Estimation of Normal Boiling Temperatures, Critical Properties, and

Article pubs.acs.org/jced

Estimation of Normal Boiling Temperatures, Critical Properties, and Acentric Factors of Deep Eutectic Solvents Nouman Rafique Mirza, Nathan J. Nicholas, Yue Wu, Sandra Kentish, and Geoffrey W. Stevens* Department of Chemical and Biomolecular Engineering, The University of Melbourne, Parkville, Victoria 3010, Australia ABSTRACT: Deep eutectic solvents (DESs) are novel solvents that have shown the ability to capture carbon dioxide from flue gases. Thermodynamic modeling is needed to validate the experimental vapor−liquid equilibria (VLE) of the CO2− DES systems. To establish thermodynamic models of these solvents, their critical properties must be estimated. In the present study, a combination of the modified Lydersen−Joback−Reid (LJR) method and the Lee−Kesler mixing rules has been applied to estimate the critical properties of 39 different DESs. Normal boiling temperatures and acentric factors have also been determined. The accuracy of this method has been tested by comparison of theoretical densities determined from the estimated critical properties with experimental values. Absolute deviations ranging from 0 % to 17.4 % were observed for the estimated density values. An overall average absolute deviation of 4.9 % was observed for the studied DESs. Absolute deviations for DESs consisting of aliphatic precursors ranged from 0 % to 9.5 %, whereas for DESs consisting of at least one aromatic precursor, these ranged from 5.8 % to 17.4 %. The accuracy fell as the percentage of hydrogen-bond donors (HBD) increased. The method was also found to accurately take into account the variation in density due to a temperature change. intensive purification steps common in the synthesis of ILs.2 As a result, DESs have found potential utilization in many different areas such as innovative organic synthesis, 15 catalytic processes,16 biodiesel purification,17 drug solubilization,18 electrodeposition,19 electropolishing of metals, and metal oxide processing.20 DESs and aqueous mixtures of DESs have also shown promising results for the absorption of acid gases.21−26 In order to develop processes based upon DESs, their physical, physicochemical, and transport properties (i.e., density, viscosity, conductivity, pH, vapor pressure, critical properties, normal boiling temperature, Gibbs free energy, etc.) need to be determined. However, the focus of present-day research has mainly been on the determination of only the physicochemical and transport properties (mainly density, viscosity, and conductivity) of these solvents.12,27−29 In order to develop thermodynamic models for these solvents, an understanding of their phase equilibria is also needed. More importantly, the development of a database for the critical properties of these solvents is needed so that thermodynamic models can be applied to validate the experimental data. Because of their tendency to thermally decompose at high temperatures,14 their critical properties are extremely difficult to determine experimentally and thus have to be predicted theoretically. In this study, the critical temperatures (Tc), critical pressures (Pc), critical molar volumes (Vc), normal boiling temperatures

1. INTRODUCTION Deep eutectic solvents (DESs) have attracted much attention from the scientific community in recent years, and a number of studies have been published outlining various applications of these solvents.1,2 A DES is a combination of a salt and a hydrogen-bond donor (HBD), which when mixed in a certain molar ratio and heated mildly at a moderate temperature form a clear liquid.3 The liquid has a freezing point considerably lower than that predicted from ideal solution theory using the fusion enthalpies of the original precursors4 and thus is termed a “deep eutectic solvent”. There are a large number of precursors that can develop affiliations with each other and hence formulate deep eutectic solvents.5 These solvents share properties similar to those of low-transition-temperature mixtures (LTTMs)5 and have also been called natural deep eutectic solvents (NADES)6,7and ionic liquid analogues8,9 in the literature. Deep eutectic solvents share many similarities with ionic liquids (ILs)2 yet are regarded as different. This is due to the fact that DESs are not always composed entirely of ionic species, as the precursors for DESs can be neutral entities, e.g., a DES resulting from ZnCl2 and urea.10 Furthermore, as DESs are formed from the mixing of neutral species, they are not limited by a charge balance ratio, and therefore, the molar ratio of its precursors can be varied to obtain the eutectic solvent. Furthermore, unlike protic ionic liquids,11 a complete proton transfer is not necessarily required to form a eutectic solvent. Some major advantages of DESs over ILs are that they can be biodegradable, nontoxic, and nonflammable and can have negligible vapor pressure.12−14 Another major advantage is that they can be manufactured cheaply and readily without requiring © 2015 American Chemical Society

