Study on thermodynamic properties and estimation of polarity of ionic liquids {[Cnmmim][NTf2] (n = 2, 4)}

Article abstract of DOI:10.1039/c4ra04391j

Two bis(trifluoromethyl sulfonyl)imide ionic liquids [C_nmmim] [NTf₂] (n = 2, 4) {1-alkyl-2,3-dimethyimidazolium-N,N- bis(trifluoromethyl sulfonyl)imide} were prepared and characterized by ¹H NMR spectroscopy and differential scanning calorimetry (DSC). The values of their density, surface tension and refractive index were measured in the temperature range of (298.15 to 338.15 ± 0.01) K and the average contributions to the density, surface tension, and refractive index per methyl group in the alkyl chain and the addition of a methylene group in the imidazolium ring for the ILs were discussed. The dependence of volumetric properties, surface properties and molar refraction on temperature was discussed. Based on Kabo's method and Verevkin's experimental values, the molar enthalpies of vaporization, ΔH^v, for [C_nmmim] [NTf₂] (n = 2, 4) were estimated. As a new idea, it was put forward that ΔH^v can be assumed to consist of two parts: a part corresponds with the induced energy, ΔH^v_n, and another part corresponds with orientation energy from the permanent dipole moment of the ion pair in ILs, ΔH^v_μ. The values of ΔH^v_n were calculated in terms of the Lawson-Ingham equation so that the values of ΔH^v_μ could be estimated. Using the values of ΔH^v, ΔH ^v_n and ΔH^v_μ, cohesive energy density, δ² (δ is Hildebrand solubility parameter), the contribution of induced energy, δ_n², and the contribution of orientation energy, δ_μ², were obtained. If a liquid only has δ_n then it is a non-polar liquid and if a liquid not only has δ_n, but also has δ_μ then it is a polar liquid. Since the ion pairs in ILs have a permanent dipole moment, the ionic liquid has a certain polarity. Therefore, using δ_μ as the polarity scaling of ILs is very convenient because the values of δ_μ are very easy to calculate from the enthalpy of vaporization and refractive index data.

Full text of DOI:10.1039/c4ra04391j

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PAPER
Study on thermodynamic properties and
estimation of polarity of ionic liquids {[Cnmmim]-
Cite this: RSC Adv., 2014, 4, 30725
[NTf2] (n ¼ 2, 4)}†
a
a
a
a
b
Jie Wei, Tianyou Ma, Xiaoxue Ma, Wei Guan, Qingshan Liu and Jiazhen Yanga
*
*
Two bis(trifluoromethyl sulfonyl)imide ionic liquids [Cnmmim][NTf2] (n
¼
2, 4) {1-alkyl-2,3-
1
dimethyimidazolium-N,N-bis(trifluoromethyl sulfonyl)imide} were prepared and characterized by H NMR
spectroscopy and differential scanning calorimetry (DSC). The values of their density, surface tension and
refractive index were measured in the temperature range of (298.15 to 338.15 ꢀ 0.01) K and the average
contributions to the density, surface tension, and refractive index per methyl group in the alkyl chain and
the addition of a methylene group in the imidazolium ring for the ILs were discussed. The dependence
of volumetric properties, surface properties and molar refraction on temperature was discussed. Based
on Kabo's method and Verevkin's experimental values, the molar enthalpies of vaporization, DHv, for
[Cnmmim][NTf2] (n ¼ 2, 4) were estimated. As a new idea, it was put forward that DHv can be assumed to
consist of two parts: a part corresponds with the induced energy, DHvn, and another part corresponds
with orientation energy from the permanent dipole moment of the ion pair in ILs, DHvm. The values of
DHvn were calculated in terms of the Lawson–Ingham equation so that the values of DHvm could be
estimated. Using the values of DHv, DHnv and DHmv, cohesive energy density, d2 (d is Hildebrand solubility
parameter), the contribution of induced energy, dn2, and the contribution of orientation energy, dm2, were
obtained. If a liquid only has dn then it is a non-polar liquid and if a liquid not only has dn, but also has dm
then it is a polar liquid. Since the ion pairs in ILs have a permanent dipole moment, the ionic liquid has a
certain polarity. Therefore, using dm as the polarity scaling of ILs is very convenient because the values of
dm are very easy to calculate from the enthalpy of vaporization and refractive index data.
Received 11th May 2014
Accepted 27th June 2014
DOI: 10.1039/c4ra04391j
www.rsc.org/advances
properties.6,7 As we all know, the fundamental thermodynamic
properties,8–12 as the indispensable parameters which reect the
1. Introduction
structures of compounds, play crucial role in the application
and study. In recent years, there has been a developing trend in
the literature toward estimation of the physicochemical prop-
erties for compounds by semiempirical methods, in particular,
for ILs.13–15 Although the estimated result cannot be regarded as
accurate physicochemical data, it is commended because it
provides valuable insight into the origins behavior of materials.
