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Determination of the Enthalpy of Vaporization and Prediction of Surface Tension for Ionic Liquid 1‑Alkyl-3-methylimidazolium Propionate [Cnmim][Pro](n = 4, 5, 6) Jing Tong,* Hong-Xu Yang, Ru-Jing Liu, Chi Li, Li-Xin Xia,* and Jia-Zhen Yang College of Chemistry, Liaoning University, Shenyang 110036, People’s Republic of China S Supporting Information *

ABSTRACT: With the use of isothermogravimetrical analysis, the enthalpies of vaporization, ΔglHom(Tav), at the average temperature, Tav = 445.65 K, for the ionic liquids (ILs) 1-alkyl-3methylimidazolium propionate [Cnmim][Pro](n = 4, 5, 6) were determined. Using Verevkin’s method, the difference of heat capacities between the vapor phase and the liquid phase, ΔglCpom, for [Cnmim][Pro](n = 2, 3, 4, 5, 6), were calculated based on the statistical thermodynamics. Therefore, with the use of ΔglCpom, the values of ΔglHom(Tav) were transformed into ΔglHom(298), 126.8, 130.3, and 136.5 for [Cnmim][Pro](n = 4, 5, 6), respectively. In terms of the new scale of polarity for ILs, the order of the polarity of [Cnmim][Pro](n = 2, 3, 4, 5, 6) was predicted, that is, the polarity decreases with increasing methylene. A new model of the relationship between the surface tension and the enthalpy of vaporization for aprotic ILs was put forward and used to predict the surface tension for [Cnmim][Pro](n = 2, 3, 4, 5, 6) and others. The predicted surface tension for the ILs is in good agreement with the experimental one.

1. INTRODUCTION Over the past few decades, a new class of novel reaction medium and soft functional materials, ionic liquids (ILs), have been widely applied in science, research, and industry.1−3 The knowledge of enthalpy of vaporization is indispensable for theoretical research and practical application of ILs.4,5 However, the experimental determination of the vaporization enthalpy is a challenging task because, with the exception of the Knudsen method,6,7 traditional experimental techniques for vaporization enthalpy measurement have not been applicable for ILs because of their very low vapor pressures. This has stimulated the development of new direct experimental methods such as lineof-sight mass spectrometry (LOSMS),8,9 high-temperature UV spectroscopic technique (UV),10 quartz crystal microbalance (QCM),11 and temperature-programmed desorption.12 In addition, Dai and co-workers13 first applied the isothermogravimetrical method, which was established to measure the vaporization enthalpy by Alexander and co-workers14 and Price and Hawkins,15,16 to the ILs. The TGA (thermal gravity analysis) method has some crucial advantages: small amounts of sample, short experimental time, and commercial availability of the experimental setup, as well as the simplicity of measuring technique, so that this method has attracted more and more attention from industrial and scientific communities.17−19 Recently, using a commercially available TGA, Verevkin et al.18 carefully made experimental study and recommended the optimal experimental conditions according to which the vaporization enthalpy of the ILs can be measured with a reasonable accuracy, ±3 kJ·mol−1. As a continuation of our previous investigation,19 this paper reports the following: (1) Ionic liquids [Cnmim][Pro](n = 4, 5, 6) were prepared by the neutralization method and characterized by 1H NMR spectroscopy and differential scanning calorimetry © XXXX American Chemical Society

