Post on 09-Apr-2022
S1
Supporting Information
Tunable hydrophobic eutectic solvents based on
terpenes and monocarboxylic acids
Mónia A. R. Martins1-4, Emanuel A. Crespo1,5, Paula V. A. Pontes4, Liliana P. Silva1, Mark
Bülow5, Guilherme J. Maximo4, Eduardo A. C. Batista4, Christoph Held5, Simão P.
Pinho2,3, and João A. P. Coutinho1,*
1CICECO – Aveiro Institute of Materials, Department of Chemistry, University of Aveiro,
3810-193 Aveiro, Portugal
2Associate Laboratory LSRE-LCM, Department of Chemical and Biological Technology,
Polytechnic Institute of Bragança, 5300-253 Bragança, Portugal
3Mountain Research Center – CIMO, Polytechnic Institute of Bragança, 5301-855
Bragança, Portugal
4Faculty of Food Engineering, University of Campinas, 13083-862 Campinas, Brazil
5Laboratory of Thermodynamics, Department of Biochemical and Chemical
Engineering, TU Dortmund, 44227 Dortmund, Germany
*Corresponding author: João A. P. Coutinho, E-mail address: jcoutinho@ua.pt, Phone:
+351 234401507, Fax: + 351 234370084
Number of pages: 33
Number of tables: 14
Number of figures: 14
S2
Figure S1. Structures of the compounds investigated in this work.
L(−)-menthol
Thymol
Caprylic acid
Capric acid
Lauric acid
Myristic acid
Palmitic acid
Stearic acid
Oleic acid
1 1
1
CHCl3 TMSOH
9
23
4
56
7
8
910
11
11 13
11
11
11
11
12
11
11
13
2 8
4, 5, 12
6
3
11
3
5, 8
7
4
1
Menthol + Lauric acid
S3
Menthol
Lauric acid
Menthol + Lauric acid
1 1
2
3
4
5
6
7
8
8
8
8
8
8
8
8
8
8
9
10
TMSCHCl3
Thymol + Myristic acid
9
10
1, 8
73
4
6
2
5
S4
Figure S2. 1H spectra of pure menthol, thymol, lauric acid and myristic acid; and the mixtures
menthol + lauric acid and thymol + myristic acid at a composition close to the eutectic point
and at room temperature.
Thymol
Myristic acid
Thymol + Myristic acid
260
280
300
320
340
360
0.00 0.20 0.40 0.60 0.80 1.00
T/
K
xmonocarboxylic acid
Caprylic acid
Capric acid
Lauric acid
Myristic acid
Palmitic acid
Stearic acid
S5
Figure S3. Solid-liquid phase diagrams of mixtures composed of monocarboxylic acids
and terpenes L(–)-menthol or thymol. Symbols represent the experimental data
measured in this work while the solid lines represent the ideal solubility curves.
260
280
300
320
340
360
0.00 0.20 0.40 0.60 0.80 1.00
T/
K
xmonocarboxylic acid
Caprylic acid
Capric acid
Lauric acid
Myristic acid
Palmitic acid
Stearic acid
0.60
0.80
1.00
1.20
0.0 0.2 0.4 0.6 0.8 1.0
γ
xCaprylic Acid
0.80
0.90
1.00
1.10
0.0 0.2 0.4 0.6 0.8 1.0
γ
xCapric Acid
S6
Figure S4. Activity coefficients of mixtures composed of monocarboxylic acids and L(–)-
menthol. Legend: ●, experimental; - -, Ideal; ─, PC-SAFT.
0.80
0.90
1.00
1.10
0.0 0.2 0.4 0.6 0.8 1.0
γ
xLauric Acid
0.70
0.80
0.90
1.00
1.10
0.0 0.2 0.4 0.6 0.8 1.0
γ
xMyristic Acid
0.90
1.00
1.10
1.20
0.0 0.2 0.4 0.6 0.8 1.0
γ
xPalmitic Acid
0.70
0.90
1.10
0.0 0.2 0.4 0.6 0.8 1.0
γ
xStearic Acid
0.60
0.70
0.80
0.90
1.00
1.10
0.0 0.2 0.4 0.6 0.8 1.0
γ
xCaprylic Acid
0.80
0.90
1.00
1.10
0.0 0.2 0.4 0.6 0.8 1.0
γ
xCapric Acid
S7
Figure S5. Activity coefficients of mixtures composed of monocarboxylic acids and
thymol. Legend: ●, experimental; - -, Ideal; ─, PC-SAFT.
0.90
1.00
1.10
0.0 0.2 0.4 0.6 0.8 1.0
γ
xLauric Acid
0.90
1.00
1.10
1.20
0.0 0.2 0.4 0.6 0.8 1.0
γ
xMyristic Acid
0.90
1.00
1.10
1.20
0.0 0.2 0.4 0.6 0.8 1.0
γ
xPalmitic Acid
0.90
1.00
1.10
1.20
1.30
0.0 0.2 0.4 0.6 0.8 1.0
γ
xStearic Acid
S8
Figure S6. SLE of binary mixtures composed of lauric acid and terpenes. Symbols
represent experimental data measured in this work while solid lines depict the PC-
SAFT results. Legend: ●, L(–)-menthol; , thymol.
