J. Phys. Chem. B 2008, 112, 4381-4386
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Estimation of Physicochemical Properties of Ionic Liquids 1-Alkyl-3-methylimidazolium Chloroaluminate Jing Tong, Qing-Shan Liu, Wei-Guo Xu, Da-Wei Fang, and Jia-Zhen Yang* College of Chemistry, Laboratory of Green Chemistry, Liaoning UniVersity, Shenyang 110036, People’s Republic of China ReceiVed: December 14, 2007; In Final Form: January 17, 2008
The density and surface tension of ionic liquids [C2mim][AlCl4] (1-ethlyl-3-methyl imidazolium chloroaluminate) and [C6mim][AlCl4] (1-hexyl-3-methylimidazolium chloroaluminate) were measured in the temperature range from 283.15 to 338.15 ( 0.05 K. In terms of these experimental results, the estimation of physicochemical properties of 1-alkyl-3-methylimidazolium chloroaluminate ([Cnmim][AlCl4], n ) 1-6) was carried out. With the use of the parachor, the values of surface tension of the ILs were predicted. In terms of Glasser’s theory, the standard molar entropy, lattice energy, and surface properties of the ILs were estimated. With the use of Kabo’s method and Rebelo’s method, the molar enthalpy of vaporization of the ILs, ∆lgHm0, was predicted. According to the interstice model, the values of the thermal expansion coefficient of the ILs were also estimated. Since the magnitude order of the thermal expansion coefficient estimated by the model is in good agreement with that measured experimentally, this result means that the interstice model is reasonable.
1. Introduction The rapid growth in ionic liquid literature indicates that they continue to attract much attention from both the industrial and academic communities as green solvents.1-3 As first-generation ionic liquids (ILs), the ILs based on AlCl3 have the disadvantage of being reactive with water so that they were restricted in application due to their moisture and air sensitivity. However, AlCl3-based ILs have wider and variable Lewis acidity, so they can still be very useful for the electrodeposition of pure metals and alloys4,5 and other specialized fields. Recently, there is a developing trend6,7 in the literature toward estimation of thermodynamic quantities for ILs, which is to be commended because it provides valuable insight into the origins of the behavior of materials. In order to follow this trend, this article reports that the volumetric and surface properties of the ILs [C2mim][AlCl4] (1-ethlyl-3-methylimidazolium chloroaluminate) and [C6mim][AlCl4] (1-hexyl-3-methylimidazolium chloroaluminate) were determined in the temperature range from 283.15 to 338.15 K. On the basis of these experimental results and literature data, the estimation of physicochemical properties of 1-alkyl-3-methylimidazolium chloroaluminate ([Cnmim][AlCl4], n ) 1-6), is discussed: (1) According to Deetlefs’ method,7 the values of surface tension were estimated using the parachor. (2) In terms of Glasser’s theory,8 the standard molar entropy, lattice energy, and surface properties of the ILs were estimated. (3) With the use of Kabo’s method9 and Rebelo’s method,10 the molar enthalpy of vaporization, ∆lgHm0(298 K), and ∆lgHm0(Tb) at the hypothetical normal boiling point, Tb, were estimated, respectively. (4) According to the interstice model,11,12 the values of the thermal expansion coefficient of the ILs were also estimated. 2. Experimental Section 2.1. Chemicals. Anhydrous AlCl3 (purity is 99.99%) was purchased from Aldrich. It was opened in the glovebox under * Corresponding author.
