculation of kiXj and/or liXj is available. In particular, phase equilibrium calculations are usually affected by the values of liXj to a much lesser extent compared to kiXj . Therefore, it is usually presumed that liXj = 0 regardless of X — this approach is followed in this work as well. In turn, kiXj , which may be also strongly temperaturedependent, can be fitted to other thermodynamic property, for instance the property which is much easier to measure or estimate using an auxiliary model. This methodology was successfully utilized for diverse binary systems in predicting VLE/LLE/SLE phase diagrams and hE using the binary corrections fitted to temperature-dependent γ ∞ of molecular solute in IL. 48–50,53,56,57,59 As shown previously, 56 predictive capacity of the PC-SAFT can be enhanced by using γ ∞ data estimated from modified UNIFAC (Dortmund) group contribution model. 82 In this work the strategy is generalized and extended to multicomponent systems using up-to-date compilation of experimental γ ∞ data 83 as well as the UNIFAC parameters matrix available for ILs. 84 12


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In order to keep the notation clear and consistent, IL present in a system by will be consequently denoted as 1, whereas molecular solutes will be referred to as i or j. For C-component systems C(C − 1)/2 binary corrections are needed to be specified along with their types. The following rules are proposed for establishing the type of the correction for a given pair of components i- j: 56 (1) Xi j = LB if one of the components is both non-polar and non-associating (e.g. IL, or water + hydrocarbon, or ether); (2) Xi j = KS if i is polar but not self-associating, while j is self-associating (or vice-versa; e.g. IL + ketone, alcohol + ethyl acetate); (3) Xi j = WS if both i and j are selfassociating fluids (e.g. IL + alcohol, or pyridine). Furthermore, the corrections can be divided into X1i two distinct classes, namely: (1) these corresponding to IL-based sub-binaries, i.e. k 1i , where X

i = 2, . . ., C; (2) these corresponding to binary subsystems with no IL present, i.e. ki j i j , where i > 1 and j > i. The binary parameters belonging to the former class can be fitted to γ ∞ data of solute i ∞ , at specified temperature (e.g. that of LLE tie lines). In the case of the latter in IL, denoted as γi1 X

class, such an approach could result in ambiguities in selecting whether ki j i j should be fitted to γi∞j X

ij or γ ∞ ji . In order to avoid this, it was decided to adjust ki j values to excess Gibbs energy of mixing

of equimolar mixture of i and j predicted by the UNIFAC model: 84

qi j (T ) ≡

E gUNIFAC (x i = x j = 0.5)

(3)

RT

This is the key novelty of the study presented herein compared to reference 56. The only exception from this rule are the aqueous solutions, mainly due to a significant asymmetry in size, shape and interactions of molecules forming such systems — in this case, water is treated in the same way as IL, i.e. γ ∞ value of a solute in water is adopted in fitting the respective binary correction. Summing up, the following strategies of the PC-SAFT calculations of VLE/LLE phase diagrams in multicomponent systems are proposed to investigate and highlight an effect of the way of binary corrections determination: X

(1) ki j i j = 0 for all i < j — traditional application of an equation of state with eq (2) in an entirely predictive manner; this strategy will be referred to in further text as “PC-SAFT-0” or “strategy 13



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0”; X

X1i ∞ data and k i j (where i > 1 and j > i) adjusted (i = 2, . . ., C) fitted directly to experimental γi1 (2) k1i ij

to the UNIFAC predicted qi j (T ) — γ ∞ data are allowed to be interpolated/extrapolated using regression line of ln γ ∞ versus 1/T obtained from the available datasets; this strategy will be referred to as “PC-SAFT-1” or “strategy 1”; X

X1i ∞ data and k i j (where i > 1 and j > i) (i = 2, . . ., C) fitted to the UNIFAC predicted γi1 (3) k1i ij

adjusted to UNIFAC predicted qi j (T ) — temperature dependence of both γ ∞ and g E is defined by the UNIFAC model; this strategy is an extension of the PC-SAFT-UNIFAC approach proposed previosuly, 56 but in this work it will be referred to as “PC-SAFT-2” interchangeably with “strategy 2”.

Experimental LLE Database In order to provide evaluation of the proposed modeling strategies as comprehensive as possible, extensive database of LLE tie-lines in ternary and higher systems with ILs was built of the information extracted from more than 200 papers published in open literature since the beginning of the 21st century; in total, more than 900 datasets were found and stored in the database, mostly ternaries, with only 10 higher systems (up to 7 components). However, only a part of these data regards the systems that can be represented by the proposed PC-SAFT modeling schemes, mainly because of the following reasons: (1) the PC-SAFT parameterization of many ILs was not possible due to lack of suitable experimental pure-fluid data; (2) determination of the values of binary corrections kiXj , see eq (2), was not feasible due to limited availability of experimental data on γ ∞ , or shortcomings of the modified UNIFAC (Dortmund) model at its current stage of development for ILs-based systems — missing functional groups and/or binary interaction parameters. Overall, 408 unique ternary systems were taken into account in further considerations and analyses. Nevertheless, with almost 5000 tie lines present, this remains the largest LLE data pool for evaluation of any equation-of-state model reported so far. For some systems, several LLE datasets (differing 14


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in source and/or temperature they were measured at) were available, so that the final database contained 479 datasets for ternary systems and 5 entries for higher systems, taken from 142 papers published in years from 2003 until 2017. Detailed summary of this data compilation (along with the references to experimental data) can be found in the Supporting Information, Table S1. The tables of ILs’ ions and molecular solutes cover a great variety of structures, so that performance of the PC-SAFT model in capturing different molecular effects on LLE phase diagrams is possible to be highlighted and discussed within the framework of this study. List of ions constituting the ILs with LLE data available as well as their abbreviations used herein are given in the Supporting Information. In total, LLE data for 97 different ILs were collected, including the salts belonging to a number cationic families: (abbreviations used in further text are given in parentheses): 56 imidazolium (Im), 17 pyridinium (Py), 8 pyrrolidinium (Pyr), 6 piperidinium (Pip), 5 ammonium (N), 3 morpholinium (Mo), single phospohnium (P) and single iso-quinolinium (iQuin). In total, 43 distinct cations can be encountered in the database. In turn, among 20 distinct anions, the database is predominated (in terms of the number of both ILs and datasets) by bis[(trifluoromethyl)sulfonyl]imides [NTf2 ] (37 ILs and 174 datasets) and tetrafluoroborates [BF4 ] (11 ILs and 51 datasets). The molecular solutes (in total 44 compounds) were divided into a number of chemical families, namely: 14 alkanes (including linear, branched and cyclic structures), 5 alkenes (including linear, branched and cyclic structures), 8 aromatic hydrocarbons, 2 S/N-compounds (thiophene and pyridine), 5 polar oxygenated compounds (ethers, esters and ketones), 9 alcohols (mostly 1-alkanols) and water. Table 2 summarizes the numbers of ternary systems corresponding to each class of mixture of solutes to be separated using ILs. As can be noticed, {IL + aromatic hydrocarbon + alkane} systems comprise more than a half of the database, in terms of both the number of systems as well as diversity of ILs. Major part of the database is also covered by the data for {IL + thiophene/pyridine + alkane} and {IL + alcohol + alkane} mixtures. Aqueous solutions of alcohols as well as the mixtures of alkenes with alkanes are the systems of a moderate contribution to the entire data collection, whereas LLE data for other classes of mixtures constitute a small minority. These “minor” mixtures formed by polar and/or associating 15



fluids will be also discussed in order to elucidate actual robustness of the applied molecular models in reproducing phase equilibrium data for complex systems with both solute-solute and IL-solute induced association or cross-association. Nevertheless, in further discussion on the modeling robustness and performance an emphasis will be put on pairs of solutes corresponding to ILassisted separations commonly addressed in literature, i.e. separation of aromatic from aliphatic hydrocarbons and extractive removal of sulfur compounds from gasolines.

