Computer-Aided Molecular Design of New Task-Specific Ionic Liquids

Research Article pubs.acs.org/journal/ascecg

Computer-Aided Molecular Design of New Task-Specific Ionic Liquids for Extractive Desulfurization of Gasoline Kamil Paduszyński,* Marek Królikowski, Maciej Zawadzki, and Patrycja Orzeł Department of Physical Chemistry, Faculty of Chemistry Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland S Supporting Information *

ABSTRACT: New ionic liquids (ILs) for extractive removal of organic sulfur compounds from gasoline are proposed following the results of computer-aided molecular design (CAMD), comprising application of the extensive group contribution model for infinite dilution activity coefficients of molecular solutes in ILs presented previously [J. Chem. Inf. Model. 2016, 56, 1420−1437]. Infinite dilution selectivity of model system thiophene/n-heptane was adopted as a benchmark property. The proposed structures, selected on the basis of screening of almost 25 800 cation−anion combinations, were synthesized and characterized from the point of view of their thermal behavior and fundamental physical properties, density, and dynamic viscosity. Besides, general remarks regarding an impact of cation/anion structure on extraction selectivity are highlighted and discussed based on the calculations carried out. Liquid−liquid phase equilibrium diagrams in ternary systems {IL + thiophene + n-heptane} were determined at T = 308.15 K in the entire range of feed composition in order to verify robustness and reliability of the applied CAMD approach. Finally, performance of the proposed extraction solvents in thiophene/n-heptane separation is confronted against 39 other ILs reported in the literature. KEYWORDS: Ionic liquids, Extraction, Desulfurization, CAMD

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INTRODUCTION Ionic liquids (ILs) are organic salts disclosing a number of unique and peculiar physical, chemical, and thermodynamic properties compared to traditional molecular organic compounds.1 Significant asymmetry in size and shape of the constituting ions weakens their mutual electrostatic interactions, which results in a decrease in lattice energy of ILs, consequently in solid−liquid phase transitions at temperatures much lower compared to “conventional” salts known from inorganic chemistry.2 In consequence, molten salts can be operated at ambient or mild conditions of temperature, which opens paths of possible applications in many areas of both pure and industrial chemistry.3,4 The most important benefit from employing ILs are their good thermal stability and extremely low volatilityILs are often referred to as the solvents of green chemistry and sustainable development and seen in modern and clean processes of chemical engineering as alternative media for volatile organic compounds (VOCs). The only factor that may be seen as an obstacle in applying ILs in eco-friendly processes is that in a great majority of cases they are chemicals synthesized from petroleum-derived precursorsbiobased ILs derived from renewable sources like amino acids, carbohydrates, or lignin seem to be truly sustainable alternatives.5 Another feature of ILs, which make these chemicals particularly attractive from the point of view of separation methods (like © 2017 American Chemical Society

liquid−liquid extraction or extractive distillation) is their capability of dissolving different compounds selectively. In fact, a vast amount of papers concerned with applications of ILs in several important separation problems has been published in the open literature in the past few years.6 In particular, many efforts have been put into extractive desulfurization of fuels using ILs,7−9 as sustainable alternatives for traditional hydrodesulfurization (HDS) process imposing a high level of both environmental and commercial costs due to a high level of consumption of hydrogen and energy as operating at high temperature and pressure. The properties of ILs can be tailored by modifying the chemical structures of the “cores” of cations and anions as well as their task-specific functionalization, namely, by attaching some functional groups which may differ in size, shape (linear, branched, cyclic, ...), polarity, acidity, etc. This generates a huge number of possible ILs, estimated by some authors to be of the order of 1018 (including binary and ternary salts).3 To be more specific, based on our recent viscosity data compilation, it was established that a number of possible binary cation−anion combinations was around 150 000,10 taking into account only Received: June 14, 2017 Revised: August 11, 2017 Published: August 12, 2017 9032

DOI: 10.1021/acssuschemeng.7b01932 ACS Sustainable Chem. Eng. 2017, 5, 9032−9042

Research Article

ACS Sustainable Chemistry & Engineering the ions reported in the literature. First of all, “tuneability” of ILs may be seen as their advantage since a lot of “degrees of freedom” are available for a selection of an IL proper for a given application. Of course, one can try to find some correlations between chemical structure of ions and properties of interest for some selected families of ILs and their homologous series. Nevertheless, such an experiment-based design is, in general, very ineffective. For instance, in the mentioned case of viscosity, the number of characterized ILs covers approximately 1% of the entire pool of cation−anion combinations.10 This may be perceived as a representative example showing that systematic experimental investigations of such a large library of compounds is a tough, basically unfeasible, challenge. Because of rapid development in computer science observed in the last few decades (including hardware and algorithms for processing huge data sets), the modeling methods involving large-scale and complex calculations have become readily accessible for researches, basically at desktop PCs. That is why computeraided molecular design (CAMD) has become very popular in developing new materials, in particular, these intended to be applied in separations.11−13 The CAMD approach has received an attention of many research groups studying ILs, in particular, those investigating potential applications of ILs as extractants or entrainers in separations.14 For this kind of problem, a detail knowledge of liquid−liquid equilibrium (LLE) and vapor−liquid equilibrium (VLE) phase diagrams is of fundamental importance. However, in a significant part of papers devoted to CAMD of ILs for separations, an infinite dilution activity coefficient (henceforth abbreviated by IDAC or γ∞) was used as a benchmark property. IDAC of a solute in a given IL is strongly associated with affinity of the solute to IL resulting from differences in the strength and nature between IL−solute and IL−IL interactions. Thus, the ratio of IDACs observed for a pair of solutes i and j is ∞ ∞ strongly related to the IL’s selectivity S∞ ij ≡ γj /γi in a potential process aiming to get their effective separation. Several computational methods and properties have been used to compute the IDACs. A conductor-like screening model for real solvents (COSMO-RS), a theoretical hybrid approach combining principles of quantum chemistry and molecular thermodynamics, has gained a vast amount of attention.15 In particular, this method has been intensively applied in “IDAC-based” CAMD of ILs suitable for different separation problems, e.g., desulfurization and denitrification of fuels.16−22 In order to make verifying and estimating the robustness of the COSMORS model possible, a comprehensive review of the performance of this approach in predicting IDAC of diverse solutes in more than 200 ILs has been carried out and reported very recently by our group.23 Beside COSMO-RS, several more or less sophisticated correlations involving machine-learning algorithms have been proposed as rapid and compact predictive tools for calculating IDACs; a detailed review of these methods (up to June 2016) can be found elsewhere.24 Obviously, compared with COSMO-RS, they suffer from being purely empirical, i.e., having no solid physical foundations as being equations with a number of coefficients simply fitted to databases of the measured values. Nevertheless, they are much easier in use, as their applying does not require a commercial software, as well as it does not expect from the user any expertise in quantum chemistryin other words, they seem to be the tools suited for chemical engineers rather than chemists. Very recently, a state-of-the-art method of this type has been developed and carefully analyzed by our group on the basis of

