Thermophysical properties of alkyl-imidazolium based ionic liquids through the heterosegmented SAFT-BACK equation of state

Journal of Molecular Liquids 191 (2014) 59–67

Contents lists available at ScienceDirect

Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

Thermophysical properties of alkyl-imidazolium based ionic liquids through the heterosegmented SAFT-BACK equation of state Ali Maghari ⁎, Fatemeh ZiaMajidi, Elham Pashaei Department of Physical Chemistry, School of Chemistry, College of Science, University of Tehran, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 19 September 2013 Received in revised form 14 November 2013 Accepted 15 November 2013 Available online 6 December 2013 Keywords: Ionic liquid Heterosegmented SAFT-BACK Equation of state Second derivatives

a b s t r a c t Heterosegmented molecular model combined with SAFT-BACK EOS was developed to predict the pVT and second derivative properties including speed-of-sound, isothermal compressibility and isobaric thermal expansivity of some alkyl-imidazolium ionic liquids (ILs) with [PF6]−, [BF4]− and [NTf2] anions. In this work, an IL was considered as two components, a cation and an anion. The cation of IL is treated as chain-like entity and was divided into several kinds of segments including cation head (imidazolium ring) and several segments of \CH2 (including \CH3) in the alkyl tails of the IL molecule, while the anion is not divided into segments and treated as a whole. The segment shape is described by a non-spherical parameter with using a hard convex body term as the reference. To account for the association scheme, the cation head and the anion of ILs each was considered one association site, which can only cross-associate. Moreover, we have considered a dipolar interaction between anion and cation head where the effective dipole moment is approximated as a linear function of density. The heterosegmented SAFT-BACK model was found to be able to correctly describe the second-order thermodynamic derivative properties as well as pVT properties of ILs studied in this work. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Ionic liquids (ILs) are organic molten salts with extremely low volatility, nonflammable, non-explosive and relative thermal stability which makes them good candidates for alternative solvents. ILs are generally constituted by an asymmetric organic cation and a weakly coordinating organic or inorganic anion that cannot form an ordered crystal and thus remain liquid at room temperature. The organic cation consists of a cation head and several alkyl groups, whereas the anion with smaller size and more symmetrical shape can be inorganic anion, i.e. tetrafluoroborate [BF4]−, hexafluorophosphate [PF6]− or organic anion, such as nitrate [NO3]− and bis (trifluoromethylsulfonyl) imide [NTf2]−. Asymmetry of the cation is responsible for the low melting points of ILs, while the nature of the anion is usually assumed to be responsible

Abbreviations: BACK, Boublik–Alder–Chen–Kreglewski; Hcb, hard convex body; SAFT, Statistical Associating Fluid Theory; [C2mim][BF4], 1-ethyl-3-methylimidazolium tetrafluoroborate; [C4mim][BF4], 1-butyl-3-methylimidazolium tetrafluoroborate; [C6mim][BF4], 1hexyl-3-methylimidazolium tetrafluoroborate; [C8mim][BF4], 1-octyl-3-methylimidazolium tetrafluoroborate; [C2mim][PF6], 1-ethyl-3-methylimidazolium hexafluorophosphate; [C4mim][PF6], 1-butyl-3-methylimidazolium hexafluorophosphate; [C6mim][PF6], 1-hexyl3-methylimidazolium hexafluorophosphate; [C8mim][PF6], 1-octyl-3-methylimidazolium hexafluorophosphate; [C3mim][NTf2], 1-propyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide; [C4mim][NTf2], 1-butyl-3-methylimidazolium bis[(trifluoromethyl) sulfonyl]imide; [C5mim][NTf2], 1-pentyl-3-methylimidazolium bis[(trifluoromethyl) sulfonyl]imide; [C6mim][NTf2], 1-hexyl-3-methylimidazolium bis[(trifluoromethyl) sulfonyl]imide. ⁎ Corresponding author. Tel.: +98 21 6111 3307; fax: +98 21 6640 5141. E-mail address: [email protected] (A. Maghari). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.11.017

for many of the physical properties of ILs [1]. For example IL with [C4mim] cation and PF6 anion is immiscible with water, whereas IL with same cation and BF4 anion is water soluble. The alkyl-chain length of the cations has been known to significantly influence the physical and chemical properties of ILs, especially liquid crystal formation [2]. The flexibility of molecular tuning by ability to vary different cations and anions allows for synthesis of numerous ILs for many specific applications. Properties such as density, heat capacities, surface tension and viscosity are affected. Motivated by these interesting properties, some experimental and theoretical studies on ILs have been investigated by several groups in the last two decades and have still been the subject of many academic and industrial researches, since the study of the molecular ILs is still in its early stages. In recent years, many theoretical approaches have been proposed for the representation of the thermodynamic characteristics and phase behavior of systems containing ILs. The group contribution methods [3–8], activity coefficient models [9–11] and cubic equations of state [12–17] have been applied to calculate the thermodynamic properties of ILs. Moreover, the statistical associating fluid theory (SAFT) provides an excellent model for the estimation and prediction of the thermophysical properties and phase behavior of ILs and their mixtures. SAFT is based on the first-order perturbation theory of Wertheim [18–21], and is first proposed by Chapman et al. [22] and have been converted into a very useful engineering equation [23,24]. An important feature of the SAFT theory is that it explicitly takes into account nonsphericity and association interactions and has since been used to predict the phase equilibria behavior of a wide variety of pure components and their mixtures. It is considered one of the most powerful predictive tools for the study

