Estimation of Thermodynamic Properties

Estimation of Normal Boiling Temperatures, Critical Properties, andAcentric Factors of Deep Eutectic SolventsNouman Raque Mirza, Nathan J. Nicholas, Yue Wu, Sandra Kentish, and Georey 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 shownthe ability to capture carbon dioxide from ue gases. Thermodynamic modeling isneeded to validate the experimental vaporliquid equilibria (VLE) of the CO2DES systems. To establish thermodynamic models of these solvents, their criticalproperties must be estimated. In the present study, a combination of the modiedLydersenJobackReid (LJR) method and the LeeKesler mixing rules has beenapplied to estimate the critical properties of 39 dierent DESs. Normal boilingtemperatures and acentric factors have also been determined. The accuracy of thismethod has been tested by comparison of theoretical densities determined fromthe estimated critical properties with experimental values. Absolute deviationsranging from 0 % to 17.4 % were observed for the estimated density values. Anoverall average absolute deviation of 4.9 % was observed for the studied DESs.Absolute deviations for DESs consisting of aliphatic precursors ranged from 0 % to9.5 %, whereas for DESs consisting of at least one aromatic precursor, these ranged from 5.8 % to 17.4 %. The accuracy fell as thepercentage of hydrogen-bond donors (HBD) increased. The method was also found to accurately take into account the variationin density due to a temperature change.

1. INTRODUCTIONDeep eutectic solvents (DESs) have attracted much attentionfrom the scientic community in recent years, and a number ofstudies have been published outlining various applications ofthese solvents.1,2 A DES is a combination of a salt and ahydrogen-bond donor (HBD), which when mixed in a certainmolar ratio and heated mildly at a moderate temperature form aclear liquid.3 The liquid has a freezing point considerably lowerthan that predicted from ideal solution theory using the fusionenthalpies of the original precursors4 and thus is termed adeep eutectic solvent. There are a large number of precursorsthat can develop aliations with each other and henceformulate deep eutectic solvents.5 These solvents shareproperties similar to those of low-transition-temperaturemixtures (LTTMs)5 and have also been called natural deepeutectic solvents (NADES)6,7and ionic liquid analogues8,9 inthe literature.Deep eutectic solvents share many similarities with ionic

liquids (ILs)2 yet are regarded as dierent. This is due to thefact that DESs are not always composed entirely of ionicspecies, as the precursors for DESs can be neutral entities, e.g.,a DES resulting from ZnCl2 and urea.

10 Furthermore, as DESsare formed from the mixing of neutral species, they are notlimited by a charge balance ratio, and therefore, the molar ratioof its precursors can be varied to obtain the eutectic solvent.Furthermore, unlike protic ionic liquids,11 a complete protontransfer is not necessarily required to form a eutectic solvent.Some major advantages of DESs over ILs are that they can be

biodegradable, nontoxic, and nonammable and can havenegligible vapor pressure.1214 Another major advantage is thatthey can be manufactured cheaply and readily without requiring

intensive purication steps common in the synthesis of ILs.2 Asa result, DESs have found potential utilization in many dierentareas such as innovative organic synthesis,15 catalyticprocesses,16 biodiesel purication,17 drug solubilization,18

electrodeposition,19 electropolishing of metals, and metaloxide processing.20 DESs and aqueous mixtures of DESs havealso shown promising results for the absorption of acidgases.2126

In order to develop processes based upon DESs, theirphysical, physicochemical, and transport properties (i.e.,density, viscosity, conductivity, pH, vapor pressure, criticalproperties, normal boiling temperature, Gibbs free energy, etc.)need to be determined. However, the focus of present-dayresearch has mainly been on the determination of only thephysicochemical and transport properties (mainly density,viscosity, and conductivity) of these solvents.12,2729 In orderto develop thermodynamic models for these solvents, anunderstanding of their phase equilibria is also needed. Moreimportantly, the development of a database for the criticalproperties of these solvents is needed so that thermodynamicmodels can be applied to validate the experimental data.Because of their tendency to thermally decompose at hightemperatures,14 their critical properties are extremely dicult todetermine experimentally and thus have to be predictedtheoretically.In this study, the critical temperatures (Tc), critical pressures

