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Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Determination of Density and Viscosity of Binary Mixtures of Water and Dimethyl Sulfoxide with 1‑Ethyl-3-methylimidazolium Diethylphosphate [EtMeIm]+[Et2PO4]− at Atmospheric Pressure Laura de Pablo,†,‡ José Juan Segovia Puras,‡ Carmen Martín,‡ and María Dolores Bermejo*,† †

High Pressure Process Group, Department of Chemical Engineering and Environmental Technology and ‡Research Group TERMOCAL, Thermodynamics and Calibration, University of Valladolid, E-47011 Valladolid, Spain ABSTRACT: In this work, the densities and viscosities of 1-ethyl-3methylimidazolium diethylphosphate ([EtMeIm]+ [Et2PO4]−) in binary mixtures with water and dimethyl sulfoxide (DMSO) at atmospheric pressure and temperatures between 293.15 and 373.15 K were determined. The properties were measured in a Stabinger densimeter−viscosimeter SVM 3000 model. In addition, a correlation of the viscosity data was made with a modification of the Grunberg and Nissan correlation, in which corrections for the interaction between the ionic liquid and the water, DMSO, or both were introduced. For the mixture H2O + ([EtMeIm]+ [Et2PO4]−), the %AARD is 13% with a maximum deviation (%max) of 49%; for the mixture DMSO + ([EtMeIm]+ [Et2PO4]−), the %AARD is 9.5% and the %max is 49%.

diethylphosphate, [EtMeIm]+[Et2PO4]−, is the most suitable for cellulose processing because it does not cause any degradation of cellulose. Lall-Ramnarine et al.9 found that alkylimidazolium IL’s with alkylphosphate-derived anions are more stable for enzymatic reactions and less toxic for the fermentative bacteria than the imidazolium acetate ionic liquids. Alkylphosphate ILs also present advantages over other cellulose-dissolving ILs of having a much lower melting point (20 vs 80 °C), lower viscosity, and being able to dissolve cellulose at room temperature.3,10 Some physical properties of ionic liquids of this family can be found in the literature. Ficke et al.11 show that ionic liquids with diethylphosphate anions have a large negative excess enthalpy. Wang et al.12 measured the density of pure 1-methyl-3methylimidazolium dimethylphosphate and pure 1-ethyl-3methylimidazolium diethylphosphate at atmospheric pressure. Other authors have studied the physical properties of [EtMeIm]+[Et2PO4]−, Ge et al.13 measured activity coefficients at infinite dilution of [EtMeIm]+[Et2PO4]− with aromatic and aliphatic compounds, Cao et al.14 discovered that it is possible to break the azeotrope of methyl acetate and methanol by adding 1alkyl-3-methylimidazolium dialkylphosphate ionic liquids by studying the vapor−liquid equilibrium of the three components, and Ghani et al.15 measured the density, surface tension, and viscosity of ternary mixtures of water + N-methyldiethanolamine (MDEA) + [EtMeIm]+[Et2PO4]−/1,3-dimethylimidazolium dimethylphosphate ([Me2 Im]+[Me2PO4]−). Nevertheless,

1. INTRODUCTION Ionic liquids are substances composed entirely of ions. Their complex structures hinder the crystallization process, making them substances with a very low fusion temperature. They are also considered to be “green” solvents because they have very low vapor pressures. In addition, they have high thermal and chemical stability. Their properties are easily tunable by changing the ion substituents,1 making ionic liquids highly versatile. Thus, ionic liquids have become a promising alternative to conventional solvents.2 In the past few years, the global interest in the use of environmentally sustainable resources has increased. Therefore, the biopolymers, and more specifically cellulose, have received most of the attention in the search for new natural, biodegradable, and renewable resources. However, cellulose, due to its complex structure, is not easily processed because it is not soluble in water at room temperature or in other conventional solvents. Some ionic liquids have demonstrated their capacity to dissolve cellulose;3 however, the solution of cellulose in ionic liquids dramatically increases the viscosity of the mixture. Therefore, cosolvents are frequently added to these mixtures. One of the most common cosolvents is dimethyl sulfoxide (DMSO). This substance is frequently used in cellulose processing with ILs because it decreases the friction between monomers4 and does not affect cellulose solubility.5,6 The recovery of the dissolved cellulose is frequently made using water as an antisolvent.7 Thus, physical properties of mixtures of water and DMSO with cellulose dissolving ILs are of great interest for the development of the processing of cellulose in ionic liquid media. After studying the dissolution of cellulose in several ionic liquids, Vitz et al.8 concluded that 1-ethyl-3-methylimidazolium © XXXX American Chemical Society