the very comprehensive database of IDACs.24 In particular, three distinct machine-learning algorithms were tested, with the least-squares support vector machine (LSSVM) finally recommended to be the most reliable in terms of generalization capacity.24 An interesting contribution by Song et al.25 presenting a systematic method for screening ILs as extraction solvents for extractive desulfurization has been published very recently in this journal. This paper is particularly worth mentioning as it demonstrates a “combined” approach of CAMD, in which the COSMO-RS method was used in preselection of ILs based on LLE, whereas empirical group contribution (GC) models were employed to finally select the best ILs meeting certain physical property (melting point and viscosity) constraints. The major drawback of the work of Song et al.25 is, however, that the performance of the proposed ILs in continuous extraction was analyzed in an Aspen Plus process simulator only, whereas neither synthesis nor LLE/viscosity measurements were carried out by the authors. Besides, the ILs finally proposed in ref 25 were based on lactate or formate anions, known for forming rather viscous (and hygroscopic) ILs. Unfortunately, the authors did not point out that experimental viscosity of the ILs proposed by them may be about one order of magnitude higher compared to the simulated data, which can be readily checked using our previous viscosity data compilation.10 This is a good example showing that one should rely on purely simulated data with special care taken if supporting experimental evidence is not demonstrated. In this paper, new ILs are proposed for a model extractive desulfurization process, simulated by LLE in model ternary systems {IL + thiophene + n-heptane}. The chemical structures of ILs have been established on the basis in silico screening of a predefined 432 × 65 cation−anion matrix with the previously reported LSSVM-based model24 allowing to predict IDACs solely from GCs of ions and the Abraham’s molecular descriptors of solutes. n-Heptane/thiophene infinite dilution selectivity was employed as the criterion to be maximized during the screening process. The ILs having the structures revealed by the performed CAMD were synthesized, and their basic physical properties (thermal behavior, density, and viscosity) were measured. Ternary LLE phase diagrams were determined experimentally in order to verify the robustness of the applied CAMD tool.

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CAMD PROCEDURE Despite the fact that gasoline is a complex multicomponent mixture consisting of a great diversity of hydrocarbons (aliphatic/aromatic, linear/cyclic/branched, ...) and other organic compounds, CAMD of new ILs intended to be applied in extractive desulfurization was performed employing the following reference system: pure n-heptane was considered as a model fuel, whereas thiophene was taken as a model organic sulfur compound treated as the only impurity. In fact, nheptane is certainly present in gasoline; however, it cannot be considered as a fuel in a spark-ignition engine in a pure state because the octane rating of n-heptane is, by definition, equal to zero. Furthermore, (di)benzothiophene and its alkylated derivatives are another sulfur compounds difficult to eliminate using available techniques; thus, they should be also taken into account. Finally, the results and conclusions obtained by representing a fuel with n-heptane should not be extrapolated to heavier fractions like diesel fuel or kerosene. The assumption of such a simplified picture of a real system was dictated first of 9033


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ACS Sustainable Chemistry & Engineering

0.000, A3 = 0.000, B3 = 0.000, L3 = 3.130) were predicted and transformed into infinite dilution selectivity S∞ 23, so that the CAMD proposed in this work can be finally formulated as the following optimization problem:

all by the limitations of the applied CAMD tool, which permits representing binary systems {IL + molecular solute} only. Furthermore, there are a significant amount of LLE data reported in the literature for ternary systems {IL + thiophene + n-heptane}, including 39 distinct ILs.26−42 By using these data, the ILs designed in silico in this work (thus, used CAMD protocol as a whole) can be confronted to other ILs in terms of such measures like distribution ratio or selectivity. Evaluation of an IL in extractive removal of thiophene from n-heptane was carried out by using the GC model for predicting IDACs based on (1) formal decomposition of IL’s cation and anion structures into functional groups, (2) Abraham’s solvation descriptors of solutes (dipolarity E, polarizability S, acidity A, basicity B, lipophilicity L). To our best knowledge, this the very first attempt to use these kinds of calculations in CAMD of ILs. All the computational details regarding LSSVM algorithm as well as the descriptors can be found in our previous paper24 and references therein. We found the LSSVMbased tool very attractive as it allows us to estimate IDAC of any solute in ILs composed of any ions given that their chemical structure can be represented by the model’s predefined functional groups. Since the number of the groups is relatively high (in total 81, including 18 cation cores, 33 anions cores, and 30 substituted groups24), the number of available ionic structures becomes enormous. In particular, the model was established on the basis on experimental IDAC data reported for 188 ILs, composed of 84 and 40 distinct cations and anions, respectively. This means that the experimental data pool used covered only a small fraction, 188/(84 × 40) ≈ 0.055, of all the possible binary cation−anion combinations. Of course, predictions can be performed not only for the possible 84 × 40 = 3360 binary salts that can be built of the ions considered in development of the model. However, it should be kept in mind that for these particular ILs, the predictions returned by the proposed LSSVM model should be seen as the most reliablethe empirical models, particularly those employing machine-learning algorithms, are always more stable in interpolating than in extrapolating from applicability domain. Nevertheless, we decided to extend the investigated “chemical space” of ILs by taking into account more cations and more anions. However, in order to minimize a risk of resulting in extraordinarily complex or chemically unstable structures, only the ions forming the ILs reported in the literature were taken into consideration. The final lists of both cations and anions were established based on our in-house databases of different physical properties of pure ILs, first of all the revised version of viscosity data reported by our group in 2014.10 A detailed summary of basic chemical information on the ions, including their names and molecular weights, is given in the Microsoft Excel spreadsheet provided in the Supporting Information. Summing up, the list covers 430 cations (including 138 imidazolium, 58 pyridinium and quinolinium, 115 ammonium, 22 pyrrolidinium, 26 piperidinium, 16 morpholinium, 48 phosphonium, and 7 sulfonium) and 60 anions, respectively, so the proposed CAMD will be based on screening the of 430 × 60 = 25800 binary 1:1 ILs. Di- and tricationic ILs, as well as these based on very “unusual” bicyclic cations, were excluded from this study. For each (i, j) cation−anion pair, the values of IDACs of thiophene (henceforth, denoted by 2 in all the equations; solvation parameters:24 E2 = 0.687, S2 = 0.560, A2 = 0.000, B2 = 0.150, L2 = 2.819) and n-heptane (henceforth, denoted by 3 in all the equations; solvation parameters:24 E3 = 0.000, S3 =