280
290
300
310
320
330
0.0 0.2 0.4 0.6 0.8 1.0
T/
K
xLauric Acid
0.83
0.85
0.87
0.89
0.91
0.93
278 298 318 338 358 378
ρ/
g·cm
-3
T / K
L(–)-menthol L(–)-menthol_CaprylicAcid L(–)-menthol_CapricAcid L(–)-menthol_LauricAcid
L(–)-menthol_MyristicAcid L(–)-menthol_PalmiticAcid L(–)-menthol_StearicAcid
a)
0.869
0.875
0.881
320 325 330
S9
Figure S7. Density of eutectic mixtures involving monocarboxylic acids and: a) L(–)-
menthol or b) thymol. Symbols represent experimental density data measured in this
work while dashed lines represent PC-SAFT modelling results.
0.87
0.89
0.91
0.93
0.95
0.97
278 298 318 338 358 378
ρ/
g·cm
-3
T / K
Thymol Thymol_CaprylicAcid Thymol_CapricAcid Thymol_LauricAcid
Thymol_MyristicAcid Thymol_PalmiticAcid Thymol_StearicAcid
b)
S10
Figure S8. Excess molar volumes, VmE, versus temperature for the binary mixtures
investigated in this work.
-0.5
-0.3
-0.1
0.1
310 320 330 340 350 360
Vm
E/
cm3·m
ol-1
T / K
L(–)-menthol_CaprylicAcid L(–)-menthol_CapricAcid L(–)-menthol_LauricAcid
L(–)-menthol_MyristicAcid L(–)-menthol_PalmiticAcid L(–)-menthol_StearicAcid
-0.3
0.0
0.3
0.6
320 330 340 350 360 370
Vm
E/
cm3 ·
mo
l-1
T / K
Thymol_CaprylicAcid Thymol_CapricAcid Thymol_LauricAcid
Thymol_MyristicAcid Thymol_PalmiticAcid Thymol_StearicAcid
S11
0
20
40
60
278 298 318 338 358 378
η/
mP
a·s
T / K
L(–)-menthol L(–)-menthol_CaprylicAcid L(–)-menthol_CapricAcidL(–)-menthol_LauricAcid L(–)-menthol_MyristicAcid L(–)-menthol_PalmiticAcidL(–)-menthol_StearicAcid
a)
0
5
10
15
20
278 298 318 338 358 378
η/
mP
a·s
T / K
Thymol Thymol_CaprylicAcid Thymol_CapricAcid Thymol_LauricAcid
Thymol_MyristicAcid Thymol_PalmiticAcid Thymol_StearicAcid
b)
S12
Figure S9. Experimental viscosity of eutectic mixtures involving monocarboxylic acids
and: a) L(–)-menthol or b) thymol. Lines correspond to the Vogel–Tammann–Fulcher
correlations.
0
10
20
30
40
50
60
270 285 300 315 330 345 360 375
η/
mP
a·s
T / K
L(–)-menthol_CaprylicAcidThymol_CaprylicAcidCaprylic AcidL(–)-mentholThymol
0
10
20
30
40
50
270 285 300 315 330 345 360 375η
/ m
Pa·
s
T / K
L(–)-menthol_CapricAcidThymol_CapricAcidCapricAcidL(–)-mentholThymol
0
5
10
15
20
25
30
295 315 335 355 375
η/
mP
a·s
T / K
L(–)-menthol_LauricAcidThymol_LauricAcidLauricAcidL(–)-mentholThymol
0
10
20
30
40
290 310 330 350 370 390
η/
mP
a·s
T / K
L(–)-menthol_MyristicAcidThymol_MyristicAcidMyristicAcidL(–)-mentholThymol
0
3
6
9
12
15
18
310 320 330 340 350 360 370 380
η/
mP
a·s
T / K
L(–)-menthol_PalmiticAcidThymol_PalmiticAcidPalmiticAcidL(–)-mentholThymol
0
3
6
9
12
15
18
310 320 330 340 350 360 370 380
η/
mP
a·s
T / K
L(–)-menthol_StearicAcidThymol_StearicAcidStearicAcidL(–)-mentholThymol
S13
Figure S10. Comparison between the viscosity of pure compounds and their mixtures.
Figure S11. Sigma profiles of the terpenes used in this work computed by COSMO-RS
((COnductor-like Screening MOdel for Real Solvents, BP_TZVP_C30_1401,
COSMOconfX v3.0, COSMOlogic GmbH & Co KG. Leverkusen, Germany).
0
5
10
15
20
25
30
35
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
p(σ
)
σ/e·nm-2
Water Thymol L(-)-menthol
H-Bond Donor Region
H-Bond Acceptor Region
Non-polar Region
d)
S14
Table S1. Experimental (x2, T)a and calculated (γi) data of the SLE of systems involving
L(–)-menthol.