16


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Results and Discussion Pure Fluid PC-SAFT Parameters For majority of ILs under study (mainly these based on bistriflamide anion, [NTf2 ]) the parameters were taken directly from literature 49,50,52,54,56,74 without refitting. For the remaining ones, the parameters were regressed using experimental densities (ρ) at atmospheric pressure and/or the Hildebrand solubility parameters (δH ) calculated on the basis of γ ∞ data using regular solution theory (all details regarding this procedure can be found elsewhere 49,50,57–59 ). For a number of ILs, molar enthalpy of vaporization (∆vl h) was used instead of δH . The experimental data were extracted from literature, including careful data analysis and revision prior to fitting. In terms of average absolute relative error, the model was capable of representing all pure-fluid properties data within 0.1%. A full list of the PC-SAFT pure-fluid parameters for all the ILs considered in this study along with the references to relevant experimental data is presented in the Supporting Information, Table S2. In order to reduce the number of optimization degrees of freedom several simplifying assumptions were made. First, the parameters related to dispersion (u/k B ) and association (ε AB /kB and κ AB ) were fitted only for a single member of homologous series or anionic family of ILs for which both ρ and δH (or ∆vl h) were available — then, the optimized values were transferred to other similar compounds, while m and σ of them were adjusted to density data only. In particular, for [NTf2 ]-based ILs separate values of ε AB /kB and κ AB were assigned to distinct cationic families of ILs, as well as ILs differing in chemical nature of the cation’s side chains (saturated, unsaturated, oxygenated). Besides, the parameter m was fixed as constant in the case of isomeric pyridinium cations to capture structural similarity of their ILs. In the case of ILs with no experimental ρ data available, the parameters were either extrapolated assuming linear relationship between m, mσ 3 and mu/k B and molecular weight of fluid or estimated by using group contribution scheme proposed by Tihic et al. 78 The latter approach was applied to obtain parameters for 1-benzyl-3-vinylimidazolium bistriflamide, [C1Ph Cv Im][NTf2 ], based on the pa17



rameters obtained for 1-benzyl-3-methylimidazolium bistriflamide, [C1Ph C1 Im][NTf2 ], namely, it was assumed that π([C1Ph Cv Im][NTf 2 ]) = π([C1Ph C1 Im][NTf 2 ]) − π(CH3 ) + π(CH2 −CH), where π ∈ {m, mσ 3, mu/k B }. Quality and/or physical significance of the obtained set of the PC-SAFT parameters is, in general, quite difficult to assess. Nevertheless, it is always a good practice to check how do the parameters and their combinations vary with molecular weight of fluid (M). In particular, mσ 3 is proportional to hard-chain volume, so that it is supposed to change in a regular fashion within a given homologous series as well as to correlate with experimentally observed molar volume. Such analyses were performed using the parameters listed in Table S2 in the Supporting Information. The results are recapitulated in Figure 1. As seen from Figure 1a, good correlation between mσ 3 and M is obtained in the case of ILs based on different anions (not all the anions were included in the figure to make it more legible), what can be expressed in terms of determination coefficient R2 varying from 0.878 ([NTf2 ]-based ILs) to 0.999 (alkylsulfates). Deviations from the linear trends (mainly in the case of bistriflamides) are due to differences in associating parameters assigned to ILs differing in type of the cation (especially, in the cation’s side chains). It is also worth to notice that hard-chain volume Vhc ≡ πmσ 3 /6 is strongly correlated (R2 = 0.973) with molecular volume derived from ρ data V ≡ M/( ρNAv ) (at T = 298.15 K) taken from the literature. On average, V is twice as high as Vhc regardless of the kind of cation and anion, as depicted in Figure 1b. If maximum atomic packing factor (APF) of 0.74 is taken into account, one can establish that the volume occupied by ILs’ molecules is approximately 1.5 higher compared to closely-packed PCSAFT segments. Surprisingly, this is in a fair agreement with independent results obtained using entirely different methodology. 85 For molecular solutes, the PC-SAFT pure-fluid parameters were taken directly from the literature in a great majority of cases. Only in the case of styrene and some ethers the parameters were fitted in this work following the standard procedure of simultaneous regression vapor pressure and saturated liquid density data taken from DIPPR database. 86 All the parameters are summarized in the Supporting Information, Table S3. 18


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LLE Phase Diagrams Because of a large number of experimental ternary LLE datasets considered in this study, detailed analysis of all the obtained results is not feasible within the body of a single research paper. However, calculated versus experimental LLE tie lines of each individual dataset are depicted in the Supporting Information, Figures S1 to S477, in order to give the reader a possibility to evaluate more closely the proposed modeling strategies on his/her own. Furthermore, the systems discussed with the paper are in some cases referred to in terms of their numeric identifiers used in X

the Supporting Information, Table S1. The values of adjusted binary interaction parameters (ki j i j ) used in the LLE predictions are also listed in the Supporting Information in a separate Microsoft Excel spreadsheet, along with all details on the properties they were fitted to. In further text, concise review of predictive capacity of the PC-SAFT model is provided for selected representative systems. First, some general remarks on an effect of using binary interaction parameters adjusted to γ ∞ data on the quality of predictions are presented and addressed to “pure” PC-SAFT-0 calculations carried out for a number of representative ternary systems. Then, comparative analysis of accuracy of the three proposed modeling strategies is presented using a common quantitative measure, taking into account all the systems contained in the database, but also considering separately all relevant types of molecular subsystems listed in Table 2. Finally, capabilities of the model of capturing effect on chemical structure of IL on LLE phase diagrams and LLE-derived properties (distribution ratio and selectivity) are highlighted. It is noteworthy that most of discussion is concerned with ternary systems. Nevertheless, modeling of the systems with higher number of components is also examined and the obtained results are summarized in the end of the section. General Remarks Figure 2 presents PC-SAFT predicted versus experimental 87–90 LLE phase diagrams for six systems formed by 1-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide, [C2 C1 Im][NTf2 ], and molecular solutes representing different types of ternary mixtures. First of all, an effect of param19



eterization strategy (0 versus 1 or 2) on performance of the model is shown. As seen from Figure 2a, for {[C2 C1 Im][NTf2 ] + benzene + n-hexane} the PC-SAFT model properly reproduces experimental 87 phase diagram of type II according to Treybal classification (i.e. immiscibility of the IL with both molecular solutes, while complete miscibility of the molecular solutes), irrespective of modeling strategy applied. This is an unquestionable advantage of the PCSAFT over the COSMO-RS, which has serious problems with capturing LLE split in the mixtures of ILs with aromatic hydrocarbons. 75 However, the prediction based solely on pure-fluid parameters displays much broader miscibility gap in {IL + benzene} subsystem compared to the experimental data. 87 Of course, this significantly affects the quality of predicted LLE in ternary system, especially the composition of IL-rich phase (extract), thus the slope of tie lines. As demonstrated previously, 56 using binary interaction parameters fitted to experimental γ ∞ data substantially enhances accuracy of predictions of LLE in binary systems with aromatics. The results shown in Figure 2a indicate that this also take a positive effect on ternary LLE. In fact, PC-SAFT-1 approach predicts LLE data much closer to the measured ones, taking into account binodal curve defining the range of compositions of liquid phase instability region, tie lines compositions and thier slopes. Significant improvement in the PC-SAFT model performance when using strategy 1 is also observed in the systems {[C2 C1 Im][NTf2 ] + thiophene + n-hexane/toluene}, 88 see Figure 2b and Figure 2c. In the case of the system with n-hexane, basically the same experimental and predicted phase behavior is observed as for the system {[C2 C1 Im][NTf2 ] + benzene + n-hexane}. Particularly enhanced quality of predictions is observed for the system with toluene, which disclose very similar miscibility with the IL as thiophene. 88 This is represented by PC-SAFT-1 approach with reasonably good accuracy compared to PC-SAFT-0 in the entire range of feed compositions. Ternary mixtures disclosing LLE behavior with one miscibility gap in their binary subsystems (i.e. type I of phase diagram) are also reasonably described by the proposed strategies of PCSAFT modeling, as can be seen in Figure 2d and e. In the case of the system {[C2 C1 Im][NTf2 ] + pyridine + n-hexane}, 88 see Figure 2d, it seems that PC-SAFT model properly predicts LLE region, even if none binary interaction parameters are applied. Nevertheless, quality of predictions 20


