Modeling the Volumetric Properties of Ionic Liquids Using Modified

ARTICLE pubs.acs.org/IECR

Modeling the Volumetric Properties of Ionic Liquids Using Modified Perturbed Hard-Sphere Equation of State: Application to Pure and Binary Mixtures S. M. Hosseini,*,† J. Moghadasi,† M. M. Papari,‡ and F. Fadaei Nobandegani† † ‡

Department of Chemistry, Shiraz University, Shiraz 71454, Iran Department of Chemistry, Shiraz University of Technology, Shiraz 71555-313, Iran ABSTRACT: In this paper, an alternative corresponding states correlation was applied to the perturbed hard-sphere equation of state (PHS EOS) to improve the predictive power of this EOS for modeling the volumetric properties of ionic liquids (ILs) and their mixtures. Two temperature-dependent parameters appearing in the EOS have been determined using two reliable scaling constants, the surface tension and the liquid density, both at room temperature. The predictive power of the proposed model has been assessed by comparing the results with 2366 experimental data points over a broad range of pressures and temperatures. The overall average absolute deviation (AAD) of the calculated densities from literature data was found to be 0.77%. Generally, this work shows that the PHS EOS based on the surface tension property of ILs outperforms the PHS EOS based on critical properties. Moreover, the improved PHS EOS has been applied to predict the volumetric properties of 16 binary mixtures involving ILs. The second partners of binary mixtures studied in this work are water, ethanol, methanol, acetone, acetonitrile, propylene carbonate, and 1-propanol. Furthermore, the binary mixtures of ILs have also been studied. From 1685 data points examined for the aforementioned binary mixtures, the AAD of the calculated densities and the excess volumes from those reported in the literature were found to be 0.38 and 0.56%, respectively. Finally, the nonadditivity behavior of the studied mixtures is also investigated. The sign of the nonadditivity parameter indicates a tendency toward attraction between the unlike molecules in the mixture. However, the value of this parameter is not large, which implies that the hard-sphere model is able to model the excess properties of the present mixtures.

1. INTRODUCTION Generally, ionic liquids (ILs) came into focus recently as new materials offering several highly promising applications. The unique properties of these liquids, such as nonflammability, electrical conductivity, thermal stability, low vapor pressure, and high heat capacity, lead to this fact: they are more considered than conventional organic solvents. Their potential applications can be briefly cited: (1) they are favorite electrolytes in lithium rechargeable batteries1 and supercapacitors;2 (2) these materials can also be used as thermal fluids for heat storage by combining their high heat capacity, thermal stability, and negligible vapor pressure;3 (3) their interesting solvent properties make them well-known as green solvents for the future.4 Therefore, accurate knowledge of the thermophysical properties of ILs is valuable as it is required to decide whether the use of ILs could be extended from the laboratory level to large-scale industrial applications. To improve the above-mentioned processes based on ILs, the thermophysical properties of these liquids must be exactly characterized. In other words, the design of industrial processes and new products based on ILs can only be achieved when their thermophysical properties are exactly known. Under this circumstance, the development of equation of state (EOS) and correlation methods for modeling their thermophysical properties such as density and viscosity can be considerably useful. The present work is the extension of our previous works on modeling the volumetric properties of ILs and their mixtures using perturbed hard-sphere equation of state (PHS EOS).57 Hosseini et al.57 developed a PHS EOS for predicting the r 2011 American Chemical Society

pressurevolumetemperature (PVT) properties of several classes of pure ionic liquids and their mixtures. The major aim of this work is to reconstruct the previous equation of state by applying the surface tension property of ILs rather than their critical points developed in our previous works.57 The reason for this selection is that the surface properties of ILs can be measured easily and accurately. It should be mentioned that the critical properties cannot be obtained experimentally for ILs. There are only several methods to estimate this property for ILs in the literature.8,9 Furthermore, recently, Hosseini and Sharafi10 have shown that selection of surface tension as a scaling property helped to improve the predictive power of thermophysical property models. For the evaluation of the present EOS, we compare the results with literature data as well as those obtained from the group contribution method reported by Gardas and Coutinho.11 Extension of the present EOS to binary mixtures including IL + water, IL + ethanol, IL + methanol, IL + acetone, IL + acetonitrile, IL + propylene carbonate, IL + 1-propanol and IL + IL will also be discussed. The ILs studied in this work are listed in Table 1. Basically, the density and the excess volumetric properties of fluid mixtures, which depend on the composition and/or temperature and are of great importance in understanding the nature of molecular aggregation that exists in binary mixtures, have been Received: June 11, 2011 Accepted: December 12, 2011 Revised: November 15, 2011 Published: December 12, 2011 758