(Pc), critical molar volumes (Vc), normal boiling temperatures

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

Article

pubs.acs.org/jced

2015 American Chemical Society 1844 DOI: 10.1021/acs.jced.5b00046J. Chem. Eng. Data 2015, 60, 18441854

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

Journal of Chemical & Engineering Data Article

DOI: 10.1021/acs.jced.5b00046J. Chem. Eng. Data 2015, 60, 18441854

1845

Table 1. continued



1846

(Tb), and acentric factors () of 39 dierent DESs have beenestimated. The accuracy of the estimation has been tested bypredicting the densities of the DESs using the estimated criticalproperties and comparing the results with the values alreadyquoted in the literature. Table 1 presents the structures andmolar ratios of the precursors for the 39 deep eutectic solventsstudied in this work.

2. ESTIMATING CRITICAL PROPERTIES

Presently there exist a number of methods in the literature forestimating critical properties. Group contribution methods havebeen reported by Constantinou et al.,30 Constantinou andGani,31 Lydersen,32 Ambrose and Young,33 and Klincewicz andReid34 In group contribution methods, the type and frequencyof individual atoms or groups of atoms are considered and their

individual contributions to the critical properties are summatedto obtain the nal estimate for critical properties. The accuracyof these methods varies, and the choice of method is basedupon the spectrum of its applicability, ease of use, and theadditional data required for estimating critical properties.35

The methods proposed by Lydersen,32 Ambrose andYoung,33 and Klincewicz and Reid34 require prior knowledgeof normal boiling temperatures to further estimate the criticalproperties of the chemical compounds. Joback and Reid36

proposed a method that also included estimation of the normalboiling points and is still used with slight modications toestimate the properties. Constantinou et al.30 initially proposeda complex contribution method in which the molecule, on thebasis of a rearrangement of the valence electrons, is consideredto be composed of its dominant and recessive conjugate forms.

Table 1. continued



1847

The method provides good estimates of the properties;however, its application can be tedious because of the variousconjugate forms of many organic molecules. Constantinou andGani31 later proposed another group contribution method inwhich a molecule is divided into two dierent levels. Theprimary level consists of the rst-order functional groups suchas those used in the Lydersen method.32 The secondary levelcontains functional groups that are worked up by consideringthe rst-order functional groups as building blocks and providemore information about the molecular structure of the chemicalcompound. Property estimation is done on the basis of theprimary level and then extended to the secondary level to makeit more accurate and applicable for isomers.Lydersen32 dened 43 dierent structural groups and

proposed the following equations to estimate the criticalproperties of organic compounds:

=+

TT

n T n T0.567 ( )i i i ic

b

L L2

(1)

=+

PM

n P(0.34 )i ic

L2

(2)

= + V n V40 i ic L (3)In these equations, Tb is the normal boiling temperature (K), niis the frequency of appearance of the ith group of atoms in themolecule, TL is their contribution to the critical temperature(K), PL is their contribution to the critical pressure (bar),VL is their contribution to the critical molar volume (cm3mol1), and M is the molar mass of the entire molecule (gmol1).Later on, Joback and Reid36 dened 41 structural groups and,

on the basis of the elemental analysis of molecules, proposedthe following equations to estimate the critical properties:

=+

TTn T n T0.584 0.965 ( )i i i i

cb

J J2

(4)

=+

PN n P1

(0.113 0.0032 )i ic

J2

(5)

= + V n V17.5 i ic J (6)In these equations, N is the number of atoms in the molecule,Tb is the normal boiling temperature (K), ni is the frequency ofappearance of the ith group of atoms in the molecule, TJ istheir contribution to the critical temperature (K), PJ is theircontribution to the critical pressure (bar), and VJ is theircontribution to the critical molar volume (cm3mol1).Alvarez and Valderrama37 combined the Lydersen32 and

JobackReid36 methods to give the modied LydersenJobackReid (LJR) method, which is specically applicable tohigh-molecular-weight compounds. The method uses the sameequations for estimation of critical properties as were originallyproposed by Lydersen32 and JobackReid36 but with dierentparameters. The equations proposed in the method are thefollowing:

= + T n T198.2 i ib bM (7)

=+

TTn T n T0.5703 1.0121 ( )i i i i

cb

M M2

(8)

