Measurement of vaporization enthalpy by isothermogravimetrical method and prediction of the polarity for 1-alkyl-3-methylimidazolium acetate {[C_nmim][OAc] (n = 4, 6)} ionic liquids

Abstract

Ionic liquids 1-butyl-3-methylimidazolium acetate [C₄mim][OAc] and 1-hexyl-3-methylimidazolium acetate [C₆mim][OAc] were prepared by the neutralization method and confirmed by ¹H NMR spectroscopy and differential scanning calorimetry (DSC). Using isothermogravimetrical analysis, the enthalpy of vaporization, Δ^g_lH^°_m(T_av), at the average temperature, T_av, for [C_nmim][OAc] (n = 4, 6) were determined. Using the established method, the difference of heat capacities between the vapor phase and the liquid phase, Δ^g_lC^°_pm, for [C_nmim][OAc] (n = 4, 6) were calculated based on the statistical thermodynamics. Therefore, the value of Δ^g_lH^°_m(T_av) can be transformed into Δ^g_lH^°_m(298) by using Δ^g_lC^°_pm. The vaporization enthalpies were also further tested by molecular dynamic (MD) simulations, and the results were in good agreement with the corresponding experimental values. In terms of the new scale of polarity for ILs, the order of the polarity of [C_nmim][OAc] (n = 4, 6) was also predicted and good agreement with our experiences.

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1. Introduction

Ionic liquids (ILs) are a novel class of green solvents. They have many distinct advantages such as chemical and thermal stability, non-flammability, and chemical tunabilities, and promise widespread application in industry.¹ Acetic acid ionic liquids (AcAILs) have strong solubility and good catalytic properties, which are useful for a indispensable part of solvent systems for cellulose,¹ an enzyme-friendly cosolvent for the resolution of amino acids,² assisted transdermal delivery of sparingly soluble drugs.³ Thus, considering the fact that acetate ionic liquids have a variety of applications, we prepared acetate ionic liquids [C_nmim][OAc] (n = 4, 6) with a fixed alkyl chain length and measured the vaporization enthalpy in this paper.

The knowledge of enthalpy of vaporization is indispensable for the theoretical research and practical application of ILs.⁴ However, experimental techniques of determining the vaporization enthalpy are challenging, and the main problem depend on their negligible vapor pressure at ambient temperatures. This has stimulated the development of new direct experimental methods such as transpiration,^5,6 temperature-programmed desorption and line-of-sight mass spectrometry (LOSMS),^7–10 thermogravimetry,^11–13 high-temperature spectroscopic techniques,¹⁴ drop microcalorimetry,¹⁵ and the Knudsen effusion method.^16,17

Recently, isothermogravimetrical analysis is broadly applied in the research for vaporization enthalpy, which was established by Alexander et al.¹⁸ and Price et al.^19,20 Dai et al.¹¹ firstly extended this method to IL systems. Notably, the method has some crucial advantages: small amounts of sample, short experimental time, and the commercial availability of the experimental setup, and the simplicity of measuring technique. As a result, isothermogravimetrical analysis has attracted more and more attention from the industrial and scientific communities.^13,21,22 Lately, Verevkin et al.²¹ made great efforts to improve experimental conditions and recommended the optimal ones according to which the vaporization enthalpy of the ILs can be measured with a reasonable accuracy of ±3 kJ mol⁻¹.

In order to obtain accurate values of vaporization enthalpy for [C_nmim][OAc] (n = 4, 6) and predict the new scale of polarity that we have ever put forward, this paper reports the following: (1) the preparation of ionic liquids 1-butyl-3-methylimidazolium acetate [C₄mim][OAc] and 1-hexyl-3-methylimidazolium acetate [C₆mim][OAc] using the neutralization method and confirmation by ¹H NMR spectroscopy and differential scanning calorimetry (DSC); (2) determination the enthalpy of vaporization for ionic liquids [C_nmim][OAc] (n = 4, 6) at the average temperature by using isothermogravimetrical analysis and further test by molecular dynamic (MD) simulations; (3) prediction the polarity of [C_nmim][OAc] (n = 4, 6) in terms of the new scale of polarity for ILs.

