Practical Determination of the Solubility Parameters of 1-Alkyl-3-methylimidazolium Bromide ([CnC1im]Br, n = 5, 6, 7, 8) Ionic Liquids by Inverse Gas Chromatography and the Hansen Solubility Parameter

The physicochemical properties of four 1-alkyl-3-methylimidazolium bromide ([CnC1im]Br, n = 5, 6, 7, 8) ionic liquids (ILs) were investigated in this work by using inverse gas chromatography (IGC) from 303.15 K to 343.15 K. Twenty-eight organic solvents were used to obtain the physicochemical properties between each IL and solvent via the IGC method, including the specific retention volume and the Flory–Huggins interaction parameter. The Hildebrand solubility parameters of the four [CnC1im]Br ILs were determined by linear extrapolation to be δ2([C5C1im]Br) = 25.78 (J·cm−3)0.5, δ2([C6C1im]Br) = 25.38 (J·cm−3)0.5, δ2([C7C1im]Br) =24.78 (J·cm−3)0.5 and δ2([C8C1im]Br) = 24.23 (J·cm−3)0.5 at room temperature (298.15 K). At the same time, the Hansen solubility parameters of the four [CnC1im]Br ILs were simulated by using the Hansen Solubility Parameter in Practice (HSPiP) at room temperature (298.15 K). The results were as follows: δt([C5C1im]Br) = 25.86 (J·cm−3)0.5, δt([C6C1im]Br) = 25.39 (J·cm−3)0.5, δt([C7C1im]Br) = 24.81 (J·cm−3)0.5 and δt([C8C1im]Br) = 24.33 (J·cm−3)0.5. These values were slightly higher than those obtained by the IGC method, but they only exhibited small errors, covering a range of 0.01 to 0.1 (J·cm−3)0.5. In addition, the miscibility between the IL and the probe was evaluated by IGC, and it exhibited a basic agreement with the HSPiP. This study confirms that the combination of the two methods can accurately calculate solubility parameters and select solvents.