x2 T / K γ1 x2 T / K γ2
Solid Phase: L(–)-menthol (1) Solid Phase: Monocarboxylix Acid (2)
Caprylic Acid
0.00 315.68 1.00 0.47 267.57 1.11 0.16 301.09 0.93 0.50 268.65 1.09 0.20 295.81 0.90 0.60 273.22 1.05 0.31 285.87 0.87 0.70 277.54 1.03 0.39 275.80 0.81 0.80 281.42 1.02 0.44 265.57 0.71 0.90 284.76 1.00
1 288.20 1.00
Capric Acid
0.00 315.68 1.00 0.40 280.65 0.99 0.10 304.31 0.93 0.45 284.12 1.02 0.20 293.46 0.86 0.50 286.20 0.98 0.30 284.35 0.83 0.60 291.95 1.03 0.35 280.61 0.83 0.70 294.42 0.98
0.81 300.65 1.06 0.90 301.76 1.00 1 304.75 1.00
Lauric Acid
0.00 315.68 1.00 0.31 291.54 0.99 0.10 306.18 0.95 0.40 296.17 0.97 0.15 303.47 0.97 0.50 301.12 0.98 0.20 296.83 0.91 0.60 306.65 1.05 0.25 289.49 0.85 0.70 308.19 0.96
0.80 312.62 1.02 0.90 315.27 1.01 1.00 317.48 1.00
Myristic Acid
0.00 315.68 1.00 0.30 303.76 0.92 0.10 306.35 0.96 0.40 310.93 1.04 0.20 296.17 0.91 0.50 314.17 1.00
0.60 317.10 0.99 0.70 319.74 0.98 0.80 322.84 1.00 0.90 324.97 1.00 1.00 327.03 1.00
Palmitic Acid
0.00 315.68 1.00 0.20 308.61 0.94 0.10 308.53 0.99 0.30 317.07 1.07
0.40 322.82 1.13 0.50 325.36 1.04 0.59 327.30 0.99 0.70 329.91 0.97 0.80 332.20 0.97 0.90 333.43 0.92 1.00 336.84 1.00
Stearic Acid
0.00 315.68 1.00 0.20 316.14 0.77 0.10 308.60 0.99 0.30 322.99 0.85
0.40 330.76 1.09
S15
0.50 332.85 1.00 0.60 335.17 0.97 0.69 336.77 0.93 0.80 338.68 0.91 0.90 340.88 0.93 1.00 343.67 1.00
aStandard uncertainties, u, are u(T) = 0.1 K and ur(x) = 0.002.
Table S2. Experimental (x2, T)a and calculated (γi) data of the SLE of systems involving
thymol.
x2 T / K γ1 x2 T / K γ2
Solid Phase: Thymol (1) Solid Phase: Monocarboxylix Acid (2)
Caprylic Acid
0.00 323.50 1.00 0.70 275.45 0.97 0.09 318.49 0.98 0.80 280.16 0.99 0.20 312.05 0.96 0.90 285.13 1.02 0.30 302.51 0.86 1.00 288.20 1.00 0.40 296.95 0.86 0.50 284.16 0.73 0.59 274.98 0.68
Capric Acid
0.00 323.50 1.00 0.55 289.87 1.04 0.10 318.01 0.98 0.64 292.35 0.98 0.20 314.51 1.01 0.70 293.36 0.94 0.30 306.47 0.95 0.90 301.25 0.98 0.40 301.49 0.98 1.00 304.75 1.00 0.45 294.95 0.90 0.51 287.84 0.83
Lauric Acid
0.00 323.50 1.00 0.60 304.76 0.96 0.10 318.22 0.98 0.70 309.36 1.01 0.21 311.60 0.96 0.80 311.51 0.97 0.30 306.96 0.97 0.90 314.17 0.97 0.40 303.22 1.03 1.00 317.48 1.00 0.45 301.54 1.07
Myristic Acid
0.00 323.50 1.00 0.35 309.05 1.07 0.10 318.44 0.99 0.40 312.14 1.12 0.20 312.30 0.96 0.50 313.95 0.99 0.30 309.05 1.01 0.60 317.42 1.01
0.70 319.51 0.97 0.80 322.41 0.98 0.90 325.83 1.05 1.00 327.03 1.00
Palmitic Acid
0.00 323.50 1.00 0.30 318.25 1.15 0.10 317.70 0.97 0.40 320.48 0.99 0.20 311.83 0.95 0.50 324.31 1.00
0.60 327.45 1.00 0.70 329.00 0.92 0.79 331.72 0.95 0.89 334.10 0.96 1.00 336.84 1.00
S16
Stearic Acid
0.00 323.50 1.00 0.20 322.48 1.19 0.10 316.71 0.95 0.30 325.51 1.01
0.40 329.42 0.99 0.50 332.62 0.98 0.60 334.71 0.93 0.70 337.45 0.96 0.80 339.37 0.95 0.90 341.05 0.94 1.00 343.67 1.00
aStandard uncertainties, u, are u(T) = 0.1 K and ur(x) = 0.002.
Table S3. Binary parameters applied within the PC-SAFT model and average absolute
deviations (AAD / K) for each system investigated.
