Temperature-Dependent Linear Solvation Energy Relationship for the Determination of Gas-Liquid Partition Coefficients of Organic Compounds in Ionic Liquids

*Amel Ayad, Fabrice Mutelet and Amina Negadi*

## **Abstract**

In this work, a new group contribution method was used for calculating gas-to-ionic liquid partition coefficients (log *KL*) of molecular solutes in ILs with a temperature-dependent linear solvation energy relationship. About 36 group parameters are used to correlate 14,762 log KL data points of organic compounds in ionic liquids. The experimental log *KL* data have been collected from the published literature for different solutes in ionic liquids at different temperatures within the range of 293.15–396.35 K. The calculated log *KL* data showed a satisfactory agreement with experimental data with an average absolute relative deviation (AARD) of 6.39%.

**Keywords:** inverse gas chromatography, solvation model, thermodynamic properties, ionic liquids, polarity

## **1. Introduction**

Gas chromatography is a widely used technique for the characterization of complex systems in chemical industries but also for the determination of physicochemical properties of solute in the stationary phase. This approach is also known as inverse gas chromatography (IGC) is used to quantify the solute-stationary interactions or the polarity of the last one. At the end of the twentieth century, numerous solvation models were proposed to represent retention data from chromatography. The most well-known models are called Linear Free Energy Relationship (LFER) or Linear Solvation Energy Relationship (LSER). The most recent representation of the LSER model proposed by Abraham [1–4] is given by Eq. (1).

$$\text{logSP} = \text{c} + \text{eE} + \text{sS} + \text{aA} + \text{bB} + \text{lL} \tag{1}$$

Where SP is a solvation parameter related with the free energy change such as gas–liquid partition coefficient, specific retention volume, or adjusted retention

time at a given temperature. The capital letters represent the solutes properties and the lowercase letters the complementary properties of the ionic liquids. The solute descriptors are the excess molar refraction *E*, dipolarity/polarizability *S*, hydrogen bond acidity basicity, *A* and *B*, respectively, and the gas–liquid partition coefficient on n-hexadecane at 298 K, *L*. The solute descriptors may be determined using inverse gas chromatography or estimated using a group contribution method. A databank of descriptors for about 4000 compounds may be found in the literature [5–7]. The coefficients c, e, s, a, b, and l are not simply fitting coefficients, but they reflect complementary properties of the solvent phase. These coefficients are determined by multiple linear regression of Eq. (1). This model was strongly applied to characterize complex fluids.

A large databank of experimental LSER parameters for organic compounds can be found in the literature. Platts et al. proposed to determine these parameters using group contribution methods [5, 6].

In order to improve the predictive applicability of the Abraham model for ionic liquids, Sprunger et al. [8–11] have proposed a method for predicting log *KL* for solute dissolved in ILs by splitting each of the six equation coefficients as a cation plus anion sum contribution. In their paper, the gas–liquid partition of solutes in ILs is represented by:

$$\begin{aligned} \log \mathbf{K}\_{\text{L}} &= (\mathbf{c}\_{\text{KL}, \text{ cation}} + \mathbf{c}\_{\text{KL}, \text{ anion}}) + (\mathbf{e}\_{\text{KL}, \text{cation}} + \mathbf{e}\_{\text{KL}, \text{ anion}}), \mathbf{E} \\ &+ (\mathbf{s}\_{\text{KL}, \text{ cation}} + \mathbf{s}\_{\text{KL}, \text{ anion}}).\mathbf{S} + (\mathbf{a}\_{\text{KL}, \text{ cation}} + \mathbf{a}\_{\text{KL}, \text{ anion}}).\mathbf{A} \\ &+ (\mathbf{b}\_{\text{KL}, \text{ cation}} + \mathbf{b}\_{\text{KL, anion}}).\mathbf{B} + (\mathbf{l}\_{\text{KL}, \text{ cation}} + \mathbf{l}\_{\text{KL}, \text{ anion}}).\mathbf{L} \end{aligned} \tag{2}$$

