J Therm Anal Calorim (2016) 124:399–405 DOI 10.1007/s10973-015-5127-6
Thermophysical and transport properties of binary mixtures containing triethylene glycol and alcohols at different temperatures Mohammad Almasi1
Received: 9 May 2015 / Accepted: 24 October 2015 / Published online: 3 November 2015 Akade´miai Kiado´, Budapest, Hungary 2015
Abstract Densities and viscosities have been measured for the binary mixtures of triethylene glycol with ? 2propanol, 2-butanol and 2-pentanol over the entire range of mole fraction at T = 293.15–323.15 K. From experimental data, the excess molar volume, thermal expansion coefficient, excess thermal expansion coefficient and deviation in viscosity were calculated. The experimental results have been discussed in terms of molecular interactions and formation of molecular complexes between unlike molecules. Influence of temperature and carbon chain length of alcohols on mentioned properties was discussed. Moreover, the friction theory coupled with PC-SAFT equation of state was applied to produce the viscosities of pure data and binary mixtures. Keywords theory
k m 2AB kij e x
Attractive viscosity scaling parameter Reduced viscosity Linear attractive viscous friction coefficient Linear repulsive viscous friction coefficient Quadratic repulsive viscous friction coefficient Helmholtz energy Segment molar Helmholtz energy (seg), per mole of segments Boltzmann’s constant Effective number of segments within the molecule Association energy of interaction between sites A and B Binary interaction parameter Molecular segment energy parameter Acentric factor
Density Viscosity PC-SAFT Friction
List of symbols MWi Molecular weight of component i pa Attraction pressure pr Repulsion pressure z Mass-weighted fraction of component g Total viscosity g0 Dilute gas viscosity gf Friction viscosity Electronic supplementary material The online version of this article (doi:10.1007/s10973-015-5127-6) contains supplementary material, which is available to authorized users. & Mohammad Almasi
[email protected] 1
ga gr ja jr jrr A a0
Department of Chemistry, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
Introduction The excess parameters derived from densities, viscosities and ultrasonic velocities of pure liquids and liquid mixtures have been investigated in scientific laboratories for many years. The significance of excess parameters has been recognized by the chemical industries to carry out the design calculations such as chemical process, chemical separations, mass transfer operations (adsorption, evaporation precipitation), heat transfer and fluid flow [1]. One of the most important atmospheric pollutants is sulfur dioxide (SO2) that has crucial effects on human health and environment, and as a consequence, receives more and more attention, so the ways of reducing SO2 emissions are very significant. Triethylene glycol (TEG) is used in the removal of SO2 from flue gas due to its low vapor pressure, low toxicity, high chemical stability and
123
400
M. Almasi
low melting point. On the other hand, the organic solvents are used in gas sweetening absorption processes, and among them, alcohols show favorable absorption and desorption properties for acid gases in industrial processes [2]. So the knowledge of physicochemical properties of TEG ? alcohol mixtures over a wide range of temperatures is important for practical applications in flue gas desulfurization. Also because of their favorable properties, all of the studied substances could be used in the cleaning of exhaust air and gas streams from industrial production plants. This paper is a part of our systematic program of research concerning the experimental and theoretical study of several thermodynamic and transport properties of mixtures containing alcohols (–OH) functional groups [3, 4]. The aim of this work is to improve our understanding of the molecular interaction of this functional group with triethylene glycol molecules. In this paper, liquid densities and viscosities are reported for binary mixtures of triethylene glycol and 2-alkanols at seven temperatures (293.15–323.15 K) within the entire composition range. To the best of our knowledge, no literature data are available for the density and viscosity of the binary systems reported here, but some thermodynamic properties for solutions containing ethylene glycols were reported elsewhere [5, 6]. Furthermore, the friction theory coupled with PC-SAFT model was used to correlate the viscosities of pure state and binary mixtures. Applicability of these models to mentioned mixtures has not been verified in the literature until the present time.