System kij_eps AAD / K (Ideal) AAD / K (PC-SAFT)
L(–)-menthol
Caprylic Acid -0.0667 4.99 1.11
Capric Acid -0.0501 3.41 1.20
Lauric Acid -0.0281 2.08 1.10
Myristic Acid -0.0265 1.23 0.47
Palmitic Acid -0.0155 0.89 1.28
Stearic Acid 0.0072 1.30 1.02
Thymol
Caprylic Acid - 4.49 1.36
Capric Acid - 1.90 1.36
Lauric Acid - 1.28 1.31
Myristic Acid - 1.35 1.24
Palmitic Acid - 0.99 1.16
Stearic Acid - 0.96 1.28
Table S4. Eutectic points calculated using PC-SAFT and considering an ideal behavior
for the systems investigated in this work.
xE
Ideal TE Ideal xE PC-SAFT TE PC-SAFT xE
Ideal TE Ideal xE PC-SAFT TE PC-SAFT
L(–)-menthol Thymol
Caprylic Acid 0.57 269.69 0.46 263.18 0.71 276.76 0.65 270.82
Capric Acid 0.43 283.01 0.36 279.16 0.57 289.98 0.56 287.00
Lauric Acid 0.32 292.42 0.29 290.97 0.45 299.33 0.44 297.71
Myristic Acid 0.22 300.29 0.20 299.48 0.33 306.92 0.33 306.30
Palmitic Acid 0.15 305.41 0.14 305.57 0.24 312.25 0.24 312.29
Stearic Acid 0.09 309.55 0.09 310.04 0.16 316.45 0.16 316.69
S17
Table S5. Experimental density results, ρ, at 0.1 MPa as a function of temperature, for
the mixtures of L(–)-menthol and monocarboxylic acids. The mole fraction of the acid
(xacid) is provided.a
ρ / g·cm-3
L(–)-menthol +
Caprylic acid
Capric acid
Lauric acid
Myristic acid
Palmitic acid
Stearic acid
xacid T / K
0.400 0.400 0.250 0.200 0.150 0.100
278.15 0.9148
283.15 0.9110 0.9075
288.15 0.9073 0.9039
293.15 0.9036 0.9002
298.15 0.8998 0.8965 0.8930 0.8921
303.15 0.8961 0.8929 0.8894 0.8884
308.15 0.8924 0.8892 0.8859 0.8848
313.15 0.8887 0.8855 0.8823 0.8812 0.8814 0.8810
318.15 0.8849 0.8818 0.8787 0.8776 0.8777 0.8774
323.15 0.8811 0.8780 0.8751 0.8739 0.8741 0.8737
328.15 0.8773 0.8743 0.8714 0.8702 0.8703 0.8700
333.15 0.8735 0.8705 0.8677 0.8665 0.8666 0.8662
338.15 0.8697 0.8667 0.8639 0.8628 0.8629 0.8624
343.15 0.8658 0.8629 0.8601 0.8590 0.8591 0.8587
348.15 0.8619 0.8591 0.8562 0.8553 0.8553 0.8549
353.15 0.8580 0.8553 0.8523 0.8515 0.8513 0.8511
358.15 0.8541 0.8514 0.8485 0.8476 0.8475 0.8472
363.15 0.8502 0.8476 0.8447 0.8438 0.8436 0.8433
368.15 0.8462 0.8437 0.8410 0.8398 0.8396 0.8393
373.15 0.8422 0.8397 0.8372 0.8359 0.8355 0.8353 aUncertainties are u(T) = 0.02 K, u(ρ) = 0.0005 g·cm-3 and ur(p) = 0.05.
Table S6. Experimental density results, ρ, at 0.1 MPa as a function of temperature, for
the mixtures of thymol and monocarboxylic acids. The mole fraction of the acid (xacid) is
provided.a
ρ / g·cm-3
Thymol +
Caprylic acid
Capric acid Lauric acid
Myristic acid
Palmitic acid
Stearic acid
xacid T / K
0.579 0.500 0.450 0.250 0.200 0.100
278.15 0.9461
283.15 0.9421
288.15 0.9381
293.15 0.9341 0.9340
S18
298.15 0.9301 0.9301
303.15 0.9261 0.9263 0.9221
308.15 0.9221 0.9224 0.9183
313.15 0.9181 0.9186 0.9145 0.9279 0.9294
318.15 0.9140 0.9147 0.9107 0.9240 0.9255 0.9357
323.15 0.9100 0.9108 0.9069 0.9202 0.9217 0.9318
328.15 0.9060 0.9070 0.9031 0.9164 0.9179 0.9279
333.15 0.9020 0.9031 0.8992 0.9126 0.9140 0.9240
338.15 0.8979 0.8992 0.8954 0.9087 0.9102 0.9201
343.15 0.8939 0.8953 0.8916 0.9049 0.9063 0.9162
348.15 0.8898 0.8914 0.8878 0.9010 0.9024 0.9123
353.15 0.8858 0.8874 0.8842 0.8971 0.8986 0.9083
358.15 0.8817 0.8835 0.8803 0.8933 0.8946 0.9044
363.15 0.8776 0.8795 0.8764 0.8893 0.8906 0.9003
368.15 0.8735 0.8755 0.8724 0.8853 0.8867 0.8963
373.15 0.8694 0.8715 0.8685 0.8814 0.8828 0.8923 aUncertainties are u(T) = 0.02 K, u(ρ) = 0.0005 g·cm-3 and ur(p) = 0.05.
Table S7. Average absolute relative deviations (ARD / %) of the densities calculated
with PC-SAFT and the ones measured experimentally for each system investigated.