Received: January 13, 2015 Accepted: May 15, 2015 Published: June 2, 2015 1844

DOI: 10.1021/acs.jced.5b00046 J. Chem. Eng. Data 2015, 60, 1844−1854

Journal of Chemical & Engineering Data

Article

Table 1. Structures and Molar Ratios of Organic Salts and Hydrogen-Bond Donors for the Studied DESs

1845



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Table 1. continued

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Table 1. continued

individual contributions to the critical properties are summated to obtain the final estimate for critical properties. The accuracy of these methods varies, and the choice of method is based upon the spectrum of its applicability, ease of use, and the additional data required for estimating critical properties.35 The methods proposed by Lydersen,32 Ambrose and Young,33 and Klincewicz and Reid34 require prior knowledge of normal boiling temperatures to further estimate the critical properties of the chemical compounds. Joback and Reid36 proposed a method that also included estimation of the normal boiling points and is still used with slight modifications to estimate the properties. Constantinou et al.30 initially proposed a complex contribution method in which the molecule, on the basis of a rearrangement of the valence electrons, is considered to be composed of its dominant and recessive conjugate forms.

(Tb), and acentric factors (ω) of 39 different DESs have been estimated. The accuracy of the estimation has been tested by predicting the densities of the DESs using the estimated critical properties and comparing the results with the values already quoted in the literature. Table 1 presents the structures and molar ratios of the precursors for the 39 deep eutectic solvents studied in this work.

2. ESTIMATING CRITICAL PROPERTIES Presently there exist a number of methods in the literature for estimating critical properties. Group contribution methods have been reported by Constantinou et al.,30 Constantinou and Gani,31 Lydersen,32 Ambrose and Young,33 and Klincewicz and Reid34 In group contribution methods, the type and frequency of individual atoms or groups of atoms are considered and their 1847



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The method provides good estimates of the properties; however, its application can be tedious because of the various conjugate forms of many organic molecules. Constantinou and Gani31 later proposed another group contribution method in which a molecule is divided into two different levels. The primary level consists of the first-order functional groups such as those used in the Lydersen method.32 The secondary level contains functional groups that are worked up by considering the first-order functional groups as building blocks and provide more information about the molecular structure of the chemical compound. Property estimation is done on the basis of the primary level and then extended to the secondary level to make it more accurate and applicable for isomers. Lydersen32 defined 43 different structural groups and proposed the following equations to estimate the critical properties of organic compounds: Tc = Pc =

Pc =

Vc = 6.75 +

(1)

M (0.34 + ∑ niΔPLi)2

(2)

Vc = 40 +

∑ niΔVLi

(3)

In these equations, Tb is the normal boiling temperature (K), ni is the frequency of appearance of the ith group of atoms in the molecule, ΔTL is their contribution to the critical temperature (K), ΔPL is their contribution to the critical pressure (bar), ΔVL is their contribution to the critical molar volume (cm3· mol−1), and M is the molar mass of the entire molecule (g· mol−1). Later on, Joback and Reid36 defined 41 structural groups and, on the basis of the elemental analysis of molecules, proposed the following equations to estimate the critical properties: Tc = Pc =

TcD =

1 (0.113 + 0.0032N − ∑ niΔPJi)2

∑ niΔVMi

(10)

1 VcD0.25

∑ ∑ yyi j Vcij 0.25Tcij i

j

(11)

where

Tcij = (TciTcj)0.5 kij′

Tb 0.584 + 0.965 ∑ niΔTJi − (∑ niΔTJi)2

(9)