Special Issue: In Honor of Cor Peters Received: September 2, 2017 Accepted: January 29, 2018

A

DOI: 10.1021/acs.jced.7b00788 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Materials and Purification Methods

a

chemical name

source

initial mole fraction purity

purification method

1-ethyl-3-methylimidazolium diethylphosphate dimethyl sulfoxide water

Iolitec Sigma Sigma

0.98 0.999 1

none none none

final mole fraction purity

analysis method KFa KFa

Karl Fischer coulometric titration.

Figure 1. 1-Ethyl-3-methylimidazolium diethylphosphate ionic liquid.

2.2. Measurements with a Stabinger Viscometer. The Stabinger viscometer used in this work is a SVM 3000 model. It is based on the principle of Couette. It consists of two rotating concentric tubes and between them the fluid of interest. It measures the torque difference between the rotating cylinders that is proportional to the viscosity of the fluid. For the calculations, it is necessary to know the density of the fluid, so the Stabinger viscometer has a vibrating tube densimeter integrated into its structure. Both measurements were carried out simultaneously, with the densimeter and the viscometer being filled in a single step. The measurements were performed thought a cycle of temperatures. The range of temperature of the equipment is from 233.15 K to 373.15 K in a viscosity range from 0.2 mPa·s to 20 000 mPa·s and in a density range from 0.65 g· cm−3 to 2 g·cm−3. The uncertainty in the temperature is ±0.21 K (k = 2, 95.45% coverage factor) from 278.15 K to 343.15 K. The apparatus performs five measurements automatically with a relative uncertainty in the viscosity of 2.0% (k = 2), and the expanded uncertainty of the density is ±0.26 kg·m−3 (k = 2) (level of confidence = 95.45%). The expanded uncertainty (k = 2) of the mole fraction is ±0.001. After the measurements, the water content of the mixture was not possible to determine. The uncertainty in the density and the viscosity of the Stabinger viscometer was calculated following the law of propagation of uncertainty described in GUM 2008.17 The results are summarized in Tables 2 and 3. The final uncertainty is similar to those obtained by other authors18,19 using the same equipment.

representation of the chemical structure can be observed. Because of the low moisture of the ionic liquid, it was not dried before use. Nevertheless, the final humidity of every binary mixture was determined by Karl Fischer coulometric titration using a Mettler Toledo C20 KF. The mixtures were prepared gravimetrically by using a high-precision balance (Sartorius Basic BA 310P, precision = 0.001 g) and then isolated from the environment using a hermetically sealed crystal vial until a sample was extracted for the measurements in order to avoid water absorption. The measurements were carried out just after the preparation of the mixture.

3. EXPERIMENTAL RESULTS 3.1. Densities and Determination of Excess Molar Volumes. The density measurements in the systems H2O + [EtMeIm]+[Et2PO4]− and DMSO + [EtMeIm]+[Et2PO4]− are reported in Tables 4 and 5, respectively. Our experimental data of pure [EtMeIm]+[Et2PO4]− were compared to literature data reported by several authors.11,12,20−23 The relative deviations of the density measurements are presented in Figure 2. The discrepancies between our data and the literature data can be caused by the different amounts of water present in the samples and different purities of the ionic liquid. It can be

more work has to been done in order to fully understand the dissolution and recovery process of cellulose in ionic liquids.16 In this work, the density (ρ) and the viscosity (μ) of pure 1ethyl-3-methylimidazolium diethylphosphate and its binary mixtures with water and DMSO were measured over 9 isotherms within the temperature range of 293.15−373.15 K at atmospheric pressure. In addition, experimental viscosity data were correlated.

