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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