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of phase equilibrium compositions is not acceptable, not only because they significantly deviate from the experimental data (including both extract and raffinate phases), but also due to the fact that the qualitatively wrong predictions of the slope of tie lines are provided by the model. In turn, an incorporation of binary correction fitted to experimental γ ∞ data (i.e. PC-SAFT-1) results in a significant improvement of predictions of both immiscibility region as well as tie lines. However, it should be noted that the compositions of extract phase are captured by the model more accurately compared to the raffinate — in fact, the model predicts that this phase is almost pure alkane. This finding may be attributed to the fact that pyridine was modeled as self-associating fluid (rationale for that can be found elsewhere 57 ), whereas not adopting this simplification resulted in LLE split in binary mixture with IL. Besides, binary correction corresponding to pyridine-n-hexane interaction was relatively small, but positive — thus, the “corrected” cross-term corresponds with weaker mutual interaction between dislike molecules, which is revealed in the macroscopic behavior as deterioration of miscibility. Results obtained for the system with “naturally” self-associating component are shown in Figure 2e, where experimental LLE data of {[C2 C1 Im][NTf2 ] + ethanol + n-hexane} 89 are confronted with PC-SAFT predictions. As seen, PC-SAFT predictions with all binary corrections set to zero resulted in quite accurate representation of LLE split region. However, accuracy of tie lines compositions gets worse as ethanol content increases, even though the signs of the slope of the computed and experimental tie lines are the same. Substantial improvement in overall accuracy was observed when the PC-SAFT calculations followed strategy 1. In particular, differences between predicted and experimental compositions of the extract phase remain at approximately the same level regardless of feed composition. It is interesting to note that the deviations observed for the raffinate are the lowest in the case of tie lines corresponding to the lowest and highest concentrations of ethanol in the feed. In fact, the shape of the predicted LLE region suggest that close to the LLE critical point the sign of tie line slope switches from positive to negative. Although such behavior is not clearly evidenced in the dataset presented in Figure 2e, it has emerged in LLE determinations in systems with other ILs, e.g. [Cn C1 Im][PF6 ] (where n = 6, 8) 91 — unfortunately, the presented modeling is 21



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not capable to capture such a peculiar phase behavior of these systems, especially when strategy 2 is used to estimate the binary interaction parameters (see the results obtained for datasets no. 251, 264 and 265 in the Supporting Information, Table S1). Figure 2f presents the results obtained for ternary system {[C2 C1 Im][NTf2 ] + 1-propanol + water} 90 representing the most complicated case, i.e. the mixture consisting of self-associating compounds only; thus, six distinct specific interactions are allowed to be encountered in the solution: IL-IL, alcohol-alcohol, water-water, IL-alcohol, IL-water and alcohol-water. Experimental data indicate the phase diagram of type I with miscibility gap in binary subsystem {IL + water}. Unfortunately, this is not the phase behavior predicted by the PC-SAFT, including pure predictions as well as the computations based on binary corrections to Wolbach-Sandler combining rules fitted following the strategy 2. In fact, LLE split in molecular subsystem {1-propanol + water} is wrongly predicted by the calculations by the both PC-SAFT-0 and PC-SAFT-2 parameterization schemes. Nevertheless, employment of the binary corrections fitted to γ ∞ data results in a significant improvement of quality of the predictions, especially in the case of the IL-rich phase. Furthermore, miscibility region for {1-propanol + water} predicted by PC-SAFT-2 is twice as narrow as in the case of PC-SAFT-0, the same as accuracy of {IL + water} LLE gap calculation is also substantially enhanced. Assessing the quality of the demonstrated calculations based on phase diagrams is not always straightforward due to limited legibility of ternary plots. In order to make the final evaluation easier, the “raw” LLE data can be transformed into some useful quantities derived from equilibrium mole fractions in extract (x 0i ) and raffinate (x 00i ). Usually, distribution ratio of component “2” denoted by β2 and selectivity of separation component “2” from “3” denoted by S23 , are the properties used for the purpose. They are defined as follows: x 02 β2 ≡ 00 x2

(4a)

β2 β3

(4b)

S23 ≡

22


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Experimental and calculated values of β2 and S23 of the selected systems from Figure 2 are plotted in Figure 3 as a function of the mole fraction of component “2” in the feed. It is clearly seen that, employing γ ∞ data (either experimental or predicted from UNIFAC model) results, in general, in a significant improvement of the performance of the PC-SAFT model in representing ternary LLE diagrams for complex systems with ILs. Some surfactant-like ILs (i.e. these consisted of cations substituted with long alkyl chains) have been shown to be capable of inducing Treybal’s type III of phase diagram with three-phase region corresponding to liquid-liquid-liquid equilibrium (LLLE). Although modeling of such complex behavior may seem to be very challenging problem, the PC-SAFT model has been recently demonstrated by Soto et al. 40 as very efficient tool for representing both LLE and LLLE data. In fact, average absolute deviations (AADs) between computed and experimental equilibrium compositions (mass fractions) in the systems {[Cn C1 Im][NTf2 ] + n-dodecane + water} (where n = 10, 12) were of the order of 0.005, even with all the binary corrections set as zeros. Pure predictions (i.e. calculations following strategy 0) resulted, however, in much higher values of AAD when temperature was changed from T = 298.15 K to T = 348.15 K. The data reported in reference 40 are used in this work to test the proposed PC-SAFT-2 predictive approach. The results are depicted in Figure 4 for the system with [C12 C1 Im][NTf2 ] at T = 348.15 K. As seen, significant improvement in accuracy of prediction is observed for PC-SAFT-2 compared to PC-SAFT-0, including both twoand three-phase regions. The data plotted in Figure 4 are presented in mole-fraction basis. In terms of mass fractions, AAD obtained for PC-SAFT-0 (Figure 4a) is 0.175, which is way higher compared to the work of Soto et al., 40 who obtained 0.020. Obviously, such very high value of AAD is due to the fact that the model assigned all the tie lines to incorrect LLE region. As demonstrated in Figure 4b, the problem is resolved, when γ ∞ data are involved in calculations. In fact, AAD of 0.006 is observed in the case of the PC-SAFT model with strategy 2. The value reported in reference 40 is the same, but obtained with binary correction fitted to LLE/LLLE data, not estimated independently in the way presented in this work. Finally, some exemplary results obtained for the systems with induced association are demon23



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strated in Figure 5. Experimental 92,93 versus PC-SAFT predicted LLE phase diagrams mixtures {[C4 C1 Im][PF6 ] + butanone + alcohol (ethanol, or 2-propanol)} with the ketone playing the role of hydrogen bond acceptor are shown in Figure 5a and b. As seen, the model applied in an entirely predictive mode does predict miscibility gap in {IL + ketone} subsystem, whereas the experiments reveal LLE only in the case of {IL + alcohol} binary mixture. In the case of the system with ethanol, LLE split is not observed at all in the calculated phase diagram, since the feed compositions from experimental tie lines are outside the LLE region designated by binodal curve; in the case of the system with 1-propanol, only one LLE split is properly captured by the model. The quality of computations changes drastically when γ ∞ data are involved. In fact, the PC-SAFT combined with strategy 1 of binary interaction parameters fitting yield, first of all, in qualitatively correct results, but also in a substantial improvement of accuracy of tie lines compositions. The calculations for the system {[C4 C1 Im][BF4 ] + tetrahydrofuran + water} reported by Jork et al. 93 are summarized in Figure 5c. In this case, pure PC-SAFT predictions result in a completely different phase behavior compared with the experimental evidence, including the existence of LLLE. Again, employing binary corrections adjusted to γ ∞ data result in a significantly improved description. The presented results are strongly encouraging, taking into account complexity of the the systems under study and a variety of molecular interactions present in the solution. Modeling Performance Root-mean-square error (RMSE) between calculated and experimental LLE mole fractions, defined as 1/2 X N X C ( xˆ 0 − x 0 ) 2 + ( xˆ 00 − x 00 ) 2  i j i j i j i j  RMSE =   2NC  i=1 j=1 

(5)

is adopted throughout the discussion as a quantitative measure of goodness of prediction. In definition given in eq (5), N stands for the number of tie lines for which the value of RMSE is computed, C denotes the number of components of the system, prime and double prime denote