∞ max (i , j)[S23 ](i , j)

≡

∞ γ3,( i , j) ∞ γ2,( i , j)

(1)

The reference temperature assumed was T = 308.15 K. This value of T represents typical conditions at which both IDAC and phase equilibrium data are usually measured and reported. ∞ One can speculate that β∞ 2 ≡ 1/γ2 , i.e., thiophene’s infinite dilution distribution ratio, would be better choice for the objective function for the CAMD proposed. The reason for ∞ which one can justify application of S∞ 23 instead of β2 is that the former quantity has a much broader range of values. In fact, S∞ 23 may vary by several orders of magnitude (approx from 1 to 1000), whereas β2∞ is, in general, in the narrow range (approximately between 0.1 and 5). Therefore, one may expect that capturing (at least qualitatively) the variability of S∞ 23 with the chemical structure of a cation/anion will be more effective than in the case of β∞ 2 . An unquestionable drawback of the definition of selectivity given in eq 1 is that it accounts only for the effect of the extract phase on the partitioning behavior nevertheless, S∞ 23 quantifies somewhat the difference in mutual affinity between IL and solute (n-heptane or thiophene); thus, one may expect that it correlates with the selectivity derived based on LLE data (i.e., the ratio of distribution coefficients), which are key in real extraction processes. Furthermore, it should be stressed that the assumption of using eq 1 as an objective function for selecting the best ILs is indeed adequate, nevertheless, only for the model gasoline employed. Formulation of a real gasoline, whose desulfurization with ILs is the ultimate purpose of this and similar studies, additionally comprises significant concentrations of other hydrocarbons disclosing, in general, higher solubility in ILs compared to nalkanes (this especially regards the aromatics). This may bring likely significant discrepancies in the selectivity of thiophene on the real gasoline/IL biphasic system compared to eq 1, first of all due to an influence of the raffinate phase on partitioning. The MATLAB integrated development environment (Mathworks, Inc., version 2016A) was employed to perform the proposed screening. All the operations related to the data storage, import/export, analysis, and visualization were run by using in-house subroutines, whereas the calculations with the LSSVM model were carried out with LSSVMlab Toolbox.43

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EXPERIMENTAL METHODS

Thermal Behavior. Thermal behavior of the synthesized ILs was determined with differential scanning calorimetry (DSC) by using a DSC 1 STARa calorimeter from Mettler Toledo. Prior to the measurements, the apparatus was calibrated with a 0.999999 mass fraction purity indium sample, as well as a set of several high purity organic compounds (n-heptane, n-octane, n-decane, 1-undecanol) and water. Thermograms were recorded in the heating/cooling/heating regime, with the temperature scanning rate of ±10 K·min−1. Temperatures of the observed phase transitions were determined from the second heating scan. We checked that applying a lower heating/cooling rate does not significantly affect the measured data (e.g., onset temperature and area of a peak). The standard uncertainty of the determined temperatures has been estimated to be 0.5 K. Density and Viscosity. The temperature-dependent ambient pressure density of pure ILs was measured by using an Anton Paar 4500 M vibrating tube densimeter calibrated with doubly distilled and 9034


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Figure 1. Results of screening of various cation−anion combinations to find ILs exhibiting infinite dilution n-heptane/thiophene selectivity as high as possible. The lowest and the highest values of |log10 S∞ 23| are marked in blue and red, respectively. The abbreviations used to classify cations are as follows: Im, imidazolium; Py and Quin, pyridinium and (iso)quinolinium; N, ammonium; Pyr, pyrrolidinium; Pip, piperidinium; Mo, morpholinium; P, phosphonium; S, sulfonium. The names of cations and anions corresponding to the plotted IDs are provided in the Supporting Information.

IDs, as well as all the calculated values of S∞ 23, can be found in the Microsoft Excel spreadsheet provided in the Supporting Information. Although the data presented in Figure 1 may be perceived as complex and difficult to discuss in detail, some general conclusions on the predicted impact of a cation/anion structure can be drawn from them. First of all, it should be noted that the proposed CAMD suggests that some types of cations, as well as some types of anions, seem to be completely useless from the point of view of thiophene/n-heptane separations as they disclose selectivity very close to 1. For example, this is the case of many long-chained phosponium- and ammonium-based ILs, as one can easily notice from Figure 1. This result may be treated as a rationale for considering these “classic” ILs in future investigations on S-compound/alkane separations only if they have a short alkyl chain substituted at the P or N atom. On the other hand, one can also find the anions that form the ILs with no potential to be applied in the considered separation problem, irrespective of the accompanying cation. In particular, this is the case of the anions like dodecyl sulfate, bis(2ethylhexyl)phosphate, palminate, or stearate. In general, the anions having in their structures as long, nonfunctionalized alkyl chains seem to be the worst choice when selecting the ILs for separation of thiophene from n-heptane; surface activity (due to amphiphilic character) of these anions can be recognized as another obstacle in applying the ILs formed by them. It is worth pointing out that the presented screening reveals several anions disclosing an enhanced selectivity for a great diversity of cations. The anions like thiocyanate [S−C − ∞ N]− (S̅∞ 23 = 92.1), chloride [Cl] (S̅23 = 83.6), methylsulfonate − ∞ [CH3SO3] (S̅23 = 71.7), nitrate [NO3]− (S̅∞ 23 = 66.8), and dicyanamide [N(CN)2]− (S̅∞ 23 = 64.4) can serve here as representative examples. In particular, the very promising predictions obtained for thiocyanates are actually not a surprise since ILs based on this anion have been suggested several years ago as very effective in separation of aromatic from aliphatic hydrocarbons.45−48 For each cationic family presented in Figure 1, the respective cations were sorted with respect to their functionalization and molecular weight (MW). First, the cations with no extra functional groups attached to the alkyl chains were listed with increasing MW, followed by the “task-specific” cations. Thus, the LSSVM model properly predicts that for a given anion (1) an increase in the both nonfunctionalized and