Other approaches reported in the literature to calculate log KL are based on group contribution methods (GC). This method is useful because we need only to know the structure of the material (IL). Revelli et al. [12] proposed to splits the cation with its alkyl chains into 21 different contributions to estimate log *KL* for other IL whose cation does not define in the correlation but their groups appear in this method. A new approach was developed by Mutelet et al. [13] who proposed temperaturedependent GC-LSER (TDGC-LSER) for correlating log *KL* data measured of various solutes in ILs at different temperatures. A reliable prediction was obtained with a standard deviation of 0.13 log units and a coefficient of determination *R*<sup>2</sup> of 0.995. To evaluate the predictive capacity of this model, Mutelet et al. have been used data from five ILs not included in the regression. The deviations vary from 0.09 log units and 0.27 log units depending on the number of data for the groups defined by the IL. The TDGC-LSER model is given by the following equation:

$$\begin{aligned} \log K\_L &= -2.84418 + \sum\_{i}^{21} n\_i c\_i + \sum\_{i}^{21} n\_i e\_i \mathbf{E} + \sum\_{i}^{21} n\_i s\_i \mathbf{S} + \sum\_{i}^{21} n\_i a\_i \mathbf{A} + \sum\_{i}^{21} n\_i b\_i \mathbf{B} \\ &+ \sum\_{i}^{21} n\_i l\_i \mathbf{L}/T \end{aligned} \tag{3}$$

In this chapter, we propose to extend the model temperature-dependent GC-LSER (TDGC-LSER) based on the group contribution method to correlate and analysis of log KL values for different solutes in ILs as a function of the temperature from 293.15 to 396.35 K. A new decomposition but also new groups are proposed in this approach. The database includes the alkyl-based ILs as well as functionalized ILs (task-specific ILs) such as alcohols and ethers. The largest number of ILs used in this database was composed of imidazolium cation-based ILs (73 ILs). Three new cations were included, choline, quinolinium, and octanium, each cation occurs only once in the database as well as Sulphonium-Based ILs.

*Temperature-Dependent Linear Solvation Energy Relationship for the Determination… DOI: http://dx.doi.org/10.5772/intechopen.102733*

## **2. Calculation of gas-liquid partition coefficients from inverse gas chromatography data**

Partition coefficients *KL* maybe then calculated from the activity coefficients at infinite dilution, *γ*<sup>∞</sup> 1,2, using Eq. (4):

$$K\_L = \frac{RT}{\eta\_{1,2}^{\infty} P\_1^0 V\_{solvent}}\tag{4}$$

## **3. Data sets and methodology**

The objective of this study is to extend the potential applicability of the TDGC-LSER model for the prediction of log *KL* to different ILs include new functional groups. The ILs used in this study and their abbreviations are listed in **Table 1**.



*Temperature-Dependent Linear Solvation Energy Relationship for the Determination… DOI: http://dx.doi.org/10.5772/intechopen.102733*



*Temperature-Dependent Linear Solvation Energy Relationship for the Determination… DOI: http://dx.doi.org/10.5772/intechopen.102733*


**Table 1.**

*Names and abbreviations of ionic liquids.*

**Figure 1.** *Number of cation-based ILs used for the prediction of log* KL*.*

The families of ILs represent 11 cation types are imidazolium, pyridinium, pyrrolidinium, piperidinium, phosphonium, morpholium, sulphonium, ammonium, choline, quinolinium, octanium. From **Figure 1**, we can see ILs with respect to their cations used for the correlation of log *KL*. The largest number of ILs used in this database was composed of imidazolium cation-based ILs. Three new cations were included, choline, quinolinium, and octanium. For the anions, 20 different structures are used, for example tris(pentafluoroethyl)trifluorophosphate, nitrate, bis(trifluoromethylsulfonyl)imide, hexafluorophosphate, tetrafluoroborate, and sulfates.

The collection of organic solutes includes alkanes, cycloalkanes, alkenes, alkynes, aromatics, alcohols, ethers, aldehydes, ketones, chloroalkanes cyanoalkanes, thiophene, pyridine, water, and other solutes. The values of the five solute descriptors for different organic compounds considered in this work can be found in the literature [1–6]. The solute descriptors used in the calculations were taken from earlier studies on ILs and cover the range from: *E* = �0.020 to *E* = 0.851, *S* = 0.000 to *S* = 0.950, *A* = 0.000 to *A* = 0.82, *B* = 0.000 to *B* = 0.79, *L* = 0.26 to *L* = 6.705. A databank containing 107 ILs corresponding to 14,762 experimental log *KL* were used for the development of the model. The 36 groups used for the representation of ILs are given in **Table 2**.


