Thermodynamic, transport and optical properties of ...

Journal of Molecular Liquids 233 (2017) 222–235

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Thermodynamic, transport and optical properties of formamide + 1,2-ethanediol, 1,3-propanediol and poly (ethylene glycol) 200 binary liquid mixtures Meysam Hemmat a, Mehrdad Moosavi b,⁎, Marzieh Dehghan a, Esmaeel Mousavi a, Abbas Ali Rostami a,b a b

Faculty of Chemical Engineering, Shomal University, P.O. Box 731, Amol, Mazandaran, Iran Faculty of Chemistry, University of Mazandaran, P.O. Box 453, Babolsar, Mazandaran, Iran

a r t i c l e

i n f o

Article history: Received 11 December 2016 Accepted 2 March 2017 Available online 07 March 2017 Keywords: Formamide Diols Excess properties Prediction equations

a b s t r a c t Densities and viscosities of formamide (FA) + 1,2-ethanediol (1,2-ED), 1,3-propanediol (1,3-PD) and poly (ethylene glycol) 200 (PEG 200) binary liquid mixtures at temperatures of 293.15, 298.15 and 303.15 K and refractive indices at T = 298.15 K were measured over the entire range of composition and atmospheric pressure (0.1 MPa). From the experimental measurements, several thermophysical properties including the excess molar volumes (VEm), coefficient of thermal expansion αP, excess coefficient of thermal expansion αEP, partial molar volume V mi, excess refractive index nE and excess viscosity ηE were calculated. The obtained excess parameters were used to discuss the inter-intra molecular interactions in the liquid mixtures. Moreover, the excess properties were correlated with Redlich-Kister polynomial equation and the viscosities were correlated with Eyring–Margules, McAllister and Andrade models. Finally, Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) equation of state were applied to the densities of studied binary mixtures to examine the ability of these models to predict thermodynamic properties. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Thermodynamic and transport properties of fluids are essential in chemical engineering calculations such as fluids flow and heat and mass transfer [1]. Knowledge of the dependence of these properties on the composition, temperature and pressure is important in understanding the intermolecular interactions and phase behavior of fluids [2]. Moreover, study on deviations of thermodynamic properties to ideal behavior, excess properties, are well candidates to obtain the information about the nature of solute-solute, solvent-solvent and solute-solvent interactions and structural accommodation in the mixtures that leads to the extending or modification of theoretical models [3–5]. The multi-component solvent systems, containing amides are interesting because of these family of components are the common solvents in chemical reactions, industrial processes and biological systems [6]. Formamide is the simplest amide family members with the following resonance structure,

⁎ Corresponding author. E-mail address: [email protected] (M. Moosavi).

http://dx.doi.org/10.1016/j.molliq.2017.03.008 0167-7322/© 2017 Elsevier B.V. All rights reserved.

ð1Þ Formamide structure and reactivity is conventionally interpreted within the framework of resonance theory. Its planar geometry, large rotation barrier (18–19 kcal mol− 1), and red-shifted carbonyl stretching frequency can be readily understood in terms of the strong resonance mixing of the dipolar form. In contrast to typical pyramidal amine geometries, the planar amino group is stabilized by the resonance interaction of the p-type nitrogen atom lone pair with the carbonyl π system [7]. This molecule can develop cyclic dimers and chain like aggregations. Formamide molecules are highly polar (3.37 D at T = 298.15 K) and are strongly self-associated through extensive three-dimensional network of hydrogen bonds. Thus, it is favorable to use this amide to model and study of the phase behavior of association systems in pure and the mixtures with other polar systems [8,9]. Alkanediols are the class of strong associating components with the ability to form inter-intra molecular hydrogen bonding [10]. It is of

M. Hemmat et al. / Journal of Molecular Liquids 233 (2017) 222–235

great interest to perform a study on the mixtures involving FA + diols at different composition and temperature to see the effects of various parameters on the extension of system's H-bonding. Furthermore, it should be mention that these components have found the huge application in industries [8]. Survey of literature shows the different researches have been performed on the thermophysical behavior of mixtures including the formamide or alkanediols. Ultrasonic and viscosity measurements of formamide + ethanol, 1-propanol, 1,2-ethanediol and 1,2-propanediol at temperatures of 293.15 to 318.15 K were performed by Nain [11]. The obtained negative values of viscosity deviations and isentropic compressibility deviations decrease and increase, respectively, with increase of temperatures. Experimental measurements of density and viscosity as well as density functional theory (DFT) methods combined with molecular dynamics simulations study of FA + 1,2-ethanediol or 1,2-

223

propanediol binary mixtures were performed by Alcalde et al. [8]. For FA + 1,2-ED mixtures, positive values of VEm and negative values of ηE shift to zero point by increasing the temperatures. The simulation study shows that the hydroxyl groups in diols shows a large affinity for amide carbonyl groups, and thus, very efficient H-bonding is developed through these positions. Rani and Maken [12], reported the densities and volumetric properties of FA + 1-propanol, 1-butanol and 2methyl-1-propanol binary mixtures. The negative values of VEm were obtained and attributed to the presence of intermolecular H-bonding between unlike molecules. Also, the VEm increases with volumes follow the sequence 1-butanol N 1-propanol N 2-methyl-1-propanol. Awasthi and Awasthi [9] obtained the negative values of VEm for FA + 2alkoxyethanols binaries and the results was ascribed to the formation of strong hydrogen bonds between the hydroxyl group of 2alkoxyethanols and amidic group of FA acting as hydrogen acceptor.