degassed water, benzene, and dried air. The apparatus allows us to control the temperature of the sample within 0.05 K and measure its specific density with results of 0.01 kg·m−3. Taking into account impurities of the samples, standard uncertainty of the measurements was estimated to be 1 kg·m−3 (based on the assumptions proposed by NIST44). The dynamic viscosity of pure ILs was determined as a function of temperature with an Anton Paar AMVn rheometer based on the “falling ball” principle. The apparatus allows us to control the temperature within 0.05 K. The relative standard uncertainty of the measured viscosity was estimated to be 5%. LLE Phase Diagrams. LLE tie-lines were determined for ternary mixtures {IL + thiophene + n-heptane} by using a static method, coupled with gas chromatography analysis employed to obtain the composition of coexisting liquid phases. Detailed procedures were found by our group to be optimum for LLE measurements for these kinds of systems and were reported previously.30 Herein, we provide a brief description including some details specific for the systems under study. Heterogeneous mixtures were prepared in jacketed and thermostated (T = 308.15 K at ambient conditions of pressure, p = 0.1 MPa) glass cells (closed tightly in order to avoid any losses by evaporation or moisture absorbing) and then vigorously stirred with a coated magnetic bar for 6 h, followed by resting for 12 h in order to obtain the phase separation and equilibrium state. The samples were taken from both phases and dissolved in a well-defined amount of acetone in order to prevent the mixture from phase splitting. The capillary column of the chromatograph was protected with a precolumn to prevent it from reaching it by the nonvolatile IL. All the analyses followed internal standard protocol with 1-propanol applied in this work. A PerkinElmer Clarus 580 gas chromatograph equipped with FID and TCD detectors was used in all determinations. More details on the experimental setup used is given in Table S1 in the Supporting Information. Finally, accepted values of concentration were established based on the average of three subsequent analyses. The estimated uncertainties in the determination of mole fraction compositions were 0.003 and 0.005 for the compositions of the raffinate (i.e., hydrocarbon-rich phase) and extract (i.e., IL-rich phase), respectively.

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RESULTS AND DISCUSSION CAMD Results. The results of the LSSVM screening of cation−anion combinations are summarized in Figure 1, where the values of S∞ 23 (in logarithmic scale) are represented as a color map plot: blue and red correspond to extremely low and high selectivity, respectively. The anions were ranked in terms of mean values of selectivity calculated over all 430 cations. Full list of names of cations and anions corresponding to the plotted 9035


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to ILs based on other families of cations, e.g., pyrrolidinium- or piperidinium-based ones. In order to address these findings, thus to combine the results of calculations with our general empirical knowledge on the ILs, we decided to select and test not “the best” IL revealed by the calculations but their pyrrolidnium and piperidinium counterparts differing in functionalization. Finally, proposed ILs are 1-(3-hydroxypropyl)-1-methylpyrrolidinium thiocyanate [C3OHC1Pyr][SCN], 1-(3-hydroxypropyl)-1-methylpiperidinium thiocyanate [C3OHC1Pip][SCN], 1-(3-cyanopropyl)-1methylpyrrolidinium thiocyanate [C3CNC1Pyr][SCN], and 1(3-cyanopropyl)-1-methylpiperidinium thiocyanate [C3CNC1Pip][SCN] (the chemical structures are summarized in Figure 2). Synthesis of Designed ILs. The syntheses of the in silicodesigned thiocyanates shown in Figure 2 were carried out by means of the metathesis reaction of the corresponding chlorides with NaSCN. Chlorides were synthesized according to the procedure described in detail elsewhere.51 A drying socket was used instead of the nitrogen atmosphere originally proposed in ref 51. The thiocyanates were synthesized following the procedure used in the same work51 for the preparation of 1-butyl-3-methylimidazolium tetrafluoroborate. Due to the significantly low solubility of the final product in dichloromethane, acetone was used as the solvent in this work. Details regarding the syntheses and analyses of all the presented ILs are given in the Supporting Information, including 1H and 13 NMR spectra of the obtained products given in Figures S1−S8. All the prepared compounds were dried under vacuum prior to the measurements of thermal behavior, physical properties, and liquid−liquid equilibrium phase diagrams. The water mass fractions were measured by using Karl Fischer titration. The final results of these determinations were 767 ppm for [C3OHC1Pyr][SCN], 206 ppm for [C3OHC1Pip][SCN], 438 ppm for [C3CNC1Pyr][SCN], and 847 ppm for [C3CNC1Pip][SCN]. Thermal Behavior. DSC thermograms of the ILs under investigation are presented in Figure 3. The curves presented were recorded in the second heating run, which was basically indistinguishable from the first one. As noticed, all the compounds were thermally stable up to T = 373 K. In the case of ILs based on the cations incorporating the CN group,

functionalized cation’s MW (associated usually with an increase in the length and/or branching of alkyl chains) results in a decrease in selectivity and (2) “grafting” the functional group(s) (like −OH, −CN, −C(O)O−, ...) usually increases the selectivity (these cations are located roughly in the second half of the lists). Finally, all the 430 × 60 = 25 800 ILs taken into account during screening were ranked with respect to the calculated S∞ 23. ∞ A complete list of S23 obtained for each cation−anion combination can be found in the Microsoft Excel spreadsheet provided in the Supporting Information, whereas the chemical structures selected on the basis of the proposed CAMD are summarized in Figure 2. According to the used LSSVM model,

Figure 2. Chemical structure of in silico-designed ILs, their abbreviations used throughout the text, and the physical state of the synthesized compounds at laboratory conditions prior the measurements.

the IL pretending to be the most effective extractant in thiophene/n-heptane separation was 4-(3-hydroxypropyl)-4methylmorpholinium thiocyanate (S∞ 23 = 402.9). Besides, many other [SCN]-based ILs were found in the “lead” of the obtained ranking. Although several chlorides and methylsulfonates were also predicted to disclose high selectivity, the idea of considering this IL was abandoned due to (1) high melting points expected for chloridesin fact, these ILs (actually, the ILs’ precursors) usually form solid phase at ambient conditions and (2) potentially higher dynamic viscosity (η) of methylsulfonates compared to thiocyanates, for example, in the case of common 1-ethyl-3-methylimidazolium ILs at T = 298.15 K, η = 155 mPa·s for methylsulfonate49 and η = 22.5 mPa·s for thiocyanate.50 In general, the [SCN] anion combined with the cations with OH and CN groups attached to the alkyl chains seems to form the most promising ILs for the analyzed separation problem. This can be illustrated by considering ILs ranked in the first 50 places: 20 of them are based on the thiocyanate anion, whereas only 7 of them are composed of cations which have in their chemical structure neither hydroxyl nor cyano groups. Besides, morpholiniumbased ILs have been shown to be much more viscous compared