60

A. Maghari et al. / Journal of Molecular Liquids 191 (2014) 59–67

of fluid phase equilibria. In SAFT a molecule is composed of m segments correspond to atoms, functional groups, or complete molecules. Each segment has the same volume and interaction energy parameters. Molecules are represented as covalently bonded chains of segments that may contain sites capable of forming associative complexes. Several versions of SAFT have been developed by different methods to calculate the free energy of monomers (segments). Although SAFT approach has been widely used to predict the thermophysical properties of real fluids, there has been relatively small work about the ability of SAFT in predicting thermodynamic properties of ionic fluids, such as ILs. Blas and Vega [25] have predicted the thermophysical properties of ILs using the soft-SAFT equation of state (EOS). Moreover, the soft-SAFT EOS has been used to study the solubility of carbon dioxide, hydrogen, carbon monoxide and xenon in the alkylimidazolium [Cnmim]+ with some fluorinated anions [BF4]−, [PF6]− and [NTf2]−, achieving quantitative agreement with experimental data [26,27]. Rahmati and coworkers have used the SAFT-VR and PC-SAFT to predict the solubility of hydrogen sulfide in six imidazolium-based ILs [28]. Domańska et al. [29–33] have recently used the PC-SAFT EOS to reproduce diverse thermophysical data, such as phase diagrams and excess enthalpies for pure ILs as well as their mixtures with organic or inorganic solvents. Polishuk [34] has also provided an estimate of the second derivatives of ILs using the PC-SAFT, generalized (G) SAFT-plus-Cubic and Cubic-PlusAssociating (CPA) models. It showed that the PC-SAFT substantially overestimates heat capacities and underestimates the temperature and pressure dependencies of sound velocities and compressibilities, whereas the GSAFT + Cubic model can predict these more reliably. The ability of the PC-SAFT equation to represent the solubility of carbon dioxide in ionic liquids has been investigated by Chen et al. [35]. Ji et al. [36] have applied the ePC-SAFT with six strategies to model the density of imidazolium-based ILs and the solubility of CO2 and CH4 in these ILs. It was shown that all strategies can be used to accurately represent the density of pure ILs, but only the ion-based model accounting for Coulomb interactions provides reliable prediction results with respect to the CO2 solubility in ILs. Llovell et al. [37] have recently studied the solubility of three common pollutants, SO2, NH3 and H2S, in three types of ILs using the soft-SAFT EOS. Ji and Adidharma have developed a new version of SAFT, called heterosegmented SAFT model to predict the densities of pure ILs [38] and molar volumes of CO2/IL mixtures [39,40]. They have divided the IL in four different parts, including the anion, the cation head, the methyl group and the alkyl chain as independent components with their molecular parameters. In our recent work [41], we have extended the SAFT-BACK model to predict the pressure–volume–temperature (pVT) and second-order thermodynamic properties of pure alkyl-imidazolium ionic liquids (ILs) with [PF6]− and [BF4]− anions. In our previous work, we assumed that the IL is modeled as a chain-like dipolar ion-pairs composed of nonspherical molecules, which interact with other dipolar ion-pairs. We achieved very good results for densities and speed of sound of ILs over a wide range of temperature and pressure, whereas the extended SAFT-BACK EOS overestimates the isobaric thermal expansion coefficients of [Cnmim][BF4] with respect to experimental data. In the present work, a heterosegmented SAFT-BACK model (hetero-SAFT-BACK for short) is developed to describe the first and second derivative properties of ILs. In this study, twelve kinds of ILs including [Cnmim][PF6], [Cnmim][BF4] with n = 2, 4, 6, 8 and [Cnmim][NTf2] with n = 3, 4, 5 and 6 in a wide range of temperatures and pressures have been extensively evaluated. 2. Theory and thermodynamic modeling Based on statistical mechanical description for systems composed of non-spherical molecules, an EOS for hard convex body (hcb) fluids was proposed by Boublik [42] from the scaled particle theory. Chen and Kreglewski [43] used this equation combined with the equation of Alder et al. [44] to establish an EOS called Boublik–Alder–Chen–

Kreglewski (BACK). Chen and co-workers combined BACK with SAFT and proposed two modifications for a better description of the properties of chain fluids [45] as well as polar [46] and association [47] fluids in the whole region: (i) the chain formation term is modified for a more accurate description of the long chain fluids; (ii) the effect of chain formation on the dispersion term is included. This new version of SAFT, the so-called modified SAFT-BACK EOS has been recently developed by Maghari et al. [48–51] to determine the thermodynamic derivative properties of some pure fluids and their mixtures in the wide density and temperature ranges including critical temperature. The SAFT type equations of state are usually written in terms of the residual Helmholtz energy as A

res

id

≡ A−A ¼ A

ref

dis

þA

þA

chain

þA

polar

þA

assoc

ð1Þ

where the superscripts “id”, “ref”, “dis”, “chain”, “polar” and “assoc” stand for ideal, reference, dispersion, chain, polar, and association terms, respectively. In this work, we assume that a pure IL is composed of two components, which are designated by i, where i = 1, 2 represent the anion and cation, respectively. Each component may be divided into several segments, which are designated by a (a = 1, 2, ⋯ s). Since the anion (as component 1) is not divided into segments, we have s1 = 1, and there is no chain term for anion component. The cation of IL (component 2) is divided into s2 segments including cation head (imidazolium ring) and several segments of \ CH2 (including \CH3) in the alkyl tails of the IL molecule. Clearly, these alkyl segments are not chained as a straight line, but are zigzag or crooked ones, so that we consider a shape parameter for the alkyl segments. The number of segment a of si ma;i is the component i (= 1, 2) is designated by ma,i and mi ¼ ∑a¼1 total number of segments in component i. For example, the IL [C4mim] [PF6] is composed two components: (i) component 1 is the anion [PF6]; (ii) component 2 is cation [C4mim]. The anion is treated as one segment and the cation [C4mim] is composed of 5 segments of –CH2 (including \CH3) and one segment of imidazolium ring (cation head). In our model, the cation head and the anion have one association site, which can only cross-associate. The detailed expressions required for the individual terms in Eq. (1) are briefly described below. 2.1. Reference term The reference term in the hetero-SAFT-BACK version has been chosen as hard convex body (hcb) proposed by Boublik [42] given by " # hcb 2 2  A α α −3α
2 ln ð 1−η Þ−3α ¼m − − 1−α NkB T 1−η ð1−ηÞ2

ð2Þ

where m = m1 + m2 is the total segment number and α is a parameter which is related directly to the geometry of the hard-convex body. The average non-spherical parameter α can be obtained from the following mixing rules: α¼

1 ðα þ α 2 Þ 2 1

ð3Þ


 where α1 and α 2 ≡ α CH2 þ α cation head are the shape parameters of anion and cation, respectively. The packing factor η, appeared in Eq. (2) is defined as:

η≡

2 X π 3 xi mi di NAv ρs 6 i¼1

ð4Þ

where xi and mi are mole fraction and the total segment number of component i, respectively, NAv is the Avogadro's number, ρs ≡ cρ in which ρ

A. Maghari et al. / Journal of Molecular Liquids 191 (2014) 59–67

is the molar density, c is an adjustable parameter and di is the temperature-dependent segment diameter of component i (anion and cation) calculated through the following expression: " di ¼ σ i 1−0:12 exp −

3u0i kB T

!#

00

π 3 N σ 6 Av i

ði ¼ 1; 2Þ

00


1=2 0 0 0 u2 ¼ uCH2 ucation head

ðdÞ ¼

ð7Þ

ð8Þ

ð14Þ

as Achain;dis λAchain;hcb m2 Adis ¼ NkB T m NkB T Ahcb

2.4. Polar term We assume that the charges on the cation head and anion have distributed homogeneously, since there is a strong electrostatic interaction. The contribution due to the electrostatic interactions between polar groups can then be approximated by the multipole expansion [52,53]. In this work, only the leading term of the point dipole-point dipole interaction is included: polar

2.2. Dispersion term The dispersion contribution of Helmholtz energy Adis, appeared in Eq. (1), is expressed with the results of Alder et al. [44] for squarewell fluid as in Eq. (9): ð9Þ

in which Dij is a series of 36 universal constants fitted by Chen pffiffiffi and Kreglewski [43] from the experimental data of argon and τ ≡ 2π=6 is the close packed reduced density. In Eq. (9), the interaction energy of segment u is given by

ð15Þ

in which λ = 0.9 for the best results of our model of ILs.

