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Article

The Hildebrand Solubility Parameters of Ionic Liquids—Part 2

Department of Physical Chemistry, Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland
Int. J. Mol. Sci. 2011, 12(6), 3553-3575; https://doi.org/10.3390/ijms12063553
Submission received: 6 April 2011 / Revised: 19 May 2011 / Accepted: 26 May 2011 / Published: 3 June 2011
(This article belongs to the Special Issue Advances in Green Chemistry and Sustainable Chemistry 2011)

Abstract

:
The Hildebrand solubility parameters have been calculated for eight ionic liquids. Retention data from the inverse gas chromatography measurements of the activity coefficients at infinite dilution were used for the calculation. From the solubility parameters, the enthalpies of vaporization of ionic liquids were estimated. Results are compared with solubility parameters estimated by different methods.

1. Introduction

Ionic liquids (ILs) are a relatively new class of salts with a melting temperature below 373.15 K. In general, ILs are composed of organic cations with either inorganic or organic anions. Ionic liquids have unique properties, namely, a wide liquid range, stability at high temperatures and negligible vapor pressure. Because of the last mentioned property, the inverse gas chromatography (IGC) is a suitable method for measuring thermodynamic properties of pure substances and their mixtures [1]. From the IGC measurements, the activity coefficients at infinite dilution, Flory-Huggins interaction parameters as well as the Hildebrand solubility parameters can be determined. By this method the solubility parameters were determined previously for different ionic liquids [26].
The Hildebrand solubility parameters have numerous applications including gas-liquid solubility, solvent extraction and many others as described in detail in the literature [7,8]. The solubility parameter is the square root of the cohesive energy density, which is defined as the ratio of the energy of vaporization, ΔvapU, to the molar volume, υ:
δ = Δ vap U υ = Δ vap H - R T υ
Because ILs have negligible vapor pressure, experimental measurements of their energy of vaporization are difficult. For this reason, experimental data of ΔvapU are unavailable. Alternative methods have been considered for estimation of the solubility parameters of ionic liquids: From melting temperatures of ILs [9], from intrinsic viscosity measurements [10], from the activation energy of viscosity [11,12], from surface tension measurements [13], from Kamlet-Taft equation [14], using non random hydrogen bonding (NRHB) and PC-SAFT models [15], from lattice energy density [16].
This paper provides information on the Hildebrand solubility parameters determined for eight ionic liquids as a function of temperature and the enthalpies of vaporization calculated from the values of the solubility parameters. The solubility parameters were calculated using the experimental data from the activity coefficients at infinite dilution measurements. The list of investigated ionic liquids is shown in Table 1. The values of the activity coefficients at infinite dilution for the investigated ionic liquids were published earlier [1724].

2. Results and Discussion

The Hildebrand solubility parameters were calculated for the ionic liquids presented (with abbreviations and structures) in Table 1. The results are presented in Table 2. For ionic liquids based on [FAP] and [NTf2] anions with the same cation, [N-C3OHPY]+, the solubility parameter is higher for IL with [NTf2] anion. Estimated enthalpy of vaporization is higher for [N-C3OHPY][FAP] than for [N-C3OHPY][NTf2], the higher molar mass and more complex structure of [FAP] anion causes higher enthalpy of vaporization. For ionic liquids [bmPIP][SCN] and [bmPIP][NTf2] the solubility parameter as well as the enthalpy of vaporization is higher for ionic liquid with [SCN] anion. In this case the structure of [SCN] anion is much simpler than for [NTf2] and the molar mass is lower, but very strong interaction of thiocyanate group increases the enthalpy of vaporization. With an increase of the alkyl chain in the cation structure of an ionic liquid the solubility parameter decreases. Due to increase of molar mass and alkyl chain length the enthalpy of vaporization also increases. This is typical behavior observed with increasing of alkyl chain length for example in linear alkanes or alkylbenzenes. This effect is visible in two pairs of ionic liquids, namely [emim][TCB][dmim][TCB] and [pmPIP][NTf2][bmPIP][NTf2].
Table 3 presents comparison of the Hildebrand solubility parameters determined by different methods for selected ionic liquids based on [NTf2] anion. Camper et al. presents different values of δ for ionic liquid [emim][NTf2] estimated from the IL melting point [9] and from lattice energy density [16]. These values differ about 2.4 times and are inconsistent with δ obtained by other methods. Solubility parameters determined from enthalpy of vaporization are in good agreement with values of δ obtained by IGC for [emim][NTf2] and [hmim][NTf2] and with values of δ estimated from surface tension for [bmim][NTf2] and [bmPYR][NTf2]. Kilaru et al. estimated solubility parameters from activation energy of viscosity using the equation presented below [11]:
δ = [ K v R T υ ln ( 10 - 9 μ υ h N A ) ] 0.5
where: μ is the dynamic viscosity of IL (in units of mPa·s), υ is the molar volume (in units of cm3·mol−1), h is Planck constant (in units of J·s), NA is Avogadro constant (in units of mol−1), and Kv is a proportionality constant. They calculated Kv value of 7.8 for ILs based on [NTf2] anion from solubility parameters determined from intrinsic viscosity [10]. Consequently the solubility parameters estimated from Equation 2 are consistent with those estimated from intrinsic viscosity. In this work Kv value of 5.23 was obtained from the solubility parameters determined from experimental enthalpy of vaporization (the procedure is described in Supporting Information). Based on this value the solubility parameters were determined for [N-C3OHPY][NTf2], [pmPIP][NTf2] and [bmPIP][NTf2] ionic liquids for which the molar volumes and viscosities were determined (see Table 3S). Results are presented in Table 4. The differences in results are in the range from 3 to 10%.