=+

PM

n P(0.2573 )i ic

M2

(9)

= + V n V6.75 i ic M (10)In these equations, ni is the frequency of appearance of the ithgroup of atoms in the molecule, TbM is their contribution tothe normal boiling temperature (K), TM is their contributionto the critical temperature (K), PM is their contribution to thecritical pressure (bar), VM is their contribution to the criticalmolar volume (cm3mol1), and M is the molar mass of themolecule (gmol1).In this work, the modied LydersenJobackReid method

has been applied to estimate the critical properties of theprecursors constituting the 39 deep eutectic solvents understudy. This method was chosen because it gives an accurateestimation of the critical properties of high-molecular-weightorganic molecules and is relatively simple to apply. A summaryof the functional groups used in the modied LJR method andtheir contributions to the critical properties is presented inTable 2.Since DESs are mixtures of two or more precursors, the

method used to estimate the properties of the pure precursorsmust be extended to estimate the properties of the nalmixture. After the critical properties of the precursors weredetermined, the LeeKesler mixing rules, as recommended byKnapp et al.,39 were used to estimate the nal critical propertiesof the DESs. These rules are given by the following equations:

=TV

yy V T1

i ji j ij ijcD

cD0.25 c

0.25c

(11)

where

= T T T k( )ij i j ijc c c 0.5 (12)

=V yy Vi j

i j ijcD c(13)

where

= +V V V18( )ij i jc c

1/3c1/3 3

(14)

= P RTV

(0.2905 0.085 )cD DcD

cD (15)

where

= yi

i iD(16)

In the above equations, the subscript D refers to the nalproperties of the mixture, i and j refer to the pure components,yi and yj are the mole fractions of the pure components, andTcD, PcD, VcD, kij, and D are the critical temperature (K),critical pressure (bar), critical molar volume (cm3mol1),binary interaction parameter, and acentric factor, respectively,for the eutectic mixture. The acentric factors of the precursors(i) were estimated using the correlation proposed byValderrama and Robles:38



1848

=

+

T TT T T

PP

TT T

PP

PP

( 43 K)( 43 K)( )(0.7 43 K)

log

( 43 K)( )

log log 1

ib c

c b c

c

b

c

c b

c

b

c

b (17)

To estimate the density from these critical properties, acorrelation based upon the work of Spencer and Danner41 wasused. The correlation42 requires knowledge of the normalboiling temperature, molecular weight, and critical properties toestimate the density of the compound. The correlation, which

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

=

MPRT

P VT

0.3445L

cD

cD

cD cD1.0135

cD (18)

where

= + +

TT

1 (1 )

1 (1 )R

2/7

bR2/7

(19)

in which

=T TTR c (20)

and

=T TTbRb

C (21)

In these equations, L is the density of the DES (gcm3), M is

the molar mass (gmol1), Pc is the critical pressure (bar), R isthe universal gas constant (8.314 Jmol1K1), Tc is the criticaltemperature (K), Vc is the critical molar volume (cm

3mol1),TR is the reduced temperature, and TbR is the reduced normalboiling point.Binary interaction parameters (kij) for DESs have not yet

been reported in the literature. Labinov and Sand40 studied 12binary mixtures of other chemical species and reported that formixtures of nonpolar substances the value of kij should rangefrom 1.0 to 1.3, while for mixtures of polar substances the valueshould range from 0.95 to 1.06. In the present study, because ofthe unavailability of experimental data, a value of unity for kijwas assumed in all of the calculations. To ensure that thisassumption was reasonable, optimum kij values were estimatedfor four dierent DESs, each chosen from one of the categoriesdened in this study, by minimizing the error in the densityafter the critical properties were estimated from the currentmethodology. These kij values ranged from 0.81 to 1.56. Asensitivity analysis was also carried out, and the results showedthat the absolute deviation of the density remained within 10 %across this range of kij values. This qualies the assumption thatin the absence of experimental data a value of unity for kij yieldssatisfactory results.

