Chinese Journal of Chemical Engineering, 16(2) 256—262 (2008)
Densities and Viscosities of the Ionic Liquid [C4mim][PF6]+
N,N-dimethylformamide Binary Mixtures at 293.15 K to 318.15 K*
GENG Yanfang (耿彦芳), WANG Tengfang (王腾芳), YU Dahong (虞大红), PENG Changjun
(彭昌军)**, LIU Honglai (刘洪来) and HU Ying (胡英)
State Key Laboratory of Chemical Engineering and Department of Chemistry, East China University of Science and
Technology, Shanghai 200237, China
Abstract Viscosities and densities for 1-butyl-3-methylimidazolium hexafluorophosphate ([C4mim][PF6]) and N,
N-dimethylformamide (DMF) binary mixtures have been measured at the temperature range from 293.15 K to
318.15 K. It is shown that the viscosities and densities decrease monotonously with temperature and the content of
DMF. Various correlation methods including Arrhenius-like equation, Seddon et al.’s equation, Redlich-Kister
equation with four parameters, and other empirical equations were applied to evaluate these experimental data. A
model based on an equation of state for estimating the viscosity of mixtures containing ionic liquids were proposed
by coupling with the excess Gibbs free energy model of viscosity, which can synchronously calculate the viscosity
and the molar volume. The results show that the model gives a deviation of 8.29% for the viscosity, and a deviation
of 1.05% for the molar volume when only one temperature-independent adjustable parameter is adopted. The correlation accuracy is further improved when two parameters or one temperature-dependent parameter is used.
Keywords ionic liquid, N, N-dimethylformamide, density, viscosity, [C4mim][PF6], correlation
1
INTRODUCTION
Room-temperature ionic liquids (RTILs), also
considered as room temperature molten salts (RTMS),
are a class of organic salts consisting solely of cations
and anions; they keep liquid state at or near ambient
temperature. Many unique advantages are exhibited
by those RTILs compared with the conventional organic solvents, such as a larger temperature range of
liquid state, lower vapor pressures, nonflammable,
good thermal stability, and favorable solubility of polar or non-polar organic and inorganic compounds [1].
Nowadays, there are many available interesting
air-stable RTILs that are increasingly employed as
replacement for organic solvents in basic research and
applications.
However, despite their many unique properties,
there are still several obstacles in the practical applications for RTILs because of the difficulties encountered in the purification and separation process as well
as the higher production cost. As a way out, one can
mix an ionic liquid with another ionic liquid or with
certain organic solvent, the difficulties might be
eliminated effectively, and sometimes, it is possible to
gain some new favorable performance. Therefore,
many studies have addressed the physicochemical
properties of ionic liquids mixture. For example,
Wang et al. [2] measured densities and viscosities for
mixtures of 1-n-butyl-3-methylimidazolium tetrafluoroborate ([C4mim][BF4]) ionic liquid with
acetonitrile, dichloromethane, 2-butanone, and
N,N-dimethylformamide at 298.15 K. Arce et al. [3]
measured densities, refractive indices, speeds of sound,
and dynamic viscosities of 1-methyl-3-octylimidazolium
tetrafluoroborate ([C8mim][BF4]) in binary mixtures
with methanol, ethanol, 1-propanol, and 2-propanol at
298.15 K. Alan et al. [4] reported that the viscosities of
RTILs decrease and their specific conductivity increases after adding organic solvents. Every et al. [5]
obtained the similar results for the blends of various
RTILs, consequently, the mixtures exhibit a better capability and have a promising application in the field
of electrochemistry. Orchillés et al. [6] measured densities of 1-butyl-3-methylimidazolium octylsulfate
solutions in water and 1-propanol. Volumetric data of
(RTIL+RTIL) mixtures and (RTIL+non-aqueous organic liquids) have been reported in the Refs. [7, 8].