**Table 2.**

*Description of the 36 groups used for the estimation of log* KL*.*

## **4. Results and discussion**

In the present study, the database contains 14,762 experimental data for about 107 ILs at the temperature range of 293.15–396.35 K, the main objective of this study is to extend the predictive applicability of the TDGC-LSER model to a new cation and anion based ILs, that have not been reported previously, as the ILs having cyano-based anions (thiocyanate [SCN]─; dicyanamide, [N(CN)2] ─; tricyanomethanide, [C(CN)3] ─ and perfluorinated anions (e.g. trifluorotris(perfluoroethyl) phosphate, [FAP]). The model adopted in this work is capable of representing log *KL* over a wide range of temperatures. The quality of regression analysis was determined by calculating the average absolute relative deviation (AARD) defined as follows:

$$AARD\left(\log K\_L\right) = \frac{1}{N} \sum\_{i=1}^{N} \left| \frac{\log \mathbf{K}\_L^{cal} - \log \mathbf{K}\_L^{cap}}{\log \mathbf{K}\_L^{cap}} \right| \times 100\tag{5}$$

The TDGC-LSER model may represent the partition coefficient of solutes in ILs using the Eq. 6:

$$\log K\_L = -3.1729 + \sum\_{i}^{36} n\_i c\_i + \sum\_{i}^{36} n\_i c\_i \mathbf{E} + \sum\_{i}^{36} n\_i \mathbf{s}\_i \mathbf{S} + \sum\_{i}^{36} n\_i a\_i \mathbf{A} + \sum\_{i}^{36} n\_i b\_i \mathbf{B} + \sum\_{i}^{36} n\_i l\_i \mathbf{L}/T \tag{6}$$

### *Temperature-Dependent Linear Solvation Energy Relationship for the Determination… DOI: http://dx.doi.org/10.5772/intechopen.102733*

Where ni is the number of group i present in the ionic liquid. Values of ci, ei, si, ai, bi, and li and their standard errors in parentheses are given in **Table 3**.

The experimental log KL data for all ILs were reproduced using Eq. (6) with average absolute deviation (AARD) at the level of 6.39%. The model developed is statistically good, and describes the experimental log *KL* to within a standard deviation of 0.134 log units, squared correlation coefficient *R*<sup>2</sup> = 96.9%, and a Fisher's *F* statistic *F* = 2106.87.



#### **Table 3.**

*TDGC-LSER coefficients for the calculation of log* KL*.*

The average absolute deviation AARD *<sup>γ</sup>*<sup>∞</sup> <sup>ð</sup> ) on the prediction of activity coefficients at infinite dilution *γ*<sup>∞</sup> for each IL considered in this study are determined by the following equation:

$$AARD(\chi^{\circ \circ}) = \frac{1}{N} \sum\_{i=1}^{N} \left| \frac{\chi\_{cal}^{\circ \circ} - \chi\_{exp}^{\circ \circ}}{\chi\_{exp}^{\circ \circ}} \right| \times \mathbf{100} \tag{7}$$

The AARD values on the prediction of log *KL* and *γ*<sup>∞</sup> for each IL considered in this work are reported in **Table 4**.

The values obtained for each ILs vary from 0.87 to 35.41%. **Figure 2** shows a plot of calculated log *KL* from TDGC-LSER versus experimental log KL for 107 ILs. The derived equation provides a good description of solute transfer into cyano-based anion such as [BMIM]<sup>+</sup> [C(CN)3] �, [BMPY]+ [C(CN)3] �, [BMPYR]<sup>+</sup> [C(CN)3] � for which the values of AARD are at the level of about 3% except for [BMMOR]+


*Temperature-Dependent Linear Solvation Energy Relationship for the Determination… DOI: http://dx.doi.org/10.5772/intechopen.102733*


#### **Table 4.**

*Average absolute deviation for the ionic liquids that are used in this study.*

#### **Figure 2.**

*Comparison of calculated log KL values based on Eq. (6) versus experimental data.*

[C(CN)3] � with AARD of 5.94%. For the IL [HMIM]<sup>+</sup> [Tf2N]� the AARD was less than 1%. The same all piperidinium cation-based ILs studied in this work have a small AARD lower than 4%.

*Temperature-Dependent Linear Solvation Energy Relationship for the Determination… DOI: http://dx.doi.org/10.5772/intechopen.102733*

The ILs with the highest AARD are [MMIM]<sup>+</sup> [MeSO4] �, [PM2IM]<sup>+</sup> [BF4] �, [BMIM]<sup>+</sup> [NO3] �, [OMIM]<sup>+</sup> [NO3] �, This may be related to the quality of the experimental data or the number of experimental data.