3. RESULTS AND DISCUSSIONThe estimated critical properties (Tc, Pc, and Vc), normalboiling temperatures (Tb), molar masses (M), acentric factors(), and ratios of the normal boiling point to the criticaltemperature (Tb/Tc) as well as the resultant estimated DESdensities (est), their values previously reported in the literature(lit), and the deviations between the estimated andexperimental densities () are presented in Table 3. It shouldbe pointed out that the correlation used to estimate the densityvalues (eqs 18 to 21) is completely independent of themodied LJR method and the LeeKesler mixing rules.Therefore, it can be said that density estimation andcomparison with published values is a reliable, independenttest of the accuracy of the estimated properties. Table 3 showsthat the estimated densities are in good agreement with thepublished values. The minimum absolute deviation is observedfor (ChCl:EG)1:3 (0 %), while the maximum deviation is 17 %for (Me-tri-PBR:TEG)1:5. The overall average absolute

Table 2. Groups of Atoms and Their Contributions to theCritical Properties for the Modied LJR Method38

TbMa TM PM VMgroup K K bar cm3mol1

Without RingsCH3 23.58 0.0275 0.3031 66.81CH2 22.88 0.0159 0.2165 57.11>CH 21.74 0.0002 0.114 45.7>C< 18.18 0.0206 0.0539 21.78CH2 24.96 0.017 0.2493 60.37CH- 18.25 0.0182 0.1866 49.92C< 24.14 0.0003 0.0832 34.9C 26.15 0.0029 0.0934 33.85CH 0.0078 0.1429 43.97C 0.0078 0.1429 43.97OH (alcohol) 92.88 0.0723 0.1343 30.4O 22.42 0.0051 0.13 15.61>CO 94.97 0.0247 0.2341 69.76CHO 72.24 0.0294 0.3128 77.46COOH 169.06 0.0853 0.4537 88.6COO- 81.1 0.0377 0.4139 84.76HCOO 0.036 0.4752 97.77O (others) 10.5 0.0273 0.2042 44.03NH2 73.23 0.0364 0.1692 49.1>NH 50.17 0.0119 0.0322 78.96>N 11.74 0.0028 0.0304 26.7N 74.6 0.0172 0.1541 45.54CN 125.66 0.0506 0.3697 89.32NO2 152.54 0.0448 0.4529 123.62F 0.03 0.0228 0.2912 31.47Cl 38.13 0.0188 0.3738 62.08Br 66.86 0.0124 0.5799 76.6I 93.84 0.0148 0.9174 100.79

With RingsCH2 27.15 0.0116 0.1982 51.64>CH 21.78 0.0081 0.1773 30.56CH 26.73 0.0114 0.1693 42.55>C< 21.32 0.018 0.0139 17.62C< 31.01 0.0051 0.0955 31.28O 31.22 0.0138 0.1371 17.41OH (phenol) 76.34 0.0291 0.0493 17.44>CO 94.97 0.0343 0.2751 59.32>NH 52.82 0.0244 0.0724 27.61>N 0.0063 0.0538 25.17N 57.55 0.0011 0.0559 42.15

Other GroupsB 24.56 0.0352 0.0348 22.45P 34.86 0.0084 0.1776 67.01SO2 147.24 0.0563 0.0606 112.19

aMissing values were assumed to be equal to zero.



1849

deviation of the density is 4.9 %, showing good agreement withthe published data.An attempt was made to classify the DESs on the basis of the

functional groups they contain, and this resulted in four distinctgroups (Table 1): amide-containing DESs, aromatic-containingDESs, carboxylic acid-containing DESs, and alcohol-containingDESs. It is clear that all of the DESs containing at least oneamide group result in a negative deviation in the predicteddensity. The deviation ranges from 1.8 % to 9.5 %. DESscontaining two amide groups exhibit an absolute deviation ofmore than 6 %. A maximum deviation of 9.5 % is observed for(ChCl:U)1:2, which contains two amide groups, while theminimum deviation is 1.8 % for (EtACl:TFA)1:1.5, whichcontains only one amide group.Greater deviations are exhibited by DESs containing one or

more aromatic rings. Aromatics are small molecules withstronger interaction forces between them.51 In addition to thehydrogen bonding that exists between the precursors of DESs,

the presence of these stronger interactions aects the accuracyof the LRJ and LeeKesler methods, both of which assume nointeractions within the chemical species.3941,44,47 DESscontaining a greater number of aromatic rings are observedto show larger deviations. For example, (ChCl:Ph)1:3, whichcontains only one ring, shows a deviation of 8.1 %, while (Me-tri-PBr:EG)1:3, which contains three rings, shows a deviation of13.6 %. It is also observed that as the mass percentage of ring-containing precursor is increased in a certain DES, the resultingdeviation 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 DESsinvolving (ChCl:LA). This could be attributed to an additionalcarboxylic radical present in the (ChCl:MA)1:2 DES. Anincrease in the number of functional groups means that there

