Estimation of Surface Tension of Ionic LiquidâCosolvent Binary

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Estimation of Surface Tension of Ionic Liquid−Cosolvent Binary Mixtures by a Modified Hildebrand−Scott Equation Yingjie Xu,* Hongye Zhu, and Lulu Yang Department of Chemistry, Shaoxing University, Shaoxing, Zhejiang 312000, China ABSTRACT: The correlation model of gas−liquid interfacial tension (surface tension) of nonaqueous mixtures containing ionic liquids (ILs) is still in its infancy. The purpose of this work is to develop a modified Hildebrand−Scott equation based on local composition concept and the group surface area parameters of UNIFAC model as well as to evaluate the capability of this model. The surface tension of 33 IL− cosolvent binary systems were correlated by the modified Hildebrand−Scott equation with two energy parameters and an overall average relative deviation of only 0.92%. The ILs in the study included imidazolium-based, pyridinium-based, and isoquinolinium-based ones, and the cosolvents included methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, acetonitrile, and tetrahydrofuran. Using the energy parameters obtained from the surface tension of a given IL−cosolvent binary system at 298.15 K, the surface tension of the same system at other different temperatures was predicted by the modified Hildebrand−Scott equation, with an overall average relative deviation of 1.06%.

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INTRODUTION Ionic liquids (ILs) are organic salts with a melting point below a conventional temperature of 373.15 K. Due to their unique thermophysical properties, such as negligible vapor pressure, high thermal stability, and excellent solubility for polar or nonpolar substances, they have been used widely in chemical processing,1 catalytic reactions,2,3 and separation processes.4 The interest in their thermophysical properties and applications are still growing. Among the many unique properties of ILs, their surface tension which is the main property of any liquid−gas interface plays a special role in several industrial processes for different reasons.5,6 For example, the low vapor pressures of ILs can influence their surface tension, thereby determining mass transfer processes like distillation, absorption, separation, and extraction. In the past decade, most of the experimental methods commonly used to determine the surface tension of conventional liquids have been applied to pure ILs and mixtures containing ILs, and the corresponding works have been reported. Recently, Tariq and co-workers gave a critical assessment of the available literature on the subject of surface tension of pure ILs and mixtures containing ILs, and the different experimental methods used to determine the surface tension are presented and critically discussed.6 Besides the direct measurement methods to obtain the surface tension of pure ILs and mixtures containing ILs, the estimation or prediction method is another important approach, which is of engineering interest and physicochemical interest. Therefore, there are a few models available for estimation of surface tension of pure ILs in the recent literature, including parachors methods,7−9 group contribution methods,10,11 and corresponding state theory.12 However, the estimation method for surface © XXXX American Chemical Society

tension of IL−cosolvent mixtures is extremely rare, even though the ILs to be treated in the chemical industry are usually coexisting with other cosolvents. To better understand the influence of the cosolvents on the surface tension of ILs, it is necessary to estimate or correlate the surface tension of IL− cosolvent mixtures using some semitheoretical models. When comparing the surface tension of IL−cosolvent mixtures and conventional liquid mixtures, there may be an obvious difference because of the ionic nature of ILs, which exhibit low vapor pressures even at conditions well above the ambient temperatures.6 According to the literature,13 the methods for calculating the surface tension of the conventional liquid mixtures can be divided into two categories: those based on empirical relations and those derived from thermodynamics. Some thermodynamics-based equations have been developed to calculate the surface tension of the conventional liquid mixtures, such as the Butler type equation,14 the Eberhart equation,15 the Hildebrand−Scott equation,16 the Sprow− Prausnitz equation,17 the Fu−Wang equation,18 the Li−Wang equation,19 etc. For example, Fu et al.18 developed an equation by modifying the Hildebrand−Scott equation for ideal binary systems with the local composition concept proposed by Wilson.20 To improve usability, they had the local area fractions instead of the area fractions of the original Hildebrand−Scott equation and assumed that the numerical value of the dimensionless group was equal to unity. The Fu−Wang equation was used to correlate the surface tension data of 251 binary systems and 14 ternary systems including polar Received: April 8, 2013 Accepted: July 9, 2013

