Correlation of viscosity's Arrhenius' Parameters for

  ‫ ﻟﺔ اﻟ اﻟﻌﻠﻲ ﻘ اﻟﺎء دﻋﺗ ﻟر‬ ‫اﻟ ﺎ اﻟﻲ‬ ‫ ﻧ راﻟﯾ اﻟ رﻓﻠﻲ‬:‫"!ر‬#‫ﻟﻠ‬ ‫ﻌ ـ ـ ـ ـ ـ ـ ـ ـ ـ ـ ـ ـ ـ ـان‬

Correlation of viscosity Arrhenius’ parameters of pure solvents and its binary mixtures. ‫ﻫـ‬1438-3-5 ‫ اﻻﺣ اﻟ اﻓ‬: ‫اﻟ م‬ Chemistry Department, College of Science, Dammam, KSA, Dec. 4, 2016

‫ﺎر‬9:‫ ﻗﺎﻋﺔ اﻟ‬: ‫ﺎن‬8‫اﻟ‬ 1:30-12:30:>‫اﻟ ﻗ‬ 1

MINISTRY OF HIGHER EDUCATION

UNIVERSITY OF DAMMAM COLLEGE OF SCIENCE

‫وزارة اﻟﺘﻌﻠﻴـﻢ اﻟﻌﺎﻟـﻲ‬ ‫ﺟﺎﻣﻌـﺔ اﻟـﺪﻣـﺎم‬ ‫ﻛﻠﻴﺔ اﻟﻌﻠ ــﻮم‬

Conference Title Title::

“CORRELATION OF VISCOSITY’S ARRHENIUS’ PARAMETERS FOR PURE SOLVENTS AND ITS BINARY MIXTURES.” Presented by :

Noureddine Ouerfelli Associate Professor College of Science Science-- Chemistry Department Department..

Dynamic

; Shear ; Absolute Viscosity

η ‫ﺍﻟﻠﺰﻭﺟﺔ‬ ‫ﺍﻟﻤﻄﻠﻘﺔ ; ﺍﻟﻘﺺ ; ﺍﻟﺪﻳﻨﺎﻣﻴﻜﻴﺔ‬ 3

(Rheometer) ‫ﺍﻟﺮﺍﻳﻮﻣﻴﺘﺮ‬

for dynamic viscosity measurements

4

(Ostwald Viscometer)

for kinematic viscosity measurements 5

Dynamic viscosity = Kinematic viscosity × Density 6

Viscosity

Pure Liquids of

7

1.4

Viscosity

η /

mPa.s

1.3 1.2 1.1 1 0.9 0.8 0.7 0.6

270

280

290

300

310

320

330

T/K 8

-6.6

Linear Dependence

mPa.s

-6.7 -6.8

/

-6.9

lnη

Natural logarithm of Viscosity

-6.5

-7

ARRHENIUS BEHAVIOR

-7.1 -7.2 -7.3

0.003

0.0032

0.0034

0.0036

0.0038

-1

1/T / K

9

Arrhenius Type-Equation

10

-6

Ea / R = (Y - Y ) / (X - X ) 2

1

2

1

Y = ln (η / mPa.s)

-7

Y

2

Straight line equation has two parameters: Ea : Activity energy / J.mol-1. Slope of the curve. lnAs : dimensionless constant. Intercept to the ordinate. As : pre-exponential factor.

-8

-9

Y

1

-10

-11

lnAs X

-12

0

0.001

X

1

2

0.002

0.003

0.004

-1

X = 1 / T (K ) 11

In the Case of non Arrhenius Behavior 0,4 0,2

The two Arrhenius parameters

0 -0,2

ln η Water

The plot of logarithm of viscosity of liquid water versus 1/T it’s non linear.

Ea and lnAs

-0,4

become non constants and dependent on temperature.

-0,6 -0,8 -1 -1,2 0,0028

0,003

0,0032

0,0034

0,0036

-1

1 / T (K ) 12

(Vogel-Tammann-Fulcher) V.T.F

13

T/K 290

295

300

305

310

315

320

325 22

22 Ea / kJ .mol-1

Ea

18

16

16

14

14

12

12

Ea / kJ.mol

-1

18

260

280

300

320

340

360

-1

20

Ea / kJ.mol

20

380

T/K

Variation of Arrhenius activation energy (Ea) of two pure liquids as function of the absolute temperature (T): (●): Water ; (○): Dioxane. 14

25 As /m icroPa.s eth a vapou r As

As /µ Pa.s

20

15

10

5

0 260

280

300

320

340

360

380

T /K

Variation of the viscosity of water vapor and of the entropic factor as function of absolute temperature: (●): liquid water ; (▲ ): liquid dioxane ; (□): water vapor. 15