3. Calculation of Solubility Parameters

3.1. Experimental Procedure

On the basis of the experimental data from the activity coefficients at infinite dilution measurements, the Hildebrand solubility parameters have been calculated using the equations presented below. 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 relevant papers [1724].

3.2. Theoretical Basis

Retention data were used for the calculation of Hildebrand 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, J23 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 at the column outlet, Pw is the vapor pressure of water at Tf and U is the flow rate measured with the flow meter. The interaction parameter χ12 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 8 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. The thermophysical properties required in calculations were calculated using equations and constants taken from the literature [30].
Values of χ12 were determined from Equation 2 and are presented in Table 1S. If the left side of Equation 9 is plotted against δ1, a straight line having a slope of 2δ2/RT and an intercept of −δ22 /RT is obtained. The solubility parameter of the solvent δ2 (ionic liquid) can be calculated from the slope. Example of calculations is presented in the Supporting Information. Hildebrand solubility parameters of the investigated ionic liquids and the estimated enthalpies of vaporization calculated using Equation 10 are listed in Table 2.

4. Conclusions

The Hildebrand solubility parameters estimated by different methods are divergent. The most reliable results are from the experiment especially from the enthalpies of vaporization. As presented in Table 3, solubility parameters calculated from enthalpies of vaporization and determined by IGC are in good consistency for [emim][NTf2] and [hmim][NTf2] ionic liquids. Therefore, the inverse gas chromatography is an appropriate method to determine Hildebrand solubility parameters of ionic liquids. While the ionic liquids have negligible vapor pressure, experimental measurements of their enthalpy of vaporization are difficult; therefore, this property can be estimated from the solubility parameters.

Acknowledgements

Funding for this research was provided by the Ministry of Sciences and Higher Education in years 2008–2011 (Grant No. N209 096435).

Appendix Electronic Supporting Information

Table S1, interaction parameters, χ12 Example of calculation of the solubility parameter. Calculation of the Kv constant from Equation 2; Table S2, data used in calculation of Kv constant; Table S3, densities and viscosities for [N-C3OHPY][NTf2], [pmPIP][NTf2] and [bmPIP][NTf2] ionic liquids.
Table S1. Interaction parameters, χ 12.
Table S1. Interaction parameters, χ 12.
χ 12
[N-C3OHPY][FAP]

T/Kn-pentanen-hexanen-heptanen-octanen-nonanen-decane
308.153.623.964.324.685.045.42
318.153.503.834.174.524.865.24
328.153.393.714.044.384.725.08
338.153.273.583.914.244.574.93
348.153.183.483.784.114.444.78
358.153.093.373.673.994.304.64
T/Kcyclopentanecyclohexanecycloheptanecyclooctane1-pentene1-hexene
308.153.193.553.814.082.753.07
318.153.083.423.673.932.662.97
328.152.973.293.543.802.582.88
338.152.863.173.423.672.502.80
348.152.753.053.303.552.432.72
358.152.672.943.193.432.362.64
T/K1-heptene1-octene1-hexyne1-heptyne1-octynebenzene
308.153.403.792.012.332.690.482
318.153.313.681.962.282.630.495
328.153.223.581.922.232.570.505
338.153.143.481.872.182.510.519
348.153.063.381.832.132.450.528
358.152.973.291.792.082.400.537
T/Ktolueneethylbenzeneo-xylenem-xylenep-xylenemethanol
308.150.7321.120.9441.011.061.01
318.150.7431.120.9501.021.070.979
328.150.7511.120.9551.031.070.944
338.150.7611.120.9611.041.080.913
348.150.7691.120.9661.041.080.882
358.150.7771.110.9711.051.090.855
T/Kethanol1-propanol1-butanolwaterthiophenetetrahydrofuran
308.150.8731.011.202.950.557−0.967
318.150.8320.9651.142.850.564−0.859
328.150.7960.9161.082.770.572−0.776
338.150.7610.8781.032.690.578−0.683
348.150.7300.8360.9742.610.585−0.601
358.150.6990.8030.9262.540.591−0.529
T/Kmethyl tert-butyl etherdiethyl etherdi-n-propyl etherdi-n-butyl ether2-pentanone3-pentanone
308.15−0.01040.1681.292.14
318.150.0830.2451.322.15−1.09−0.988
328.150.1700.3241.362.15−1.01−0.907
338.150.2620.3901.392.16−0.933−0.831
348.150.3350.4501.432.16−0.860−0.759
358.150.4140.5041.452.16−0.792−0.694
T/Kacetone
308.15−1.66
318.15−1.56
328.15−1.47
338.15−1.38
348.15−1.30
358.15−1.23