In these equations, ni is the frequency of appearance of the ith group of atoms in the molecule, ΔTbM is their contribution to the normal boiling temperature (K), ΔTM is their contribution to the critical temperature (K), ΔPM is their contribution to the critical pressure (bar), ΔVM is their contribution to the critical molar volume (cm3·mol−1), and M is the molar mass of the molecule (g·mol−1). In this work, the modified Lydersen−Joback−Reid method has been applied to estimate the critical properties of the precursors constituting the 39 deep eutectic solvents under study. This method was chosen because it gives an accurate estimation of the critical properties of high-molecular-weight organic molecules and is relatively simple to apply. A summary of the functional groups used in the modified LJR method and their contributions to the critical properties is presented in Table 2. Since DESs are mixtures of two or more precursors, the method used to estimate the properties of the pure precursors must be extended to estimate the properties of the final mixture. After the critical properties of the precursors were determined, the Lee−Kesler mixing rules, as recommended by Knapp et al.,39 were used to estimate the final critical properties of the DESs. These rules are given by the following equations:

Tb 0.567 + ∑ niΔTLi − (∑ niΔTLi)2

M (0.2573 + ∑ niΔPMi)2

(12)

(4)

VcD =

∑ ∑ yyi j Vcij i

(13)

j

(5)

where Vc = 17.5 +

∑ niΔVJi

(6)

Vcij =

In these equations, N is the number of atoms in the molecule, Tb is the normal boiling temperature (K), ni is the frequency of appearance of the ith group of atoms in the molecule, ΔTJ is their contribution to the critical temperature (K), ΔPJ is their contribution to the critical pressure (bar), and ΔVJ is their contribution to the critical molar volume (cm3·mol−1). Alvarez and Valderrama37 combined the Lydersen32 and Joback−Reid36 methods to give the “modified Lydersen− Joback−Reid” (LJR) method, which is specifically applicable to high-molecular-weight compounds. The method uses the same equations for estimation of critical properties as were originally proposed by Lydersen32 and Joback−Reid36 but with different parameters. The equations proposed in the method are the following: Tb = 198.2 +

Tc =

∑ niΔTbMi

PcD = (0.2905 − 0.085ωD)

(14)

RTcD VcD

(15)

where

ωD =

∑ yi ωi i

(16)

In the above equations, the subscript D refers to the final properties of the mixture, i and j refer to the pure components, yi and yj are the mole fractions of the pure components, and TcD, PcD, VcD, kij′ , and ωD are the critical temperature (K), critical pressure (bar), critical molar volume (cm3·mol−1), binary interaction parameter, and acentric factor, respectively, for the eutectic mixture. The acentric factors of the precursors (ωi) were estimated using the correlation proposed by Valderrama and Robles:38

(7)

Tb 0.5703 + 1.0121 ∑ niΔTMi − (∑ niΔTMi)2

1 (Vci1/3 + Vcj1/3)3 8

(8) 1848



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has successfully been used to predict the densities of ionic liquids,38 is given by the following equation:

Table 2. Groups of Atoms and Their Contributions to the Critical Properties for the Modified LJR Method38 ΔTbMa group

K

−CH3 −CH2− >CH− >C< CH2 CHC< C CH C− −OH (alcohol) −O− >CO −CHO −COOH −COOHCOO− O (others) −NH2 >NH >N− −N −CN −NO2 −F −Cl −Br −I −CH2− >CH− CH− >C< C< −O− −OH (phenol) >CO >NH >N− −N −B −P −SO2 a

ΔTM

ΔPM

K

Without Rings 23.58 0.0275 22.88 0.0159 21.74 0.0002 18.18 −0.0206 24.96 0.017 18.25 0.0182 24.14 −0.0003 26.15 −0.0029 0.0078 0.0078 92.88 0.0723 22.42 0.0051 94.97 0.0247 72.24 0.0294 169.06 0.0853 81.1 0.0377 0.036 −10.5 0.0273 73.23 0.0364 50.17 0.0119 11.74 −0.0028 74.6 0.0172 125.66 0.0506 152.54 0.0448 −0.03 0.0228 38.13 0.0188 66.86 0.0124 93.84 0.0148 With Rings 27.15 0.0116 21.78 0.0081 26.73 0.0114 21.32 −0.018 31.01 0.0051 31.22 0.0138 76.34 0.0291 94.97 0.0343 52.82 0.0244 0.0063 57.55 −0.0011 Other Groups −24.56 0.0352 34.86 −0.0084 147.24 −0.0563