A ¼ NkB T

dis X X  u i
η j A ¼m Dij NkB T kB T τ i j

1 3α ηð1 þ α Þ 2α 2 η2 þ þ 2 1−η ð1−ηÞ ð1 þ 3α Þ ð1−ηÞ3 ð1 þ 3α Þ

The chain dispersion term Achain,dis, appeared in Eq. (12) is expressed

The average segment volume and dispersion energy of component 2 (cation) are given by

v2

hcb

ð5Þ

ð6Þ

 1=3 3 1
00 1=3
00 ¼ þ vcation head vCH2 2

where the radial distribution function for hard convex body (hcb) is given by g

in which u0i is the segment dispersion energy parameter and σi is the temperature-independent segment diameter of component i, which is related to the segment volume parameter v00 i by vi ¼

61

2 X

! mi xi

i¼1

A2 =NkB T 1−ðA3 =NkB T Þ=ðA2 =NkB T Þ

ð16Þ

where A2 and A3 are the second- and third-order perturbation terms, respectively, is given by   A2 4η u 2 μ 4 ¼−
3 NkB T 3 kB T σ =σ

ð17aÞ

  A3 10η2 u 3 μ 6 ¼
3 NkB T 9 kB T σ =σ

ð17bÞ

p

p

where σp is the effective polar interaction, adjusted as 4.1 × 10−10m for ffiffiffiffiffiffiffiffi. Since the diall ILs and the reduced dipole moment μ  ¼ 170:24 pμ=m u σ3

1=2

u ¼ ðu1 u2 Þ

ð10Þ

pole moment is changed with density due to the induction, we adopted the following linear relation for the dipole moment in liquid phase as

where u1 and u2 are the interaction energy of anion and cation, respectively, which can be defined as

μ ¼ μ ∘ ð1 þ ςρÞ

  e 1=2 0 ui ¼ ui 1 þ i kB T

where μ∘ is the dipole moment for dilute gas and ς is an adjustable parameter. The theoretical basis for density-dependence of dipole moment was discussed by Kraska and Gubbins [54].

ð11Þ

ð18Þ

where ei/kB is an adjusted parameter, equals to 10 for all selected ILs.

2.5. Association term

2.3. Chain term

The Helmholtz energy contribution due to association sites on the molecule derives from the first-order Wertheim's perturbation theory, expressed as the sum of the contributions of all associating sites of component i

Based on the polymerization limit of Wertheim's theory, the chain contributions of Helmholtz energy for alkyl groups (anion and cation head have no chain contribution) are obtained as A

chain

¼A

chain;hcb

chain;dis

þA

ð12Þ

where Achain,hcb is the incremental Helmholtz energy due to chain formation of hard convex body, is the same as that in SAFT but with the mean radial distribution function ghcb for the hard convex body fluids: A

chain;hcb

NkB T

¼ ð1−m2 Þ ln g

hcb

" X Aassoc X ¼ xi NkB T a i

ð13Þ

X Ai 2

! þ

Mi 2

# ð19Þ

with Mi as the number of associating sites of component i and XAi as the mole fraction of molecules of component i non-bonded at sites A. The value of XAi comes from the solution of the mass-action equation A

ðdÞ

A

ln X i −

Xi ¼

1þρ

X

x j j

1 Xs b¼1

B

Ai B j

XjΔ

:

ð20Þ

62

A. Maghari et al. / Journal of Molecular Liquids 191 (2014) 59–67

The function ΔAi B j , which characterizes the association strength between association site A of molecule i and association site B of molecule j, can be written by

Ai B j

Δ

¼g

hcb

" ! # 
 εAi B j 6 0 Ai B j −1 dij vij κ exp kB T π

ð21Þ

in which κ Ai B j and ε Ai B j are the site-site bonding-volume of association and site-site association energy, respectively. It should be noted that the measurements by show stronger interaction between the cation head and the anion which can be attributed to the hydrogen bonding between hydrogen atoms at C+ 2 in the imidazolium ring (cation head) and anion terminated atoms (such as fluorine in PF− 6 ) [55]. In our model, the cation head and anion each have one association site, in which the association interactions were allowed between two different sites of two IL molecules, that is only cross-association to each other.

3. Model parameters As mentioned in section 2, the IL of the present model is composed of two components including anion and cation. The anion of IL is treated as one segment, whereas the cation is divided into two kinds of segments including imidazolium ring (cation head) and several segments of \CH2 (including \CH3) in the alkyl tails of the IL molecule. To obtain the thermodynamic properties of ILs with hetero-SAFT-BACK model, a set of parameters for groups representing –CH2, imidazolium ring (imi+) and anion need to be adjusted, including segment number ma, 0 segment volume v00 a , segment dispersion energy ua /kB and segment shape αa. In addition to these parameters two adjustable dipole moment parameters μ∘ and ς of IL as well as two association parameters characterize the association contribution, i.e., the well depth of the association site-site potential εab and the parameter related to the volume available for bonding κab must be adjusted. In addition the parameter c is defined as ρs ≡ cρ in which ρs is the segment density, appeared in Eq. (4). In order to decrease the number of parameters for fitting, the association parameters between all pairs of cations and anions were kept constant for the whole considered ILs, with values κab = 4.63 × 10−3 and εab/kB = 1374 K, which were transferred from those of [Cnmim] [PF6] ILs reported in our previous work [41]. It is noteworthy that the number of parameters to describe a group of ILs seems to be excessive, but most of parameters including the size, shape, volume and energy for all segments –CH2, imi+ and anion are similar to all other ILs. For example, in all 12 ILs considered in this work, formed by combining one imidazulium ring (cation head), three different anions (BF4, PF6 and NTf2) and 4 different alkyls, using hetero-SAFT-BACK model, the number of parameters needed to describe all of them is 56. These parameters were estimated by fitting to a group of available experimental pρT data from the sources listed in Table 1. The range of temperature and pressure and fitting errors of each IL density are also given in Table 1. The fit results for the segment and molecular parameters are listed in Tables 2 and 3. It is emphasized that most of ILs have very low or negligible saturation vapor pressure and there are no available experimental vapor pressure data for most ILs. Thermodynamic properties and vapor pressure of [C4mim][PF6] in the ideal gas state were reported by Paulechka et al. [56,57] from molecular and spectral data. The evaluated saturated vapor pressure of [C4mim][PF6] was 1 × 10−10 Pa at room-temperature and 2 × 10−4 and 5 × 10−1 Pa at 400 and 500 K, respectively. The uncertainties of these reported values of vapor pressures were clearly much greater than the values themselves, and the results were inconclusive. Therefore, only experimental liquid densities are used to obtain the EOS parameters.