System L(–)-menthol Thymol
Caprylic Acid 0.61 1.35
Capric Acid 0.35 0.74
Lauric Acid 0.18 0.47
Myristic Acid 0.37 0.05
Palmitic Acid 0.56 0.02
Stearic Acid 0.67 0.15
Table S8. Experimental viscosity results, η, at 0.1 MPa and as a function of
temperature, for the mixtures of L(–)-menthol and monocarboxylic acids. The mole
fraction of the acid (xacid) is provided.a
η / mPa·s
L(–)-menthol + - Caprylic acid Capric acid Lauric acid Myristic acid Palmitic acid Stearic acid
xacid T / K
0.000 0.400 0.400 0.250 0.200 0.150 0.100
278.15 50.64
283.15 35.97 45.50
288.15 26.38 33.05
293.15 19.83 24.68
298.15 15.29 18.85 28.10 33.99
303.15 12.01 14.70 20.91 24.78
S19
308.15 9.58 11.68 15.93 18.54
313.15 7.80 9.43 12.40 14.21 15.25 16.61
318.15 6.43 7.73 9.84 11.11 11.78 12.62
323.15 9.43 5.37 6.42 7.94 8.85 9.29 9.81
328.15 7.19 4.54 5.39 6.50 7.17 7.46 7.77
333.15 5.62 3.88 4.58 5.40 5.89 6.09 6.27
338.15 4.48 3.34 3.92 4.54 4.91 5.04 5.14
343.15 3.63 2.91 3.40 3.86 4.14 4.21 4.27
348.15 2.99 2.55 2.97 3.32 3.53 3.57 3.59
353.15 2.50 2.25 2.61 2.87 3.04 3.06 3.06
358.15 2.12 2.00 2.31 2.51 2.65 2.65 2.63
363.15 1.82 1.79 2.06 2.21 2.32 2.32 2.29
368.15 1.57 1.61 1.84 1.96 2.05 2.04 2.00
373.15 1.37 1.45 1.66 1.75 1.82 1.81 1.77 aUncertainties are u(T) = 0.02 K, ur(η) = 0.35% and ur(p) = 0.05.
Table S9. Experimental viscosity results, η, at 0.1 MPa and as a function of
temperature, for the mixtures of thymol and monocarboxylic acids. The mole fraction
of the acid (xacid) is provided.a
η / mPa·s
Thymol + - Caprylic acid Capric acid Lauric acid Myristic acid Palmitic acid Stearic acid
xacid T / K
0.000 0.579 0.500 0.450 0.250 0.200 0.100
278.15 19.22
283.15 15.02
288.15 11.97
293.15 9.71 15.28
298.15 8.00 12.16
303.15 6.68 9.86 12.43
308.15 5.65 8.12 10.12
313.15 4.83 6.78 8.37 8.69 9.21
318.15 4.17 5.74 7.01 7.16 7.54 6.88
323.15 3.64 4.91 5.95 5.98 6.29 5.68
328.15 3.60 3.20 4.24 5.10 5.07 5.31 4.77
333.15 3.05 2.83 3.70 4.42 4.34 4.53 4.06
338.15 2.62 2.53 3.26 3.86 3.76 3.91 3.49
343.15 2.27 2.27 2.88 3.40 3.28 3.41 3.03
348.15 1.99 2.05 2.57 3.02 2.89 3.00 2.66
353.15 1.76 1.86 2.31 2.70 2.57 2.65 2.35
358.15 1.57 1.69 2.08 2.42 2.30 2.37 2.10
363.15 1.41 1.54 1.89 2.19 2.06 2.12 1.88
368.15 1.27 1.41 1.72 1.98 1.86 1.92 1.70
373.15 1.15 1.30 1.57 1.80 1.69 1.74 1.54
S20
aUncertainties are u(T) = 0.02 K, ur(η) = 0.35% and ur(p) = 0.05.
Table S10. Kamlet-Taft solvatochromic parameters of pure components and mixtures
investigated in this work at 323.15 K, along with the standard deviations, and of other
common solvents1 (standard temperature and pressure).
β π* α
Terpenes L(–)-menthol 0.66 ± 0.01 0.42 ± 0.01 0.53
Monocarboxylic acids Caprylic Acid 0.14 ± 0.02 0.30 ± 0.01 0.91
Capric Acid 0.17 ± 0.00 0.27 ± 0.01 0.86
Lauric Acid 0.26 ± 0.04 0.25 ± 0.01 0.85
Other solvents1 Water 0.14 1.09 1.17
Ethanol 0.75 0.51 0.83
Methanol 0.66 0.58 0.93
Acetone 0.48 0.71 0.08
Heptane 0.00 -0.08 0.00
Cyclohexane 0.00 0.00 0.00
o-xylene 0.16 0.48 0.00
Mixtures
L(–)-menthol + Caprylic Acid 0.43 ± 0.01 0.39 ± 0.01 0.85
Capric Acid 0.45 ± 0.01 0.35 ± 0.01 0.84
Lauric Acid 0.54 ± 0.02 0.37 ± 0.01 0.79
Myristic Acid 0.50 ±0.02 0.38 ± 0.01 0.75
Palmitic Acid 0.57 ± 0.01 0.38 ± 0.01 0.71
Stearic Acid 0.64 ± 0.02 0.38 ± 0.01 0.68
Thymol + Caprylic Acid 0.05 ± 0.02 0.67 ± 0.01 1.10
Capric Acid 0.05 ± 0.02 0.71 ± 0.01 1.11
Lauric Acid 0.02 ± 0.01 0.75 ± 0.01 1.05
Myristic Acid 0.02 ± 0.02 0.84 ± 0.01 1.13
Palmitic Acid 0.01 ± 0.01 0.87 ± 0.01 1.11
S21
Stearic Acid 0.05 ± 0.01 0.94 ± 0.01 1.10
Table S11. Solubility of water in the eutectic mixtures, xw, and solubility of thymol (+
monocarboxylic acids), xthymol, in water at 298.15 K.