2. EXPERIMENTAL SECTION 2.1. Materials. The DMSO used in the experiments was provided by Sigma−Aldrich and has a purity of 99.90% and a water content of ∼200 ppm. Deionized water was provided by Sigma-Aldrich and used to prepare the aqueous solutions. The compound data are summarized in Table 1. Ionic liquid 1-ethyl3-methylimidazolium diethylphosphate was purchased from Iolitec (assay (NMR, nuclear magnetic resonance) = 98%; 1ethyl-3-methylimidazolium (IC, ion chromatography) = 99.1%; diethylphosphate (IC) = 98.2%, and 1-methylimidazole (IC) < 1% with a water content of 0.012 mole fraction). In Figure 1, a

Table 2. Uncertainty Budget of Density for the Stabinger Viscometera uncertainty u(T)

u(ρ)

U(ρ) U(ρ) a

units calibration resolution repeatability calibration resolution repeatability

K

g·cm−3

g·cm−3 g·cm−3/g·cm−3

estimate

divisor

u(x)/kg·m−3

0.020 0.001 0.005 0.0005 0.0001 0.0001

1 2√3 1 2 2√3 2 k=2 k=2

1.1 × 10−4

2.6 × 10−1

5.2 × 10−1 4.6 × 10−1

Values were calculated for xH2O = 0.259, T = 333.15 K, and ρ = 1126.0 kg·m−3. B



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Table 3. Uncertainty Budget of Viscosity for the Stabinger Viscometera uncertainty

units

u(T)

calibration resolution repeatability calibration resolution repeatability

u(μ)

K

mPa·s

U(μ) U(μ) a

estimate

divisor

u(x)/mPa·s

0.020 0.001 0.005 1.3 0.0001 0.13

1 2√3 1 1 2√3 1 k=2 k=2

0.11

mPa·s mPa·s/mPa·s

1.3

2.6 1.9 × 10−2

Values calculated for xH2O = 0.183, 313.15 K, and μ = 135 mPa·s.

Table 4. Experimental Values of Density ρ for the System Water (1) + [EtMeIm]+[Et2PO4]− as a Function of Temperature T and Mole Fraction of Water x1a Measured at Pressure p = (0.10 ± 0.01) MPa x1 T/K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

0.012 ρ/kg·m−3 1151.2 1144.2 1137.4 1130.7 1124.1 1117.5 1111.0 1104.5 1098.2

0.061

0.123

0.183

0.259

0.502

0.765

0.880

1.000

1151.7 1144.7 1137.9 1131.2 1124.6 1118.0 1111.5 1104.9 1098.5

1152.1 1145.2 1138.4 1131.7 1125.0 1118.4 1111.9 1105.2 1098.9

1152.4 1145.5 1138.7 1132.0 1125.4 1118.8 1112.1 1105.6 1099.1

1153.0 1146.1 1139.3 1132.6 1126.0 1119.3 1112.7 1106.1 1099.6

1154.6 1147.8 1141.1 1134.3 1127.4 1120.5 1113.7 1106.8 1099.9

1150.2 1143.1 1135.9 1128.6 1121.2 1113.8 1106.3 1098.7 1091.2

1124.0 1116.7 1109.2 1101.7 1094.0 1086.1 1078.1 1070.0 1061.9

1000.1 998.0 994.3 990.2 985.2 979.6 973.3 b b

Standard uncertainties are u(x1) = 0.001, u(T) = 0.21 K, and U(ρ) = 5.2 × 10−1 kg·m−3 (0.95 level of confidence). bBecause of the limitations of the equipment used, it was not possible to measure densities and viscosities at temperatures close to the boiling point of the water.

a

Table 5. Experimental Values of Density ρ for the System Water (1) + DMSO (2) + [EtMeIm]+[Et2PO4]− as a Function of Temperature T and Mole Fraction of the DMSO x2a and Water (1) Impurities Mole Fraction x1a Measured at Pressure p = (0.10 ± 0.01) MPa x1 x2 T/K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 a