Introduction
Ionic liquids (ILs), as demonstrated by green and neoteric solvent research in recent years [1,2], are salts that are commonly made up of asymmetric organic cations, and either inorganic or organic anions [3]. ILs have been widely used as novel electrolytes, separation solvents, and reaction media [4,5], due to their excellent thermal stability, adjustable density, low melting point, strong solvation and high electrochemical stability [6,7]. However, their cost and high viscosity hinders their application. Knowledge about the thermophysical properties of each ionic liquid is essential for scaling up its potential applications. Moreover, 1-alkyl-3-methylimidazolium bromides ([C n C 1 im]Br) are one of the most commonly investigated types of ILs, solely for their use as an intermediate compound.
The specific retention volume, V 0 g , at the zero-pressure standard state was determined experimentally from Equation (1) [23,24], which is: 15 mT a F P 0 − P w P 0 (t r − t 0 ) 3 2 (P i /P 0 ) 2 − 1 where t r is the retention time of the probe, T a is the room temperature, and F is the flow rate of carrier gas, m is the mass of the IL on the column, t 0 is the retention time of the non-interacting probe, P w represents the saturated vapor pressure, and P 0 and P i are the outlet and inlet pressures of the column, respectively. The specific retention volume, V 0 g , is an important term used in determining the thermodynamic parameters of the IL by the IGC. V 0 g of 28 probes on four ILs from 303.15 K to 343.15 K were calculated by Equation (1). The results are listed in Table S1. To obtain the retention graph of the probes, InV 0 g was plotted with the temperatures from 303.15 K to 343.15 K. For [C 5 C 1 im]Br, Figure 1 demonstrates that the InV 0 g value decreased with increasing temperature. In addition, a linear relationship between the probe and [C 5 C 1 im]Br was obtained within the range of the experimental temperature. This results indicated that a balance had been established between the probe and [C 5 C 1 im]Br. For the n-alkane series, the V 0 g increased as the numbers of CH 2 groups increased because of the increase of the interaction forces between the IL and the probe caused by the greater amount of CH 2 added into the probe.  (1) where tr is the retention time of the probe, Ta is the room temperature, and F is the flow rate of carrier gas, m is the mass of the IL on the column, t0 is the retention time of the non-interacting probe, Pw represents the saturated vapor pressure, and Po and Pi are the outlet and inlet pressures of the column, respectively.
The specific retention volume, V 0 g , is an important term used in determining the thermodynamic parameters of the IL by the IGC. V 0 g of 28 probes on four ILs from 303.15 K to 343.15 K were calculated by Equation (1). The results are listed in Table S1. To obtain the retention graph of the probes, V In 0 g was plotted with the temperatures from 303.15 K to 343.15 K. For [C5C1im]Br, Figure 1 demonstrates that the V In 0 g value decreased with increasing temperature. In addition, a linear relationship between the probe and [C5C1im]Br was obtained within the range of the experimental temperature. This results indicated that a balance had been established between the probe and [C5C1im]Br. For the n-alkane series, the V 0 g increased as the numbers of CH2 groups increased because of the increase of the interaction forces between the IL and the probe caused by the greater amount of CH2 added into the probe. (c) cyclohexene, octene, pentanone, 3-pentanone, thiophene, nitromethane, p-xylene; (d) methanol, ethanol, propanol, isopropanol, butanol, 2-butanol, isobutanol.
The Flory-Huggins interaction parameter, χ 12 , which was obtained using IGC experiments, was calculated by using the expression [13,25].
where V 2 is the specific volume of the IL, T is the column temperature, V 1 is the molar volume of the probes, P 0 1 represents the probe vapor pressure at the column temperature, R represents the gas constant, and B 11 is the second viral coefficient of the probe, where the probe solvent solubility parameter, δ 1 , can be obtained from the literature acquired by using Equation (3) [26], which is: where V c is the critical molar volume of the solvent, T c represents the critical temperature of the solvent [27], and n is the number of carbon atoms in the solute. The Flory-Huggins interaction parameter, χ 12 , plays a significant role in predicting the miscibility between the IL and the probe. The χ 12 values were calculated according to Equation (2), as listed in Table 1, which shows that χ 12 of some probes, such as thiophene, increased when the temperature increased. However, χ 12 of other probes, such as n-butyl benzene, o-xylene, m-xylene, p-xylene, ethyl benzene, toluene, nitromethane, methanol, ethanol, n-propyl benzene, cyclohexene, octene, pentanone, 3-pentanone, propanol, benzene, isopropanol, butanol, n-C 6 to n-C 12 , 2-butanol, and isobutanol decreased when the temperature increased. The reasons for this change in χ 12 may include: enthalpy, χ H , and entropic, χ S [28]. χ H is related to the intermolecular forces between the IL and the probe, which gradually decrease with increasing temperature. Compared with the enthalpy, χ S displays an opposite, trend, and it is associated with the free solvent volume. The decrease in the χ 12 value means that the IL-probe interactions are becoming strong. According to the Flory-Huggins theory, an χ 12 value below 0.5, indicates that the IL and the probe are completely miscible. By contrast, an χ 12 value above 0.5 indicates that the IL and probe are insoluble or partially dissolved. In other words, a low χ 12 value reflects good compatibility. The following rules have been developed for the system [29,30]: an χ 12 value that is lower than 0.5 indicates that the solvent is good, and a value of between 0.5 and 1 indicates a moderately suitable solvent, whereas a χ 12 value that is larger than 1 indicates a poor solvent. The results are listed in Table 1. The χ 12 values indicated that nitromethane, methanol, ethanol, butanol, thiophene, 2-butanol, isopropanol, propanol, and isobutanol were excellent solvents for all of the examined ILs. By contrast, n-propyl benzene, cyclohexene, ethyl benzene, o-xylene, m-xylene, p-xylene, the n-alkanes (n-C 6 to n-C 12 ), octane, and n-butyl benzene were poor solvents for all of the examined ILs. Table 1 shows that at the same temperature, the best solvents for dissolving the four ILs were alcohols, followed by benzenes and n-alkanes. This finding was related to the polarities of the solvents.

The Hildebrand Solubility Parameter
The Hildebrand solubility parameter is defined as the square root of the cohesive energy (CED) [31].
where ∆E v is the energy of vaporization, V 1 is the molar volume, and ∆H v is molar enthalpy of evaporation.
For the ILs, the calculation formula for the Hildebrand solubility parameter, δ 2 , was calculated using the following equation [32,33]: By plotting the left-hand side of Equation (5) as a function of the probe solubility parameter δ 1 at different temperatures [34], δ 2 was obtained from the slope of the straight line.
The variable δ 2 plays a significant role in selecting solvents to dissolve or swell materials, judging the compatibility of blends, and selecting the pharmaceutical solvents. The δ 2 for the IL [C 5 C 1 im]Br from 303.15 K to 343.15 K was calculated from δ 2 1 /RT − χ 12 /V 1 versus δ 1 , as shown in Figure 2. The δ 2 1 /RT − χ 12 /V 1 versus δ 1 graphs for the three ILs are shown in Figures S1-S3. The δ 2 of the four examined ILs and the literature are given in Table 2. As shown in Table 2 respectively. The δ 2 shows a slight decrease with increasing temperature, something that has also been observed by Marciniak [35] and Moganty [36]. As the temperature increases, the δ 2 values decrease, because the molar enthalpy of evaporation decreases with temperature, and the molar volume increases with temperature. We also found that δ 2 decreases with increasing alkyl chain length at same temperature, due to the molar enthalpy of evaporation decreasing with the molar mass increase of cations, which is in agreement with the results reported by Alavianmehr [37] and Marciniak [38]. In other words, the more aliphatic the character of the imidazolium cation, the lower the solubility parameters. In addition, we were able to obtain the δ 2 of the ILs at room temperature, using the extrapolation method, based on the relationship curve seen in Figure 3. The δ 2 values of three ILs at 298.15 K are shown in Table 2. They also follow the rule: [C 5 C 1 im]Br > [C 6