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dx.doi.org/10.1021/je400331r | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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surface tension of ideal systems. For the IL−cosolvent mixtures, there exist significant interactions between the components such as hydrogen bonding and electrostatic interactions, which can affect the surface tension of system.6 To better investigate the surface tension of IL−cosolvent mixtures, the local composition concept is introduced in the present work, which is proposed by Wilson to describe the microscopic solution structure and extensively used to correlate vapor− liquid equilibrium data of ideal and nonideal solution mixtures.20,27,28 According to Wilson’s local composition concept for a binary mixture, the ratios of the probability of finding the molecule j around the central molecule i can be defined in terms of bulk mole fractions xj and xi and interaction energies between i−j pair gji and i−i pair gii shown below:20,27

mixtures with hydrogen bonding, organic, inorganic, aqueous, nonaqueous, and fused salt mixtures.18 The correlation results showed that the Fu−Wang equation could be applied to a much larger variety of systems. These results suggest that surface tension calculations may also be enhanced when applying the Fu−Wang equation to IL−cosolvent mixtures. However, it is difficult to obtain the molar cross-sectional area of ILs, which is an essential component of the Fu−Wang equation. Moreover, the numerical value of the dimensionless group of IL−cosolvent mixtures is not always equal to unity because of the notable difference in the shape of the molecule between ILs and cosolvent. Therefore, there may be some inaccuracies if the Fu−Wang equation is applied directly to correlate the surface tension of IL−cosolvent mixtures. In fact, results of previous research indicated that the numerical value of the molar cross-sectional area could affect the surface tension of systems.21 Recently, the original and modified UNIFAC models for ILs have been applied to predict the thermodynamic properties of IL−cosolvent mixtures, using the surface area parameters of subgroups of ILs obtained by correlating the experimental activity coefficients of the cosolvents at infinite dilution in ILs or vapor−liquid equilibria data of IL−cosolvent mixtures at different temperatures.22−26 The results provide us some suggestions on how to obtain the molar cross-sectional area of IL−cosolvent mixtures based on the surface area parameters of UNIFAC model. Therefore, the purpose of this work is to develop a modified Hildebrand−Scott equation based on local composition concept and the surface area parameters of UNIFAC model to describe the surface tension of IL−cosolvent mixtures. The modified Hildebrand−Scott equation presented in this work considers the effect of the interactions as well as differences of the molar cross-sectional area of IL−cosolvent mixtures and has two energy parameters representing the interactions between IL and cosolvent. The surface tension data of 33 IL−cosolvent binary mixtures reported in the literature at different temperatures were correlated to evaluate the capability of this model with two energy parameters. Furthermore, supposing the energy parameters were not significantly affected by temperature, the surface tension of the same binary system at different temperatures was predicted through this model.

xji xii

θii =

xiAi xiAi + xjAj

(3)

Ai xii Ai xii + Aj xji

(4)

Aki /m 2·mol−1 = 2.5 × 105∑ vk , iQ k = 2.5 × 105qi k

(5)

where vk,i is the number of groups of type k in molecule i and qi is the surface area parameter of the pure component. The group surface area parameter Qk of UNIFAC model for pure ILs and cosolvents can be obtained from the literature;25,26,29,31 hence, the van der Waals area Aki and surface area parameter qi of the pure components can also be obtained. Based on the UNIFAC model and using the group surface area parameters Qk of ILs obtained by correlating the experimental activity coefficients of the cosolvents at infinite dilution in ILs, Lei et al. successfully predicted the vapor−liquid equilibria of systems with ILs at finite concentration and screened suitable ILs as entrainer in separation processes recently.25,26 The above-mentioned results sufficiently show that the group surface area parameters Qk of ILs are effective. Therefore, in the present work, we have the van der Waals area Aki instead of the molar cross-sectional area Ai of pure substances. Substituting eqs 3 and 5 into eq 4 and the definition of Λji as below qj Λji = exp[− (gji − gii)/RT ] qi (6)

