The Hildebrand Solubility Parameters of Ionic Liquids—Part 2

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.


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 [2][3][4][5][6].
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, Δ vap U, to the molar volume, υ: Because ILs have negligible vapor pressure, experimental measurements of their energy of vaporization are difficult. For this reason, experimental data of Δ vap U 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 [17][18][19][20][21][22][23][24].

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 where: µ is the dynamic viscosity of IL (in units of mPa· s), υ is the molar volume (in units of cm 3 · mol -1 ), h is Planck constant (in units of J· s), N A is Avogadro constant (in units of mol -1 ), and K v is a proportionality constant. They calculated K v value of 7.8 for ILs based on [NTf 2 ]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 K v 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-C 3 Table 3S). Results are presented in Table 4. The differences in results are in the range from 3 to 10%.

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 [17][18][19][20][21][22][23][24].

Theoretical Basis
Retention data were used for the calculation of Hildebrand 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 at the column outlet, P w is the vapor pressure of water at T f and U is the flow rate measured with the 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: can be rewritten as: The solubility parameters δ 1 of the solutes were calculated using following equation:  Table 2.

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          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).