Figure 3. DSC thermograms of the in silico-designed ILs. 9036


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ILs. The impact of the chemical structure of the cation on ρ and η on the investigated ILs is presented in Figure 4.

no thermal phenomena except glass transition were detected. The values of the determined glass transition temperatures (Tg) were as follows: Tg = 223.3 K for [C3OHC1Pyr][SCN], Tg = 206.3 K for [C 3OH C 1 Pip][SCN], T g = 193.1 K for [C3CNC1Pyr][SCN], and Tg = 211.5 K for [C3CNC1Pip][SCN]. On the other hand, for the ILs involving the OH group in their chemical structure, endothermic peaks corresponding to melting were recorded at (onset temperatures are given) Tm = 282.5 K for [C3OHC1Pyr][SCN] and Tm = 307.4 K for [C3OHC1Pip][SCN]. In the case of the latter IL, an exothermic cold crystallization peak at Tcc = 251.7 K was disclosed. Despite the fact that the results of the DSC thermal analysis suggest that [C 3OHC1Pip][SCN] should form a solid in laboratory conditions, we did not observe any spontaneous precipitation or crystallization processes of this IL when handling and operating it at “room” temperature (T ≈ 293 K). Keeping all the ILs in the refrigerator overnight did not result in solidification of the samples either. These results suggest that [C3OHC1Pip][SCN] in its molten state can persist as a subcooled liquid until cooled to extremely low temperatures as these applied in DSC measurements. Physical Properties. All the measured temperaturedependent data on liquid density (ρ) and dynamic viscosity (η) of the synthesized ILs can be found in the Supporting Information, Tables S2 and S3. In order to make interpolations/extrapolations of the experimental data to other temperatures, the results of measurements were fitted using, respectively, the exponential model in the case of ρ (resulting in temperature-independent value of thermal expansion coefficient αp) and the Arrhenius equation in the case of η. The coefficients of the obtained correlations are given in Tables 1 and 2 along with their uncertainties as well as the

Figure 4. Physical properties of the in silico-designed and -synthesized ILs as a function of temperature T: (a) liquid density, ρ; (b) dynamic viscosity, η. Markers designated by experimental data: circles, [C 3OH C 1 Pyr][SCN]; squares, [C 3OH C 1 Pip][SCN]; triangles, [C3CNC1Pyr][SCN]; diamonds, [C3CNC1Pip][SCN]. Solid lines designated by the correlations given in Tables 1 and 2, respectively.

Table 1. Coefficients of the Exponential Model Used To Represent the Measured Density of ILs Studied Along with Their Margin Errors u (Defined as Half the Width of the 95% Confidence Intervals) and Root-Mean-Square Errors σ between Fitted and Experimental Dataa Ionic liquid

ρ0 ± 2u(ρ0)/kg·m−3

[C3OHC1Pyr][SCN] [C3OHC1Pip][SCN] [C3CNC1Pyr][SCN] [C3CNC1Pip][SCN] a

1117.3 1112.4 1108.8 1105.8

± ± ± ±

0.06 0.19 0.05 0.09

αp ± 2u(αp) /10−4 K−1

σ/kg·m−3

± ± ± ±

0.05 0.09 0.04 0.07

4.64 4.67 4.72 4.78

0.02 0.05 0.01 0.02

In general, all the ILs exhibit relatively low densities varying in a very narrow range from 1105 to 1115 kg·m−3 at T = 298.15 K, see Figure 4a. It can be seen that pyrrolidinium-based ILs disclose higher density compared to their piperidinium counterparts, regardless of the type of the terminal functional group. Besides, the ILs based on OH-functionalized cations are denser than these involving CN groups. The observed differences in density are closely related with cation−cation interactions affecting molecular packing. In terms of molar volume V ≡ M/ρ, where M denotes the molecular weight, the lower V value is the stronger the interactions are and the better ordered molecular packing is. At T = 308.15 K, the values of V obtained (given in cm3·mol−1) are as follows: 181.9 for [C3OHC1Pyr][SCN], 195.4 for [C3OHC1Pip][SCN], 191.5 for [C3CNC1Pyr][SCN], and 204.8 for [C3CNC1Pip][SCN]. As seen, replacing pyrrolidinium by a piperidinium core results in

ρ = ρ0 exp[−αp(T − T0)], where T0 = 298.15 K.

root-mean-square errors between the fitted and measured properties (σ). Based on the very low values of σ, it is clearly seen that the presented equations allow us to reproduce the experimental data with an excellent accuracy irrespective of the

Table 2. Coefficients of the Arrhenius Equation Used To Represent the Measured Viscosity of ILs Studied Along with Their Margin Errors u (Defined as Half the Width of the 95% Confidence Intervals) and Root-Mean-Square Errors between Fitted and Experimental Data (σ)a Ionic liquid [C3OHC1Pyr][SCN] [C3OHC1Pip][SCN] [C3CNC1Pyr][SCN] [C3CNC1Pip][SCN] a

ln A ± 2u(ln A) −9.73 −13.66 −10.68 −13.92

± ± ± ±

0.80 0.44 0.23 0.72

Ea ± 2u(Ea)/kJ·mol−1

σ/mPa·s

± ± ± ±

5.9 9.4 5.3 17.9

37.3 51.6 41.7 53.8

2.1 1.2 0.6 2.0

ln η/mPa·s = ln A + Ea/RT. 9037


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Figure 5. LLE phase diagrams (in mole fraction basis) of ternary mixtures of the is silico-designed ILs with thiophene and n-heptane at temperature T = 308.15 K and pressure p = 0.1 MPa.

