Density and Refractive Index of Binary Mixtures of Two 1-Alkyl-3

Article pubs.acs.org/jced

Density and Refractive Index of Binary Mixtures of Two 1‑Alkyl-3-methylimidazolium Ionic Liquids with 1,4-Dioxane and Ethylene Glycol Oana Ciocirlan,*,† Oana Croitoru,† and Olga Iulian† †

Department of Inorganic Chemistry, Physical Chemistry and Electrochemistry, Politehnica University of Bucharest, 1-7 Gh. Polizu Street, 011061 Bucharest, Romania ABSTRACT: This paper reports experimental data of density and refractive index for the binary systems of 1-butyl-3-methylimidazolium tetrafluoroborate, [Bmim][BF4], with 1,4-dioxane, and 1-ethyl-3-methylimidazolium tetrafluoroborate, [Emim][BF4], with 1,4-dioxane and ethylene glycol (EG). Moreover, for the system [Bmim][BF4] + EG we report here refractive index data. The measurements for the systems with EG were made over the entire composition range at atmospheric pressure (101 ± 2 kPa) and in the temperature range from (293.15 to 353.15) K for densities and from (298.15 to 323.15) K for refractive indices. Because at room temperature the mixtures of both ionic liquids with 1,4-dioxane have indicated partial immiscibility, liquid−liquid phase equilibrium was determined. The excess molar volumes, VE, and deviations in refractive index, Δn, were calculated by using the measured experimental data and correlated by the Redlich−Kister type equations. VE values are positive for the system with EG and negative for both systems with 1,4-dioxane, Δn presenting an opposite sign. To probe the interactions in mixtures and to correlate the excess molar volumes of the mixtures the Prigogine−Flory−Patterson (PFP) theory has been used. Moreover, to correlate VE and predict density and refractive index of the mixtures the Lorentz− Lorenz equation was applied.

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INTRODUCTION Ionic liquids (ILs) are a special kind of organic salts, liquids at room temperature and with voluminous cations commonly derived from quaternary ammonium groups like imidazolium, pyridinium, pyrrolidinium. Owing to their ionic character, very small vapor pressures, and unique physicochemical properties, ILs are studied as possible substitutes for organic solvents in different fields, both in pure state or in mixtures. ILs have been already successfully employed as solvents for applications in electrochemistry, biotechnology, materials chemistry, nanotechnology, polymer science, and organic and inorganic synthesis.1−4 1,4-Dioxane and ethylene glycol (EG) are important organic solvents with many uses in industrial applications. Studies of the mixtures of ILs and 1,4-dioxane are less reported in the literature; we found some studies concerning activity coefficients at infinite dilution in the ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate.5 Because of partial immiscibility of the investigated binary systems of ILs with 1,4-dioxane they can be considered for use in extraction/separation processes. The binary mixtures of ILs and EG can serve as thermal fluids, with properties better than that of pure components, and can be used in various chemical processes; a few studies are reported in the literature concerning the physicochemical properties of mixtures of ILs with EG.6−10 In this work, the densities and refractive indices data for the binary systems of 1-butyl-3-methylimidazolium tetrafluoroborate, © 2014 American Chemical Society

[Bmim][BF4], with 1,4-dioxane, and 1-ethyl-3-methylimidazolium tetrafluoroborate, [Emim][BF4], with 1,4-dioxane and ethylene glycol (EG) were reported. For the [Bmim][BF4] + EG system we have added here refractive index data. The excess molar volumes, VE, and deviations in refractive index, Δn, were calculated by using the measured experimental data and correlated by the Redlich−Kister type equations. Moreover, correlation of excess molar volume and prediction of density and refractive index by using the Lorentz−Lorenz equation have been done. Because of the existence of partial immiscibility for the binary systems [Bmim][BF4] + 1,4-dioxane and [Emim][BF4] + 1,4-dioxane, the liquid−liquid phase equilibrium was determined. This work is a continuation of our previous investigations on the thermodynamic properties of ILs with organic solvents.10−12 Since our last investigation, no volumetric and refractive index data have become available in literature for the binary systems [Bmim][BF4] + 1,4-dioxane, [Emim][BF4] + 1,4dioxane, and [Emim][BF4] + EG. The volumetric properties of the [Bmim][BF4] +EG system were studied by some authors7,8 and by us;10 therefore, for this system refractive indices data only at 298.15 K and at atmospheric pressure are reported.7,8 Received: July 16, 2013 Accepted: March 13, 2014 Published: March 21, 2014 1165

dx.doi.org/10.1021/je400659p | J. Chem. Eng. Data 2014, 59, 1165−1174

Journal of Chemical & Engineering Data

Article

Table 2. Comparison of Measured Densities and Refractive Indices with Literature Values for Pure Components at T = (298.15 and 323.15) K ρ/g·cm−3 component [Bmim] [BF4]

Figure 1. Liquid−liquid phase equilibria in the binary systems of [Bmim][BF4] + 1,4-dioxane (△) and [Emim][BF4] + 1,4-dioxane (◇). The lines are given only as guides to eye.

