**4. Predictive models based on LSER model coupled to a group contribution method**

Solvation model may be also used to set up correlation between thermodynamic properties and LSER parameters. Abraham et al. [41,42] reported mathematical correlations based on the general Abraham solvation parameter model for the gas-to-solvent, *KL*, and water-tosolvent, *P*, partition coefficients. Recently, [43-46] modified the Abraham solvation parameter model:

$$\begin{aligned} \text{Log}K\_{L} &= \mathbf{c}\_{\text{cation}} + \mathbf{c}\_{\text{anion}} + (\mathbf{e}\_{\text{cation}} + \mathbf{e}\_{\text{anion}}) \cdot \mathbf{E} + (\mathbf{s}\_{\text{cation}} + \mathbf{s}\_{\text{anion}}) \cdot \mathbf{S} + \\ &+ (\mathbf{a}\_{\text{cation}} + \mathbf{a}\_{\text{anion}}) \cdot \mathbf{A} + (\mathbf{b}\_{\text{cation}} + \mathbf{b}\_{\text{anion}}) \cdot \mathbf{B} + (\mathbf{l}\_{\text{cation}} + \mathbf{l}\_{\text{anion}}) \cdot \mathbf{L} \end{aligned} \tag{18}$$

$$\begin{aligned} \text{LogP} &= \mathbf{c}'\_{\text{cation}} + \mathbf{c}'\_{\text{anion}} + \left(\mathbf{e}'\_{\text{cation}} + \mathbf{e}'\_{\text{anion}}\right) \cdot \mathbf{E} + \left(\mathbf{s}'\_{\text{cation}} + \mathbf{s}'\_{\text{anion}}\right) \cdot \mathbf{S} \\ &+ \left(\mathbf{a}'\_{\text{cation}} + \mathbf{a}'\_{\text{anion}}\right) \cdot \mathbf{A} + \left(\mathbf{b}'\_{\text{cation}} + \mathbf{b}'\_{\text{anion}}\right) \cdot \mathbf{B} + \left(\mathbf{v}\_{\text{cation}} + \mathbf{v}\_{\text{anion}}\right) \cdot \mathbf{V} \end{aligned} \tag{19}$$

by rewriting each of the six solvent equation coefficients as a summation of their respective cation and anion contribution. The dependent variables in equations (18) and (19) are solutes descriptors as follows: **E** and **S** refer to the excess molar refraction in units of (cm3.mol-1)/10 and dipolarity/polarizability descriptors of the solute, respectively, **A** and **B**


**Table 3.** LSER descriptors of ionic liquids determined at 313.15 K.

376 Chromatography – The Most Versatile Method of Chemical Analysis

scales developed for polar molecular solvents.

dialkylimidazolium salts.

**contribution method** 

parameter model:

bromide [36], 1-butyl-3-methylimidazolium octyl sulfate and 1-ethyl-3-methylimidazolium tosylate [37], Triethylsulphonium bis(trifluoromethylsulfonyl)imide [38], 1-Methyl-3 ethylimidazolium bis(trifluorosulfonyl)-amide and 1.2-Dimethyl-3-ethylimidazolium bis(trifluorosulfonyl)-amide [39] were taken from the sources indicated. Poole & Poole [40] found that the system constants of LSER model for the room temperature ionic liquids fall into the range *e* = −0.62 to 0.86, *s* = 1.7–2.8, *a* = 2.1–7.3, *b* = 0–1.07, and *l* = 0.35–0.96. Compared with the scale of the polar organic solvents *e* = −0.60 to 0.82, *s* = 0.54–2.8, *a* = 0.28–5.50, *b* = 0– 4.8, and *l* = −0.21 to 0.98, we can see that both scales are similar indicating that the solvation properties for the room temperature ionic liquids are classical and fit quite well into the

The (c + lL) term gives information on the effect of cohesion of the ionic liquids on solute transfer from the gas phase. In general, the ionic liquids are cohesive solvents; they interact weakly via nonbonding and π-electrons (*r* system constant is zero) and are not much different to other polar non-ionic liquids. The ionic liquids are roughly as dipolar/polarizable as classical solvents. The hydrogen-bond basicity of the ionic liquid (*a*  system constants) are considerably larger than values obtained for non phases (0-2.1) [1]. The hydrogen-bond basicity of Ils depends on the anion grafted on the cation. ionic liquids can be slightly more hydrogen-bond basic than dimethyl sulfoxide and *N*methylpyrrolidinone, and are weak to moderate hydrogen-bond acids, similar to the aliphatic alcohols. From Table 3 and data collected in the reference [40], we can see that the hydrogen-bond acidity of the ionic liquids depends largely on the cation and is lower for the 1,3-dialkylimidazolium salts with an alkyl group at C-2 position than 1,3-