0.019 0.048 ρ/kg·m−3 1150.9 1143.8 1137.0 1130.3 1123.7 1117.1 1110.4 1103.8 1097.3

0.003 0.100

0.004 0.150

0.004 0.249

0.004 0.497

0.005 0.768

0.008 0.886

0.000 1.000

1150.2 1143.1 1136.3 1129.4 1122.8 1116.1 1109.4 1102.8 1096.2

1149.6 1142.6 1135.7 1128.8 1121.9 1115.2 1108.5 1101.8 1095.2

1148.2 1141.2 1134.2 1127.3 1120.3 1113.4 1106.6 1099.9 1093.2

1143.7 1136.4 1129.0 1121.2 1113.4 1106.0 1098.8 1091.5 1084.3

1132.3 1124.6 1116.3 1108.1 1099.9 1091.7 1083.6 1075.6 1067.5

1120.7 1111.6 1102.6 1093.5 1084.7 1075.6 1066.8 1057.8 1049.0

1101.2 1091.2 1081.1 1071.1 1061.2 1051.3 1041.1 1031.3 1021.4

Standard uncertainties u are u(x1) = 0.001, u(x2) = 0.001, u(T) = 0.21 K, and U(ρ) = 5.2 × 10−1 kg·m−3 (0.95 level of confidence).

99% ≥99% >99% >98% 95.2% >98%

Figure 3. Relative deviations Δρ = ρ(expt) − ρ(lit) of experimental densities ρ of pure DMSO in this work and those reported by Campbell24 (□), Casteel et al.25 (◊), Wang et al.26 (Δ), Ivanov et al.27 (○), Iulian et al.28 (+), Krakowiak et al.29 (■), Zarei et al.30 (⧫), and Clever et al.31 (▲) (uncertainty not reported) as a function of temperature T.

excess molar volume calculations of H 2 O + [EtMeIm]+[Et2PO4]−, pure water density data at 363 and 373 K was taken from Refprop software.32 The mixtures of ionic liquid with water are less ideal than the mixtures with DMSO, as observed in Figures 6 and 7, where the excess volume is represented versus the mole fractions of H2O and DMSO, respectively. In both mixtures, there is a negative excess volume; however, the influence of the temperature of both systems in the excess volume is completely reversed. While in the aqueous mixtures the absolute value of the excess molar volume

decreases with temperature, in the mixtures with DMSO the absolute excess volume is higher with temperature. In aqueous mixtures, an increase in the temperature indicates a weakening of the interactions between the molecules, resulting in a higher ideality in the mixture.33 On the other hand, the mixtures with DMSO presents the reverse behavior. The explanation of this behavior can be that the temperature increases the free-volume availability and the mixture has, in this way, a larger capacity to accommodate DMSO molecules in its structure.34 D



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Figure 4. Experimental densities ρ of H2O(1) + [EtMeIm]+[Et2PO4]− at 293.15 K (□), 303.15 K (◊), 313.15 K (Δ), 323.15 K (○), 333.15 K (■), 343.15 K (⧫), 353.15 K (▲), 363.15 K (●), and 373.15 K (+) as a function of water mole fraction x1.

Figure 5. Experimental densities ρ of mixtures of DMSO(2) + [EtMeIm]+[Et2PO4]− at 293.15 K (□), 303.15 K (◊), 313.15 K (Δ), 323.15 K (×), 333.15 K (○), 343.15 K (+), 353.15 K (■), 363.15 K (⧫), and 373.15 K (▲) as a function of DMSO mole fraction x2.

Figure 6. Excess volumes (VE) of H2O (1) + [EtMeIm]+[Et2PO4]− at 293.15 K (□), 303.15 K (◊), 313.15 K (Δ), 323.15 K (○), 333.15 K (+), 343.15 K (■), 353.15 K (⧫), 363.15 K (▲), and 373.15 K (●) as a function of water mole fraction x1.