(1)

where σ1, σ2, and σm are surface tensions of pure substances 1, 2, and their mixtures, respectively. A1 and A2 are the molar cross-sectional areas of pure substances 1 and 2, respectively. y1 and y2 are area fractions of pure substances 1 and 2, respectively, which can be defined by following expression: yi =

xi exp( −gii /RT )

According to the literature, the relationship between the van der Waals area of molecule i Aki and group surface area parameter Qk of the UNIFAC model can be written as29,30

THEORY SECTION According to the Hildebrand−Scott equation, surface tension of binary mixture can be expressed as follows:16 (σ1 − σ2)2 (y1A 2 + y2 A1)y1y2 2RT

xi exp( −gji /RT )

where xii and xji denote the local mole fraction of molecules i and j around the central molecule i, respectively. Replacing mole fraction xi and xj in eq 2 by local composition xii and xji, respectively, the area fraction yi can be transformed into the local surface area fraction θii

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σm = y1σ1 + y2 σ2 −

=

(2)

then the original eq 4 can be rewritten as xi θii = xi + xj Λji

Although the differences in the sizes of the molecules have been taken into consideration in the original Hildebrand−Scott equation, the interactions between the components as well as the differences between the bulk and local surface concentration have not been mentioned. Therefore, the original Hildebrand−Scott equation is mainly applied to describe the

(7)

Replacing the area fraction yi in eq 1 by the local surface area fraction θii, then the resultant equation of the surface tension of the IL−cosolvent binary mixture can be given by B



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Table 1. Correlation Results of Surface Tension for IL−Cosolvent Binary Mixtures T/K

systems 32

[C2mim]BF4 (1) + ethanol (2) [C4mim]BF4 (1) + ethanol (2)32 [C6mim]BF4 (1) + ethanol (2)32 [C8mim]BF4 (1) + ethanol (2)32 [C1mim]CH3SO4 (1) + methanol (2)33 [C1mim]CH3SO4 (1) + ethanol (2)33 [C1mim]CH3SO4 (1) + 1-butanol (2)33 [C4mim]CH3SO4 (1) + methanol (2)33 [C4mim]CH3SO4 (1) + ethanol (2)33 [C4mim]CH3SO4 (1) + 1-butanol (2)33 [C4mim]OcSO4 (1) + methanol (2)33 [C4mim]OcSO4 (1) + 1-butanol (2)33 [C2mim]NTf2 (1) + THF (2)34

[C2mim]NTf2 (1) + acetonitrile (2)34

[C8iQuin]NTf2 (1) + 1-hexanol (2)35

[C4mim]NTf2 (1) + 1-propanol (2)36 [C4mim]NTf2 (1) + 1-butanol (2)36 [C2mim]EtSO4 (1) + ethanol (2)37 [C2mim]BuSO4 (1) + ethanol (2)37 [C2mim]HeSO4 (1) + ethanol (2)37 [C2mim]OcSO4 (1) + ethanol (2)37 [C8py]NO3 (1) + 1-butanol (2)38 [C8py]NO3 (1) + ethanol (2)38 [C8py]NO3 (1) + methanol (2)38 [C2mim]CH3SO4 (1) + methanol (2)39 [C2mim]CH3SO4 (1) + ethanol (2)39 [C2mim]CH3SO4 (1) + 1-butanol (2)39 [C2mim]EtSO4 (1) + ethanol (2)40 [C4mim]SCN (1) + 1-pentanol (2)41

[C4mim]SCN (1) + 1-butanol (2)41

[C4mim]SCN (1) + 1-hexanol (2)41

[C2mim]NO3 (1) + methanol (2)42 [C2mim]NO3 (1) + ethanol (2)42 total

σm = θ11σ1 + θ22σ2 −

(g21−g11)/J·mol−1 −3155.8 −3589.0 −2669.0 −3153.0 −2059.0 −4561.9 −5858.8 −2709.4 −4404.3 −7067.7 −3036.9 −10926.8 −1813.3 −1809.3 −1133.2 −837.6 −173.7 −1260.0 −518.5 −534.6 −548.5 −992.3 −777.1 −1067.7 −1383.3 −1644.2 −3974.8 −3425.5 −2548.5 491.3 −4482.1 −2431.1 −73.1 −1885.7 −4297.8 −6212.5 −2591.7 −5476.7 −5307.3 −5198.1 −5061.1 −4814.4 −4757.5 −4634.3 −4469.2 −4156.4 −3267.9 −6525.4 −6284.2 −6003.0 −6056.6 −5923.9 −1355.4 −4354.9