Table 1 Comparison of ILs density with hetero-SAFT-BACK EOS against the experimental data. Ionic liquids

Temperature range (K)

Pressure range (MPa)

NP

313–472 0.1–200 189 [C2mim][BF4] 298–472 0.1–200 212 [C4mim][BF4] 313–472 0.1–200 189 [C6mim][BF4] 298–348 0.1–26 79 [C8mim][BF4] 352–472 10–200 140 [C2mim][PF6] [C4mim][PF6] 298–323 0.1–100 138 313–472 0.1–200 189 [C6mim][PF6] 312–472 0.1–200 189 [C8mim][PF6] 352–472 0.1–60 165 [C3mim][NTf2] 298–328 0.1–60 151 [C4mim][NTf2] 298–333 0.1–60 165 [C5mim][NTf2] 298–333 0.1–60 88 [C6mim][NTf2] N P ρ −ρ cal exp ARDðρÞ ≡ 100 ; NP, number of data points. NP ∑ ρ exp i¼1

ARD(ρ)

Data source

0.03 0.05 0.10 0.12 0.06 0.09 0.11 0.13 0.06 0.09 0.11 0.13

[73] [58,66,74,75] [62,63,73,74] [66,69,76] [73] [58,66,69,75] [62,66,73] [66,69,73,76] [77] [59] [77] [59,62]

4. Results and discussion The hetero-SAFT-BACK EOS with obtained molecular parameters is directly used to pρT properties of pure ILs. In this work, twelve kinds of ILs including [Cnmim][PF6] and [Cnmim][BF4] with n = 2, 4, 6, 8 and [Cnmim][NTf2] with n = 3, 4, 5, 6 were taken into account. As illustrative examples, the pρT behaviors of [C4mim][BF4], [C4mim] [PF6] and [C4mim][NTf2] ILs are shown in Figs. 1, 2 and 3, respectively. The solid lines represent the hetero-SAFT-BACK calculations, while symbols represent experimental data taken from [58–61]. Satisfactory results are obtained for densities of ILs over a wide range of temperatures and pressures. Values of mean deviations between hetero-SAFTBACK calculated and experimental densities for [Cnmim][BF4], [Cnmim][PF6] and [Cnmim][NTf2] are given in Table 1. Furthermore, the molecular parameters fitted to liquid densities of ILs are further used in a predictive manner to obtain the vapor pressure as well as thermodynamic derivative properties, such as speed of sound, thermal expansion coefficient and isothermal compressibility. According to the thermodynamic relation, in phase equilibria, the Gibbs free energy of liquid phase equals that of the vapor phase, i.e. V

L

G ¼G

ð22Þ

or alternatively V

V

L

A þ pV ¼ A þ pV

L

ð23Þ

where the superscripts V and L denote vapor and liquid phase, respectively. Therefore, one can obtain the saturated vapor pressure from the hetero-SAFT-BACK EOS. The calculated saturated vapor pressure for [C4mim][BF4], [C4mim][PF6] and [C4mim][NTf2] at 500 K is about 1.6 × 10−3 Pa, 6.5 × 10−2 Pa and 1.8 × 10−2 Pa, respectively. The experimental value of vapor pressure for [C4mim][NTf2] at 497.53 K is 1.59 × 10−1 Pa [64] and for [C4mim][PF6] at 500 K is 5 × 10−1 Pa [56]. Moreover, the calculation of speed of sound is of particular interest, as it represents a strong test for any EOS, since it involves the temperature and density partial derivatives of pressure. To achieve this the EOS must describe with great accuracy for the p (ρ,T). The speed of sound is a

Table 2 Optimized parameters for segments \CH2, imi+ and anions [BF4]−, [PF6]− and [NTf2]−.

MW α u0/kB v00

\CH2

[imi]+

[BF4]−

[PF6]−

[NTf2]−

14.02 1 83 1.54

67.07 1.1 490 16.2

86.8 1.23 1400 11.3

144.96 1.25 1550 15.0

280.27 1.26 1657 23.0

A. Maghari et al. / Journal of Molecular Liquids 191 (2014) 59–67

120

Table 3 Optimized influence Parameters for the compounds studied in this work.

T = 298.15K T = 303.15K

4

μ∘

ς × 10

c

0.805 0.900 1.00 1.127 0.805 0.928 1.013 1.125 0.885 0.950 0.998 1.055

−0.30 −0.28 −0.26 −0.24 −0.30 −0.28 −0.26 −0.24 −0.29 −0.28 −0.27 −0.26

1.00 1.01 1.01 1.035 1.102 1.109 1.094 1.096 1.532 1.500 1.610 1.440

100

T = 318.15K

1 ¼ ρκ S

2

vs ¼

∂p ∂ρ

 :

80

T = 323.15K

60

40

20

0 1340 1350 1360 1370 1380 1390 1400 1410 1420 1430

mechanical property of a fluid and is related to the thermodynamic isentropic compressibility κS as 

T = 308.15K T = 313.15K

pressure (MPa)

[C2mim][BF4] [C4mim][BF4] [C6mim][BF4] [C8mim][BF4] [C2mim][PF6] [C4mim][PF6] [C6mim][PF6] [C8mim][PF6] [C3mim][NTf2] [C4mim][NTf2] [C5mim][NTf2] [C6mim][NTf2]

63

density (kg m-3)

ð24Þ

Fig. 2. Predicted densities for [C4mim][PF6] at several temperatures compared with literature data. Symbols correspond to experimental data taken from Azevedo et al. [58,60] and Machida et al. [63].

ð25Þ

in which Cid V is ideal gas heat capacity at constant volume. Since the experimental values of ideal gas heat capacities for ILs are not available, we obtained the ideal gas heat capacity at constant pressure Cid p as a function of temperature based on the summation parameters for the functional groups using the following equation [59,65]:

S

Alternatively, the speed of sound vs can be written as  vs ¼

γ MW



∂p ∂ρ

 1=2 T

where MW is the molecular mass and γ ≡ Cp/CV is the specific heat ratio. We can determine the speed of sound at each pressure and temperature by initially solving the (∂p/∂ρ)T from the hetero-SAFT-BACK EOS. The heat capacity ratio γ can be determined by calculating the ratio of the specific heats at constant pressure Cp and volume CV, given by the derivative of the Helmholtz energy and the pressure, which are directly calculated from the hetero-SAFT-BACK EOS: ! 2 ∂2 A T ð∂p=∂T Þρ ¼ C þ C p ¼ −T V ∂T 2 ρ2 ð∂p=∂ρÞT

CV ¼

2 res

∂ A ∂T 2

X

! N i AC pi −37:93

Ni BC pi þ 0:210 T i i! ! X X −4 2 −7 3 T þ T þ N i C C pi −3:91  10 Ni DC pi þ 2:06  10

! ð27Þ

where AC pi , BC pi , C C pi and DC pi are group contribution parameters and Ni is the number of groups of type i in the molecule. The calculated speed of sound for [C4mim][PF6], [C4mim][BF4] and [C4mim][NTf2] up to 100 MPa are shown as illustrative examples in Figs. 4–6. For the sake of comparison the experimental speed of sound data for [C4mim][PF6]

70 T = 298.15K

T = 303.23K

60

T = 313.1K

50

T = 372.7K

pressure (MPa)

pressure (MPa)

T = 303.14K T = 308.09K

T = 332.6K T = 352.6K

T =392.8K T = 412.9K T = 432.6K

100

i

ð28Þ

T = 298.34K

150

!