bar

ΔVM

ρL =

−1

cm ·mol 3

0.3031 0.2165 0.114 0.0539 0.2493 0.1866 0.0832 0.0934 0.1429 0.1429 0.1343 0.13 0.2341 0.3128 0.4537 0.4139 0.4752 0.2042 0.1692 0.0322 0.0304 0.1541 0.3697 0.4529 0.2912 0.3738 0.5799 0.9174

66.81 57.11 45.7 21.78 60.37 49.92 34.9 33.85 43.97 43.97 30.4 15.61 69.76 77.46 88.6 84.76 97.77 44.03 49.1 78.96 26.7 45.54 89.32 123.62 31.47 62.08 76.6 100.79

0.1982 0.1773 0.1693 0.0139 0.0955 0.1371 0.0493 0.2751 0.0724 0.0538 0.0559

51.64 30.56 42.55 17.62 31.28 17.41 −17.44 59.32 27.61 25.17 42.15

0.0348 0.1776 −0.0606

22.45 67.01 112.19

⎡ 1 + (1 − T )2/7 ⎤ R ⎥ β = −⎢ ⎢⎣ 1 + (1 − TbR )2/7 ⎥⎦

⎛P ⎞ ⎛P ⎞ (Tc − 43 K) log⎜ c ⎟ + log⎜ c ⎟ − 1 (Tc − Tb) ⎝ Pb ⎠ ⎝ Pb ⎠

(19)

in which TR =

T Tc

(20)

and TbR =

Tb TC

(21)

In these equations, ρL is the density of the DES (g·cm−3), M is the molar mass (g·mol−1), Pc is the critical pressure (bar), R is the universal gas constant (8.314 J·mol−1·K−1), Tc is the critical temperature (K), Vc is the critical molar volume (cm3·mol−1), TR is the reduced temperature, and TbR is the reduced normal boiling point. Binary interaction parameters (kij′ ) for DESs have not yet been reported in the literature. Labinov and Sand40 studied 12 binary mixtures of other chemical species and reported that for mixtures of nonpolar substances the value of k′ij should range from 1.0 to 1.3, while for mixtures of polar substances the value should range from 0.95 to 1.06. In the present study, because of the unavailability of experimental data, a value of unity for k′ij was assumed in all of the calculations. To ensure that this assumption was reasonable, optimum kij′ values were estimated for four different DESs, each chosen from one of the categories defined in this study, by minimizing the error in the density after the critical properties were estimated from the current methodology. These kij′ values ranged from 0.81 to 1.56. A sensitivity analysis was also carried out, and the results showed that the absolute deviation of the density remained within 10 % across this range of k′ij values. This qualifies the assumption that in the absence of experimental data a value of unity for kij′ yields satisfactory results.

3. RESULTS AND DISCUSSION The estimated critical properties (Tc, Pc, and Vc), normal boiling temperatures (Tb), molar masses (M), acentric factors (ω), and ratios of the normal boiling point to the critical temperature (Tb/Tc) as well as the resultant estimated DES densities (ρest), their values previously reported in the literature (ρlit), and the deviations between the estimated and experimental densities (Δρ) are presented in Table 3. It should be pointed out that the correlation used to estimate the density values (eqs 18 to 21) is completely independent of the modified LJR method and the Lee−Kesler mixing rules. Therefore, it can be said that density estimation and comparison with published values is a reliable, independent test of the accuracy of the estimated properties. Table 3 shows that the estimated densities are in good agreement with the published values. The minimum absolute deviation is observed for (ChCl:EG)1:3 (0 %), while the maximum deviation is 17 % for (Me-tri-PBR:TEG)1:5. The overall average absolute

⎛P ⎞ (Tb − 43 K)(Tc − 43 K) log⎜ c ⎟ (Tc − Tb)(0.7Tc − 43 K) ⎝ Pb ⎠ −

(18)

where

Missing values were assumed to be equal to zero.