(DSC). (2) The vaporization enthalpies for the ILs were determined using the thermogravimetric approach. (3) A new scale of polarity, δμ (δμ2 is the contribution of dipole moment to the cohesive energy), for the ILs was proposed, and the value of δμ can be estimated. (4) A new theory model on the relationship between the surface tension and the enthalpy of vaporization for aprotic ILs is put forward and used to predict the surface tension.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Propionic acid was distilled and dried under reduced pressure. N-Methylimidazole, 1-bromobutane, 1-bromopentane, and 1-bromohexane were vacuum distilled prior to use. Ethyl acetate and acetonitrile were distilled and then stored over molecular sieves in tightly sealed glass bottles. Anionexchange resin (type 717) was activated by the regular method before use. The source and purity of the materials are listed in Table 1. 2.2. Preparation of the ILs. The ILs, [Cnmim][Pro](n = 4, 5, 6), were prepared by a neutralization method according to Fukumoto et al.20 The structures of the resulting materials were confirmed by 1H NMR spectroscopy (see Figure A in the Supporting Information). Differential scanning calorimetric (DSC) measurements showed that the ILs had no obvious melting point (see Figure B in the Supporting Information). 2.3. Isothermal Gravimetric Analysis for the ILs. In this work a Mettler Toledo Instruments TGA/SDTA851e was used and calibrated for temperature according to Stewart’s method21 Received: September 12, 2014 Revised: October 27, 2014

A

dx.doi.org/10.1021/jp509240w | J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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Table 1. Source and Purity of the Materials mass fraction purity N-methylimidazole ≥ 0.99 propionic acid ≥ 0.99 1-bromobutane > 0.98 1-bromopentane > 0.98 1-bromohexane > 0.98 ethyl acetate > 0.99 acetonitrile > 0.99 anion-exchange resin (type 717, granularity > 0.95)

source ACROS Shenyang Reagent Co. Ltd. Shenyang Reagent Co. Ltd. Shenyang Reagent Co. Ltd. Shenyang Reagent Co. Ltd. Shanghai Reagent Co. Ltd. Shanghai Reagent Co. Ltd. Shanghai Reagent Co. Ltd.

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 was checked with standard milligram masses. First, to determine the range of temperature, conventional TGA curves with ∼12 mg sample weight for [Cnmim][Pro](n = 4, 5, 6) were measured in argon at a flow rate of 60 mL·min−1. Then, the isothermal gravimetric analysis curve for the ILs was measured according to optimal conditions recommended by Verevkin et al.18 and our preliminary work,19 and some suitable experimental parameters were selected: (1) The masses of samples, m, used for isothermal gravimetric analysis were ∼50 mg. (2) A heating ramp of 20 K· min−1 was used, and it stayed for 1 h at 413 K to remove the volatile impurities, such as traces of propionic acid and water. (3) According to the stability of the ILs, the temperature and the length of the experimental time, t, at each isotherm were taken: 35 min at 423 K, 30 min at 433 K, 25 min at 443 K, 20 min at 453 K, 15 min at 458 K, and 10 min at 463 K. (4) The purge gas of 60 mL·min−1 was used. (5) The same platinum crucible was used for each sample, to maintain a uniform cross-sectional area. According to the isothermal gravimetric experiments, by plotting (m0 − m)/kg versus (t−t0)/s (m is the sample mass, t is the time, subscript 0 means the initial state) for the ILs at each isotherm in the temperature range from 423.15 to 463.15 K, a series of good straight lines were obtained (see Figure 1). These straight lines are typical time-course isothermal TGA mass loss curves, and the values of the slopes of the ILs, −dm/dt, are listed in Table 2. As can be seen from Figure 1, 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.22