2. Experimental section

2.1 Chemicals

Distilled deionized water with a conductance of (0.8–1.2) × 10⁻⁴ S m⁻¹ was used in all experiments. The sources and purities of all other chemicals are listed in Table S1.† Acetic acid was distilled and dried under reduced pressure. N-Methylimidazole (AR-grade reagent) was vacuum-distilled prior to use, 1-bromobutane and 1-chlorohexane (AR-grade reagent) were distilled before use. Anion-exchange resin (type 717) was activated by the regular method before use.

2.2 Preparation of the ILs

The [C_nmim][OAc] (n = 4, 6) were prepared by a neutralization method according to Fukumoto et al.²³ Using ion selective electrode, halogen content in [C_nmim][OAc] (n = 4, 6) was less than 230 ppm and the water contents in two samples determined by a Karl Fischer moisture titrator (ZSD-2 type) were 4600 ppm and 4700 ppm, respectively. Structures of the two ILs were confirmed by ¹H NMR spectroscopy (see Fig. S1 and Fig. S2 in ESI†). Differential scanning calorimetry (DSC) measurements showed that two ILs had no obvious melting point, but the values of their glass transition temperatures are −70.5 °C and −63.2 °C, respectively, which are given in Fig. S3 and Fig. S4 in ESI.† The estimated purities of the synthesized ionic liquids [C_nmim][OAc] (n = 4, 6) were greater than 0.990 in terms of the combination of precursor purities and the ¹H NMR spectra.

2.3 TGA experiments for the ILs

Thermogravimetric analysis (TGA) was carried out on a Netzsch Instrument TG209F1 apparatus which is calibrated for temperature according to the method of Stewart²⁴ using indium, tin, bismuth and lead. The accuracy of the temperature measurements was adjusted to be better than ±0.2 K, the magnitude and linearity of the balance response were checked with standard milligram masses.

In order to obtain the range of constant temperature, temperature-ramp TGA experiments were performed for on ca. 10 mg of the ionic liquids, using a heating rate of 10 K min⁻¹ and nitrogen flow of 100 mL min⁻¹ (see Fig. S5 and Fig. S6 in ESI†), from the Fig. S5 and Fig. S6,† it shows that the thermal decomposition temperature, T_onset, were 491.6 K and 495.3 K and were listed in Table 1. Some values of T_onset were collected from literature^25,26 and were also listed in Table 1.

Table 1 The values of T_onset(exp.), T_onset(lit.), and the isothermal temperature range, T-range^b

Ionic liquids	Tonset(exp.)^a/K	Tonset(lit.)/K	T-range/K
a The standard uncertainty (0.68 level of confidence): u(T) = 0.02 K for temperature.b Tonset: thermal decomposition temperature, T-range: the isothermal temperature range which is used to calculate the enthalpy of vaporization in our work.
[C4mim][OAc]	491.6	497 (ref. 25), 489 (ref. 26)	408–448
[C6mim][OAc]	495.3	493 (ref. 26)	408–448

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The isothermal TGA was performed according to our experiments: (1) the sample weights used for isothermal gravimetric analysis were in ca. 50 mg range; (2) nitrogen flow of 100 mL min⁻¹ which was recommended the optional experimental condition (see Fig. S7 in ESI†) was used as the inert purge gas rate; (3) a heating ramp of 10 K min⁻¹ was used followed by a 1.5 h static hold period at 403 K, allowing for the slow removal of volatile impurities such as acetic acid and traces of water prior to a stepwise temperature programmed run; (4) taking the stability of the two ILs into account, 5 K interval as the stepwise temperature and hold period, t, at each isotherm was taken: 40 min at 408 K, 35 min at 413 K, 35 min at 418 K, 30 min at 423 K, 30 min at 428 K, 25 min at 433 K, 25 min at 438 K, 20 min at 443 K, 20 min at 448 K; (5) in the experiments, the same platinum crucible was used for each sample, in order to maintain a uniform cross-sectional area.

