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Int. J. Mol. Sci. 2010, 11(5), 1973-1990; doi:10.3390/ijms11051973

Article
The Solubility Parameters of Ionic Liquids
Department of Physical Chemistry, Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland
Received: 1 March 2010; in revised form: 21 April 2010 / Accepted: 22 April 2010 / Published: 27 April 2010

Abstract

:
The Hildebrand’s solubility parameters have been calculated for 18 ionic liquids from the inverse gas chromatography measurements of the activity coefficients at infinite dilution. Retention data were used for the calculation. The solubility parameters are helpful for the prediction of the solubility in the binary solvent mixtures. From the solubility parameters, the standard enthalpies of vaporization of ionic liquids were estimated.
Keywords:
ionic liquid; Hildebrand’s solubility parameter; standard enthalpy of vaporization

1. Introduction

Ionic liquids (ILs) have become the subject of an increasing number of investigations due to their unique properties such as wide liquid range, stability at high temperatures, no flammability and negligible vapor pressure. Ionic liquids as green solvents can be used in separation processes, synthesis, catalysis and electrochemistry, successfully replacing the conventional volatile, flammable and toxic organic solvents. Since the ILs have a negligible vapor pressure, the inverse gas chromatography (IGC) is a suitable method for measuring thermodynamic properties of pure substances and their mixtures [1]. From the retention data, the activity coefficients at infinite dilution, Flory-Huggins interaction parameters as well as the Hildebrand’s solubility parameters can be determined. Activity coefficients at infinite dilution are very important for calculations of selectivity and capacity of entrainers for the different separation problems, characterizing the behavior of liquid mixtures, estimation of mutual solubilities, fitting the excess molar energy (GE) model parameters (e.g., Wilson, NRTL, UNIQUAC), predicting the existence of an azeotrope, analytical chromatography, calculation of Henry constant and partition coefficients, development of thermodynamic models based on the group contribution methods such as mod. UNIFAC [2]. The values of the activity coefficients at infinite dilution for the investigated ionic liquids were published earlier [318].
The Hildebrand’s solubility parameters have numerous applications including gas-liquid solubility, solvent extraction and many others as described in detail in the literature [19,20]. Solubility parameters are available for only some of the ionic liquids determined by IGC [2124], intrinsic viscosity method [25] or estimated from Kamlet-Taft equation [26]. This paper provides information on the Hildebrand’s solubility parameters determined for 18 ionic liquids as a function of temperature and the standard enthalpies of vaporization calculated from the values of the solubility parameters.