Case of Arrhenius Behavior 1,5 Ln étha Etylamine Ln etha Benzyl alcohol Ln etha Methanol Ln etha DMA

ln(η η) of some liquids

1

0,5

y= y= y= y=

-8,1405 + 2408,4x -9,5785 + 3220,5x -4,9694 + 1300,4x -4,7545 + 1400,1x

R= 0,99978 R= 0,99918 R= 0,99969 R= 0,99479

0

-0,5

-1 0,00315

0,0032

0,00325

0,0033

-1

1 / T (K ) 16

Y = ln(η) 4 2 1/T

b

0

1/T

m

1/T

A

-2

X = 1/T

Arrhenius Temperature

-4 -6

Slope = Ea/R

-8 -10

lnAs

-12 0

0.00375

0.0075

0.01125

0.015

This plot shows how to determine graphically (Ea/R), (lnAs) and (TA). We have proceeded by extrapolation to reach these two parameters…

17 17

ARRHENIUS PARAMETERS

SOLVENT

Ea kJ.mol-1

lnAs -

As µPa.s

TA K

Toluene

8.8153

-11.05276

15.843

95.922

Ethylamine

20.0253

-15.04826

0.29149

160.19

Benzyl alcohol

26.7777

-16.48625

0.069201

195.34

Methanol

10.8125

-11.87716

6.94728

109.49

DMA

11.6415

-11.66256

8.61023

121.37

18

MUTUAL CORRELATIONS BETWEEN ARRHENIUS PARAMETERS

19

#

Pure Component /

Arrhenius parameters of some pure liquids

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

DMA FA DMF MOE EOE 1,4-dioxane IBA EtOH MetOH p-X / 1,4-DMB DMSO DMSO DMSO o-X / 1,2-DMB EG TEA Glycerol TEGMME n-Heptane 1-propanol 2-propanol t-butanol Allyl alcohol Propargyl alcohol Benzene Ethylbenzene Chlorobenzene bromobenzene 1,4-dioxane EtOH 2-propanol isoamyl alcohol 3-amino-1-propanol Water 2-MOE propylene carbonate 1,2-diethoxyethane N,methylacetamide acetonitrile MetOH Tetrahydrofuran

Ea

T* = Ea/R

lnAs

TA

Tm

Tb

kJ.mol-1

/K 1173.7 1973.7 1088.8 1826.3 1900.7 1522.6 1338.1 1588.1 1194.8 1009.3 1690.8 1723.9 1409.7 1151.4 3601.1 987.68 7169.2 2555.2 1725.2 2139.9 2640.0 3852.2 1840.8 1816.7 1798.7 1022.5 954.13 2017.1 1452.2 1885.9 3058.5 2602.7 4336.9 1872.4 1744.4 1706.9 910.34 2300.6 840.64 1226.5 810.42

-10.914 -12.442 -10.780 -12.602 -12.682 -11.853 -11.200 -12.166 -11.528 -10.761 -11.872 -12.002 -10.975 -11.044 -16.146 -11.248 -24.143 -13.638 -12.613 -13.415 -15.032 -18.476 -12.866 -12.607 -13.254 -10.807 -10.406 -13.450 -11.607 -12.997 -16.403 -14.322 -18.036 -13.307 -12.662 -11.729 -10.819 -13.155 -10.793 -11.629 -10.393

/K 107.54 158.63 101.00 144.93 149.87 128.47 119.48 130.50 103.64 93.800 142.42 143.63 128.44 104.26 223.03 87.810 296.95 187.36 136.78 159.51 175.63 208.50 143.07 144.10 135.71 94.617 91.687 149.98 125.11 145.10 186.46 181.72 240.46 140.70 137.77 145.53 84.142 174.88 77.885 105.47 77.977

/ K 253.15 275.65 212.15 188.15 183.15 284.15 226.15 159.15 175.55 285.65 290.65 290.65 290.65 248.65 260.15 158.15 293.15 229.15 182.15 149.15 183.65 298.84 144.15 220.15 278.65 178.15 228.15 242.15 284.15 159.15 183.65 156.15 284.15 273.15 188.15 218.15 199.15 300.15 222.15 175.55 165.15

/ K 438.55 483.15 425.00 397.65 408.15 374.15 426.65 351.15 337.75 411.15 462.15 462.15 462.15 417.15 470.15 361.95 455.15 395.15 371.15 370.15 355.15 355.55 370.15 387.65 353.15 409.15 405.15 429.15 374.15 351.15 355.15 403.15 458.65 373.15 397.65 513.15 394.15 478.15 354.65 337.75 339.15