X

ð26Þ

250

200

þ

i

where the heat capacity at constant volume is given by id C V −T

id

Cp ¼

T = 452.3K T = 472.2K

T = 313.15K T = 318.14K T = 323.14K

40

T =328.2K

30 20

50 10 0 1050

1100

1150

1200

density (kg

1250

1300

m-3)

0 1400

1420

density (kg Fig. 1. Predicted densities for [C4mim][BF4] at several temperatures compared with literature data. Symbols correspond to experimental data taken from Azevedo et al. [58,60] and Machida et al. [63].

1460

1440

1480

m-3)

Fig. 3. Predicted densities for [C4mim][NTf2] at several temperatures compared with literature data. Symbols correspond to experimental data taken from Azevedo et al. [59,60].

64

A. Maghari et al. / Journal of Molecular Liquids 191 (2014) 59–67

1700

2000

1600

speed of sound (m s-1)

speed of sound (m s-1)

1900

1800

1700

1600

1500

1400 T = 283.15K

1300

T = 303.15K T = 313.15K

1200

T = 283.15K

T = 323.15K

T = 303.15K T = 313.15K

1500

1100

T = 323.15K

0

50

100

150

200

pressure (MPa) 1400 0

50

100

150

200

Fig. 6. Calculated speed of sound for [C4mim][NTf2] at several temperatures compared with literature data. Symbols correspond to experimental data taken from [58].

pressure (MPa) Fig. 4. Calculated speed of sound for [C4mim][PF6] at several temperatures compared with literature data. Symbols correspond to experimental data taken from Azevedo et al. [58].

and [C4mim][BF4] were taken from Ref. [58] and for [C4mim][NTf2], were taken from Ref. [59]. The hetero-SAFT-BACK calculations of speed of sounds for selected ILs are in good agreement with the experimental data. The maximum uncertainty of speed of sound results is 2.12% for [C4mim][BF4] at 323.15 K and 150 MPa. As the anions of different ILs increase in size, i.e. [BF4]− b [PF6]− b [NTf2]−, the speed of sound decreases. We have also investigated the effect of temperature on the speed of sound. Fig. 7 shows the evolution of the speed of sound of [Cnmim][NTf2] with n = 3, 4 and 5 at 0.1 MPa as compared to experimental data. Table 4 is also shown the ARDs for the calculated speed of sound from the available experimental data of some ILs. The experimental data of speed of sound for [Cnmim][PF6], [Cnmim][BF4] with n = 2, 6 and 8 and [Cnmim][NTf2] with n = 6 are not available. Moreover, two important derivative properties, including the isothermal compressibility κT and the isobaric thermal expansion coefficient αp have been calculated from the hetero-SAFT-BACK EOS. These two properties are related to the variation of the density with pressure and temperature. The effect of pressure in density can be best described

by the isothermal compressibility κT, which is calculated from the following expression κT ≡

    ∂ρ 1 ∂p −1 ¼ : ∂p T ρ ∂ρ T

1 ρ

ð29Þ

Similarly the isobaric thermal expansion coefficient αp, could also be obtained analytically by differentiating of density with respect to temperature, or alternatively, differentiating of pressure with respect to temperature and multiplying by the isothermal compressibility according to the following equation αp ≡ −

    1 ∂ρ ∂p ¼ κT : ρ ∂T p ∂T ρ

ð30Þ

The calculated αp and κT over wide temperature and pressure ranges are given in Tables 5, 6 and 7 for [Cnmim][BF4], [Cnmim][PF6] and [Cnmim][NTf2], respectively. The predicted isothermal compressibility of ILs varied from about 0.32 to 0.60 GPa− 1. This is significantly lower than that of other organic liquids. Within the studied T and p ranges, the isothermal compressibilities as well as isobaric thermal expansivities decrease as pressure is raised. Moreover, the isothermal

1280 1800

speed of sound (m s-1)

speed of sound (m s-1)

exp (C3mim)

1260

1750 1700 1650 1600 1550 1500 T = 283.15K

1450

T = 303.15K

1400

T = 313.16K

cal (C3mim) exp (C4mim)

1240

cal (C4mim) exp (C5mim)

1220

cal (C5mim)

1200 1180 1160

T = 323.25K

1350

1140 280

1300 0

50

100

150

200

290

300

310

320

330

340

350

Temperature (K)

pressure (MPa) Fig. 5. Calculated speed of sound for [C4mim][BF4] at several temperatures compared with literature data. Symbols correspond to experimental data taken from Azevedo et al. [58].

Fig. 7. Speed of sound of [Cnmim][NTf2] as a function of temperature at a fixed pressure of 0.1 MPa. Symbols represent experimental data [59,77] and solid lines are hetero-SAFTBACK prediction.

A. Maghari et al. / Journal of Molecular Liquids 191 (2014) 59–67 Table 4 Comparison of ILs' speed of sound with hetero-SAFT-BACK EOS against the available experimental data. Ionic liquids

Temperature range (K)

Pressure range (MPa)

NP

ARD(vs)

Data source

[C4mim][BF4] [C4mim][PF6] [C3mim][NTf2] [C4mim][NTf2] [C5mim][NTf2]

283–323 283–323 298–338 283–323 288–338

0.1–150 0.1–151 0.5–200 0.1–150 0.5–150

41 44 113 39 114

2.12 1.45 1.78 1.92 2.10

[58] [58] [77] [59] [77]



Table 6 Calculated values of isothermal compressibility (κT) and isobaric thermal expansivity (αp) for [Cnmim][PF6] by hetero-SAFT-BACK model. P/Mpa T/K

0.1

20

40

0.3892 0.4100 0.4387 0.4696

0.3642 0.3824 0.4080 0.4340

0.3410 0.3583 0.3812 0.4045

0.4131 0.4368 0.4715 0.5021

0.3848 0.4051 0.4331 0.4628

0.3586 0.3778 0.4030 0.4272

0.7077 0.6752 0.6532 0.6425

0.6823 0.6492 0.6260 0.6141

0.6581 0.6259 0.6025 0.5897

0.7263 0.6910 0.6651 0.6439

0.6978 0.6614 0.6333 0.6143

0.6708 0.6360 0.6070 0.5869

0.1

20

40

0.3549 0.3719 0.3959 0.4197

0.3333 0.3485 0.3698 0.3920

0.3867 0.4078 0.4361 0.4649

0.3614 0.3807 0.4059 0.5757

0.6445 0.6078 0.5798 0.5633

0.6221 0.5858 0.5591 0.5415

0.6913 0.6541 0.6228 0.6014

0.6649 0.6284 0.5972 0.5759

−1



NP v 100 s ;cal −vs ;exp ; NP ∑ vs ;exp i¼1

ARDðvs Þ ≡

65

NP, number of data points.