dx.doi.org/10.1021/ie2012455 | Ind. Eng. Chem. Res. 2012, 51, 758–766

Industrial & Engineering Chemistry Research

ARTICLE

Table 1. Input Constants Used in Equations 3 and 4 Mwa

γ*

F*a

(g/mol)

(mN/m)a

(mol/m3)

[C2mim][NTf2]

391.3

35.71

3881.16

[C4mim][NTf2]

419.2

32.80

3427.00

[C2mim][EtSO4]

236.3

45.43

5252.22

[C2mim][Triflate]

260.2

44.40

5302.84

[C8mim][BF4]

226.2

32.70

1114.40

ionic liquid

a

[(C6H13)3P(C14H29)][Cl]

519.3

33.40

1716.92

[(C6H13)3P(C14H29)][NTf2] [(C6H13)3P(C14H29)][N(CN2)]

764.0 549.9

33.00 35.00

1396.07 1635.80

[C6mim][NTf2]

447.3

32.31

3079.14

[C8mim][NTf2]

475.5

30.63

2778.12

[C4mim][Triflate]

288.2

35.52

1306.10

[C4mim][BF4]

226.0

44.81

1206.90

[C2mim][OcSO4]

320.5

31.00

1097.48

[C7mim][NTf2]

461.0

32.00

1352.80

[C10mim][NTf2] [C4mim][MeSO4]

503.5 250.3

32.12 43.30

1282.40 1212.22

[C4mim][PF6]

284.2

44.10

4819.85

[C6mim][PF6]

312.2

39.02

4154.39

[C8mim][PF6]

340.3

35.16

3646.19

[C2mim][MeSO3]

206.3

50.72

1244.96

[N1114][NTf2]

396.4

32.46

3516.60

[C6mim][BF4]

312.2

37.33

3668.8

[C2mim][BF4] [C2mim][PF3(C2F5)3]

198.0 556.2

44.30 34.80

6752.20 3073.20

Figure 1. Plot for the calculated (P/FRT) using eq 1 versus temperature for [C4mim][NTf2] at 1 MPa ([), 5 MPa (]), 10 MPa (9), 20 MPa (2), 30 MPa (b), and 40 MPa (4).

be expressed in terms of the following universal functions: aðTÞ ¼

2π kT Fa ðTrÞ 3F

ð3Þ

bðTÞ ¼

2π Fb ðTrÞ 3F

ð4Þ

Here F* represents the liquid density at room temperature and T* is the room temperature (298.15 K). We have presented an empirical formula for universal functions Fa(Tr) and Fb(Tr) in terms of reduced temperature, which can be written as

These values have been taken from the literature.1425

determined. In this respect, another aim of the present work is the extension of the improved EOS to mixtures involving ILs.

Fa ðTr Þ ¼ a1 þ a2 Tr þ a3 Tr2

ð5Þ

Fb ðTr Þ ¼ b1 þ b2 Tr þ b3 Tr2

ð6Þ

where

2. THEORY

a1 ¼ 62:6800

2.1. Equation of State for Pure ILs. The general frame of the EOS proposed by Hosseini et al.5,6 for pure ILs has the form

a2 ¼ 112:8300

P 1 þ η þ η2 η3 aðTÞF ¼ FkT kT ð1 ηÞ3

a3 ¼ 106:3020

ð1Þ

b2 ¼ 0:2852 b3 ¼ 0:8639

It should be mentioned that the coefficients a1b3 have been determined by the use of experimental PVT data. The reduced temperature Tr is

where P is the pressure, F is the number (molar) density, kT is the thermal energy per molecule, and η is the packing fraction defined as bðTÞF η¼ 4

b1 ¼ 1:4974

Tr ¼ ðT 3=2 =T 1=2 Tref Þ3=4

ð2Þ

ð7Þ

Tref is the reference temperature, which is expressed by the equation Tref ¼ γF2=3 N 1=3 =R