As a continuation of our previous investigation,16–18 this paper
reports: (1) two bis(triuoromethyl sulfonyl)imide ionic liquids
[Cnmmim][NTf2] (n ¼ 2, 4) {1-alkyl-2,3-dimethy imidazolium-
N,N-bis(triuoromethyl sulfonyl)imide} were prepared and
characterized. (2) The values of density, surface tension and
refractive index for [Cnmmim][NTf2] (n ¼ 2, 4) were measured in
the temperature range of (298.15 to 338.15 ꢀ 0.01) K. (3) The
dependence of volumetric properties, surface properties and
molar refraction on temperature were discussed. (4) Based on
the Kabo's method and Verevkin's experimental values, the
molar enthalpies of vaporization, DHv, for the [Cnmmim][NTf2]
(n ¼ 2, 4) were estimated. (5) A new scale of polarity, dm, for the
ILs was put forward and values of dm can be estimated easily
based on the vaporization enthalpy and refractive index data.
Ionic liquids are attracting increasing attention in many elds
with their special physical and chemical properties, such as
non-ammability, dual natural polarity, thermal stability,
liquidity over a wide temperature range, easy recycling, and
being a good solvent for a wide variety of organic and inorganic
chemical compounds. Actually, most ILs are water miscible;
therefore, the anions for bis(triuoromethyl sulfonyl)imide
(NTf2ꢁ) ILs attracted much concern as water immiscible
compounds when they appeared.1–4 Bis(triuoromethyl
sulfonyl)imide ionic liquids have attracted considerable atten-
tion from industry and the academic community, because they
have several unique properties including negligible vapor
pressure at ambient temperatures,5 good thermal stability
aCollege of Chemistry, Liaoning University, Shenyang 110036, P. R. China. E-mail:
guanweiy@sina.com
bAdvanced Rechargeable Batteries Laboratory, Dalian Institute of Chemical Physics,
Chinese Academy of Sciences, Dalian 116023, P. R. China. E-mail: liuqingshan@
dicp.ac.cn
† Electronic supplementary information (ESI) available. See DOI:
10.1039/c4ra04391j
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Differential scanning calorimetry (DSC) measurements
showed that [Cnmmim][NTf2] (n ¼ 2, 4) had no obvious melting
point, but the glass transition temperature, Tg(n¼2) ¼ ꢁ16.47 ꢃC
in Fig. S3 of ESI.† The traces of DSC for [C4mmim][NTf2]are
listed Fig. S4 of ESI.†
2. Experimental section
2.1 Chemicals
Deionized water was distilled in a quartz still, and its conduc-
tance was (0.8–1.2) ꢂ 10ꢁ4 S mꢁ1. 1,2-Dimethyimidazolium (AR-
grade reagent) was vacuum-distilled prior to use. 1-Bromo-
ethane and 1-bromobutane, (AR-grade reagent) were distilled
before use. The purity of HN(SO2CF3)2 is 99.9%. Aer absorbing
the water by molecular sieves, ethyl acetate and acetonitrile
were distilled and used in the synthesis process. The source and
purity of the materials are listed in Table 1.
2.3 Determination of the density, surface tension and
refractive index of [Cnmmim][NTf2] (n ¼ 2, 4)
The density (r/g cmꢁ3), surface tension (g/mJ mꢁ2) and refrac-
tive index (nD) were measured at atmospheric pressure in the
temperature range of (298.15 to 338.15 ꢀ 0.01) K. Since the trace
water still exists in the ILs aer drying by common methods, the
presence of water becomes the most problematic impurity and
needs to be conrmed before and aer measurement. The mass
2.2 Preparation of [Cnmmim][NTf2] (n ¼ 2, 4)
Fig. 1 is a schematic of this synthetic route. [Cnmmim][NTf2] (n fraction of water is the average of three measurements carried
¼ 2, 4) were synthesized according to the ion exchange reaction. out Karl Fischer moisture titrator (ZSD-2 type) for [Cnmmim]-
First, 1,2-dimethylimidazole (1 mol) was placed in a round- [NTf2] (n ¼ 2, 4) were listed in Table 2.
bottomed ask and stirred, and 1-bromoethane or 1-bromo-
An Anton Paar DMA 4500 oscillating U-tube densitometer
ꢃ
butane (1.1 mol) was added dropwise into the ask at 70 C. A was used to measure the density of [Cnmmim][NTf2] (n ¼ 2, 4).
slight excess of the 1-bromoethyl or 1-bromobutane was used to The temperature in the cell was regulated to ꢀ0.01 K with solid
guarantee the consumption of 1,2-dimethylimidazole. Ethyl state thermostat. Before the measurement, the apparatus was
acetate was added to reduce the viscosity of the mixture, which calibrated once a day with dry air and double-distilled freshly
ꢃ
was le to stir under reux at 70 C for 48 h. The halide salt degassed water. Then the values of density of pure water were
separated as a second phase from the ethyl acetate. Excess of measured by the calibrated apparatus from (298.15 to 338.15 ꢀ
ethyl acetate was removed by decantation.