an increase in V by about +13 cm3·mol−1, whereas the substitution of the hydroxyl group by the cyano group corresponds to an increase in V approximately by +10 cm3· mol−1. An effect of the size of the ring can be explained in terms of the ring itself but also by an enhanced conformational flexibility of the 6-membered piperidinium ring. On the other hand, the observed impact of the type of functional group can be easily explained considering the fact that, compared to hydroxyl, the CN group is built of two “heavy” atoms. It is also interesting to note that the obtained density−structure relationships are in quite good agreement with the additivity model proposed by our group a few years ago.52 The molar volume increments predicted by this model due to cation core and functional group replacement are 14.6 and 7.7 cm3·mol−1, respectively; therefore, the experimental results confirm the adequacy of the model. Although all the obtained ILs form a liquid phase at ambient conditions and can be easily operated, the dynamic viscosity of them is relatively high, as seen in Figure 4b. Of course, this can hinder applications of the proposed compounds in real industrial separation processes. Eventually, they could be used at elevated temperature, but unfortunately, such conditions usually affect the separation efficiency. Furthermore, η varies with the chemical structure of the cation as follows: [C3OHC1Pyr][SCN] < [C3CNC1Pyr][SCN] < [C3OHC1Pip]-

[SCN] < [C3CNC1Pip][SCN]. This trend is preserved along the entire range of temperature under study. It is interesting that it also follows the order of increasing viscous flow activation energy obtained from the Arrhenius fits, see Table 2. In general, this means that the combination of pyrrolidinium-based cations with hydroxyl group functionalization promotes the lower viscosity compared to the piperidinium core and cyano group attached to it. This can be perceived as a surprising result because it has been demonstrated many times that the ILs consisting of cyano-based anions disclose very low viscosity. In order to confirm our observation, one should compare an effect of CN to OH substitution measured for other ILs. For example, one can confront the viscosity η = 65.5 mPa·s of [C2CNC1Im][BF4] at T = 293 K reported by Zhao et al.53 with η = 153.6 mPa·s reported at the same temperature for [C2OHC1Im][BF4] by Song et al.54 Based on these results, one could claim that the effect of the functional group is reverse. However, it has to be kept in mind that in the “task-specific” ILs, as these presented in this work, the interaction between the functional group and the anion may play the most dominant role in governing bulk phase behavior and physical properties. Besides, uncertainty of the single data point reported for [C2CNC1Im][BF4] is very difficult to be estimated as no information on the sample purity (e.g., water content) was provided by the authors.53 We only 9038


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proposed ILs are the distribution ratio of thiophene β2 and the selectivity in thiophene/n-separation S23, computed in mole fraction basis. The quantities β2 and S23 are usually defined as follows:

can speculate that the determined viscosity could be significantly lowered by moisture absorbed by the sample. Liquid−Liquid Equilibrium. All the determined LLE data in ternary systems {IL + thiophene + n-heptane} are listed in Table S4 in the Supporting Information. The phase diagrams plotted on the basis of the measured equilibrium mole fractions are given in Figure 5. First of all, it should be emphasized that the miscibility gap covers basically the entire range of concentrations, irrespective of the kind of both cation and substituent. This means that even a very small amount (in terms of number of moles) of any of the studied ILs induces a liquid phase split when added to a completely miscibible binary system {thiophene + n-heptane}. Furthermore, the raffinate phase of each system does not contain ILs within the uncertainty of the analysis method applied. On the other hand, the concentration of n-heptane in the IL-rich phase is also very low and varies from 0.001 to 0.003 mol/mol. These results indeed confirm a potential usefulness of the in silico-designed ILs in extraction processes from nonpolar phases like aliphatic hydrocarbons’ mixtures. They also demonstrate that an incorporation of functional groups in the cation’s alkyl chain deteriorates miscibility with hydrocarbons compared with “plain” alkylated ILs. In fact, nonfunctionalized [SCN]-based ILs dissolve much more n-heptane, as evidenced by previous studies carried out in our group several years ago.55 One can speculate that can such behavior is associated with stronger cation−cation interactions (in particular, dipole− dipole or hydrogen bonding like in the of ILs composed of case cyano- and hydroxyl-based cations, respectively) compared with the “plain” alkyl chain. In the case of the binary mixtures {IL + thiophene}, the range of the IL’s concentration corresponding to the miscibility gap is much narrower and visibly depends on both the cation type and the functional group. In particular, the liquid phase split appears above the thiophene mole fraction (corresponding to the solubility of thiophene in IL) of 0.493 for [C3OHC1Pyr][SCN], 0.591 for [C3OHC1Pip][SCN], 0.547 for [C3CNC1Pyr][SCN], and 0.625 for [C3CNC1Pip][SCN]. Therefore, the following apply: (1) Piperidinium cations promote higher solubility of thiophene (by about 0.08−0.1 mol/mol), possibly due to higher contribution of dispersive van der Waals forces from an extra CH2 unit. (2) An increase in solubility by about 0.03−0.05 mol/mol is observed when OH is replaced by CNbased on this observation, one can draw a conclusion that n−π cross interaction is slightly more preferable than induced association between a sulfur atom of in heterocyclic thiophene and OH group of the cation. Furthermore, it is noteworthy that all the considered ILs dissolve less thiophene than nonfunctionalized ILs [CnC1Im][SCN] (where n = 2, 4, 6).56 In turn, solubility of thiophene in the studied ILs is so low that it could not be accurately determined with the utilized analytical setup. These final findings can be perceived as another argument supporting a proposition that cation−cation (or, in general, IL−IL) interactions seem to be much stronger than IL−thiophene interactions, thus dominant in governing the macroscopic phase behavior of mixtures “task-specific” ILs with organic sulfur compounds. From the utilitarian point of view, a usefulness of the studied ILs as extractants in fuels’ desulfurization should be discussed not in terms of molecular interactions or direct phase equilibrium data plotted in Figure 5 but rather in terms of some auxiliary properties derived from LLE tie-lines. The properties used in this work to express the efficiency of the

β2 ≡

S23 ≡

x 2′ x 2″

β2 β3

(2)

=

x 2′/x 2″ x3′/x3″

(3)

where the symbols denoted by ′ and ′′ correspond to the extract and the raffinate phase, respectively. It should be noted that the latter property is thermodynamically related to the “benchmark” property defined in eq 1 and used in the presented CAMD. Therefore, high values of selectivity derived from LLE data have been expected and hoped to be disclosed by the in silico-designed ILs before any LLE experiments. Figure 6 presents the calculated values of maximum max selectivity S23 (usually corresponding to very low feed