24


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extract phase (i.e. IL-rich phase) and raffinate phase, respectively. Finally, x i j is the mole fraction of j-th component of i-th tie line with the “hat” assigned to the PC-SAFT calculated value. Mid-points of the experimental tie lines were taken to be feed composition of LLE flash calculations. It was also assumed that feed composition is assigned to both extract and raffinate if the model does not predict the LLE split. The results obtained for three different PC-SAFT modeling strategies are confronted in this section with the outcomes of the COSMO-RS model (combined with BP-TZVP-COSMO level of quantum chemical calculations) discussed in detail previously. 75 RMSE values calculated on the basis of all the ternary LLE data represented by the studied modeling approaches are summarized in Table 3. Obviously, only PC-SAFT-0 and COSMO-RS were capable of reproducing all the systems and datasets collected in the LLE database, as requiring pure-fluid information only. The number of represented systems is substantially reduced in the case of strategies 1 and 2 of PC-SAFT modeling, because of lack of experimental infinite dilution data or missing UNIFAC functional groups constituting the ions forming ILs (or the parameters corresponding to interactions involving these groups), respectively. PC-SAFT-0 has turned out to be globally the most inaccurate modeling approach with RMSE at the level of 0.15, whereas the remaining approaches resulted in RMSE lower than 0.10. Irrespective of the model, raffinate phase mole fractions are reproduced more precisely compared to extract. Among them, PCSAFT-1 provides the most accurate description of tie lines — unfortunately, this means that some experimental binary data like γ ∞ are strongly recommended to get satisfactory results for ternary systems. In turn, PC-SAFT-2 discloses basically the same global accuracy if one compares it with COSMO-RS. However, it should be pointed out that the latter approach does not predict LLE split for greater (relatively) number of feed compositions. To make the comparison of all the models “fairer”, one can recalculate the RMSEs listed in Table 3 considering only the systems which can be represented by all the models — the number of such systems is 125, including 147 datasets and 1543 tie lines. The resulting values are (the numbers of LLE splits not captured by respective models are given in parentheses): 0.140 for PC-SAFT-0 (31), 0.059 for PC-SAFT-1 (5), 0.060 for PC-SAFT-2 (4) and 0.069 for COSMO-RS (47). Hence, it is clearly seen that the analysis based 25



on such limited pool of data leads to the conclusions which are consistent with these that can be drawn from Table 3. Accuracy of the proposed PC-SAFT modeling schemes should be analyzed more minutely by taking into account variation of RMSE data obtained for different systems, rather than considering the global values only. Results of such analysis is presented in Figure 6. In Figure 6a, distribution of RMSE values (calculated for each ternary system individually) is depicted in the form of boxplot. In general, the values of RMSE vary from < 0.001 to ≈ 0.4, irrespective of the model. The numbers of systems, for which the value of RMSE was below 0.1 were: 162 for PC-SAFT-0 (40% of the systems represented by the model), 262 for PC-SAFT-1 (92%), 206 for PC-SAFT-2 (83%) and 339 for COSMO-RS (83%). Thus, the PC-SAFT-1 modeling not only resulted in the lowest global RMSE, but disclosed the narrowest distribution of RMSE among all tested approaches as well. Nevertheless, entirely predictive PC-SAFT-2 and COSMO-RS disclose very promising modeling performance as well. Furthermore, there is a number of systems which displayed noticeably high RMSE — in Figure 6a such systems are marked as outliers. Their presence might be due to poor quality of experimental data, what is illustrated (and confirmed, to some extent) in Figure 6b for the system {[C4 C1 Im][BF4 ] + 1-pentanol + n−heptane} reported by Revelli et al. 94 The calculations carried out for this particular systems result in the highest values of RMSE of all the considered models except PC-SAFT-0. Of course, high RMSE is because of erroneous experimental tie lines, which suggest that the presented LLE phase diagram is of type II, with miscibility gaps in binary subsystems {IL + n-heptane} and {1-pentanol + n-heptane}. However, in the case of the latter subsystem, miscibility gap is not observed experimentally — none binary LLE data for this mixture can be found neighter in widely known thermodynamic databases, like these provided by DDBST or NIST. Furthermore, the results reported by Revelli et al. 94 suggest that the IL forms homogeneous solutions with 1-pentanol regardless of mixture composition. This is, however, in contradiction with independent binary LLE measurements reported elsewhere 3 years before the discussed ternary data were published. 95 A general remark that can raised on the basis of this specific example it that a special care must taken when comparing modeled versus experimental 26


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tie lines, particularly if the observed RMSE is in the “outlier range” of values. In the case of PC-SAFT, inaccurate predictions may be also attributed to unreliable pure-fluid data used in model parameters fitting, or high uncertainty of γ ∞ data used in binary correction estimation. Finally, modeling failure can be caused simply by incapacity of the molecular pictures adopted to mimic real systems of representing their thermodynamic properties. In order to present mutual relationships between accuracy of the studied models more specifically, the following scoring scheme is proposed when comparing model i to model j in representing LLE data for a given system: (1) the model i “wins” if RMSEi < c and RMSE j > c; (2) the model j “wins” if RMSE j < c and RMSEi > c; (3) “draw” is set if either RMSE < c or RMSE > c for both models. The enter value c classifying the model as the better “one” can be fixed arbitrarily; in this work c = 0.05 was assumed. The results of such RMSE data treatment are given in Table 4 in the format “wins–draws–losses” of model i against model j. As seen, strategy 0 of PC-SAFT modeling evidently fails against two strategies based on γ ∞ data as well as against the COSMO-RS. However, for more than a half of all ternary systems PC-SAFT-0 and COSMO-RS preserve the same order of accuracy. This is not the case of PC-SAFT-1 and PC-SAFT-2, for which better (still compared with PC-SAFT-0) predictions were recorded for almost two thirds and more than half of systems, respectively. These strategies yield in more accurate LLE data representation also when compared with the COSMO-RS. Nevertheless, only in the case of PC-SAFT-1, prevailing over the COSMO-RS is noticeable. It is finally interesting to compare PC-SAFT-1 versus PC-SAFT-2, what can be done only for the systems with both measured and UNIFAC-predicted γ ∞ data. In general, both strategies display similar accuracy of predictions for a great majority (almost 80%) of such systems. Furthermore, PC-SAFT-2 provides the results closer to experimental data in a greater number of cases, what can be seen as surprising taking into account the overall RMSE values listed in Table 3. Accuracy of the modeling methods studied in this work depends on a kind of chemical families of components forming molecular subsystem (“component 2 + component 3”). RMSE data computed for all the types of mixtures listed in Table 2 are presented in Figure 7. In general PC-SAFT-1/2 27



provides better representation of ternary LLE data compared to PC-SAFT-0 irrespective of kind of molecular components — systems with polar components and water are the only exception from this rule. Possible reason for that can be related to rarity and scarcity γ ∞ data for polar components and water in ILs, thus high uncertainty of binary interaction parameters fitted to them. Moreover, PC-SAFT predictions following strategy 1 result in lower RMSE compared to strategy 2. Only in the case of {alkene + aromatic hydrocarbons} and {alcohol + water} subsystems, the opposite is true. In turn, COSMO-RS yielded in more accurate description of LLE data than PC-SAFT for {alkane + alkane}, {alkane + polar compound}, {alkene + alcohol} and all subsystems with water. In fact, improvement in modeling performance of COSMO-RS over PC-SAFT is particularly seen in the case of aqueous systems. Predictions of the Structure Effect on LLE Apart from detailed analysis of RMSE, i.e. the quantitative measure of modeling accuracy, it is also important to test how does the model perform in predicting qualitative trends in variation of a property under study with structure of chemicals forming the system. In this work, an effect of structure of IL on maximum values of β2 and S23 is checked for two types of systems corresponding to common separation problems with potential application of ILs in extractions, namely: toluene (2) / n-heptane (3) 96–99,99–105 and thiophene (2) / n-heptane (3). 106–109 The results of such analysis are summarized in Figure 8. The plots shown therein were constructed as follows. For each system with respective LLE data available: (1) experimental tie lines with maximum β2 and S23 were max resulting from experimental LLE data were computed and sorted in identified; (2) β2max and S23 max resulting from modeled LLE data were computed and sorted a decreasing order; (3) β2max and S23

following the order obtained in step no. 2. max are calculated with reasonable accuracy As can be noticed from Figure 8, both β2max and S23

only in the case of PC-SAFT-1 and PC-SAFT-2, irrespective of the separation under consideration. Predictions resulted from strategy 0 yield in systematically underestimated both distribution ratio and selectivity. Obviously, none of the modeling strategies applied perfectly reproduce the qual28


