Surface Tension Prediction of Ionic Liquid Binary Solutions - American

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Surface Tension Prediction of Ionic Liquid Binary Solutions Ensieh Ghasemian Lemraski* and Zohre Pouyanfar Faculty of Science, Ilam University, P.O. Box 69315516, Ilam, Iran S Supporting Information *

ABSTRACT: An ionic liquid is a salt in which the ions are poorly coordinated, which results in these solvents being liquid below 100 °C, or even at room temperature. At least one ion has a delocalized charge, and one component is organic, which prevents the formation of a stable crystal lattice. In the present work three classical thermodynamic models has been selected to predict the surface tensions of ionic liquid binary mixtures based on the CSGC model (corresponding-states group-contribution method), HSEG model (extended Guggenheim’s ideal solution model), and parachor model. To predict the surface tension of ionic liquid binary solution, we calculated critical parameters, density, and surface tension of pure component. To compare, theoretical and experimental data average standard deviation values have been calculated. These values for the studied ionic liquid binary systems show the HSEG model has good accordance in comparison with other predictive equations.

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for calculating surface tension of binary and ternary mixtures.10−14 In the most of the predictive models, physicochemical parameters, such as density, surface composition, or critical parameters, hasve been used directly or indirectly in determining the surface tension. In the next section the mentioned models in order to prediction of surface tension in the present work have been described briefly. Corresponding-States Group-Contribution Theory. In the first section the corresponding-states group-contribution theory (CSGC) to calculate surface tensions of ionic liquid−ionic liquid and ionic liquid−organic binary mixtures has been proposed. This classical thermodynamic model was introduced by Brock and Bird (BBT) and relates surface tension of pure compounds and critical parameters.17−21 The following equations were developed for mixtures as shown as below:

INTRODUCTION Ionic liquids are composed of an organic cation and an inorganic anion. At least one ion has a delocalized charge, and one component is organic, which prevents the formation of a stable crystal lattice.1,2 Because of their interesting physical and chemical properties ionic liquids have many applications, such as powerful solvents and electrically conducting fluids (electrolytes). Many experimental and theoretical studies to investigate physical and chemical properties of ionic liquids such as melting point, viscosity, density, thermal and electrochemical stability, solvent properties, and surface tension3−8 have been performed.9 Besides experimental study, the theoretical method is another important strategy, which is of chemical and chemical engineering interest. Recently a few theoretical model have been used for predicting surface tension of pure ionic liquids, including parachor methods,10,11 group contribution methods,12 and corresponding state theory.13 However, the theoretical surface tension data of ionic liquid binary solution are extremely rare.14,15 To obtain information about the surface tension of ionic liquid binary solution, it is necessary to prediction or correlates the surface tension of ionic liquid−solvent mixtures using theoretical and semi empirical models. In the present work we focused on surface tension prediction of ionic liquid−ionic liquid and ionic liquid−organic binary solution in the whole mole fraction of component using HSEG, parachor, and CSGC models.16−18 The main goal of the present work is to overcome the shortage of information about surface tension and surface properties of ionic liquids. It will be shown that by using the HSEG model it can be possible to obtain good results for surface tensions of ionic liquid binary solutions. Theoretical Section: Short Description of Applied Models for Predicting Surface Tension in the Present Work. Different classical thermodynamic models are available © XXXX American Chemical Society

σmix

⎛ ∑ x P * ⎞a i ci ⎟⎟ (∑ xiTc*i )b (c ∑ xiαci − d) = ⎜⎜ i ⎝ 101.325 ⎠ i i × (1 −

∑ xiTr*i )e i

(1)

⎛ T * ln(Pc*/101.325) ⎞ ⎟ αc = f ⎜1 + br * 1 − Tbr ⎠ ⎝

(2)

Where

Tr* =

T Tc*

(3)

Received: May 28, 2014 Accepted: November 20, 2014

A

dx.doi.org/10.1021/je500479f | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

*= Tbr

Article

Tb Tc*

According to the modified Lydersen−Jobarck−Reid method density of pure component can be calculated from eq 12

(4)

In the above expressions Tb is the normal boiling point of components, T*c and P*c are supposed-critical temperature and supposed-critical pressure of components, respectively, which have been calculated using eqs 5 and 6.21 Tc* =

ρ=

[A T +

+

i CT(∑M niΔTi )2

+

A̅ = a +

i DT (∑M niΔTi )3 ]