Equation 1 has two parts: (1) the CarnahanStarling expression12 taken as reference hard-sphere model and (2) a van der Waals (vdW) attraction term. To utilize the proposed EOS for ILs, two temperaturedependent terms, a(T) and b(T), must be evaluated. The above-mentioned parameters are related to the volume of hard spheres and the attraction between spheres, respectively. For this purpose, a simple procedure based on the corresponding states correlation has been previously developed using critical properties of ILs.57 In this work, the parameters a(T) and b(T) are calculated using a new correlation based on the surface tension and liquid density of ILs at room temperature as two scaling constants: The temperature-dependent parameters of eq 1 can

ð8Þ

where γ* is the surface tension, F* is the liquid density at the room temperature, N is Avogadro’s number, and R is the universal gas constant. Equations 18 represent that by knowing just two reliable scaling constants (γ* and F*), one can reconstruct a new version of the PHS EOS. 2.2. Extension of Improved Equation of State to Mixtures. The mixture version of eq 1 has the structure P 1 þ η þ η2 η3 F ¼ 3 FkT kT ð1 ηÞ 759

m

m

∑i ∑j xi xjaðTÞij

ð9Þ

dx.doi.org/10.1021/ie2012455 |Ind. Eng. Chem. Res. 2012, 51, 758–766


ARTICLE

Table 2. Predicted Results for the Density of ILs Studied in This Work ionic liquid

ΔP (MPa)

ΔT (K)

AADb (%)

ref

[C2mim][NTf2]

0.130

293393

096

0.51

28

[C4mim][NTf2]

0.160

298328

168

0.96

29

140

322415

030

0.62

28

[C2mim][EtSO4]

0.135

293393

080

0.31

30

[C2mim][Triflate]

0.135

293393

091

0.60

30

[(C6H13)3P(C14H29)][Cl]

0.265

298333

134

0.71

31

0.135

273318

072

0.46

33

[(C6H13)3P(C14H29)][NTf2] [(C6H13)3P(C14H29)][N(CN2)]

0.265 0.135

298333 273318

126 100

0.75 0.45

31 33

[C6mim][NTf2]

0.165

293338

155

0.80

32

[C8mim][NTf2]

0.130

293393

096

0.97

27

[C4mim][Triflate]

0.110

293393

076

0.27

26

[C8mim][BF4]

0.110

293393

077

0.35

26

[C4mim][BF4] [C7mim][NTf2] [C10mim][NTf2]

0.1150

293452

127

1.35

37

10

293393

011

0.56

26

0.130 0.135

293333 298353

096 060

0.98 0.71

27 35 25

[C2mim][OcSO4]

0.1

293363

018

0.32

[C4mim][MeSO4]

0.1

278363

039

0.60

25, 36, 37

[C4mim][PF6]

10100

312.8472

100

1.05

38

[C6mim][PF6]

0.110

293393

077

0.89

26

[C8mim][PF6]

0.110

293393

077

0.85

26

10100

312.8472

081

1.24

38

[C2mim][PF3(C2F5)3] [N1114][NTf2]

0.1 140

283338 293415

012 036

0.68 0.50

23 39

[C2mim][BF4]

10200

313472

140

1.20

17

[C6mim][BF4]

10120

313472

093

1.31

17

[C2mim][MeSO3]

0.1

273363

018

0.60

24

2366

0.77

overall a

NPa

NP represents the number of data points examined. b AAD = 100/NP∑NP i = 1|Fi,calcd Fi,exptl|/Fi, exptl.

where x i and x j are the mole fractions of the ith and jth components, respectively. η is the packing fraction of mixtures of hard sphere.13 This parameter is defined by the following expression: η¼

F 4

m

∑i xi bðTÞi

ð10Þ

In the case of binary mixtures, the hard-sphere covolumes, b(T)ij, are additive according to following expression: 3 þ bðTÞ1=3 bðTÞij ¼ 1=8½bðTÞ1=3 i j