Table 3. Estimated Critical Properties and Comparison of Densities (at 40 C) with Literature Values for 39 Dierent DESs

M Tb Tc Pc Vc est lit

DES gmol1 K K bar cm3mol1 Tb/Tc gcm3 gcm3 %

(ChCl:U)1:2 86.58 445.6 644.4 49.35 254.37 0.661 0.69 1.076 1.18944 9.5

(ChCl:EG)1:2 87.92 439.0 602.0 40.39 259.67 0.952 0.73 1.097 1.10945 1.1

(ChCl:G)1:2 107.93 515.4 680.67 33.06 315.17 1.251 0.76 1.211 1.18346 2.4

(ChCl:MA)1:2 115.91 550.3 738.71 37.90 319.65 1.097 0.74 1.284 1.18525 8.4

(ChCl:B)1:3 102.50 471.0 637.97 33.42 330.34 0.968 0.74 1.057 1.052a,47 0.5

(ChCl:TFA)1:2 121.90 408.8 589.24 39.58 303.67 0.532 0.69 1.248 1.342b,1 7.0

(ChCl:LA)1:1.3 111.62 495.2 671.26 35.26 328.35 0.977 0.74 1.152 1.15748 0.4

(ChCl:Ph)1:2 109.28 445.3 651.15 44.53 297.58 0.538 0.68 1.150 1.08749 5.8

(AcChCl:U)1:2 100.60 461.6 667.24 45.80 287.55 0.624 0.69 1.131 1.206b,1 6.2

(EtACl:U)1:1.5 68.65 381.6 582.07 63.13 192.20 0.468 0.66 1.055 1.140b,1 7.5

(EtACl:AA)1:1.5 68.06 351.8 544.27 57.73 203.09 0.369 0.65 0.974 1.041b,1 6.4

(EtACl:TFA)1:1.5 100.44 348.5 531.92 49.52 232.77 0.351 0.66 1.250 1.273b,1 1.8

(di-EtACl:EG)1:2 92.60 446.5 611.68 38.38 270.13 1.019 0.73 1.120 1.09027 2.8

(di-EtACl:G)1:2 112.61 522.9 690.79 31.42 326.30 1.317 0.76 1.248 1.173b,27 6.4

(Me-tri-PBr:G)1:2 180.50 635.4 832.40 26.87 455.97 1.334 0.76 1.511 1.306b,27 15.7

(Me-tri-PBr:EG)1:3 135.86 526.7 708.03 35.16 335.88 1.058 0.74 1.409 1.24027 13.6

(Me-tri-PBr:TEG)1:5 184.68 608.0 799.52 25.56 517.16 1.078 0.76 1.323 1.186b,28 11.6