Table 1. Liquid−Liquid (Cloud-Points) Phase Boundaries (T(K)) at Atmospheric Pressure (101 ± 2 kPa) for the Studied [Bmim][BF4] (1) + 1,4-Dioxane (2) and [Emim][BF4] (1) + 1,4-Dioxane (2) Binary Systemsa system

x1

T/K

[Bmim][BF4] + 1,4-dioxane

0.1452 0.1591 0.1806 0.1830 0.1897 0.2201 0.2332 0.2380 0.2450

293.2 310.2 338.2 347.2 293.2 314.2 329.2 343.2 353.2

[Emim][BF4] + 1,4-dioxane

[Emim] [BF4]

1,4-dioxane

a

Expanded uncertainty (k = 2) in temperature was U(T) = 2.0 K and uncertainty in mole fractions was 0.0002.

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EG

EXPERIMENTAL SECTION Materials. The ionic liquids were 1-ethyl-3-methylimidazolium tetrafluoroborate (mass fraction > 0.98) from Sigma Aldrich and 1-butyl-3-methylimidazolium tetrafluoroborate (mass fraction > 0.99) from Merck. The organic solvents 1,4-dioxane (mass fraction > 0.99) and ethylene glycol (mass fraction > 0.995) were supplied by Merck and were stored overnight on 3A molecular sieves to remove the water traces. Because of the ionic liquids hygroscopicity they were treated for about 11 h at 333 K in vacuum. Then they were manipulated under nitrogen atmosphere to avoid any contact with the atmosphere. Afterward we used a Schlenk tube and syringes equipped with a Luer Lock valve to prepare the binary mixtures and to load them into the apparatus. Apparatus and Procedure. The binary mixtures of ILs with 1,4-dioxane or EG were prepared by mass on a HR-120 (A&D Japan) electronic balance, precision of ± 10−4 g. The experimental uncertainty in mole fractions did not exceed ± 0.0002. Measurement of Density. The densities of the pure ionic liquids and of binary mixtures with organic solvents were measured with an Anton Paar DMA 4500 densimeter, the precision of measurements being ± 0.05 kg·m−3. The thermostatted sample was controlled to ± 0.01 K. The densimeter

T/K

exptl

298.15

1.20089

303.15

1.19734

313.15

1.19027

323.15

1.18324

298.15

1.28682

303.15

1.28302

313.15

1.27545

323.15

1.26797

298.15

1.02792

303.15

1.02227

313.15 323.15 298.15

1.01091 0.99949 1.10996

303.15

1.10645

313.15

1.09938

n lit.

1.20127 1.201418 1.2012918 1.2010019 1.2013420 1.1975518 1.1976019 1.197422 1.1906818 1.1908019 1.190122 1.1836718 1.1840019 1.182722 1.282323 1.2855124 1.278723 1.2817424 1.271423 1.2741724 1.264223 1.2666924 1.0277225 1.0281226 1.028627 1.0222326 1.0227129 1.0113229 0.9991229 1.11007 1.10995530 1.1054631 1.1066332 1.0983531 1.0996432

exptl 1.4215

lit. 1.42087 1.421920 1.419721

1.4202

1.420620 1.418121

1.4179

1.415521

1.4153

1.413221

1.4111

1.410923

1.4100

1.409823

1.4073 1.4051 1.4205

1.4171 1.4112 1.4063 1.4300

1.4199926 1.420327 1.420328 1.4177126

1.4285

1.43047,8,30 1.431031 1.428731

1.4258

1.425431

included an automatic viscosity correction. The U-cell of apparatus was calibrated with dry air and ultrapure water at atmospheric pressure. The uncertainty in the density measurement is ± 5·10−5 g·cm−3 and for the excess molar volume calculation, about ± 10−2 cm3·mol−1. Measurement of Refractive Index. Refractive indices values for the D-line, n, were measured with an Abbe refractometer with a precision of ± 0.0001, connected to a thermostat maintained at ± 0.05 K. Liquid−liquid Phase Equilibria. In this work a dynamic (synthetic) method for the liquid−liquid phase equilibria determination was used. Solubility measurements have been done at atmospheric pressure and in the temperature range 293.15 K to 353.15 K using a cloud-point methodvisual observation of the turbidity that accompanies phase separation. The measurements were made into a double-walled glass cell connected to a temperature-controlled thermostatic bath, with an accuracy of ± 0.1 K, a similar procedure being used previously.13 The mixtures of known composition were heated 1166