dry argon and used without further purification. 1-Ethyl-3methylimidazolium chloride ([C2mim]Cl) was produced by Aldrich and was recrystallized twice from acetonitrile/ethyl acetate. 1-Methylimidazole AR grade reagent was obtained from ACROS and was vacuum-distilled prior to being used. Chlorohexane AR grade reagent was obtained from Beijing Chemicals Co. and distilled before use. Ethyl acetate and acetonitrile were distilled and then stored over molecular sieves in tightly sealed glass bottles. 2.2. Preparation of Ionic Liquids. All glassware that contacted the ILs was cleaned in hot dilute nitric acid and rinsed repeatedly in doubly deionized water, then baked dry at 393 K and stored in desiccators before use. According to Huddleston’s method,13 1-hexyl-3-methylimidazolium chloride ([C6mim]Cl) was synthesized whose color is slightly yellow. The yield is approximately 80%. Analysis of [C6mim]Cl by 1H NMR resulted in a spectrum (see Figure A of the Supporting Information) in good agreement with the literature.13 AlCl3 was added slowly with stirring to a small glass vial containing equal molar [C6mim]Cl under dry argon, and then the slightly yellow and transparent ionic liquid compound [C6mim][AlCl4] was obtained. Analysis of the product by 1H NMR gave a spectrum identical to that for [C6mim][AlCl4] (see Figure B of the Supporting Information). The thermal decomposition temperature of the IL, Td ) 721 K, was determined by thermogravimetric analysis using a TA Instruments (SDT) model Q600 thermogravimetric analyzer (see Figure C of the Supporting Information). [C2mim][AlCl4] was obtained by the same method and was a colorless and transparent ionic liquid compound. 2.3. Measurement of Density and Surface Tension. First, the densities of deionized and degassed water were measured by a Westphal balance and were in good agreement with those in the literature14 within experimental error, (0.0002 g‚cm-3 at 283.1-338.15 ( 0.05 K. Then, the densities of ionic liquids [C2mim][AlCl4] and [C6mim][AlCl4] were measured by the same method, respectively, under dry argon in the same
10.1021/jp711767z CCC: $40.75 © 2008 American Chemical Society Published on Web 03/18/2008
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TABLE 1: Values of Density, G/g‚cm-3, of [Cnmim][AlCl4] (n ) 2, 6) at 283.15-338.15 K
TABLE 3: Values of Parachors, P, of [Cnmim][AlCl4] (n ) 1-6) at 283.15-338.15 K
T/K ionic liquid
T/K
283.15 288.15 293.15 298.15 303.15 308.15
[C2mim][AlCl4] 1.3060 1.3020 1.2979 1.2947 1.2908 1.2870 [C6mim][AlCl4] 1.2065 1.2026 1.1987 1.1953 1.1904 1.1859 T/K ionic liquid
313.15 318.15 323.15 328.15 333.15 338.15
ionic liquid [C1mim][AlCl4]a [C2mim][AlCl4] [C3mim][AlCl4]a [C4mim][AlCl4]b [C5mim][AlCl4]c [C6mim][AlCl4]
283.15 288.15 293.15 298.15 303.15 308.15 550.3 581.1 611.9 642.7 673.5 704.3
551.1 581.9 612.7 643.5 674.3 705.2
[C2mim][AlCl4] 1.2833 1.2798 1.2759 1.2725 1.2689 1.2651 [C6mim][AlCl4] 1.1820 1.1782 1.1742 1.1702 1.1661 1.1622
γ/mJ‚m-2,
TABLE 2: Values of Surface Tension, [Cnmim][AlCl4] (n ) 2, 6) at 283.15-338.15 K T/K ionic liquid [C2mim][AlCl4] [C6mim][AlCl4]
283.15 288.15 293.15 298.15 303.15 308.15 53.5 40.4
53.2 40.1
52.9 39.8
52.4 39.6
52.2 39.3
51.9 38.9
T/K ionic liquid [C2mim][AlCl4] [C6mim][AlCl4]
313.15 318.15 323.15 328.15 333.15 338.15 51.6 38.7
51.3 38.5
50.7 38.2
50.5 37.9
50.2 37.6
551.8 582.9 614.0 645.2 676.3 707.4
553.0 584.2 615.4 646.6 677.8 709.0
553.9 585.1 616.2 647.4 678.6 709.7
T/K ionic liquid
of
551.9 582.7 613.5 644.4 675.2 706.1
[C1mim][AlCl4]a [C2mim][AlCl4] [C3mim][AlCl4]a [C4mim][AlCl4]b [C5mim][AlCl4]c [C6mim][AlCl4]
313.15 318.15 323.15 328.15 333.15 338.15 554.5 585.8 617.1 648.4 679.7 711.0
555.0 586.4 617.9 649.3 680.7 712.1
555.0 586.6 618.2 649.8 681.4 713.0
555.9 587.5 619.1 650.6 682.2 713.8
556.7 588.4 620.1 651.8 683.4 715.1
557.0 588.9 620.8 652.7 684.7 716.6
a The values of density are taken from ref 15. b The values of density are taken from ref 16. c The values of density are taken from ref 17.