9.7590 16.410 9.0530 15.185 15.803 12.660 11.126 13.204 9.9340 8.3920 14.058 14.333 11.721 9.5730 29.941 8.2120 59.608 21.245 14.344 17.792 21.950 32.029 15.305 15.105 14.955 8.5016 7.9331 16.771 12.074 15.680 25.430 21.640 36.059 15.568 14.504 14.192 7.5690 19.128 6.9895 10.198 6.7382

20

Arrhenius parameters and temperatures Table : Descriptive statistics on temperatures` parameters: Arithmetic means (Ti), Confidence Interval (CI), standard-deviation (σ), coefficient of variation (CV) and standard error (SE). Temperatures Arrhenius T TA Temp.

(Ti) /K

CI

σ

CV (%)

SE

146.25

133.73 – 158.76

54.189

37.05

6.2572

Melting Point

Tm

228.57

216.99 – 240.15

50.142

21.94

5.7899

Boiling Point

Tb

403.63

392.10 – 415.16

49.929

12.37

5.7653

Activation Temp.

T*

2096.1

1781.8 – 2410.4

1361.0

64.93

157.16

100

1000

T

0

T

A

100

T

m

Tb

T*

Ti / K

1000

Classification of different mean temperatures 21

60

Ea / kJ.mol-1

50

40

30

20

10

0 -25

-20

-15

lnAs

-10 22

60

Ea / kJ.mol-1

50

40

30

20

10

0 50

100

150

200

TA / K

250

300 23

-10

lnAs

-15

-20

-25 50

100

150

200

TA / K

250

300 24

60 Ea / kJ.mol-1

Data Arrhenius parameters

Ea / kJ.mol

-1

50

40

30

20

10

0 -0.1

-0.09

-0.08

-0.07

-0.06

-0.05

-0.04

1/ln(As / mPa.s) 25

1500 Data Arrhenius parameters

Ea (-ln(As / mPa.s) / kJ.mol-1

Ea*(-lnAs)

8

9

Y = M0 + M1*x + ... M8*x + M9*x M0 -10.9655658 M1 9.84553965 M2 0.243581005 R 0.999082627

1000

500

x

0 0

10

20

30

40

50

60

-1

Ea / kJ.mol

26

9 lnT*

ln(T* / K) ln(

8.5

8

7.5

7

6.5 50

100

150

200

250

300

T /K A

27

9 lnT*

ln(T* T* / K)

8.5

8

7.5

7

6.5 4.2

4.4

4.6

4.8

5

5.2

ln(TA / K)

5.4

5.6

5.8 28

First Suggestion: Empirical Model:

HajKacem-Ouerfelli equation

Fluid Phase Equilibria, Vol. 383, (2014) 11-20. doi: 10.1016/j.fluid.2014.09.023

We start from the following dependence:

with α0 = 2.933 and (λ ≈1−ε), where (ε) is a small positive quantity. Arrhenius-type equation becomes with only one parameter (Ea or lnAs):

29

Comparison between the experimental and estimated activation energy values 80

-5

70 -10

50 est

-15

lnAs

40

Ea

est

/ kJ.mol -1

60

30

-20

20 -25 10 0

0

10

20

30

Ea

40

50

60

70

-1

exp

/ kJ.mol

(6 < Ea < 30 kJ·mol-1)

80

-30 -30

-25

-20

lnAs

-15

-10

-5

exp

(- 17 < ln(As /Pa·s) < - 10)

Second Suggestion: Semi-Empirical Model:

Messaâdi-Dhouibi equation

Journal of Chemistry, Vol. 2015 (2015), Article ID 163262, http://dx.doi.org/10.1155/2015/163262

We start from the following dependence:

(T0) is the limiting Arrhenius temperature and, (α0 = 9.894 ± 0.536) and (γ0 = 44.86 ± 1.91) 103 are two dimensionless constants. Arrhenius-type equation becomes with only one parameter (Ea or lnAs):

31

Comparison between the experimental and estimated activation energy values 60

-10

(a)

(b) / mPa.s)

40

30

-15

ln(As ln

Ea

cal

cal

/ kJ.mol

-1

50

20

-20

10

0 0

10

20

30

Ea

exp

40 -1

50

/ kJ.mol

(5 < Ea < 60 kJ·mol-1)

60

-25 -25

-20

-15

ln(As

exp

-10

/ mPa.s)

(-25 < ln(As /Pa·s) < -9) 32

Viscosity of

Binary Liquids Mixtures 33

0.9

{Met (1) + DMA (2)} mixtures 0.8

η / mPa.s

0.7

0.6

0.5

étha (ma.Pa) pour T=303.15K. étha (ma.Pa) pour T=303.15K. étha (ma.Pa) pour T=308.15K. étha (ma.Pa) pour T=308.15K. étha (ma.Pa) pour T=313.15K. étha (ma.Pa) pour T=313.15K. étha (ma.Pa) pour T=318.15K. étha (ma.Pa) pour T=318.15K.