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Table 3. Experimental Densities for the Binary Systems [Bmim][BF4] + 1,4-Dioxane, [Emim][BF4] + 1,4-Dioxane, and [Emim][BF4] + EG at Different Temperatures and Atmospheric Pressure of 101 kPaa ρ/g·cm−3 x1

a

T/K = 293.15

T/K = 298.15

0.0000 0.2559 0.3956 0.4988 0.6000 0.7021 0.8993 1.0000

1.03357 1.11875 1.14631 1.16137 1.17310 1.18304 1.19809 1.20444

1.02792 1.11431 1.14223 1.15744 1.16926 1.17930 1.19453 1.20089

0.0000 0.3292 0.4547 0.4923 0.6409 0.6838 0.7851 0.8336 1.0000

1.03357 1.17162 1.20347 1.21184 1.24074 1.24689 1.26350 1.27018 1.29063

1.02792 1.16726 1.19931 1.20773 1.23677 1.24294 1.25961 1.26632 1.28682

0.0000 0.1249 0.2084 0.3046 0.4124 0.4763 0.5565 0.7170 0.7826 0.9010 1.0000

1.11345 1.16163 1.18410 1.20575 1.22493 1.23472 1.24569 1.26434 1.27114 1.28220 1.29063

1.10996 1.15785 1.18023 1.20179 1.22094 1.23074 1.24172 1.26043 1.26725 1.27835 1.28682

T/K = 303.15

T/K = 313.15

T/K = 323.15

T/K = 333.15

T/K = 343.15

T/K = 353.15

0.98797 1.08347 1.11385 1.13018 1.14279 1.15344 1.16960 1.17625

0.97637 1.07465 1.10580 1.12247 1.13531 1.14614 1.16253 1.16932

0.96463 1.06580 1.09777 1.11480 1.12787 1.13889 1.15557 1.16244

0.98797 1.13698 1.17056 1.17933 1.20933 1.21568 1.23277 1.23964 1.26055

0.97637 1.12837 1.16244 1.17131 1.20162 1.20802 1.22524 1.23215 1.25318

0.96463 1.12041 1.15435 1.16332 1.19395 1.20041 1.21775 1.22541 1.24587

1.08500 1.13139 1.15319 1.17439 1.19347 1.20336 1.21449 1.23360 1.24056 1.25189 1.26055

1.07765 1.12378 1.14548 1.16665 1.18576 1.19568 1.20688 1.22611 1.23311 1.24449 1.25318

1.07017 1.11615 1.13777 1.15894 1.17810 1.18807 1.19933 1.21868 1.22573 1.23716 1.24587

[Bmim][BF4] (1) + 1,4-Dioxane (2) 1.02227 1.01091 0.99949 1.10987 1.10106 1.09228 1.13814 1.13001 1.12191 1.15351 1.14569 1.13792 1.16545 1.15784 1.15029 1.17557 1.16815 1.16077 1.19095 1.18380 1.17668 1.19734 1.19027 1.18324 [Emim][BF4] (1) + 1,4-Dioxane (2) 1.02227 1.01091 0.99949 1.16300 1.15424 1.14514 1.19516 1.18692 1.17843 1.20363 1.19548 1.18738 1.23279 1.22492 1.21710 1.23889 1.23117 1.22340 1.25572 1.24801 1.24036 1.26245 1.25479 1.24718 1.28302 1.27545 1.26797 [Emim][BF4] (1) + EG (2) 1.10645 1.09938 1.09224 1.15408 1.14654 1.13898 1.17636 1.16863 1.16091 1.19784 1.18998 1.18217 1.21696 1.20907 1.20124 1.22677 1.21890 1.21109 1.23777 1.22992 1.22217 1.25653 1.24881 1.24118 1.26337 1.25569 1.24809 1.27451 1.26690 1.25936 1.28302 1.27545 1.26797

Standard uncertainty u are u(ρ) = 5·10−5 g·cm−3, u(x1) = 0.0002, u(T) = 0.01 K, u(p) = 2 kPa.

slowly with continuous stirring until two phases appeared, and then they were cooled very slowly until the disappearance of two phases was detected. These measurements of LLE temperatures have been influenced by the differences in density and refractive index of the two emerged phases, but also by the kinetic hindrance of phase separation. Accordingly, the expanded uncertainty in temperature (k = 2) was U(T) = 2.0 K (0.95 level of confidence), given by the repeatability of determination of the transition temperatures. The same procedure of the cloud-point temperatures determination is well-known in the literature.14,15