N, N-dimethyllformamide (DMF), a nonproton
polar organic solvent with high dielectric constant, is
conceived as an omnipotent organic liquid because of
its good solubility for both organic solvents and many
inorganic liquids. It has also been used for improving
activity of some polymerization reactions [9]. Zhang et
al. [10] fabricated cobalt and nickel nanoparticles in
DMF solution, in which DMF acts not only as solvent
but also as reductant. The mixtures of ionic liquid and
DMF may provide a potential application for the
utilization of both ionic liquids and DMF.
In the following, we measured viscosities and densities for the binary mixture 1-butyl-3-methylimidazolium
hexafluorophosphate [C4mim][PF6]+DMF at temperatures from 293.15 K to 318.15 K. We then correlate
the experimental results with various methods including a model proposed in this work.
2
2.1
EXPERIMENTAL
Chemicals
[C4mim][PF6] was prepared and purified using the
Received 2007-06-20, accepted 2007-10-03.
* Supported by the National Natural Science Foundation of China (20476025, 20776040), Shanghai Municipal Science and
Technology Commission of China (05DJ14002) and Hubei Key Laboratory of Novel Chemical Reactor and Green Chemical
Technology of China (XLHX2007002).
** To whom correspondence should be addressed. E-mail: [email protected]
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Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
procedures described in Refs. [11-13]. The structure of
final product was confirmed by 1H-NMR [DMSO, δ
relative to TMS: δCH3(1):3H, 3.85; δH(2):1H,9.04;
δCH2(3):2H, 4.16; δH(4):1H,7.74; δH(5):1H,7.62;
δCH2(6):2H,1.76;
δCH2(7):2H,1.29;
δCH3(8):3H,0.86). The presence of water in the samples has a strong impact on the physicochemical
properties such as viscosity and density [14]. In this
work, the ionic liquid was dried under vacuum at
343.15 K for one day before use. The water content was
0.2 % (by mass) after measurements by Karl-Fisher
titration analysis. Another impurity that can also affect
the properties is the halogen ion. The content of bromine ion in IL was determined by qualitative analysis
using sodium hypochlorite oxidation.
N,N-dimethylformamide (A.R.grade) with a
minimum mass fraction purity of 99.0% (Shanghai
Chemical Reagent Co., LTD) was rectified, and the
distillate at temperatures from 425 K to 427 K was
collected before use. Visser [15], Chittleborough [16]
and Marchettl [17] have studied the density or viscosity of the mixture of DMF and water, it indicated that
the presence of water has an obvious effect on the
properties of DMF. Here, the water content in DMF,
0.002% in mass fraction, was measured using
Karl-Fisher. The density of DMF obtained in this context has good accordance with Ref. [16], but there are
slight differences between our viscosity values and
those reported by Chittleborough [16] and Marchettl
[17] due to the presence of water.
Mixtures were gravimetrically prepared over the
whole composition range by using an analytical balance with a standard uncertainty of 0.1mg. The mixtures were maintained under ultrasonic for several hours
to assure homogeneity and then stored in desiccator.
2.2
Property measurements
Viscosities of the binary mixtures were measured
using Ubbelohde viscometer, which was obtained
from SCHOTT-Instruments, Mainz. Two viscometers
were used in order to improve precision and a statistical analysis of our results indicates a precision in the
viscosities of 1.3%. Densities were determined in the
same temperature bath using pycnometer of approximately 20cm3. The pycnometer used was calibrated
with distilled water of known density. The precision of
－
－
the density measurement is of the order 10 4 g·cm 3.
3
RESULTS AND DISCUSSION
3.1 Experimental data of viscosities and corresponding correlations
Most RTILs are viscous liquids, their viscosities
ranging between 10 mPa·s and 500 mPa·s, with two or
three orders of magnitude greater than traditional organic solvents. The high viscosity badly affects mass
transfer and more energy is needed when mixing them
with another liquid. More and more attentions have
been paid to the design of ionic liquids with lower
viscosity. It has been found that the viscosity of
[Cnmim][BF4] with n equal to 2, 4, and 6 increases
from 66.5 mPa·s to 314 mPa·s [1], whereas for
[Cnmim][Tf2N] [11] with alkyl chain lengths from 1 to
4 the viscosity first decreases and then increases again.