0.4

0.3 0

0.2

0.4

x

0.6

1

0.8

1 34

-7

-7.2

ln(η / mPa.s)

y = -12.172 + 1556.4x R= 0.99829 y = -12.233 + 1574.6x R= 0.99853 y = -12.278 + 1588.4x R= 0.99876

-7.4

y = -12.319 + 1600.5x R= 0.99899 y = -12.334 + 1604.3x R= 0.99912 y = -12.317 + 1597.5x R= 0.99885

-7.6

y = -12.325 + 1599.8x R= 0.99922

-7.8

-8 0.00316

0.0032

0.00324 -1

0.00328

1 / T (K )

35

x1 0.0000 0.020202 0.040404 0.070707 0.10101 0.12500 0.14141 0.17172 0.20202 0.23200 0.27273 0.30303 0.32400 0.35354 0.38384 0.40500 0.44444 0.49495 0.54545 0.59596 0.64400 0.68687 0.72727 0.77778 0.82828 0.87879 0.91500 0.93900 0.96100 0.97980 0.98990 1.0000

Ea/ kJ·mol−1 12.941 13.092 13.207 13.307 13.339 13.339 13.301 13.231 13.137 13.030 12.872 12.755 12.653 12.544 12.478 12.402 12.319 12.223 12.156 12.108 12.074 12.026 11.973 11.876 11.733 11.537 11.384 11.240 11.147 11.014 10.957 10.849

As /10−6 Pa·s 5.1733 4.8672 4.6530 4.4661 4.3996 4.3864 4.4394 4.5427 4.6857 4.8477 5.1065 5.2937 5.4767 5.5818 5.7231 5.8154 5.9210 5.9865 5.9686 5.8974 5.7633 5.7288 5.6775 5.6718 5.7575 5.9388 6.0406 6.2683 6.4334 6.5634 6.6360 6.8449

∆H*/ kJ·mol−1 12.260 12.420 12.536 12.622 12.625 12.581 12.537 12.425 12.289 12.154 11.942 11.799 11.680 11.583 11.472 11.396 11.290 11.174 11.078 10.987 10.889 10.784 10.661 10.474 10.258 10.037 9.8820 9.7912 9.6755 9.5962 9.5465 9.4588

∆S*/J·K-1·mol-1 -3.8394 -3.2098 -2.7213 -2.2681 -2.0767 -2.0275 -2.1066 -2.2668 -2.4921 -2.7239 -3.0737 -3.2870 -3.4517 -3.5387 -3.6160 -3.6575 -3.6005 -3.4357 -3.1739 -2.8653 -2.5122 -2.3573 -2.2018 -2.0840 -2.0238 -1.9364 -1.8318 -1.6596 -1.3167 -0.91371 -0.67496 -0.42284

36

13.5

103 Ea / kJ.mol-1

-R.lnAs / J.K-1.mol-1

12.5 101 12

-1

Ea / kJ.mol

102

-R.lnAs / J.K .mol

-1

13

100

-1

11.5 99

11

10.5

98 0

0.2

0.4

x

0.6

0.8

1

1 37

13.5 Ea / kJ.mol-1

(pure DMA)

13 (x = 0.125)

Ea / kJ.mol

-1

1

12.5 (x = 0.50) 1

(x = 0.75) 1

12

11.5

11 (pure Methanol)

10.5 98

99

100

101 -1

-R.lnAs / J.K .mol

102

103

-1 38

Extended HajKacem-Ouerfelli equation for binary liquid mixtures

50 40 30 10

20

-1

Eaest /k.J.mol

-10 -12 -14 -16 -18

0

-20

ln(Asest /Pa.s)

-8

60

-6

70

Comparison between the experimental and estimated Arrhenius parameters values



-20

-18

-16

-14

-12

-10

ln(Asexp /Pa.s)

-8

-6

0

10

20

30

40

50

60

70

-1

Eaexp /k.J.mol

39

Extended Messaâdi-Dhouibi equation for binary liquid mixtures 

Comparison between the experimental and estimated Arrhenius parameters values

-10

50

J

(a)

(b)

(Ea)est / kJ.mol-1

Data for calc Data for calc

-12

/ kJ.mol

-1

40

30

est

-16

(Ea)

ln(As/Pa.s)

est

-14

20

-18 10

-20

-22 -22

0

-20

-18

-16

ln(As/Pa.s)

-14 exp

-12

-10

0

10

20

(Ea)

exp

30

/ kJ.mol

-1

40

50

40

Thank You for You Attention

Merci pour Votre Attention!