Hansen Solubility Parameter
According to the HSP concept, the total solubility parameter (δ t ) of an IL can be divided into partial solubility parameters, namely, polar (δ P ), hydrogen bonding (δ H ) and dispersion (δ D ) [39][40][41]: The distance (R a ) between the solvent and the IL within a three-dimensional (3D) diagram was calculated using Equation (7) [42,43]: The relative energy difference (RED), which plays a significant role in predicting the compatibility of the IL and the solvent, can be calculated by Equation (8): where R 0 is the interaction radius of the IL, R a is the distance between the solvent and center of the solubility sphere, δ 1 i represents the HSP for the IL, and δ 2 i is the HSP for the solvent. RED ≤ 1 indicates a good solvent, while a progressively higher RED value implies a poor solvent.
The double-sphere is divided into two domains (the blue solid blue ball at the center represents D 1 , and the green ball represents D 2 ). The Hansen solubility parameters of the ILs can be acquired by Equation (9)-(11) [44], which are: a = R 01 /(R 01 + R 02 ) where δ i1 and δ i2 are the solubility parameters of the D 1 and D 2 domains, R 01 are the interaction radii of the D 1 domain, R 02 represent the interaction radii of the D 2 domain, and δ i (the Midpoint) is a solubility parameter that considers the volume of spheres.

Solubility Test for ILs
The solubility test results of each ionic liquid in 51 pure solvents are summarized in Table 3. We found that good and poor solvents could be obtained from the RED values. The four ILs were found to be poorly dissolved in n-propyl benzene, m-xylene, cyclohexene, o-xylene, ethyl benzene, p-xylene, n-C 6 , n-C 7 , n-C 8 , n-C 9 , n-C 10 , n-C 11 , n-C 12 , octane, and n-butyl benzene, whereas nitromethane, methanol, ethanol, butanol, thiophene, 2-butanol, isopropanol, propanol, and isobutanol were favorable solvents for the four examined ILs. These results are basically consistent with those derived from IGC, based on the χ 12 values. The determination of the miscibility between the IL and the probe by HSPiP is a supplement to the determination of IGC, due to the huge amount of HSPiP data. In practical applications, the combination of the two methods can accurately select solvents.

HSPs of the ILs
Considering [C 5 C 1 im]Br as an example, 51 solvents were used to dissolve this. The results of the 3D solubility parameter spheres and the two-dimensional (2D) graphs of the Hansen space are shown in Figure 4. From Figure 4a, we can see that the green sphere is [C 5 C 1 im]Br, the blue solid blue ball at the center represents the D 1 domain, and the green ball represents D 2 . The blue ball points represent good solvents, and the red data points without the sphere represent solvents, which will, advantageously, not dissolve the IL. Moreover, we can clearly see the solvent distribution from the 2D graphs (Figure 4b). The graphs of HSPs for the other ILs are listed in Figures S4-S6. The simulation results of the four ILs are given in Table 4. The δ t values of the four ILs fitted the following rule: [C 5 C 1 im]Br > [C 6 C 1 im]Br > [C 7 C 1 im]Br > [C 8 C 1 im]Br. The δ 2 values of the ILs decreased with an increase of the alkyl chain. It should be added that the values δ 2 of the four ILs obtained by the HSPiP were higher than those obtained by IGC. However, the results obtained by both methods were within an error range of 0.01-0.1 (J·cm −3 ) 0.5 . The harmony between the calculated and experimental values of the solubility parameters is remarkable. The IGC method calculates the δ 2 values through a series of formulas, producing theoretical values, while the HSPiP method is based on solubility testing used to obtain the HSPs of ILs, producing experimental values, which are closer to the true values. Br as an example, 51 solvents were used to dissolve this. The results of the 3D solubility parameter spheres and the two-dimensional (2D) graphs of the Hansen space are shown in Figure 4. From Figure 4(a), we can see that the green sphere is [C5C1im]Br, the blue solid blue ball at the center represents the D1 domain, and the green ball represents D2. The blue ball points represent good solvents, and the red data points without the sphere represent solvents, which will, advantageously, not dissolve the IL. Moreover, we can clearly see the solvent distribution from the 2D graphs (Figure 4(b)). The graphs of HSPs for the other ILs are listed in Figures S4-S6. The simulation results of the four ILs are given in Table 4