ð11Þ

The attractive forces between two hard-sphere species of mixture including i and j components can be written as follows: aðTÞij ¼

2π kT ðFa Þij 3ðFÞij

Figure 2. Maximum deviation percent of estimated densities of ILs including [C2mim][NTf2] (a), [C4mim][NTf2] (b), [C2mim][EtSO4] (c), [C2mim][Triflate] (d), [(C6H13)3P(C14H29)][Cl] (e), [C2mim][MeSO3] (f), [C4mim][PF6] (g), [C6mim][PF6] (h), [C8mim][PF6] (i), [(C6H13)3P(C14H29)][N(CN2)] (j), [(C6H13)3P(C14H29)][NTf2] (k), [C6mim][NTf2] (l), [C4mim][Triflate] (m), [C4mim][BF4] (n), [C7mim][NTf2] (o), [C10mim][NTf2] (p), [C2mim][OcSO4] (q), and [C4mim] [MeSO4] (r).

ð12Þ

In this study, we have applied the following combining rules to Tref and F* and the universal function Fa: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð13Þ ðTref Þij ¼ Tref ;i Tref ;j 1 ðFij Þ1=3 ¼ ½ðFi Þ1=3 þ ðFi Þ1=3 2

ð14Þ

ðFa Þij ¼ 760

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðFa Þii ðFa Þjj

ð15Þ



ARTICLE

Table 3. AAD of the Estimated Densities by Use of the Proposed Model, Our Previous Works,5,6 and the Method of Gardas and Coutinho,11 Compared with the Experiment AADa (%) ionic liquid

ΔT (K)

previous works5,6

this work

Gardas and Coutinho11

ref

[C2mim][NTf2]

293353

013

2.85

0.45

0.38

40

[C4mim][NTf2]

298328

168

1.15

0.96

0.22

29

[(C6H13)3P(C14H29)][Cl] [(C6H13)3P(C14H29)][NTf2]

298333 298333

134 126

1.00 1.37

0.71 0.75

2.43 0.24

31 31

[C6mim][NTf2]

293338

155

1.34

0.80

0.34

32

[C8mim][BF4]

293393

007

3.82

0.82

2.02

40

273363

013

1.60

0.37

0.44

41

298343

096

2.26

0.56

0.20

27

298.2323.2

006

1.54

0.88

1.69

40

273363

013

2.80

0.54

0.11

41

730

1.44

0.75

0.67

[C8mim][NTf2] [C8mim][PF6] overall a

NPb

b AAD = 100/NP∑NP i = 1|Fi,calcd Fi,exptl|/Fi, exptl. NP represents the number of data points examined.

Table 4. AAD of the Predicted Densities of Binary Mixtures Using Equation 9 from the Experiment ΔT(K)

NPa

AADb (%)

MDc (%)

ref

[C2mim][EtSO4] + acetone

278308

139

0.41

1.38

42

[C2mim][EtSO4] + acetonitrile

278308

167

0.44

1.63

42

[C2mim][EtSO4] + dichloromethane [C2mim][EtSO4] + ethanol

278308 278308

131 125

0.32 0.28

1.82 1.18

42 42

[C2mim][EtSO4] + methanol

278308

146

0.31

1.26

42

[C2mim][EtSO4] + propylene carbonate

278308

132

0.17

0.92

42

[C2mim][EtSO4] + water

278308

111

0.31

1.29

42

[C8mim][BF4] + ethanol

283343

077

0.33

0.96

43

mixture

[C4mim][BF4] + water

303353

083

0.38

1.34

44


293323

057

0.32

1.02

45

[C2mim][Triflate] + methanol [C2mim][Triflate ] + 1-propanol

278318 278338

090 090

0.51 0.25

1.24 0.92

46 46

[C2mim][Triflate ] + water

278338

132

0.21

0.59

46

[C2mim][Triflate ] + ethanol

278338

077

0.24

0.90

46

[C4mim][PF6] + [C4mim][BF4]

298308

125

0.67

1.26

47

[C4mim][BF4] + [C4mim][MeSO4]

298308

143

0.48

1.26

47

1685

0.38

overall

a NP represents the number of data points examined. b AAD = 100/NP∑NP i = 1|Fi,calcd Fi,exptl|/Fi, calculated Fmix.