(5) Pc* =

101.325 ln(Tb − 273.15) i

i

i

[AP + BP ∑M niΔ Pi + CP(∑M niΔ Pi )2 + DP (∑M niΔ Pi )3 ] (6)

where ΔTi and ΔPi are the contribution values of group i to calculate supposed-critical temperature Tc* and supposed-critical pressure P*c of the pure component. Parameters AT ∼ DT and AP ∼ DP as well as a, b, c, d, e, and f in eqs 1 to 6 have been calculated using experimental surface tension data. HSEG Model. In the second section the HSEG model has been used to prediction surface tension of ionic liquid solution. The HSEG model is extended Guggenheim’s ideal solution equation22 and used for mixtures with same size of the molecules. Based on HSEG model σ can be written as σ − σ2 σ = Y1σ1 + Y2σ2 − 1 (Y1A 2 + Y2A1)Y1Y2 (7) 2RT

Ai xi1 A1x1 + A 2 x 2

Also A1 and A2 are the molar areas of the pure component and have been defined using different forms, but in the present work, we have used the popular form of surface area calculations23 from the density, ρ, molecular weight, M, of pure components, and Avogadro number, NA, as shown as in eq 9.

(10) 11

Using reported parachors of some ionic liquids, the surface tension of ionic liquid binary solution has been calculated using eq 11.

⎛ ρP ⎞ 4 σ=⎜ ⎟ ⎝ MW ⎠

⎛ cm 3 ⎞ VC⎜ ⎟=D+ ⎝ mol ⎠

∑ nΔVc

(15)

Tb(K) = 198.2 +

∑ nΔTb

(16)

Tb A + B ∑ nΔTc − (∑ nΔTc)2

(17)

RESULTS AND DISCUSSION In the present research, the experimental surface tensions of 37 ionic liquid systems between 0 and 1 range of mole fraction of components at different temperatures have been collected from literature. On the basis of necessary input data to prediction surface tension of mixtures, imidazolium, pyridinium, and isoquinolinium-based ionic liquids and methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, acetonitrile, dimethyl sulfoxide, and tetrahydrofuran (THF) as organic solvents have been selected. As shown as in Table 1, the calculated surface tensions of ionic liquid binary mixtures using each of the three calculation models show very little deviation from experimental data. (Experimental and predicted surface tension and values of MRSD for studied binary solutions are shown in Supporting Information.) Also the relative percent error range versus number of data points from three models are given in Figure 1. The mean relative standard deviation values obtained for all ionic liquid binary mixtures using eq 18 has presented in Table 1, where Np shows the number of experimental data.

(9)

Mi ρi

(14)

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Parachor Model. Sudgen’s equation (SE)18 is the third theoretical model which we used to calculation surface tension of binary solution. Sudgen defined the parachor parameter based on (Mi) the molar mass of the pure compound i, (ρi), and its density and surface tension of component as shown as in eq 10. [Pi ] = σi1/4

(13)

where Tc and Tb are the critical temperature and boiling temperature of molecule respectively, M is molecular weight of component, VC is the critical volume of component, n is the number of groups, ΔVc, ΔTb, and ΔTc are the critical volume, boiling temperature, and critical temperature of each group, respectively. In eq 12 the parameters of A, B, and D are constant (A = 0.5703, B = 1.0121, and D = 6.75), and a = 0.3411, b = 2.0443, c = 0.5386, and d = 0.02111 in eqs 13 and 14 are system independent constants. In the present work density of components have been calculated based on the proposed method.

(8)

Ai = (Mi /ρi )2/3 NA1/3

bM VC

⎛c d⎞ B̅ = ⎜ + ⎟V cb M⎠ ⎝ Vc

Tc(K) =

In this expression, Yi is molar area fraction for the molecule i and defined by the following equation: Yi =

(12)

In the above equation

Tb i BT ∑M niΔTi

A̅ 2⎛ B ⎞ (T − TC) + ⎜A ln ⎟ B 7⎝ B̅ ⎠ (TC − TB)

(11)

⎡ 1 MRSD% = 100·⎢ ⎢ Np ⎣

To prediction of surface tension, by eq 11, density is the necessary input data. But density data for all ionic liquid has not been reported in the literature, so we suggested the modified group contribution method (modified Lydersen−Jobarck−Reid method)24,25 to predicting of ionic liquids densities in the different temperature.