According to the isothermal gravimetric experiments, plotting (m₀ − m) vs. (t − t₀) (m is sample mass, t is time, subscript 0 means initial state) for the ILs at each isotherm in the temperature range from 408 K to 448 K, two good straight lines were obtained (see Fig. S8 and Fig. S9†). Both lines are typical time-course isothermal TGA mass loss curves and the values of their slopes of the ILs, −dm/dt, are listed in Table S2.† From Fig. S8 and Fig.S9,† the isothermal TGA mass loss curves are all rigorously linear with correlation coefficients exceeding 0.999. The high linearity associated with the isothermal TGA curves reveals zero-order mass loss kinetics, providing strong evidence that the observed decrease in mass over time at constant temperature results from vaporization of the IL and does not originate from evolution of thermal degradation product or from impurity.²⁷ And in order to confirm the absence of decomposition of ILs in the experimental conditions, the residual ILs in the crucible were analyzed by ¹H NMR spectroscopy (see Fig. S10 and Fig. S11†). No decomposition of ILs in the experimental conditions was detected.

3. Results and discussion

3.1 The vaporization enthalpy of the ILs

Alexander¹⁸ and Price^19,20 have conducted extensive research to establish the measurement of vaporization enthalpy based on TGA methodology. Only an abbreviated derivation of the regression formula is given below. The relationship between vapor pressure, p, and the rate of mass loss, −dm/dt, under the conventional TGA conditions can be described by the Langmuir equation:¹⁹

−dm/dt = pα(M/2πRT)^1/2 (1)

where p is the pressure, α is the vaporization constant, T is the absolute temperature, R is the universal gas constant, and M is the molar mass. Under vacuum conditions, α has a value of unity. In the presence of a purge gas α can be considered as a constant. The Langmuir equation holds true for a certain rate of mass loss if the interface of a given TGA crucible maintains a constant area. Because the values of vaporization rates of ILs are very small, the condition of negligible change in interfacial area between the ILs sample and the atmosphere is satisfied during slow isothermal vaporization experiments.

Eqn (1) can be recast as

p ∝ (T)^1/2(−dm/dt) (2)

The Clausius–Clapeyron equation can be used to interrelate vapor pressure with vaporization enthalpy and temperature:

ln p = b − Δ^g_lH^°_m/RT (3)

where b is an empirical parameter. Taking into account the positive relationship between p and (−dm/dt)T^1/2, the following regression equation can be easily derived by inserting eqn (2) into eqn (3):

ln[(−dm/dt)T^1/2] = c − Δ^g_lH^°_m/RT (4)

where c is another empirical parameter.

According eqn (4), the values of ln[(−dm/dt)T^1/2] of the samples in a given temperature range were calculated and are listed in Table S2.†

Plotting ln[(−dm/dt)T^1/2] against 1/T according to eqn (4) [ln[(−dm/dt)T^1/2] = c − Δ^g_lH^°_m/RT], two good straight lines with r² exceeding 0.997 were obtained (see Fig.1). The slopes of the straight lines were used to calculate the vaporization enthalpy of the ILs [C_nmim][OAc] (n = 4, 6) at an average temperature, T_av:

Δ^g_lH^°_m(T_av) = −RS_L (5)

where S_L is slope, T_av is the average temperature. The values of S_L for the two ILs are −1.5376 × 10⁴ and −1.6004 × 10⁴, respectively. According to eqn (5), the calculated values of Δ^g_lH^°_m(T_av) for [C_nmim][OAc] (n = 4, 6) are 127.8 kJ mol⁻¹ and 133.1 kJ mol⁻¹ at the average temperature 428 K, respectively, and they are listed in Table 2. From Table 2, it can be seen that the value of the average vaporization enthalpy of [C₆mim][OAc] is bigger than that of [C₄mim][OAc].