The excess molar volume, VE, of binary mixtures was calculated from the following equation, the single-component and mixture version of eq 1: VE ¼

x 1 M1 þ x 2 M2 x 1 M 1 x 2 M2 Fmix F1 F2

exptl.

c

MD represents the maximum deviation of

constants: the surface tension and the liquid density of ILs at room temperature. The numerical values of surface tension together with the values of molecular weight of ionic liquids considered in this study are given in Table 1. These values have been taken from the literature.1425 To show the distinctive features of the present work, a typical plot for the calculated values of P/FRT using eq 1 versus temperature for [C4mim][NTf2] is exemplified in Figure 1. As seen in Figure 1, the data at constant T will be nearly proportional to P. Because the variable on the vertical axis is P/FRT, this proportionality would imply F to be independent of P, which means incompressibility of ionic liquids. Therefore, eq 1 could successfully describe a liquid that apparently is not far from incompressibility. The only way we can see is that, according to the fitted parameters a(T) and b(T), the packing fraction, η, comes out to be slightly close to unity.

ð16Þ

Fmix is the density of mixture involving IL, x1 and x2 are mole fractions, and M1 and M2 are molar masses associated with two components, 1 and 2, respectively.

3. RESULTS AND DISCUSSION As we mentioned earlier, in the present study the PHS EOS was modified using the surface tension property of ILs. In this study, an alternative procedure was employed to fit the temperaturedependent parameters of the PHS EOS based on two reliable scaling 761



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Table 5. AAD of the Calculated Excess Molar Volumes of Several Binary Mixtures Involving ILs Using Modified PHS EOS from the Experiment AADb

MDc

(%)

(%)

ref

ΔT(K)

NP


283343

077

0.51

1.14

43


303343

071

0.14

0.76

44

[C2mim][Triflate] + methanol

278318

064

0.46

1.02

46

[C2mim][Triflate ] + 1-propanol [C2mim][Triflate ] + water

278338 278338

090 132

0.51 0.55

1.89 1.78

46 46

[C2mim][Triflate ] + ethanol

278338

077

0.42

1.49

46


303343

062

0.32

0.83

48

438

0.56

mixture

overall

a

a

NP represents the number of data points examined. b AAD = 100/ E E E c NP∑NP i = 1|V i,calcd V i,exptl|/V i, exptl. MD represents the maximum deviation of calculated VE.

Figure 3. Deviation plot for the calculated liquid density of [C4mim][PF6] (1) + [C4mim][BF4] (2) mixture at 298.15 K ([), 303.15 K (0), 305.15 K (2), and 308.15 K, compared with experiment.47

Table 6. AAD of the Calculated Density of Binary Mixtures Obtained by Equation 9 and Those Obtained in the Previous Work,7 from the Literature Values mixture

a

NPa

this work

Hosseini et al.7

ref

[C2mim][EtSO4] + water

030

0.47

1.48

49


080

0.38

0.65

44

[C2mim][Triflate] + methanol

090

0.51

0.30

46

[C2mim][Triflate ] + 1-propanol

085

0.25

0.15

46


132

0.21

0.40

46

[C2mim][Triflate ] + ethanol overall

075 492

0.22 0.31

0.21 0.41

46

NP represents the number of data points examined.

At first, we examined the predictive power of improved EOS for the prediction of the liquid density of pure ILs. For this purpose, 24 ILs with various anions have been chosen. Our calculation results have been summarized as average absolute deviation percent (AAD%) from the literature data2339 in Table 2. As Table 2 shows from 2366 data points examined for the studied ILs over a broad pressures ranging from 0.1 to 200 MPa and temperatures ranging from 273 to 472.15 K, AAD was found to be 0.77%. It should be mentioned that the uncertainty of our calculations was of the order of (2.9%. Also, to show the accuracy of the present work, the maximum deviations (in %) of the predicted densities using eq 1 from the measured values for all ILs studied in this work have been demonstrated in Figure 2. To assess further the reliability of the improved PHS EOS, we have compared the present EOS with the model developed by Gardas and Coutinho11 as well as our previous model.5,6 The outcomes of the calculations are given in Table 3. From 730 data points taken from the literature,27,29,31,32,40,41 the AAD of the predicted densities using the present model and those obtained from the work of Gardas and Coutinho11 were found to be 0.75 and 0.67%, respectively. As is clear from Table 3, the predicted densities obtained from our improved PHS EOS have almost the same accuracy as those obtained from ref 11. The interesting point of the present study is that the average AAD of the present model by the usage of surface tension is 0.75%, which is lower than those obtained from our previous model (i.e., 1.44%), which uses the critical properties.