The comparison with literature of the pure compounds data for density and refractive index are presented in Table 2 at different temperatures. Table 3 shows the density data for [Bmim][BF4] + 1,4-dioxane, [Emim][BF4] + 1,4-dioxane, and [Emim][BF4] + EG at temperatures of (293.15, 298.15, 303.15, 313.15, 323.15, 333.15, 343.15, and 353.15) K. Table 4 presents the refractive index data at temperatures of (298.15, 303.15, 313.15, and 323.15) K for the same systems, in addition the data for [Bmim][BF4] + EG system. The refractive index data at 298.15 K for the binary system of [Bmim][BF4] + EG correspond well with those of Iglesias-Otero et al.,8 less well with those of Singh et al.7 (Figure 2). The densities of the investigated binary systems increase with the increase of ionic liquid content in the mixture, as expected. The refractive indices decrease continuously from the value for pure EG until reaching the value corresponding to pure ILs, while both systems with 1,4-dioxane present curves with a maximum. The experimental excess molar volumes, VE, deviations in refractive index, Δn, and molar refraction, R, for the binary mixtures were calculated with the equations

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RESULTS AND DISCUSSION The LL equilibrium data for the studied [Bmim][BF4] + 1,4-dioxane and [Emim][BF4] + 1,4-dioxane binary systems are given in Figure 1. Here are presented the miscibility data of 1,4-dioxane in ionic liquids at atmospheric pressure (101 ± 2 kPa). As can be observed the solubilities of 1,4-dioxane, a nonpolar cyclic solvent, in [Bmim][BF4] and [Emim][BF4], respectively, are quite high (see Table 1). Unfortunately, the solubilities of both ionic liquids in 1,4-dioxane were very small (x1 < 0.001 at 293.15 K) and difficult to be measured. Both systems present lower critical solution temperature (LCST)-type behavior, as was observed in literature for other mixtures of ILs with nonpolar solvents.16,17

VE =

⎛1

∑ xiMi⎜⎜ i

1167

⎝ρ

−

1⎞ ⎟⎟ ρi ⎠

(1)



Article

Table 4. Experimental Refractive Indices for the Binary Systems [Bmim][BF4] + 1,4-Dioxane, [Bmim][BF4] + EG, [Emim][BF4] + 1,4-Dioxane, [Emim][BF4] + EG at Different Temperatures and Atmospheric Pressure of 101 kPaa n x1 0.0000 0.2559 0.3956 0.4988 0.6000 0.7021 0.8993 1.0000 0.0000 0.0895 0.1758 0.3578 0.4397 0.6482 0.8121 1.0000 0.0000 0.3292 0.4547 0.4923 0.6409 0.6838 0.7851 0.8336 1.0000 0.0000 0.1249 0.2084 0.3046 0.4124 0.4763 0.5565 0.7170 0.7826 0.9010 1.0000

T/K = 298.15

T/K = 303.15

T/K = 313.15

[Bmim][BF4] (1) + 1,4-Dioxane (2) 1.4205 1.4171 1.4112 1.4253 1.4236 1.4196 1.4258 1.4244 1.4210 1.4256 1.4242 1.4211 1.4249 1.4235 1.4206 1.4241 1.4225 1.4199 1.4222 1.4207 1.4183 1.4215 1.4202 1.4179 [Bmim][BF4] (1) + EG (2) 1.4300 1.4285 1.4258 1.4276 1.4258 1.4231 1.4257 1.4239 1.4212 1.4231 1.4216 1.4188 1.4224 1.4211 1.4182 1.4217 1.4205 1.4178 1.4216 1.4204 1.4179 1.4215 1.4202 1.4179 [Emim][BF4] (1) + 1,4-Dioxane (2) 1.4205 1.4171 1.4112 1.4214 1.4195 1.4163 1.4197 1.4181 1.4154 1.4191 1.4176 1.4149 1.4165 1.4150 1.4126 1.4157 1.4143 1.4118 1.4140 1.4125 1.4100 1.4132 1.4118 1.4092 1.4111 1.4100 1.4073 [Emim][BF4] (1) + EG (2) 1.4300 1.4285 1.4258 1.4239 1.4224 1.4199 1.4206 1.4192 1.4167 1.4176 1.4163 1.4136 1.4151 1.4138 1.4110 1.4140 1.4127 1.4099 1.4130 1.4117 1.4089 1.4120 1.4105 1.4079 1.4118 1.4103 1.4077 1.4115 1.4101 1.4076 1.4111 1.4100 1.4073

T/K = 323.15 1.4063 1.4161 1.4179 1.4181 1.4177 1.4169 1.4155 1.4153

Figure 2. Comparison of our refractive index data at 298.15 K for the binary systems [Bmim][BF4] (1) + EG (2) (⧫) with literature data, ref 7 () and ref 8 (□).