Fig. 1 Plot of ln[(−dm/dt)T^1/2] vs. T⁻¹[C_nmim][OAc] (n = 4, 6) [C₄mim][OAc] y = 28.88–1.5376 × 10⁴x, r² = 0.9977, s = 0.05 [C₆mim][OAc] y = 30.46–1.6004 × 10⁴x, r² = 0.9979, s = 0.05.

Table 2 The values of Δ^g_lH^°_m(T_av)^a, Δ^g_lC^°_pm, Δ^g_lH^°_m(298) and Δ^g_lH^°_m for [C_nmim][OAc](n = 4, 6)

ILs	Δ^glH^°m(Tav)/kJ mol^−1	Tav/K	Δ^glC^°pm/J K^−1 mol^−1	Δ^glH^°m(298)/kJ mol^−1	Δ^glH^°m^b/kJ mol^−1
a The standard uncertainty (0.68 level of confidence): u(T) = 0.02 K for temperature and the expanded uncertainties Uc (0.95 level of confidence) for the vaporization enthalpy of the ILs [Cnmim][OAc] (n = 4, 6) at an average temperature, Δ^glH^°m(Tav) were given inside the table, respectively.b The vaporization enthalpy values were obtained by molecular dynamics simulations for [Cnmim][OAc](n = 4, 6) at 298 K.
[C4mim][OAc]	127.8 ± 4.3	428	−53.4	134.8	134.2933
[C6mim][OAc]	133.1 ± 4.2	428	−58.7	140.7	142.8351

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In order to compare the values of enthalpy of vaporization obtained from different experimental methods, Δ^g_lH^°_m(T_av) should be converted into Δ^g_lH^°_m(298) at reference temperature 298 K, using the following equation:

Δ^g_lH^°_m(298) = Δ^g_lH^°_m(T_av) + Δ^g_lC^°_pm(298 − T_av) (6)

where Δ^g_lC^°_pm is the difference in heat capacity of gaseous state and liquid of the ILs at constant pressure (Δ^g_lC^°_pm = C^°_pg − C^°_p1). At first, in order to facilitate, Δ^g_lC^°_pm was considered to be a constant,^7,21,22 −94 J K⁻¹ mol⁻¹ or −100 J K⁻¹ mol⁻¹. However, Verevkin et al.^28,29 have clearly pointed out that the estimated value of Δ^g_lC^°_pm is excessively overestimated. Thus, even having reliable experimental vaporization enthalpies at T_av, the simple adjustment of the experimental values to the 298 K provides an additional uncertainty to the experimental results. For example, if T_av = 450 K, the deviation of 10 J K⁻¹ mol⁻¹ in Δ^g_lC^°_pm corresponds to 1.5 kJ mol⁻¹ in the enthalpy of vaporization at 298 K. Verevkin et al.²⁸ had discussed a variety of estimation methods, but we think that the method of estimating Δ^g_lC^°_pm proposed by Paulechka et al.¹⁶ and Zaitsau et al.³⁰ is appropriate which is based on the statistical thermodynamics. According to this approach, the new estimation values of Δ^g_lC^°_pm based on statistical thermodynamics and some auxiliary experimental data are carried out and values of Δ^g_lC^°_pm for [C_nmim][OAc] (n = 4, 6) are −53.4 J K⁻¹ mol⁻¹ and −58.7 J K⁻¹ mol⁻¹, respectively and are listed in Table 2. The detailed procedures of calculating Δ^g_lC^°_pm are placed in ESI.† From Table 2 can be seen, the estimation values of Δ^g_lC^°_pm increase along with increasing the number of methylene group in the alkyl chains of the ILs [C_nmim][OAc] (n = 4, 6). According to eqn (6), Δ^g_lH^°_m(298) of [C_nmim][OAc] (n = 4, 6) were calculated and also listed in Table 2. From Table 2, it can be seen that the values of the vaporization enthalpy increase along with increasing the number of methylene group in the alkyl chains of the ILs.

