# Estimation of the Critical Temperatures of Some More Deep Eutectic Solvents from Their Surface Tensions

Authors: Yizhak Marcus
Journal: Advances in Materials Science and Engineering
 (2018)

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## Abstract

The critical temperatures of two dozen deep eutectic solvents, for only some of which these have been estimated previously, were estimated from the temperature dependences of their surface tensions and densities available in the literature according to the Eötvös and the Guggenheim expressions.


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## Body

## 1. Introduction

Deep eutectic solvents are binary mixtures of a hydrogen bond accepting component (HBA), typically quaternary ammonium or phosphonium salt, and a hydrogen bond donating component (HBD), typically polyol, at a definite molar ratio. These mixtures are liquid at room temperature and freeze at a temperature considerably below the freezing points of the components, and hence, they are eutectics. Mirza et al. [1] reported a group additivity method for the estimation of the critical temperatures Tc (also the boiling points and densities) of deep eutectic solvents. An alternative path for the estimation of the critical temperatures is described here for deep eutectic solvents that for most of them no previous estimates were reported.The surface tensionsσ of liquids over a temperature range are related to their critical temperatures Tc according to either of two relationships. One relationship, according to Eötvös [2], is(1)σV2/3=A1−TTc,where V=M/ρ is the molar volume of the liquid, M is its molar mass, and ρ is its density. The other relationship, according to Guggenheim [3], is(2)σσ0=1−TTc11/9.These relationships may be inverted in order to deduce the critical temperatures fromσT and ρT data that are available in the literature. In order to apply these expressions, it is necessary to determine the parameters A of (1) and σ0 of (2). The experimental functions σT and ρT are linear over a wide temperature range:(3)σT=σT=298.15K−∂σ∂TTK−298.15,(4)ρT=a−bTK−273.15.The molar volumeV=M/ρ is therefore also linear with the temperature (because b≪a). Therefore, extrapolation to the nominal temperature T=0 yields according to (1) and (2), respectively, A0=σ0V02/3andσ0=σ0.Thus, the critical temperatureTcE according to (1) is(5)TcE=T1−σTVT2/3/A0,and TcG according to (2) is(6)TcG=T1−σT/σ09/11.