compressibilities increase as temperature is increased, whereas the isobaric thermal expansivities decrease when the temperature is raised. These features are representative of the behavior of αp and κT for studied ILs and are mutually consistent with literature data [66]. Some explanations of the unusual behavior of the isothermal compressibility and isobaric thermal expansivity of liquids are discussed in [67,68]. Furthermore, the behavior of αp for our [C4mim][PF6], [C8mim][PF6] and [C8mim][BF4] ILs versus temperature and pressure agrees with those reported by other work [69]. The most often method for determining αp is from fitting precise density data against temperature. This requires high quality density data, not always available, and is extremely dependent on the choice of the type of equation for fitting the data. On the other hand, the isobaric thermal expansivity can be directly determined by exploiting the exact thermodynamic relation [70]

κT/GPa [C2mim] 298 313 333 353 [C6mim] 298 313 333 353 P/Mpa [C2mim] 298 313 333 353 [C6mim] 298 313 333 353

[C4mim] 0.3799 0.3992 0.4267 0.4516 [C8mim] 0.4187 0.4431 0.4753 0.5073

[C4mim] 0.6678 0.6322 0.6062 0.5873 [C8mim] 0.7225 0.6838 0.6548 0.6312

ð32Þ

where δQ/δt is heat flux and δp/δt is the pressure variation against time. If the pressure of the system is varied isothermally, a heat transfer appears between the thermostat and the sample. The obtained experimental values by Navia et al. for isobaric thermal expansivities of [Cnmim][BF4] and [Cnmim][NTf2] in the range 298–343 K and from 0.1 to 40 MPa were compared to those of present work by means of the avcal cal − αexp erage absolute deviation, AAD = (1/n) ∑ni = 1|(αp,i p,i )/αp,i |. For [C4mim][BF4] and [C4mim][NTf2] ILs, the comparison between the isobaric thermal expansivities of this work and the measured values [71] resulted in AAD are less than 7.8% and 4.7%, respectively. The comparisons of αp values in this work with the reported values [72] for [C2mim][BF4], [C6mim][BF4], [C8mim][BF4] and [C6mim][NTf2] show the AAD are less than 8.7%, 7.4%, 5.3% and 5.5%, respectively. It is seen

Table 5 Calculated values of isothermal compressibility (κT) and isobaric thermal expansivity (αp) for [Cnmim][BF4] by hetero-SAFT-BACK model.

Table 7 Calculated values of isothermal compressibility (κT) and isobaric thermal expansivity (αp) for [Cnmim][NTf2] by hetero-SAFT-BACK model.

 α p ¼ −ρ

∂S ∂p

 T


ρ ∂Q  ¼− T ∂p T

ð31Þ

where Q is the heat exchange between the sample and thermostat. Navia et al. [71,72] determined the isobaric thermal expansivity of some ILs by using the scanning calorimetric method and applying the following equation: αp ¼ −

ρ δQ =δt T δp=δt

P/Mpa

P/Mpa T/K

0.1

20

40

0.1

20

40

−1

κT/GPa [C2mim] 298 313 333 353 [C6mim] 298 313 333 353

0.3678 0.3872 0.4121 0.4389

0.3458 0.3624 0.3858 0.4098

0.3261 0.3412 0.3629 0.3838

0.4015 0.4232 0.4530 0.4835

0.3729 0.3918 0.4188 0.4442

0.3486 0.3671 0.3908 0.4138

103αp/K−1 [C2mim] 298 0.6692 313 0.6482 333 0.6372 353 0.6289 [C6mim] 298 0.6871 313 0.6761 333 0.6538 353 0.6383

0.6344 0.6291 0.6192 0.6098

0.6131 0.6069 0.5978 0.5848

0.6551 0.6472 0.6259 0.6091

0.6368 0.6231 0.6015 0.5845

[C4mim] 0.3863 0.4080 0.4369 0.4656 [C8mim] 0.3973 0.4168 0.4443 0.4735

[C4mim] 0.6892 0.6671 0.6511 0.6373 [C8mim] 0.6660 0.6362 0.6110 0.5911

0.3620 0.3801 0.4052 0.4321

0.3398 0.3571 0.3793 0.4005

0.3672 0.3881 0.4132 0.4365

0.3458 0.3629 0.3850 0.4068

0.6647 0.6411 0.6232 0.6098

0.6418 0.6182 0.5996 0.5867

0.6274 0.6109 0.5865 0.5642

0.6082 0.5875 0.5619 0.5427

T/K κT/GPa−1 [C3mim] 298 313 333 353 [C5mim] 298 313 333 353

0.1

20

40

0.4975 0.5234 0.5582 0.5936

0.4536 0.4774 0.5062 0.5368

0.4202 0.4396 0.4651 0.4916

0.5032 0.5302 0.5675 0.6048

0.4589 0.4813 0.5133 0.5440

0.4220 0.4430 0.4702 0.4981

0.6483 0.6028 0.5671 0.5464

0.6205 0.5752 0.5393 0.5192

0.6978 0.6242 0.5879 0.5641

0.6708 0.5955 0.5582 0.5361

103αp/K−1 [C3mim] 298 0.6802 313 0.6349 333 0.6008 353 0.5790 [C5mim] 298 0.7263 313 0.6596 333 0.6224 353 0.5993

0.1 [C4mim] 0.4890 0.5141 0.5475 0.5818 [C6mim] 0.5051 0.5331 0.5718 0.6098

[C4mim] 0.6755 0.6286 0.5918 0.5685 [C6mim] 0.7151 0.6676 0.6304 0.6061

20

40

0.4470 0.4691 0.4978 0.5264

0.4132 0.4325 0.4568 0.4824

0.4604 0.4852 0.5161 0.5483

0.4239 0.4449 0.4722 0.5008

0.6433 0.5966 0.5593 0.5367

0.6162 0.5695 0.5326 0.5103

0.6795 0.6321 0.5936 0.5699

0.6496 0.6028 0.5638 0.5402

66

A. Maghari et al. / Journal of Molecular Liquids 191 (2014) 59–67

0.68

0.68 0.66

[C4mim][BF4 ]

0.64

0.64

0.62

0.62

103α p(K-1)

103α p(K-1)

0.66

0.6 0.58

[C6mim][BF4 ]

0.6 0.58

0.56

0.56

0.54

0.54

0.52

0.52 0.5

0.5 0

20

40

60

0

20

pressure (MPa) 0.68

60

0.68

[C4mim][NTf2]

0.66

[C6mim][NTf2]

0.66

0.64

0.64

0.62

0.62

103α p(K)

103α p(K-1)

40

pressure (MPa)