Figure 4. Deviation plot for the calculated excess molar volumes of mixture [C2mim][Triflate] (2) + water (1) at 278.15 K ([), 398.15 K (0), 318.15 K (4), and 338.15 K (]), compared with experiment.46

As already mentioned, we have extended our calculations to mixtures of ionic liquids with several solvents using eq 9. Tables 4 and 5 contain, respectively, the AAD of the calculated densities and the excess molar volumes of studied binary mixtures at various mole fractions and temperatures from the measurements.4248 Besides, the maximum deviations (MD) of the calculations have also been included in Tables 4 and 5. In the case of binary mixtures, from 1685 and 438 experimental data points for density and excess molar volumes, examined in this study, the overall AAD’s were found to be 0.38 and 0.56%, respectively. It should be mentioned that the maximum deviation of the calculated volumetric properties of all binary mixtures studied in this work was found to be 1.89%. Table 6 compares the accuracies of the results obtained from the present model and those reported in our previous work.7 Interestingly, the results are in favor of superiority of the present model over our last model.7 The experimental volumetric data were taken from refs 44, 46, and 49. In general, a wide space of experimental data points regarding the binary mixtures has been taken to check the predictive power of the improved EOS. To show how the mixture version of 762



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Figure 5. Excess molar volume of mixture [C4mim][BF4] + H2O as a function of volume fraction of ionic liquid (ϕ) at temperatures 303.15 K ([) and 343 K (2). The solid line represents the calculated VE with nonadditivity effects, and the dashed line represents the calculated VE without nonadditivity effects, compared with the experiment44 (markers).

Figure 7. Excess molar volume of mixture [C8mim][BF4] + ethanol as a function of volume fraction (ϕ) of ionic liquid at temperatures 298.15 K (2) and 333 K ([). The solid line represents the calculated VE with nonadditivity effects, and the dashed line represents the calculated VE without nonadditivity effects, compared with the experiment43 (markers).

fraction of ILs, respectively. The numerical values of the nonadditivity parameter for the above-mentioned mixtures are 0.053, 0.042, and 0.049. A nonzero nonadditivity parameter implies some interaction between the unlike components. The low values of this parameter are in favor of this fact that the volumes are nearly additive. As Figures 57 illustrate, the nonadditivity parameter improves slightly the results of excess molar volumes of mixtures involving ILs. It is apparent the hard-sphere model can be successfully applied to the present mixtures. In Figure 5, the positive deviation of the excess molar volumes for [C4mim][BF4] + water over the whole range of compositions and temperatures indicates a repulsive intermolecular potential energy between unlike particles in the mixture. This can be attributed to the high relative permittivity of water, which weakens or breaks the strong electrostatic attractions between the ions, which results in expanding the volume of the binary mixture from the pure IL. It should be added that the increase of the VE with temperature indicates that the mixture is more expansible than the pure compounds. Thus, the temperature increase gives rise to loosening aggregation in pure ILs. On the other hand, the negative deviations in Figures 6 and 7 have been generally related to more efficient packing and attractive interactions in the mixtures than in the pure liquids. Actually, the interaction between polar solvent molecules (e.g., ethanol and methanol studied in this work) and ILs can give rise to local packing effects. The weight of such effects depends on the probability that a solvent molecule interacts with IL.