3.2 Molecular dynamics simulations for Δ^g_lH^°_m

A molecular-based understanding is a great challenge by molecular dynamic (MD) simulations, which are now widely applied to determine the structural, dynamic, and thermodynamic properties of ILs. In this study, the enthalpy of vaporization Δ^g_lH^°_m for [C_nmim][OAc] (n = 4, 6) were performed using the Tinker 4.2 molecular modeling package.³¹ For the ILs, the usually force field was based on an AMBER-type parametrization,³² which has been specifically optimized for imidazolium-based ILs and widely used in other studies.³³ The restraint electrostatic potential (RESP) charges were fitted to determine the ionic charges of the [C_nmim][OAc] by the RED III scheme. The labeling scheme and the corresponding completed set of force field parameters are shown in Fig. S12, Tables S3 and S4,† respectively. Initial system geometries were generated by randomly inserting 126 [C_nmim][OAc] (n = 4, 6) into the simulation cell and then allowing the system to relax for 3 ns with an NVT ensemble.³⁴ This step was followed by equilibrating the system for 3 ns within the NPT ensemble. Berendsen thermostat and barostat were used to control the temperature and pressure at 298 K and 0.1 MPa, respectively.³⁵ Finally, because of the specific viscosity of the IL system, the production stage was continued for 3 ns using an NVT ensemble.

The enthalpy of vaporization Δ^g_lH^°_m of the [C_nmim][OAc] (n = 4, 6) systems are related to the change in the internal energy, U_inter, which can be directly extracted from the simulation. Our estimations for Δ^g_lH^°_m is calculated as:

Δ^g_lH^°_m = RT − (U_inter − U_iponpair) (7)

where R is the gas constant, U_ionpair represents the average intermolecular energy of an ionic pair at the ideal gas state, which can be simulated in terms of a single ion pair at the same temperature with a large enough simulation box. The corresponding U_inter and U_ionpair values are listed in the Table S5 in ESI.† Thus, Δ^g_lH^°_m for [C_nmim][OAc] (n = 4, 6) ILs at 298 K are listed in Table 2, in which the simulated values of Δ^g_lH^°_m agree excellently with the results of TGA experimental measurements.

3.3 The polarity of the ILs

In previous papers,²² we have pointed out that dielectric constant can't accurately descript the polarity of ionic liquids. For example, the dielectric constant value of [C₄mim][NTf₂] measured by Daguenet et al.³⁶ is 11.7 which is the same with [C₄mim][BF₄] measured by Wakai et al.³⁷ However, as we known, the polarity should be different for [C₄mim][NTf₂] and [C₄mim][BF₄], because the former is hydrophobic and the later is hydrophilic. Therefore, based on Hildebrand's theory,³⁸ we put forward a new scale of polarity, δ_μ, for ILs in previous papers:²²

δ_μ² = Δ^g_lH^°_mμ/V_m − (1 − x_n)RT/V_m (8)

where V_m is molar volume, Δ^g_lH^°_mμ is contribution part from the average permanent dipole moment of ion pair in the IL.