xw xw 105 xthymol
L(–)-menthol Thymol
Caprylic Acid 0.177 ± 0.009 0.240 ± 0.009 3.328 ± 0.022
Capric Acid 0.157 ± 0.011 0.224 ± 0.011 3.210 ± 0.362
Lauric Acid 0.148 ± 0.003 0.222 ± 0.004 3.029 ± 0.031
Myristic Acid 0.136 ± 0.013 0.204 ± 0.016 2.663 ± 0.207
Palmitic Acid - a - a 2.463 ± 0.052
Stearic Acid - a - a 2.078 ± 0.045
aSolid at 298.15 K.
S22
PC-SAFT EoS
SAFT-type equations are written as a sum of free energy terms, each of them
mimicking a specific interaction, yielding the system’s residual Helmholtz energy, resA .
For classical PC-SAFT, which was used in this work, the residual Helmholtz energy can
be expressed as:
TNk
A
TNk
A
TNk
A
TNk
A
B
assoc
B
disp
B
hc
B
res
(S1)
where res, hc, disp and assoc refer to residual, hard-chain reference fluid, dispersive
and associative interactions, respectively. N and kB stand for number of molecules and
the Boltzmann constant, respectively. For non-associating molecules, three pure-
component parameters are required: the number of segments in the chain ( seg
im ), the
diameter of the segments (i ) and the dispersive energy between segments (
Bi ku / ).
The extension to mixtures requires the value of the unlike size and energy parameters
for which the conventional Lorentz-Berthelot combining rules are commonly applied
and whenever required, one adjustable binary interaction parameter, kij, for
adjustment of the cross-dispersion energy can be used:
jiij
2
1 (S2)
jiijij uuku 1 (S3)
When dealing with self-associating components as those studied in this work, a proper
association scheme, establishing the number and type of association sites and the
interactions between them, needs to be specified a priori based on the structure and
knowledge of the molecule and its interactions. Furthermore, the inclusion of the
association term in a SAFT-type equation (assocA in Equation S1) requires two
additional pure-component parameters related to the association energy ( AiBi ) and
association volume ( AiBi ).
S23
The extension to mixtures requires the evaluation of the cross-association parameters
for which the mixing rules proposed by Wolbach and Sandler2 are considered:
)1(2
1_ epsij
AjBjAiBiAiBj k (S4)
3
21
jjii
jjiiAjBjAiBiAiBj
(S5)
In order to account for deviations from the value calculated through the selected
mixing rules, a binary interaction parameter, kij_eps, for correction of the cross-
association energy can be applied when required for an accurate description of the
data.
PC-SAFT Pure-Component Parameters
As previously mentioned, within the framework of PC-SAFT, a total of five pure-
component parameters are required to model each associating compound. To better
describe the thermodynamic behavior of real substances, these parameters are usually
regressed from experimental data on thermodynamic properties and/or phase
equilibria, preferably of the pure substance. The molecular parameters regressed in
this work are reported in Table S12 along with the average relative deviation (%ARD)
values for the thermodynamic properties considered in the fitting procedure (for those
regressed in this work):
1001
%1
exp
exp
exp
N
i i
i
calc
i
X
XX
NARD (S6)
where Nexp is the total number of experimental points and Xicalc and Xi
exp are the
calculated and the experimental values of the physical property being evaluated.
The PC-SAFT modelling of systems involving monocarboxylic acids was addressed by
several authors3–6 with the 2B association scheme (according to the nomenclature of
Huang and Radosz7) as being the most appropriate for long-chain monocarboxylic
S24
acids. Therefore, PC-SAFT pure-component parameters are available in the literature
for the monocarboxylic acids investigated in this work except for caprylic acid, which
are here regressed from experimental liquid densities (at 1 atm) and vapor pressures
as depicted in Figure S12 and reported in Table S12.
600
650
700
750
800
850
900
950
250 300 350 400 450 500 550 600
ρ/
kg·m
⁻³
T / K
a)
8
9
10
11
12
1.8 2.0 2.2 2.4
ln(p
/Pa)
1000 / T / K⁻¹
b)
900
925
950
975
1000
260 300 340 380
ρ/
kg·m
⁻³
T / K
c)
5
7
9
11
13
1.7 2.1 2.5 2.9
ln(p
/Pa)
1000 / T / K⁻¹
d)
S25
Figure S12. Liquid densities (at 1 atm) and vapor pressures of: a,b) caprylic acid; c,d)
thymol; and e,f) L(–)-menthol. The symbols represent experimental data8–10 while the
lines depict the PC-SAFT results with the parameters proposed here (solid lines) and
those of Okuniewski et al.11 (dashed lines).