[N-C3OHPY][NTf2]

T/Kn-pentanen-hexane3-methylpentane2,2-dimethylbutanen-heptanen-octane
318.153.674.043.903.814.454.86
328.153.593.943.803.714.344.73
338.153.503.843.703.614.224.61
348.153.433.763.623.534.134.50
358.153.353.673.543.444.034.40
T/K2,2,4-trimethylpentanen-nonanen-decanecyclopentanecyclohexanemethylcyclohe xane
318.154.405.275.703.083.453.78
328.154.305.135.542.993.353.68
338.154.205.005.412.913.263.58
348.154.114.895.292.843.183.49
358.154.034.775.162.783.103.41
T/Kcycloheptanecyclooctane1-pentene1-hexenecyclohexene1-heptene
318.153.734.032.893.282.753.67
328.153.633.922.833.202.683.59
338.153.533.812.763.122.623.51
348.153.443.712.713.062.573.44
358.153.363.632.653.002.523.38
T/K1-octene1-decene1-hexyne1-heptyne1-octynebenzene
318.154.094.912.102.482.890.886
328.154.004.802.082.452.840.887
338.153.914.702.052.412.790.888
348.153.834.612.032.392.760.888
358.153.754.512.012.352.710.888
T/Ktolueneethylbenzeneo-xylenem-xylenep-xylenemethanol
318.151.181.621.381.511.510.896
328.151.181.611.381.511.510.850
338.151.181.601.381.511.510.805
348.151.181.581.381.511.510.761
358.151.181.581.381.511.510.719
T/Kethanol1-propanol1-butanolwateracetic acidthiophene
318.150.8851.021.232.21−0.6140.754
328.150.8360.9681.172.13−0.5340.756
338.150.7880.9181.112.06−0.4640.756
348.150.7450.8681.051.99−0.3970.757
358.150.6980.8220.9951.94−0.3340.756
T/Ktetrahydrofuran1,4-dioxanemethyl tert-butyl ethermethyl tert-pentyl etherdiethyl etherdi-n-propyl ether
318.150.125−0.2051.261.691.342.43
328.150.166−0.1571.291.701.352.40
338.150.201−0.1121.311.711.362.38
348.150.230−0.0701.331.731.372.36
358.150.260−0.0321.351.741.382.35
T/Kdi-n-butyl etheracetone2-pentanone3-pentanone
318.153.30−0.3510.1930.253
328.153.25−0.3140.2170.277
338.153.20−0.2840.2420.301
348.153.16−0.2550.2610.322
358.153.12−0.2290.2810.341

[emim][TCB]

T/Kn-pentanen-hexanen-heptanen-octane2,2,4-trimethylpentanen-nonane
298.153.263.634.054.464.144.90
308.153.163.543.944.344.034.76
318.153.113.473.864.253.964.65
328.153.023.383.754.143.874.52
338.152.963.303.674.043.784.41
348.152.903.243.603.953.714.31
358.152.843.183.523.863.634.21
T/Kn-decanecyclopentanecyclohexanemethylcyclohe xanecycloheptanecyclooctane
298.155.322.643.013.353.233.49
308.155.182.572.923.243.133.38
318.155.062.522.863.173.073.31
328.154.922.442.773.082.983.21
338.154.812.392.703.002.903.14
348.154.692.342.642.942.833.06
358.154.582.282.572.882.772.98
T/K1-pentene1-hexenecyclohexene1-heptene1-octene1-hexyne
298.152.422.802.213.183.611.50
308.152.372.732.163.103.521.49
318.152.342.692.143.063.461.49
328.152.292.622.092.993.371.48
338.152.252.572.042.923.301.48
348.152.222.532.012.893.241.47
358.152.152.481.982.833.181.47
T/K1-heptyne1-octynebenzenetolueneethylbenzeneo-xylene
298.151.862.230.4330.7101.100.922
308.151.842.210.4430.7211.100.927
318.151.832.180.4550.7301.100.933
328.151.812.160.4620.7391.100.937
338.151.802.140.4710.7471.100.943
348.151.782.120.4770.7571.090.949
358.151.772.110.4830.7621.090.950
T/Km-xylenep-xylenemethanolethanol1-propanol1-butanol
298.151.081.020.9681.041.111.29
308.151.081.030.8860.9441.011.17
318.151.091.030.8120.8560.9091.06
328.151.091.040.7390.7700.8160.953
338.151.101.050.6740.6930.7340.861
348.151.101.060.6120.6200.6600.780
358.151.101.060.5530.5510.5910.701
T/Kwaterthiophenetetrahydrofuranmethyl tert-butyl ethermethyl tert-pentyl etherdiethyl ether
298.152.390.316−0.01641.191.531.21
308.152.270.3250.01041.201.541.21
318.152.190.3310.03351.211.541.21
328.152.100.3370.04581.221.551.21
338.152.010.3450.06261.231.551.21
348.151.920.3480.08781.241.561.21
358.151.850.3550.1011.241.561.20
T/Kdi-n-propyl etherdi-n-butyl etheracetone2-pentanone3-pentanone2-hexanone
298.152.243.06−0.445−0.0425−0.07900.210
308.152.212.99−0.421−0.0239−0.05280.225
318.152.182.94−0.398−0.0018−0.02080.238
328.152.142.87−0.3790.01550.00470.247
338.152.122.83−0.3580.02980.02660.261
348.152.092.78−0.3440.04270.04640.272
358.152.062.73−0.3250.06010.06780.283
T/K3-hexanone
298.150.276
308.150.294
318.150.314
328.150.330
338.150.343
348.150.355
358.150.371