49.8 37.5
temperature range, and the sample to be measured was placed in a cell with a jacket which was thermostated at each temperature with an accuracy (0.05 K. With the use of the tensiometer of the forced bubble method (DP-AW type produced by Sang Li Electronic Co.), the surface tension of water was measured from 283.15 to 338.15 K and was in good agreement with that in the literature14 within experimental error, (0.1 mJ‚m-2. The surface tensions of ionic liquids [C2mim][AlCl4] and [C6mim][AlCl4] were measured by the same method under dry argon in the same temperature range. The uncertainties of the measurements were (0.2 mJ‚m-2. Figure 1. Plot of parachor P vs number of carbons (n) in the alkyl chains of the ILs at 298.15 K. The fitting equation: P ) 31.1n + 520.6.
3. Results and Discussion The measured values of density and surface tension of the ionic liquids [C2mim][AlCl4] and [C6mim][AlCl4] are listed in Tables 1and 2, respectively. Each value in Tables 1 and 2 is the average of three determinations. In comparison of F ) 1.2947 g‚cm-3 at 298.15 K in this work with F ) 1.2941 g‚cm-3 at the same temperature obtained by Fannin et al.,15 they are in good agreement. Both the density and surface tension of the ILs decreased with rising temperature. 3.1. Using Parachors Predicting Surface Tension of ILs. Recently, Deetlefs et al.7 pointed out that the parachor, P, can be used as a link between the structure, density, and surface tensions of ionic liquids:
P ) (Mγ1/4)/F
(1)
where M is molar mass. According to eq 1, the experimental values of the parachor of [C2mim][AlCl4], [C4mim][AlCl4],16 [C5mim][AlCl4],17 and [C6mim][AlCl4] are listed in Table 3. From Table 3 it is shown that the parachors increase slightly with the temperature for the given IL, and the parachors are linear with the number (n) of carbons in the alkyl chain of the ILs at a given temperature. When the values of P at given temperature T were plotted against n, a good straight line was obtained (see Figure 1). The linear relation between the parachor and the number of carbons in the alkyl chain of ILs is expressed as the following empirical equation:
P ) an + b
(2)
where a and b are empirical constants; the value of the slope a ) 31.1 at 298.15 K; it is a mean contribution per methylene to the parachor and is much less than neutral parachor contribution values of methylene (39.9).18 With the use of eq 2, values of the parachor of [C1mim][AlCl4] and [C3mim][AlCl4] are calculated and are also listed in Table 3. Then, surface tensions of ILs may be predicted from eq 1 using data of the parachor and density. The predicted values of surface tension, γ(cal), of [Cnmim][AlCl4] (n ) 1-6) at 298.15 K are listed in Table 4. The predicted values at other temperatures are listed in Table D of the Supporting Information. From Table 4, it can be seen that the corresponding predicted values of the parachor obtained by eq 1 are close to experimental data. In the absence of sufficient data of parachor contribution values for ions, Deetlefs et al.7 considered that the parachor of ionic liquids may be calculated using neutral parachor contribution values18 so that the parachor may become as a tool to predict physical properties of ILs. With the use of Deetlefs’s method, calculated values of the parachor of [Cnmim][AlCl4] (n ) 1-6) are also listed in Table 4. When the above values of the parachor are compared with the predicted one obtained using the neutral parachor contribution values, the relative deviations are larger than 3%. 3.2. Estimation of Surface Properties and Volumetric Properties for ILs. The experimental values of ln F against (T
1-Alkyl-3-methylimidazolium Chloroaluminate ILs
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TABLE 4: Predicted Surface Tensions of ILs, [Cnmim][AlCl4] (n ) 1-6), at 298.15 K ionic liquid
M /g‚mol-1
F /g‚cm-3
[C1mim][AlCl4] [C2mim][AlCl4] [C2mim][AlCl4] [C3mim][AlCl4] [C4mim][AlCl4] [C4mim][AlCl4] [C5mim][AlCl4] [C6mim][AlCl4]
266.0 280.0 280.0 294.0 308.0 308.0 322.0 336.0
1.3289a 1.2947 1.2941a 1.2624a 1.2381b 1.2380a 1.2133c 1.1952
a
γ(exp) /mJ‚m-2 52.4 45.6 42.6 40.8
γ(cal) /mJ‚m-2
∆γ /mJ‚m-2
57.8 52.8 52.7 48.3 45.2 45.2 42.2 40.1
P(exp)
0.4 0.3
581.8
-0.4 -0.4 -0.4 -0.7
646.5 678.1 705.4
P(cal) 551.8 582.9 582.9 614.0 645.2 645.1 676.3 707.4
∆P 1.1 -1.3 -1.8 2.0
P(ref)
δ%
487.3 527.2 527.2 567.1 607.0 607.0 646.9 686.8
13 11 11 8 6 6 5 3
Ref 15. b Ref 16. c Ref 17; ∆γ ) γ(cal) - γ(exp); ∆P ) P(cal) - P(exp); P(ref), ref 18; δ% ) (P(cal) - P(ref))/P(ref).