Δ^g_lH^°_mμ = Δ^g_lH^°_m(298) − Δ^g_lH^°_mn (9)

where Δ^g_lH^°_mn is the contribution part from the induced dipole moment of the ILs and its value can be calculated by Lawson–Ingham equation:³⁹

Δ^g_lH^°_mn = C[(n_D² − 1)/(n_D² + 2)]V_m (10)

where C is an empirical constant which equals 1.297 kJ cm⁻³ for organic liquids, n_D is the refractive index, R_n is the molar refraction. In addition, x_n = Δ^g_lH^°_mn/Δ^g_lH^°_m(298) in eqn (8). Using the experimental data in our previous paper,⁴⁰ the values of δ_μ for [C₄mim][OAc] and [C₆mim][OAc] were 18.2 J^1/2 cm^−3/2 and 16.0 J^1/2 cm^−3/2 according to eqn (8), and were listed Table 3. As listed in Table 3, the values of δ_μ decrease with increasing the number of methylene (–CH₂–) group in the alkyl chains of the ILs, that is, polarity of the ILs reduces with increasing the number of the methylene.

Table 3 The values of n_D, D, M, ρ, Δ^g_lH^°_mn, Δ^g_lH^°_m(exp), Δ^g_lH^°_mμ and δ_μ for [C_nmim][OAc] (n = 4, 6) and others at 298 K

Ionic liquids	nD	D	M/g mol^−1	ρ/g cm^−3	Δ^glH^°mn/kJ mol^−1	Δ^glH^°m(exp)/kJ mol^−1	Δ^glH^°mμ/kJ mol^−1	δμ/J^1/2 cm^−3/2
a This work; nD is refractive index; M is molecular mass; D is dielectric constant; Δ^glH^°mμ is the contribution part from the average permanent dipole moment; Δ^glH^°mn is the contribution part from the induced dipole moment; δμ is the new scale of polarity.
[C4mim][OAc]	1.4869 (ref. 40)		198.264	1.04740 (ref. 40)	70.6	134.8	64.2	18.2^a
[C6mim][OAc]	1.4829 (ref. 40)		226.316	1.01700 (ref. 40)	82.4	140.7	58.3	16.0^a
[C2mim][NTf2]	1.421 (ref. 41)		391.31 (ref. 41)	1.50 (ref. 11)	85.8	132.7 (ref. 30)	46.9	13.28
[C4mim][NTf2]	1.427 (ref. 41)	11.7 (ref. 30)	419.37 (ref. 41)	1.42 (ref. 11)	98.4	137.8 (ref. 30)	39.5	11.45
[C6mim][NTf2]	1.431 (ref. 41)		447.42 (ref. 41)	1.33 (ref. 11)	112.9	142.3 (ref. 30)	29.4	9.26
[C8mim][NTf2]	1.434 (ref. 41)		475.47 (ref. 41)	1.31 (ref. 11)	122.6	147.0 (ref. 30)	24.4	8.13
[C10mim][NTf2]	1.436 (ref. 41)		503.53 (ref. 41)	1.21 (ref. 11)	141.1	147.5 (ref. 30)	6.4	3.88
[C2mim][BF4]	1.409 (ref. 41)	12.8 (ref. 37)	197.97	1.2798 (ref. 42)	85.8	132.7 (ref. 30)	46.9	23.35
[C4mim][BF4]	1.420 (ref. 41)	11.7 (ref. 37)	226.02	1.2015 (ref. 42)	98.4	137.8 (ref. 30)	39.5	21.72
[C2C1im][SCN]	1.5506 (ref. 43)		169.15	1.117 (ref. 43)	62.7	153.7 (ref. 28)	91.0	24.3
[C2C1im][N(CN)2]	1.5112 (ref. 43)		177.11	1.104 (ref. 43)	62.4	156.4 (ref. 28)	94.0	24.0
[C2C1im][C(CN)3]	1.5124 (ref. 43)		201.13	1.0819 (ref. 43)	72.4	138.5 (ref. 28)	66.1	18.7
[C2C1im][B(CN)4]	1.4469 (ref. 43)		225.95	1.0361 (ref. 43)	75.6	135.6 (ref. 28)	60.0	16.4