[dmim][TCB]

T/Kn-pentanen-hexanen-heptanen-octane2,2,4-trimethylpentanen-nonane
328.151.982.112.272.442.352.62
338.151.942.072.232.392.302.57
348.151.902.032.182.342.252.52
358.151.851.992.132.302.212.47
368.151.811.942.092.252.172.42
T/Kn-decanecyclopentanecyclohexanemethylcyclohe xanecycloheptanecyclooctane
328.152.821.581.731.841.781.88
338.152.761.541.681.791.731.83
348.152.711.501.631.751.691.79
358.152.651.461.591.711.651.74
368.152.601.421.541.671.611.70
T/K1-pentene1-hexenecyclohexene1-heptene1-octene1-hexyne
328.151.491.631.281.781.960.853
338.151.471.591.251.751.930.857
348.151.451.561.231.731.900.860
358.151.421.531.211.701.870.859
368.151.401.511.181.681.840.861
T/K1-heptyne1-octynebenzenetolueneethylbenzeneo-xylene
328.150.9831.140.06980.1820.3820.266
338.150.9871.140.08260.2010.3960.283
348.150.9901.140.09570.2180.4090.302
358.150.9911.140.1050.2330.4210.318
368.150.9921.140.1140.2470.4290.330
T/Km-xylenep-xylenemethanolethanol1-propanol1-butanol
328.150.3610.3430.9970.8350.6820.635
338.150.3810.3660.9290.7590.6130.565
348.150.4020.3860.8700.6930.5550.507
358.150.4160.4010.8030.6250.4970.452
368.150.4370.4220.7520.5660.4410.392
T/Kwateracetic acidbutyric acidthiophenetetrahydrofuranmethyl tert-butyl ether
328.152.78−0.3320.1180.0626−0.3380.547
338.152.68−0.2840.1160.0761−0.3070.565
348.152.57−0.2380.1140.0845−0.2790.585
358.152.49−0.1980.1110.0968−0.2550.605
368.152.42−0.1640.1090.107−0.2300.619
T/Kmethyl tert-pentyl etherdiethyl etherdi-n-propyl etherdi-n-butyl etheracetone2-pentanone
328.150.7110.6261.151.49−0.450−0.462
338.150.7280.6351.141.48−0.428−0.431
348.150.7460.6411.131.47−0.409−0.404
358.150.7600.6461.131.46−0.394−0.380
368.150.7720.6491.121.45−0.378−0.353
T/K3-pentanone
328.15−0.497
338.15−0.460
348.15−0.426
358.15−0.395
368.15−0.364

[bmPIP][SCN]

T/Kn-hexanen-heptanen-octanen-nonanen-decanecyclopentane
318.154.905.195.495.826.193.55
328.154.735.005.365.696.073.42
338.154.574.895.245.605.973.32
348.154.444.755.115.465.843.21
358.154.304.675.035.375.743.15
T/Kcyclohexanecycloheptanecyclooctane1-hexene1-heptene1-octene
318.153.853.914.173.824.164.54
328.153.743.844.073.714.084.46
338.153.643.743.973.644.004.38
348.153.543.653.883.563.924.30
358.153.463.603.813.493.874.24
T/K1-hexyne1-heptyne1-octynebenzenetolueneethylbenzene
318.151.942.302.660.9071.321.76
328.151.942.302.660.9161.331.76
338.151.952.302.660.9241.331.75
348.151.952.302.660.9301.331.75
358.151.952.302.660.9381.341.74
T/Ko-xylenem-xylenep-xylenemethanolethanolwater
318.151.541.771.72−0.1870.1030.413
328.151.551.771.73−0.1900.08220.429
338.151.551.771.73−0.1910.06000.445
348.151.561.771.73−0.1960.04050.460
358.151.561.771.74−0.1980.02410.476
T/Kthiophenetetrahydrofuranmethyl tert-butyl etherdiethyl etherdi-n-propyl etherdi-n-butyl ether
318.150.4341.142.702.673.634.39
328.150.4591.152.662.623.564.31
338.150.4861.162.632.573.504.24
348.150.5041.162.592.543.444.17
358.150.5251.172.572.503.394.12
T/Kacetone2-pentanone3-pentanone
318.150.7951.291.30
328.150.7941.291.30
338.150.7921.291.30
348.150.7901.291.30
358.150.7891.291.30