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max . However, the “scatter” of computed data along the experimental itative trends in β2max and S23

ones is significantly reduced, when γ ∞ data are involved in binary interaction parameters fitting. In order to present the performance in predicting qualitative structure-property relationship more precisely, one can use the relative numbers of pairs (i, j) of ILs, for which the computed change in max due to change IL from i to j is consistent with respective experimentally observed β2max and S23 max , effect. In the case of toluene/n-heptane separation the percentages obtained for β2max and S23

respectively, are as follows: 65% and 61% for PC-SAFT-0, 77% and 80% for PC-SAFT-1, 81% and 76% for PC-SAFT-2. For thiophene/n-heptane, the respective values are: 57% and 50% for PC-SAFT-0, 84% and 83% for PC-SAFT-1; the values for strategy 2 are not shown because of the lack of UNIFAC interaction parameters between the groups forming ILs and thiophene. Therefore, it is much more likely to correctly predict an impact of variation of chemical structure of IL on its extractive performance, when either PC-SAFT-1 or PC-SAFT-2 are used — hence, the results obtained with PC-SAFT-0 will be no longer discussed in this paper. More detailed analysis of is not so easy to carry out, mainly because of diversity of systems, for which the experimental LLE data are listed in the presented database. Nevertheless, some selected structural effects on both β2 and S23 in toluene/n-heptane and thiophene/n-heptane separation are depicted in Figure 9 and Figure 10, respectively. In particular, Figure 9a and Figure 10a demonstrates experimental versus PC-SAFT-1/2 predicted effect of ILs’ cation core. As seen, in the case of toluene/n-heptane separation the modeling is not entirely capable of capturing this subtle variation (imidazolium, pyridinium, pyrrolidinium) in chemical structure correctly — in fact, the predicted trend observed for both β2 and S23 is in the opposite to the experimental one. This is not the case of thiophene/n-heptane separation, for which modeled and measured data of β2 and S23 follow exactly the same trends. An impact of the length of the side chain attached to cation cores is correctly predicted for both separations under study — as seen from Figure 9b and Figure 10b, PC-SAFT-1/2 captures that elongating alkyl chains (of imidazolium or piperidinium cations) results in a decrease of extractive capacity of ILs. In turn, an effect of cation’s functionalization is not captured so precisely. In Figure 9c, it can be noticed that changing 29



terminal functional group in [C2 C1 Im]-derived cations from methyl to allyl, phenyl or hydroxyl group affects both β2 and S23 indeed. Nevertheless, the variations of these properties are so small that reproducing them using such simple molecular scheme as adopted in the proposed modeling is virtually impossible. Moreover, it should be emphasized that the scatter of the experimental data is quite significant, so that the “real” effects are extremely difficult to be highlighted on the basis of them. For some systems, however, such delicate variations due to functionalization are nicely captured by the PC-SAFT modeling, as demonstrated in Figure 10c, including not only the order of β2 and S23 , but also their dependence on feed’s composition. Finally, an impact of IL’s anion on extraction performance is tested. As seen in Figure 9d, for toluene / n-heptane separation, the model reproduces experimentally observed anion dependency of distribution ratio of toluene in the systems with [C4 C1 Im]-based ILs, including the order of β2 values as well as their variation with feed’s composition; it is worth noticing that minima of β2 indicated by the experimental data for [SCN] and [N(CN)2 ] ILs is also present in the modeled curves. Unfortunately, predicted S23 data do not follow the experimental trend exactly. According to the model’s outcomes, increasing the number of C− −N groups in the anion results in an increase in β2 and decrease in S23 . However, this is experimentally observed only for β2 . For thiophene / n-heptane separation (Figure 10d) anion effect is illustrated by comparing predicted versus experimental β2 and S23 for ILs based on [C4 C1 Pyr] cation. In contrary to toluene / n-heptane, the PC-SAFT displays problems with reproducing correct trend in β2 . On the other hand, the PC-SAFT properly predicts that IL based on [OTf] (triflate) anion is better extractant compared with its tris(pentafluoroethyl)trifluorphosphate-based ([FAP]) counterpart, at least in terms of S23 . The model does not, however, capture that both [OTf] and [B(CN)4 ] ILs disclose basically the same selectivity in the entire range of composition. In fact, this is quite unexpected, thus difficult to model, taking into account significant differences in chemical structure of the anions under consideration. Furthermore, experimental β2 values are more distinctive, so that the corresponding S23 data seems to be inconsistent with them. Obviously, one can make a proposition that the observed inconsistencies justify or explain the modeling failure.

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Multinary Systems Extension of the presented and discussed modeling methodology to the mixtures with higher number of molecular components is straightforward. In this work, 5 such systems with available experimental LLE data 110–114 were taken into consideration; the matrices of binary interaction parameters can be found in the Microsoft Excel spreadsheet provided in the Supporting Information. In further text, robustness of PC-SAFT applied with the proposed strategies of binary corrections fitting, two representative systems will be presented. It is worth mentioning that, to my best knowledge, this is the very first time when PC-SAFT equation of state is applied to model LLE phase diagrams of higher than ternary ILs-based systems. Figure 11 presents LLE in quaternary system {[C2 C1 Im][N(CN)2 ] + toluene + cyclohexane + n-heptane} at T = 298 K reported recently by Corderi et al. 111 As can be noticed from Figure 11a, PC-SAFT-0 strategy of modeling results in reasonable predictions of raffinate phase compositions, whereas rather poor predictions are obtained in the case of extract — in fact, predicted content of molecular compounds in this phase is much lower compared to experimental ones. By using six binary interaction parameters obtained following PC-SAFT-1 strategy, the results are substantially enhanced, see Figure 11b. In terms of RMSE defined in eq (5), the accuracy of calculations is improved by an order of magnitude, namely from 0.027 for PC-SAFT-0 to 0.002 for PC-SAFT-1. Taking into account all the quaternary LLE tie lines available, the global RMSE for strategies 0, 1 and 2 of PC-SAFT modeling were, respectively, 0.090, 0.001 and 0.001. Thus, it is clearly seen that an essentially better description of phase behavior is provided using combining rules with binary corrections fitted to γ ∞ data. Al-Rashed et al. 114 have measured and published LLE data for mixtures formed by [C4 C1 Im][PF6 ] and six hydrocarbons (n-hexane, n-heptane, n-octane, benzene, toluene and o-xylene) representing naphtha reformate. In Figure 12, experimental data reported in their paper are plotted along with respective PC-SAFT-0 and PC-SAFT-1 predictions. Of course, direct LLE data are impossible to visualize, therefore they were transformed into pseudo-ternary diagram, with aliphatic hydrocarbons and aromatic hydrocarbons treated as single components, see Figure 12a, or transformed into 31



distribution ratios defined for each component in the same way as in eq (4a) (Figure 12b). As seen, experimental pseudo-ternary LLE phase diagram does not differ so much from a typical ternary phase diagram of system {IL + aromatic hydrocarbon + alkane}. Performance of PC-SAFT-0 approach is, as usual, quite poor, particularly in describing IL-rich phase. In turn, incorporation of 21 distinct binary corrections kiLB j fitted to either experimental or UNIFAC predicted auxiliary data yields in a noticeable improvement of accuracy. This can be expressed as RMSE, namely, 0.066 for strategy 0, 0.014 for strategy 1 and 0.022 for strategy 2. The observed enhancement in RMSE in LLE mole fractions is confirmed, when PC-SAFT-0 and PC-SAFT-1 distribution ratios are confronted to the respective experimental values. Furthermore, it is seen in Figure 12b that PC-SAFT does properly predict the order of variation of distribution ratio with chemical structure of hydrocarbon, irrespective of the modeling strategy applied. However, in the case of aromatic fraction, proposed modeling does not capture that for each solute i, βi decrease with its concentration in the feed, see Figure 12b. For aliphatic hydrocarbons, modeled trends are consistent with experimentally observed ones, as depicted in Figure 12c.