⎛ σi ,exp − σi ,cal ⎞2 ⎤ ⎟⎟ ⎥ ∑ ⎜⎜ σ ⎝ ⎠ ⎥⎦ i ,exp i

1/2

(18)

According to the observed deviation of calculated surface tension data from experimental data, it can be seen each of three B



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Table 1. Mean Relative Standard Deviation (MRSD) with Maximum Deviation (MD) Values of All Studied Binary Mixtures in the Present Work MRSD (%) binary system

T/K

[EMIM][NTf2] (1) + THF (2)26 [EMIM][NTf2] (1) + acetonitrile (2)26 [BMIM][NTf2] (1) + THF (2)27 [BMIM][NTf2] (1) + acetonitrile (2)27 [BMIM][NTf2] (1) + DMSO (2)27 [EMIM][NTf2] (1) + DMSO (2)27 [BMIM][L-lactate] (1) + methanol (2)28 [BMIM][L-lactate] (1) + ethanol (2)28 [BMIM][L-lactate] (1) + butanol (2)28 [EMIM][NO3] (1) + methanol (2)29 [EMIM][NO3] (1) + ethanol (2)29 [C4mim][NTf2] (1) + [C4 C1mim][NTf2] (2)30 [C4mim][NTf2] (1) + [C3mpyr][NTf2] (2)30 [C4mim][NTf2] (1) + [C3mpy][NTf2] (2)30 [C4mim][NTf2] (1) + [C3mpip][NTf2] (2)30 [EMIM][BF4] (1) + ethanol (2)31 [BMIM][BF4] (1) + ethanol (2)31 [HMIM][BF4] (1) + ethanol (2)31 [MOIM][BF4] (1) + ethanol (2)31 [C4MIM][NTf2] (1) + butanol (2)32 [BMIM][NTf2] (1) + propanol (2)32 [C8iQuin][NTf2] (1) + 1-hexanol (2)33 [EMIM][CH3SO4] (1) + methanol (2)34 [MMIM][CH3SO4] (1) + ethanol (2)34 [MMIM][CH3SO4] (1) + butanol (2)34 [C6H13OCH2MIM][BF4] (1) + methanol (2)35 [C6H13OCH2MIM][BF4] (1) + butanol (2)35 [C6H13OCH2MIM][BF4] (1) + hexanol (2)35 [(C6H13OCH2)2IM][BF4] (1) + methanol (2)35 [(C6H13OCH2)2IM][BF4] (1) + butanol (2)35 [(C6H13OCH2)2IM][BF4] (1) + hexanol (2)35 [MMIM][NTf2] (1) + [BMIM][NTf2] (2)36 [BMIM][NTf2] (1) + [EMIM][NTf2] (2)36 [BMIM][NTf2] (1) + [PMIM][NTf2] (2)36 [BMIM][NTf2] (1) + [HMIM][NTf2] (2)36 [BMIM][NTf2] (1) + [OMIM][NTf2] (2)36 [BMIM][NTf2] (1) + [DMIM][NTf2] (2)36 total

(293.15−308.15) (293.15−313.15) (293.15−308.15) (293.15−313.15) (293.15−313.15) (293.15−313.15) (298.15−318.15) (298.15−318.15) (298.15−318.15) 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 (298.15−318) 298.15 298.15 298.15 308.15 (308−318) (308−318) (308−318) (308−318) (308−318) 298.15 298.15 298.15 298.15 298.15 298.15

MD (maximum deviation)

data point

CSGC-ST model

HSEG model

parachor model

CSGC model

HSEG model

parachor model

44 40 40 40 40 40 48 45 48 11 11 7 7 7 7 6 11 11 11 12 12 21 8 8 8 5 8 8 8 8 8 7 7 7 7 7 7 614

2.10 4.10 3.76 4.75 7.05 4.35 16.93 3.88 5.84 12.70 8.12 4.72 11.56 8.91 11.19 19.51 8.78 14.87 30.19 7.10 2.58 7.92 4.45

0.82 2.43 1.19 2.60 2.42 2.56 8.60 3.68 7.49 14.99 8.44 0.94 0.66 0.08 0.55 5.23 13.36 5.25 2.70 7.62 2.89 4.40 15.76 18.49 11.34

2.22 6.07 3.51 6.35 10.52 6.28 14.02 16.57 23.74

1.03 2.72 2.59 2.72 5.02 6.92 6.35 7.1 7.58 6.79 3.71 2.17 6.27 4.78 6.08 7.11 4.89 6.79 14.8 2.81 1.35 2.93 1.85

0.56 1.39 0.58 1.38 2.04 1.67 5.11 3.99 1.99 5.13 9.45 0.43 0.31 0.05 0.24 2.94 5.95 2.40 1.27 3.01 1.43 1.86 7.77 10.66 8.65