2. Results and Discussion

The Hildebrand’s solubility parameters (δ2) were calculated for the ionic liquids presented (with abbreviations and structures) in Table 1. The solubility parameters show a slight dependence on the temperature, which was also observed by Mutelet et al. [2123]. The results are presented in Table 2 and are compared to results taken from the literature [2126].
The values of δ2 calculated using the IGC method are not consistent with those obtained by the intrinsic viscosity method or estimated from the Kamlet-Taft equation. For ionic liquid [bmim][CF3SO3] the values of δ2 are 22.67, 24.9 [25] and 25.4 [26] obtained by IGC, intrinsic viscosity method or estimated from Kamlet-Taft equation, respectively. For ionic liquid [hmim][NTf2] the difference is much greater, values of δ2 are 20.25 and 25.6 [25] for the IGC and intrinsic viscosity methods, respectively. It was found that values of δ2 determined using the IGC method by Mutelet et al. [2123] and Foco et al. [24] are also not consistent with those determined by the two methods mentioned above (Table 2). On the other hand, values obtained by different research groups by IGC are coherent as is shown in Figure 1. From Figure 1, it is obvious that for an ionic liquid of general cation formula [Rmim]+, the solubility parameter decreases with an increasing of the alkyl chain R. In the other words, the more aliphatic the cation character, the lower the solubility parameter. The slope of all three lines is similar – it confirms that the data are consistent (except for [emim][BF4] ionic liquid).
Figure 2 shows the anion influence on the solubility parameter for ionic liquids based on 1-alkyl-3-methyl-imidazolium cations [Rmim]+, 1-butyl-(3 or 4)-methyl-pyridinium [bmPY]+ and 1-butyl-1-methyl-pyrrolidinium [bmPYR]+ cations. The solubility parameter increases in the following order: [Cl] < [NTf2] < [CF3SO3] < [OcSO4] < [PF6] < [BF4] < [TOS] < [SCN] < [MDEGSO4] < [TFA]. The highest values of δ2 are for [BF4], [TOS], [SCN], [MDEGSO4] and [TFA] anions, whilst the lowest value is for the [Cl] anion.
Figure 3 shows influence of the cation structure on the solubility parameter for ionic liquids based on [SCN] and [CF3SO3] anions. The lowest values of δ2 are for butyl-methyl-pyridinium [bmPY]+ cations ([1,3bmPY][CF3SO3] and [1,4bmPY][SCN]).
The influence of the cation on the solubility parameter for the bis(trifluoromethylsulfonyl)-amide based ionic liquids ([NTf2]) is shown in Figure 4. The solubility parameter increases in the following order: [(C6OC)2im]+ < [hmim]+ < [C6OCmim]+ < [1,4bmPY]+ < [Et3S]+ < [emim]+. The difference in solubility parameters between [hmim]+ and [C6OCmim]+ cations are very small. It is caused by the similar structure of these two cations. The [C6OCmim]+ cation has an additional methoxy group (–O–CH2–) in the structure, which causes a little augmentation of δ2 value. From this figure, it can be concluded again that the solubility parameter is higher for the ionic liquids with less aliphatic character. It is also presented in Figure 1 and was mentioned previously.
Standard enthalpies of vaporization ΔvapH298.15 calculated according to equation 8 and molar volumes of ionic liquids necessary in enthalpy calculations are presented in Table 3, and are contrasted the results taken from the literature [2529]. The larger differences in values of enthalpies of vaporization are for ionic liquids based on the [SCN] anion. For ionic [bmim][CF3SO3] the difference is not so high: 22 and 13 kJ·mol−1 according to references [27] and [28], respectively. Due to the difference in solubility parameters, values of the enthalpies of vaporization calculated from data from references [25,26] are of course different and larger. For ionic liquid [1,4bmPY][NTf2] value of the enthalpy of vaporization is lower by 20 kJ·mol−1 than for that obtained by Deyko et al. [27]. A very good consistency in results of enthalpies of vaporization is found for [hmim][NTf2] ionic liquid. Result obtained from IGC measurements is only of about 2 and 4 kJ·mol−1 lower than for that obtained by Deyko et al. [27] and Zaitsau et al. [29], whilst the enthalpy of vaporization obtained from the solubility parameter determined by intrinsic viscosity method is much higher at of 216.4 kJ·mol−1 [25].

3. Calculation of Solubility Parameters

3.1. Experimental Procedure

The activity coefficients at infinite dilution for all investigated ionic liquids were measured using inverse gas chromatography. Detailed descriptions of materials, apparatus and methods used in each experiment are presented in the certain papers [318]. On the basis of the experimental data from the activity coefficients at infinite dilution measurements, the Hildebrand’s solubility parameters have been calculated using equations presented below.