1.4229 1.4203 1.4184 1.4159 1.4154 1.4150 1.4152 1.4153

The experimental values of excess properties have been fitted to Redlich−Kister type polynomials: Y E = x1x 2 ∑ Ak (x1 − x 2)k k

1.4063 1.4129 1.4123 1.4119 1.4097 1.4090 1.4074 1.4067 1.4051

where YE is the excess properties and Ak is the Redlich−Kister parameters obtained by fitting the equations to the experimental values. These values are given in Table 5, together with the standard deviation, σ, calculated as follows: n E E 2 0.5 σ = [∑ (Yexp , i − Ycalc, i) /(N − M )] i=1

Standard uncertainty u are u(n) = 0.0001, u(x1) = 0.0002, u(T) = 0.05 K, u(p) = 2 kPa.

∑ ϕini i

R=

M n2 − 1 ρ n2 + 2

(5)

where N is the number of experimental data points and M is the number of parameters. The VE values are negative for the systems with 1,4-dioxane at all investigated temperatures over the whole composition range, more negative for [Emim][BF4] + 1,4-dioxane (Figures 3 to 4). For these systems VE values become more negative when temperature increases. Figure 5 shows the VE variation for the [Emim][BF4] + EG system, which is positive and increases as the temperature increases. The minimum/maximum values in VE were observed at around x1 = 0.4. The deviation in refractive indices presents an opposite sign than the VE values, being positive for the systems with 1,4-dioxane, more positive for the system with [Emim][BF4] (Figures 6 and 8), and negative for the systems with EG, more negative for the system with [Emim][BF4], also (Figures 7 and 9). Correlation of Excess Molar Volume with the Prigogine−Flory−Patterson (PFP) Theory. Both to probe the interactions in mixtures and to correlate the volumetric properties of the mixtures with ILs the Prigogine−Flory− Patterson (PFP) theory has been applied.33−35 According with this, the VE value can be regarded as a sum of three contributions: an interactional, a free volume, and an internal pressure contribution, which indicate the influence of intermolecular interactions and different structural factors on excess property. The expression for VE is given by

1.4229 1.4174 1.4142 1.4111 1.4085 1.4074 1.4064 1.4054 1.4054 1.4053 1.4051

a

Δn = n −

(4)

(2)

(3)

where ρi, Mi, ni, are the densities, molar masses, and refractive indices, respectively, of the pure compounds, in a similar way being notations for mixtures; xi and ϕi are the mole fractions and volume fractions of the mixtures. 1168



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Table 5. Parameters, Ak, and Standard Deviations, σ (eq 5), for the Redlich−Kister Equation T/K

A0

A1

A2

σ

[Bmim][BF4] + 1,4-Dioxane VE/(cm3·mol−1)

−4.908 2.383 −5.117 2.495 −5.338 2.597 −5.811 2.866 −6.321 3.166 −6.880 3.473 −7.467 3.826 −8.108 4.177 0.0174 −0.0111 0.0195 −0.0153 0.0209 −0.0161 0.0226 −0.0188 [Bmim][BF4] + EG −0.0058 0.0021 −0.0053 0.0043 −0.0070 0.0046 −0.0079 0.0045 [Emim][BF4] + 1,4-Dioxane −5.736 3.829 −5.983 3.975 −6.228 4.224 −6.778 4.458 −7.307 4.507 −7.971 5.198 −8.635 5.596 −9.315 6.474 0.0185 −0.0154 0.0200 −0.0179 0.0246 −0.0200 0.0251 −0.0217 [Emim][BF4] + EG 1.804 0.564 1.899 0.536 1.992 0.513 2.163 0.449 2.322 0.381 2.465 0.319 2.590 0.248 2.697 0.183 −0.0101 0.0022 −0.0104 0.0009 −0.0111 0.0008 −0.0116 −0.0003

293.15 298.15 303.15 313.15 323.15 333.15 343.15 353.15 298.15 303.15 313.15 323.15

Δn

Δn

298.15 303.15 313.15 323.15

VE/(cm3·mol−1)

293.15 298.15 303.15 313.15 323.15 333.15 343.15 353.15 298.15 303.15 313.15 323.15

Δn

VE/(cm3·mol−1)

293.15 298.15 303.15 313.15 323.15 333.15 343.15 353.15 298.15 303.15 313.15 323.15