Figure 6. Comparison of the performance of the new in silico-desiged ILs in extractive separation of thiophene from n-heptane with different ILs, expressed in terms of maximum thiophene/n-heptane selectivity max Smax 23 as a function of corresponding thiophene’s distribution ratio β2 : circle, [C3OHC1Pyr][SCN]; square, [C3OHC1Pip][SCN]; triangle, [C3CNC1Pyr][SCN]; diamond, [C3CNC1Pip][SCN]; crosses, literature max are listed in the Microsoft data.26−42 All values of both Smax 23 and β2 Excel spreadsheet provided in the Supporting Information.

concentration of thiophene) plotted as a function of the corresponding thiophene’s distribution ratio βmax 2 . The values obtained for the ILs studied in this work are compared with 39 different ILs, for which LLE data in ternary mixtures with thiophene and n-heptane has been found in literature.26−42 All max the values of both Smax 23 and β23 required to obtain the plot in Figure 6 can be found in the Microsoft Excel file provided in the Supporting Information. As seen, one of the lowest values of βmax was obtained for all the ILs under study. At first sight, 2 this can be seen as a very disappointing result. However, a low distribution ratio of thiophene is accompanied by high selectivity; thus, a selection of optimal ILs for a given separation process is a matter of balance. This is also confirmed in this work because Smax 23 of ILs proposed in this paper exhibits one of the highest values among all of those plotted in Figure 6. In order to provide more detailed comparison, Smax 23 values observed for each IL were sorted in an ascending order and plotted in Figure 7. As seen, there is no significant impact of the cation’s or substituent’s nature on the final results. Never9039


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26−42 Figure 7. Ranking of experimental maximum thiophene/n-heptane selectivity Smax for 23 calculated on the basis LLE data reported in the literature different ILs. The bars highlighted in colors correspond to the ILs investigated in this work. Key for the abbreviations used is as follows: [C1C1Im], 1,3-dimethylimidazolium; [C2C1Im], 1-ethyl-3-methylimidazolium; [C4C1Im], 1-butyl-3-methylimidazolium; [C5C1Im], 3-methyl-1-pentylimidazolium; [C6C1Im], 3-hexyl-1-methylimidazolium; [C8C1Im], 3-methyl-1-octylimidazolium; [C1PhC1Im], 1-benzyl-3-methylimidazolium; [C2OHC1Im], 1-(2-hydroxyethyl)-3-methylimidazolium; [C4CCN(3)Py], 3-cyano-1-butylpyridinium; [C4CCN(4)Py], 4-cyano-1-butylpyridinium; [C6CCN(4)Py], 4cyano-1-hexylpyridinium; [C4C1Pyr], 1-butyl-1-methylpyrrolidinium; [C3OHC1Pyr], 1-(3-hydroxypropyl)-1-methylpyrrolidinium; [C2O1C1Pyr], 1-(2methoxyethyl)-1-methylpyrrolidinium; [C3CNC1Pyr], 1-(3-cyanopropyl)-1-methylpyrrolidinium; [C3C1Pip], 1-methyl-1-propylpiperidinium; [C4C1Pip], 1-butyl-1-methylpiperidinium; [C5C1Pip], 1-methyl-1-pentylpiperidinium; [C6C1Pip], 1-hexyl-1-methylpiperidinium; [C3OHC1Pip], 1(3-hydroxypropyl)-1-methylpiperidinium; [C2O1C1Pip], 1-(2-methoxyethyl)-1-methylpiperidinium; [C3CNC1Pip], 1-(3-cyanopropyl)-1-methylpiperidinium; [C2O1C1Mor], 4-(2-methoxyethyl)-4-methylmorpholinium; [(C4)3C2P], tributyl(ethyl)phosphonium; [(C2OH)3C1N], tris(2-hydroxyethyl)(methyl)ammonium; [C2O1C2C1C1N], ethyl(2-methoxyethyl)dimethylammonium; [NTf2], bis(trifluoromethylsulfonyl)imide; [OTf], trifluoromethanesulfonate; [TCB], tetracyanoborate; [TCM], tricyanomethanide; [FAP], trifluorotris(pentafluoroethyl)phosphate; [DEP], diethyl phosphate; [MP], hydrogen methylphosphonate; [C1SO4], methyl sulfate; [C2SO4], ethyl sulfate; [NO3], nitrate; [SCN], thiocyanate; [Ac], acetate.

complex chemicals as ILs should involve a combination of several properties, e.g., selectivity + viscosity + melting point, as proposed very recently by Song et al.25 That is definitely true, nevertheless the primary goal of this contribution was to check robustness and reliability of a specific model published previously.24 Unfortunately, a great majority of authors do not follow this pathusually, some more or less interesting empirical structure−property relationships are published and not developed or applied/tested in subsequent works. Of course, the next step of this research should involve real fuel or some mixtures simulating it to evaluate the actual efficiency and usefulness of the proposed ILs in real extractive desulfurization and related processes. We believe that this study will be perceived by the scientific community dealing with ILs as a significant achievement in “collaboration” of chemical engineering and/or thermodynamics with artificial intelligence tools, which may open many new paths of possible applications of machine-learning algorithms in developing other modern (“greener” thus cleaner) separation processes and technologies.

theless, the synthesized and characterized ILs take four out of the first seven positions in the ranking shown with [C3CNC1Pyr][SCN] posing as a very promising extractant. The ILs with higher maximum selectivity were 1,3-dimethylimidazolium hydrogen methylphosponate [C1C1Im][MP] and [C2C1Im][SCN] proposed and investigated from the point of view of desulfuriaztion capabilities by Kȩdra-Królik et al.33 However, it should be stressed that most of the data presented in Figures 6 and 7 were determined at temperatures lower than T = 308.15 K, including those measured and published for the two mentioned “competitive” ILs reported in ref 33. An increase in temperature to T = 308.15 K, at which the data presented in this paper were collected, would result in a shift of the reference Smax 23 data at T = 298.15 K or T = 303.15 K toward lower values. Therefore, if an effect of temperature is taken into account, one can speculate that in silico-designed ILs described in this work may be perceived as the most promising candidates for the novel solvents for extractive removal of thiophene from n-heptane, at least in terms of Smax 23 .