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Using the values of literature,^{11,30,36,37,41,42} δ_μ = 11.45 J^1/2 cm^−3/2 for [C₄mim][NTf₂] and δ_μ = 21.72 J^1/2 cm^−3/2 for [C₄mim][BF₄] were obtained, from which it is obvious that the values of polarity for [C₄mim][BF₄] is much larger than for [C₄mim][NTf₂]. This result is in good agreement with our experience, that is, [C₄mim][NTf₂] is hydrophobic and [C₄mim][BF₄] is hydrophilic. Using the method in this work, the values of δ_μ for other ILs were calculated from literature^{11,28,30,36,37,41–43} as shown in Table 3. The polarity order of ILs in Table 3 is consistent with the magnitude of δ obtained by Schröder's method.⁴⁴ From Table 3, it is concluded that the δ_μ can be used as a criterion to determine the order of polarity.

4. Conclusions

Two ILs [C_nmim][OAc] (n = 4, 6) were prepared and confirmed. Using isothermogravimetrical analysis, the enthalpy of vaporization at the average temperature, T_av, for the ILs were determined. The difference of heat capacity between the vapor phase and the liquid phase, Δ^g_lC^°_pm, were calculated based on the statistical thermodynamics, and the values of Δ^g_lC^°_pm are −53.4 J K⁻¹ mol⁻¹ and –58.7 J K⁻¹ mol⁻¹ which correspond to [C₄mim][OAc] and [C₆mim][OAc], respectively. In terms of Δ^g_lC^°_pm, the values of Δ^g_lH^°_m(T_av) can be transformed into Δ^g_lH^°_m(298), which are 134.8 kJ mol⁻¹ and 140.7 kJ mol⁻¹ for [C_nmim][OAc] (n = 4, 6) at the reference temperature 298 K, respectively. Simultaneously, the experimental vaporization enthalpy Δ^g_lH^°_m(298 K) is further testified by MD simulations, and the calculated results are in good agreement with corresponding experimental results. Based on the vaporization enthalpy and in terms of Hildebrand solubility parameter theory, the new scale of polarity values, δ_μ, for the ILs can be estimated easily, the satisfactory results were obtained and good agreement with our experiences.

List of symbols

C	1.297 kJ cm^−3, an empirical constant for organic liquids
D	Dielectric constant (−)
−dm/dt	The rate of mass loss (g min^−1)
Δ^glC^°pm	The difference of heat capacities between the vapor phase and the liquid phase (J K^−1 mol^−1)
Δ^glH^°m	The enthalpy of vaporization (kJ mol^−1)
Δ^glH^°m(Tav)	The enthalpy of vaporization at the average temperature Tav (kJ mol^−1)
Δ^glH^°m(298)	The enthalpy of vaporization at 298 K (kJ mol^−1)
Δ^glH^°mμ	The contribution part from the average permanent dipole moment of ion pair in the IL (kJ mol^−1)
Δ^glH^°mn	The contribution part from the induced dipole moment of the ILs (kJ mol^−1)
M	The molar mass (g mol^−1)
nD	The refractive index
p	The pressure (Pa)
R	The universal gas constant (J K^−1 mol^−1)
Rn	The molar refraction (cm^3 mol^−1)
SL	Slope (−)
T	The absolute temperature (K)
Tav	The average temperature (K)
Tonset	The thermal decomposition temperature (K)
T-range	The isothermal temperature range which is used to calculate the enthalpy of vaporization in our work (K)
Uinter	The internal energy (kJ mol^−1)
Uionpair	The average intermolecular energy of an ionic pair at the ideal gas state (kJ mol^−1)
Vm	Molar volume (cm^3 mol^−1)
xn	Δ^glH^°mn/Δ^glH^°m(298)

Greek letters

α	The vaporization constant
δμ	The new scale of polarity (J^1/2 cm^−3/2)
ρ	The density (g cm^−3)

Acknowledgements

This project was supported by the NSFC (21173107, 21373104 and 21373005), Peoples Republic of China.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra12626f

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