Experimental Chemicals All pure materials used in this study are reagent grade, and their purity is [99 % (by mass). Mentioned materials were supplied by Merck and used without further purifications. Measured densities and viscosities at T = 298.15 K are presented in Table 1 along with the values available in the literature [7, 8]. Table 1 Densities, q, and viscosities, g, of pure components at T = 298.15 K and P = 0.1 MPa Chemical name
q/g cm-3 exptl.
g/mPa s Lit.
exptl.
Lit. 37.31 [7]
Triethylene glycol
1.1189
1.11875 [6]
37.34
2-Propanol
0.7811
0.7810 [6]
2.08
2.105 [7]
2-Butanol 2-Pentanol
0.8027 0.8053
0.80270 [6] 0.80524 [6]
3.04 3.28
3.114 [7] 3.316 [7]
123
Equipment and procedure Density and viscosity values were measured using a fully automated SVM 3000 Anton-Paar rotational Stabinger viscometer. The viscometer is based on a modified Couette principle with a rapidly rotating outer tube and an inner measuring bob which rotates more slowly. Uncertainty for density measurements is 1 9 10-4 g cm-3 and for viscosity measurements is 1 %. Three to five sets of readings for the flow times were taken for each sample. The mixtures were prepared just before use by mass on an electronic balance (Mettler AE 163, Switzerland) accurate to 0.01 mg and kept in airtight stoppered glass bottles to avoid evaporation. The maximum estimated uncertainty in the mole fractions is 1 9 10-4.
Results and discussion Densities and excess molar volumes The experimental values of densities for binary mixtures at various temperatures are listed in Table 2. Values of excess molar volumes, VmE , were calculated by the following equation VmE ¼
N X
xi Mi ðq1 q1 i Þ
ð1Þ
i¼1
where q is the density of the mixture, qi is the density of pure component i, xi is the mole fraction, Mi is the molar mass of component i, and N stands for the number of components in the mixture. VmE values for binary mixtures are reported in SI (Supplementary Information) file. The plots of excess molar volumes against the mole fraction of triethylene glycol at T = 298.15 K are given in Fig. 1. The values of excess molar volumes are negative for all studied mixtures. Negative values mean that there is a volume contraction which can be explained by the specific intermolecular interactions occurring in the mixing process. Formation of strong intermolecular hydrogen bonds yields large negative VmE values. This behavior is more important in the lower carbon chain length of alcohols. The values of VmE at equimolar concentrations of triethylene glycol and 2-alkanols follow the order 2-propanol [ 2butanol [ 2-pentanol. By increasing the chain length of the alcohol, the interactions between unlike molecules decrease and VmE values become less negative. For the triethylene glycol ? alcohol systems, the temperature effect is opposite and VmE becomes more negative when temperature increases. Such behavior may be explained by the packing effects which become more dominant and increase with temperature. The next step of this study is analysis of
Thermophysical and transport properties of binary mixtures containing triethylene glycol and…
401