0.01) K with 5 K interval and were in good agreement with
The products were recrystallized from acetonitrile. The literature19 within experimental error ꢀ0.00001 g cmꢁ3. Finally,
volume of acetonitrile used for the recrystallization was the densities of the samples were measured at the same
approximately half that of the halide salt. Acetonitrile was then temperature.
decanted aer crystallization; this step was repeated twice. Aer
By use of the tensiometer of the forced bubble method
the third cycle, the remaining acetonitrile and 1-bromoethane (DPAW type produced by Sang Li Electronic Co.), the surface
or 1-bromobutane were removed under reduced pressure using tension of water was measured at 298.15 ꢀ 0.01 K and was in
a rotary evaporator at 70 C, and the bromide salt was nally good agreement with the literature19 within experimental
ꢃ
ꢃ
dried in high vacuum at 70 C.
error ꢀ0.1 mJ mꢁ2. Then, the values of surface tension of the
A certain quality of [Cnmmim][Br] (n ¼ 2, 4) was placed in a samples were measured by the same method at (298.15 to
round-bottomed ask and dissolved in deionized water. Then, 338.15 ꢀ 0.01) K.
the equivalent amount of bis(triuoromethyl sulfonyl)imide
The refractive index, nD, of the samples was measured by an
HN(SO2CF3)2 purchased from Rhodia Co. was added dropwise Abbe refractometer. First, the refractive index of degassed water
into the ask at room temperature and stirred for 3 h. The was measured by the instrument at 298.15 ꢀ 0.01 K and was in
HN(SO2CF3)2 was dissolved in the deionized water, and the good agreement with the literature19 within experimental error
mass fraction of the aqueous solution is 70%. The lower liquid ꢀ0.0001. Then, the values of the samples were measured by the
was washed several times with 30 mL of distilled water until no instrument at (298.15 to 338.15 ꢀ 0.01) K.
Brꢁ was indicated by the solution of AgNO3/HNO3. The nal
The values of density, surface tension, and refractive index
product was dried under the vacuum at 353.15 K for 24 h. for the samples of the ILs [Cnmmim][NTf2] (n ¼ 2, 4) at different
Structures of the [Cnmmim][NTf2] (n ¼ 2, 4) were conrmed by temperatures are listed in Table 3. Each value in the table is the
1H NMR spectroscopy (see Fig. S1 and S2 in the ESI†).
average of triple measurements.
Table 1 The source and purity of the materials
Chemical name
Source
Purication method
Mass fraction purity
1,2-Dimethyimidazolium
1-Bromoethane
1-Bromobutane
HN(SO2CF3)2
Ethyl acetate
Acetonitrile
ACROS
Further purication
Further purication
Further purication
Molecular sieves
Further purication
Further purication
$0.998
>0.985
>0.985
>0.999
>0.985
>0.995
Shanghai Reagent Co. Ltd.
Shanghai Reagent Co. Ltd.
Rhodia Co. Ltd.
Shanghai Reagent Co. Ltd.
Shanghai Reagent Co. Ltd.
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Fig. 1 Preparation of [Cnmmim][NTf2] (n ¼ 2, 4) by the ion exchange method.
Table 2 Mass fraction of water before and after the measurement of
caused by the different water content of the samples. From the
Table 2, the water content of the samples is very low, the ILs
samples may be regarded as pure ionic liquids.