Figure 1. Plot of (m0 − m)/kg vs (t − t0)/s from the bottom to top: 423.15, 433.15, 443.15, 453.15, 458.15, and 463.15 K, respectively. (a) [C4mim][Pro] ■ 423.15 K: y = 9.83 × 10−9 + 3.81 × 10−10x, r = 0.9996, s = 5.94 × 10−9; ● 433.15 K: y = 2.68 × 10−9 + 7.56 × 10−10x, r = 0.9997, s = 8.16 × 10−9; ▲ 443.15 K: y = −3.65 × 10−8 + 1.50 × 10−9x, r = 0.9995, s = 1.74 × 10−8; ▼ 453.15 K: y = −7.26 × 10−8 + 3.37 × 10−9x, r = 0.9997, s = 2.34 × 10−8; ⧫ 458.15 K: y = −5.85 × 10−9 + 4.68 × 10−9x, r = 0.9999, s = 6.38 × 10−9; ◀ 463.15 K: y = 4.57 × 10−8 + 6.31 × 10−9x, r = 0.9997, s = 2.02 × 10−8. (b) [C5mim][Pro] ■ 423.15 K: y = 2.58 × 10−8 + 3.32 × 10−10x, r = 0.9985, s = 9.68 × 10−9; ● 433.15 K: y = −1.95 × 10−8 + 5.96 × 10−10x, r = 0.9997, s = 6.55 × 10−9; ▲ 443.15 K: y = −3.80 × 10−8 + 1.32 × 10−9x, r = 0.9995, s = 1.49 × 10−8; ▼ 453.15 K: y = −4.50 × 10−8 + 2.96 × 10−9x, r = 0.9997, s = 1.73 × 10−8; ⧫ 458.15 K: y = −2.29 × 10−8 + 4.25 × 10−9x, r = 0.9999, s = 8.05 × 10−9; ◀ 463.15 K: y = −1.25 × 10−8 + 5.66 × 10−9x, r = 0.9999, s = 4.54 × 10−9. (c) [C6mim][Pro] ■ 423.15 K: y = 2.75 × 10−8 + 3.05 × 10−10x, r = 0.9954, s = 1.68 × 10−8; ● 433.15 K: y = −1.87 × 10−8 + 5.70 × 10−10x, r = 0.9995, s = 8.40 × 10−9; ▲ 443.15 K: y = −2.91 × 10−8 + 1.10 × 10−9x, r = 0.9995, s = 1.26 × 10−8; ▼ 453.15 K: y = −4.61 × 10−8 + 2.54 × 10−9x, r = 0.9996, s = 1.82 × 10−8; ⧫ 458.15 K: y = 4.60 × 10−8 + 4.28 × 10−9x, r = 0.9997, s = 2.38 × 10−8; ◀ 463.15 K: y = −1.42 × 10−8 + 6.50 × 10−9x, r = 0.9996, s = 2.62 × 10−8; x: (m0−m)/kg; y: (t−t0)/s.

3. RESULTS AND DISCUSSION 3.1. Vaporization Enthalpies of the ILs. On the basis of the thermogravimetric method, which was established to measure vaporization enthalpy by Alexander and co-workers14 and Price and Hawkins,15,16 Dai and co-workers derived a working equation for the calculation of vaporization enthalpies for the ILs (for the derivation process, see refs 13 and 19), ln[( −dm /dt )T1/2] = c − Δg l H o m/RT

(1)

where T is the absolute temperature, c is an empirical parameter, ΔglHom is the vaporization enthalpy of the IL at the average temperature Tav (Tav = (ΣinTi)/n), and R is the gas constant. According to eq 1, the values of ln[(−dm/dt)T1/2] of the samples at different temperatures were calculated and are listed

in Table 2. By plotting ln[(−dm/dt)T1/2] against 1/T, a good straight line was obtained (see Figure 2). The slopes of the B



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Table 2. Values of −dm/dt and ln[T1/2(−dm/dt)] for [Cnmim][Pro](n = 4, 5, 6) from 423.15 to 463.15 K T/K

T−1/K−1

423.15 433.15 443.15 453.15 458.15 463.15 slope ra sb

0.002363 0.002309 0.002257 0.002207 0.002183 0.002159 −1.423 × 104 −0.999 0.05218

423.15 433.15 443.15 453.15 458.15 463.15 slope ra sb

0.002363 0.002309 0.002257 0.002207 0.002183 0.002159 −1.529 × 104 −0.994 0.1466

1010(−dm/dt)/kg·s−1

ln[T1/2·(−dm/dt)]

T/K

T−1/K−1

3.806 7.562 15.01 33.70 46.80 63.06

−18.6653 −17.9671 −17.2701 −16.4504 −16.1165 −15.8128

423.15 433.15 443.15 453.15 458.15 463.15 slope ra sb

0.002363 0.002309 0.002257 0.002207 0.002183 0.002159 −1.460 × 104 −0.998 0.08125

[C6mim][Pro] 3.046 5.699 10.97 25.41 42.79 64.95

−18.8883 −18.2499 −17.5838 −16.7328 −16.2060 −15.7832

1010(−dm/dt)/kg·s−1

[C4mim][Pro]

a

ln[T1/2·(−dm/dt)]