3.2. Theoretical Basis

Retention data were used for the calculation of Hildebrand’s solubility parameters, δ2. According to the Flory-Huggins theory the interaction parameter at infinite dilution can be determined using the following expression:
χ 12 = ln ( 273.15 R P 1 * V g M 1 ) P 1 * ( B 11 V 1 * ) R T + ln ( ρ 1 ρ 2 ) ( 1 V 1 * V 2 * )
where R denotes the gas constant, T the temperature, P1* the saturated vapor pressure of the solute at temperature T, B11 the second virial coefficient of pure solute, V1* and V2* the molar volume of the solute and solvent respectively, M1 the molar mass of solute, ρ1 and ρ2 density of solute and solvent respectively, Vg specific retention volume which is given by:
V g = 273.15 V N T m 2
where m2 denotes the mass of the solvent on the column packing and VN the net retention volume of the solute given by:
V N = J 2 3 U o ( t R t G )
where tR and tG are the retention times for the solute and an unretained gas, respectively, Uo is the column outlet flow rate, J 2 3 the pressure correction term given by:
J 2 3 = 2 3 ( P i / P o ) 3 1 ( P i / P o ) 2 1
where Pi and Po denote the inlet and the outlet pressure, respectively.
The column outlet flow rate corrected for the vapor pressure of water Uo is given by:
U o = U ( 1 P w P o ) T T f
where Tf is the temperature of the flow meter, Pw is the vapor pressure of water at Tf and U is the flow rate measured with the bubble flow meter.
The interaction parameter χ 12 may be expressed as a function of δ1 and δ2 which denote the solubility parameters of the solute and of the solvent, respectively by:
χ 12 = V 1 * ( δ 1 δ 2 ) 2 R T
Equation 6 can be rewritten as:
( δ 1 2 R T χ 12 V 1 * ) = ( 2 δ 2 R T ) δ 1 δ 2 2 R T
The solubility parameters δ1 of the solutes were calculated using following equation:
δ 2 = Δ vap H R T υ
where ΔvapH denotes enthalpy of vaporization and υ the molar volume. Enthalpies of vaporization of solutes were taken from literature [35] and molar volumes were calculated from densities taken from literature [36]. The values of B11 were calculated using the McGlashan and Potter [37] equation for alkanes and Tsonopolous [38] equation for the rest of solvents. The vapor pressure values were calculated using equation and constants taken from the literature [36,39,40]. Critical data used to calculate B11 were obtained from literature [41,42].
Values of χ 12 were determined from equation 1. If the left side of equation 7 is plotted against δ1, a straight line having a slope of 2δ2/RT and an intercept of δ 2 2 / R T is obtained. The solubility parameter of the solvent δ2 (ionic liquid) can be calculated from the slope and from the intercept of the straight line. The agreement of both δ2 values confirms the applicability of the method to the considered system. An example plot δ 1 2 R T χ 12 V 1 * versus δ1 is given in Figure 5 for ionic liquid [(C6OC)2im][NTf2] at T = 368.15 K. From the slope and interception of straight line the solubility parameter was determined, giving results of 20.30 and 20.40, respectively. Then the average of these values was taken as a final result. The correlation coefficient in this example is 0.996. Hildebrand’s solubility parameters of the investigated ionic liquids and the estimated standard enthalpy of vaporization calculated using equation 8 are listed in Tables 2 and 3, respectively.

4. Conclusions

Inverse gas chromatography is a reliable method to determine Hildebrand’s solubility parameters. Data obtained for 18 ionic liquids are coherent with those obtained by different research group by the same method. From the solubility parameters the standard enthalpies of vaporization can be calculated. Obtained values of enthalpies of vaporization are in acceptable consistency with the data available in literature except for ionic liquids based on thiocyanate anion.

Acknowledgments

Funding for this research was provided by the Ministry of Science and Higher Education in years 2008–2011 (Grant No. N209 096435). The author would like to thank Urszula Domańska for very helpful discussion and guidance.

Electronic Supporting Information

Table 1S, interaction parameters, χ 12 .