Recently, a practical and effective method is adding
organic liquids into ionic liquid to adjust the viscosity
because it has been found that the viscosity of ionic
liquids decreases sharply with the increasing amount
of organic liquids [4, 5]. Values of viscosity for
[C4mim][PF6] and DMF as well as their mixtures from
293.15 K to 318.15 K measured in this work are presented in Table 1.
Table 1
xDMF
The experimental results of viscosities for
xDMF+(1－x)[C4mim][PF6]
η/mPa·s
293.15 K 298.15 K 303.15 K 308.15 K 313.15 K 318.15 K
0.0000
265.19
205.57
165.71
133.89
110.79
95.75
0.1002
151.11
114.49
88.20
68.75
54.88
44.63
0.2000
94.60
73.44
58.02
45.91
37.38
31.22
0.3002
59.64
47.42
38.13
30.91
25.68
21.55
0.3999
39.70
32.09
26.34
21.74
18.30
15.57
0.5000
23.41
19.44
16.30
13.74
11.82
10.24
0.6000
12.37
10.57
9.11
7.89
6.94
6.16
0.7000
6.86
6.02
5.32
4.71
4.22
3.82
0.7999
3.71
3.35
3.03
2.73
2.51
2.30
0.8999
1.90
1.77
1.62
1.50
1.40
1.31
1.0000
0.91
0.87
0.82
0.78
0.75
0.72
As presented above, the trends in the evolution of
viscosity are consistent with information available in
the literature. For pure components, it has been illuminated that the values for molecular liquid are acceptable. However, for the viscosity data for
[C4mim][PF6] there is a discrepancy between our
work and literatures. Besides the effect of temperature
and experimental method, the presence of trace
amounts of impurities such as water and halogen ion
in sample can greatly modify the values of thermodynamic properties. Our data are lower than that of dried
sample with 0.019% of water in mass fraction but
higher than that of the water-saturated sample containing 2.68% of water by Jacquemin [14]. Zhu and
co-workers [18] have obtained a value of 217.9 mPa·s
at 298.15 K, which is somewhat higher than our results with 205.57 mPa·s. Okoturo and VanderNoot [19]
have reported a lower viscosity of 173 mPa·s at
298.15 K and alleged that their sample was checked
only by NMR spectroscopy without specific contents
of water as well as other impurities. In addition, Harris
[20] has reported a higher value of 273 mPa·s at
298.15 K. Up to now, the highest values of viscosity
are obtained by Huddleston et al. [21] of 397 mPa·s for
water equilibrated sample and 450 mPa·s for dried one.
Therefore, a detailed comparison for viscosities is difficult due to the quantity of diverse impurities, the
experimental condition, and higher viscosity of ILs. It
must be a very hard job to synthesize a pure standard
ILs sample.
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Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
It was found that the viscosities of the
[C4mim][PF6] are notably greater than that of DMF
and the viscosities of the mixture decrease with the
content of DMF. The van der Waals interaction and
weak hydrogen bonding play the principle part in
DMF, whereas the nitrogen and fluorine atoms in anion can form hydrogen bonding with hydrogen in
imidazole ring and the electrostatic attraction between
cation and anion in RTILs is strong for ionic liquids.
Therefore, the much higher viscosity for [C4mim][PF6]
than DMF is of no wonder. This leads to the fact that
the viscosity of the mixture decreases sharply first,
then decreases much slower with the increase of DMF.
On the other hand, it is also found that the influence of
temperature on the viscosity of ionic liquid is much
greater than that of organic solvent. Along with the
increase of organic solvent, the impact of temperature
on viscosities of the mixture is more and more slender.