[pmPIP][NTf2]

T/Kn-pentanen-hexanen-heptanen-octanen-nonanen-decane
308.153.313.403.583.814.084.38
318.153.023.213.443.703.984.30
328.152.983.143.353.603.884.18
338.152.853.063.293.533.804.09
348.152.752.953.193.433.703.99
358.152.722.933.143.373.633.91
T/Kcyclopentanecyclohexanecycloheptanecyclooctane1-pentene1-hexene
308.152.722.933.053.232.482.64
318.152.522.772.943.152.302.52
328.152.472.712.863.042.272.48
338.152.382.622.782.982.322.41
348.152.292.512.702.892.132.34
358.152.262.482.642.822.132.31
T/K1-heptene1-octene1-hexyne1-heptyne1-octynebenzene
308.152.843.111.471.711.980.418
318.152.763.041.461.701.980.427
328.152.712.961.451.681.950.430
338.152.652.921.461.691.940.433
348.152.592.851.441.671.950.444
358.152.552.811.441.671.910.456
T/Ktolueneethylbenzeneo-xylenem-xylenep-xylenemethanol
308.150.6150.9130.7520.8220.8121.62
318.150.6190.9150.7720.8510.8451.54
328.150.6350.9320.7750.8490.8491.44
338.150.6420.9300.7870.8650.8641.36
348.150.6550.9360.7950.8750.8761.28
358.150.6680.9420.8110.8920.8941.20
T/Kethanol1-propanol1-butanolwaterthiophenetetrahydrofuran
308.151.541.551.643.360.3770.355
318.151.451.461.563.270.3860.363
328.151.351.351.423.140.3890.370
338.151.261.261.323.040.4010.385
348.151.181.171.232.900.4040.384
358.151.101.101.152.780.4160.398
T/Kmethyl tert-butyl etherdiethyl etherdi-n-propyl etherdi-n-butyl etheracetone2-pentanone
308.151.381.472.162.78−0.03290.181
318.151.371.412.122.72−0.02170.200
328.151.361.412.102.68−0.01510.209
338.151.351.392.072.630.00070.225
348.151.341.362.022.57−0.00290.229
358.151.331.362.012.530.00710.244
T/K3-pentanone
308.150.161
318.150.178
328.150.208
338.150.225
348.150.235
358.150.256

[bmPIP][NTf2]

T/Kn-pentanen-hexane3-methylpentane2,2-dimethylbutanen-heptanen-octane
308.152.622.852.742.663.133.42
318.152.512.722.622.543.003.27
328.152.392.622.502.422.893.16
338.152.342.562.452.372.823.09
348.152.292.512.402.332.763.02
358.152.232.472.352.282.692.95
T/K2,2,4-trimethylpentanen-nonanen-decanecyclopentanecyclohexanemethylcyclohe xane
308.153.033.714.012.222.482.67
318.152.923.553.842.112.362.54
328.152.813.423.712.022.262.44
338.152.743.353.631.962.202.38
348.152.693.283.541.902.122.31
358.152.633.203.471.872.092.27
T/Kcycloheptanecyclooctane1-pentene1-hexenecyclohexene1-heptene
308.152.702.912.002.261.952.51
318.152.572.781.912.161.872.41
328.152.472.671.832.081.792.33
338.152.402.601.812.031.752.29
348.152.322.511.761.971.702.23
358.152.282.471.731.941.642.21
T/K1-octene1-hexyne1-heptyne1-octynebenzenetoluene
308.152.801.281.521.790.3040.486
318.152.701.241.471.720.3150.498
328.152.601.201.431.670.3170.508
338.152.551.201.421.660.3240.518
348.152.491.181.401.650.3380.534
358.152.461.201.401.630.3540.550
T/Kethylbenzeneo-xylenem-xylenep-xylenemethanolethanol
308.150.7930.6320.7020.6981.601.49
318.150.8000.6460.7230.7161.521.40
328.150.7950.6440.7180.7191.421.31
338.150.7970.6500.7290.7331.341.21
348.150.8070.6670.7480.7471.251.12
358.150.8160.6710.7590.7581.161.04
T/K1-propanol1-butanolwaterthiophenetetrahydrofuranmethyl tert-butyl ether
308.151.471.543.490.2990.2061.06
318.151.381.423.340.3020.2151.06
328.151.281.333.210.3010.2051.05
338.151.181.223.070.3060.2071.04
348.151.091.122.940.3080.2071.04
358.151.011.042.810.3230.2191.04
T/Kdiethyl etherdi-n-propyl etherdi-n-butyl etheracetone2-pentanone3-pentanone
308.151.191.862.46−0.08410.05580.0284
318.151.181.852.43−0.07820.06670.0492
328.151.111.752.33−0.07640.08850.0770
338.151.121.752.29−0.07390.09430.0842
348.151.111.732.25−0.07320.1060.114
358.151.101.702.21−0.07060.1150.124