References and Notes

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Figure 1. The solubility parameter versus the number of carbon atoms n in the alkyl chain R for the ionic liquids based on 1-alkyl-3-methyl-imidazolium cation [Rmim]+ obtained by IGC method. ( Ijms 11 01973i1) [SCN]; ( Ijms 11 01973i2) [BF4]; ( Ijms 11 01973i3) [NTf2]. The lines are drawn to guide the eye.
Figure 1. The solubility parameter versus the number of carbon atoms n in the alkyl chain R for the ionic liquids based on 1-alkyl-3-methyl-imidazolium cation [Rmim]+ obtained by IGC method. ( Ijms 11 01973i1) [SCN]; ( Ijms 11 01973i2) [BF4]; ( Ijms 11 01973i3) [NTf2]. The lines are drawn to guide the eye.
Ijms 11 01973f1
Figure 2. Anion influence on the solubility parameter for ionic liquids based on 1-alkyl-3-methyl imidazolium cations [Rmim]+, [bmPY]+ and [bmPYR]+ cations. ( Ijms 11 01973i4) [emim]+; ( Ijms 11 01973i5) [bmim]+; ( Ijms 11 01973i6) [hmim]+; ( Ijms 11 01973i7) [omim]+; ( Ijms 11 01973i8) [1,4bmPY]+; ( Ijms 11 01973i9) [1,3bmPY]+; ( Ijms 11 01973i10) [bmPYR]+.
Figure 2. Anion influence on the solubility parameter for ionic liquids based on 1-alkyl-3-methyl imidazolium cations [Rmim]+, [bmPY]+ and [bmPYR]+ cations. ( Ijms 11 01973i4) [emim]+; ( Ijms 11 01973i5) [bmim]+; ( Ijms 11 01973i6) [hmim]+; ( Ijms 11 01973i7) [omim]+; ( Ijms 11 01973i8) [1,4bmPY]+; ( Ijms 11 01973i9) [1,3bmPY]+; ( Ijms 11 01973i10) [bmPYR]+.
Ijms 11 01973f2
Figure 3. Influence of cation structure on the solubility parameter for ionic liquids based on ( Ijms 11 01973i11) [SCN] and ( Ijms 11 01973i12) [CF3SO3] anions. The lines are drawn to guide the eye.
Figure 3. Influence of cation structure on the solubility parameter for ionic liquids based on ( Ijms 11 01973i11) [SCN] and ( Ijms 11 01973i12) [CF3SO3] anions. The lines are drawn to guide the eye.
Ijms 11 01973f3
Figure 4. Cation influence on the solubility parameter for ionic liquids based on [NTf2] anion. The line is drawn to guide the eye.
Figure 4. Cation influence on the solubility parameter for ionic liquids based on [NTf2] anion. The line is drawn to guide the eye.
Ijms 11 01973f4
Figure 5. An example of the determination of solubility parameter δ2. Plot of δ 1 2 R T χ 12 V 1 * versus δ1 according to the equation 7 for ionic liquid [(C6OC)2im][NTf2] at T = 368.15 K.
Figure 5. An example of the determination of solubility parameter δ2. Plot of δ 1 2 R T χ 12 V 1 * versus δ1 according to the equation 7 for ionic liquid [(C6OC)2im][NTf2] at T = 368.15 K.
Ijms 11 01973f5
Table 1. Abbreviations, names and structures of investigated ionic liquids.
Table 1. Abbreviations, names and structures of investigated ionic liquids.
AbbreviationNameStructureReference
[emim][TFA]1-Ethyl-3-methyl-imidazolium trifluoroacetate Ijms 11 01973i13[3]
[emim][SCN]1-Ethyl-3-methyl-imidazolium thiocyanate Ijms 11 01973i14[4]
[bmim][SCN]1-Butyl-3-methyl-imidazolium thiocyanate Ijms 11 01973i15[5]
[hmim][SCN]1-Hexyl-3-methyl-imidazolium thiocyanate Ijms 11 01973i16[6]
[1,4bmPY][SCN]1-Butyl-4-methyl-pyridinium thiocyanate Ijms 11 01973i17[7]
[bmPYR][SCN]1-Butyl-1-methyl-pyrrolidinium thiocyanate Ijms 11 01973i18[7]
[bmim][CF3SO3]1-Butyl-3-methyl-imidazolium trifluoromethanesulfonate Ijms 11 01973i19[8]
[1,3bmPY][CF3SO3]1-Butyl-3-methyl-pyridinium trifluoromethanesulfonate Ijms 11 01973i20[9]
[bmPYR][CF3SO3]1-Butyl-1-methyl-pyrrolidinium trifluoromethanesulfonate Ijms 11 01973i21[10]
[bmim][MDEGSO4]1-Butyl-3-methyl-imidazolium 2-(2-methoxyethoxy)ethyl sulfate Ijms 11 01973i22[11]
[bmim][OcSO4]1-Butyl-3-methyl-imidazolium octyl sulfate Ijms 11 01973i23[12]
[P1,i4,i4,i4][TOS]Triisobutyl-methyl-phosphonium tosylate Ijms 11 01973i24[13]
[1,4bmPY][TOS]1-Butyl-4-methyl-pyridinium tosylate Ijms 11 01973i25[14]
[1,4bmPY][NTf2]1-Butyl-4-methyl-pyridinium bis(trifluoromethylsulfonyl)-amide Ijms 11 01973i26[15]
[C6OCmim][NTf2]1-Hexyloxymethyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)-amide Ijms 11 01973i27[16]
[(C6OC)2im][NTf2]1,3-Dihexyloxymethyl-imidazolium bis(trifluoromethylsulfonyl)-amide Ijms 11 01973i28[16]
[Et3S][NTf2]Triethyl-sulfonium bis(trifluoromethylsulfonyl)-amide Ijms 11 01973i29[17]
[hmim][NTf2]1-Hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)-amide Ijms 11 01973i30[18]
Table 2. Hildebrand’s solubility parameters δ2 for the different ionic liquids.
Table 2. Hildebrand’s solubility parameters δ2 for the different ionic liquids.
Ionic liquidT/Kδ2/MPa0.5
[emim][TFA]298.1525.561
328.1525.58
338.1525.59
348.1525.60
358.1525.60