Table 1 Density (ρ), viscosity (η) and refractive index (n) of pure liquids with the available corresponding literature values at T = 293.15, 298.15 and 303.15 K. ρ/g·cm−3

η/mPa·s

n

EXP

LIT

AAD%

EXP

LIT

AAD%

Formamide T = 293.15 K

1.1325

3.7542 [23]

0.541

1.129

3.32

3.322 [11] 3.305 [13] 3.322 [23] 3.230 [30]

0.060 0.451 0.060 2.711

T = 303.15 K

1.1247

0.062 0.044 0.000 0.044 0.014 0.008 0.002 0.004 0.018 0.044 0.020 0.012

3.734

T = 298.15 K

1.1332 [22] 1.1320 [23] 1.1290 [13] 1.1295 [24] 1.1288 [25] 1.1291 [26] 1.1290 [27] 1.1290 [28] 1.1245 [9] 1.1252 [24] 1.1244 [27] 1.1245 [29]

2.964

2.966 [11] 2.975 [13] 2.876 [29] 2.950 [30] 2.830 [31] 2.941 [32]

0.076 0.371 2.945 0.472 4.520 0.776

PEG200 T = 293.15 K

1.1248 1.1207

T = 303.15 K

1.1166

0.196 0.000 0.015 0.025 0.009 0.000 0.036 0.034 0.028 0.037

64.74

T = 298.15 K

1.1270 [33] 1.1248 [34] 1.1208 [35] 1.1209 [36] 1.1208 [37] 1.1207 [18] 1.117 [33] 1.1169 [34] 1.1169 [35] 1.1170 [36]

66.79 [34] 63.011 [38] 49.724 [35] 48.157 [36] 49.33 [37] 49.456 [39] 37.682 [34] 38.912 [35] 37.682 [36] 37.670 [38]

3.167 2.671 0.554 2.615 0.243 0.012 0.085 3.352 0.085 0.053

1,2-Ethanediol T = 293.15 K

1.1138

1.1102

20.86 [19] 21.19 [44] 20.83 [45] 18.68 [19] 17.14 [44] 17.12 [44]

2.065 0.516 2.206 7.356 1.494 1.609

T = 303.15 K

1.1067

0.026 0.044 0.053 0.036 0.045 0.063 0.036 0.009 0.045 0.117 0.027

21.30

T = 298.15 K

1.1135 [41] 1.1133 [42] 1.1132 [19] 1.1098 [41] 1.1097 [42] 1.1095 [19] 1.1098 [43] 1.1068 [41] 1.1062 [42] 1.1054 [19] 1.1064 [43]

14.33

13.86 [19] 14.02 [44] 13.64 [45]

3.279 2.163 4.815

1,3-Propanediol T = 293.15 K

1.0527

52.01 [49]

4.621

1.0495

42.89

41.11 [49] 40.06 [20] 41.69 [52]

4.150 6.598 2.797

T = 303.15 K

1.0463

0.085 0.104 0.028 0.009 0.066 0.038 0.019 0.009 0.066 0.019 0.028 0.038

54.53

T = 298.15 K

1.0536 [41] 1.0538 [42] 1.0530 [48] 1.0528 [49] 1.0502 [41] 1.0499 [48] 1.0497 [49] 1.0496 [50] 1.0470 [41] 1.0465 [42] 1.0466 [49] 1.0467 [51]

34.62

32.88 [49] 33.57 [52]

5.026 3.033

49.45

37.65

17.40

EXP

LIT

AAD%

1.4459

1.4461 [25] 1.4458 [27] 1.4461 [28] 1.4609 [21]

0.014 0.007 0.014 1.042

1.4582

1.4588 [5] 1.4583 [35] 1.4585 [36] 1.4570 [40]

−0.041 −0.007 −0.021 0.082

1.4293

1.4304 [46] 1.4292 [47] 1.4300 [48]

0.076 0.006 0.048

1.4372

1.4379 [49] 1.4382 [51] 1.4379 [53]

0.048 0.062 0.048

Standard uncertainties are u(T) = 0.01 K, u(p) = 10 kPa, u(x1) = 0.0002; relative standard uncertainties are ur(ρ) = 0.002; ur(η) = 0.1 and ur(n) = 0.01