[C5mim][Pro] −18.8015 −18.2054 −17.3949 −16.5811 −16.2138 −15.9204

3.322 5.959 13.25 29.57 42.45 56.62

The correlation coefficient of fitting ln[(−dm/dt)T1/2] vs 1/T. bThe standard deviation.

calculated values of ΔglHom(Tav) for the ILs at Tav = 445.65 K are listed in Table 3. To compare the values of enthalpy of vaporization obtained from different experimental methods, ΔglHom(Tav) should be converted into ΔglHom(298) at the reference temperature, 298.15 K, using the following equation, Δg l H o m(298) = Δg l H o m(Tav) + Δg Cpo (298 − Tav) l

m

(3)

ΔglCpom

where is the difference in heat capacity of the gaseous and liquid state of the IL at constant pressure (ΔglCpom = CPog − CPol). To facilitate the adjustment of enthalpies of vaporization to 298 K, according to Armstrong et al.,8 we used a tentative estimate of ΔglCpom = −94 J·K−1·mol−1 in our previous paper.19 However, Verevkin and co-workers23,24 have clearly pointed out that the estimated value of ΔglCpom is excessively overestimated. Thus, even having reliable experimental vaporization enthalpies at Tav, the simple adjustment of the experimental values to 298 K provides an additional uncertainty to the experimental results. For example, the deviation of 10 J·K−1·mol−1 in ΔglCpom corresponds to 1.4 kJ·mol−1 in the enthalpy of vaporization at 298.15 K. Recently, Verevkin et al.25 suggested a new approach for estimating ΔglCpom based on statistical thermodynamics and some auxiliary experimental data:

Figure 2. Plot of ln[ (−dm/dt) T1/2] vs 1/T: ■ [C4mim][Pro]: y = 14.93 − 1.424 × 104x, r = −0.999, s = 0.05; ● [C5mim][Pro]: y = 15.63 − 1.461 × 104x, r = −0.998, s = 0.08; ▲ [C6mim][Pro]: y = 17.14 − 1.530 × 104x, r = −0.994, s = 0.14. x: 1/T; y: ln[(−dm/dt)T1/2].

straight lines for each IL were used to calculate the evaporation enthalpy of the ILs at an average temperature Tav, Δg l H o m(Tav) = −RSL

(2)

Δg C po = (3/2)R + (3/2)R + R − 3R − 3R − (C po − C V o m)l

where SL is the slope. The value of SL for [C4mim][Pro] is −1.423 × 104, that for [C5mim][Pro] is −1.460 × 104, and that for [C6mim][Pro] is −1.529 × 104. According to eq 2, the

l

m

m

= − 2R − (C p

o

o

m

− C V m)l

(4)

Table 3. Values of ΔglCpom/J·K−1·mol−1, ΔglHom(298)/ kJ·mol−1, and δμ/J1/2·cm−3/2 for [Cnmim][Pro](n = 2, 3, 4, 5, 6)

a

IL

ΔglHom(Tav)/ kJ·mol−1

[C2mim][Pro] [C3mim][Pro] [C4mim][Pro] [C5mim][Pro] [C6mim][Pro]

111.2 ± 5.9 115.8 ± 2.9a 118.3 ± 2.5 121.5 ± 3.7 127.2 ± 6.8 a

δμ/J1/2·cm−3/2

Tav/K a

a

438.15 438.15a 445.65 445.65 445.65

18.10 17.13a 15.99 14.99 14.44

ΔgloCp m/J·K−1·mol−1

ΔglHom(298)/kJ·mol−1

−51.7 −55.8a −57.8 −60.8 −63.3

118.6 123. 9 126.8 130.3 136.5

a

Ref 19. C



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It is apparent that the contribution (Cpom − CVom)l in eq 4 is the main part of the heat capacity difference, ΔglCpom, and is vitally important for the proper temperature adjustments of vaporization enthalpies. Fortunately, the contribution (Cpom − CVom)l could be easily calculated from the volumetric properties,26 (Cpo − Cv o m)l = (αp2/κT)VmT m

structural corrections of the jth type in the IL. For example, the calculation formula for [C5mim][Pro] (C12H22N2O2) is Δg l H o m(C12H 22N2O2 ) = 12ΔHC + 2ΔHN + 2ΔHO