Figure 6. Excess molar volume of mixture [C2mim][Triflate] + methanol as a function of volume fraction (ϕ) of ionic liquid at temperatures 288 K (4), 308.15 K (/), and 318.15K (b). The solid line represents the calculated VE with nonadditivity effects, and the dashed line represents the calculated VE without nonadditivity effects, compared with the experiment46 (markers).

improved eq 1 passes through the experimental points, two deviation plots for the calculated density and excess molar volume of binary mixtures including [C4mim][PF6] + [C4mim][BF4] and [C2mim][Triflate] + water have been shown in Figures 3 and 4. The experimental values were taken from refs 46 and 47. It should be mentioned that the scaling parameters F* and γ* of the solvents have been taken from the literature.5052 As we know, the excess thermodynamic properties of different liquid mixtures can be a reliable source to gain information about the nature of intermolecular potential interactions. In this respect, the nonadditivity effect on our proposed model has been investigated. We followed the procedure proposed in refs 5355 and took into account the nonadditivity effect in our numerical calculation of excess molar volumes of mixtures involving ILs. Typically, Figures 57 show the excess molar volumes with and without considering the nonadditivity effect for three mixtures, [C4mim][BF4] + water, [C2mim][Triflate] + methanol, and [C8mim][BF4] + ethanol, in terms of volume

4. CONCLUSION In the present work, we have developed a new version of the PHS EOS. This work showed that using the surface tension property of liquids provides a good opportunity to scale the temperature-dependent parameters of the PHS EOS for ILs. This procedure is a good alternative for developing models for especially ILs because the surface tension property of ILs can be determined experimentally. In general, the results summarized in Tables 3 and 6 reveal that the modified model is capable of providing 763


Industrial & Engineering Chemistry Research more accurate volumetric properties of ILs and their mixtures with solvents than our previous model. The predicted densities and excess molar volumes for mixtures involving ILs were in good agreement with experimental data showing that the improved PHS EOS could provide a good estimate for densities of mixtures as well as pure ILs. Considering the nonadditivity effect in our calculations showed that this effect can improve slightly the results of excess properties such as excess molar volumes.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Fax: +98-711726-1288.

’ ACKNOWLEDGMENT We are grateful to the Research Committee of Shiraz University and Shiraz University of Technology for supporting this project. ’ ABBREVIATIONS [C2mim][NTf2] = 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [C4mim][NTf2] = 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [C2mim][EtSO4] = 1-ethyl-3-methylimidazolium ethyl sulfate [C2mim][Triflate] = 1-ethyl-3-methylimidazolium trifluoromethanesulfonate [C8mim][BF4] = 1-octyl-3-methylimidazolium tetrafluoroborate [(C6H13)3P(C14H29)][Cl] = trihexyltetradecylphosphonium chloride [(C6H13)3P(C14H29)][NTf2] = trihexyltetradecylphosphoniumbis[(trifluoromethyl)sulfonyl] imide [(C6H13)3P(C14H29)][N(CN2)] = trihexyltetradecylphosphonium dicyanamide [C6mim][NTf2] = 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [C8mim][NTf2] = 1-octyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [C4mim][Triflate] = 1-butyl-3-methylimidazolium trifluoromethanesulfonate [C4mim][BF4] = 1-butyl-3-methylimidazolium tetrafluoroborate [C2mim][OcSO4] = 1-ethyl-3-methylimidazolium octylsulfate [C7mim][NTf2] = 1-hepyl-3-methylimidazolium bis (trifluoromethylsulfonyl)imide [C10mim][NTf2] = 1-decyl-3 methylimidazolium bis[(trifluoromethyl)sulfonyl]imide [C4mim][MeSO4] = 1-butyl-3-methylimidazolium methylsulfate [C4mim][PF6] = 1-butyl-3-methylimidazolium hexafluorophosphate [C6mim][PF6] = 1-hexyl-3-methylimidazolium hexafluorophosphate [C8mim][PF6] = 1-octyl-3-methylimidazolium hexafluorophosphate [N1114][NTf2] = 1-butyltrimethylammonium bis(trifluoromethylsulfonyl)imide [C2mim][BF4] = 1-ethyl-3-methylimidazolium tetrafluoroborate [C6mim][BF4] = 1-hexyl-3-methylimidazolium tetrafluoroborate [C2mim][MeSO3] = 1-ethyl-3-methylimidazolium methansulfonate

ARTICLE

[C2mim][PF3(C2F5)3] = 1-ethyl-3-methylimizazolium tris(pentafluoroethyl) trifluorophosphate

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