The specific retention volume V_g⁰,which is used to describe the elution behavior of probes,can be calculated using the following equation ^[23]:

The specific retention volume V_g⁰ can be used for the calculation of thermodynamic properties. The weight fraction activity coefficient,Ω ₁^∞,and the molar heat (enthalpy) of sorption,Δ H₁^S,of the probe absorbed by [BMIM]BF₄ are given by the following equations ^{[24, 25]}:

From the obtained weight fraction activity coefficient values,the molar enthalpy of mixing Δ H_l^∞,and values of heats of vaporization Δ H_v,can be calculated according to the following thermodynamic relations ^{[26, 27]}:

Using Flory-Huggins theory,the interactions between [BMIM]BF₄ and the probes may be expressed by means of Flory-Huggins parameter,χ ₁₂^∞,which is calculated by the equations ^{[28, 29]}:

The solubility parameter of each probe,δ ₁,or the square root of cohesive energy density (CED) for the volatile solute is related to enthalpy of vaporization,Δ E_v,and the molar volume as follows ^[17]:

The solubility parameter of [BMIM]BF₄,δ ₂,can be calculated by using the following equation ^{[30, 31]}:

By plotting the left hand side of this equation versus δ ₁,a straight line having a slope of 2 δ ₂/RT and an intercept of (- δ ₂²/RT) is obtained. The solubility parameter of [BMIM]BF₄ can be determined from the slope or the intercept of the straight line. This relation has been widely used in IGC to estimate the solubility parameters of the stationary ^[32].

The ionic liquid [BMIM]BF₄ investigated in this work was obtained from Chengjie Chemical Co.,Ltd. (China)with a quoted purity of greater than 0.99 mass fraction. A homologous series of n-alkanes from n-C₁₀ to n-C₁₂ were used as non-polar probes. Dichloromethane,acetone,chloroform,ethyl acetate,carbon tetrachloride,methyl acetate,cyclohexane,toluene,ethanol and methanol were used as polar probes. All chemicals used in this work were of analytical purity and without further purification.

The stationary phase used in this work was prepared by dissolving a weighed sample of the [BMIM]BF₄ in dichloromethane and depositing the solution on a weighed amount of silicon alkylation 102 monomer support (60-80 mesh). The mixture was allowed to dry under rotary evaporator by slow evaporation,being stirred to ensure a homogeneous mixture. The stationary phase consisted of 20% (mass percentage) of the [BMIM]BF₄. The coated support was packed into a stainless steel column with 0.2 cm inner diameter and 120 cm length. Before experiment,the column was conditioned by blowing nitrogen at 393 K for 8 h.

The IGC measurements were performed on a commercial Shimadzu QP 2010 gas chromatograph,equipped with a thermal conductivity detector. The GC solution (2.30.00) was used to trace detector signals in the analysis. The injector and detector temperatures were kept at 503 K and 533 K,respectively. Dried nitrogen was used as carrier gas with a flow-rate of about 20 mL/min throughout the experiment. The flow rate of nitrogen was measured with a soap bubble flowmeter at room temperature. The temperature of the oven ranged from 333 K to 373 K varied in 10 K increments. In this experiment,air was used to act as the non-interacting void volume maker to determine the column hold-up time of other probe solvents. The mass of the stationary phase,retention time,dead time,column temperature,flow rate,and input and output pressures,all have experimental errors. Based on the error propagation law,the δ ₂ was estimated to have a relative uncertainty within ±5%.

The V_g⁰ data are essential in the determination of physicochemical or thermodynamic properties of a material by IGC ^{[33, 34]}. The V⁰_g values of the solvents on the [BMIM]BF₄ obtained from the IGC measurements from 333 K to 373 K with 10 K intervals were determined using equation (1). Figs. 1 and 2 give examples of plotting ln V_g⁰ versus 1/T for the [BMIM]BF₄. It can be seen that the values of ln V_g⁰ varied with the reciprocal temperatures. ln V_g⁰ decreased with increasing temperatures.