[OQuin][NTf2]

T/Kn-pentanen-hexanen-heptanen-octanen-nonanen-decane
328.151.902.002.172.302.462.65
338.151.861.972.122.262.422.60
348.151.821.932.072.212.372.54
358.151.791.902.032.182.332.50
368.151.751.871.992.142.292.45
T/Kcyclopentanecyclohexanecycloheptanecyclooctane1-pentene1-hexene
328.151.571.701.761.851.501.60
338.151.541.661.721.811.481.58
348.151.501.611.681.761.461.55
358.151.471.581.641.721.431.53
368.151.431.541.611.681.411.51
T/K1-heptene1-octene1-hexyne1-heptyne1-octynebenzene
328.151.741.890.9771.091.220.188
338.151.721.870.9821.091.220.194
348.151.701.840.9811.091.210.206
358.151.681.820.9831.091.220.216
368.151.661.800.9871.081.220.224
T/Ktolueneethylbenzeneo-xylenem-xylenep-xylenemethanol
328.150.2470.4710.2550.3860.3991.62
338.150.2670.4850.2820.4020.4161.54
348.150.2850.4950.3030.4190.4241.43
358.150.3020.5050.3220.4300.4371.35
368.150.3200.5170.3400.4450.4471.27
T/Kethanol1-propanol1-butanol1-pentanolwaterthiophene
328.151.431.291.241.153.530.215
338.151.321.201.141.073.400.223
348.151.221.101.020.9793.240.227
358.151.141.020.9430.8963.120.231
368.151.060.9420.8650.8272.980.236
T/Ktetrahydrofuranmethyl tert-butyl etherdiethyl etherdi-n-propyl etherdi-n-butyl etheracetone
328.150.03260.7780.8791.331.65−0.0485
338.150.05060.7870.8801.311.63−0.0465
348.150.06530.7930.8811.301.60−0.0456
358.150.07420.7960.8791.281.57−0.0458
368.150.08530.8030.8771.261.54−0.0465
T/K2-pentanone3-pentanone
328.15−0.0778−0.0596
338.15−0.0694−0.0483
348.15−0.0621−0.0372
358.15−0.0521−0.0285
368.15−0.0461−0.0216

Example of Calculation of the Solubility Parameter

Experimental data for n-octane + [emim][TCB] system at T = 298.15 K:
  • T = 298.15 K
  • pi = 137423 Pa
  • po = 97423 Pa
  • Tf = 297.15 K
  • U = 41.2 mL·min−1
  • tRtG = 270.66 s
  • m2 = 2.1053 g
  • Pw (at Tf) = 2986.2 Pa (from [30])
  • Uo = 6.679·10−7 m3·s−1 (from Equation 6)
  • J23 = 1.217 (from Equation 5)
  • VN = 1.485·10−4 m3 (from Equation 4)
  • Vg = 6.464·10−5 m3·g−1 (from Equation 3)
  • P1* = 1871.0 Pa (from [30])
  • M1 = 114.2285 g·mol−1 (from [30])
  • B11 = −4.496·10−3 m3·mol−1 (from [30])
  • V1* = 1.6256·10−4 m3·mol−1 (from [30])
  • V2* = 2.1818·10−4 m3·mol−1 (calculated from density from [19])
  • ρ1 = 0.70268 g·cm−3 (from [30])
  • ρ2 = 1.03627 g·cm−3 (from [19])
  • χ12 = 4.463 (from Equation 2)
  • δ1 = 15486 (J·m3)0.5 (from [30])
Analogous calculations were made for the rest of solutes. The results are presented in the Table 1S. Based on these values the Equation 7 can be plotted (see Figure S1).
Figure S1. 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 [emim][TCB] at T = 298.15 K. ( Ijms 12 03553ig1) n-octane, ( Ijms 12 03553ig2) rest of solutes.
Figure S1. 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 [emim][TCB] at T = 298.15 K. ( Ijms 12 03553ig1) n-octane, ( Ijms 12 03553ig2) rest of solutes.
Ijms 12 03553f1
From the slope (2δ2/RT) the value of 20.874 is obtained. From this value the δ2 is calculated giving value 25.9 MPa0.5 (see Table 2).