ωi =

β MPcD ⎛ 0.3445PcDVcD1.0135 ⎞ ⎜ ⎟ RTcD ⎝ TcD ⎠

(17)

To estimate the density from these critical properties, a correlation based upon the work of Spencer and Danner41 was used. The correlation42 requires knowledge of the normal boiling temperature, molecular weight, and critical properties to estimate the density of the compound. The correlation, which 1849



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Table 3. Estimated Critical Properties and Comparison of Densities (at 40 °C) with Literature Values for 39 Different DESs DES (ChCl:U)1:2 (ChCl:EG)1:2 (ChCl:G)1:2 (ChCl:MA)1:2 (ChCl:B)1:3 (ChCl:TFA)1:2 (ChCl:LA)1:1.3 (ChCl:Ph)1:2 (AcChCl:U)1:2 (EtACl:U)1:1.5 (EtACl:AA)1:1.5 (EtACl:TFA)1:1.5 (di-EtACl:EG)1:2 (di-EtACl:G)1:2 (Me-tri-PBr:G)1:2 (Me-tri-PBr:EG)1:3 (Me-tri-PBr:TEG)1:5 (ChCl:G)1:1 (ChCl:G)1:3 (di-EtACl:TFA)1:2 (ChCl:EG)1:3 (ChCl:Ph)1:3 (ChCl:Ph)1:4 (ChCl:LA)1:1.5 (ChCl:LA)1:2 (ChCl:LA)1:2.5 (ChCl:LA)1:3 (ChCl:LA)1:3.5 (ChCl:LA)1:4 (ChCl:LA)1:5 (ChCl:LA)1:8 (ChCl:LA)1:10 (ChCl:LA)1:15 (Me-tri-PBr:G)1:1.75 (Me-tri-PBr:EG)1:4 (ChCl:F)2.5:1 (ChCl:F)2:1 (ChCl:F)1.5:1 (ChCl:F)1:1 a

M

Tb

Tc

Pc

Vc

g·mol−1

K

K

bar

cm3·mol−1

86.58 87.92 107.93 115.91 102.50 121.90 111.62 109.28 100.60 68.65 68.06 100.44 92.60 112.61 180.50 135.86 184.68 115.86 103.97 126.58 81.46 105.49 103.21 109.90 106.59 104.23 102.47 101.09 99.99 98.34 95.58 94.58 93.18 188.5 121.1 151.2 153.13 155.84 159.89

445.6 439.0 515.4 550.3 471.0 408.8 495.2 445.3 461.6 381.6 351.8 348.5 446.5 522.9 635.4 526.7 608.0 500.9 522.6 416.4 436.7 443.8 442.9 497.5 502.0 505.2 507.6 509.4 510.9 513.1 516.8 518.2 520.1 643.7 507.3 574.9 594.5 621.9 663.0

644.4 602.0 680.67 738.71 637.97 589.24 671.26 651.15 667.24 582.07 544.27 531.92 611.68 690.79 832.40 708.03 799.52 664.90 688.98 596.14 600.48 655.66 658.52 674.60 681.14 685.93 689.60 692.50 694.85 698.42 704.52 706.78 710.00 843.77 684.72 737.10 756.99 785.24 828.52

49.35 40.39 33.06 37.90 33.42 39.58 35.26 44.53 45.80 63.13 57.73 49.52 38.38 31.42 26.87 35.16 25.56 31.05 34.20 37.82 43.41 47.91 50.12 35.97 37.42 38.53 39.39 40.09 40.67 41.57 43.14 43.74 44.62 26.41 37.58 25.71 25.46 25.05 24.28

254.37 259.67 315.17 319.65 330.34 303.67 328.35 297.58 287.55 192.20 203.09 232.77 270.13 326.30 455.97 335.88 517.16 345.17 300.50 320.32 239.41 281.06 271.30 321.82 309.42 300.66 294.15 289.11 285.10 279.12 269.24 265.68 260.69 475.58 303.04 451.68 453.53 456.15 460.06