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Conclusions A study on the performance of the PC-SAFT model in modeling of LLE phase diagrams in ILsbased systems was presented and analyzed on the basis of extensive compilation of experimental data (mostly ternary) extracted from literature. It was shown that accurate (in many cases very accurate) and qualitatively correct results can be obtained using relatively simple molecular scheme of ILs and their interactions with diverse molecular compounds, including non-polar, polar and self-associating fluids. However, incorporation of infinite dilution data for the IL-based binary subsystems of the investigated multinary system as well as some extra outcome from UNIFAC model, see eq (3), was necessary to achieve that. One should keep in mind that the proposed modeling protocol is limited by the availability of these auxiliary data. The comparative analysis with the COSMO-RS model allows to address the key question raised in the end of introductory part of this paper. The results obtained suggest that the PC-SAFT, i.e. the approach simpler in terms of the mathematics, physical background and so on, yields in basically the same quality of LLE predictions as the COSMO-RS. Thus, both models should be considered as being equally appropriate for IL-based solutions. However, if the calculations performed for each system are analyzed individually, the PC-SAFT approach provides better results in a greater number of cases. It is noteworthy that only in the case of aqueous solutions, the COSMO-RS provides globally better accuracy of predictions. The “cost” of this success of the PC-SAFT is a necessity of having experimental pure-IL data at hand as they are required in adjusting the model’s parameters. However, due to equation-of-state nature of the core model, it provides general and thermodynamically consistent description of both pure fluids and mixtures composing them (including both temperature- and density-dependence). This is in contrast with the COSMO-RS, which is given in terms of activity coefficients, so that neither pure fluid nor effect of pressure on the systems can be accounted for. Summing up, one can propose the PC-SAFT method as a robust thermodynamic tool for estimating phase behavior of the systems with ILs, thus assisting in design of novel separations and purification methods involving extraction with ILs. I believe that this work will be also found useful by physical chemists and encourage the community to further explore 33



molecular-level aspects of ILs and their impact on macroscopic behavior of their systems.

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Supporting Information Available (1) PDF file: List of abbreviations of the ions composing ILs considered in this study; Table S1 — summary of ternary LLE data compilation; Table S2 and S3 — list of the PC-SAFT pure fluid parameters of ILs and molecular solutes, respectively; Figures S1-S478 — experimental versus PCSAFT predicted ternary LLE phase diagrams obtained for different modeling strategies. (2) XLS file: all the details regarding the presented PC-SAFT calculations, in particular the RMSEs and the values of binary interaction parameters (along with the data used to obtained them) for each dataset. This material is available free of charge via the Internet at http://pubs.acs.org/.

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

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Nomenclature Roman letters a

Helmholtz free energy, see eq (1)

A, B

associating sites

C

number of components

g

Gibbs free energy

m

PC-SAFT parameter

i, j

components

k

binary interaction parameter

kB

the Boltzmann constant

l

binary interaction parameter

N

number of tie lines

q

reduced excess Gibbs free energy, see eq (3)

R

universal gas constant

S

selectivity, see eq (4b)

T

absolute temperature

u

PC-SAFT parameter

x

mole fraction

Greek letters β

distribution ratio, see eq (4a)

γ

activity coefficient

ε

PC-SAFT parameter

κ

PC-SAFT parameter

σ

PC-SAFT parameter

Subscripts/superscripts 0

extract phase

37



00

raffinate phase

∞

infnite dilution

1, 2, 3, . . .

components

assoc

association term

disp

dispersive term

E

excess property

hc

hard-chain term

KS

Kleiner-Sadowski combining rule

LB

Lorentz-Berthelot combining rule

res

residual property

WS

Wolbach-Sandler combining rule

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Larriba, M.;

García, J.;

Torrecilla, J. S.;

Rodríguez, F. Liquid-

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García, S.;

Torrecilla, J. S.;

Rodríguez, F. N-Butylpyridinium Bis-

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Ternary

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the 1-Alkylpiperidinium-Based Ionic Liquids on Desulfurization of Fuels. J. Chem. Thermodyn. 2014, 72, 31–36. (108) Domańska, U.; Walczak, K.; Królikowski, M. Extraction Desulfurization Process of Fuels with Ionic Liquids. J. Chem. Thermodyn. 77, 40–45. (109) Domańska, U.; Lukoshko, E. V.; Królikowski, M. Separation of Thiophene from Heptane with Ionic Liquids. J. Chem. Thermodyn. 2013, 61, 126–131. (110) Corderí, S.; Calvar, N.; Gómez, E.; Domínguez, A. Quaternary (Liquid+liquid) Equilibrium Data for the Extraction of Toluene from Alkanes Using the Ionic Liquid [EMim][MSO4 ]. J. Chem. Thermodyn. 2014, 76, 79–86. (111) Corderí, S.; Gómez, E.; Domínguez, A.; Calvar, N. (Liquid + liquid) Equilibrium of Ternary and Quaternary Systems Containing Heptane, Cyclohexane, Toluene and the Ionic Liquid [EMim][N(CN)2 ]. Experimental Data and Correlation. J. Chem. Thermodyn. 2016, 94, 16– 23. (112) Requejo, P. F.; Calvar, N.; Domínguez, A.; Gómez, E. Application of the Ionic Liquid Tributylmethylammonium Bis(Trifluoromethylsulfonyl)Imide as Solvent for the Extraction of Benzene from Octane and Decane at T = 298.15 K and Atmospheric Pressure. Fluid Phase Equilib. 2016, 417, 137–143. (113) Requejo, P. F.; Calvar, N.; Domínguez, A.; Gómez, E. Comparative Study of the LLE of the Quaternary and Ternary Systems Involving Benzene, n-Octane, n-Decane and the Ionic Liquid [BMpyr][NTf2 ]. J. Chem. Thermodyn. 2016, 98, 56–61. (114) Al-Rashed, O. A.; Fahim, M. A.; Shaaban, M. Prediction and Measurement of Phase Equilibria for the Extraction of BTX from Naphtha Reformate Using BMIMPF6 Ionic Liquid. Fluid Phase Equilib. 2014, 363, 248–262.

52


Page 52 of 68

62 2

water

40

S/N-compound

alcohol

230

aromatic

2

16

alkene

polar

9

alkane


53 2

31

2

31

69

9

9

1

11

1

11

44

2

1

8

5

6

4

NILs

Ns

Nbin

Ns

NILs

alkene

alkane

3

3

Nbin

3

Ns

2

NILs

aromatic

2

Nbin

2

9

Ns

polar

2

7

NILs

1

5

Nbin

20

Ns

15

NILs

alcohol

5

Nbin

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 2. Summary of the Database of Ternary LLE Data Given in Terms of the Number of Distinct Systems (Ns ), ILs (NILs ) and Binaries (Nbin ) Available for Each Type of Binary Subsystems of Molecular Solutes.

Page 53 of 68 Industrial & Engineering Chemistry Research


Page 54 of 68

Table 3. Summary of Ternary LLE Calculations with the PC-SAFT Equation of State Presented in This Work and the COSMO-RS Model Reported Previously in the Literature, Given in Terms of the Numbers of Systems, Datasets and Tie Lines Represented by the Models and Root Mean Square Deviations (RMSE) Between Calculated and Experimental Mole Fraction Composition of Equilibrium Phases. Model

Number of represented:

RMSEa

systems datasets tie linesb

overall extract raffinate

PC-SAFT-0

408

477 4706 (96%)

0.151

0.184

0.089

PC-SAFT-1

285

325 3384 (97%)

0.058

0.063

0.033

PC-SAFT-2

248

299 2932 (99%)

0.079

0.084

0.066

COSMO-RSc

408

477 4588 (93%)

0.079

0.083

0.068

a

See eq (5).

b

Percentage of correctly predicted LLE splits is given in the parenthesis.

c

BP-TZVP-COSMO level. Obtained based on the data published elsewhere. 75

54


Page 55 of 68 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4. Modeling Score Records Obtained Based on RMSE Values Resulted from Different Calculations Mathods/Strategies. a Model i

Model j PC-SAFT-0

PC-SAFT-1

179–102–4

PC-SAFT-2

127–114–7

PC-SAFT-1 PC-SAFT-2

16–98–11

COSMO-RS 166–231–11 25–172–88 a

25–190–33

Format: wins of model i – draws – wins of model j (details in text).