(7)

According to Verevkin, ΔHC = 2.5, ΔHN = 26.3, and ΔHO = 23.6, so that the values of ΔglHom(298) for [Cnmim][Pro](n = 4, 5, 6) are 127.3, 129.8, and 132.3 kJ·mol−1, respectively, and the values are close to the experimental ones. 3.2. Polarity of [Cnmim][Pro](n = 4, 5, 6). In the previous paper,19 we pointed out that the dielectric constant cannot accurately describe the polarity of ionic liquids. For example, the dielectric constant of [C4mim][NTf2] measured by Daguenet et al.29 is 11.7, which is the same as that for [C4mim][BF4] measured by Wakai et al.30 However, there is a great difference in polarity between them: [C4mim][NTf2] is hydrophobic and [C4mim][BF4] is hydrophilic. Therefore, on the basis of the theory of Hildebrand and Scott,31 we put forward a new scale of the polarity, δμ, for the ILs in the previous paper:19 28

(5)

where αp is the thermal expansion coefficient, K−1; κT is the isothermal compressibility in Pa−1, and Vm is the molar volume in m3·mol−1. The molar volume, as well as the thermal expansion coefficient, is usually derived from the density of ILs and the temperature dependence. The values of κT can be calculated from the speed of sound W (T, p).24 The data needed in the calculation of the values of ΔglCpom are listed in Table S1 of the Supporting Information. Using the values of ΔglCpom, the experimental vaporization enthalpy at Tav can be adjusted to the experimental one at 298.15 K. The calculated values of ΔglCpom and ΔglHom(298) are listed in Table 3. In Table 3, ΔglHom(298) of [Cnmim][Pro](n = 2, 3) were calculated using the values of ΔglHom(Tav) in our previous paper.15 By plotting ΔglHom(298) versus n (n is the number of methylene (−CH2−) groups in the alkyl chains of the ILs), a good straight line (see Figure 3) was obtained, and

δμ 2 = ΔH v μ/Vm − (1 − xn)RT /Vm

(8)

where Vm is the molar volume and ΔHvμ is the contribution from the average permanent dipole moment of the ion pair in the IL, ΔH v μ = Δg l H o m(298) − ΔH v n

(9)

where ΔHvn is the contribution from the induced dipole moment of the IL. Its value can be calculated by the Lawson−Ingham equation,32 ΔH v n = C[(nD2 − 1)/(nD2 + 2)]Vm

where C is an empirical constant that equals 1.297 kJ·cm−3 for organic liquids and nD is the refractive index. In addition, xn = ΔHvn/ΔglH om(298) in eq 8. Using the experimental data in our previous paper,33 the values of δμ for [Cnmim][Pro](n = 4, 5, 6) were calculated from eq 8 and are listed in the fourth column of Table 3. From Table 3 it can be seen that the values of δμ decrease with the increasing number of methylene (−CH2−) groups in the alkyl chains of the ILs, that is, the polarity of the IL reduces with the increase of the number of methylenes. Using the data of Seddon and co-workers,34 δμ = 20.42 J1/2·cm−3/2 for [C4mim][BF4] and δμ = 10.23 J1/2·cm−3/2 for [C4mim][NTf2] were obtained according to the above-described method, so that it is seen that the polarity of [C4mim][BF4] is much larger than that of [C4mim][NTf2]. This result is in good agreement with our experience, that is, [C4mim][NTf2] is hydrophobic and [C4mim][BF4] is hydrophilic. 3.3. Prediction of Surface Tension Using the Vaporization Enthalpy of ILs. To predict the surface tension of the ILs with the use of the vaporization enthalpy, a new theory modelthe surface tension model of the vaporization process of the ILwas put forward. Surface tension is produced due to the mutual attractions between molecules in a liquid; a molecule in the interior is attracted in all directions, but one at the surface is only attracted inward from the surface. Because the saturation vapor pressure is extremely low at the equilibrium between the IL and its vapor at room temperature, the attraction force from the vapor phase can be ignored. With the use of the aprotic ionic liquid of 1−1 type as an example, in the inside of the ionic liquid each ion interacts with Z counterions (Z is the number of counterions), so that the total energy of a pair of cation and anion, εc(l) + εa(l), is