**4. Predictive models based on LSER model coupled to a group** 

Solvation model may be also used to set up correlation between thermodynamic properties and LSER parameters. Abraham et al. [41,42] reported mathematical correlations based on the general Abraham solvation parameter model for the gas-to-solvent, *KL*, and water-tosolvent, *P*, partition coefficients. Recently, [43-46] modified the Abraham solvation

cation anion cation anion cation anion

= ++ + + + + + + + ++

 + a a b b l l *KL ( )· ( )·*

cation anion cation anion cation anion

by rewriting each of the six solvent equation coefficients as a summation of their respective cation and anion contribution. The dependent variables in equations (18) and (19) are solutes descriptors as follows: **E** and **S** refer to the excess molar refraction in units of (cm3.mol-1)/10 and dipolarity/polarizability descriptors of the solute, respectively, **A** and **B**

*P ' ' ( ' ' )· ( ' ' )·*

Log c c e e s s

Log c c e e s s

cation anion cation anion cation anion

cation anion cation anion cation anion

a a b b v v

*( ' ' )· ( ' ' )· ( )·*= ++ + + + + + + + ++

*( )· ( )· ( )·*

**E S A BL** (18)

**E S A BV** (19)

are measures of the solute hydrogen-bond acidity and basicity, **V** is the McGowan volume in units of (cm3.mol-1)/100 and **L** is the logarithm of the gas-to-hexadecane partition coefficient at 298 K. Sprunger et al. calculated equation coefficients for 8 cations and 4 anions using a database that contained 584 experimental log *KL* and 571 experimental log *P* values. No loss in predictive accuracy was observed by separating the equation coefficients into individual cation-specific and anion-specific values. The major advantage of splitting the equation coefficients into individual cation-specific and anion-specific contributions is that one can make predictions for more ILs. In Sprunger's approach, the major advantage of splitting the equation coefficients into individual cation-specific and anion-specific contributions is that one can make predictions for more Ils. Most of the cations are alkylimidazolium. The use of this model is somewhat limited since it can not be extrapolated to alkylimidazolium ionic liquids not initially defined by the method (e.g. with long alkyl chains).

The Use of Solvation Models in Gas Chromatography 379

− − N . Nine groups are used for

<sup>6</sup> PF ,

2 CN N .

<sup>2</sup> TF N , hexafluorophosphate: <sup>−</sup>

imidazolium based ionic liquids, 3 ammonium, 3 pyridinium and 4 pyrolidinium based ionic liquids. The authors also add sulphonium and phosphonium ionic liquids although only one set of *KL* (or *P*) data may be found for these families. The twenty one groups which are defined in this method are listed in Table 4. The decomposition into groups of the ionic liquids is very easy, that is as simple as possible. No substitution effects are considered. No exceptions are defined. In Figure 3 are represented all ionic liquids studied in this work. Five groups are defined to describe the chains R1, R2, R3 and R4 grafted on the cation: CH3, CH2, -O-, -O-Ncycl and –OH. These groups allow the calculation of partition coefficients of alkyl based ionic liquids but also functionalized ionic liquids such as ether, alcohols. The remaining seven groups are: CH2cyclic, CHcyclic, Ccyclic, Ncyclic, N+ (ammonium cation), P+

> ⏐ − = N and

trifluoromethylsulfonate : <sup>−</sup> CF SO3 3 , trifluoroacetate : <sup>−</sup> ACF3 and dicyanamide: ( ) <sup>−</sup>

As an example, let's have a look at the decomposition of 1-butyl-3-methylimidazolium hexafluorophosphate. In this case, the decomposition of the molecule into elementary groups is: 2 group 1 (-CH3) + 3 group 2 (-CH2) + 3 group 7 ( Ccyclic) + 2 group 9 (Ncyclic) + 1

> N+ R1

R2

Imidazolium Pyridinium Pyrolidinium

P + R4 R1 R3 R2

Ammonium Phosphonium Sulphonium

Group contribution model coupled to LSER (GC-LSER) for estimating the gas-to-ionic liquids partition coefficients and water-to-ionic liquids partition coefficients allows to predict with good accuracy Log *KL* and Log *P* at 298 K of not only alkyl based ionic liquids but also functionalized ionic liquids. The parameters of the group contribution methods were determined for imidazolium, pyridinium, pyrrolidinium, phosphonium, ammonium and sulphonium based ionic liquids containing several different anions. A comparison between the experimental and calculated values showed that the proposed models describe

⏐

<sup>4</sup> EtSO , octylsulfate: <sup>−</sup> OcSO4 , thiocyanate: <sup>−</sup> SCN ,

S + R1

N+ R1 R2

R2 R3

(phosphonium cation) and S+ (sulphonium cation).