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 293.15 298.15 303.15 308.15 293.15 298.15 303.15 308.15 313.15 298.15 308.15 318.15 298 298 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 293.15 298.15 308.15 318.15 328.15 338.15 298.15 308.15 318.15 328.15 338.15 298.15 308.15 318.15 328.15 338.15 298.15 298.15

(σ1 − σ2)2 (θ11Ak 2 + θ22Ak1)θ11θ22 2RT

(g12−g22)/J·mol−1 379.3 2138.4 1821.3 3161.4 578.6 1337.6 2399.1 2694.9 3175.5 4964.4 3042.2 10932.9 1820.3 1818.6 926.4 512.0 176.8 1487.3 579.0 573.9 571.1 96.4 −144.4 109.1 516.5 353.9 4024.2 3457.0 2568.7 −1099.2 4496.9 2440.3 79.1 1974.8 5619.2 6269.5 1692.9 5518.6 5353.8 5249.6 5116.5 4876.5 4804.6 4485.0 4523.8 4214.1 2439.7 6570.5 6330.2 6052.4 6107.6 5981.2 17.4 5084,6

ARD 0.34 0.61 0.30 0.62 0.42 5.20 5.64 0.50 1.24 1.23 0.50 0.48 0.16 0.11 0.09 0.10 0.04 0.04 0.10 0.07 0.10 0.54 0.81 0.61 0.65 1.03 0.49 0.97 0.89 0.22 2.61 3.51 1.20 0.46 1.57 2.82 1.68 0.71 0.63 0.62 0.51 0.79 1.12 0.92 0.58 0.38 0.67 0.36 0.54 1.03 0.63 0.68 0.84 0.47 0.92

AAD/mN·m−1 0.14 0.17 0.09 0.17 0.16 1.68 1.90 0.16 0.30 0.32 0.13 0.12 0.05 0.04 0.03 0.03 0.01 0.01 0.04 0.02 0.04 0.16 0.22 0.17 0.18 0.27 0.17 0.29 0.24 0.06 0.72 1.05 0.38 0.16 0.51 0.86 0.47 0.23 0.20 0.18 0.15 0.23 0.35 0.28 0.16 0.10 0.20 0.11 0.16 0.29 0.18 0.18 0.35 0.19 0.28

where Ak1 and Ak2 are the van der Waals areas of pure substances 1 and 2, respectively, which can be calculated from eq 5. As can be seen from eq 8, there are two energy parameters, (g21−g11) and (g12−g22), which have definite

(8)

C



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physical significance and denote interaction energies in the IL− cosolvent mixture. Therefore, the relationships between the surface tension and composition of IL−cosolvent binary mixtures are established by modifying the Hildebrand−Scott equation based on the local composition and the group surface area parameters Qk of UNIFAC model.

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RESULTS AND DISCUSSION Correlation of Surface Tension for IL−Cosolvent Binary Mixtures. The concentration-dependent surface tension of IL−cosolvent binary mixtures can be correlated through eq 8 with two energy parameters, (g21−g11) and (g12− g22), which can be obtained using the least-squares fitting method when the following function is a minimum: ⎡ 1 O.F. = ⎢ ⎢m − 2 ⎣

⎛ σm,cal − σm,exp ⎞2 ⎤ ⎟⎟ ⎥ ∑ ⎜⎜ σ ⎝ ⎠ ⎥⎦ m ,exp i=1

Figure 1. Comparison of the correlated and experimental surface tension from the literature for [C8iQuin]NTf2 (1) + 1-hexanol (2) system35 at different temperatures: □, 298.15 K; Δ, 308.15 K; ▽, 318.15 K. The symbols represent experimental values, and the solid curves represent the values calculated from the eq 8.