Calculation of the Kv Constant from Equation 2

Using data presented in the Table S2 and the Kv value of 7.8 the solubility parameters were determined using Equation 2. Then the Kv value was optimized using the objective function OF = i = 1 n ( δ experimental - δ calculated ) i 2 using MS Excel Solver. Densities and viscosities were taken from the ILThermo database available at http://ilthermo.boulder.nist.gov/ILThermo/. Solubility parameters were calculated from enthalpies of vaporization [2529].
Table S2. Data used in calculation of Kv constant.
Table S2. Data used in calculation of Kv constant.
Ionic Liquidρ/g·cm−3M/g·mol−1μ/mPa·sυ/cm3·mol−1δ2/MPa0.5
[emim][NTf2]1.5192391.3234.29257.621.3
1.5192391.3234.29257.622.6
1.5192391.3234.29257.622.7

[bmim][NTf2]1.4366419.3750.70291.921.2
1.4366419.3750.70291.919.8
1.4366419.3750.70291.922.9

[hmim][NTf2]1.3706447.4270.96326.520.5
1.3706447.4270.96326.519.0
1.3706447.4270.96326.522.9

[omim][NTf2]1.3206475.4892.51360.120.2
1.3206475.4892.51360.120.2
1.3206475.4892.51360.123.0
1.3206475.4892.51360.118.9

[dmim][NTf2]1.2780499.50108.20390.817.8

[bmPYR][NTf2]1.3940422.4176.92303.022.2
Table S3. Densities and viscosities for [N-C3OHPY][NTf2], [pmPIP][NTf2] and [bmPIP][NTf2] ionic liquids.
Table S3. Densities and viscosities for [N-C3OHPY][NTf2], [pmPIP][NTf2] and [bmPIP][NTf2] ionic liquids.
Ionic LiquidT/Kρ/g·cm−3aμ/m Pa·s b
[N-C3OHPY][NTf2]308.151.545167.03
318.151.535743.85
328.151.526630.56
338.151.517522.21
348.151.508516.90

[pmPIP][NTf2]308.151.401086.70
318.151.392355.24
328.151.383737.75
338.151.375127.17
348.151.366620.32

[bmPIP][NTf2]308.151.370697.76
318.151.362161.05
328.151.353640.92
338.151.345229.01
348.151.336921.28
adetermined using Anton Paar DMA 4500 densitometer;
bdetermined using Anton Paar AMVn viscometer.

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Table 1. Abbreviations, names, sources, purities and structures of investigated ionic liquids.
Table 1. Abbreviations, names, sources, purities and structures of investigated ionic liquids.
Abbreviation, Name, Source, PurityStructureReference
abbreviation: [N-C3OHPY][FAP]
name: 1-(3-hydroxypropyl)pyridinium trifluorotris(perfluoroethyl)phosphate
source: MERCK
purity > 0.999 mass fraction
water content < 100 ppm
halide content < 100 ppm
Ijms 12 03553f2[17]
abbreviation: [N-C3OHPY][NTf2]
name: 1-(3-hydroxypropyl)pyridinium bis(trifluoromethylsulfonyl)-amide
source: MERCK
purity > 0.999 mass fraction
water content < 100 ppm
halide content < 100 ppm
Ijms 12 03553f3[18]
abbreviation: [emim][TCB]
name: 1-ethyl-3-methylimidazolium tetracyanoborate
source: MERCK
purity > 0.99 mass fraction
water content < 200 ppm
halide content < 100 ppm
Ijms 12 03553f4[19]
abbreviation: [dmim][TCB]
name: 1-decyl-3-methylimidazolium tetracyanoborate
source: MERCK
purity > 0.9996 mass fraction
water content: < 100 ppm
halide content < 100 ppm
Ijms 12 03553f5[20]
abbreviation: [bmPIP][SCN]
name: 1-butyl-1-methylpiperidinium thiocyanate
source: IoLiTec
purity > 0.98 mass fraction
water content: < 100 ppm
halide content < 100 ppm
Ijms 12 03553f6[21]
abbreviation: [pmPIP][NTf2]
name: 1-propyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)-amide
source: IoLiTec
purity > 0.99 mass fraction
water content: < 100 ppm
halide content < 100 ppm
Ijms 12 03553f7[22]
abbreviation: [bmPIP][NTf2]
name: 1-butyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)-amide
source: IoLiTec
purity > 0.99 mass fraction
water content: < 250 ppm
halide content < 100 ppm
Ijms 12 03553f8[23]
abbreviation: [OiQuin][NTf2]
name: N-octyl-isoquinolinium bis(trifluoromethylsulfonyl)-amide
source: synthesized
purity > 0.99 mass fraction
water content: < 180 ppm
halide content < 100 ppm
Ijms 12 03553f9[24]
Table 2. Hildebrand solubility parameters, δ2 and standard enthalpies of vaporization for the investigated ionic liquids.
Table 2. Hildebrand solubility parameters, δ2 and standard enthalpies of vaporization for the investigated ionic liquids.
Ionic LiquidT/Kδ2/MPa0.5ΔvapH/kJ·mol−1
[N-C3OHPY][FAP]298.1525.0a212.3
308.1524.7209.6
318.1524.5206.6
328.1524.2203.3
338.1523.9199.6
348.1523.6196.2
358.1523.3192.1

[N-C3OHPY][NTf2]298.1526.0a186.1
318.1525.6182.0
328.1525.3179.5
338.1525.1176.9
348.1524.8174.2
358.1524.5171.2