TABLE 5: Values of Volume Properties and Surface Properties of ILs [Cnmim][AlCl4] (n ) 1-6) at 298.15 K
a
ionic liquid
F /g‚cm-3
Vm /nm3
S0 /J‚K-1‚mol-1
103Sa /mJ‚K-1‚m-2
Ea /mJ‚m-2
UPOT /kJ‚mol-1
[C1mim][AlCl4] [C2mim][AlCl4] [C3mim][AlCl4] [C4mim][AlCl4] [C5mim][AlCl4] [C6mim][AlCl4]
1.3289a 1.2947 1.2624a 1.2381b 1.2133c 1.1953
0.3324 0.3592 0.3867 0.4130 0.4407 0.4670
444 477 511 544 579 612
66.3 68.9 69.5 60.7 48.5 58.7
77.5 73.3 69.0 63.3 56.6 57.6
442 434 426 419 412 406
Ref 15. b Ref 16. c Ref 17.
- 298.15) were fitted by the method of least-squares as the following equation:
According to Glasser’s theory,8 the standard molar entropy for ionic liquids, S0, is given by
ln[F/(g‚cm-3)] ) c - R(T/K - 298.15)
S0(298)/J‚K‚mol-1 ) 1246.5(Vm/nm3) + 29.5
(3)
where c is an empirical constant and R ) -(∂ln F/∂T)p is the coefficient of thermal expansion. Then R ) 5.75 × 10-4 and 6.86 × 10-4 K-1 obtained by the fitting of ln F versus (T 298.15) (see Figure D of the Supporting Information) for [C2mim][AlCl4] and [C6mim][AlCl4], respectively. From the experimental density, the molecular volume, Vm, was calculated using following equation:
Vm ) M/(NF)
(4)
where M is the molar mass of ILs and N is Avogadro’s constant. The molecular volume, Vm, of [C2mim][AlCl4], [C6mim][AlCl4], and the other ionic liquids based on aluminate taken from Fannin et al.’s data15 and our previous investigation16,17 at 298.15 K were calculated by eq 4 and are listed in Table 5. By the leastsquares method, the slope, 0.0270 nm3, of the linear regression of Vm against n (the number of carbons in the alkyl chains of the ILs) (see Figure 2) is a mean contribution per methylene (-CH2-) to the molecular volume and is in good agreement with that of methylene contributions of 0.0280 nm3 from n-alcohols, 0.0272 nm3 from n-amines, and 0.0267 nm3 from n-paraffins.8
so that the values of S0 of [Cnmim][AlCl4] at 298.15 K are also listed in Table 5. By the least-squares method, the slope of the linear regression of S0(298)/J‚K‚mol-1 against n is 33.7 J‚K-1‚mol-1 (see Figure 2). This implies that the contribution per methylene group to the standard entropy of the ILs is 33.7 J‚K-1‚mol-1. This value is in excellent agreement with the value of 33.9 J‚K-1‚mol-1 from [Cnmim][BF4].8 The values of γ estimated using the parachor for [Cnmim][AlCl4] have been fitted against T by the least-squares to a linear equation (see Figure E of the Supporting Information), and the correlation coefficients r are larger than 0.99. The values of the surface excess entropy, Sa ) -(∂γ/∂T)p, may be obtained from the slope of the fitting line and are listed in Table 5. In addition, the values of the surface excess energy Ea likewise may be obtained from the surface tension: Ea ) γ - T(∂γ/∂T)p at 298.15 K and are also listed in Table 5. In comparison with fused salts, for example, Ea ) 146 mJ‚m-2 for fused NaNO3, the values of Ea for [Cnmim][AlCl4] are much lower and are close to those of organic liquids, for example, 67 mJ‚m-2 for benzene and 51.1 mJ‚m-2 for n-octane.19 This fact shows that interaction energy between ions in the ILs is much less than that in inorganic fused salts because the surface excess energy is dependent on interaction energy between ions; that is, this means the crystal energy of ILs is much less than that of inorganic fused salts. The crystal energy, UPOT, of ILs may be estimated in terms of Glasser’s empirical equation:8
UPOT/kJ‚mol-1 ) 1981.2(F/M)1/3 + 103.8
Figure 2. Plots of Vm and S0 vs number of carbons (n) in the alkyl chains of the ILs at 298.15 K, respectively. [ Fitting equation: Vm ) 0.0270n + 0.3054. 2 Fitting equation: S0 ) 34n + 410.