More precisely, Ncyclic represents two structures: <sup>+</sup>

tetrafluoroborate: <sup>−</sup>

).

**Figure 3.** Cation of six families of ionic liquids.

N+ R4 R1 R3 R2

N N+ R1 R2 R3

group 14 (PF6-

anions: bis(trifluoromethylsulfonyl)imide :( ) <sup>−</sup>

<sup>4</sup> BF , ethylsulfate: <sup>−</sup>

In the development of Mutelet et al. [47], the cation with its alkyl chains is splitted in different contributions: (CH3, CH2, N, CHcyclic…). The approach allows to have a predictive model. The aim of this work was to develop a group contribution method allowing to estimate the log *KL* and Log *P* of organic compounds in ionic liquids at 298 K. Using the LSER model proposed by Abraham, the group contribution method expresses LSER coefficients ci, ei, si, ai, bi and li of equation (19). or ' <sup>i</sup> <sup>c</sup> , ' <sup>i</sup> <sup>e</sup> , ' <sup>i</sup> <sup>s</sup> , ' <sup>i</sup> <sup>a</sup> , ' <sup>i</sup> b and i v of equation (20) by:

$$\begin{aligned} \text{LogK}\_{\text{L}} &= \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{c}\_{\text{i}} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{e}\_{\text{i}} \cdot \mathbf{E} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{s}\_{\text{i}} \cdot \mathbf{S} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{a}\_{\text{i}} \cdot \mathbf{A} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{b}\_{\text{i}} \cdot \mathbf{B} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{l}\_{\text{i}} \cdot \mathbf{L} \\ \text{LogP} &= \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{c}\_{\text{i}} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{e}\_{\text{i}} \cdot \mathbf{E} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{s}\_{\text{i}} \cdot \mathbf{S} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{a}\_{\text{i}} \cdot \mathbf{A} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{b}\_{\text{i}} \cdot \mathbf{B} + \sum\_{\text{i}}^{21} \mathbf{n}\_{\text{i}} \times \mathbf{v}\_{\text{i}} \cdot \mathbf{V} \end{aligned} \tag{20}$$

Where ni is the number of group i present in the ionic liquid.

Mutelet et al. [47] proposed to extend the temperature dependent GC-LSER in view of determining the partition coefficient of organic compounds in ionic liquids. The GC-LSER can be rewriting as followed:

$$\text{LogK}\_{\text{L}} = \text{const} + \frac{\sum\_{i}^{21} \mathbf{n}\_{i} \times \mathbf{c}\_{i} + \sum\_{i}^{21} \mathbf{n}\_{i} \times \mathbf{e}\_{i} \cdot \mathbf{E} + \sum\_{i}^{21} \mathbf{n}\_{i} \times \mathbf{a}\_{i} \cdot \mathbf{A} + \sum\_{i}^{21} \mathbf{n}\_{i} \times \mathbf{b}\_{i} \cdot \mathbf{B} + \sum\_{i}^{21} \mathbf{n}\_{i} \times \mathbf{l}\_{i} \cdot \mathbf{L}}{\text{T}} \tag{21}$$