Δn

E VPFP E = Vint + VfvE + VipE x1V1* + x 2V 2*

=

(v1̃ − v2̃ )2 ((14/9)v −̃ 1/3 − 1)ψ1ψ2

[(4/3)v −̃ 1/3 − 1]v ̃ (v1̃ − v2̃ )(P1* − P2*)ψ1ψ2 + P2*ψ + P1*ψ 1

2

0.0040 0.0008 0.0015 0.0033

2.8 × 10−5 2.8 × 10−5 2.6 × 10−5 2.6 × 10−5

−2.286 −2.362 −2.565 −2.576 −2.330 −2.892 −3.059 −4.799

0.036 0.036 0.040 0.037 0.040 0.039 0.040 0.045 1.3 × 10−5 0.6 × 10−5 0.3 × 10−5 0.1 × 10−5

−0.388 −0.402 −0.415 −0.456 −0.482 −0.491 −0.520 −0.558 0.0072 0.0055 0.0090 0.0109

0.0112 0.0111 0.0112 0.0115 0.0120 0.0126 0.0132 0.0141 2.9 × 10−5 2.9 × 10−5 2.9 × 10−5 2.8 × 10−5

characteristic volume and characteristic pressure, respectively, and χ12 is the interaction parameter. Table 6 shows some physicochemical data and parameters of the pure components used in PFP theory required for VE correlation and calculated into a similar manner as in our previous articles.9,10 It can be observed that for both systems with 1,4-dioxane the interactional contribution is negative and represents the most important factor in deciding the sign of VE (Table 7 and Figures 10a,b), indicating the presence of interactions in mixtures, especially due to the hydrogen bonding between the oxygen atoms of 1,4-dioxane and the hydrogen atom at position 2 of the imidazole ring of ILs. It is also interesting to observe the value of the interactional contribution for the [Emim][BF4] + EG system which is

(v 1/3 ̃ − 1)v 2/3 ̃ ψ1θ2χ12 −1/3 − 1]P1* [(4/3)v ̃ −−

0.009 0.012 0.014 0.017 0.019 0.021 0.022 0.025 0.2 × 10−5 0.7 × 10−5 1.5 × 10−5 8.5 × 10−5

(6)

where θi is the surface site fraction, ψi is the contact energy fraction, ṽi is the reduced volume; Vi* and Pi* are the 1169



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Figure 5. Excess molar volumes, VE, for the [Emim][BF4] (1) + EG (2) binary system at different temperatures: ◇, 293.15 K; ◆, 298.15 K; △, 303.15 K; ∗, 313.15 K; +, 323.15 K; , 333.15 K; □, 343.15 K; ×, 353.15 K; solid line, Redlich−Kister correlation.

Figure 3. Excess molar volumes, VE, for the [Bmim][BF4] (1) + 1,4dioxane (2) binary system at different temperatures: ◇, 293.15 K; ◆, 298.15 K; △, 303.15 K; ∗, 313.15 K; +, 323.15 K; , 333.15 K; □, 343.15 K; ×, 353.15 K; solid line, Redlich−Kister correlation.

Figure 6. Deviation in refractive index, Δn, for the [Bmim][BF4] (1) + 1,4-dioxane (2) binary system at different temperatures: ◆, 298.15 K; △, 303.15 K; ∗, 313.15 K; +, 323.15 K; solid line, Redlich−Kister correlation.

Figure 4. Excess molar volumes, VE, for the [Emim][BF4] (1) + 1,4dioxane (2) binary system at different temperatures: ◇, 293.15 K; ◆, 298.15 K; △, 303.15 K; ∗, 313.15 K; +, 323.15 K; , 333.15 K; □, 343.15 K; ×, 353.15 K; solid line, Redlich−Kister correlation.

positive, suggesting relatively weak intermolecular specific interactions on mixing, or rather that breaking of self-interactions prevail over interactions between the ionic liquid and EG, as stated in literature.7,40 A perusal of Table 7 reveals that the differences between characteristic pressures and reduced volumes of ILs and organic solvents are bigger for the systems of ILs with 1,4-dioxane than with EG, being more accentuated in the case of [Bmim][BF4] + 1,4-dioxane system than [Emim][BF4] + 1,4-dioxane. This leads to an important contribution to VE of the internal pressure factor in the case of [Bmim][BF4] + 1,4-dioxane system comparative with [Emim][BF4] + 1,4-dioxane, and practically no influence on VE of this factor in the case of the [Emim][BF4] + EG system (Table 7). In this last system the two contributions due to the free volume and internal pressure are negligible (Table 7 and Figure 10c). This leads us to the idea that for the systems with 1,4-dioxane there is a more efficient steric packing or geometrical accommodation between unlike molecules than in the case of

Figure 7. Deviation in refractive index, Δn, for the [Bmim][BF4] (1) + EG (2) binary system at different temperatures: ◆, 298.15 K; △, 303.15 K; ∗, 313.15 K; +, 323.15 K; solid line, Redlich−Kister correlation.