(5)
(6)
With the use of eq 6, the values of UPOT are obtained and listed in Table 5. From Table 5, it is shown that crystal energies of ILs are much less than those of inorganic fused salts, for example, UPOT ) 613 kJ‚mol-1 for fused CsI14 which is the least crystal energy among alkali halides. However, the largest value among [Cnmim][AlCl4] is only 442 kJ‚mol-1. The low
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TABLE 6: Molar Enthalpy of Vaporization, ∆lgHm0(298 K), ∆lgHm0(Tb), and the Contribution to the Molar Enthalpy of Vaporization of the ILs [Cnmim][AlCl4] (n ) 1-6), [C5mim][GaCl4], and [C5mim][InCl4] ionic liquid [C1mim][AlCl4] [C2mim][AlCl4] [C3mim][AlCl4] [C4mim][AlCl4] [C5mim][AlCl4] [C6mim][AlCl4] [C5mim][GaCl4]a [C5mim][InCl4]b a
107k /J‚K-1
Tc /K
Tb /K
1.610 1.774 1.883 1.678 1.333 1.759
1530 1373 1272 1366 1606 1275
918 824 763 820 964 765
∆lgHm0(Tb) ∆lgHm0(298 K) /kJ‚mol-1 /kJ‚mol-1 82.6 74.2 68.7 73.8 86.8 68.9
189.5 182.4 175.5 171.8 167.2 165.3 170.8 174.6 Figure 3. Plot of γV2/3 of ILs vs temperature T: [ [C1mim][AlCl4] (y ) -0.01610x + 24.64); 2 [C2mim][AlCl4] (y ) -0.01774x + 24.35); s [C3mim][AlCl4] (y ) -0.01883x + 23.95); 9 [C4mim][AlCl4] (y ) -0.01678x + 22.93); × [C5mim][AlCl4] (y ) -0.01333x + 21.41); b [C6mim][AlCl4] (y ) -0.01759x + 22.42).
Ref 20. b Ref 21.
crystal energy is the underlying reason for forming ionic liquids at room temperature. 3.3. Estimation of Vaporization Enthalpies for ILs. Kabo’s group9 put forward an empirical equation for estimation of the enthalpy of vaporization, ∆lgHm0(298 K), of ionic liquids:
∆lgHm0(298 K) ) A(γV2/3N1/3) + B
temperature, Tc, of the ILs was estimated using the Eo¨tvo¨s equation:19
γV2/3 ) k(Tc - T)
(7)
(8)
where V is the molar volume of the ILs, Tc is the critical temperature, and k is an empirical constant. The linear regressions of the product of γ and V2/3 for [Cnmim][AlCl4] against absolute temperature T were made, and straight lines were obtained (see Figure 3). From the slopes and the intercepts of the straight lines, the values of k and Tc, respectively, were obtained and are listed in Table 6. According to Rebelo’s method, the predicted values of ∆lgHm0(Tb) of the ILs are also listed in Table 6. From Table 6, the difference between ∆lgHm0(Tb) estimated in terms of Rebelo’s method and ∆lgHm0(298 K) estimated in terms of Kabo’s method is very large. This is because of the heat capacity difference between the liquid and gas phases at different temperatures. We suppose a linear change of ∆lgHm0 with temperature in the range between 298 K and Tb, the vapor pressure, p, of the ILs at various temperatures may be estimated using the Clapeyron-Clausius equation, and the calculated values of ∆lgHm0 and p at various temperatures are listed in Table 7. Figure 4 is the plot of vapor pressure, p, and ∆lgHm0 of the ILs against temperature, T. 3.4. Interstice Model for Ionic Liquids. For pure ionic liquids a new theoretical model11,12 is put forward on the basis of the following assumptions: (1) Because of the large size and the asymmetric shape, the ions may not be closely packed and lots of interstices of ions come into existence. (2) In order to calculate the volume easily, the interstice is regarded as a