Figure 3. Plot of ΔglHom (298) vs n (n is the number of methylene (−CH2−) groups in the alkyl chains of the ILs), y = 110.4 + 4.2x, r = 0.992, s = 0.976; x: n; y: ΔglHom (298)/kJ·mol−1.

the slope of the line, ΔglHom(−CH2−) = 4.2 ± 0.3 kJ·mol−1, is the contribution of each methylene (−CH2−) group in the alkyl chains of the imidazolium-based ILs. The value of ΔglHom(−CH2−), which is between ΔglHom(−CH2−) = 4.85 ± 0.3 kJ·mol−1 recommended by Archer et al.27 and ΔglHom(−CH2−) = 3.89 kJ·mol−1 obtained by Zaitsau et al.,24 has certain rationality. Verevkin28 has derived a simple straightforward additive approach based on the empirical formula of an IL. It seems to be reasonable to separate the bulk enthalpy of vaporization of an IL into two parts: a main contribution, which comes from the constituent elements (regardless of their position in the cation or anion), and an auxiliary contribution due to specified structural peculiarities of some ILs. The general formula for the vaporization enthalpy calculations of ILs at 298.15 K is eq 6: Δg l H o m(298) = ΣniΔHi + ΣnjΔHj

(10)

(6)

Herein, ΔHi is the contribution of the ith element, ni is the number of elements of the ith type in the IL, ΔHj is the contribution of the jth structural correction, and nj is the number of D



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Table 4. Data Required by Eq 23 and Predicted Values of Surface Tension IL [C2mim][Pro] [C3mim][Pro] [C4mim][Pro] [C5mim][Pro] [C6mim][Pro] [C2mim][NTf2]b [C4mim][NTf2]b [C6mim][NTf2]b [C8mim][NTf2]b [C2mim]EtSO4 [C2Py][NTf2] [C3Py][NTf2] [C4Py][NTf2] [C5Py][NTf2] [C6Py][NTf2] a

γ/mJ·m−2

104V/m3·mol−1

a

38.6 37.3a 36.1a 35.0a 33.9 34.90 31.76 30.94 30.24 48.79c 34.0f 33.3e 32.8f 32.4f 31.7e

γV 2/3/mJ·mol−2/3

ΔglH om (298) /kJ·mol−1

γ(Pre)/mJ·m−2

0.1192 0.1226 0.1255 0.1282 0.1304 0.1412 0.1397 0.1472 0.1548 0.1678 0.1359 0.1390 0.1425 0.1462 0.1484

118.6 123.9 126.8 130.3 136.5 135.3 136.2 139.8 150.0 164.0b 131.4c 134.5d 138.1d 141.7d 145.9d

38.7 37.4 35.9 34.7 34.1 34.6 32.0 30.4 30.1 48.8 34.1 33.4 32.9 32.4 32.1

a

1.717 1.884a 2.050a 2.218a 2.386a 2.575 2.918 3.280 3.663 2.018b 2.527f 2.696e 2.863f 3.030f 3.204e

Ref 19. bRef 28. cRef 40. dRef 24. eRef 41. fEstimated values.