0.6 0.58

0.6 0.58

0.56

0.56

0.54

0.54

0.52

0.52

0.5

0.5 0

20

40

0

60

20

pressure (MPa)

40

60

pressure (MPa)

Fig. 8. Calculated isobaric thermal expansivity for some ILs as a function of pressure at two different temperatures T = 298 K (solid line) and T = 338.15 K (dashed line). Symbols represent experimental data [71,72] at T = 298 K (■) and T = 338.15 K (▲).

that the hetero-SAFT-BACK EOS showed good agreement with available experimental data. In Fig. 8 we also compare the available isobaric thermal expansivities of [C4mim][BF4], [C6mim][BF4], [C4mim][NTf2] and [C6mim][NTf2], directly determined by exploiting the exact thermodynamic Eq. (32), with the values calculated with the hetero-SAFT-BACK EOS. 5. Conclusion In this work, the hetero-SAFT-BACK EOS is developed to predict the pressure–density–temperature (pρT) and thermodynamic derivative properties of pure alkyl-imidazolium ILs with the [PF6]− and [BF4]− and [NTf2]− anions. We assumed that a pure IL is composed of two components, including anion and cation. The anion is treated as one segment and there is no chain term for anion component. The cation of IL is divided into several segments including cation head (imidazolium ring) and segments of \CH2 (including \CH3) in the alkyl tails of the IL molecule. In our model, the cation head and the anion have one association site, which can only cross-associate. The hetero-SAFT-BACK EOS parameters were estimated by fitting to available experimental liquid density and pρT data in liquid phase region. We obtained very good results for densities of ILs over a wide range of temperature and pressure. A robust test for reliability of obtained parameters has been done by calculating the saturated vapor pressure from the hetero-SAFT-BACK EOS. The obtained saturated vapor pressure for [C4mim][PF6] was extremely low and smaller than the values predicted by Paulechka et al. [56,57]. Moreover, we have checked the capability of the model for predicting the second derivative properties, including speed of sound, isothermal compressibility and isobaric

thermal expansivity over the wide pressure and temperature ranges. We have obtained a good agreement between experimental and predicted values of these derivative properties. Nomenclature and units Superscripts assoc association term cal calculated chain chain term dis dispersion exp experimental hcb hard convex body id ideal gas L liquid V vapor ref reference term res residual Subscripts a, b site index Greeks α αp γ ΔAi B j εAi B j η

shape parameter thermal expansion coefficient (K−1) specific heat ratio association strength between sites A and B (Å3) association energy between sites A and B (J) packing factor

A. Maghari et al. / Journal of Molecular Liquids 191 (2014) 59–67

κ Ai B j κS κT μ μ∘ μ* v00 ρ σ σp τ ς

bonding-volume of association between sites A and B (mol m−3) isentropic compressibility (Pa−1) isothermal compressibility (Pa−1) dipole moment (D) dipole moment parameter (D) reduced dipole moment segment volume (m3mol−1) molar density (mol m−3) temperature-independent segment diameter (Å) effective polar interaction, 5.485 × 10−10m close packed reduced density dipole moment parameter (mol−1 m3)

Acknowledgment We thank Dr. Morteza Farnia for helpful discussions. References [1] J.L. Anthony, J.L. Anderson, E.J. Maginn, J.F. Brennecke, J. Phys. Chem. B 109 (2005) 6366–6374. [2] B. Qiao, C. Krekeler, R. Berger, L.D. Site, C. Holm, J. Phys. Chem. B 112 (2008) 1743–1751. [3] R.L. Gardas, J.A.P. Coutinho, Fluid Phase Equilib. 263 (2008) 26–32. [4] R.L. Gardas, J.A.P. Coutinho, Fluid Phase Equilib. 265 (2008) 57–65. [5] R.L. Gardas, J.A.P. Coutinho, Fluid Phase Equilib. 266 (2008) 195–201. [6] R.L. Gardas, J.A.P. Coutinho, Fluid Phase Equilib. 267 (2008) 188–192. [7] R.L. Gardas, J.A.P. Coutinho, Ind. Eng. Chem. Res. 47 (2008) 5751–5757. [8] R.L. Gardas, J.A.P. Coutinho, AIChE J 55 (2009) 1274–1290. [9] M.B. Shiflett, M.A. Harmer, C.P. Junk, A. Yokozeki, Fluid Phase Equilib. 242 (2006) 220–232. [10] M.B. Shiflett, A. Yokozeki, Fluid Phase Equilib. 259 (2007) 210–217. [11] M.B. Shiflett, A. Yokozeki, Ind. Eng. Chem. Res. 47 (2008) 926–934. [12] A. Yokozeki, Mark B. Shiflett, J. Supercrit. Fluids 55 (2010) 846–851. [13] P.J. Carvalho, V.H. Álvarez, J.J.B. Machado, J. Paulyb, J.L. Daridon, I.M. Marrucho, M. Aznar, J.A.P. Coutinho, J. Supercrit. Fluids 48 (2009) 99–107. [14] P.J. Carvalho, V.H. Alvarez, B. Schröder, A.M. Gil, I.M. Marrucho, M. Aznar, L.M.N.B.F. Santos, J.A.P. Coutinho, J. Phys. Chem. B 113 (2009) 6803–6812. [15] J.O. Valderrama, P.A. Robles, Ind. Eng. Chem. Res. 46 (2007) 1338–1344. [16] A. Yokozeki, M.B. Shiflett, J. Phys. Chem. B 111 (2007) 2070–2074. [17] P.J. Carvalho, V.H. Álvarez, I.M. Marrucho, M. Aznar, J.A.P. Coutinho, J. Supercrit. Fluids 52 (2010) 258–265. [18] M.S. Wertheim, J. Stat. Phys. 35 (1984) 19–34. [19] M.S. Wertheim, J. Stat. Phys. 35 (1984) 35–47. [20] M.S. Wertheim, J. Stat. Phys. 42 (1986) 459–476. [21] M.S. Wertheim, J. Stat. Phys. 42 (1986) 477–492. [22] W.G. Chapman, K.E. Gubbins, G. Jackson, M. Radosz, Fluid Phase Equilib. 52 (1989) 31–38. [23] S. Huang, M. Radosz, Ind. Eng. Chem. Res. 29 (1990) 2284–2294. [24] S. Huang, M. Radosz, Ind. Eng. Chem. Res. 30 (1991) 1994–2005. [25] F.J. Blas, L.F. Vega, Mol. Phys. 92 (1997) 135–150. [26] J.S. Andreu, L.F. Vega, J. Phys. Chem. C 111 (2007) 16028–16034. [27] J.S. Andreu, L.F. Vega, J. Phys. Chem. B 112 (2008) 15398–15406. [28] M. Rahmati-Rostami, B. Behzadi, C. Ghotbi, Fluid Phase Equilib. 309 (2011) 179–189. [29] U. Domańska, M. Zawadzki, K. Paduszyński, M. Królikowski, J. Phys. Chem. B 116 (2012) 8191–8200.