where N is Avogadro’s constant; A and B are empirical parameters; their values are A ) 0.01121 and B ) 2.4 kJ‚mol-1, respectively. The values of the molar enthalpy of vaporization, ∆lgHm0(298 K), for the ionic liquids [Cnmim][AlCl4] were calculated from eq 7 and are listed in Table 6. From Table 6, the estimated enthalpy of vaporization of ILs at 298.15 K decreases with length of the aliphatic chains of the cation, and it can be interpreted considering that longer side chains decrease the relative importance of Coulomb forces leading to smaller values of ∆lgHm0(298 K). In addition, as will be readily seen from Table 6, the sequence of the vaporization enthalpies is ∆lgHm0([C5mim][AlCl4]) < ∆lgHm0([C5mim][GaCl4])20 < ∆lgHm0([C5mim][InCl4]);21 that is, the greater the mass of anion, the greater is its molar standard vaporization enthalpy. This fact shows that in contradiction to the effect of the cation on the molar standard vaporization enthalpy, the nonelectrostatic force for the anion is primary. Rebelo et al.10 put forward a method of estimating the hypothetical temperature of the normal boiling point (NBP) of ionic liquids, Tb, in terms of the critical temperature, Tc. They thought that the relationship between Tb and Tc is Tb ≈ 0.6Tc for ionic liquids. The molar enthalpy of vaporization for ionic liquids [Cnmim][AlCl4] at NBP, ∆lgHm0(Tb), can be estimated by the Trouton constant (≈90 J‚mol-1‚K-1). The critical
TABLE 7: Values of ∆lgHm0 and p of [Cnmim][AlCl4] (n ) 2, 6) at Various Temperatures T/K ∆lgHm0/kJ‚mol-1 p/Pa
800 79.1 7.1 × 104
∆lgHm0/kJ‚mol-1 p/Pa
750
650
600
89.4 3.1 × 104
[C2mim][AlCl4] 99.7 1.0 × 104
700
550
110.0 2.6 × 103
120.2 4.4 × 102
130.5 45
71.9 8.0 × 104
[C6mim][AlCl4] 82.3 3.3 × 104
92.6 1.0 × 104
102.9 2.3 × 103
113.2 3.2 × 102
T/K
500
450
400
350
300
250
∆lgHm0/kJ‚mol-1 p/Pa
140.8 2.3
151.1 4.7 × 10-2
[C2mim][AlCl4] 161.4 2.5 × 10-4
171.7 2.0 × 10-7
182.0 7.9 × 10-12
192.3 2.4 × 10-18
∆lgHm0/kJ‚mol-1 p/Pa
123.6 24
133.9 7.8 × 10-1
[C6mim][AlCl4] 144.2 7.5 × 10-3
154.5 1.2 × 10-5
164.8 1.3 × 10-9
175.2 1.6 × 10-15
1-Alkyl-3-methylimidazolium Chloroaluminate ILs
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TABLE 8: Parameters of Interstice Model for ILs, [Cnmim][AlCl4] (n ) 1-6), at 298.15 K ionic liquid
F /g‚cm-3
γ /mJ‚m-2
10-24ν/cm3
∑ν/cm3
102∑ν/V
104R/K-1 (cal
104R/K-1 (exp)
[C1mim][AlCl4] [C2mim][AlCl4] [C3mim][AlCl4] [C4mim][AlCl4] [C5mim][AlCl4] [C6mim][AlCl4]
1.3289a 1.2947 1.2624a 1.2381b 1.2133c 1.1952
57.8 52.8 48.3 45.2 42.2 40.1
12.92 14.79 16.89 18.63 20.71 22.34
15.56 17.81 20.33 22.44 24.94 26.90
7.8 8.2 8.7 9.0 9.4 9.6
3.91 4.39 4.39 4.54 4.73 4.81
5.11 5.75 6.30 6.22 5.89 6.86
a
Ref 15. b Ref 16. c Ref 17.