[emim][SCN]298.1525.191
308.1525.24
318.1525.33
328.1525.41
338.1525.46
348.1525.55
358.1525.57

[bmim][SCN]298.1524.641
318.1524.70
328.1524.72
338.1524.75
348.1524.77
358.1524.80

[hmim][SCN]298.1523.651
318.1523.74
328.1523.79
338.1523.84
348.1523.90
358.1523.93
368.1523.98

[1,4bmPY][SCN]298.1524.53
308.1524.57
318.1524.62
328.1524.67
338.1524.71
348.1524.74
358.1524.77

[bmPYR][SCN]298.1524.96
308.1524.98
318.1525.00
328.1525.01
338.1525.02
348.1525.04
358.1525.05

[bmPYR][SCN]298.1524.96
308.1524.98
318.1525.00
328.1525.01
338.1525.02
348.1525.04
358.1525.05

[bmim][CF3SO3]298.1522.671
308.1522.74
318.1522.81
328.1522.87
338.1522.97
348.1523.03
358.1523.09

[1,3bmPY][CF3SO3]298.1522.471
318.1522.61
328.1522.68
338.1522.75
348.1522.84
358.1522.89

[bmPYR][CF3SO3]298.1522.831
318.1522.94
328.1523.01
338.1523.06
348.1523.13
358.1523.17
368.1523.24

[bmim][MDEGSO4]298.1524.80
303.1524.80
308.1524.81

[bmim][OcSO4]298.1522.83
313.1523.00
328.1523.25

[P1,i4,i4,i4][TOS]298.1524.331
318.1524.20
328.1524.13
338.1524.05
348.1523.99
358.1523.93

[1,4bmPY][TOS]298.1523.061
328.1523.24
333.1523.27
338.1523.29
343.1523.33

[1,4bmPY][NTf2]298.1520.611
318.1520.82
328.1520.92
338.1521.05
348.1521.15
358.1521.25
368.1521.35