67

[30] K. Paduszyński, J. Chiyen, D. Ramjugernath, T. Letcher, U. Domańska, Fluid Phase Equilib. 305 (2011) 43–52. [31] K. Paduszyński, U. Domańska, J. Phys. Chem. B 115 (2011) 12537–12548. [32] K. Paduszyński, U. Domańska, J. Phys. Chem. B 116 (2012) 5002–5018. [33] K. Paduszyński, M. Królikowski, U. Domańska, J. Phys. Chem. B 117 (2013) 3884–3891. [34] I. Polishuk, J. Phys. Chem. A 117 (2013) 2223–2232. [35] Y. Chen, F. Mutelet, J.N. Jaubert, J. Phys. Chem. B 116 (2012) 14375–14388. [36] X. Ji, C. Held, G. Sadowski, Fluid Phase Equilib 335 (2012) 64–73. [37] F. Llovell, R.M. Marcos, M. MacDowell, L.F. Vega, J. Phys. Chem. B 116 (2012) 7709–7718. [38] X. Ji, H. Adidharma, Chem. Eng. Sci. 64 (2009) 1985–1992. [39] X.Y. Ji, H. Adidharma, Fluid Phase Equilib. 293 (2010) 141–150. [40] X.Y. Ji, H. Adidharma, Fluid Phase Equilib. 315 (2012) 53–63. [41] A. Maghari, F. ZiaMajidi, Fluid Phase Equilib. 356 (2013) 109–116. [42] T. Boublik, J. Phys. Chem. 63 (1975) 4084–4085. [43] S.S. Chen, A.A. Kreglewski, Ber. Bunsenges. Phys. Chem. 81 (1977) 1048–1052. [44] B.J. Alder, D.A. Young, M.A. Mark, J. Chem. Phys. 56 (1972) 3013–3029. [45] J. Chen, J.G. Mi, Fluid Phase Equilib. 186 (2001) 165–184. [46] J.G. Mi, J. Chen, G.H. Gao, W.Y. Fei, Fluid Phase Equilib. 201 (2002) 295–307. [47] J. Chen, J.G. Mi, Y.M. Yu, G. Luo, Chem. Eng. Sci. 59 (2004) 5831–5838. [48] A. Maghari, M.S. Sadeghi, Fluid Phase Equilib. 252 (2007) 152–161. [49] A. Maghari, Z. Safaei, S. Sarhangian, Cryogenics 48 (2008) 48–55. [50] A. Maghari, Z. Safaei, J. Mol. Liq. 142 (2008) 95–102. [51] A. Maghari, M. Hamzehloo, Fluid Phase Equilib. 302 (2011) 195–201. [52] C.H. Twu, K.E. Gubbins, Chem. Eng. Sci. 33 (1978) 863–878. [53] C.H. Twu, K.E. Gubbins, Chem. Eng. Sci. 33 (1978) 879–887. [54] T. Kraska, K.E. Gubbins, Ind. Eng. Chem. Res. 35 (1996) 4727–4737. [55] S. Keskin, D. Kayrak-Talay, U. Akman, . Horta su, J. Supercrit. Fluids 43 (2007) 150–180. [56] Y.U. Paulechka, G.J. Kabo, A.V. Blokhin, O.A. Vydrov, J.W. Magee, M. Frenkel, J. Chem. Eng. Data 48 (2003) 457–462. [57] G.J. Kabo, A.V. Blokhin, Y.U. Paulechka, A.G. Kabo, M.P. Shymanovich, J.W. Magee, J. Chem. Eng. Data 49 (2004) 453–461. [58] R. Gomes de Azevedo, J.M.S.S. Esperanca, V. Najdanovic-Visak, Z.P. Visak, H.J.R. Guedes, M. Nunes da Ponte, L.P.N. Rebelo, J. Chem. Eng. Data 50 (2005) 997–1008. [59] R. Gomes de Azevedo, J.M.S.S. Esperanc, J. Szydlowski, Z.P. Visak, P.F. Pires, H.J.R. Guedes, L.P.N. Rebelo, J. Chem. Thermodyn. 37 (2005) 888–899. [60] J. Jacquemin, R. Ge, P. Nancarrow, W. Rooney, M.F. Costa Gomes, A.A.H. Pádua, C. Hardacre, J. Chem. Eng. Data 53 (2008) 716–726. [61] H. Machida, Y. Sato, R.L. Smith Jr., Fluid Phase Equilib. 264 (2008) 147–155. [62] A. Muhammad, M.I. Abdul Mutalib, C.D. Wilfred, T. Murugesan, A. Shafeeq, J. Chem. Thermodyn. 40 (2008) 1433–1438. [63] J. Safarov, E. Hassel, J. Mol. Liq. 153 (2010) 153–158. [64] K.G. Joback, R.C. Reid, Chem. Eng. Commun. 57 (1987) 233–243. [65] B.E. Poling, J.M. Prausnitz, J.P. O'Connell, The Properties of Gases and Liquids, McGraw-Hill, New York, 2001. [66] R.L. Gardas, M.G. Freire, P.J. Carvalho, I.M. Marrucho, I.M.A. Fonseca, A.G.M. Ferreira, J.A.P. Coutinho, J. Chem. Eng. Data 52 (2007) 80–88. [67] J. Troncoso, C.A. Cerdeiriña, P. Navia, Y.A. Sanmamed, D.G. Salgado, L. Romaní, J. Phys. Chem. Lett. 1 (2010) 211–214. [68] J. Troncoso, P. Navia, L. Romaní, D. Bessieres, T. Lafitte, J. Chem. Phys. 134 (2011) 094502. [69] Z. Gu, J.F. Brennecke, J. Chem. Eng. Data 47 (2002) 339–345. [70] P. Navia, J. Troncoso, L. Romaní, J. Chem. Thermodyn. 40 (2008) 1607–1611. [71] P. Navia, J. Troncoso, L. Romaní, J. Chem. Eng. Data 55 (2010) 590–594. [72] P. Navia, J. Troncoso, L. Romaní, J. Chem. Eng. Data 55 (2010) 595–599. [73] R. Taguchi, H. Machida, Y. Sato, R.L. Smith, J. Chem. Eng. Data 54 (2009) 22–27. [74] G. García-Miaja, J. Troncoso, L. Romaní, J. Chem. Thermodyn. 41 (2009) 334–341. [75] C. Frez, G.J. Diebold, C.D. Tran, S. Yu, J. Chem. Eng. Data 51 (2006) 1250–1255. [76] K.R. Harris, M. Kanakubo, L.A. Woolf, J. Chem. Eng. Data 51 (2006) 1161–1167. [77] J.M.S.S. Esperanca, Z.P. Visak, N.V. Plechkova, K.R. Seddon, H.J.R. Guedes, L.P.N. Rebelo, J. Chem. Eng. Data 51 (2006) 2009–2015.