[Emim][BF4] + EG, where probably the correct term is steric hindrance between IL and EG. 1170



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approximation (assuming molar refraction to behave ideally), the excess molar volume can be calculated with V E = ( −Δn)

3R(n id − n) 2

(n − 1)(n id2 − 1)

= ( −Δn)f (R , n id , n) (7)

where the refractive index of an ideal mixture, nid, is given by ⎛ n 2n 2 + 2ϕ n 2 + 2ϕ n 2 ⎞1/2 1 2 1 1 2 2 ⎟ n id = ⎜⎜ ⎟ 2 2 2 + ϕ n + ϕ n ⎝ ⎠ 1 1 2 2

(8)

The Lorentz−Lorenz approximation is used also for predicting the density and refractive index with the following expressions, calculating a standard deviation according to eq 11. n2 − 1 n2 + 2

( )(x M + x M ) ρ= ( )x + ( )x

Figure 8. Deviation in refractive index, Δn, for the [Emim][BF4] (1) + 1,4-dioxane (2) binary system at different temperatures: ◆, 298.15 K; △, 303.15 K; ∗, 313.15 K; +, 323.15 K; solid line, Redlich−Kister correlation.

n12 − 1 n12 + 2

1 1

M1 1ρ 1

2

2

2

n2 − 1

n2 2 + 2

M2 2 ρ 2

(9)

⎛ ⎡ n12 − 1 ⎞1/2 M1 n2 2 − 1 M2 ⎤ ⎜ 2ρ⎢⎣ n 2 + 2 x1 ρ + n 2 + 2 x 2 ρ ⎥⎦ + (x1M1 + x 2M 2) ⎟ 1 2 1 2 ⎟ n=⎜ ⎡ n12 − 1 ⎜ M1 n2 2 − 1 M2 ⎤ ⎟ ( x M + x M ) − ρ x + x ⎜ 1 1 ⎟ ⎢⎣ n12 + 2 1 ρ1 2 2 2ρ ⎥ n2 2 + 2 2⎦ ⎠ ⎝ (10)

( )

( ) ( )

(

)

n

σ = [∑ (Yexp , i − Ycalc, i)2 /N ]0.5

(11)

i=1

Hence, if the densities, the refractive indices for the pure products, and n for the mixture are known, one can estimate the density of the mixture, but also the inverse prediction can be obtained. Table 8 presents the standard deviation for excess molar volume, density, and refractive index for the binary mixtures at T = (298.15, 303.15, 313.15, and 323.15) K. As can be seen the differences between the experimental and predicted density values were all less than 0.003 g·cm−3 and even less than 0.00093 g·cm−3 for two from the four investigated systems: [Bmim][BF4] + 1,4-dioxane and [Emim][BF4] + EG systems. It must be emphasized that anyway the reported density values from the literature often exhibit larger differences than 0.005 g·cm−3. As Iglesias-Otero et al. have noticed, the proposed prediction method is an effective choice for the fast, reliable estimation of density in binary mixtures with ILs.8 For refractive indices predictions the obtained results were good for all studied systems. Thus, differences were all less than 0.0012 and even less than 0.00037 in the same systems for density predictions. So, the proposed method provides quite accurate refractive index data for binary systems containing ILs. From Table 8 it can be observed that the VE correlations are better for [Bmim][BF4] + 1,4-dioxane and [Emim][BF4] + EG

Figure 9. Deviation in refractive index, Δn, for the [Emim][BF4] (1) + EG (2) binary system at different temperatures: ◆, 298.15 K; △, 303.15 K; ∗, 313.15 K; +, 323.15 K; solid line, Redlich−Kister correlation.

Even though the PFP theory leads to a one-parameter model, the agreement between experimental and calculated values of VE is good, better for the systems with 1,4-dioxane than with EG, with standard deviations in the range of 0.040−0.052·cm3·mol−1, as is shown in Table 7. Correlation and Prediction of Excess Molar Volume, Density and Refractive Index by the Lorentz−lorenz Approximation. According to Iglesias-Otero et al.8 which have studied the correlations between volumetric properties and refractive index of binary mixtures of ionic liquids and organic solvents within the framework of the Lorentz−Lorenz

Table 6. Physico-chemical Data of Pure Components Used in the Prigogine−Flory−Patterson Theory at T/K = 298.15