density, surface tension, and refractive index
Surface
Refractive
index
The values of density, surface tension, refractive index and
the average contributions to the density, surface tension, and
refractive index of per methyl group (–CH2–) in alkyl chain of
[Cnmmim][NTf2] (n ¼ 2, 4) at 298.15 K are listed in Table 4, and
the values of [Cnmim][NTf2] (n ¼ 2, 4) at 298.15 K were taken
from the literature24–26 are also listed in Table 4. It shows that
the average contributions to the density, surface tension, and
refractive index of per methyl group (–CH2–) in alkyl chain for
[Cnmmim][NTf2] (n ¼ 2, 4) are in good agreement with [Cnmim]-
[NTf2] (n ¼ 2, 4). The average contributions to the addition of a
methylene group (–CH3) in the imidazolium ring for [Cnmmim]-
Density
Before
tension
104w
Aer
Before
Aer
Before
Aer
[C2mmim][NTf2]
[C4mmim][NTf2]
2.12
1.78
2.88
2.67
2.67
2.19
4.12
3.58
2.67
2.19
3.01
2.53
In order to compare with this work, the experimental data of
these properties in literature were collected and are also listed
in Table 3. It can be seen that the experimental values of
density, surface tension and refractive index for [C2mmim]-
[NTf2] and [C4mmim][NTf2] at 298.15 K are different by different
authors from the literature.20–23 The crucial reason is mainly
[NTf2] (n ¼ 2, 4) vs. [Cnmim][NTf2] (n ¼ 2, 4) are 0.02521 g cmꢁ3
,
2.82 mJ mꢁ2, and 0.0063, respectively, and they are much larger
Table 3 Values of density, r, surface tension, g, and refractive index, nD, the molar refraction, Rm, the mean molecular polarizability, ap, of
[Cnmmim][NTf2] (n ¼ 2, 4) in the temperature range of 298.15–338.15 Ke
T/K
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
338.15
[C2mmim][NTf2]
r/g cmꢁ3
1.49107
1.4931a
33.5
1.48624
33.3
1.48142
33.0
1.47662
32.8
1.47183
32.6
1.46706
32.4
1.46231
32.2
1.45757
32.0
1.45284
31.8
g/mJ mꢁ2
39.98a
1.4280
1.4296a
69.95
nD
1.4265
1.4250
1.4235
1.4220
1.4205
1.4190
1.4175
1.4161
Rm/cm3 molꢁ1
1024ap
69.96
27.76
69.97
27.76
69.98
27.77
69.99
27.77
70.00
27.77
70.01
27.78
70.02
27.78
70.04
27.79
27.75
[C4mmim][NTf2]
r/g cmꢁ3
1.41852
1.4224a
1.4159b
1.40c
1.41391
1.40929
1.40468
1.40007
1.39548
1.3909
1.38633
1.38178
g/mJ mꢁ2
32.5
32.2
32.0
31.8
31.6
31.4
31.2
31.0
30.7
38.21a
1.4325
1.4334a
79.32
35.54d
1.4311
33.83d
1.4286
32.20d
1.4260
30.49d
1.4232
nD
1.4298
1.4273
1.4247
1.4218
Rm/cm3 molꢁ1
1024ap
79.36
31.49
79.41
31.51
79.48
31.53
79.53
31.55
79.57
31.57
79.62
31.59
79.64
31.6
79.67
31.61
31.47
a
b
c
d
e
Ref. 21. Ref. 22. Ref. 20. Ref. 23. The standards uncertainty m(r) ¼ 0.00005 g cmꢁ3; the standards uncertainty m(g) ¼ 0.5 mJ mꢁ2; the
standards uncertainty m(nD) ¼ 0.0005.
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Table 4 Values of density, r, surface tension, g, refractive index, nD and D(–CH2–) of [Cnmmim][NTf2] (n ¼ 2, 4) and [Cnmim][NTf2] (n ¼ 2, 4) at
298.15 K, respectivelya,e
[C2mmim][NTf2]
[C4mmim][NTf2]
D(–CH2–)
[C2mim][NTf2]
[C4mim][NTf2]
D(–CH2–)
r/g cmꢁ3
g/mJ mꢁ2
nD
1.49107
33.5
1.4280
1.41852
32.5
1.4325
0.036
0.50
0.0023
1.52a
1.44b
0.040
0.36
0.0030
36.17b
1.421c
35.46c
1.427d
a
D(–CH2–) the average contributions to r, g, and nD per methyl group (–CH2–) in alkyl chain for [Cnmmim][NTf2] and [Cnmim][NTf2] (n ¼ 2, 4).
b
c
d
e
Ref. 24. Ref. 25. Ref. 26. The standards uncertainty m(r) ¼ 0.00005 g cmꢁ3; the standards uncertainty m(g) ¼ 0.5 mJ mꢁ2; the standards
uncertainty m(nD) ¼ 0.0005.
than that of per methyl group (–CH2–) in alkyl chain, it means [Cnmim][NTf2]. The calculated values of molar volume, V, and
that the addition of a methylene group (–CH3) in the imidazo- molecular volume, Vm, for [Cnmmim][NTf2] (n ¼ 2, 4) are listed
lium ring of [Cnmmim][NTf2] (n ¼ 2, 4) can have a stronger in Table 5.
impact in some properties, for example the density, surface
tension, and refractive index in the work.