bubble. (3) There are 2N interstices for 1 mol of 1-1 ionic liquid, where N is Avogadro’s number. (4) The interstice in ionic liquids can move about like an ion or other particles; in the movement the interstice does not vanish but can be compressed and expanded, which has an extra feature of motion of an interstice called the breathing motion. According to the same procedure of the hole model of molten salts, an expression for calculation of interstice volume, V, was obtained by classical statistical mechanics:
V ) 0.6791(kbT/γ)3/2
(9)
where kb is Boltzmann’s constant, T is the thermodynamic temperature, and γ is the surface tension of ionic liquids. According to eq 9, the values of average volume of the interstices of ILs may be obtained, V ) 14.93 × 10-24 cm3 for [C2mim][AlCl4] and V ) 22.78 × 10-24 cm3 for [C6mim][AlCl4], because the surface tensions of [C2mim][AlCl4] and [C6mim][AlCl4] at 298.15 K are 52.4 and 39.6 mJ‚m-2, respectively. Then, the molar volume of the interstice is ∑V ) 2NV ) 17.98 cm3 for [C2mim][AlCl4] and 27.43 cm3 for [C6mim][AlCl4]. The volume fractions of interstice, ∑V/V, are about 8.2% and 9.6% for ILs [C2mim][AlCl4] and [C6mim][AlCl4], respectively, and this is in good agreement with that of the majority of materials which exhibit 10% to ∼15% volume expansion in the process from the solid to liquid state. This result means that the interstice model is reasonable. The volume of ionic liquids, V, consists of the inherent volume, Vi, and total volume of the all interstices, ∑V ) 2Nν, that is,
V ) Vi + 2Nν
(10)
If the expansion of IL volume only results from the expansion
of the interstices when the temperature increases, then calculation expression of R was derived from the interstice model:
R ) (1/V)(∂V/∂T)p ) 3Nν/VT
(11)
The values of R (calculated) calculated using eq 11 and of corresponding experimental values, R (experimental), for ILs [Cnmim][AlCl4] at 298.15 K are listed in Table 8. The magnitude order of the thermal expansion coefficients R (calculated) are in good agreement with R (experimental) so that this result means that the interstice model is reasonable and may be used to estimate thermal expansion coefficient of ILs. It is noted that there are probably certain semantic confusions of the name of this theory with that of the hole model of fused salts.22 In fact, there is a great difference between the interstice theory and the hole model. The hole theory is designed to describe spontaneous density fluctuations of molecular extent that occur in liquids, as the constituent particles move about under thermal agitation. In the unmelted crystal, one such important density fluctuation that appears in equilibrium at high temperatures is the unoccupied lattice site, or missing particle. On account of the rigid geometrical structure of the crystal, such a small low-density region can be equal in size to only one characteristic elementary volume, determined by the crystal structure. Furthermore, motion of these empty regions can proceed only by discrete jumps, produced by a shift of a particle in the crystal into a neighboring unoccupied site. However, the situation in the liquid is much less restrictive, since extra freedom of particle movement attending the melting of the rigid crystal implies not only a continuum of possible sizes and shapes for the low-density regions, or “holes”, but movement of these holes may occur by a relatively continuous drift, rather than by discrete jumps. However, in the interstice theory, the inherent interstices exist in ionic liquids on account of the large size and great asymmetry of ions and cannot vanish during thermal movement. Acknowledgment. This project was supported by NSFC (20773056) and the Bureau of Liaoning Province (20060359), People’s Republic of China. Supporting Information Available: Additional figures and table. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
Figure 4. Plot of vapor pressure, p, and ∆lgHm0 of the ILs vs temperature T: [ [C2mim][AlCl4] (∆lgHm0 ) -0.2057T + 243.7); b [C6mim][AlCl4] (∆lgHm0 ) -0.2064T + 226.8); 2 [C2mim][AlCl4] (p vs T); × [C5mim][AlCl4] (p vs T).
(1) Rogers, R. D., Seddon, K. R., Eds. Ionic Liquids Industrial Applications for Green Chemistry; ACS Symposium Series 818; American Chemical Society: Washington, DC, 2002. (2) Rogers, R. D., Seddon, K. R., Eds. Ionic Liquids as Green SolVent; ACS Symposium Series 856; American Chemical Society: Washington, DC, 2003; Chapter 12. (3) Dupout, J.; de Souza, R. F.; Suarez, P. A. Z. Ionic liquid (molten salt) phase organometallic catalysis. Chem. ReV. 2002, 102, 3667-3692.