Fig. 1

Fig. 1 Plots of ln Vg0 versus 1/T for some probes

Fig. 2

Fig. 2 Plots of ln Vg0 versus 1/T for other probes

The Δ H₁^S value was obtained from the slope of ln V_g⁰ versus 1/T using equation (3). Δ H_l^∞ was obtained from the slope of ln Ω ₁^∞ versus 1/T using equation (4). Table 1 shows experimentally obtained Δ H_l^S,Δ H_l^∞ and Δ H_v in the temperature range of 333-373 K. The sorption process was dependent on the chemical natures of IL and the interactions between [BMIM]BF₄ and the probes. From the data in Table 1,it can be seen that the molar heats of sorption of the probes increased as the numbers of CH₂ groups in probe molecule increased,indicating that longer CH₂ chains in the probe molecule resulted in stronger interaction between the probe and [BMIM]BF₄. As more CH₂ groups are added to probes,the heat of sorption becomes more exothermic,because the chemical nature and the number of carbons of each probe are different from each other. The polar probes have higher molar heats of sorption than the nonpolar probes,because the nonpolar probes exhibited dispersive forces during interaction with the n-alkane groups of [BMIM]BF₄,whereas the polar probes have dipole-dipole forces and dispersive forces during interaction with the polar groups of [BMIM]BF₄.

Table 1

Table 1 Thermodynamic parameters between the probes and [BMIM]BF Probe - Δ H1S/(kJ/mol) Δ Hl∞/(kJ/mol) Δ Hv/(kJ/mol) n-C10 48.18 -3.749 44.44 n-C11 51.42 -2.643 48.78 n-C12 55.33 -2.455 52.87 Dichloromethane 32.10 -8.217 23.89 Acetone 34.04 -7.846 26.20 Chloroform 35.92 -10.30 25.61 Ethyl acetate 36.62 -6.759 29.86 Carbon tetrachloride 33.15 -5.923 27.23 Methyl acetate 34.57 -6.808 27.77 Cyclohexane 29.70 -2.005 27.70 Benzene 34.99 -6.552 28.44 Toluene 38.38 -5.860 32.52 Ethanol 29.38 8.033 37.41 Methanol 26.31 6.829 33.14

Table 1 Thermodynamic parameters between the probes and [BMIM]BF4

The value of the weight fraction activity coefficient at infinite dilution is especially important. It has been proposed that Ω ₁^∞ values can be used to evaluate the compatibility ^[35]. The following rule has been formulated: Ω ₁^∞＜5,good solvents; 5＜ Ω ₁^∞＜10,the probe is characterized as “moderate solvents”; Ω ₁^∞＞10,poor solvents. The Ω ₁^∞ value was calculated based on equation (2) and listed in Table 2. As shown in Table 2,n-C₁₀ to n-C₁₂,carbon tetrachloride,cyclohexane and toluene are poor solvents for [BMIM]BF₄,while dichloromethane and chloroform are good solvents for [BMIM]BF₄.

Table 2

Table 2 Ω 1∞ values of the probes at various temperatures Probe 333 K 343 K 353 K 363 K 373 K n-C10 170.7 177.1 183.5 190.5 197.4 n-C11 188.7 194.6 199.8 204.7 209.1 n-C12 203.7 208.4 212.8 218.9 223.9 Dichloromethane 3.457 3.762 4.070 4.424 4.744 Acetone 5.108 5.531 5.972 6.449 6.916 Chloroform 2.790 3.090 3.423 3.787 4.151 Ethyl acetate 9.265 9.914 10.61 11.34 12.01 Carbon tetrachloride 10.59 11.25 11.93 12.61 13.33 Methyl acetate 6.481 6.963 7.444 7.938 8.439 Cyclohexane 122.9 126.5 128.4 130.2 133.5 Benzene 8.639 9.161 9.739 10.45 11.11 Toluene 11.29 11.92 12.62 13.38 14.15 Ethanol 6.438 5.690 5.298 4.931 4.697 Methanol 5.355 5.271 4.991 4.504 4.150