Plotting the experimental values of ln V for [Cnmmim][NTf2]
(n ¼ 2, 4) against DT, (DT/K ¼ T/K – 298.15 K), a set of good
straight lines were obtained (see Fig. 2). The correlation coeffi-
cients of these regression lines are larger than 0.999, and their
empirical equation is:
3. Results and discussion
ln V ¼ A + a(T ꢁ 298.15)
(2)
3.1 Dependence of volumetric and surface properties of
[Cnmmim][NTf2] (n ¼ 2, 4) on temperature
Using the experimental values of density, the molecular volume
(the sum of positive and negative ion volumes), Vm, of
[Cnmmim][NTf2] (n ¼ 2, 4), were calculated from the following
equation:
Vm ¼ M/(Nr) ¼ V/N
(1)
where V is molar volume, M is molar mass and N is Avogadro
constant. According to eqn (1), Vm (n ¼ 2, 4) ¼ 0.4516 nm3,
0.5075 nm3 for [Cnmmim][NTf2] (n ¼ 2, 4) at 298.15 K. The
difference between the molecular volumes of [C2mmim][NTf2]
and [C4mmim][NTf2] (0.0559 nm3) can be seen as the contri-
bution of two methylene (–CH2–) groups to the molecular
volume; this means that the contribution per methylene (–CH2–)
group to the molecular volume is 0.0280 nm3, which is in good
agreement with the value of 0.0278 nm3 for the ILs [Cnmim][Ala]
(n ¼ 2–6), found in our previous investigation,27 and with the
mean contribution of 0.0275 nm3 per methylene (–CH2–) group,
obtained by Glasser28 for the ILs [Cnmim][BF4] and
Fig. 2 The plot of ln V against DT. - [C2mmim][NTf2]: ln V ¼ 5.6054–
6.4867 ꢂ 10ꢁ4 DT, s ¼ 3.24 ꢂ 10ꢁ5, r ¼ 0.9999; C [C4mmim][NTf2]:
ln V ¼ 5.7220–6.5700 ꢂ 10ꢁ4 DT, s ¼ 3.05 ꢂ 10ꢁ5, r ¼ 0.9999.
Table 5 The values of molar volume, V, molecular volume, Vm, and Gibbs energy of surface formation, Ea, for ILs [Cnmmim][NTf2] (n ¼ 2, 4) at
298.15–338.15 K
T/K
298.15
303.15
308.15
313.15
318.15
323.15
328.15
333.15
338.15
[C2mmim][NTf2]
V/cm3 molꢁ1
271.8786
5.6054
0.4516
46.1
272.7621
5.6086
0.4531
46.1
273.6496
5.6118
0.4546
46.0
274.5392
5.6151
0.4560
46.1
275.4326
5.6183
0.4575
46.1
276.3282
5.6216
0.4590
46.1
277.2258
5.6248
0.4605
46.1
278.1273
5.6281
0.4620
46.1
279.0328
5.6313
0.4635
46.1
ln(V/cm3 molꢁ1
Vm/nm3
)
Ea/mJ mꢁ2
[C4mmim][NTf2]
V /cm3 molꢁ1
305.5227
5.7220
0.5075
45.2
306.5188
5.7253
0.5092
45.1
307.5236
5.7286
0.5108
45.1
308.5329
5.7318
0.5125
45.2
309.5488
5.7351
0.5142
45.2
310.5670
5.7384
0.5159
45.2
311.5896
5.7417
0.5176
45.2
312.6168
5.7450
0.5193
45.2
313.6462
5.7483
0.5210
45.1
ln(V/cm3 molꢁ1
Vm/nm3
)
Ea/mJ mꢁ2
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where A is the intercept and a is the slope. According to the
denition, the slope, a, is the coefficient of thermal expansion:
a h (1/V)(vV/vT)p ¼ (v ln V/vT)p
(3)
From Table 6, it can be seen that, with the increase in the
number of methylene on alkyl side chains, the values of thermal
expansion coefficients are increased only slightly.
The Gibbs energy of surface formation Ea likewise may be
obtained from the surface tensions measured in this work:
Ea ¼ g – T(vg/vT)p
(4)
The calculated values of Ea for the ILs [Cnmmim][NTf2] (n ¼
2, 4) are also listed in Table 5. According to Table 5, we can see
that the values of Ea for [Cnmmim][NTf2] (n ¼ 2, 4) are nearly
equivalent in the temperature range of (298.15–338.15) K, that
is, the Gibbs energy of surface formation is temperature-
independent.
Fig. 3 Plot of gV2/3 vs. T for [Cnmmim][NTf2] (n ¼ 2, 4). - [C2mmim]-
[NTf2]: gV2/3 ¼ 1760.745 + 1.194 T, s ¼ 1.29, r ¼ 0.997; C [C4mmim]-
[NTf2]: gV2/3 ¼ 1865.791 + 1.320 T, s ¼ 1.68, r ¼ 0.996.
In comparison with fused salts, for example, Ea ¼ 146 mJ mꢁ2
(for fused NaNO3),29 the values of Ea for the ILs are much lower
and are close to organic liquids, for example, Ea ¼ 67 mJ mꢁ2 for
benzene and 51.1 mJ mꢁ2 for n-octane.30 This fact shows that
interaction energy between ions in the ILs is much less than
that in inorganic fused salts because the Gibbs energy of surface
formation is dependent on interaction energy between ions.
The low Gibbs energy of surface formation is the underlying
reason for forming ILs [Cnmmim][NTf2] (n ¼ 2, 4) at room
temperature.
that the relationship between Tb and Tc is Tb z 0.6 Tc for ionic
liquids. The values of Tc and Tb are listed in Table 6.