As a result, viscosities of mixture present a concave
curve with increasing DMF.
It is found that an Arrhenius-like equation [14]
can be used to fit the temperature effect on the viscosity of the ionic liquid mixtures,
η = η∞ exp ( Ea / RT )
(1)
where η is the viscosity of the system, and η∞ and Ea
are characteristic parameters. In fact, Eq. (1) is a simplified version of Eyring’s absolute rate theory. Table
2 lists the correlated parameters and the relative deviation Δ. It is indicated clearly that Eq. (1) is quite
satisfactory for correlating viscosities of system
[C4mim][PF6]＋DMF with temperature.
Table 2 The correlated results for xDMF+(1-x)
[C4mim][PF6] by Arrhenius-like equation
4
－1
xDMF
η∞×10 /mPa·s
Ea/kJ·mol
0.0000
5.60
31.79
0.0277
0.1002
0.26
37.93
0.1901
0.2000
0.64
34.61
0.0891
0.3002
1.34
31.67
0.0176
0.3999
2.58
29.09
0.1351
0.5000
6.09
25.71
0.0150
0.6000
16.61
21.71
0.0112
0.7000
38.65
18.22
0.0086
0.7999
82.59
14.88
0.0154
0.8999
162.12
11.62
0.0108
1.0000
418.15
7.51
0.0149
(4)
η = η0 exp ( − xDMF / a )
−4
with η0 = 0.1142 × 10 exp ( 41.81/ RT ) and a = RT /
(33.662 − 8.1739 RT ) , where η0 should be the viscosity of pure ionic liquid [C4mim][PF6] with xDMF = 0 .
However, the linear relation Eq. (2) does not apply to
the case of xDMF = 0 , therefore, η0 is an empirical
parameter. We can use Eq. (4) to predict approximately the viscosity for mixture containing ionic liquids at given temperatures and compositions except for
the pure ionic liquid. It was found that the result predicted has a deviation of 11.61% due to error transfer.
To correlate viscosity with composition, Seddon
et al. [22] have stated that viscosities for ionic liquid
mixtures can generally be described by the exponential expression
η = ηRTIL exp ( − xDMF / a )
(5)
where a is a constant characteristic for the mixture,
and ηRTIL is the viscosity of the pure ionic liquid.
Compared with the above Eq. (4), it is obvious that
the two equations are virtually the same except for the
physical meanings of the pre-exponential factor. We
have used Eq. (5) to fit the viscosities of the mixtures.
It was found that the total average relative deviation
for viscosity is about 11.01%, indicating that Seddon
et al.’s equation, Eq. (5), is not suitable for correlating
the viscosity data in this work. That is because the
equation uses the viscosity of the pure ionic liquid as
the pre-exponential factor.
Another model for correlating viscosity with
composition is Redlich-Kister equation [23]
n
Δη = η − ( x1η1 + x2η 2 ) = x1 x2 ∑ Bi ( x1 − x2 ) ,
Δ
i
(6)
i =1
where x1 and x2 are molar fractions of DMF and
[C4mim][PF6], respectively. Redlich-Kister equation
provides in fact an excess property of a solution by
defining the difference between the real mixture property and that of an ideal solution at the same temperature, pressure, and composition. We have correlated
experimental values with four parameters [n equals to
3 in Eq. (6)] by Redlich-Kister equation and found
that the total average relative error for viscosity is
11.02%, indicating that the results are comparable
with Seddon et al.’s equation with a total relative deviation of 11.01%. Of course, we can also increase the
number of parameters to improve the correlation accuracy.