ω 0.661 0.952 1.251 1.097 0.968 0.532 0.977 0.538 0.624 0.468 0.369 0.351 1.019 1.317 1.334 1.058 1.078 1.137 1.307 0.542 0.968 0.511 0.496 0.989 1.012 1.028 1.040 1.049 1.056 1.067 1.084 1.091 1.100 1.311 1.064 1.188 1.259 1.359 1.510

Tb/Tc 0.69 0.73 0.76 0.74 0.74 0.69 0.74 0.68 0.69 0.66 0.65 0.66 0.73 0.76 0.76 0.74 0.76 0.75 0.76 0.70 0.73 0.68 0.67 0.74 0.74 0.74 0.74 0.74 0.74 0.73 0.73 0.73 0.73 0.76 0.74 0.78 0.79 0.79 0.80

ρest

ρlit

Δρ

g·cm−3

g·cm−3

%

1.076 1.097 1.211 1.284 1.057 1.248 1.152 1.150 1.131 1.055 0.974 1.250 1.120 1.248 1.511 1.409 1.323 1.182 1.235 1.239 1.117 1.170 1.183 1.160 1.175 1.185 1.193 1.199 1.204 1.212 1.224 1.229 1.235 1.514 1.395 1.260 1.296 1.347 1.425

44

1.189 1.10945 1.18346 1.18525 1.052a,47 1.342b,1 1.15748 1.08749 1.206b,1 1.140b,1 1.041b,1 1.273b,1 1.09027 1.173b,27 1.306b,27 1.24027 1.186b,28 1.156b,27 1.19527 1.29027 1.117b,27 1.08249 1.08049 1.16548 1.16948 1.17448 1.17948 1.18248 1.18248 1.18948 1.19648 1.19948 1.19948 1.290b,27 1.233b,27 1.259b,50 1.278b,50 1.304b,50 1.337b,50

−9.5 −1.1 2.4 8.4 0.5 −7.0 −0.4 5.8 −6.2 −7.5 −6.4 −1.8 2.8 6.4 15.7 13.6 11.6 2.3 3.4 −4.0 0.0 8.1 9.5 −0.4 0.5 0.9 1.2 1.4 1.9 1.9 2.3 2.5 3.0 17.4 13.1 0.1 1.4 3.3 6.6

At 293.15 K. bAt 298.15 K.

the presence of these stronger interactions affects the accuracy of the LRJ and Lee−Kesler methods, both of which assume no interactions within the chemical species.39−41,44,47 DESs containing a greater number of aromatic rings are observed to show larger deviations. For example, (ChCl:Ph)1:3, which contains only one ring, shows a deviation of 8.1 %, while (Metri-PBr:EG)1:3, which contains three rings, shows a deviation of 13.6 %. It is also observed that as the mass percentage of ringcontaining precursor is increased in a certain DES, the resulting deviation is also increased. For example, the deviations for (ChCl:Ph)1:2, (ChCl:Ph)1:3, and (ChCl:Ph)1:4 are 5.8 %, 8.1 %, and 9.5 %, respectively. There are only two DESs in the group containing carboxylic acids. Deviations for these two DESs range from −0.4 % to 8.4 %. (ChCl:MA)1:2 shows a higher deviation than all of the DESs involving (ChCl:LA). This could be attributed to an additional carboxylic radical present in the (ChCl:MA)1:2 DES. An increase in the number of functional groups means that there

deviation of the density is 4.9 %, showing good agreement with the published data. An attempt was made to classify the DESs on the basis of the functional groups they contain, and this resulted in four distinct groups (Table 1): amide-containing DESs, aromatic-containing DESs, carboxylic acid-containing DESs, and alcohol-containing DESs. It is clear that all of the DESs containing at least one amide group result in a negative deviation in the predicted density. The deviation ranges from −1.8 % to −9.5 %. DESs containing two amide groups exhibit an absolute deviation of more than 6 %. A maximum deviation of −9.5 % is observed for (ChCl:U)1:2, which contains two amide groups, while the minimum deviation is −1.8 % for (EtACl:TFA)1:1.5, which contains only one amide group. Greater deviations are exhibited by DESs containing one or more aromatic rings. Aromatics are small molecules with stronger interaction forces between them.51 In addition to the hydrogen bonding that exists between the precursors of DESs, 1850