Kabo and colleagues32 put forward an empirical equation for
the estimation of the standard molar enthalpy of vaporization,
DHv at 298.15 K, for the ILs:
DHv ¼ A(gV2/3
N
1/3) + B
(6)
where V is the molar volume, g is surface tension, N is Avoga-
dro's constant, A and B are the empirical parameters,32 their
values are A ¼ 0.01121 and B ¼ 2.4 kJ molꢁ1, respectively. The
values of molar enthalpy of vaporization for [Cnmmim][NTf2]
(n ¼ 2, 4) calculated from eqn (6) are listed in Table 7. The mean
contribution to vaporization enthalpy per methylene (–CH2–)
¨
¨
3.2 Eotvos equation and estimation of the enthalpy of
vaporization
group, DHv (–CH2–) ¼ 3.3 kJ molꢁ1
.
In general, the dependence of surface tension, g, on tempera-
29
Based on the Verevkin's experimental data,33 and the
contribution to vaporization enthalpy of per methylene (–CH2–)
group (3.89 kJ molꢁ1), the molar enthalpies of vaporization,
DHv, for the ILs [Cnmmim][NTf2] (n ¼ 2, 4) were estimated and
are also listed in Table 7.
¨ ¨
ture may be expressed in Eotvos equation:
gV2/3 ¼ k (Tc – T)
(5)
where V is molar volume, Tc is critical temperature, and k is an
empirical constant. The linear regressions of product of g and
V2/3 for the ILs against absolute temperature T were made and
good straight lines were obtained (see Fig. 3).
From the slopes and the intercepts of the straight lines, the
values of k and Tc were obtained respectively, and they are listed
in Table 6.
From Table 7, the values of dm for the [Cnmmim][NTf2] (n ¼ 2,
4) based on the Verevkin's experimental data are a little bit
larger than that of using Kabo's method.
Rebelo et al.31 put forward a method of estimating the
hypothetical temperature of normal boiling point (NBP) of ionic
liquids, Tb, in terms of critical temperature, Tc. They thought
Table 7 The values of vaporization enthalpy and dm of ILs [Cnmmim]
[NTf2] (n ¼ 2, 4)
DHvn/kJ
DHvm/kJ
Ionic liquids
DHv/kJ molꢁ1
molꢁ1
molꢁ1
dm/J1/2 cmꢁ3/2
Kabo's
[C2mmim][NTf2]
[C4mmim][NTf2]
Table 6 The values of a, k, Tc, and Tb of ILs [Cnmmim][NTf2] (n ¼ 2, 4)
135.5
142.0
90.7
102.9
44.8
39.1
12.72
11.21
Ionic liquids
a ꢂ 10ꢁ4/Kꢁ1
107k/J Kꢁ1
Tc/K
Tb/K
[C2mmim][NTf2]
[C4mmim][NTf2]
6.49
6.57
1.194
1.320
1475
1414
885
848
Verevkin's
[C2mmim][NTf2]
[C4mmim][NTf2]
130.79
136.29
130.79
136.29
40.07
33.41
12.02
10.36
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Table 8 The values of n, D, M, r, Rn, DvapHn, DvapH(exp), DvapHm and dm for some ILs
Dvap
n/kJ molꢁ1
H
DvapH(exp)/kJ
DvapHm/kJ
Ionic liquids
nD
D
M/g molꢁ1
r/g cmꢁ3
Rm/cm3 molꢁ1
molꢁ1
molꢁ1
dm/J1/2 cmꢁ3/2
[C2mim][NTf2]
[C4mim][NTf2]
[C6mim][NTf2]
[C8mim][NTf2]
[C10mim][NTf2]
[C2mim][BF4]
1.421a
1.427a
1.431a
1.434a
1.436a
1.409a
1.420a
1.5506b
1.5112b
1.5124b
1.4469b
391.31a
419.37a
447.42a
475.47a
503.53a
197.97
226.02
1.50e
85.8
98.4
112.9
122.6
141.1
49.6
61.7
62.7
62.4
72.4
132.7g
137.8g
142.3g
147.0g
147.5g
135.5h
152.5i
153.7h
156.4h
138.5h
135.6h
46.9
39.5
29.4
24.4
6.4
85.9
90.3
91.0
94.0
66.1
60.0
13.28
11.45
9.26
8.13
3.88
23.35
21.72
24.3
24.0
18.7
11.7c
1.42e
1.33e
1.31e
1.21e
12.8d
11.7d
1.2798f
1.2015f
[C4mim][BF4]
[C2C1im][SCN]
[C2C1im][N(CN)2]
[C2C1im][C(CN)3]
[C2C1im][B(CN)4]
48.32b
48.1b
55.84b
58.28b
75.6
16.4
a
c
h
Ref. 26. b Ref. 44. Ref. 38. d Ref. 37. e Ref. 39. f Ref. 40. g Ref. 41. Ref. 43. i Ref. 42.
enthalpy of vaporization for ionic liquids by using eqn (9) are
too small because this equation may be applied only to non-
polar van der Waals liquid. The polarization of non-polar van
der Waals liquid in the electric eld is caused only by induced
dipole moment. But, for the ionic liquids the polarization in
electric eld is caused by both self-induced dipole moment and
mean permanent dipole moment of ion pair in ILs.