1/2

m

(9)

where m is the number of experimental surface tension data, σm,cal is the calculated surface tension according to eq 8, and σm,exp is the experimental surface tension. In this work, the experimental surface tensions of 33 nonaqueous binary mixtures containing ILs over the whole concentration range at different temperatures available in the literature were collected, which was determined by different methods, such as capillary rise and pendant drop, du Noüy ring and Wilhelmy plate, drop weight/volume, maximum bubble pressure, etc. The uncertainty of the measurements can be found in the corresponding literatures. The ILs in the studied systems included imidazolium-based, pyridinium-based, and isoquinolinium-based, and the cosolvents included methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, acetonitrile, and tetrahydrofuran (THF). Performance of eq 8 for calculating the surface tension of IL−cosolvent binary mixtures have been extensively tested with the above-mentioned systems. The energy parameters, (g21−g11) and (g12−g22), average relative deviation (ARD) and average absolute deviation (AAD) between the experimental and calculated values are shown in Table 1, in which ARD and AAD are defined respectively as below ARD =

AAD =

100 % m

1 m

m

∑ i=1

Figure 2. Comparison of the correlated and experimental surface tension from the literature for 1-ethyl-3-methyl imidazolium alkyl sulfate (1)+ethanol (2) systems37 at 298.15 K: □, [C2mim]EtSO4 (1) + ethanol (2) system; Δ, [C2mim]BuSO4 (1) + ethanol (2) system; ▽, [C2mim]HeSO4 (1) + ethanol (2) system; ○, [C2mim]OcSO4 (1) + ethanol (2) system. The symbols represent experimental values, and the solid curves represent the values calculated from the eq 8.

|σm,cal − σm,exp| σm,exp

(10)

m

∑ |σm,cal − σm,exp| i=1

(11)

It can be seen from Table 1 that the eq 8 gives good correlation results of the surface tension data for 33 IL− cosolvent binary systems, with an overall ARD of only 0.92 %, as well as an overall AAD of only 0.28 mN·m−1. Figures 1−3 show three examples of the correlation results for Noctylisoquinolinium bis{(trifluoromethyl)sulfonyl}imide ([C8iQuin][NTf2]) (1) + 1-hexanol (2) system, 1-ethyl-3methylimidazolium alkyl sulfate (1) + ethanol (2) system, and 1-ethyl-3-methyl imidazolium nitrate ([C2mim]NO3) (1) + alcohol (2) system, respectively. As can be seen from Figures 1−3, the experimental and calculated values are in good agreement. It is also clear from Figure 1 that the eq 8 can be applied to correlate concentration-dependent surface tension of IL−cosolvent binary mixtures, even of the systems with a turning point on the plot of surface tension versus mole

Figure 3. Comparison of the correlated and experimental surface tension from the literature for [C2mim]NO3 (1) + alcohol (2) systems42 at 298.15 K: □, [C2mim]NO3 (1) + methanol (2) system; Δ, [C2mim]NO3 (1) + ethanol (2) system. The symbols represent experimental values, and the solid curves represent the values calculated from the eq 8.

fraction. According to the correlation results listed in Table 1, the modified Hildebrand−Scott equation presented in this work could facilitate the estimation of surface tension of these IL−cosolvent systems. Prediction of Surface Tension for IL−Cosolvent Binary Mixtures. As can be seen from Table 1, all of the correlations D



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be 1.06 %. The comparison between the predicted and experimental data of surface tension for 1-ethyl-3-methylimidazolium bis[(trifluoromethylsulfonyl]imide ([C2mim]NTf2) (1) + acetonitrile (2) system and [C8iQuin][NTf2]) (1) + 1-hexanol (2) system is shown in Figures 4 and 5, respectively. As a whole, the accuracy of the prediction of the eq 8 is acceptable, and it can be applied to a certain temperature range.