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CONCLUSIONS The idea of CAMD of cations/anions forming ILs interesting from the point of view extractive removal of sulfur compounds from model gasolines was presented, discussed, applied, and finally verified by syntheses and measurements. The most important and encouraging result of this work is that the ILs designed by employing purely empirical correlation of γ∞ data based on GCs and the LSSVM method have turned out to be in fact the extraction solvents exhibiting the highest thiophene/nheptane selectivity among the other ILs consisting of a variety of ions reported in the literature so far. One can argue that the proposed optimization was based on optimization of a single benchmark property only, whereas a detailed CAMD of such

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acssuschemeng.7b01932. Table S1: Gas chromatograph setup used in experimental determination of LLE tie-lines. Table S2: Experimental data on density of the studied ILs as a function of temperature. Table S3: Experimental data on dynamic viscosity of the studied ILs as a function of temperature. Table S4: Experimental data on LLE tie line compositions of the studied ternary systems. Synthetic 9040


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(15) Diedenhofen, M.; Klamt, A. COSMO-RS as a Tool for Property Prediction of IL Mixtures − A Review. Fluid Phase Equilib. 2010, 294, 31−38. (16) Kumar, A. A. P.; Banerjee, T. Thiophene Separation with Ionic Liquids for Desulphurization: A Quantum Chemical Approach. Fluid Phase Equilib. 2009, 278, 1−8. (17) Anantharaj, R.; Banerjee, T. COSMO-RS-Based Screening of Ionic Liquids as Green Solvents in Denitrification Studies. Ind. Eng. Chem. Res. 2010, 49, 8705−8725. (18) Anantharaj, R.; Banerjee, T. COSMO-RS Based Predictions for the Desulphurization of Diesel Oil Using Ionic Liquids: Effect of Cation and Anion Combination. Fuel Process. Technol. 2011, 92, 39− 52. (19) Anantharaj, R.; Banerjee, T. Fast Solvent Screening for the Simultaneous Hydrodesulfurization and Hydrodenitrification of Diesel Oil Using Ionic Liquids. J. Chem. Eng. Data 2011, 56, 2770−2785. (20) Devi Wilfred, C.; Man, Z.; Phak Chan, Z. Predicting Methods for Sulfur Removal from Model Oils Using COSMO-RS and Partition Coefficient. Chem. Eng. Sci. 2013, 102, 373−377. (21) Gao, S.; Chen, X.; Abro, R.; Abdeltawab, A. A.; Al-Deyab, S. S.; Yu, G. Desulfurization of Fuel Oil: Conductor-like Screening Model for Real Solvents Study on Capacity of Ionic Liquids for Thiophene and Dibenzothiophene. Ind. Eng. Chem. Res. 2015, 54, 9421−9430. (22) Song, Z.; Zhou, T.; Zhang, J.; Cheng, H.; Chen, L.; Qi, Z. Screening of Ionic Liquids for Solvent-Sensitive Extraction with Deep Desulfurization as an Example. Chem. Eng. Sci. 2015, 129, 69−77. (23) Paduszyński, K. An overview of performance of COSMO-RS approach in predicting activity coefficients of molecular solutes in ionic liquids and derived properties at infinite dilution. Phys. Chem. Chem. Phys. 2017, 19, 11835−11850. (24) Paduszyński, K. In Silico Calculation of Infinite Dilution Activity Coefficients of Molecular Solutes in Ionic Liquids: Critical Review of Current Methods and New Models Based on Three Machine Learning Algorithms. J. Chem. Inf. Model. 2016, 56, 1420−1437. (25) Song, Z.; Zhou, T.; Qi, Z.; Sundmacher, K. Systematic Method for Screening Ionic Liquids as Extraction Solvents Exemplified by an Extractive Desulfurization Process. ACS Sustainable Chem. Eng. 2017, 5, 3382−3389. (26) Alonso, L.; Arce, A.; Francisco, M.; Soto, A. Thiophene Separation from Aliphatic Hydrocarbons Using the 1-Ethyl-3Methylimidazolium Ethylsulfate Ionic Liquid. Fluid Phase Equilib. 2008, 270, 97−102. (27) Alonso, L.; Arce, A.; Francisco, M.; Soto, A. Phase Behaviour of 1-Methyl-3-Octylimidazolium Bis[Trifluoromethylsulfonyl]Imide with Thiophene and Aliphatic Hydrocarbons: The Influence of n-Alkane Chain Length. Fluid Phase Equilib. 2008, 263, 176−181. (28) Domańska, U.; Lukoshko, E. V.; Królikowski, M. Separation of Thiophene from Heptane with Ionic Liquids. J. Chem. Thermodyn. 2013, 61, 126−131. (29) Domańska, U.; Walczak, K.; Zawadzki, M. Separation of Sulfur Compounds from Alkanes with 1-Alkylcyanopyridinium-Based Ionic Liquids. J. Chem. Thermodyn. 2014, 69, 27−35. (30) Domańska, U.; Walczak, K.; Królikowski, M. Extraction Desulfurization Process of Fuels with Ionic Liquids. J. Chem. Thermodyn. 2014, 77, 40−45. (31) Domańska, U.; Walczak, K. Ternary Liquid-Liquid Equilibria for Mixtures of {Ionic Liquid + Thiophene or Benzothiophene + Heptane} at T = 308.15 K. J. Solution Chem. 2015, 44, 382−394. (32) Kȩdra-Królik, K.; Mutelet, F.; Moïse, J.-C.; Jaubert, J.-N. Deep Fuels Desulfurization and Denitrogenation Using 1-Butyl-3-Methylimidazolium Trifluoromethanesulfonate. Energy Fuels 2011, 25, 1559− 1565. (33) Kȩdra-Królik, K.; Fabrice, M.; Jaubert, J.-N. Extraction of Thiophene or Pyridine from n-Heptane Using Ionic Liquids. Gasoline and Diesel Desulfurization. Ind. Eng. Chem. Res. 2011, 50, 2296−2306. (34) Królikowski, M.; Walczak, K.; Domańska, U. Solvent Extraction of Aromatic Sulfur Compounds from n-Heptane Using the 1-Ethyl-3Methylimidazolium Tricyanomethanide Ionic Liquid. J. Chem. Thermodyn. 2013, 65, 168−173.

procedures for all the ILs studied in this work, including NMR spectra.(PDF) Full list of all cations and anions considered in the screening process and n-heptane/thiophene selectivity of each cation−anion combination predicted by using LSSVM model, as well as the data required to obtain Figure 6. (ZIP)

AUTHOR INFORMATION

Corresponding Author

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

Kamil Paduszyński: 0000-0003-2489-6983 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding for this research was provided by the Ministry of Science and Higher Education in the years 2015−2016 within the framework of the project “Iuventus Plus” No. 0347/IP3/ 2015/73.

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