Carefully analyzing the characteristic parameters
obtained, we found that the parameter, Ea, decreases
linearly with increasing composition of DMF except
for xDMF = 0 . The linear relation can be represented by
Ea / kJ ⋅ mol−1 = −33.662 xDMF + 41.81
(2)
with correlation coefficients greater than 0.99. On the
other hand, we have also noted that the parameter η∞
in Eq. (1) increases exponentially with increasing
composition of DMF except for xDMF = 0 . A simple
exponential equation
η∞ × 104 / mPa ⋅ s = 0.1142exp (8.1739xDMF )
can be used to fit η∞ with a correlation coefficient of
0.999. Inserting Eq. (2) and Eq. (3) into Eq. (1), we have
(3)
3.2 Experimental data of densities and corresponding correlations
Table 3 presents the densities of mixture
[C4mim][PF6]+DMF measured in this work. The density data for pure ionic liquid obtained in this work
have discrepancy with literatures. Nevertheless, comparison is difficult due to the quantity of diverse impurities in their samples. The density for [C4mim][PF6]
with approximately 0.15 % (by mass) water content
by Blanchard [24] is lower than that of sample with
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Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
Table 3 The experimental densities of
xDMF+(1－x)[C4mim][PF6]
－3
xDMF
ρ/g·cm
293.15K 298.15K 303.15K 308.15K 313.15K 318.15K
0.0000
1.3689
1.3635
1.3592
1.3555
1.3520
1.3474
0.1002
1.3493
1.3454
1.3409
1.3367
1.3323
1.3283
0.2000
1.3298
1.3256
1.3213
1.3170
1.3127
1.3086
0.3002
1.3095
1.3053
1.3008
1.2965
1.2923
1.2881
0.3999
1.2899
1.2856
1.2812
1.2769
1.2723
1.2683
0.5000
1.2628
1.2586
1.2541
1.2498
1.2453
1.2411
0.6000
1.2244
1.2200
1.2155
1.2111
1.2067
1.2023
0.7000
1.1819
1.1778
1.1732
1.1689
1.1643
1.1599
0.7999
1.1292
1.1247
1.1201
1.1154
1.1110
1.1065
0.8999
1.0550
1.0505
1.0457
1.0409
1.0363
1.0318
1.0000
0.9491
0.9449
0.9402
0.9355
0.9307
0.9259
0.2% (by mass) water content by our work. However,
the quantity of other impurities weren’t detected and
reported in Blanchard’s work. The higher values of
Harris [20] have reported for ILs without specific impurity. The densities reported by Troncoso [25] are
higher by 0.1% to 0.2% than our data. Jacquemin [14]
observed a difference of 1% to 2% between
water-saturated and dried sample, which is negligible
for practical application. Therefore, it is believed that
the values determined in this work are acceptable.
As shown in Table 3, the density decreases with
increasing temperature at a fixed composition and
decreases with increasing composition of DMF at
fixed temperature. Jacquemin et al. [14] have measured a large number of data on the density of ionic
liquids and reported a linear decrease of density with
increasing temperature. The length of the alkyl-chain
in cation as well as the variety of anion has a great
impact on density of RTILs. Usually, the density decreases with increasing length of the alkyl-chain and
increases with increasing volume of the anion. The
densities are little affected by the temperature, whereas
viscosities decrease dramatically when the temperature
increases. The influence of temperature on density can
be expressed by using the equation as follows
ρ = α + β (T − 273.15 )
(7)
Equation (7) was applied to correlate the experimental densities and it was found that the influence of
temperature on densities can be fitted by Eq. (7), and
the relative deviation of density at given composition
is popularly smaller than 1%. Analyzing the parameters obtained, namely, α and β, we found that the parameter α in Eq. (7) decreases monotonously with increasing composition of DMF as shown in Fig. 1.
These relations can be represented by
3
2
α = −0.4891xDMF
+ 0.3296 xDMF
− 0.2552 xDMF + 1.387,
(8)
with correlation coefficients greater than 0.99. Another parameter β is linearly increased with increasing
composition of DMF (see Fig. 1). A simple equation,
β × 104 = 0.9765 xDMF + 8.3163 ,
(9)
Figure 1 The effect of xDMF on parameters α and β
△ α; ◇ β
can be fitted to parameter β with a correlation coefficient of 0.98. Therefore, one can use Eq. (7) associating it with Eq. (8) and Eq. (9) to predict approximately the densities of mixture containing ionic liquids at any temperature and composition.