− ε(vib, l)] ≈ 0. From the common statistical thermodynamics knowledge, a sum of contributions of the free rotation and free translational motion into the kinetic energy in the ideal gas state is equal to 3RT. According to the oscillation theory,39 the molecules have no free rotation or linear motion in the liquid state. The translational motion is converted into vibrations with low frequencies, and the rotation is converted into librations or hindered rotation. Their contribution to kinetic energy, ε(transl, l) + ε(rot, l), is

εc(l) + εa(l) = εc(kin, l) + εc(int , l) + Zcεc − a + εa(kin, l) + εa(int , l) + Zaεa − c

(11)

where the subscripts c and a represent cation and anion and εc−a and εa−c represent the interaction energy between cation and anion, respectively, and kin and int in parentheses represent the kinetic energy and the internal energy, respectively. To describe it conveniently, we suppose that Zεc−a = Zcεc−a = Zaεa−c in the following statements. On the surface layer of the IL, each ion interacts with Z(sur) counterions. Because the interaction is missing in the gas-phase direction, Z(sur) < Z, or Z(sur) = xZ, x < 1, so that the total energy, εc(sur) +εa(sur), for a pair of cation and anion is

ε(transl, l) + ε(rot, l) = 3RT + Δε(kin)

where Δε(kin) is the difference between the kinetic energies of the liquid and gaseous states. Therefore, the difference, Δε(l↔g), between the energy of the liquid phase and that of the gaseous phase is

εc(sur) + εa(sur) = εc(kin, sur) + εc(int , sur) + εa(kin, sur) + εa(int , sur) + 2xZεa − c

Δε(l ↔ g) = −Δε(kin) − 2Zεc − a

(12)

Δg lU o m = N Δε(l ↔ g) = −N Δε(kin) − 2NZεc − a

(13)

The energy difference, ΔU(sur), of 1 mol of the ion pairs is ΔU (sur) = 2N (x − 1)Zεc − a

ΔU (sur) = (1 − x)[Δg lU o m + N Δε(kin)]

where N is the Avogadro constant. Nevertheless, many studies have shown that the vapor phase of aprotic ionic liquids is neutral contact ion-pairs,8,35−38 so that the total energy, ε(pair, g), of the ion-pairs is

γ = N −1/3V −2/3(1 − x)Δg lU o m + (1 − x)(N /V )2/3 Δε(kin)

ΔglUom

(17)

(22)

where = − RT, and is the enthalpy of vaporization, which may be measured by experiments. Substituting ΔglHom into eq 22, the RT term and (1 − x)(N/V)2/3Δε(kin) can be combined in a constant term for ionic liquid homologies or similar structure systems. However, (1 − x) and Δε(kin) are very difficult to determine via theoretical calculation. Therefore, we used an empirical method to determine these parameters, and an empirical equation could be obtained,

If it cannot produce a big error, we suppose that εC(int, g) = εC(int, l) and εa(int, g) = εa(int, l). However, εC(kin, g) ≠ εC(kin, l) and εa(kin, g) ≠ εa(kin, l). It is well-established that the kinetic energy in the liquid and gaseous states could be considered as the sum of the translational energy, the rotational energy, and the vibrational energy:

ε(kin g) = ε(transl, g) + ε(rot, g) + ε(vib, g)

(21)

On a unit surface area, the molar number of the ion-pair is N−1/3V−2/3 so that the surface tension may be obtained from eq 21,

ε(pair, g) = [εC(kin, g) + εa(kin, g)] + [εC(int , g) + εa(int , g)] (15)

(16)

(20)

Combining eq 20 with eq 14, we obtain eq 21:

(14)

ε(kin l) = ε(transl, l) + ε(rot, l) + ε(vib, l)

(19)

so that, for 1 mol of the ion-pair, the difference, ΔglUom, is the molar vaporization energy:

The energy difference, Δεc(sur) + Δεa(sur), of a pair of cation and anion between the liquid inside and on the surface layer is Δεc(sur) + Δεa(sur) = 2(x − 1)Zεc − a

(18)

ΔglHom

ΔglHom

γV 2/3 = A + BΔg l H o m

(23) −1/3

where A = (1 − xc)(N) [Δε(kin) − RT/N] and B = N (1 − x). To evaluate A and B, the experimental values of γ and V for 2/3

Usually the difference between the kinetic energy of liquid and gaseous vibrational motion is very small, that is, [ε(vib, g) E



Article

experimental one. Figure 5 shows that the predicted values are highly correlated (r = 0.9986) and extremely similar (gradient = 1.002, close to 1; intercept = −0.07683, close to zero) with the experimental one.