1.10 3.19 1.13 2.69 8.34 5.23 10.78 11.75 10.93

5.66 2.40 5.64 13.82 2.92 6.83 7.88 6.51 2.42 1.80 1.61 1.61 7.56

1.74 1.34 1.16 2.20 4.03 5.62 5.18

6.37 8.94 5.95 7.08 14.76 14.46 11.34 14.05 12.88 10.03 13.24

0.98 0.77 2.17 2.10 0.70 4.34 8.44

2.46 0.79 1.53 2.71 1.85 5.37 3.84 1.06 1.067 0.99 1.23 1.12

0.86 0.61 0.52 0.99 1.79 2.46

2.27 3.88 3.80 2.47 10.74 5.21 4.06 4.98 4.73 3.74 10.81

0.72 0.51 1.03 1.19 0.41 2.26

(1) + [C3mpy][NTf2](2) mixture shows a minimum relative error. Remaining systems show an error percentage greater than 10 %. For the [C6H13OCH2MIM][BF4] (1) + alcohol (2) binary mixture, data for the pure component were not reported, so we could not calculate surface tension of mixture using the HSEG model. Finally MRSD values of the parachor model show that about 19 % of the studied mixtures show deviations under 5 %, and 26 % studied mixtures show deviation under 10 %. The highest value of MRSD can be seen in the binary [BMIM][L-lactate] (1) + butanol (2) at 298.15 K with a value of 23.74 %, whereas [BMIM][NTf2](1) + [OMIM][NTf2] (2) mixture shows minimum deviation. The other systems in this section show an error percentage greater than 10 %. Unfortunately our calculation in the present work has been limited due to lack of full access to experimental surface tension data. Generally average percentage deviation values show that the CSGC model predicts the surface tension of ionic liquid binary

models can be used to estimation surface tension of two types of studied ionic liquid solution in this work very well. Average percentage deviation values show that the CSGC model predicts the surface tension of ionic liquid binary solutions with mean percentage errors of 7.59 %. Also from MRSD value of CSGC model, one can conclude that nearly 42 % of the studied binary mixtures in the present work show relative deviations under 5 %, and 31 % of studied solution show an deviation below 10 %. The maximum deviation between experimental and theoretical data occurs for the binary [MOIM][BF4] (1) + ethanol (2) at 298.15 K with a value of 30.19 %, whereas [BMIM][NTf2] (1) + [OMIM][NTf2] (2) and [BMIM][NTf2] (1) + [DMIM][NTf2] (2) mixtures show a minimum relative standard error. Remaining solutions show a percentage error greater than 10 %. Results of HSEG model show the maximum deviation observed for the [MMIM][CH3SO4] (1) + ethanol (2) mixture at 298.15 K with a value of 18.49 %, whereas the [BMIM][NTf2] C



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Figure 1. Mean relative standard deviation versus number of data points, from studied three methods in this study: △, HSEG model; □, CSGC-ST model; ●, parachor model.

Figure 3. Experimental and predicted surface tension of [EMIM][NTf2] (1) + acetonitrile (2) against the molar fraction of the first component, x1. Black continuous line, experimental surface tension; ▲, HSEG model; □, CSGC-ST model; ○, parachor model.

Figure 2. Experimental and predicted surface tension of [EMIM][NTf2] (1) + THF (2) against the molar fraction of the first component, x1. Black continuous line, experimental surface tension; ▲, HSEG model; □, CSGC-ST model; ○, parachor model.

Figure 4. Experimental and predicted surface tension of BMIM-BF4 (1) + ethanol (2) against the molar fraction of the first component, x1. Black continuous line, experimental surface tension; ▲, HSEG model; □, CSGC-ST model; ○, parachor model.

solution with mean percentage errors of 7.59 %, whereas HSEG model predicted the surface tension of same ionic liquids binary mixtures with percentage errors of 5.30 %, and finally the parachor model predicts the surface tension with percentage errors of 8.77 % for the same condition. The results show that the structure and intermolecular forces play a decisive role in the deviation. Results of calculated data using presented three models with experimental surface tension data in Figures 2 to 5 show that the HSEG model has the best accordance with experimental data for ionic liquid−organic solvent binary mixtures, but for ionic liquid−ionic liquid binary mixtures the parachor model presents the best agreement between experimental and theoretical surface tension data (see Figure 5). In the studied system, results of CSGC model are a good method to predict surface tension of liquid−ionic liquid systems. In spite of CSGC model we observed that the prediction of HSEG model is accordance with experimental surface tension