The isobaric expansion coefficient, αp, was calculated from experimental density data, and it is presented for each concentration in Tables 7 and 8.

3.2. Viscosity. Viscosity data of systems H2O(1) + [EtMeIm]+[Et2PO4]− and DMSO(2) + [EtMeIm]+[Et2PO4]− are reported in Tables 9 and 10. The experiments were E



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Figure 7. Excess volumes (VE) of DMSO(2) + [EtMeIm]+[Et2PO4]− at 293.15 K (□), 303.15 K (◊), 313.15 K (Δ), 323.15 K (○), 333.15 K (+), 343.15 K (■), 353.15 K (⧫), 363.15 K (▲), and 373.15 K (●) as a function of DMSO mole fraction x2.

Table 7. Isobaric Compressibility αp of H2O(1) + [EtMeIm]+[Et2PO4]− as a Function of the Mole Fraction of Water, x1a

a

x1

αp

0.012 0.061 0.123 0.183 0.259 0.502 0.765 0.880 1.000

5.88 × 10−4 5.90 × 10−4 5.91 × 10−4 5.91 × 10−4 5.92 × 10−4 6.07 × 10−4 6.59 × 10−4 7.11 × 10−4 5.40 × 10−4

present lower viscosities than those reported by Tenney et al.35 (10% discrepancy) and a 20% maximum deviation with the data reported by Hiraga et al.20 Discrepancies are more important at lower temperatures. Maybe this can be explained by the fact that the viscosity is higher at these temperatures, with the influence of the impurities also being higher. While Tenney et al.,27 with a purity similar to that in Hiraga et al.,20 reported a data content of 1000 ppm water, which is much higher than the 175 ppm reported in this work, they present higher instead of lower viscosities, as would be expected. The data of Hiraga et al.20 present higher viscosities as expected by the lower water content of 60 ppm reported by the authors. In order to better compare, an extrapolation of the viscosity to zero water content has been calculated. In the literature data, it was not possible to make this correction due to the lack of experimental data at other water concentrations. Despite this, extrapolation causes the data to become closer to the data of Hiraga et al.20 (with only 60 ppm water reported versus 175 ppm for the samples measured in this work), and an important deviation can still be found between them. This can be explained by the fact not only that water impurities can be found in the samples but also that other impurities can affect the viscosity and can influence the temperature. In this work, we reported the presence of 1methylimidazole; however, others authors have not reported impurities other than water in their respective articles. The influence of chlorine as an impurity in ionic liquids has been already measured36 and shows a high increase in viscosity in the presence of a low concentration of chlorine. Maybe the presence of 1-methylimidazole has a similar effect on the system studied in this article. On the other hand, Normazlan et al.22 reports lower viscosity values, which it is consistent with the high humidity of his sample (3400 ppm). The viscosity of pure DMSO has been compared with data found in the literature in Figure 9.25,37−44 All of the authors report a purity that varies between 98 and 99.9% in mass fraction. However, some discrepancy is found between the literature data itself and between the same data and this article’s data. Discrepancies can be caused by different water contents in the samples. Most of the authors report a purification/drying process before the measurements25,37,39,41,43 but do not report the water content in the samples. The data of Zhao et al.,43 with an initial 98% mass fraction purity before a desiccation and degasification process, are in agreement with the uncertainty in our data.

Standard uncertainty u is u(αp) = 2%.

Table 8. Isobaric Compressibility αp of DMSO(2) + [EtMeIm]+[Et2PO4]− as a Function of DMSO Mole Fraction, x2a

a

x2

αp

0.000 0.048 0.100 0.150 0.249 0.497 0.768 0.886 1

5.89 × 10−04 5.94 × 10−04 6.00 × 10−04 6.06 × 10−04 6.14 × 10−04 6.70 × 10−04 7.40 × 10−04 8.26 × 10−04 9.44 × 10−04

Standard uncertainty u is u(αp) = 2%.