Materials
The 1-pentyl-3-methylimidazolium bromide ([C 5 C 1 im]Br), 1-hexyl-3-methylimidazolium bromide ([C 6 C 1 im]Br), 1-heptyl-3-methylimidazolium bromide ([C 7 C 1 im]Br), and 1-octyl-3-methylimidazolium bromide ([C 8 C 1 im]Br) were supplied by Chengjie Chemical Co., Ltd. (Shanghai, China). The water content and volatile compounds in the ILs were reduced by vacuum evaporation before the experiment. The vacuum evaporation pressure was 0.8 KPa, and the temperature was 363 K. The water content after vacuum evaporation was determined by using the Karl-Fisher titration technique [45], and the mass fraction of the water was less than 600 ppm. The required solvents for the experiment were purchased from J & K Scientific Ltd. (JULABO TitroLine 7750, Germany). All of the studied solvents were used without further purification. The solutes (J & K Scientific Ltd.) with purities better than 0.97 were used without further purification. The CASRN, initial mole fraction purity, initial mole fraction purity, source, and chemical name of the ILs are given in Table S2 in the Supplementary Materials.

Inverse Gas Chromatography
All experiments were performed on an Agilent 6890 gas chromatograph (Santa Clara, CA, USA) equipped with a flame ionization detector. The detector temperature was kept at 503.15 K and the injector was operated at 523.15 K during all of the experiments. Methane was used to determine the column holdup time, to calculate the retention times of the various probe solvents. High-purity nitrogen was used as a carrier gas, and the flow rate was 20 mL/min. The oven temperature was varied in 10 K intervals, between 303.15 and 343.15 K. Each experiment was repeated at least three times to check its reproducibility.
The stationary phase used in the experiments was prepared by dissolving a weighed sample of the IL in dichloromethane, and then adding it into a weighed amount of 102 silicon alkylation monomer support (80-100 mesh). The mixture was allowed to dry under a rotary evaporator by slow evaporation, to ensure a homogeneous mixture. The chromatographic column was a stainless steel column, with an inner diameter of 2 mm and a length of 1.2 m, and it was purchased from Dalian Ripley Technological Instruments Co., Ltd. (Dalian, China). The coated support was packed into the stainless steel column, and the stationary phase consisted of 20% IL, which was finally heated for 8 h under nitrogen conditions.

HSPiP Method
To determine the HSP of each IL, its interactions with 51 organic solutes were used to plot the Hansen spheres. A total of 0.2 g IL was placed in a test tube containing 2 mL test solvent. After thorough stirring, the solution was allowed to stand for 24 h at 298.15 K, and dissolution was visually observed. The solvents which could be categorized as good, i.e., those which were totally dissolved in the IL, were given a score of "1", and poor solvents, which were partially dissolved or insoluble, were given a score of "0". The experimental data were inputted via HSPiP (Ver.4.1.07, Louisville, KY, USA) to obtain the Hildebrand solubility parameters and HSPs of the ILs.

Conclusions
It is necessary to know the solubility parameters of ILs. In this study, the δ 2 values of four ILs were calculated by IGC, and the HSPs of the ILs were determined using the HSPiP method, based on solubility testing. It was found that δ 2 decreased with increasing alkyl chain length, as well as when the temperature increased. At room temperature, the δ 2 values of the four [C n C 1 im]Br ILs considered were consistent across both methods. In addition, the miscibility between the IL and the probe was successfully determined, using χ 12 values and solubility testing, the results were basically consistent across both methods.  Figure S4: (a) The 3D graph with the coordinates of [C 6 C 1 im]Br; (b) The 2D graphs corresponding to the 3D graph of [C 6 C 1 im]Br. Figure S5: (a)The 3D graph with the coordinates of [C 7 C 1 im]Br; (b) The 2D graphs corresponding to the 3D graph of [C 7 C 1 im]Br. Figure S6: (a) The 3D graph with the coordinates of [C 8 C 1 im]Br; (b) The 2D graphs corresponding to the 3D graph of [C 8 C 1 im]Br, Table S1:The specific retention volume, V 0 g , between the probe and IL at various temperatures for the hypothetical liquids at zero pressure, Table S2

Conflicts of Interest:
The authors declare no conflict of interest.