4386 J. Phys. Chem. B, Vol. 112, No. 14, 2008 (4) Yang, J.-Z.; Zhang, Q.-G.; Wang, B.; Tong, J. Study on the properties of amino acid ionic liquid EMIGly. J. Phys. Chem. B 2006, 110, 22521-22524. (5) Endres, F. Ionic liquids: solvents for the electrodeposition of metals and semiconductors. ChemPhysChem 2002, 3, 144-154. (6) Krossing, I.; Slattery, J. M. Semi-empirical methods to predict the physical properties of ionic liquids: An overview of recent developments. Z. Phys. Chem. 2006, 220 (10-11), 1343-1359. (7) Deetlefs, M.; Seddon, K. R.; Shara, M. Predicting physical properties of ionic liquids. Phys. Chem. Chem. Phys. 2006, 8, 642-649. (8) Glasser, L. Lattice and phase transition thermodynamics of ionic liquids. Thermochim. Acta 2004, 421, 87-93. (9) Zaitsau, D. H.; Kabo, G. J.; Strechan, A. A.; Paulechka, Y. U.; Tschersich, A.; Verevkin, S. P.; Heintz, A. A. Experimental vapor pressures of 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfony)imides and correlation scheme for estimation of vaporization enthalpies of ionic liquids. J. Phys. Chem. A 2006, 110, 7303-7306. (10) Rebelo, L.; Canongia, L.; Esperanc¸ a, J.; Filipe, E. On the critical temperature, normal boiling point, and vapor pressure of ionic liquids. J. Phys. Chem. B 2005, 109, 6040-6043. (11) Yang, J.-Z.; Lu, X.-M.; Gui, J.-S.; Xu, W.-G. A new theory for ionic liquidsthe interstice model part 1. The density and surface tension of ionic liquid EMISE. Green Chem. 2004, 6, 541-543. (12) Yang, J.-Z.; Gui, J.-S.; Lu, X.-M.; Zhang, Q.-G.; Li, H. W. Studies on properties of ionic liquid BMIBF4. Acta Chim. Sin. 2005, 63, 577-580. (13) Huddleston, J. G.; Visser, A. E.; Reichert, W. M.; Willauer, H. D.; Broker, G. A.; Rogers, R. D. Characterization and comparison of hydrophilic
Tong et al. and hydrophobic room temperature ionic liquids incorporating the imidazolium cation. Green Chem. 2001, 3, 156-164. (14) Lide, D. R., Ed. Handbook of Chemistry and Physics, 82nd ed.; CRC Press: Boca Raton, FL, 2001-2002. (15) Fannin, A. A., Jr.; Floreani, D. A.; King, L. A.; Landers, J. S.; Piersma, B. J.; Stech, D. J.; Vaughn, R. L.; Wilkes, J. S.; Williams, J. L. Properties of 1,3-dialkylimdazoum chloride-aluminate chloride ionic liquids. 2. Phase transitions, densities, conductivities and viscosities. J. Phys. Chem. 1984, 88, 2614. (16) Tong, J.; Zhang, Q.-G.; Hong, M.; Yang, J.-Z. Acta Phys.-Chim. Sin. 2006, 22 (1), 71-75. (17) Tong, J.; Hong, M.; Guan, W.; Yang, J. Z. J. Chem. Thermodyn. 2006, 38, 1416-1421. (18) Knotts, T. A.; Wilding, W. V.; Oscarson, J. L.; Rowley, R. L. Use of the DIPPR database for development of QSPR correlations: surface tension. J. Chem. Eng. Data 2001, 46, 1007-1012. (19) Adamson, A. W. Physical Chemistry of Surfaces, 3rd ed.; JohnWiley: New York, 1976; Gu, T. R., Translator; Science Press: Beijing, 1986. (20) Tong, J.; Liu, Q.-S.; Guan, W.; Yang, J.-Z. Estimation of physicochemical properties of ionic liquid C6MIGaCl4 using surface tension and density. J. Phys. Chem. B 2007, 111 (12), 3197-3120. (21) Tong, J.; Liu, Q.-S.; Zhang, P.; Yang, J.-Z. The surface tension and density of 1-methyl-3-hexylimidazolium chloroindium. J. Chem. Eng. Data 2007, 52 (4), 1497-1500. (22) Bockris, J. O’M.; Reddy, A. K. N. Modern Electrochemistry; Macdonald: London, 1970; p 533.