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Table 4. Comparison of Absolute Deviations of Densities from the Present Work and a Previous Study29 (Obtained Using Same Methods) |Δρ|/%

a

Salt

HBD

DES

this work

ref 29a

choline chloride choline chloride choline chloride N,N-diethylethanolammonium chloride N,N-diethylethanolammonium chloride methyltriphenylphosphonium bromide methyltriphenylphosphonium bromide

ethylene glycol trifluoroacetamide glycerol glycerol trifluoroacetamide glycerol ethylene glycol

(ChCl:EG)1:2 (ChCl:TFA)1:2 (ChCl:G)1:1 (di-EtACl:G)1:2 (di-EtACl:TFA)1:2 (Me-tri-PBr:G)1:2 (Me-tri-PBr:EG)1:4

1.1 7.0 2.3 6.4 4.0 15.7 13.1

23.4 28.9 17.4 12.3 22.6 21.8 0.30

Deviations for estimated densities at 35 and 45 °C are given. Interpolation was done to obtain deviation values for 40 °C.

Figure 1. Variation of the deviation in densities with different mole fractions of precursors in the DESs. Dotted lines represent linear fits to the deviations.

exception of (Me-tri-PBr:EG)1:4] were observed in the present work. It is to be noted that the authors of the previous study29 used a different correlation for the density to check the accuracy of the estimated critical properties. This suggests that the correlation described by Valderrama and co-workers38,42 (eqs 18 to 21) results in better estimates of the density values of DESs. Figure 1 shows the variation in density predictions with HBD content for choline chloride:glycerol (ChCl:G)-based and choline chloride:lactic acid (ChCl:LA)-based DESs. For both type of DESs, the absolute deviation tends to increase with increasing mole fraction of HBD in the deep eutectic solvent. An increase in the amount of HBD results in the introduction of more potential sites to develop weak bonding between HBDs and anions of the organic salt. This more complex bonding reduces the accuracy of the current method for estimating the critical properties. Therefore, with an increase in the amount of HBD, a larger deviation in the density estimate is observed. In the case of ChCl:G-based DESs, the absolute deviation ranges from 1.4 % to 3.4 %, while in the case of ChCl:LA-based DESs it ranges from −0.4 % to 3.0 %. In the literature it is a common practice to draw an analogy between ionic liquids and DESs because of their similar physicochemical properties.2,8,9 This analogy is not completely valid with regard to the estimation of critical properties.

are more potential active sites and hence greater potential for more inter- and intramolecular forces, resulting in more complex bonding forces. Since the method does not take into account the effect of bonding forces, their existence reduces the accuracy of the method. Alcohol-containing DESs are the largest group. The minimum deviation within this group is 0 % for (ChCl:EG)1:3, while the maximum deviation of 6.6 % is observed for (ChCl:F)1:1. In all of the DESs, an increase in the mass percentage of precursor containing a larger number of −OH groups results in higher deviations. For example, the mass percentages of glycerol in (ChCl:G)1:1, (ChCl:G)1:2, and (ChCl:G)1:3 are 39.74 %, 56.89 %, and 69.07 %, respectively, and the deviations for these DESs are 2.2 %, 2.4 %, and 3.4 %, respectively. In a previous study, Shahbaz et al.29 compared different methods of estimating the critical properties of DESs and applied these to the same density evaluation test. One of the methods they applied was the same as the one used in this study. However, their results differ from those presented here. Table 4 shows seven of the nine DESs studied by these authors and compares their results with the ones obtained in the current study. It is clear from Table 4 that in comparison to the previous study,29 significantly lower absolute deviations [with the 1851



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Figure 2. Variation of estimated and experimental densities with temperature for various DESs. Open symbols are estimated values, and solid symbols are experimental values; dashed and solid lines are linear fits to the data points.