[C6OCmim][NTf2]298.1520.261
318.1520.48
328.1520.59
338.1520.71
348.1520.82
358.1520.93
368.1521.05

[(C6OC)2im][NTf2]298.1519.601
318.1519.81
328.1519.92
338.1520.03
348.1520.14
358.1520.25
368.1520.35

[Et3S][NTf2]298.1521.051
308.1521.13
318.1521.25
328.1521.35
338.1521.47
348.1521.55
358.1521.66
368.1521.72

[hmim][NTf2]298.1520.25
308.1520.36
313.1520.44
328.1520.58
333.1520.64
338.1520.70
348.1520.83

Solubility parameters taken from the literature

[mmim][(CH3)2PO4] [21]312.5526.54
332.6525.96
352.7525.16

[emim][(C2H5)2PO4] [21]312.6525.81
332.5525.44
352.6525.32

[emim][NTf2] [23]313.1522.31

[emim][NTf2] [25]298.1527.6

[emim][BF4] [24]298.1524.4

[bmim][BF4] [24]298.1524.3

[bmim][BF4] [25]298.1531.6

[bmim][NTf2] [25]298.1526.7

[bmim][NTf2] [26]298.1525.5

[bmim][CF3SO3] [25]298.1524.9

[bmim][CF3SO3] [26]298.1525.4

[bmim][PF6] [23]313.1523.2
323.1522.62
333.1522.05

[bmim][PF6] [25]298.1529.8

[bmim][PF6] [26]298.1530.2

[bmim][SbF6] [26]298.1531.5

[bmmim][NTf2] [26]298.1524.2

[hmim][BF4] [24]298.1523.3

[hmim][NTf2] [25]298.1525.6

[hmim][PF6] [25]298.1528.6

[omim][BF4] [24]298.1522.5

[omim][NTf2] [25]298.1525.0

[omim][PF6] [25]298.1527.8

[omim][Cl] [23]313.1517.91

[C16mim][BF4] [22]323.1519.52
333.1519.61
343.1519.60

[OH-C2mim][BF4] [21]302.5522.77
312.6522.87
332.6522.88

[OH-C2mim][PF6] [21]302.6521.84
312.5521.93
332.4522.45
1extrapolated values.
Table 3. Molar volumes Vm at T = 298.15 K and standard enthalpies of vaporization ΔvapH298.15 for investigated ionic liquids.
Table 3. Molar volumes Vm at T = 298.15 K and standard enthalpies of vaporization ΔvapH298.15 for investigated ionic liquids.
Ionic liquidVm/cm3·mol−1ΔvapH298.15/kJ·mol−1
[emim][TFA]173.71115.97
[emim][SCN]151.6298.671518
[bmim][SCN]184.43114.571488
[hmim][SCN]200.04114.37
[1,4bmPY][SCN]196.25120.5
[bmPYR][SCN]188.85120.1
[bmim][CF3SO3]222.05116.671398130.29140.110145.711
[1,3bmPY][CF3SO3]234.75121.07
[bmPYR][CF3SO3]232.65123.77
[bmim][MDEGSO4]284.25177.6
[bmim][OcSO4]327.75173.0
[P1,i4,i4,i4][TOS]363.46217.67
[1,4bmPY][NTf2]304.85132.071528
[C6OCmim][NTf2]349.95146.07
[(C6OC)2im][NTf2]460.25179.27
[Et3S][NTf2]273.75123.77
[hmim][NTf2]326.45136.71398141.612216.410
1from reference [30];
2from reference [31];
3from reference [32];
4from reference [33];
5from density measurements performed on Anton Paar Density Meter DMA 4500;
6from reference [34];
7calculated from extrapolated values of δ2;
8from reference [27];
9from reference [28];
10calculated from δ2 from reference [25];
11calculated from δ2 from reference [26];
12from reference [29]
Int. J. Mol. Sci. EISSN 1422-0067 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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