[Bmim][BF4] [Emim][BF4] 1,4-dioxane EG a

α*

kT*

Vi

Vi*

Pi*

K−1

cm3·J−1

Ṽ i

cm3·mol−1

cm3·mol−1

J·cm−3

T̃ i

K

0.000588a 0.000582a 0.001118a 0.000652a

0.000386b 0.000337c 0.000738d 0.000373e

1.1567 1.1553 1.2714 1.1717

188.21 153.84 85.72 55.92

162.72 133.17 67.42 47.72

607.5 687.2 730.1 715.5

0.04094 0.04066 0.06050 0.04392

7278 7329 4925 6785

Ti*

This work. bReference 36. cReference 37. dReference 38. eReference 39 1171



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Table 7. Experimental and Calculated VE Using PFP Theory and the Three PFP Contributions at around x1= 0.4 and T/K = 298.15 VEexp systems [Bmim][BF4] + 1,4-dioxane [Emim][BF4] + 1,4-dioxane [Emim][BF4]+ EG

cm ·mol 3

VEPFP −1

−1.3617 −1.6765 0.4361

VEint −1

cm ·mol 3

−1.3322 −1.6037 0.4357

VEfv −1

cm ·mol 3

−1.3500 −1.3046 0.4311

cm ·mol 3

−1

−0.5172 −0.4555 −0.0078

VEip

χ12

σ

cm ·mol−1

J·cm−3

cm3·mol−1

0.5350 0.1564 0.0124

−133.3 −152.8 73.7

0.040 0.052 0.107

3

Table 8. Standard Deviations, σ (eq 11), Obtained from the Lorentz−Lorenz Equation for VE, ρ, and n for the Binary Mixtures at Different Temperatures σ T/K = 298.15 T/K = 303.15 T/K = 313.15 T/K = 323.15 properties VE/(cm3·mol−1) ρ/(g cm3) n VE/(cm3·mol−1) ρ/(g cm3) n VE/(cm3·mol−1) ρ/(g cm3) n VE/(cm3·mol−1) ρ/(g cm3) n

[Bmim][BF4] + 1,4-Dioxane 0.089 0.049 0.057 0.00085 0.00040 0.00049 0.00037 0.00017 0.00020 [Bmim][BF4] + EG 0.146 0.167 0.135 0.0016 0.0017 0.0014 0.00067 0.00068 0.00057 [Emim][BF4] + 1,4-Dioxane 0.299 0.300 0.171 0.0031 0.0031 0.0017 0.0013 0.0012 0.0007 [Emim][BF4] + EG 0.048 0.043 0.054 0.00051 0.00044 0.00065 0.00019 0.00017 0.00026

0.063 0.00048 0.00020 0.138 0.0015 0.00061 0.233 0.0022 0.0009 0.070 0.00093 0.00037

systems. However, the Lorentz−Lorenz approximation gives a weaker correlation for VE than for predicting the density and refractive index.

■

CONCLUSION The densities of the binary mixtures of the [Emim][BF4] with 1,4-dioxane and ethylene glycol and [Bmim][BF4] + 1,4-dioxane in the temperature range from (293.15 to 353.15) K were reported. Also, the refractive indices for the same systems in the temperature range from (298.15 to 323.15) K and also for the [Bmim][BF4] + EG system. The investigated ILs are completely miscible with EG or partially immiscible with 1,4-dioxane with LCST behavior. The excess molar volumes are negative for the systems with 1,4-dioxane and positive for the [Emim][BF4] + EG system over the whole composition range at investigated temperatures. The deviation in refractive indices presents an opposite sign than VE values. Both VE and deviations in refractive index are smaller for [Bmim][BF4] + 1,4-dioxane than for [Emim][BF4] + 1,4-dioxane. The PFP theory has a good performance in predicting the VE of the studied binary systems, better for 1,4-dioxane systems. The analysis of relative contributions suggests that the interactional contribution is the most significant term in VE values for the systems with 1,4-dioxane, with negative values, which means the presence of interactions in mixtures, and positive values for [Emim][BF4] + EG system, which means relatively weak intermolecular specific interactions on mixing or breaking/weakening of the existing ones.

Figure 10. Excess molar volume VE for the binary systems (a) [Bmim][BF4](1) + 1,4-dioxane (2), (b) [Emim][BF4](1) + 1,4-dioxane (2), and (c) [Emim][BF4](1) + EG (2), respectively, at T = 298.15 K calculated with the PFP theory: ·−·−, interactional contribution; ··−··−, free volume contribution; ----, internal pressure contribution; solid line, total excess molar volume predicted by PFP theory; ○, experimental results. 1172



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The Lorentz−Lorenz approximation gives better prediction of density or refractive index and a weaker correlation for VE.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +40214023855. Notes

The authors declare no competing financial interest.

■

REFERENCES

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Density and Refractive Index of Binary Mixtures of Two 1-Alkyl-3

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