Densities of the mixture can be also correlated
using the experimental volume. We have applied
Redlich-Kister equation with four parameters [23] to
calculate the molar volume of mixing ΔV:
ΔV = V − ( x1V1 + x2V2 )
=
M ⎞
⎛ M
− ⎜ x1 1 + x2 2 ⎟
ρ ⎝ ρ1
ρ2 ⎠
M
n
= x1 x2 ∑ Bi ( x1 − x2 )
i
,
(10)
i =0
where M is molar mass. The results that the total average relative deviation for densities is 9.35% indicate
that the Redlich-Kister equation [23] is not suitable for
correlating the experimental data in this work unless
the number of parameters is increased.
3.3 A model for correlating densities and viscosities synchronously
The other route for estimating the effect of the
composition on the viscosity of mixtures is based on
the excess Gibbs free energy model [26] represented as
follows:
K
ln(ηV ) = ∑ xi ln (ηiVi ) +
i =1
G EX
RT
(11)
where η and ηi are viscosities of the mixture and the
pure component i, respectively, and V and Vi are the
molar volume of the mixture and the pure component,
i, respectively. GEX is the excess Gibbs free energy of
the mixture. The reason for using Eq. (11) is for calculating excess Gibbs free energy and the molar volume with the same model.
In principle, an appropriate equation of state can
be used to evaluate GEX synchronously and the molar
volume of both mixture and pure components in the
Eq. (11). In this work, we adopted a molecular thermodynamic model for chain-like fluids [27] to evaluate the excess Gibbs free energy and the molar volume
for mixtures containing ionic liquid.
For an associated system, Helmholtz function, A,
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Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
and compressibility factor, Z, can be written as follows [27]:
ideal
A= A
hsm
+A
chain
+A
hsm
chain
attrc
+A
assoc
+A
attrc
(12)
assoc
Z =1+ Z
+Z
+Z
+Z
,
(13)
where superscripts “ideal”, “hsm”, “chain”, “attrc”, and
“assoc” represent contribution of ideal, hard-sphere
mixture, chain-like, square-well, and associate, to
Helmholtz function A and compressibility factor of the
system, respectively. Exact expressions and calculation method can be found in literature [27]. There are
five molecular parameters for pure compounds in this
model: chain length (r), chain diameter (σ),
square-well interaction energy (ε/k), association energy (δε), and association fraction (ω), and they can be
estimated from pVT data of pure fluid. For mixtures, a
mixing rule is introduced to calculate the reduced
temperature ( T ).
K
K
T −1 = ∑∑ xi x j ri rj ( ε ij / kT )σ ij3
i =1 j =1
ε ij = (1 − κ ij )(ε iε j )
1/ 2
K
K
∑∑ xi x j ri rjσ ij3
(14)
i =1 j =1
; σ ij = (1 − lij )(σ i + σ j ) / 2 , (15)
where κij and lij are two adjustable parameters and
they can be obtained by fitting viscosity experimental
data of the mixtures.
The Helmholtz function and the compressibility
factor of both pure liquids and mixtures can be derived through Eq. (12) and Eq. (13). The excess Gibbs
free energy can be further obtained by
K
G EX = AEX + pV EX = A + pV − ∑ xi ( Ai + pVi )
i =1
K
= A + ZRT − ∑ xi ( Ai + Z i RT )
(16)
i =1
Table 4
Systems
where
Ai = lim A ; Z i = lim Z .
xi →1
(17)
xi →1
The final expression of the model for calculating the
viscosity of mixtures can be expressed as
K
lnη = ∑ xi ln (ηi Z i RT / p ) −
i =1
K
∑ xi ( Ai / RT + Zi ) +
i =1
Z + A / RT − ln ( ZRT / p ) .