performed in nine isotherms ranging from 293.15 K to 373.15 K. All measurements were performed at atmospheric pressure. Our experimental data were compared to literature data reported by other authors.20,22,35 The relative deviations of the viscosity measurements are presented in Figure 8. It can be observed that there is some scattering among all of the authors. When comparing our data to the literature data, we found a large discrepancy in the literature data and also in our data. The discrepancies can be caused by the different amounts of water (that decreases the viscosity of the samples) and other impurities present in the samples. The water contents and purities of the ILs used by the different authors are presented in Table 11. Our data F



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Table 9. Experimental Values of the Viscosity μ of H2O(1) + [EtMeIm]+[Et2PO4]− as a Function of Temperature T and the Mole Fraction of Water x1a Measured at Pressure p = (0.10 ± 0.01) MPa x1 T/K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

0.012 μ/(mPa·s) 540 274 154 94.0 61.2 42.1 30.2 22.5 17.3

0.061

0.123

0.183

0.259

0.502

0.765

0.880

1.000

513 262 148 90.2 58.8 40.4 29.0 21.6 16.5

487 250 141 86.4 56.2 38.6 27.7 20.6 15.8

462 238 135 83.1 54.3 37.4 26.9 20.0 15.3

422 219 125 76.5 49.3 34.1 24.5 18.3 14.1

202 111 65.8 40.7 27.6 19.6 14.4 11.2 8.9

51.1 31.2 20.3 14.0 10.1 7.58 5.88 4.69 3.83

12.5 8.35 5.91 4.38 3.36 2.67 2.18 1.83 1.55

1.00 0.805 0.651 0.544 0.472 0.417 0.342

a

b b

b

Standard uncertainties u are u(x1) = 0.001, u(T) = 0.21 K, u(p) = 0.01 MPa, and ur(μ) = 0.02. Because of the limitations of the equipment used, it was not possible to measure densities and viscosities at temperatures close to the boiling point of the water.

Table 10. Experimental Values of Viscosity μ for Water(1) + DMSO(2) + [EtMeIm]+[Et2PO4]− as a Function of Temperature T, Mole Fraction of DMSO x2a, and Water (1) Impurities Mole Fraction x1a Measured at Pressure p = (0.10 ± 0.01) MPa x1 x2 T/K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 a

0.019 0.048 μ/mPa·s 481 245 137 81.1 50.6 34.8 23.9 17.8 13.4

0.003 0.100

0.004 0.150

0.004 0.249

0.004 0.497

0.005 0.768

0.008 0.886

0.000 1.000

421 217 123 73.7 48.8 33.9 22.5 16.8 12.9

329 175 102 64.6 43.1 30.2 21.7 16.5 12.8

243 134 80.6 51.8 35.3 25.2 18.7 14.3 11.2

87.0 52.9 34.6 23.9 15.7 11.8 9.22 7.36 6.01

19.0 13.2 9.59 7.14 5.72 4.60 3.80 3.18 2.71

5.91 4.50 3.54 2.87 2.38 2.02 1.73 1.51 1.32

2.31 1.89 1.57 1.33 1.15 1.01 0.893 0.799 0.721

Standard uncertainties u are u(x1) = 0.001, u(T) = 0.21 K, u(p) = 0.01 MPa, and ur(μ) = 0.02.

Figure 8. Relative deviations Δμ = μ(expt) − μ(lit) of experimental viscosity data μ of pure [EtMeIm]+[Et2PO4]− measured in this work and those reported by other authors: Hiraga et al.20 (◊), Tenney et al.35 (□), Normazlan et al.22 (Δ), and this work when viscosity is extrapolated to zero water content (○). Error bars represents the expanded uncertainty reported by the authors.