As depicted in Figure S12a) and S12b), PC-SAFT is able to provide a good description of
the experimental density and vapor pressure data of the caprylic acid. Moreover,
following the procedure applied in our previous work,6 the association volume was
kept constant and equal to 0.02 decreasing the number of parameters used in the
fitting procedure without any loss of accuracy. This supports the idea that the
associative behavior in pure carboxylic acids is induced by the presence of a carboxylic
group and thus not strongly influenced by the compounds chain length. Concerning
the consistency of the non-associative parameters proposed here for caprylic acid
when compared to those reported in previous works,4,6 correlations as a function of
the acid’s molecular weight Mw_acid can be drawn for the whole homologous series
with coefficients of determination (R2) very close to one:
,452.6004111.0 _ acidwMm 9817.02 R (S7)
,15.39778.1 _
3 acidwMm 9992.02 R (S8)
,1185211.3 _ acidwMm 9959.02 R (S9)
750
780
810
840
870
900
300 355 410 465
ρ/
kg·m
⁻³
T / K
e)
5
7
9
11
13
15
1.6 1.9 2.2 2.5 2.8 3.1
ln(p
/Pa)
1000 / T / K⁻¹
f)
S26
Regarding the terpenes, Okuniewski et al.11 used the PC-SAFT EoS to describe the solid-
liquid equilibria (SLE) phase diagrams of binary mixtures: [L(–)-menthol or thymol] + [1-
decanol, benzyl alcohol, n-decane or 2-cyclohexanethanol]. A 2B association scheme
was used to take into account the hydrogen bonding character of the hydroxyl group
present in the terpene’s structure as previously done for other hydroxyl containing
compounds.4,5 Although Okuniewski et al.11 proposed pure-component parameters for
the terpenes here investigated, a new set of parameters was proposed in this work for
L(–)-menthol and thymol as those from the literature were found to provide an
unsatisfactory description of the terpene’s liquid densities as depicted in Figure S12c) –
2e). Furthermore, the new parameters not only provide a better description of the
liquid densities (without loss of accuracy on the vapor pressures) but also allow the
model to produce a good and consistent description of the SLE data reported in this
work using no more than one binary, temperature independent interaction parameter,
as will be shown below.
Table S12. PC-SAFT pure-component parameters used in this work. The 2B association
scheme is considered for all compounds.
Compound seg
im i / Å
Bi ku / / K AiBi / K AiBi %ARD (ρL) %ARD (p*)
Thymol 4.012 3.816 290.22 1660.0 0.0616 0.10 5.97
L(–)-menthol 4.152 3.903 262.40 1785.6 0.0996 0.30 4.57
Caprylic acid6 7.048 3.136 234.36 1889.2 0.0200 1.23 1.49
Capric acid6 7.147 3.339 242.46 2263.0 0.0200 - -
Lauric acid4 7.255 3.524 252.97 3047.5 0.0034 - -
Myristic acid4 7.413 3.672 256.48 2252.5 0.0440 - -
Palmitic acid6 7.560 3.809 267.52 2291.5 0.0200 - -
Stearic acid6 7.615 3.954 275.20 2351.6 0.0200 - -
S27
Densities – Isobaric thermal expansion coefficients
The experimental density data was further correlated according to a linear
dependency on the temperature (equation S10, parameters available in Table S13),
and the isobaric thermal expansion coefficient, αp, which considers the volumetric
changes with temperature, derived from equation S11. No temperature dependence
was assigned to this property. Figure S13 illustrates the results obtained as a function
of the monocarboxylic acid.
TAA 10ln (S10)
1
ln1A
TT pp
p
(S11)
where ρ is the density, and A0 and A1 are fitting parameters.
Table S13. Estimated parameters of Equation S10, A0 and A1, for the studied mixtures.
aExpanded uncertainty with approximately 95% level of confidence.
Mixture Experimental PC-SAFT
(A0 ± σ)a 104 (A1 ± σ)a / K-1 (A0 ± σ)a 104 (A1 ± σ)a / K-1
L(–)-menthol +
Caprylic Acid 0.153 ± 0.001 -8.676 ± 0.046 0.176 ± 0.001 -9.196 ± 0.014
Capric Acid 0.148 ± 0.001 -8.614 ± 0.044 0.160 ± 0.001 -8.895 ± 0.015
Lauric Acid 0.145 ± 0.002 -8.638 ± 0.053 0.148 ± 0.001 -8.749 ± 0.019
Myristic Acid 0.144 ± 0.002 -8.651 ± 0.052 0.141 ± 0.001 -8.648 ± 0.015
Palmitic Acid 0.153 ± 0.002 -8.890 ± 0.061 0.141 ± 0.001 -8.707 ± 0.018
Stearic Acid 0.152 ± 0.002 -8.866 ± 0.055 0.139 ± 0.001 -8.691 ± 0.022
Thymol +
Caprylic Acid 0.193 ± 0.001 -8.889 ± 0.032 0.222 ± 0.001 -9.372 ± 0.013
Capric Acid 0.186 ± 0.001 -8.641 ± 0.035 0.203 ± 0.001 -8.942 ± 0.012
Lauric Acid 0.178 ± 0.001 -8.530 ± 0.029 0.190 ± 0.001 -8.758 ± 0.015
Myristic Acid 0.193 ± 0.001 -8.554 ± 0.035 0.195 ± 0.001 -8.582 ± 0.011
S28
Palmitic Acid 0.195 ± 0.001 -8.569 ± 0.034 0.197 ± 0.001 -8.599 ± 0.009
Stearic Acid 0.208 ± 0.001 -8.626 ± 0.036 0.207 ± 0.001 -8.613 ± 0.015
Figure S13. Experimental and predicted thermal expansion coefficients of eutectic
mixtures of L(–)-menthol or thymol and monocarboxylic acids.