The experimental data used to calculate Abraham's model ion-specific equation coefficients were taken from the collection of [43-46] and were updated with recent data. A total of 1450 gas-liquid partition coefficients and 1410 water-to-liquid partition coefficients were used for the calculation. Solutes were mainly n-alkanes, cycloalkanes, alkenes, alkynes, aromatics, alcohols, ethers, aldehydes, ketones, chloroalkanes. The *E*-scale varies from 0 to 1.5, the *S*scale from 0 to 1.72, the *A*-scale from 0 to 1.04, the *B*-scale from 0 to 1.28, the *L*-scale from – 1.200 to 7.833 and the *V*-scale from 0.109 to 1.799. The dataset is composed of 27 imidazolium based ionic liquids, 3 ammonium, 3 pyridinium and 4 pyrolidinium based ionic liquids. The authors also add sulphonium and phosphonium ionic liquids although only one set of *KL* (or *P*) data may be found for these families. The twenty one groups which are defined in this method are listed in Table 4. The decomposition into groups of the ionic liquids is very easy, that is as simple as possible. No substitution effects are considered. No exceptions are defined. In Figure 3 are represented all ionic liquids studied in this work. Five groups are defined to describe the chains R1, R2, R3 and R4 grafted on the cation: CH3, CH2, -O-, -O-Ncycl and –OH. These groups allow the calculation of partition coefficients of alkyl based ionic liquids but also functionalized ionic liquids such as ether, alcohols. The remaining seven groups are: CH2cyclic, CHcyclic, Ccyclic, Ncyclic, N+ (ammonium cation), P+ (phosphonium cation) and S+ (sulphonium cation).

More precisely, Ncyclic represents two structures: <sup>+</sup> ⏐ − = N and ⏐ − − N . Nine groups are used for anions: bis(trifluoromethylsulfonyl)imide :( ) <sup>−</sup> <sup>2</sup> TF N , hexafluorophosphate: <sup>−</sup> <sup>6</sup> PF , tetrafluoroborate: <sup>−</sup> <sup>4</sup> BF , ethylsulfate: <sup>−</sup> <sup>4</sup> EtSO , octylsulfate: <sup>−</sup> OcSO4 , thiocyanate: <sup>−</sup> SCN , trifluoromethylsulfonate : <sup>−</sup> CF SO3 3 , trifluoroacetate : <sup>−</sup> ACF3 and dicyanamide: ( ) <sup>−</sup> 2 CN N . As an example, let's have a look at the decomposition of 1-butyl-3-methylimidazolium hexafluorophosphate. In this case, the decomposition of the molecule into elementary groups is: 2 group 1 (-CH3) + 3 group 2 (-CH2) + 3 group 7 ( Ccyclic) + 2 group 9 (Ncyclic) + 1 group 14 (PF6- ).

**Figure 3.** Cation of six families of ionic liquids.

378 Chromatography – The Most Versatile Method of Chemical Analysis

coefficients ci, ei, si, ai, bi and li of equation (19). or '

Where ni is the number of group i present in the ionic liquid.

long alkyl chains).

can be rewriting as followed:

L

= +

by:

are measures of the solute hydrogen-bond acidity and basicity, **V** is the McGowan volume in units of (cm3.mol-1)/100 and **L** is the logarithm of the gas-to-hexadecane partition coefficient at 298 K. Sprunger et al. calculated equation coefficients for 8 cations and 4 anions using a database that contained 584 experimental log *KL* and 571 experimental log *P* values. No loss in predictive accuracy was observed by separating the equation coefficients into individual cation-specific and anion-specific values. The major advantage of splitting the equation coefficients into individual cation-specific and anion-specific contributions is that one can make predictions for more ILs. In Sprunger's approach, the major advantage of splitting the equation coefficients into individual cation-specific and anion-specific contributions is that one can make predictions for more Ils. Most of the cations are alkylimidazolium. The use of this model is somewhat limited since it can not be extrapolated to alkylimidazolium ionic liquids not initially defined by the method (e.g. with

In the development of Mutelet et al. [47], the cation with its alkyl chains is splitted in different contributions: (CH3, CH2, N, CHcyclic…). The approach allows to have a predictive model. The aim of this work was to develop a group contribution method allowing to estimate the log *KL* and Log *P* of organic compounds in ionic liquids at 298 K. Using the LSER model proposed by Abraham, the group contribution method expresses LSER

= ×+ × + × + × + × + ×

ii ii ii ii i i i i

Mutelet et al. [47] proposed to extend the temperature dependent GC-LSER in view of determining the partition coefficient of organic compounds in ionic liquids. The GC-LSER

LogK n c n e · n s · n a · n b · n l ·

21 21 21 21 21 21 L i i i i i i i i i i ii ii i i i i <sup>21</sup> <sup>21</sup> <sup>21</sup> <sup>21</sup> <sup>21</sup> <sup>21</sup> '' ' ' '

= ×+ × + × + × + × + ×

LogP n c n e · n s · n a · n b · n v ·

ii i i i i

<sup>i</sup> <sup>c</sup> , ' <sup>i</sup> <sup>e</sup> , ' <sup>i</sup> <sup>s</sup> , ' <sup>i</sup> <sup>a</sup> , '