Table 11. Source and Purity of Pure [EtMeIm]+[Et2PO4]− Used by Researchers Reporting Viscosity and Their Reported Uncertainties first author

journal

year

supplier

purity

water content

other impurities

uncertainty (k = 2) [%]

de Pablo (this article) Hiraga et al.20 Tenney et al.35 Normazlan et al.22

J. Chem. Eng. Data J. Chem. Eng. Data J. Chem. Eng. Data

2015 2014 2014

Iolitec Merck Merck Merck

98% >99% >99% 95.2%

0.09% 0.01% 0.10% 0.34%

1-methylimidazole not reported not reported not reported

2% 4.65% 0.10% 1%

G



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Figure 9. Relative deviation Δμ = μ(expt) − μ(lit) of the experimental viscosity μ of pure DMSO against the temperature between the experimental viscosity data of this work and those reported by Casteel et al.25 (◊), Ciocirlan et al.37 (Δ), Yang et al.38 (×) (uncertainty not reported), Govinda et al.39 (□), Gokavl et al.40 (○) (uncertainty not reported), Saleh et al.41 (+), Ali et al.42 (■) (uncertainty not reported), Zhao et al.43 (⧫), and Kapadi et al.44 (▲) as a function of temperature T.

Figure 10. Experimental viscosity μ of H2O(1) + [EtMeIm]+[Et2PO4]− at 293.15 K (□), 303.15 K (◊), 313.15 K (Δ), 323.15 K (○), 333.15 K (+), 343.15 K (■), 353.15 K (⧫), 363.15 K (▲), and 373.15 K (●) as a function of mole fraction of water x1. The solid line represents the correlation prediction using eq 3.

Figure 11. Experimental viscosity μ of DMSO(2) + [EtMeIm]+[Et2PO4]− at 293.15 K (□), 303.15 K (◊), 313.15 K (Δ), 323.15 K (○), 333.15 K (+), 343.15 K (■), 353.15 K (⧫), 363.15 K (▲), and 373.15 K (●) as a function of DMSO mole fraction x2. The solid line represents the correlation prediction using eq 4.

the correlation of Grunberg and Nissan45 previously used by our research group.46,47 The expression shown in eq 1 represents the viscosity of the pure ionic liquid, and it is adjusted in first place

Experimental viscosities are plotted as a function of cosolvent mole fraction in Figures 10 and 11 for the systems water + [EtMeIm]+[Et2PO4]− and DMSO + [EtMeIm]+[Et2PO4]−, respectively. It is observed that the viscosity decreases drastically with temperature and cosolvent concentration. At low cosolvent concentrations, the decreasing rate is linear. 3.3. Viscosity Correlation. The viscosity of both systems was correlated as a function of the temperature and the concentration of the cosolvent using two modifications from

⎞ ⎛ E A B ln(μ/mPa· s) = ⎜ + + ⎟ T /K ⎠ ⎝ (T /K)2

(1)

where μ is the viscosity and T is the temperature. H



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compared in Figure 10. Fitting parameters are summarized in Table 12. To correlate the viscosity of system DMSO + [EtMeIm]+[Et2PO4]−, the amount of water present in the ionic liquid was also taken into account, due to the important influence of water in the viscosity. Thus, the expression used is the one presented in eq 4, and it is also a modification of the Grunberg and Nissan correlation. Parameters E, A, B, C, D, and F, are the same for the aqueous mixtures of the IL. The rest of the parameters were adjusted for DMSO by the minimization of the average relative deviation (AARD %) in the same way as defined in eq 1. An AARD % of 9.5% was obtained with a maximum deviation of 49% at 373.15 K and xDMSO = 0. Even when in this case the behavior of the system is better described, the deviations are high. But again, due to the complex behavior of this system, these results represent a good fitting of the system for engineering purposes. The correlated and experimental data are represented in Figure 11.

Table 12. Parameters Fitted for Equations 3 and 4 E A B C D F G H I AARD % max %

eq 3

eq 4

5.18 × 105 2.51 × 103 −8.31 × 100 7.98 × 100 0.00 × 100 4.60 × 10−1

5.18 × 105 2.51 × 103 −8.31 × 100 7.98 × 100 0.00 × 100 4.60 × 10−1 9.98 × 101 2.08 × 10−1 9.61 × 10−1 9.5% 49%

13% 49%

The parameters were adjusted by minimizing the absolute average relative deviation (AARD %) objective function defined in eq 2, with n being the number of experimental data points and μexp and μcalc being the experimental and calculated viscosities, respectively.