(ChCl:G)1:1 115.86 500.9 664.90 31.05 345.17 1.137 0.75 1.182 1.156b,27 2.3

(ChCl:G)1:3 103.97 522.6 688.98 34.20 300.50 1.307 0.76 1.235 1.19527 3.4

(di-EtACl:TFA)1:2 126.58 416.4 596.14 37.82 320.32 0.542 0.70 1.239 1.29027 4.0

(ChCl:EG)1:3 81.46 436.7 600.48 43.41 239.41 0.968 0.73 1.117 1.117b,27 0.0

(ChCl:Ph)1:3 105.49 443.8 655.66 47.91 281.06 0.511 0.68 1.170 1.08249 8.1

(ChCl:Ph)1:4 103.21 442.9 658.52 50.12 271.30 0.496 0.67 1.183 1.08049 9.5

(ChCl:LA)1:1.5 109.90 497.5 674.60 35.97 321.82 0.989 0.74 1.160 1.16548 0.4

(ChCl:LA)1:2 106.59 502.0 681.14 37.42 309.42 1.012 0.74 1.175 1.16948 0.5

(ChCl:LA)1:2.5 104.23 505.2 685.93 38.53 300.66 1.028 0.74 1.185 1.17448 0.9

(ChCl:LA)1:3 102.47 507.6 689.60 39.39 294.15 1.040 0.74 1.193 1.17948 1.2

(ChCl:LA)1:3.5 101.09 509.4 692.50 40.09 289.11 1.049 0.74 1.199 1.18248 1.4

(ChCl:LA)1:4 99.99 510.9 694.85 40.67 285.10 1.056 0.74 1.204 1.18248 1.9

(ChCl:LA)1:5 98.34 513.1 698.42 41.57 279.12 1.067 0.73 1.212 1.18948 1.9

(ChCl:LA)1:8 95.58 516.8 704.52 43.14 269.24 1.084 0.73 1.224 1.19648 2.3

(ChCl:LA)1:10 94.58 518.2 706.78 43.74 265.68 1.091 0.73 1.229 1.19948 2.5

(ChCl:LA)1:15 93.18 520.1 710.00 44.62 260.69 1.100 0.73 1.235 1.19948 3.0

(Me-tri-PBr:G)1:1.75 188.5 643.7 843.77 26.41 475.58 1.311 0.76 1.514 1.290b,27 17.4

(Me-tri-PBr:EG)1:4 121.1 507.3 684.72 37.58 303.04 1.064 0.74 1.395 1.233b,27 13.1

(ChCl:F)2.5:1 151.2 574.9 737.10 25.71 451.68 1.188 0.78 1.260 1.259b,50 0.1

(ChCl:F)2:1 153.13 594.5 756.99 25.46 453.53 1.259 0.79 1.296 1.278b,50 1.4

(ChCl:F)1.5:1 155.84 621.9 785.24 25.05 456.15 1.359 0.79 1.347 1.304b,50 3.3

(ChCl:F)1:1 159.89 663.0 828.52 24.28 460.06 1.510 0.80 1.425 1.337b,50 6.6

aAt 293.15 K. bAt 298.15 K.



1850

are more potential active sites and hence greater potential formore inter- and intramolecular forces, resulting in morecomplex bonding forces. Since the method does not take intoaccount the eect of bonding forces, their existence reduces theaccuracy 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 masspercentage of precursor containing a larger number of OHgroups results in higher deviations. For example, the masspercentages 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 dierent

methods of estimating the critical properties of DESs andapplied these to the same density evaluation test. One of themethods they applied was the same as the one used in thisstudy. However, their results dier from those presented here.Table 4 shows seven of the nine DESs studied by these authorsand compares their results with the ones obtained in thecurrent study.It is clear from Table 4 that in comparison to the previous

study,29 signicantly lower absolute deviations [with the

exception of (Me-tri-PBr:EG)1:4] were observed in the presentwork. It is to be noted that the authors of the previous study29

used a dierent correlation for the density to check theaccuracy of the estimated critical properties. This suggests thatthe correlation described by Valderrama and co-workers38,42

(eqs 18 to 21) results in better estimates of the density valuesof DESs.Figure 1 shows the variation in density predictions with HBD

content for choline chloride:glycerol (ChCl:G)-based andcholine chloride:lactic acid (ChCl:LA)-based DESs. For bothtype of DESs, the absolute deviation tends to increase withincreasing mole fraction of HBD in the deep eutectic solvent.An increase in the amount of HBD results in the introductionof more potential sites to develop weak bonding betweenHBDs and anions of the organic salt. This more complexbonding reduces the accuracy of the current method forestimating the critical properties. Therefore, with an increase inthe amount of HBD, a larger deviation in the density estimate isobserved. In the case of ChCl:G-based DESs, the absolutedeviation ranges from 1.4 % to 3.4 %, while in the case ofChCl: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 similarphysicochemical properties.2,8,9 This analogy is not completelyvalid with regard to the estimation of critical properties.