55



(a)

m 3 / Å3

700

500

300

bistriﬂamides "CN" anions alkylsulfates dialkylphosphates [FAP]

100 100

300

500

700

M / g mol -1 (b) 800

600

V / Å3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

400

linear ﬁt

200 100

200

300

V hc / Å

400

3

Figure 1. Analysis of the fitted PC-SAFT parameters. (a) Combined parameter mσ 3 as a function of IL molecular weight M for different families of ILs (“CN anions” includes: [SCN], [N(CN)2 ], [C(CN)3 ] and [B(CN)4 ]). (b) Experimental molecular volume V = M/( ρNAv) derived from density ρ at T = 298.15 K versus PC-SAFT hard-chain volume Vhc = πmσ 3 /6 of all the ILs listed in the Supporting Information, Table S2.

56


Page 56 of 68

Page 57 of 68 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a)

(b)

benzene 0.8

0.2 0.4

0.2 0.6

0.6 0.8

0.4

0.6

0.8

IL

pyridine

(d) 0.2

0.2

0.8

IL

IL

toluene

0.2

0.8

0.8

0.6

0.6 0.2

0.8

IL

water

IL

0.8

0.4 0.4

0.6

0.6

1-propanol

0.6

0.4

0.4

0.2

0.8

n-hexane 0.2

0.2

0.8

(f)

0.6 0.2

0.8

0.8

0.4

0.8

0.4 0.4

0.6

0.6

ethanol

0.6

0.4

0.4

0.6

0.6 0.2

n-hexane 0.2

0.8

0.4

0.8

(e)

0.6

n-hexane 0.2

0.6 0.4

0.8

0.4

0.2

0.6 0.2

thiophene

0.8

0.4 0.4

n-hexane 0.2

(c)

thiophene

0.4 0.2

0.2

0.4

0.6

0.8

IL

Figure 2. Experimental versus PC-SAFT predicted LLE phase diagrams (in mole fraction basis) for representative ternary systems containing [C2 C1 Im][NTf2 ] (IL): (a) dataset no. 5 (strategy 1): {IL + benzene + n-hexane} at T = 298 K; 87 (b) dataset no. 15 (strategy 1): {IL + thiophene + n-hexane} at T = 298 K; 88 (c) dataset no. 16 (strategy 1): {IL + thiophene + toluene} at T = 298 K; 88 (d) dataset no. 17 (strategy 1): {IL + pyridine + n-hexane} at T = 298 K; 88 (e) dataset no. 18 (strategy 1): {IL + ethanol + n-hexane} at T = 298 K; 89 (f) dataset no. 20 (strategy 2): {IL + 1-propanol + water} at T = 283 K. 90 Key: circles, experimental data; squares, PC-SAFT-0; triangles, PC-SAFT-1/2. Numbering of the datasets according to the list given in the Supporting Information, Table S1.

57



Figure 2a Figure 2b Figure 2c Figure 2e strategy 0 strategy 1/2

β2

6

4

2

0 0

0.2

0.4

0.6

0.8

1

0.8

1

x 2 (feed) 10

S23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 58 of 68

4

102

100

0

0.2

0.4

0.6

x 2 (feed)

Figure 3. Experimental versus PC-SAFT predicted distribution ratio β2 (upper panel) and selectivity S23 (lower panel) as functions of feed’s mole fraction x 2 for representative ternary systems shown in Figure 2.

58


Page 59 of 68 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


n-dodecane

(a)

0.2

0.8

0.4

0.6

0.6

0.4

0.8

0.2

0.2

water

0.4

0.8 [C C Im]

0.6

12 1

[NTf2 ] n-dodecane

(b)

0.2

0.8

0.4

0.6

0.6

0.4

0.8

water

0.2

0.2

0.4

0.6

0.8 [C C Im] 12 1 [NTf ] 2

Figure 4. Experimental versus PC-SAFT predicted LLE phase diagram of ternary system {[C12 C1 Im][NTf2 ] + n-dodecane + water} at T = 348 K 40 (dataset no. 81 in the Supporting Information, Table S1): (a) PC-SAFT-0; (b) PC-SAFT-2. Key: circles, experimental data; squares/triangles, PC-SAFT predictions; shaded area, three-phase region.

59



(a)

(b)

ethanol 0.2 0.4

0.4

0.6

4 1

0.6

[PF6 ]

0.6

0.6 0.2

0.4

0.8

0.4 0.4

0.8

0.8 [C C Im] butanone 0.2

0.2 0.6

0.6 0.2

THF

0.8

0.4 0.4

0.8

butanone 0.2

0.2 0.6

0.6

(c)

2-propanol

0.8

Page 60 of 68

0.8 [C C Im] 4 1

[PF6 ]

0.4

0.8

water

0.2

0.2

0.4

0.6

0.8 [C C Im] 4 1

[BF4 ]

Figure 5. Experimental versus PC-SAFT predicted LLE phase diagrams (in mole fraction basis) for representative ternary systems with induced association: (a) dataset no. 243 (strategy 1): {[C4 C1 Im][PF6 ] + ethanol + butanone} at T = 298 K; 92 (b) dataset no. 244 (strategy 1): {[C4 C1 Im][PF6 ] + 2-propanol + butanone} at T = 298 K; 92 (c) dataset no. 177 (strategy 2): {[C4 C1 Im][BF4 ] + tetrahydrofuran + water} at T = 337 K. 93 Key: circles, experimental data; squares, PC-SAFT-0; triangles, PC-SAFT-1/2; shaded area, three-phase region. Numbering of the datasets according to the list given in the Supporting Information, Table S1.

60


Page 61 of 68 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) PC-SAFT-0

PC-SAFT-1

PC-SAFT-2

COSMO-RS 0

0.1

0.2

0.3

0.4

0.5

RMSE

(b)

1-pentanol

0.2

0.8

0.4

0.6

0.6

0.4

0.8

n-heptane

0.2

0.2

0.4

0.6

0.8

[C C Im] 4

1

[BF ] 4

Figure 6. (a) Distribution of RMSE values, see eq (5), obtained for different ternary systems (on each box, the central mark is the median, whereas the lower and upper edges correspond to the first and the third quartiles of the data, respectively; the “whiskers” extend to the 1.5 of the box width — approximately 99% coverage if the data are normally distributed; outliers are designated by crosses). (b) Experimental versus predicted LLE phase diagram (in mole fraction basis) for ternary system {[C4 C1 Im][BF4 ] + 1-pentanol + n-heptane} at T = 298 K 94 (dataset no. 176 in the Supporting Information, Table S1) — highlighted points in panel “a” correspond to this dataset. Key: circles, experimental data; squares, PC-SAFT-0; triangles, PC-SAFT-1; diamonds, COSMO-RS.

61



alkane

0.3

0

alkene

0.3

N/A

S/N-compound aromatic

0 0.3

N/A 0 0.3

N/A 0

polar

0.3

N/A

N/A

N/A

alcohol

0 0.3

N/A

N/A

0 0.3

water

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

N/A

N/A

0 0 1 2

0 1 2

0 1 2

0 1 2

0 1 2

alkane

alkene

aromatic

polar

alcohol

Figure 7. RMSE values, see eq (5), obtained for ternary systems differening in chemical family of molecular components. For each plot, bars from the left to the right correspond to PC-SAFT0, PC-SAFT-1, and PC-SAFT-2, respectively. The bars/areas plotted over the entire range of abscissas correspond to RMSE obtained from COSMO-RS calculations described elsewhere. 75 “N/A” indicates that experimental data for a given kind of subsystem are either not available or not represented by the model.