(18)
Molecular parameters needed are taken from
Refs. [27, 28], which were obtained by fitting pVT data
for pure component. The self association of methanol,
ethanol, 1-propanol, and 2-propanol is taken into account, whereas the corresponding association of ionic
liquid and cross association between ionic liquid and
DMF is not. We have also calculated viscosities of
other ionic-liquid mixtures from literature to examine
the applicability of Eq. (18). Table 4 gives the results.
As shown in Table 4, the model, Eq. (18), can be
used to estimate viscosities of mixtures. When only
one adjustable parameter, κij, is adopted, the total average relative deviation for viscosity is 6.88% for experimental data in this work. The corresponding result
is 5.64% by using two adjustable parameters, namely,
κij and lij.
For other mixtures containing ionic liquids from
literature selected, the total average relative deviation
for viscosity is 5.81% with κij and lowers to 3.05%
when the two parameters, κij and lij, are used. On the
other hand, if only one temperature-independent adjustable parameter, κij, is used, the total average relative deviation for viscosity is 8.29% for the 54 data
points in this work, and the corresponding result is
The correlated results for systems containing RTILs by an equation of state
T/K
One-parameter
Two-parameter
κij
Δη (ΔV)
κij
lij
Δη (ΔV)
Nm
Ref.
this work
293.15
0.0579
0.0449 ( 0.0094 )
0.0574
－0.0164
0.0449 (0.0094)
9
298.15
0.0563
0.0462 (0.0099)
0.0574
0.0319
0.0461 (0.0099)
9
303.15
0.0534
0.0538 (0.0102)
0.0791
0.4369
0.0513 (0.0101)
9
308.15
0.0499
0.0701 (0.0106)
0.1065
0.6453
0.0582 (0.0105)
9
313.15
0.0467
0.0867 (0.0111)
0.1591
0.7939
0.0647 (0.0110)
9
318.15
0.0416
0.1108 (0.0118)
0.3624
0.9235
0.0729 (0.0117)
9
[C4mim][PF6]+DMF
293-318
0.0634
0.0829 (0.0112)
0.1105
0.6672
0.0719 (0.0109)
54
this work
[C4mim][BF4]+2-butanone
298.15
0.0851
0.0329
0.1288
0.4594
0.0097
13
[2]
[C8mim][BF4]+acetonitrile
298.15
0.1106
0.0775
0.1241
0.1609
0.0708
13
[2]
[C8mim][BF4]+1-propanol
298.15
0.0139
0.0183
0.0113
－0.0265
0.0063
11
[3]
[C4mim][PF6]+DMF
[C8mim][BF4]+2-propanol
298.15
0.0023
0.0300
－0.0017
－0.0382
0.0121
11
[3]
[C8mim][BF4]+methanol
298.15
0.1297
0.0928
0.0941
－0.2244
0.0147
11
[3]
[3]
[C8mim][BF4]+ ethanol
298.15
0.0481
0.0448
0.0376
－0.0781
0.0069
11
[C4mim][BF4]+dichloromethane
298.15
0.0796
0.1425
0.0635
0.9576
0.0902
12
[2]
[C4mim][BF4]+DMF
298.15
0.0806
0.0250
0.0839
0.0439
0.0250
13
[2]
1 N m cal
1 N m cal
ηi − ηiexp /ηiexp , ΔV =
∑
∑ Vi − Viexp / Viexp , and Nm is the number of data. The numbers in parenthesis are
N m i =1
N m i =1
the results for the molar volume by Eq. (13).
Note: Δη =
Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
261
7.19% by using two temperature-independent adjustable parameters, κij and lij, which is still better than
that by using Redlich-Kister equation with four parameters. Fig. 2 and Fig. 3 show the comparison between the experimental values and the calculated results by this model. The results achieved are acceptable because the mixture is a highly asymmetrical system for viscosity. Eq. (18) can be recommended for
evaluating viscosity of ionic liquid mixtures.