Table 2 Ω 1∞ values of the probes at various temperatures

Table 3

Table 3 χ 12∞ between the probes and [BMIM]BF4 at various temperatures Probe 333 K 343 K 353 K 363 K 373 K n-C10 3.392 3.388 3.384 3.381 3.377 n-C11 3.504 3.494 3.481 3.465 3.448 n-C12 3.595 3.577 3.559 3.549 3.533 Dichloromethane 0.07192 0.1107 0.1445 0.1825 0.2074 Acetone -0.05718 -0.02356 0.007342 0.03841 0.06220 Chloroform -0.02009 0.03837 0.09745 0.1552 0.2044 Ethyl acetate 0.6718 0.6945 0.7170 0.7394 0.7521 Carbon tetrachloride 1.384 1.402 1.418 1.432 1.445 Methyl acetate 0.3483 0.3745 0.3958 0.4146 0.4303 Cyclohexane 3.118 3.105 3.077 3.049 3.032 Benzene 0.5847 0.6009 0.6201 0.6487 0.6690 Toluene 0.8434 0.8564 0.8734 0.8912 0.9080 Ethanol 0.2022 0.03393 -0.08209 -0.1985 -0.2919 Methanol 0.01182 -0.04910 -0.1485 -0.2961 -0.4232

Table 3 χ 12∞ between the probes and [BMIM]BF4 at various temperatures

The Flory-Huggins parameter χ ₁₂^∞ is a measurement of the compatibility of a material-solvent pair. The lower the values of χ ₁₂^∞ are,the higher the compatibility will be ^[36]. The values of χ ₁₂^∞ confirmed the evaluations on the values of Ω ₁^∞. Theoretically,χ ₁₂^∞ values smaller than 0.5 indicates IL-solvent systems; χ ₁₂^∞ values larger than 1 indicates an IL-non-solvent system; and 0.5＜ χ ₁₂^∞＜1 values indicates that the solvent is moderate ^[37]. The χ ₁₂^∞ values between [BMIM]BF₄ and the solvents were calculated based on equation (6) at four temperatures,and listed in Tables 3. As shown in Table 3,that parameter again indicated that dichloromethane,acetone,chloroform,methyl acetate,ethanol and methanol were good solvents for [BMIM]BF₄.

The Flory-Huggins parameter has two contributions: entropic and enthalpic ^[38]. The entropic contribution is related to the free volume of the solvent,which increased with increasing temperature. The enthalpic contribution is related to the intermolecular forces between the materials and the solvents,which decreased with increasing temperature. As can be seen from Table 3,the Flory-Huggins parameters of some probes,which include dichloromethane,acetone,chloroform,ethyl acetate,carbon tetrachloride,methyl acetate,toluene and benzene,increased with increasing temperature. It means that the entropic contribution is greater than the enthalpic contribution. The Flory-Huggins parameters of the others decreased with increasing temperature,which means the entropic contribution is greater than the enthalpic contribution,such as n-C₁₀ to n-C₁₂,cyclohexane.

Knowledge on solubility parameters of the IL used in the aforementioned technological applications is of vital importance and has been found to be a useful guide in the selection of solvents for Ils ^[39]. The solubility parameter,δ ₂,for [BMIM]BF₄ was evaluated from equation (8),which was obtained from slopes or intercepts of the plots of δ ₁²/RT- χ ₁₂^∞/V₁ versus δ ₁ as shown in Fig. 3. The solubility parameters of [BMIM]BF₄ were measured at five temperatures to obtain the temperature dependence. The solubility parameters decreased with increasing temperature,which fitted an empirical relationship from Fig. 4. The values in reported literature were mostly calculated or determined at room temperature. The extrapolated value for δ ₂ at 298 K was found to be 23.39 (J/cm³)^0.5.

Fig. 3

Fig. 3 Relation between δ 12/(RT)- χ 12∞/V1 and δ 1 at five temperatures

Fig. 4

Fig. 4 Relation between δ 2 and the temperatures

IGC was proven to be a versatile and useful technique for determining the thermodynamic properties of [BMIM]BF₄. IGC technique was successfully applied to determine [BMIM]BF₄-solvent and [BMIM]BF₄-non-solvent interactions. According to the weight fraction activity coefficient and Flory-Huggins interaction parameter of the various solvents with the [BMIM]BF₄,the results indicated that dichloromethane,acetone,chloroform,methyl acetate,ethanol and methanol were good solvents for [BMIM]BF₄; n-C₁₀ to n-C₁₂,carbon tetrachloride,cyclohexane and toluene were bad solvents for [BMIM]BF₄ at experimental temperatures. The solubility parameter of [BMIM]BF₄ was determined as 23.39 (J/cm³)^0.5 by the extrapolation at 298 K.