62


Page 62 of 68

Page 63 of 68

(a) 101

(b) 101

max

100

β2

β2

max

100

10-1

10-2

0

10

20

30

40

50

10-1

60

IL sorted w.r.t. decreasing β max 2

0

5

10

15

20

25

30

IL sorted w.r.t. decreasing β max 2

103

103 exptl. data PC-SAFT-0 PC-SAFT-1

exptl. data PC-SAFT-0 PC-SAFT-1 PC-SAFT-2

102

Smax 23

102

Smax 23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


101

100

101

0

10

20

30

40

IL sorted w.r.t. decreasing

100

50

Smax 23

0

5

10

15

20

25

30

IL sorted w.r.t. decreasing Smax 23

Figure 8. Experimental versus PC-SAFT predicted maximum distibution ratio β2max (upper panels) max (lower panels) for selected ternary systems: (a) {IL (1) + toluene (2) + n-heptane and selectivity S23 (3)}; (b) {IL (1) + thiophene (2) + n-heptane (3)}. References to experimental data can be found in the Supporting Information, Table S1.

63



1.5

1.6

1.4

(a)

1.2

(b)

(c)

1.2

(d)

1.0

β

2

0.8 1.0 0.8

0.6 0.4

0.5 30

0.4 50

0.2 50

[C4C1Im][NTf2]

25

120

[C1C1Im][NTf2]

[C4Py][NTf2]

[C2C1Im][NTf2]

[C2C1Im][NTf2]

40

[C4C1Pyr][NTf2]

20

[C4C1Im][NTf2]

100

[CaC1Im][NTf2]

40

[C3C1Im][NTf2]

[C1Ph C1Im][NTf2]

[C4C1Im][NTf2]

30

S23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 64 of 68

[C6C1Im][NTf2]

15

[C4C1Im][N(CN)2]

80

[C2OHC1Im][NTf2]

30

[C4C1Im][SCN] [C4C1Im][C(CN)3]

60

20

20

10

10

10

40

5 0

0 0

0.2

0.4

0.6

x 2 (feed)

0.8

1

20

0 0

0.2

0.4

0.6

0.8

1

x 2 (feed)

0 0

0.2

0.4

0.6

x 2 (feed)

0.8

1

0

0.2

0.4

0.6

0.8

1

x 2 (feed)

Figure 9. Experimental versus PC-SAFT predicted distribution ratio β2 and selectivity S23 in {IL (1) + toluene (2) + n-heptane} ternary systems selected to highlight relevant structural effects on LLE: (a) an effect of cation’s core in [NTf2 ]-based ILs — [C4 C1 Im], 1-butyl-3methylimidazolium 96 (dataset no. 43); [C4 Py], 1-butylpyridinium 97 (dataset no. 111); [C4 C1 Pyr], 1-butyl-1-methylpyrrolidinium 98 (dataset no. 138); (b) an effect of cation’s alkyl chain length in [NTf2 ]-based 1-alkyl-3-methylimidazolium ILs — [Cn C1 Im], n ≡ CH3 (CH2 )n − 1 96,96,99–101 (datasets no. 1, 9, 30, 43, 55); (c) an effect of cation’s side chain functionalization in [NTf2 ]based 1-R-3-methylimidazolium ILs — [C2 C1 Im], R = −CH2 CH3 99 (dataset no. 7); [Ca C1 Im], R = −CH2 CH−CH2 100 (dataset no. 89); [C1Ph C1 Im], R = −CH2 Ph 102 (dataset no. 95); [C2OH C1 Im], R = −CH2 CH2 OH 103 (dataset no. 108); (d) an effect of anion in ILs based on [C4 C1 Im] cation — [NTf2 ], bistriflamide 96 (dataset no. 43); [SCN], thiocyanate 104 (dataset no. 396); [N(CN)2 ], dicyanamide 104 (dataset no. 417); [C(CN)3 ], tricyanomethanide 105 (dataset no. 433). Key: markers and solid lines designated by PC-SAFT-1 (or PC-SAFT-2 if experimental γ ∞ data were not available), respectively.

64


Page 65 of 68

3.5

3

3.5

(a)

6

(b)

(c)

(d) 5

2.5

2.5

4

2

2

β

3 1.5

1.5

2

1

1 0.5 70

120 [C2O1C1Pyr][NTf2]

100

0.5 70 [C3C1Pip][NTf2]

60

[C2O1C1Pip][NTf2] [C2O1C1Mo][NTf2]

80

S23

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


[C6C1Pip][NTf2]

[C4C1Pyr][OTf]

[C4C1Pip][NTf2]

60

[C4C1Pip][NTf2]

50

0 120 100

[C2O1C1Pip][NTf2]

50

40

40

30

30

20

20

10

10

[C4C1Pyr][FAP] [C4C1Pyr][B(CN)4]

80 60

60

40

40 20 0

0 0

0.2

0.4

0.6

x 2 (feed)

0.8

1

20 0

0 0

0.2

0.4

0.6

0.8

1

x 2 (feed)

0

0.2

0.4

0.6

x 2 (feed)

0.8

1

0

0.2

0.4

0.6

0.8

1

x 2 (feed)

Figure 10. Experimental versus PC-SAFT predicted distribution ratio β2 and selectivity S23 in {IL (1) + thiophene (2) + n-heptane} ternary systems selected to highlight relevant structural effects on LLE: (a) an effect of cation’s core in [NTf2 ]-based ILs — [C2O1 C1 Pyr], 1-(2-methoxyethyl)-1-methylpyrrolidinium 106 (dataset no. 140); [C2O1 C1 Pip], 1(2-methoxyethyl)-1-methylpiperidinium 106 (dataset no. 149); [C2O1 C1 Mo], 1-(2-methoxyethyl)1-methylmorpholinium 106 (dataset no. 153); (b) an effect of cation’s alkyl chain length in [NTf2 ]-based 1-alkyl-1-methylpiperidinium ILs — [Cn C1 Pip], n ≡ CH3 (CH2 )n − 1 107 (datasets no. 144, 145, 148); (c) an effect of cation’s side chain functionalization in [NTf2 ]-based 1-R-1methylpiperidinium ILs — [C4 C1 Pip], R = −(CH2 )3 CH3 ; 107 [C2O1 C1 Pip], R = −CH2 CH2 OCH3 106 (datasets no. 145, 149); (d) an effect of anion in ILs based on [C4 C1 Pyr] cation — [OTf], triflate 108 (dataset no. 391); [FAP], tris(pentafluoroethyl)trifluorophosphate 109 (dataset no. 458); [B(CN)4 ], tetracyanoborate 109 (dataset no. 451). Key: markers and solid lines designated by experimental data and PC-SAFT-1, respectively.

65



(a) 1

x4

x4

1

0

0 1

x2

0 0

x3

x3

1 1

0

0

x2

0

0

x2

1

(b) 1

x4

1

x4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 66 of 68

0

x2

0 0

x3

0 1

x3

1 1

1

Figure 11. Experimental versus PC-SAFT predicted LLE phase diagram for quaternary system {[C2 C1 Im][N(CN)2 ] (1) + toluene (2) + cyclohexane (3) + n-heptane (4)} at T = 298 K: 111 (a) PCSAFT-0; (b) PC-SAFT-1. Key: circles, experimental data; squares/triangles, calculated data. Panels on the left and right present 3D views from the side of raffinate and extract, respectively.

66


Page 67 of 68

(a)

0.2

101

(b)

aromatics

100 benzene toluene o-xylene PC-SAFT-0 PC-SAFT-1

0.8 100

10-1

0.6 i

0.4

n-hexane n-heptane n-octane PC-SAFT-0 PC-SAFT-1

β

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6

0.4 10-1

0.8

0.2

10-2

aliphatics

10-2

0.2

0.4

0.6

0.8

[C C Im]

0

0.1

4 1

0.2

x i (feed)

[PF ]

0.3

10-3

0

0.1

0.2

0.3

x i (feed)

6

Figure 12. Experimental versus PC-SAFT predicted LLE data for system {[C4 C1 Im][PF6 ] + benzene + toluene + o-xylene + n-hexane, n-heptane + n-octane} at T = 298 K: 114 (a) pseudoternary phase diagram — key: circles, experimental data; squares, PC-SAFT-0; triangles, PCSAFT-1; (b) distribution ratio βi of aromatic hydrocarbons (left panel) and alkanes (right panel) as a function of their mole fractions in the feed.

67



Table of Contents (TOC) Image molecular scheme

ionic liquid (IL)

IL-based solution (real system)

thermodynamics

LLE, extraction PC-SAFT (model, interactions) (applications)

68


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Thermodynamic Modeling of Multicomponent LiquidâLiquid Equilibria

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