## **5. Prediction of partition coefficients of organic compounds in ILs not included in the database using the TDGC-LSER model**

The predictive power of TDGC-LSER was evaluated calculating log KL of organic compounds in four ILs not included in the database: 1-butyl-3-methylimidazolium chloride [BMIM]<sup>+</sup> [Cl]─ [76], 1-butyl-3-methylimidazolium dimethyl phosphate [BMIM]<sup>+</sup> [(CH3)2PO4] ─ [76], 1-butyl-3-methylimidazolium dicyanamide [BMIM]+ [N(CN)2] ─ [77], 1-Dodecyl-3-methylimidzolium Bis(trifluoromethylsulfonyl) imide [DoMIM]<sup>+</sup> [Tf2N]─ [78]. In the case of [BMIM]<sup>+</sup> [Cl]─, 224 experimental log *KL* values were predicted using the TDGC-LSER model. The difference between the calculated values and the experimental data is significant since it reaches 44.8%. In the case of alkanes, this difference is greater than 100% (for cyclopentane (173.24) and ethyl tert-butyl ether (120.38) at *T* = 358.15 K). The poor performance of the model can be explained by the limited number of experimental data containing the group [Cl]─. In addition, this ionic liquid is particularly hydrophilic and can therefore contain significant amounts of water. This presence of water can have a significant impact on the physicochemical properties of this ionic liquid. For [BMIM]<sup>+</sup> [(CH3)2PO4] ─, the AARD of log *KL* is 17.84%. The results indicate that the model correctly predicts the partition coefficients of aromatics, methanol, and ethanol. The log *KL* values of alkanes and ethers are underestimated. This can be explained by the low solubility of alkanes in the ILs and also the limited number of ethers in the database. The AARD observed with [BMIM]<sup>+</sup> [N(CN)2] ─ for the log *KL* prediction of 378 solutes is 19.78%. The TDGC-LSER model provides a good description for alkenes, alkynes, aromatic hydrocarbons (o-xylene about 4.72% at *T* = 318.15), alcohols, and ketones (acetone about 5.13% at 348.15 K). For most alkanes, the log *KL* values are underestimated, in particular for pentane (109.32% at 338.15 K), 2.2-dimethylbutane, 2.2.4-triethylpentane and cyclopentane. [DoMIM]<sup>+</sup> [Tf2N]─ contains a long alkyl chain grafted onto the imidazolium cation. 284 experimental log *KL* values were estimated using the TDGC-LSER model. The correlation provides a good description of the experimental log *KL* data (AARD = 15.77%). This result is important as it shows that the model can be used to predict solute partition coefficients in ILs not taken into account in the database. The model provides a good description for polar solutes such as aromatics (benzene 4.46% at *T* = 318.15 K) and alcohols. The most significant differences are observed for the ethers (tert-butyl methyl ether, Diethyl ether, Di-n-propyl ether, Di-iso-propyl ether).

## **6. Conclusions**

The TDGC-LSER model was used for the prediction of log *KL* for 107 ILs over a wide range of temperatures. A new set of cation and anion functional groups have been used to define the structures of the ionic liquids. The obtained correlation allows reproduce the experimental gas-to-ionic liquid partition coefficients derived from *γ*<sup>∞</sup> with satisfactory accuracy to within 0.134 log units and AARD of 6.39%. The deviation between calculated and experimental log *KL* depends strongly on the cation and anion type.

The list of groups used for the estimation of calculated log *KL* in this work can be increased to improve the predictive applicability of this model to other functional groups by the additional *γ*<sup>∞</sup> data for families of a new generation of ionic liquids.

## **Author details**

Amel Ayad<sup>1</sup> , Fabrice Mutelet<sup>2</sup> \* and Amina Negadi<sup>1</sup>

1 Université de Tlemcen, Tlemcen, Algeria

2 Ecole Nationale Supérieure des Industries Chimiques Université de Lorraine, Nancy, France

\*Address all correspondence to: fabrice.mutelet@univ-lorraine.fr

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Temperature-Dependent Linear Solvation Energy Relationship for the Determination… DOI: http://dx.doi.org/10.5772/intechopen.102733*

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## *Edited by Fabrice Mutelet*

Gas chromatography is one of the most used analytical techniques in the industry. It is a powerful tool with a wide range of applications. This book presents recent advances in gas chromatography, multidimensional gas chromatography, and gas chromatography mass spectrometry. It also discusses inverse gas chromatography. The main focus is the use of gas chromatography techniques to analyze petroleum fluids, biomass, and ionic liquids in medical and petrochemical industries.

Published in London, UK © 2022 IntechOpen © kdsoo322 / iStock

Recent Advances in Gas Chromatography

Recent Advances in

Gas Chromatography

*Edited by Fabrice Mutelet*