Figure 4 The molar volume of [C4mim][PF6]+DMF from
experimental and calculation
xDMF: 1—0.1002; 2—0.2000; 3—0.3002; 4—0.3999;
5—0.5000; 6—0.6000; 7—0.7000; 8—0.7999; 9—0.8999
◇ this work; —— by Eq. (13)
Figure 2 Viscosity of the mixture [C4mim][PF6]+DMF at
different temperatures
◆ 318.15 K; □ 313.15 K; ■ 308.15 K; △ 303.15 K;
▲ 298.15 K; ◇ 293.15 K; —— calculated by Eq. (18)
Figure 3 Viscosity of the mixture containing RTILs at
298.15 K
◇ [C4mim][BF4]/2-butanone [2]; △ [C8mim][BF4]/acetonitrile [2];
□ [C8mim][BF4]/1-propanol [3]; × [C8mim][BF4]/methanol [3];
—— calculated by Eq. (18)
Although the molar volumes of system can be
correlated directly with an equation of state such as Eq.
(13), here, we directly used κij and lij obtained by regressing the experimental viscosities, which means a
unique set of κij and lij could be used to estimate both
the viscosities and densities. The results are presented
in the Table 4 (see the number in parenthesis in the
Table). Fig. 4 shows the comparison of the molar
volume calculated by Eq. (13) with experimental. It is
found that at fixed temperature, the total average relative deviation for molar volume is 1.05% when only
κij is used and 1.04% when κij and lij are used. If
temperature-independent adjustable parameters are
further adopted, the relative deviation is 1.12% with
κij and 1.09% with κij and lij.
4
CONCLUSIONS
The viscosity and density data for the binary
mixture of [C4mim][PF6] and DMF were measured
over the whole range of composition at 293.15 K to
318.15 K and atmospheric pressure. Various correlated
methods were applied to evaluate these experimental
data. The experimental results show that the viscosities and densities for mixtures decrease monotonously
with temperature and the content of DMF.
It is found that the temperature dependence of the
viscosity can be fitted with high precision with an
Arrhenius-like equation. Seddon et al.’s equation and
Redlich-Kister equation with four parameters can not
appropriately represent the composition dependence
of the viscosity. Similarly, Redlich-Kister equation
with four parameters is also not suitable for correlating the experimental density, unless the number of
parameter is increased.
A model based on an equation of state for estimating the densities and viscosities of mixtures containing ionic liquids was presented . This model can
synchronously calculate the viscosity and the molar
volume at any composition and temperature. The results
show that the model can give the deviation of 8.29% for
the viscosity and the deviation of 1.05% for the molar
volume when only one temperature-independent adjustable parameter is adopted.
NOMENCLATURE
A
a
B
Ea
G
K
k
lij
p
R
r
T
T
V
x
Z
α, β
ε
η
η∞
κij
ρ
σ
Helmholtz function
characteristic parameters in Eq. (5)
parameters of Redlich-Kister equation
－
characteristic parameters in Eq. (1), kJ·mol 1
Gibbs free energy
number of components
－
－
Boltzmann constant, 1.38×10 23 J·K 1
adjustable parameter for collision diameter
pressure, Pa
－
－
gas constant (R＝8.315 J·mol 1·K 1)
chain length
temperature, K
reduced temperature
－
volume, m3·mol 1
molar fraction
compressibility factor
－
－
－
－
parameters in Eq. (7), g·cm 3, 10 4 g·cm 3K 1
attractive energy, J
viscosity, mPa·s
－
characteristic parameters in Eq. (1), 10 4 mPa·s
adjustable parameter for interaction energy
－
density, g·cm 3
segment collision diameter, m
262
φ
ωij
Chin. J. Chem. Eng., Vol. 16, No. 2, April 2008
segment fraction
parameter for surface fraction
Superscripts
cal
exp
calculated results
experimental results
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