AARD % =

⎛ E ⎞ A + + B⎟ ln(μ/(mPa·s)) = x IL⎜ 2 (T /K) ⎝ (T /K) ⎠ + x H2O×

⎛ |μexp − μcalc | ⎞ ⎟ ∑⎜ μ ⎝ exp ⎠

× 100 (2) n + − The viscosity of water + [EtMeIm] [Et2PO4] over the entire concentration range was correlated using eq 3, where T is the temperature and μi and xi are the viscosity and mole fraction of component i, respectively.

ln(μH O/(mPa ·s)) + 2

2

x ILx H2O x IL + F

(C + D(T /K))

(C + DT /K) ×

+ x DMSO ln(μDMSO/(mPa ·s)) +

⎛ E ⎞ A ln(μ/(mPa·s)) = x IL⎜ + + B⎟ + x H2O × 2 (T /K) ⎝ (T /K) ⎠ ln(μH O/(mPa ·s)) +

x ILx H2O x IL + F

x ILx DMSO (H + IT /K) x IL + G

(4)

In Figures 12 and 13 the relative deviation between the experimental data and the data calculated with eqs 3 and 4 can be observed. In general, deviations of as high as 49% can be found, and it is observed that deviations are higher at higher temperature. Nevertheless, the data deviation is distributed uniformly between both positive and negative sides, showing a good correlation of the equation. In Figure 14, we can see a comparison between the results of the viscosity of pure (x1 = 0.012) [EtMeIm]+[Et2PO4]− given by eq 3 and the literature data of different authors.20,22,35 The results

(3)

An AARD % of 13% and a maximum deviation of 49% occur at 373.15 K and xH2O = 0.012. Even when the deviations are high, due to the complex behavior of this system, these results represent a good fitting of system H2O + [EtMeIm]+[Et2PO4]− for engineering purposes. Correlation and experimental data are

Figure 12. Relative deviation plot of viscosities μ for H2O(1) + [EtMeIm]+[Et2PO4]− at atmospheric pressure. Values were calculated by eq 3 with parameters used in the correlation of experimental data measured in this work. I



Article

Figure 13. Relative deviation plot of viscosities μ for DMSO(2) + [EtMeIm]+[Et2PO4]− at atmospheric pressure. Values were calculated by eq 4 with parameters used in the correlation of experimental data measured in this work.

Figure 14. Comparison of literature data and authors’ data for pure (xH2O = 0.012) [EtMeIm]+[Et2PO4]− of viscosity μ with the results calculated from eq 3 as a function of temperature T. Hiraga et al.20 (◊), Tenney et al.35 (□), Normazlan et al.22 (Δ), and this work (○).

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of eq 3 show a good prediction capability despite the scattering of the data.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

4. CONCLUSIONS Experimental densities and viscosities of water(1) + 1-ethyl-3methylimidazolium diethylphosphate and DMSO(2) + 1-ethyl3-methylimidazolium diethylphosphate were determined over a range of temperature for nine isotherms between 293.15 K and 373.15 K and mole fractions of cosolvent x1 or x2 = 0, 0.05, 0.1, 0.15, 0.25, 0.5, 0.75, 0.9, and.1. It was found that density decreases linearly with temperature while the viscosity decreases exponentially with the same parameter. Excess molar volumes were also calculated. Both systems presented negative excess molar volumes. Nevertheless, while in the mixtures with water an increase in temperature increases the negative excess volume, in the mixtures with DMSO the negative excess molar volume decreases with temperature. Experimental viscosity data were correlated with modified Grunberg and Nissan correlations, achieving good results with AARD % = 13% for the mixtures with water and AARD % = 9.5% for the mixtures with DMSO.

ORCID

María Dolores Bermejo: 0000-0002-1693-2895 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank the Junta de Castilla y León for funding through project VA295U14 and MINECO for project ENE2014-53459R. M.D.B. thanks the Spanish Ministry of Economy and Competitiveness (MINECO) for the Ramón y Cajal research fellowship (RYC-2013-13976).

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