Table 2 Densities, q, and viscosities, g, for the binary mixtures as a function of the mole fraction x1 of triethylene glycol at pressure P = 0.1 MPa T/K = 293.15
x1
T/K = 298.15
T/K = 303.15
T/K = 308.15
T/K = 313.15
T/K = 318.15
T/K = 323.15
Triethylene glycol ? 2-propanol q/g cm-3 0.0000
0.7854
0.7811
0.7768
0.7724
0.7680
0.7634
0.7588
0.0810
0.8341
0.8298
0.8257
0.8214
0.8174
0.8129
0.8081
0.1598
0.8757
0.8716
0.8677
0.8635
0.8596
0.8551
0.8507
0.2401
0.9136
0.9096
0.9058
0.9017
0.8980
0.8938
0.8894
0.3501 0.4400
0.9589 0.9910
0.9551 0.9874
0.9513 0.9837
0.9474 0.9799
0.9436 0.9763
0.9397 0.9725
0.9357 0.9685
0.5601
1.0283
1.0247
1.0210
1.0173
1.0137
1.0100
1.0062
0.6501
1.0525
1.0488
1.0451
1.0414
1.0377
1.0341
1.0304
0.7400
1.0739
1.0701
1.0663
1.0627
1.059
1.0554
1.0518
0.8498
1.0967
1.0928
1.0889
1.0853
1.0816
1.0778
1.0740
0.9398
1.1131
1.1093
1.1050
1.1014
1.0977
1.0938
1.0898
1.0000
1.1229
1.1189
1.1150
1.1111
1.1073
1.1034
1.0995
0.0000
2.42
2.08
1.8
1.56
1.36
1.19
1.05
0.0810
4.61
3.54
3.21
2.65
2.22
1.97
1.80
0.1598
6.73
5.11
4.58
3.73
3.12
2.79
2.54
0.2401
9.06
6.84
5.98
4.95
4.05
3.63
3.32
0.3501
12.51
9.44
8.15
6.70
5.45
4.83
4.44
0.4400
15.58
11.82
10.07
8.26
6.71
5.88
5.39
0.5601 0.6501
20.36 24.67
15.58 18.90
13.01 15.62
10.68 12.73
8.67 10.32
7.50 8.82
6.74 7.86
0.7400
29.58
22.75
18.54
15.05
12.22
10.32
9.07
0.8498
36.45
28.15
22.62
18.28
14.86
12.42
10.68
0.9398
43.07
33.34
26.49
21.38
17.32
14.36
12.14
1.0000
48.20
37.34
29.44
23.59
19.20
15.83
13.23
g/mPa s
Triethylene glycol ? 2-butanol q/g cm-3 0.0000
0.8067
0.8027
0.7984
0.7941
0.78980
0.7852
0.7806
0.0808
0.8450
0.8410
0.8371
0.8329
0.8286
0.8243
0.8199
0.1599
0.8796
0.8758
0.8719
0.8680
0.8638
0.8596
0.8554
0.2399
0.9122
0.9084
0.9048
0.9009
0.8969
0.8928
0.8888
0.3500
0.9530
0.9493
0.9459
0.9421
0.9382
0.9344
0.9305
0.4400
0.9833
0.9797
0.9763
0.9727
0.9689
0.9651
0.9614
0.5558
1.0186
1.0151
1.0117
1.0081
1.0044
1.0007
0.9971
0.6502
1.0447
1.0411
1.0378
1.0341
1.0305
1.0268
1.0232
0.7399 0.8502
1.0673 1.0927
1.0637 1.0888
1.0603 1.0853
1.0567 1.0816
1.0530 1.0780
1.0493 1.0742
1.0457 1.0704
0.9400
1.1113
1.1073
1.1035
1.0998
1.0960
1.0922
1.0884
1.0000
1.1229
1.1189
1.1150
1.1111
1.1073
1.1034
1.0995
0.0000
3.67
3.04
2.54
2.13
1.80
1.54
1.33
0.0808
5.57
4.23
3.68
3.18
2.58
2.26
1.94
0.1599
7.33
5.59
4.84
4.17
3.33
3.02
2.54
0.2399
9.21
7.00
6.08
5.17
4.17
3.79
3.17
0.3500
12.23
9.31
7.92
6.64
5.42
4.92
4.12
g/mPa s
123
402
M. Almasi
Table 2 continued x1
T/K = 293.15
T/K = 298.15
T/K = 303.15
T/K = 308.15
T/K = 313.15
T/K = 318.15
T/K = 323.15
0.4400
15.18
11.53
9.70
7.98
6.58
5.92
4.97
0.5558
19.70
14.96
12.38
10.05
8.32
7.37
6.23
0.6502
24.16
18.37
15.03
12.09
10.01
8.75
7.40
0.7399
29.07
22.16
17.95
14.34
11.91
10.23
8.65
0.8502
36.18
27.73
22.19
17.76
14.65
12.32
10.40
0.9400
43.08
33.06
26.32
21.00
17.26
14.31
11.99
1.0000
48.20
37.34
29.44
23.59
19.20
15.83
13.23
Triethylene glycol ? 2-pentanol q/g cm-3 0.0000
0.8093
0.8053
0.8012
0.7970
0.7927
0.7884
0.7840
0.0809
0.8413
0.8375
0.8335
0.8294
0.8251
0.8210
0.8167
0.1600
0.8713
0.8675
0.8637
0.8597
0.8555
0.8515
0.8474
0.2401
0.9005
0.8968
0.8931
0.8892
0.8851
0.8812
0.8772
0.3500
0.9386
0.9349
0.9314
0.9276
0.9236
0.9198
0.9160
0.4400
0.9682
0.9646
0.9611
0.9574
0.9535
0.9498
0.9460