## 2. The Data Employed and the Results

Table1 presents the surface tension data σT=298.15K and their temperature coefficients ∂σ/∂Tp as well as the molar masses M and the density coefficients of (4), a and b, for obtaining the molar volumes. The derived critical temperature values TcE and TcG for those deep eutectic solvents are also included in Table 1, for which the required data have been reported. Table 1 also shows the values of TcM according to the group contribution estimates; the first entries are from Mirza et al. [1] and the second ones are from Mjalli et al. [4]. The following abbreviations are used for the HBA components of the solvents: ChCl = choline chloride; DEANCl = diethylethanolammonium chloride; Pr4NBr = tetrapropylammonium bromide; Bu4NCl = tetrabutylammonium chloride; MePh3PBr = methyltriphenylphosphonium bromide; BzPh3PBr = benzyltriphenylphosphonium bromide; and AllPh3PBr = allyltriphenylphosphonium bromide. The HBD components are EG = 1,2-ethanediol, Gly = glycerol, Fru = fructose, Glu = glucose, TEG = triethylene glycol, Mea = monoethanolamine, Asa = aspartic acid, Gla = glutamic acid, and Arg = arginine, and the molar ratios for the eutectics are also shown.Table 1
The surface tensionσ at 298.15 K and its temperature coefficient ∂σ/∂Tp; the molar masses M and the density coefficients of ρ=a−bt/°C of deep eutectic solvents; and the derived critical temperatures: TcE according to (3), TcG according to (4), TcM from Mirza et al. [1], and TcH from Haghbakhsh et al. [17].
HBA
HBD
σ (mN·m−1)
∂
σ
/
∂
T
p (mN·m−1·K−1)
Reference
M (g·mol−1)
a(g·cm−3)
10
3
b (g·cm−3·K−1)
Reference
T
c
E (K)
T
c
G (K)
T
c
M(K)
T
c
H (K)
ChCl
EG 1 : 2
48.91
–0.0932
[4]
263.8
1.1314
0.572
[10]
836
669
602,611
602
Gly 1 : 2
58.05
–0.1353
[5]
323.8
1.2051
0.532
[7]
832
605
681,681
681
Fru 2 : 1
74.0
–0.200
[6]
432.4
1.3081
1.179
[11]
869
564
757,903
Glu 2 : 1
71.71
–0.0516
[4]
432.4
1.267
1.000
[11]
1191
887,887
Mea 1 : 7
49.18
–0.0694
[13]
567.2
1.0843
0.73
[13]
1486
790
DEANCl
EG 1 : 4
47.51
–0.0956
[4]
402.0
1.1149
0.618
[12]
982
651
612,667
Gly 1 : 2
54.54
–0.0888
[5]
337.9
1.1881
0.599
[12]
1158
728
641,696
704
Pr4NBr
EG 1 : 4
47.05
–0.0877
[7]
514.5
1.1509
0.682
[7]
1068
677
642
Gly 1 : 3
53.12
–0.0883
[7]
536.5
1.2214
0.664
[7]
1159
720
TEG 1 : 3
46.57
–0.0814
[7]
908.4
1.1681
0.700
[7]
1146
701
Bu4NCl
EG 1 : 3
40.49
–0.0817
[8]
464.1
1.0423
0.639
[8]
1002
650
Gly 1 : 5
47.35
–0.0700
[8]
738.4
1.1579
0.650
[8]
1312
769
TEG 3 : 1
40.22
–0.0849
[8]
920.0
1.0197
0.618
[8]
963
635
Bu4NBr
Gly 1 : 4
36.57
–0.1409
[5]
690.7
1.3537
0.6
[5]
609
558
Mea 1 : 4
35.83
–0.0392
[13]
566.7
1.0729
0.73
[13]
2072
919
Asa 1 : 9
38.5
–0.1150
[14]
1520.4
0.9795
0.584
[14]
720
563
Gla 1 : 10
37.6
–0.1375
[14]
1793.8
0.9791
0.601
[14]
633
518
Arg 1 : 6
40.4
–0.0750
[14]
1367.7
1.0223
0.603
[14]
1044
708
MePh4PBr
EG 1 : 4
51.29
–0.1056
[9]
605.5
1.2504
0.709
[12]
906
642
708,989
Gly 1 : 3
58.94
–0.1259
[9]
633.5
1.3132
0.651
[12]
914
631
832,996
802
Mea 1 : 8
50.27
–0.0828
[13]
845.9
1.1209
0.81
[13]
1289
724
BzPh3PBr
Gly 1 : 16
53.24
–0.1205
[5]
1857.7
1.2512
0.7
[5]
894
613
741
AllPh3PBr
Gly 1 : 14
41.57
–0.1409
[5]
1646.5
1.2805
0.7
[5]
671
512
739
DEG 1 : 4
49.37
–0.0996
[15]
707.7
1.2160
0.74
[16]
980
748
898a
TEG 1 : 4
48.25
–0.1326
[15]
883.9
1.2150
0.74
[16]
768
581
738a
aReference [15].The resultingTcE estimates of the critical temperatures according to the Eötvös relationship are on the average by 50% larger than the TcG estimates according to the Guggenheim relationship. However, the TcG estimates are nearer the values of TcM from the group contributions according to Mirza et al. [1] than are the TcE ones. On the whole, the TcG values appear to be the more trustworthy.


## 3. Discussion

The normal boiling pointsTb of deep eutectic solvents are generally not relevant for their applications but represent the upper limit of their usage, if they do not decompose below these Tb. Therefore, the critical temperatures Tc, which are on the average about 4/3Tb/K [1], are not the quantities that are relevant to their applications but have found use for the estimation of other properties that have not been measured as functions of the temperature [1, 4]. Still, the critical temperatures are physical properties that ought to be known; hence, the present estimates for two dozens of deep eutectic solvents of which only eight had their Tc estimated previously make sense. The values are based on the nominal extrapolation of the experimental surface tension data to T=0 for the TcG estimates (to obtain σ0) and of both these and the densities for the TcE estimates (to obtain A0), but these parameters do not have any real significance.Previous estimates of the critical temperatures of deep eutectic solvents were conducted according to two paths. One was the use of the modified Lydersen−Joback−Reid group contribution method to obtain first values ofTb and from them the values of Tc, which is applicable to organic liquids for which at least Tb is known and then extended [1, 4, 17] to the deep eutectic solvents. It was applied to twenty different deep eutectic solvents (shown as TcM [1, 4] and TcH [17] in Table 1 for those also studied here) as well as to noneutectic compositions of some of them. Some disagreements between the results of the application of this method are noted in Table 1. The other path was the application of the Eötvös [4, 15] and the Guggenheim [15] expressions, but in a different manner than done here. The former expression was recast in the linear form:(7)σV2/3=A′+BT.and from the intercept and slope of its plots Tc=−A′/B resulted [4]. The agreement with the values of TcM from the group contributions is poor. Better agreement was obtained in [15] between values derived from the Eötvös and Guggenheim expressions.



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*Source: 5749479-2018-05-02.xml*