The Solubility Parameters of Ionic Liquids

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.


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 (G E ) model parameters (e.g., Wilson, NRTL, UNIQUAC), predicting the existence of an azeotrope, analytical OPEN ACCESS 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 [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].
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 [21][22][23][24], 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.

Results and Discussion
The Hildebrand's solubility parameters (δ 2 ) 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. [21][22][23]. The results are presented in Table 2 and are compared to results taken from the literature [21][22][23][24][25][26].    15 24.20 328. 15 24.13 338. 15 24.05 348. 15 23.99 358. 15 23.93  [25] for the IGC and intrinsic viscosity methods, respectively. It was found that values of δ 2 determined using the IGC method by Mutelet et al. [21][22][23] 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][BF 4 ] ionic liquid).

Figure 3 shows influence of the cation structure on the solubility parameter for ionic liquids based on [SCN]and [CF 3 SO 3 ]anions. The lowest values of δ 2 are for butyl-methyl-pyridinium [bmPY] + cations ([1,3bmPY][CF 3 SO 3 ] and [1,4bmPY][SCN]).
The influence of the cation on the solubility parameter for the bis(trifluoromethylsulfonyl)-amide based ionic liquids ([NTf 2 ] -) is shown in Figure 4. The solubility parameter increases in the following order: [(C 6 OC) 2 im] + < [hmim] + < [C 6 OCmim] + < [1,4bmPY] + < [Et 3 S] + < [emim] + . The difference in solubility parameters between [hmim] + and [C 6 OCmim] + cations are very small. It is caused by the similar structure of these two cations. The [C 6 OCmim] + cation has an additional methoxy group (-O-CH 2 -) in the structure, which causes a little augmentation of δ 2 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.   Table 3, and are contrasted the results taken from the literature [25][26][27][28][29]. The larger differences in values of enthalpies of vaporization are for ionic liquids based on the [SCN]anion. For ionic [bmim][CF 3 SO 3 ] 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][NTf 2 ] 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][NTf 2 ] 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].

Theoretical Basis
Retention data were used for the calculation of Hildebrand's solubility parameters, δ 2 . According to the Flory-Huggins theory the interaction parameter at infinite dilution can be determined using the following expression: where R denotes the gas constant, T the temperature, * 1 P the saturated vapor pressure of the solute at temperature T, B 11 the second virial coefficient of pure solute, * 1 V and * 2 V the molar volume of the solute and solvent respectively, M 1 the molar mass of solute, ρ 1 and ρ 2 density of solute and solvent respectively, V g specific retention volume which is given by: where m 2 denotes the mass of the solvent on the column packing and V N the net retention volume of the solute given by: where t R and t G are the retention times for the solute and an unretained gas, respectively, U o is the column outlet flow rate, 3 2 J the pressure correction term given by: where P i and P o denote the inlet and the outlet pressure, respectively. The column outlet flow rate corrected for the vapor pressure of water U o is given by: where T f is the temperature of the flow meter, P w is the vapor pressure of water at T f and U is the flow rate measured with the bubble flow meter. The interaction parameter  12  may be expressed as a function of δ 1 and δ 2 which denote the solubility parameters of the solute and of the solvent, respectively by: Equation 6 can be rewritten as: The solubility parameters δ 1 of the solutes were calculated using following equation: where Δ vap H 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 B 11 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 B 11 were obtained from literature [41,42].  Tables 2 and 3, respectively.

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.

Acknowledgements
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.