3.3 Molar refraction Rm and estimation of polarity for
[Cnmmim][NTf2] (n ¼ 2, 4)
The Lorentz–Lorenz relationship between the refractive index
and the mean molecular polarizability, ap, leads to the deni-
tion of the molar refraction Rm:34
2
2
Rm ¼ [(nD ꢁ 1)/(nD + 2)](M/r) ¼ (4pN/3)ap
(7)
3. In terms of the Hildebrand theory,36 DHv, DHnv , and DHvm
correspond with d2, dn2, and dm (d Hildebrand solubility
2
where M and r are molar mass and density of the ILs. ap is the
static polarizability caused by the induced dipole. According to
eqn (7), values of Rm were calculated from nD values of the ILs in
the temperature range of (298.15–338.15) K and are listed in
Table 3. As can be seen from Table 3, the values of Rm and ap
only slightly change with the increasing temperature. This fact
shows that the static polarization is caused by the dispersion
force of the ILs.
parameter), respectively:
d2 ¼ ꢁE/V ¼ (DHv ꢁ RT)/V
(10)
where E is the potential energy of a mole of material.
dn ¼ DHvn/V ꢁ xRT/V
(11)
(12)
2
2
dm ¼ DHvm/V ꢁ (1 ꢁ x)RT/V
In this work, we assume that a new method for the estima-
tion of the polarity of ILs using the enthalpy of vaporization
DHv, and there are four hypotheses as follows:
where x ¼ (DHvn/DHv) represents the fraction of contribution of
induced energy to polarity of ionic liquid, and (1 – x) ¼ (DHvm/
DHv) is the contribution fraction of orientation energy from
permanent dipole moment.
4. Non-polar organic solvent only has the induced dipole
moment dn, but orientation energy of the permanent dipole
moment dm, while dm as the new scale to the polarity, there is a
positive correlation between the dm and the polarity.
1. The enthalpy of vaporization DHv ionic liquid is composed
of two parts, a part corresponds with polarization from the
induced dipole moment, DHvn, which is contribution of induced
energy, and another part corresponds with polarization from
permanent dipole moment, DHvm, which is orientation energy:
DHv ¼ DHvn + DHvm
(8)
As we all know, the polarity of ILs is oen assessed with the
dielectric constant, for example, the values of dielectric
constant of [C2mim][BF4] and [C4mim][BF4] measured by Wakai
et al.37 are 12.8 and 11.7, respectively, however, in some case, it
is not, for example, the dielectric constant value of [C4mim]-
[NTf2] measured by Daguenet et al.38 is 11.7 which is the same
with [C4mim][BF4] by Wakai et al.37 If dm is used as criterion, it is
easy to determine the order of polarity for the two ILs. According
to the eqn (8), (9) and (12), using the values of literature26,39–42 dm
¼ 11.45 J1/2 cmꢁ3/2 for [C4mim][NTf2] and dm ¼ 21.72 J1/2 cmꢁ3/2
for [C4mim][BF4] were obtained according to the method in this
work so that it has seen that the polarity of [C4mim][BF4] is
much larger than one of [C4mim][NTf2]. This result is in good
2. Typically, the polarity of the liquid mainly depends on the
cohesive energy which may be calculated from the enthalpy of
vaporization of the liquid. Lawson and Ingham35 pointed out
that the relationship between the enthalpy of vaporization and
the refractive index can be expressed. Using the following
equation, the contribution of induced energy DHvn can be
obtained.
2
2
DHvn ¼ CRm ¼ C[(nD ꢁ 1)/(nD + 2)]V
(9)
where Rm is the molar refraction, V is molar volume of the liquid,
C is empirical constant which is equal to C ¼ 1.297 kJ cmꢁ3 for a
van der Waals liquid. However, the calculated values of the
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agreement with our experience, that is, [C4mim][NTf2] is [Cnmmim][NTf2] (n ¼ 2, 4) vs. [Cnmim][NTf2] (n ¼ 2, 4) are much
hydrophobic, [C4mim][BF4] hydrophilic. larger, it means that the addition of a methylene group of
Using the method in this work, the values of dm ¼ 12.02 [Cnmmim][NTf2] (n ¼ 2, 4) can have a stronger impact in dm, the
(12.72) J1/2 cmꢁ3/2 and 10.36 (11.21) J1/2 cmꢁ3/2 for the ILs result shows that using dm as the polarity scaling of ILs is very
[C2mmim][NTf2] and [C4mmim][NTf2] were obtained respec- convenient and reasonable.