[emim][TCB]298.1525.9149.5
308.1525.7149.0
318.1525.5147.9
328.1525.3146.8
338.1525.1145.6
348.1524.9144.4
358.1524.6142.6

[dmim][TCB]298.1524.0a205.6
328.1523.6201.9
338.1523.3199.4
348.1523.1197.1
358.1522.8194.2
368.1522.5190.5

[bmPIP][SCN]298.1530.7a198.9
318.1530.1193.4
328.1529.8190.4
338.1529.5187.2
348.1529.1183.9
358.1528.8180.5

[pmPIP][NTf2]298.1523.8b172.4
308.1523.6170.9
318.1523.3167.9
328.1523.2166.5
338.1522.9164.2
348.1522.7162.6
358.1522.5160.7

[bmPIP][NTf2]298.1523.4b175.1
308.1523.2173.4
318.1523.0171.7
328.1522.8169.7
338.1522.6168.0
348.1522.4166.4
358.1522.2164.6

[OiQuin][NTf2]298.1522.5b201.3
328.1521.9195.5
338.1521.7193.2
348.1521.6192.1
358.1521.4189.7
368.1521.2187.6
aExtrapolated values calculated using polynomial regression;
bExtrapolated values calculated using linear regression.
Table 3. Hildebrand solubility parameters, δ2 determined by different methods for selected ionic liquids based on [NTf2] anion at T = 298.15 K.
Table 3. Hildebrand solubility parameters, δ2 determined by different methods for selected ionic liquids based on [NTf2] anion at T = 298.15 K.
Ionic Liquidδ2/MPa0.5Method, Reference
[emim][NTf2]16.2melting temperature [9]
19.3activation energy of viscosity [12]
21.3benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 120.6) [25]
22.3IGC [4]
22.6benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 134) [26]
22.7benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 136) [27]
27.5aactivation energy of viscosity [11]
27.6intrinsic viscosity [10]
38.4lattice energy density [16]

[bmim][NTf2]19.8benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 118.5) [25]
20.9activation energy of viscosity [12]
21.2benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 134) [26]
21.3surface tension [13]
22.9benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 155) [27]
25.5Kamlet-Taft Equation [14]
26.5aactivation energy of viscosity [11]
26.7intrinsic viscosity [10]

[hmim][NTf2]19.0benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 124.1) [25]
19.5activation energy of viscosity [12]
20.3IGC [2]
20.5benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 139) [26]
22.9benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 173) [27]
25.2aactivation energy of viscosity [11]
25.6intrinsic viscosity [10]

[omim][NTf2]18.9benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 132.3) [25]
20.2benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 149) [28]
20.2benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 149) [26]
23.0benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 192) [27]
25.0intrinsic viscosity [10]

[bmPY][NTf2]20.6IGC [2]
21.2activation energy of viscosity [12]

[bmPYR][NTf2]21.1from surface tension [13]
22.2benthalpy of vaporization (ΔvapH298.15/kJ·mol−1 = 152) [29]

[N-C3OHPY][NTf2]25.6cIGC [this work]
23.0cactivation energy of viscosity [this work]

[pmPIP][NTf2]23.6cIGC [this work]
23.5cNRHB [15]
23.4cPC-SAFT [15]
22.2cactivation energy of viscosity [this work]

[bmPIP][NTf2]23.2cIGC [this work]
21.8cactivation energy of viscosity [this work]
aat T = 303.15 K;
bcalculated from experimental value of ΔvapH298.15;
cat T = 308.15 K.
Table 4. Hildebrand solubility parameters, δ2 determined by different methods for [N-C3OHPY][NTf2], [pmPIP][NTf2] and [bmPIP][NTf2] ionic liquids.
Table 4. Hildebrand solubility parameters, δ2 determined by different methods for [N-C3OHPY][NTf2], [pmPIP][NTf2] and [bmPIP][NTf2] ionic liquids.
Ionic LiquidT/KIGCActivation Energy of Viscosity
[N-C3OHPY][NTf2]308.1525.623.0
318.1525.322.8
328.1525.122.7
338.1524.822.6
348.1524.522.6

[pmPIP][NTf2]308.1523.622.2
318.1523.322.0
328.1523.221.9
338.1522.921.8
348.1522.721.8

[bmPIP][NTf2]308.1523.221.8
318.1523.021.6
328.1522.821.5
338.1522.621.4
348.1522.421.3

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Marciniak, A. The Hildebrand Solubility Parameters of Ionic Liquids—Part 2. Int. J. Mol. Sci. 2011, 12, 3553-3575. https://doi.org/10.3390/ijms12063553

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Marciniak A. The Hildebrand Solubility Parameters of Ionic Liquids—Part 2. International Journal of Molecular Sciences. 2011; 12(6):3553-3575. https://doi.org/10.3390/ijms12063553

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Marciniak, Andrzej. 2011. "The Hildebrand Solubility Parameters of Ionic Liquids—Part 2" International Journal of Molecular Sciences 12, no. 6: 3553-3575. https://doi.org/10.3390/ijms12063553

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