for IL−cosolvent binary systems are determined at a specified temperature. Although molecular energy must be a function of temperature, the difference in the energy parameters of eq 8, (g21−g11) and (g12−g22), may not be much affected by temperature if the temperature range covered is not very large. This treatment method of the model parameters is analogous to that in the Wilson equation20 used to calculate vapor−liquid equilibria data and that in Li-Wang equation.19 By comparing the values of energy parameters for a given system at different temperature listed in Table 1, It can be found that the difference in the energy parameters is not obvious for most systems. Therefore, supposing energy parameters (g21−g11) and (g12−g22) do not significantly affect by temperature, and then the surface tension of the IL−cosolvent binary mixture at another temperature can be predicted using the energy parameters obtained at a definite temperature through the eq 8. For example, using the energy parameters for the [C8iQuin][NTf2]) (1) + 1-hexanol (2) system obtained by correlating the surface tension at 298.15 K, the surface tension of the same system at (308.15 and 318.15) K can be predicted through eq 8. To evaluate the performance of the energy parameters in accounting for the temperature dependence of the surface tension of IL−cosolvent binary mixtures, the surface tension of 6 IL−cosolvent binary systems are predicted, and the corresponding results are listed in Table 2. The energy parameters used to predict the surface tension were obtained from the surface tension data at 298.15 K, which were listed in Table 1. It is shown that eq 8 can satisfactorily represent the variation of surface tension with temperature for the studied IL−cosolvent binary systems, and an overall ARD is found to

Figure 4. Comparison of the predicted surface tension by energy parameters obtained at 298.15 K and experimental surface tension form the literature for [C2mim]NTf2 (1) + acetonitrile (2) system34 at different temperatures: □, 293.15 K; Δ, 303.15 K; ▽, 308.15 K; ○, 313.15 K. The symbols represent experimental values, and the solid curves represent the values predicted from the eq 8.

Table 2. Surface Tension Prediction of IL−Cosolvent Binary Mixtures at Other Temperatures systems [C2mim]NTf2 (1) + THF (2)

34

T1a/K

T2b/K

298.15

293.15 303.15 308.15 293.15 303.15 308.15 313.15 308.15 318.15 308.15 318.15 328.15 338.15 308.15 318.15 328.15 338.15 308.15 318.15 328.15 338.15

[C2mim]NTf2 (1) + acetonitrile (2)34

298.15

[C8iQuin]NTf2 (1) + 1-hexanol (2)35

298.15

[C4mim]SCN (1) + 1-pentanol (2)41

298.15

[C4mim]SCN (1) + 1-butanol (2)41

298.15

[C4mim]SCN (1) + 1-hexanol (2)41

298.15

total

ARD1c ARD2d 0.16 0.09 0.10 0.04 0.10 0.07 0.10 0.81 0.61 0.63 0.62 0.51 0.79 0.92 0.58 0.38 0.67 0.54 1.03 0.63 0.68 0.48

0.17 0.22 0.33 0.17 0.20 0.13 0.13 0.82 0.69 0.81 1.13 1.54 2.58 0.94 1.21 2.22 2.61 0.84 1.95 1.55 1.99 1.06

Figure 5. Comparison of the predicted surface tension by energy parameters obtained at 298.15 K and experimental surface tension from the literature for the [C8iQuin]NTf2 (1) + 1-hexanol (2) system35 at different temperatures: □, 308.15 K; Δ, 313.15 K. The symbols represent experimental values, and the solid curves represent the values predicted from the eq 8.

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CONCLUSIONS Based on the concept of local composition and the group surface area parameters of the UNIFAC model, a modified Hildebrand−Scott equation is proposed and used to correlate the concentration-dependent surface tension of 33 IL− cosolvent binary systems with two energy parameters, and the overall ARD for the correlation is 0.92 %. Using the energy parameters obtained from the surface tension of IL−cosolvent binary system at 298.15 K, the surface tensions of the same system at other temperatures have been predicted through the modified Hildebrand−Scott equation with good accuracy, indicating that the present model is able to account for the temperature-dependent surface tension of the IL−cosolvent binary system.

a

The energy parameters were obtained by correlating experimental surface tension at this temperature. bThe surface tension was predicted at this temperature. cARD1 refers to the average relative deviations for the correlation with eq 8. dARD2 refers to the average relative deviations for the prediction. E



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +86-575-88341521. Funding

The authors are grateful to the National Natural Science Foundation of Zhejiang Province (No. Y4090453) for financial support. Notes

The authors declare no competing financial interest.

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Article

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