[Cnmim][Pro](n = 2, 3, 4, 5, 6) taken from ref 19 are listed in Table 4. Then, according to eq 23, a good straight line was obtained by plotting γV 2/3 versus ΔglHom with the correlation coefficient (r = 0.985) (see Figure 4). The fitting equation is

4. CONCLUSIONS The ILs [Cnmim][Pro](n = 4, 5, 6) were prepared and characterized. With the use of the isothermogravimetry, the vaporization enthalpies, ΔglHom(298), of these ILs were determined. The contribution of each methylene (−CH2−) group in the alkyl chains of the imidazolium-based ionic liquids to the vaporization enthalpy, ΔglHom(−CH2−) = 4.2 ± 0.3 kJ·mol−1, was obtained. In terms of the new scale of polarity for ILs, the polarity of [Cnmim][Pro](n = 2, 3, 4, 5, 6) decreases with the increase of methylene number. To predict the surface tension of ILs using the vaporization enthalpy, a new theory modelthe surface tension model of the vaporization process of the ILwas put forward. The predicted values of surface tensions are in good agreement with the corresponding experimental ones.

■

Figure 4. Plot of γV 2/3 vs ΔglHom(298): ■ [Cnmim][Pro](n = 2, 3, 4, 5, 6), y = 4.25 × 10−2 + 6.50 × 10−4x, r = 0.985, s = 9.04 × 10−4; ●[C2mim][NTf2](n = 2, 4, 5, 6), [C2mim]EtSO4, [C2Py][NTf2](n = 2, 3, 4, 5, 6) y = 9.48 × 10−3 + 9.65 × 10−4x, r = 0.991, s = 1.35 × 10−3. x: ΔglHom/kJ·mol−1; y: γV 2/3/mJ·mol−2/3.

ASSOCIATED CONTENT

S Supporting Information *

1

H NMR spectrum and differential scanning calorimetric (DSC) measurements of the PrAILs [Cnmim][Pro](n = 4, 5, 6) and Verevkin’s method for estimation of ΔglCpom. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Authors

*Tel.: +86 02462207801. Fax: +86 02462202380. E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This project was supported by NSFC (21273003, 21271095, and 21373005), the Education Bureau of Liaoning Province (LJQ2013001), Liaoning BaiQianWan Talents Program (2013921029), and the Foundation of 211 Project for Innovative Talents Training, Liaoning University.

Figure 5. Plot of predicted values of surface tension, γ(Pre), versus the corresponding experimental one, γ(Exp), y = −0.07683 + 1.002x, r = 0.9986, s = 0.2537. x: γ(Exp)/mJ·m−2; y: γ(Pre)/mJ·m−2. −2

−4

■

= 4.25 × 10 + 6.50 × 10 Δ the intercept A = γV 4.25 × 10−2, and the slope B = 6.50 × 10 . To test the extensive applicability of eq 23, by using the data of literature19,24,28,40,41 and plotting γV 2/3 versus ΔglHom, a good straight line was again obtained; the fitting equation is γV2/3 = 9.48 × 10−3 + 9.65 × 10−4ΔglHom, and the correlation coefficient is 0.991 (see Figure 4). Comparing the two fitting equations, it can be seen that (1 − x) and Δε(kin) are parameters related to the IL structure in eq 23. Because [Cnmim][NTf2](n = 2, 4, 6, 8), [C2mim]EtSO4], and [CnPy][NTf2](n = 2, 3, 4, 5, 6) have similar molecular structures, the values of (1 − xc) and Δε(kin) are also similar so that they have a common fitting equation. However, [Cnmim][Pro](n = 2, 3, 4, 5, 6) has different structures of ionic liquids so that the values of parameters A and B are also different. According to eq 23, the surface tensions of the ionic liquids can be predicted using the values of parameters A and B and employing the appropriate ΔglHom and V values (Table 4). The predicted values are also listed in Table 4. Figure 5 is the plot of predicted values of surface tension versus the corresponding 2/3

g

o lH m; −4

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