Table 4. Comparison of Absolute Deviations of Densities from the Present Work and a Previous Study29 (Obtained Using SameMethods)

||/%

Salt HBD DES this work ref 29a

choline chloride ethylene glycol (ChCl:EG)1:2 1.1 23.4choline chloride triuoroacetamide (ChCl:TFA)1:2 7.0 28.9choline chloride glycerol (ChCl:G)1:1 2.3 17.4N,N-diethylethanolammonium chloride glycerol (di-EtACl:G)1:2 6.4 12.3N,N-diethylethanolammonium chloride triuoroacetamide (di-EtACl:TFA)1:2 4.0 22.6methyltriphenylphosphonium bromide glycerol (Me-tri-PBr:G)1:2 15.7 21.8methyltriphenylphosphonium bromide ethylene glycol (Me-tri-PBr:EG)1:4 13.1 0.30

aDeviations 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 dierent mole fractions of precursors in the DESs. Dotted lines represent linear ts to thedeviations.



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Therefore, certain aspects of the estimation methods for criticalproperties applied to ILs cannot be assumed to work perfectlywell for DESs. Values of the ratio of the normal boiling point tothe critical temperature (Tb/Tc) are also given in Table 3. In aprevious study,43 a xed value of 0.60 was assumed for this ratioto estimate the normal boiling points and critical temperaturesof ionic liquids. Table 3 shows that the values of the Tb/Tc ratiorange between 0.65 and 0.80 for dierent DESs, so a xed valuefor the ratio cannot be assumed.Finally, the density values for three dierent DESs

[(ChCl:EG)1:2, (ChCl:G)1:2, and (Me-tri-PBr:G)1:2] wereestimated over the temperature range from 298.15 K to348.15 K. A comparison of these values with literature data isshown in Figure 2. The experimental value for (ChCl:EG)1:2drops suddenly at 318.15 K, which could be attributed to anexperimental error. Other than this, density values for both(ChCl:EG)1:2 and (ChCl:G)1:2 agree well with the publishedliterature. The deviations in the densities for these two DESsrange 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 thepresence of aromatic species in the DES in the form ofmethyltriphenylphosphonium bromide, which reduces theaccuracy of the method because of the additional interactionforces.In summary, on the basis of the functional groups present,

the DESs in this study have been classied into four dierentcategories: amide-containing DESs, carboxylic acid-containingDESs, alcohol-containing DESs, and aromatic-containing DESs.The critical properties of these DESs were estimated using acombination of a modied LydersenJobackReid methodand the LeeKesler mixing rules via the following procedure.First, by means of the group contribution method, individual

boiling points and the critical properties of the constituents ofthe DESs were estimated using the modied LJR method.From the boiling points and critical properties of the individualconstituents, individual acentric factors were estimated using acorrelation described by Valderrama and Robles.38 Then the

LeeKesler mixing rules were used to combined theseindividual parameters to estimate the nal critical propertiesand acentric factors of the DESs. After the nal criticalproperties of DESs were obtained, a correlation proposed byValderrama and Abu-Sharkh42 was used to estimate thedensities of these DESs. These density estimates were thencompared with experimental values to check the accuracy of theestimated 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 of1.8 % to 9.5 %), aromatic-containing DESs a higher positivedeviation (in the range of 5.8 % to 17.4 %), carboxylic acid-containing DESs a moderate deviation (in the range of 0.4 %to 8.4 %), and alcohol-containing DESs a lower deviation (inthe range of 0 % to 6.6 %). In all of the DESs studied, anincrease in mass percentage of the HBD also increased thedeviation in the density estimation.

4. CONCLUSIONSA combination of the LydersenJobackReid method and theLeeKesler mixing rules was applied to estimate the criticalproperties of 39 dierent deep eutectic solvents. Additionally,the acentric factors and normal boiling temperatures weredetermined. The consistency of the method was tested byestimating the densities of these deep eutectic solvents using anindependent correlation and comparing the values withexperimental data in the literature. The correlation used fordensity estimation was based upon the critical properties andthe molecular weight of the deep eutectic solvents andtherefore can safely be assumed to be a good test of theapplicability of the method to DESs. Comparison of theestimated and published density values shows good agreementfor DESs consisting of aliphatic precursors. However, becauseof the presence of stronger interaction forces, the method yieldshigher deviations when at least one aromatic group is present inthe DES. The method gives satisfactory results when changes inmolar ratios and density variations with temperature are takeninto account.

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



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

FundingThis research was funded by the University of Melbourne andused facilities from the Cooperative Research Centre forGreenhouse Gas Remediation, Australia.

NotesThe authors declare no competing nancial interest.

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