-9.5
-9.3
-9.1
-8.9
-8.7
-8.5
Caprylicacid
Capricacid
Lauricacid
Myristicacid
Palmiticacid
Stearicacid
104
· α
p
L(–)-menthol
L(–)-menthol PC-SAFT
Thymol
Thymol PC-SAFT
S29
Viscosity – Energy barrier
The viscosity () describes the internal resistance of a fluid to a shear stress and can be
correlated through the Vogel–Tammann–Fulcher (VTF) model,12
CT
BAT exp)( (S12)
where Aη, Bη, and Cη are adjustable parameters estimated from experimental data.
The energy barrier (E) can be estimated based on the viscosity dependence with
temperature using the following equation,13
T
TRE
/1
ln
(S13)
Experimental viscosity values were fitted using the VTF equation and the estimated
parameters are listed in Table S14 together with the energy barrier, E, calculated from
equation S13 at 318.15 K. This temperature was chosen because it is the lowest
temperature at which all mixtures are liquid. The energy barrier for the various
mixtures and the terpenes studied is represented in Figure S14.
Table S14. Fitting coefficients of the VTF equation and derived energy barrier, E, of
mixtures involving L(–)-menthol or thymol and monocarboxylic acids at 318.15 K and
0.1 MPa. aExpanded uncertainty with an approximately 95% level of confidence.
Mixture 102 (Aη ± σ)a / mPa·s (Bη ± σ)a / K (Cη ± σ)a / K (E ± σ)a / kJ·mol-1
L(–)-menthol +
Caprylic Acid 3.06 ± 0.04 768.52 ± 2.78 174.47 ± 0.21 31.33 ± 0.24
Capric Acid 2.85 ± 0.02 815.51 ± 1.54 172.57 ± 0.12 32.38 ± 0.13
Lauric Acid 2.79 ± 0.02 772.46 ± 1.92 186.42 ± 0.16 37.46 ± 0.24
Myristic Acid 2.67 ± 0.03 771.11 ± 2.58 190.27 ± 0.21 39.69 ± 0.34
Palmitic Acid 2.77 ± 0.05 740.20 ± 4.50 195.83 ± 0.40 41.63 ± 0.76
Stearic Acid 2.72 ± 0.03 716.52 ± 2.91 201.48 ± 0.26 44.30 ± 0.56
S30
Thymol +
Caprylic Acid 4.98 ± 0.06 690.54 ± 3.20 162.20 ± 0.31 23.90 ± 0.23
Capric Acid 5.33 ± 0.09 676.37 ± 4.90 173.61 ± 0.50 27.25 ± 0.46
Lauric Acid 5.41 ± 0.10 694.39 ± 5.52 175.41 ± 0.58 28.68 ± 0.57
Myristic Acid 5.61 ± 0.11 632.15 ± 5.66 187.82 ± 0.64 31.32 ± 0.80
Palmitic Acid 5.53 ± 0.17 636.51 ± 8.83 188.71 ± 0.99 31.97 ± 1.28
Stearic Acid 5.69 ± 0.15 582.28 ± 7.29 196.71 ± 0.87 33.23 ± 1.31
Figure S14. Energy barrier of the eutectic mixtures investigated at 318.15 K as a
function of the monocarboxylic acid used. Legend: , L(–)-menthol mixtures; ,
thymol mixtures; ---, pure L(–)-menthol; ···, pure thymol.
17
27
37
47
57
Caprylicacid
Capricacid
Lauricacid
Myristicacid
Palmiticacid
Stearicacid
E(3
18
.15
K)
/ kJ
·mo
l-1
S31
Kamlet Taft Solvatochromic Parameters
The dipolarity/polarizability, π*, and the hydrogen-bond acceptor basicity, β,
solvatochromic parameters were determined from the experimental measurements
according with the following equations:
)(,)(,
)(,)(,*
ecyclohexanNNDMSONN
ecyclohexanNNmixtureNN
(S14)
)(,)(,
)(,)(, 76.0
ecyclohexanNNDMSONN
ecyclohexanNNmixtureNN
(S15)
NNN 4, (S16)
4
max
101
probe (S17)
where ν is the experimental wavenumber and λmax probe is the maximum wavelength of
the probe. Subscripts N,N and 4N represent the probes N,N-diethyl-4-nitroaniline and
4-nitroaniline, respectively. The subscripts cyclohexane and DMSO indicate the
corresponding reference values for these solvents.
The hydrogen-bond donor acidity, α, was estimated using the 13C NMR chemicals
shifts, δ(Ci) (in ppm), of the carbons atoms of pyridine-N-oxide in positions i = 2 and 4:
32.215.0 24 d (S18)
where d24 = δ4 – δ2.14
S32
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