tively which are listed in Table 7 and the values of dm for other
ILs were calculated from other literature26,39,41,43,44 and are listed
in Table 8. From Table 8, the average contributions to dm of per
methyl group in alkyl chain, Ddm(–CH2–) ¼ 0.83 J1/2 cmꢁ3/2
Glossary
DSC
Ea
Differential scanning calorimetry
Gibbs energy of surface formation
Nuclear magnetic resonance
between [C2mmim][NTf2] and [C4mmim][NTf2], which is in
good agreement with the value Ddm(–CH2–) ¼ 0.82 J1/2 cmꢁ3/2
between [C2mim][BF4] and [C4mim][BF4]. Compared with the
average contributions to dm of per methyl group (–CH2–) in alkyl
chain, the average contributions to the addition of a methylene
group in the imidazolium ring, Ddm(–CH3) ¼ 1.18 J1/2 cmꢁ3/2 for
[Cnmmim][NTf2] (n ¼ 2, 4) vs. [Cnmim][NTf2] (n ¼ 2, 4) are much
larger, it also means that the addition of a methylene group in
the imidazolium ring of [Cnmmim][NTf2] (n ¼ 2, 4) can have a
stronger impact in dm. And from the table, it shows that the
polarity of the ionic liquids reduces with the increase in the
number of methylene on side chain, for example, the ILs
[Cnmim][NTf2] (n ¼ 2, 4, 6, 8, 10), the polarity of hydrophilic ILs
is larger than the hydrophobic, which these results are consis-
tent with our experience.
1H
NMR
M
Molar mass
N
Avogadro's constant
nD
Refractive index
Rm
V
Molar polarization
Molar volume
Vm
Tc
Molecular volume
Critical temperature
Tb
Temperature of normal boiling point
Enthalpy of vaporization
DHv
DHvn
The contribution to DHv from the induced dipole
moment enthalpy of vaporization
The contribution to DHv from the average permanent
dipole moment of ion pair in ILs
The fraction of contribution of induced energy to
polarity of ionic liquid
DHvm
x
4. Conclusions
Two ILs [Cnmmim][NTf2] (n ¼ 2, 4) were prepared and charac-
terized. The density, r, the surface tension, g, and the refractive
index, nD, for the two ILs were measured at (298.15 to 338.15 ꢀ
0.01) K. The average contributions to the density, surface
tension, and refractive index of per methyl group in alkyl chain
and the addition of a methylene group in the imidazolium ring
for the ILs were obtained, according to compare with the
both average contributions D(–CH2–) and D(–CH3), it turns
out the addition of a methylene group in the imidazolium ring,
D(–CH3), for [Cnmmim][NTf2] (n ¼ 2, 4) are larger than that of
[Cnmim][NTf2] (n ¼ 2, 4), which means that the addition of a
methylene group has stronger effect on the density, surface
tension, and refractive index. The values of molar volume V,
molecular volume, Vm, the thermal expansion coefficient, a,
were calculated. With the increase in the number of methylene
on alkyl side chains, the values of a are increased only slightly.
The contribution to Vm and DHv per methylene (–CH2–) group
are 0.0280 nm3 and 3.3 kJ molꢁ1, respectively. The values of
Gibbs energy of surface formation, Ea, molar refraction, Rm, and
the polarization coefficient, ap, are temperature-independent.
Based on the Kabo's method and Verevkin's experimental
values, the values of dm were estimated by enthalpy of vapor-
ization and refractive index data for [Cnmmim][NTf2] (n ¼ 2, 4),
the average contributions to dm, Ddm(–CH2–) ¼ 0.83 J1/2 cmꢁ3/2
between [C2mmim][NTf2] and [C4mmim][NTf2], which is in
good agreement with the value Ddm(–CH2–) ¼ 0.82 J1/2 cmꢁ3/2
between [C2mim][BF4] and [C4mim][BF4]. Compared with the
average contributions to dm of per methyl group in alkyl chain,
the average contributions to the addition of a methylene group
in the imidazolium ring, Ddm(–CH3) ¼ 1.18 J1/2 cmꢁ3/2 for
1 ꢁ x The fraction of contribution fraction of orientation
energy from permanent dipole moment.
Greek letters
a
Coefficient of thermal expansion
d2 Cohesive energy density
2
dn The contribution of induced energy to cohesive energy
density
2
dm The contribution of orientation energy to cohesive energy
density
d
Hildebrand solubility parameter
dn The contribution of the permanent dipole moment to
solubility parameter
dm The contribution of the induced dipole moment to
solubility parameter
g
Surface tension
Density
r
Acknowledgements
This project was supported by NSFC (21173107 and 21203193).
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