0.5601
1.0055
1.0019
0.9984
0.9948
0.9910
0.9873
0.9836
0.6499
1.0318
1.0282
1.0248
1.0212
1.0173
1.0137
1.0100
0.7401
1.0571
1.0534
1.0498
1.0463
1.0425
1.0387
1.0351
0.8501
1.0861
1.0823
1.0787
1.0750
1.0713
1.0674
1.0637
0.9401
1.1086
1.1046
1.1008
1.0971
1.0934
1.0894
1.0857
1.0000
1.1229
1.1189
1.1150
1.1111
1.1073
1.1034
1.0995
0.0000 0.0809
3.97 4.98
3.28 4.35
2.72 3.57
2.28 3.03
1.93 2.48
1.65 2.24
1.42 1.94
0.1600
6.16
5.48
4.56
3.84
3.16
2.86
2.47
0.2401
7.62
6.71
5.62
4.79
3.93
3.49
3.03
0.3500
10.23
8.84
7.33
6.20
5.10
4.48
3.87
0.4400
12.89
10.83
8.95
7.55
6.26
5.40
4.64
0.5601
17.73
14.35
11.76
9.77
8.19
6.92
5.92
0.6499
22.03
17.55
14.33
11.78
9.89
8.23
6.99
0.7401
27.33
21.36
17.37
14.16
11.86
9.81
8.27
0.8501
34.90
27.16
21.79
17.58
14.62
12.04
10.15
0.9401
42.55
32.88
26.06
21.01
17.22
14.18
11.91
1.0000
48.20
37.34
29.44
23.59
19.20
15.83
13.23
g/mPa s
x1 is the mole fraction of triethylene glycol in the (triethylene glycol ? 2-alkanol) solutions. Standard uncertainties u are u(T) = 0.01 K, u(x) = 0.0001, u(p) = 10 kPa, the combined expanded uncertainty Uc(q) = 2 9 10-4 g cm-3 (0.95 level of confidence) and for viscosity the relative combined expanded uncertainty Ur(g) = 0.02 (0.95 level of confidence)
the thermal expansion coefficient and its excess values. The thermal expansion coefficient for mixture, amix , was obtained by [9]. ! E X 1 oVm amix ¼ x i ai V ð2Þ þ V oT i where ai is thermal expansion coefficient of pure state and V is the mixture volume. The values of excess thermal expansion coefficient, aE , can be calculated from
123
aE ¼ amix
2 X
ai ui
ð3Þ
i¼1
where ui represents the volume fraction of component i. Values of amix increase with increasing temperature and decrease with increasing triethylene glycol mole fraction. As the temperature rises, breaking of hydrogen bonds becomes more important. So the rupture of hydrogen bonds is the main microscopic reason for this phenomenon. Also packing effects occur as a result of the accommodation of triethylene
Thermophysical and transport properties of binary mixtures containing triethylene glycol and…
403
0.0 0.00105 0.00100
–0.4
0.00095
α /K
VmE /cm3 mol–1
–0.2
–0.6
0.00090 0.00085
–0.8 0.00080
–1.0 0.00075
–1.2 0.0
0.2
0.4
0.6
0.8
1.0
0.00070
x1
glycol molecules in the hydrogen-bonded structure of the alcohol. This phenomenon appears at high mole fraction of triethylene glycol, since there must be enough triethylene glycol molecules to accommodate in the cavities (hydrogenbonded structure) of alcohols. So the packing effects take place at high concentration of triethylene glycol. Values of excess thermal expansion coefficient are negative over the whole composition range for all studied mixtures. These values indicate that changes of volume with temperature in the mixture are less than the amount of it in the pure state. This phenomenon could be due to the fact that there are strong interactions in the mixture in comparison with pure state. The results also are in accommodation with the negative values of excess molar volumes. Values of amix and aE for binary mixtures of triethylene glycol ? 2-pentanol at various temperatures are presented graphically in Figs. 2 and 3.