The present presentation is the fruit of some published works. works. R. Ben Haj Haj--Kacem, Kacem N. Ouerfelli. J.V. Herráez. “Viscosity Arrhenius Parameters Correlation: Extension from Pure to Binary Liquid Mixtures.” Phys. Chem. Liq. 53, (6), 2015, 776–784. R. Ben Haj Haj--Kacem, Kacem N. Ouerfelli. J.V. Herráez, M. Guettari, H. Hamda, M. Dallel. “Contribution to modeling the viscosity Arrhenius type-equation for some solvents by statistical correlation analysis.” Fluid Phase Equilibria, 383, (2014) 11-20. R. Ben Haj Haj--Kacem, Kacem N.O. Alzamel, Alzamel N.A. Al Al--Omair Omair, M.A. Alkhaldi Alkhaldi, A.A. Al Al--Arfaj, Arfaj N. Ouerfelli. “Sensitivity of viscosity Arrhenius-type equation to density of liquids.” Asian J. Chem. 28, (11), 2016, 2407–2410. H. Salhi, N.A. Al Al--Omair Omair, A.A. Al Al--Arfaj Arfaj, M.A. Alkhaldi Alkhaldi, N.O. Alzamel Alzamel, K.Y. Alqahtani Alqahtani, N. Ouerfelli. “Correlation Between Boiling Temperature and Viscosity Arrhenius Activation Energy in N,N-Dimethylformamide + 2-Propanol Mixtures at 303.15 to 323.15 K.” Asian J. Chem. 28,(9) 2016, 1972–1984. N.A. Al Al--Omair, Omair D. Das, L. Snoussi, B. Sinha, R. Pradhan, K. Acharjee, K. Saoudi Saoudi, N. Ouerfelli. “A partial derivatives approach for estimation of the viscosity Arrhenius temperature in N,N-dimethylformamide + 1,4-dioxane binary fluid mixtures at temperatures from 298.15 K to 318.15 K.” Phys. Chem. Liq. 54, (5), 2016, 615–631. Z. Trabelsi, M. Dallel, H. Salhi, D. Das, N.A. Al Al--Omair Omair, N. Ouerfelli. “On the viscosity Arrhenius temperature for methanol + N,N-dimethylformamide binary mixtures over the temperature range from 303.15 K to 323.15 K.” Phys. Chem. Liq. 53, (4), 2015, 529–552. A. Messaâdi, H. Salhi, D. Das, N.O. Alzamel Alzamel, M.A. Alkhaldi Alkhaldi, N. Ouerfelli, A.H. Hamzaoui. “A novel approach to discuss the Viscosity Arrhenius behavior and to derive the partial molar properties in binary mixtures of N,N-dimethylacetamide with 2methoxyethanol in the temperature interval (from 298.15 to 318.15) K.” Phys. Chem. Liq. 53, (4), 2015, 506–517. D. Das, H. Salhi, M. Dallel, Z. Trabelsi, A.A. Al Al--Arfaj Arfaj, N. Ouerfelli. “Viscosity Arrhenius activation energy and derived partial molar properties in isobutyric acid + water binary mixtures near and far away from critical temperature from 302.15 K to 313.15 K.” J.Solution Chem 44, (1) (2015) 54-66. H. Salhi, M. Dallel, Z. Trabelsi, N.O. Alzamel, Alzamel M.A. Alkhaldi Alkhaldi, N. Ouerfelli. “Viscosity Arrhenius activation energy and derived partial molar properties in methanol + N,N-dimethylacetamide binary mixtures the temperatures from 298.15 K to 318.15 K Phys. Chem. Liq. 53, (1), 2015 117–137. M. Dallel, D. Das, E.S. Bel Hadj Hmida, N.A. Al Al--Omair Omair, A.A. Al Al--Arfaj Arfaj, N. Ouerfelli. “Derived partial molar properties investigations of viscosity Arrhenius parameters in formamide + N,N-dimethylacetamide systems at different temperatures.” Phys. Chem. Liq. 52, (3), 2014, 442–451. 42