Lee−Kesler mixing rules were used to combined these individual parameters to estimate the final critical properties and acentric factors of the DESs. After the final critical properties of DESs were obtained, a correlation proposed by Valderrama and Abu-Sharkh42 was used to estimate the densities of these DESs. These density estimates were then compared with experimental values to check the accuracy of the estimated boiling points, acentric factors, and critical properties. The results showed that the amide-containing DESs showed a negative deviation in the density estimation (in the range of −1.8 % to −9.5 %), aromatic-containing DESs a higher positive deviation (in the range of 5.8 % to 17.4 %), carboxylic acidcontaining DESs a moderate deviation (in the range of −0.4 % to 8.4 %), and alcohol-containing DESs a lower deviation (in the range of 0 % to 6.6 %). In all of the DESs studied, an increase in mass percentage of the HBD also increased the deviation in the density estimation.

Therefore, certain aspects of the estimation methods for critical properties applied to ILs cannot be assumed to work perfectly well for DESs. Values of the ratio of the normal boiling point to the critical temperature (Tb/Tc) are also given in Table 3. In a previous study,43 a fixed value of 0.60 was assumed for this ratio to estimate the normal boiling points and critical temperatures of ionic liquids. Table 3 shows that the values of the Tb/Tc ratio range between 0.65 and 0.80 for different DESs, so a fixed value for the ratio cannot be assumed. Finally, the density values for three different DESs [(ChCl:EG)1:2, (ChCl:G)1:2, and (Me-tri-PBr:G)1:2] were estimated over the temperature range from 298.15 K to 348.15 K. A comparison of these values with literature data is shown in Figure 2. The experimental value for (ChCl:EG)1:2 drops suddenly at 318.15 K, which could be attributed to an experimental error. Other than this, density values for both (ChCl:EG)1:2 and (ChCl:G)1:2 agree well with the published literature. The deviations in the densities for these two DESs range from 0.0 % to −3.6 % over this temperature range. However, the deviation for (Me-tri-PBr:G)1:2 ranges from 14.2 % to 15.7 %. This large deviation can be attributed to the presence of aromatic species in the DES in the form of methyltriphenylphosphonium bromide, which reduces the accuracy of the method because of the additional interaction forces. In summary, on the basis of the functional groups present, the DESs in this study have been classified into four different categories: amide-containing DESs, carboxylic acid-containing DESs, alcohol-containing DESs, and aromatic-containing DESs. The critical properties of these DESs were estimated using a combination of a modified Lydersen−Joback−Reid method and the Lee−Kesler mixing rules via the following procedure. First, by means of the group contribution method, individual boiling points and the critical properties of the constituents of the DESs were estimated using the modified LJR method. From the boiling points and critical properties of the individual constituents, individual acentric factors were estimated using a correlation described by Valderrama and Robles.38 Then the

4. CONCLUSIONS A combination of the Lydersen−Joback−Reid method and the Lee−Kesler mixing rules was applied to estimate the critical properties of 39 different deep eutectic solvents. Additionally, the acentric factors and normal boiling temperatures were determined. The consistency of the method was tested by estimating the densities of these deep eutectic solvents using an independent correlation and comparing the values with experimental data in the literature. The correlation used for density estimation was based upon the critical properties and the molecular weight of the deep eutectic solvents and therefore can safely be assumed to be a good test of the applicability of the method to DESs. Comparison of the estimated and published density values shows good agreement for DESs consisting of aliphatic precursors. However, because of the presence of stronger interaction forces, the method yields higher deviations when at least one aromatic group is present in the DES. The method gives satisfactory results when changes in molar ratios and density variations with temperature are taken into account. 1852



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AUTHOR INFORMATION

Corresponding Author

*Tel.: +61 3 83446621. Fax: +61 3 83448824. E-mail: [email protected]. Funding

This research was funded by the University of Melbourne and used facilities from the Cooperative Research Centre for Greenhouse Gas Remediation, Australia. Notes

The authors declare no competing financial interest.

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Estimation of Normal Boiling Temperatures, Critical Properties, and

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