0.8
0.6
x1
Fig. 2 Thermal expansion coefficients of triethylene glycol with 2-pentanol at temperatures: 293.15 K (filled triangle), 298.15 K (filled circle), 303.15 K (filled square), 308.15 K (white circle), 313.15 K (white square), 318.15 K (filled diamond), 323.15 K (white triangle)
0 –2 –4
αE/k –1
Fig. 1 Excess molar volumes VmE versus mole fraction of triethylene glycol with (filled triangle) 2-propanol, (filled circle) 2-butanol, (filled square) 2-pentanol at T = 298.15 K. Solid curve Redlich–Kister equation
0.4
0.2
0.0
–6 –8
–10 –12
0.0
0.2
0.6
0.4
0.8
1.0
x1
Fig. 3 Excess thermal expansion coefficients of triethylene glycol with 2-pentanol at temperatures: 293.15 K (filled triangle), 303.15 K (filled square), 313.15 K (white square), 323.15 K (white triangle). Solid curve Redlich–Kister equation
Dynamic viscosities Dynamic viscosities at various temperatures are reported in Table 2. Viscosity deviation can be calculated as Dg ¼ g x1 g1 x2 g2
ð4Þ
where g is the mixture viscosity and g1 and g2 are viscosity of pure components. Deviation in viscosity is negative for all studied mixtures over the entire range of composition. The absolute values of Dg for the binary mixtures fall in the following order: 2-pentanol [ 2-butanol [ 2-propanol. This behavior indicates that specific interactions between triethylene glycol and 2-alkanols decrease when the carbon chain length increases. The viscosity deviations for the mixtures of triethylene glycol with the 2-alkanol were correlated by Redlich–Kister equation [10], and their values at T = 298.15 K are shown in Fig. 4.
Friction theory (f-theory) In the friction theory [11], total viscosity g is calculated from a mechanical viewpoint rather than a transport property and separated into two contributions: a dilute gas viscosity term g0 and a term arising from the friction between layers gf g ¼ g0 þ gf
ð5Þ
The dilute gas viscosity g0 is defined as the viscosity at the zero density limit, calculated as a function of temperature, while the other term gf is related to friction concepts of classical mechanics. This term can be expressed as follows gf ¼ jr pr þ ja pa þ jrr p2r
ð6Þ
123
404
M. Almasi
the measurements. Adjustable parameters in Eq. (8) are given in SI file along with the obtained overall AAD. Minimum ADD is obtained for 2-propanol (0.9 %), and maximum ADD was obtained for triethylene glycol (1.94 %). The extension to mixtures follows from the properties of the pure components. The dilute gas limit mixture contribution may be approximated using the following mixing rule " # n X g0;mix ¼ exp xi lnðg0;i Þ ð9Þ
0
Δη /mPa s
–2
–4
–6
–8
i¼1 0.0
0.2
0.6
0.4
0.8
1.0
x1
Fig. 4 Viscosity deviations Dg versus mole fraction of triethylene glycol for binary mixtures of triethylene glycol with (filled triangle) 2-propanol, (filled circle) 2-butanol, (filled square) 2-pentanol at T = 298.15 K. Solid curve Redlich–Kister equation
where mix stands for a mixture property, n is the number of components, and xi is the mole fraction of the ith component. The mixing rules for the friction coefficients are given by jr ¼
n X
zi jr;i
ð10Þ
zi ja;i
ð11Þ
zi jrr;i
ð12Þ
i¼1
where ja, jr and jrr are the temperature-dependent friction coefficients, pa and pr are the van der Waals attractive and repulsive pressure terms of the fluid. The dilute gas viscosity is calculated by proposed model of Chung et al. [12] and is given by: pffiffiffiffiffiffiffiffiffiffiffi MW T g0 ¼ 40:785 2=3 Fc ð7Þ vc X where X is reduced collision integral and Fc is an empirical factor. Regarding the temperature dependency of the friction constants, an exponential dependency of the following form was applied [13]
ð8Þ