data for all studied systems except the ionic liquid−alcohol system. Also from parachor model we obtain an lowest percentage errors just for [Cnmim][NTf2] + [Cnmim][NTf2] binary mixtures. As a whole, the HSEG model is a good model to theoretical study of surface tension of ionic liquid solution. The present method predicts the surface tension with mean percentage errors of 5.18 %, whereas Xu et al.15 predicted the surface tension of ionic liquids−organic solvent binary systems using a modified Hildebrand−Scott equation with percentage errors of 1.06 % for the limited number of ionic liquid binary mixtures. Oliveira et al. predict15 the surface tension of binary mixtures of 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids. But deviation values between experimental and theoretical data have not been in the mentioned paper, and only good accordance between experimental and theoretical data has been reported. D



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[HMIM][NTf2]

1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [OMIM][NTf2] 1-octyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [DMIM][NTf2] 1-decyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide [C8Quin][NTF2] N-octylisoquinoliniumbis{(trifluoromethyl)sulfonyl}imide [MOIM][BF4] 1-octyl-3-methyl imidazolium tetrafluoroborate [EMIM][CH3SO4] 1-ethyl-3-methylimidazolium methyl sulfate [MMIM][CH3SO4] 1-methyl-3-methylimidazolium methyl sulfate [EMIM][NO3] 1-ethtyl-3-methylimidazolium nitrate [C6H13OCH2MIM][Bf4] 1,3-dihexyloxymethylimidazolium bis{(trifluoromethyl)sulfonyl}imide [C3mpyr][NTf2] 1-methyl-1-propylpyrrolidinium bis(trifluoromethylsulfonyl)imide [C3mpip][NTf2] 1-methyl-1-propylpiperidinium bis(trifluoromethylsulfonyl)imide [C3mpyr][NTf2] 3-methyl-1-propylpyridinium bis(trifluoromethylsulfonyl)imide [C4C1mim][NTf2] 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide [BMIM][BF4] 1-butyl-3-methylimidazolium tetrafluoroborate [EMIM][BF4] 1-ethyl-3-methylimidazolium tetrafluoroborate [HMIM][BF4] 1-hexyl-3-methylimidazolium tetrafluoroborate [BMIM][L-lactate] 1-ethyl-3-methylimidazolium L (+)-lactate [(C6H13OCH2)2IM][BF4] 1 , 3 - d i h e x y l o x y m e t h y l imidazoliumbis(trifluoromethylsulfonyl)-imide A̅ partial molar surface area M molecular weight Np number of data points R gas constant (8.3145 J·mol−1·K−1) x2b mole fraction a−f constant parameters in eqs 1,2 AT−DT constant parameters in eq 5 AP−DP constant parameters in eq 6 P*c assumed-critical pressure (kPa) T*c assumed-critical temperature (K) Tc critical temperature Tb boiling temperature M molecular weight of component VC critical volume of component n number of groups ΔVc critical volume of each group ΔTb boiling temperature of each group ΔTc critical temperature of each group A, B, and D constants in eq 5 a, b, c, and d system independent constants in eqs 8 and 9

Figure 5. Experimental and predicted surface tension of [C4mim][NTf2] (1) + [C2mim][NTf2] (2) against the molar fraction of the first component, x1. Black continuous line, experimental surface tension; ▲, HSEG model; □, CSGC-ST model; ○, parachor model.

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CONCLUSION Surface tension of ionic liquid binary mixtures have been calculated using CSGC models (predicting surface tensions using the corresponding-states group-contribution method), HSEG model, and parachor model. Critical parameters, density and surface tension of the pure component, are used to calculate these predictions. The mean standard relative error obtained from the comparison of experimental and calculated surface tension values for studied ionic liquid binary mixtures are given using the HSEG equation in the present work.

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ASSOCIATED CONTENT

S Supporting Information *

Comparisons of the experimental and calculated surface tension by studied models in this work for ionic liquid binary mixtures. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

* E-mail: [email protected] and [email protected]. Fax: ++98-841-2227022. Funding

The authors are grateful for the support from the Research Councils of Ilam University. Notes

The authors declare no competing financial interest.

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ABBREVIATIONS [MMIM][NTf2] [EMIM][NTf2] [BMIM][NTf2] [PMIM][NTf2]

1,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide 1-pentyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide

Greek Letters

σ surface tension ρ density Subscripts

1 solvent E



Article

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2 solute B bulk phase S surface phase

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REFERENCES

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Surface Tension Prediction of Ionic Liquid Binary Solutions - American

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