**ESA B L**

**ESA B V**

× + × ⋅+ × ⋅ + × ⋅+ ×⋅

n c n eE n aA n bB n lL

i i i i i i i i ii

 21 21 21 21 21

ii i i i

LogK const T (21)

The experimental data used to calculate Abraham's model ion-specific equation coefficients were taken from the collection of [43-46] and were updated with recent data. A total of 1450 gas-liquid partition coefficients and 1410 water-to-liquid partition coefficients were used for the calculation. Solutes were mainly n-alkanes, cycloalkanes, alkenes, alkynes, aromatics, alcohols, ethers, aldehydes, ketones, chloroalkanes. The *E*-scale varies from 0 to 1.5, the *S*scale from 0 to 1.72, the *A*-scale from 0 to 1.04, the *B*-scale from 0 to 1.28, the *L*-scale from – 1.200 to 7.833 and the *V*-scale from 0.109 to 1.799. The dataset is composed of 27

<sup>i</sup> b and i v of equation (20)

(20)

Group contribution model coupled to LSER (GC-LSER) for estimating the gas-to-ionic liquids partition coefficients and water-to-ionic liquids partition coefficients allows to predict with good accuracy Log *KL* and Log *P* at 298 K of not only alkyl based ionic liquids but also functionalized ionic liquids. The parameters of the group contribution methods were determined for imidazolium, pyridinium, pyrrolidinium, phosphonium, ammonium and sulphonium based ionic liquids containing several different anions. A comparison between the experimental and calculated values showed that the proposed models describe the experimental data available with a mean absolute error of about 0.15 log unit. While the model is probably somewhat limited in prediction for pyridinium and pyrrolidinium based ionic liquids because of the poor dataset for these cations, results obtained are satisfactory.

The Use of Solvation Models in Gas Chromatography 381

The solvation parameter model is suitable for describing the retention properties of molecules in chromatographic systems. To establish the system properties requires identification of a group of compounds with well known descriptor values. We have shown that all LSER parameters of solutes may be determined using gas chromatography or experimental techniques. The solvation model may be used either for the physico-chemical characterization of the stationary phases or for the establishment of a suitable quantitative structure–property relationship to facilitate the prediction of further system properties for

*Laboratoire Réactions et Génie des Procédés (CNRS, UPR 3349), Ecole Nationale Supérieure des* 

[1] Poole, C.F. Chromatographic and spectroscopic methods for the determination of solvent properties of room temperature ionic liquids. Journal of Chromatography A

[2] Mutelet, F. & Rogalski, M. Experimental determination and prediction of the gas-liquid

[3] Russom, C.L.; Breton, R.L.; Walker, J.D.; Bradury, S.P. An overview of the use of quantitative structure-activity relationships for ranking and prioritizing large chemical inventories for environmental risk assessments Environ. Toxicol. Chem. 2003; 22 1810-

[4] Katritzky, A.R.; Maran, U.; Lobonov, V.S.; Karelson, M. Structurally Diverse Quantitative Structure-Property Relationship Correlations of Technologically Relevant

[5] Abraham, M. H.; Grellier, P. L. & Mc Gill R.A. Determination of Olive Oil-Gas and Hexadecane-Gas Partition Coefficients, and calculation of the corresponding Olive Oil-Water and Hexadecane-Water Partition Coefficients. J. Chem. Soc. PERKIN TRANS II

[6] Vitha, M. & Carr, P.W. (2006). The chemical interpretation and practice of linear solvation energy relationships in chromatography. Journal of Chromatography A 2006;

[7] Abraham, M.H., Poole, C.F. & Poole, S.K. Classification of stationary phases and other materials by gas chromatography Journal of Chromatography A, 1999; 842 79-114. [8] Kamlet, M.J.; Abboud, J.L. & Taft, R.W. (1977). The solvatochromic comparison method. 6. The π scale of solvent polarities. Journal of the American Chemical Society 1977; 18

n-hexadecane partition coefficients J. Chromatogr. A 2001; 923 153-163.

Physical Properties J. Chem. Inf. Comput. Sci. 2000; 40 1-18.

**5. Conclusion** 

**Author details** 

Fabrice Mutelet

**6. References** 

1821.

1987; 797-803.

1126 143-194.

(99) 6027-6038.

2004; 1037 49-82.

compounds lacking experimental values.

*Industries Chimiques, Nancy CEDEX, France* 


**Table 4.** Description of the 21 groups used for the estimation of LogKL and LogP.