þ b3 ðexpð3ðC 1ÞÞÞ 1ÞÞ=Pc jrr ¼ ðc4 ðexpð4CÞ 1Þ=P2c Equation (8) represents flexible model with seven adjustable parameters. By use of these parametric laws, the accuracy of the fitted model greatly depends on the quality of the experimental data and required accuracy. Also there is an issue that impacts the parameter fitting. The fitting involves numerous parameters, which leads to multivariable optimization. Multiple sets of parameters can fit the viscosity equally well for each substance. The predicted viscosity by Eq. 5 is compared with the experimental viscosities. In this case, the method to obtain adjustable parameters is optimization of them so that predicted viscosity by this model is close to the experimental values as much as possible. In other word, the difference between the predicted values and experimental values (obtained absolute average deviation) should be within the uncertainty of
123
n X i¼1
jrr ¼
n X i¼1
where zi is the mass-weighted fraction. PC-SAFT model In the PC-SAFT model [14, 15], general expression for the residual Helmholtz energy is given by ares ¼ ahc þ adisp þ aassoc
jr ¼ ða1 expðC 1Þ þ a2 ðexpð2ðC 1ÞÞ 1Þ þ a3 ðexpð3ðC 1ÞÞÞ 1ÞÞ=Pc jr ¼ ðb1 expðC 1Þ þ b2 ðexpð2ðC 1ÞÞ 1Þ
ja ¼
ð13Þ
The hard-sphere chain contribution is calculated by X hs þ ahc ¼ ma xi ðmi 1Þ ln ghs ð14Þ ij i
is mean segment number, ghs where m ij is the radial pair distribution function, and ahs is hard-sphere contribution. adis is calculated by " XX eij dis a ¼ pqnum 2I1 xi xj mi mj r3ij k BT i j ð15Þ # XX eij 2 3 xi xj mi mj rij þ mI2 C kB T i j The variable qnum is the total number density of molecules per cubic angstrom. The association contribution is described by: " # X X X Ai 1 assoc Ai a ¼ xi ln X ð16Þ þ Mi 2 2 i¼1 A i
Thermophysical and transport properties of binary mixtures containing triethylene glycol and…
References
50
η /mPa s
40
30
20
10
0
405
0.0
0.2
0.4
0.6
0.8
1.0
x1
Fig. 5 Experimental and calculated viscosities of triethylene glycol with 2-pentanol at temperatures: 293.15 K (filled triangle), 298.15 K (filled circle), 303.15 K (filled square), 308.15 K (white circle), 313.15 K (white square), 318.15 K (filled diamond), 323.15 K (white triangle). Dotted curve PC-SAFT f-theory
where Mi is the number of association sites on each molecule. XAi is the mole fraction of molecules not bonded at site A in mixture with other components [16]. The only binary interaction parameter in the PC-SAFT model, kij, which corrects the dispersive interactions, was fitted to the experimental data and reported in SI file. To couple PC-SAFT with f-theory for viscosity calculations, the pressures Pr and Pa are defined from the corresponding repulsive and attractive terms of the residual Helmholtz energy. The maximum of obtained ADD for viscosity calculation by PC-SAFT f-theory is 2 %. A comparison between the calculated viscosities using PCSAFT f-theory and experimental data is shown in Fig. 5. Agreement between experimental and calculated values is satisfactory.
Conclusions This paper reports the densities and viscosities for binary mixtures of triethylene glycol and 2-alkanols. Excess molar volumes and viscosity deviations are negative for studied mixtures. The friction theory, in combination with the PCSAFT model, was evaluated to describe the viscosities of pure components and binary mixtures. This model has been shown to provide satisfactory results for the modeling of the viscosity data.
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Acknowledgements The author thanks the Islamic Azad University (Ahvaz Branch, Ahvaz) for providing the facilities to carry out this work.
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