224


Almasi [13] determined the VEm and ηE values for FA + 2-alkanol binary mixtures. The VEm varies from negative values for FA + 2-propanol to positive values for FA + 2-heptanol mixtures. Moreover, ηE was negative at alcohol rich region and shift to positive values with increase of FA composition. Nain [14], obtained the negative VEm of Acetonitrile + FA binary mixtures and the negative values of VEm were reported to decrease with rising of temperature. Formation of new Hbonding (C≡N⋯H\\N) between nitrogen atom of \\CN group of ACN and hydrogen atom of the amino group of FA, leading to a contraction in volume, was mention as the main results of obtained negative VEm. In this paper, the experimental values of densities ρ, refractive indices nD and viscosities η of formamide (FA) and 1,2-ethanediol (1,2-ED), 1,3-propanediol (1,3-PD) or poly (ethylene glycol) 200 (PEG 200) binary liquid mixtures were reported over the entire composition range and temperatures of 293.15, 298.15 and 308.15 K and atmospheric pressure (0.1 MPa). From the experimental data, the excess molar volume VEm, coefficient of thermal expansion α P , excess coefficient of thermal expansion α EP , partial molar volume V mi , excess refractive index n E and excess viscosity ηE are calculated. The values of excess molar volume, excess viscosity and excess refractive index have been correlated with Redlich-

Kister polynomial equation to drive binary coefficients and estimate the standard deviation between experimental and calculated results. To examine the ability of different models in reproduction of experimental data, Peng-Robinson (PR) and Soave-RedlichKwong (SRK) equation of state were applied to prediction of densities. Moreover, experimental viscosities data have been reproduced with Eyring–Margules, McAllister and Andrade models. Finally, deviation between experimental and calculated thermophysical values was discussed.

2. Experimental 2.1. Materials The used components including the formamide (CAS NO: 75-12-7), 1,2-ethanediol (CAS NO: 107-21-1), 1,3-propanediol (CAS NO: 504-632) and poly (ethylene glycol) 200 (CAS NO: 25322-68-3) was purchased from Merck with purity of formamide ≥ 99.2%, 1,2-ethanediol ≥ 99.5% and 1,3-propanediol ≥ 98.0%. Their water content was around 0.2%. All these compounds were used without further purification.

Table 2 Densities ρ, viscosities η, refractive indices nD, coefficient of thermal expansion αP, excess molar volume VEm, and partial molar volume V m;i , of formamide (x1) + 1,2-ethanediol binary mixture at T = (293.15, 298.15 or 303.15) K and pressure of (0.1 MPa). T = 293.15 K x1

ρ/g·cm−3

η/mPa·s

αP ×104/K−1

VEm/cm3 · mol−1

V m1 =cm3 mol

0.0000 0.1003 0.2002 0.2990 0.3975 0.5027 0.6014 0.7027 0.7999 0.9014 1.0000

1.1138 1.1144 1.1150 1.1159 1.1169 1.1183 1.1199 1.1217 1.1239 1.1272 1.1325

21.30 16.54 13.55 11.22 9.550 7.990 6.850 5.827 4.960 4.413 3.734

6.53 6.03 6.76 7.16 6.42 7.15 6.89 6.88 5.89 4.76 25.83

0.0000 0.0378 0.0770 0.1034 0.1276 0.1423 0.1481 0.1524 0.1432 0.1032 0.0000

40.133 40.159 40.122 40.056 40.004 39.966 39.941 39.918 39.874 39.810 39.770

−1

V m2 =cm3 mol

−1

55.728 55.727 55.736 55.754 55.786 55.817 55.842 55.892 56.028 56.413 57.282

T = 298.15 K x1

ρ/g·cm−3

η/mPa·s

αP ×104/K−1

VEm/cm3 · mol−1

V m1 =cm3 mol

0.0000 0.1003 0.2002 0.2990 0.3975 0.5027 0.6014 0.7027 0.7999 0.9014 1.0000

1.1102 1.1108 1.1111 1.1120 1.1131 1.1143 1.1159 1.1178 1.1201 1.1235 1.1290

17.40 13.52 10.99 8.878 7.610 6.541 5.592 4.710 4.150 3.817 3.320

6.37 6.23 6.43 7.19 6.98 7.17 7.10 7.09 6.81 3.88 27.68

0.0000 0.0384 0.0924 0.1189 0.1388 0.1623 0.1678 0.1679 0.1547 0.1108 0.0000

40.229 40.353 40.311 40.213 40.141 40.111 40.086 40.051 39.998 39.933 39.894

−1

V m2 =cm3 mol

−1

n

55.909 55.900 55.905 55.927 55.965 55.996 56.021 56.086 56.255 56.667 57.458

1.4293 1.4302 1.4311 1.4322 1.4332 1.4344 1.4359 1.4377 1.4397 1.4425 1.4459

T = 303.15 K x1

ρ/g·cm−3

η/mPa·s

αP ×104/K−1

VEm/cm3 · mol−1

V m1 =cm3 mol

0.0000 0.1003 0.2002 0.2990 0.3975 0.5027 0.6014 0.7027 0.7999 0.9014 1.0000

1.1067 1.1071 1.1074 1.1081 1.1090 1.1103 1.1118 1.1136 1.1158 1.1192 1.1247

14.23 11.10 9.120 7.232 6.151 5.273 4.603 3.990 3.647 3.402 2.964

6.21 6.43 6.09 7.21 7.55 7.20 7.30 7.29 7.73 3.01 29.57

0.0000 0.0456 0.0969 0.1297 0.1553 0.1707 0.1769 0.1772 0.1640 0.1156 0.0000

40.431 40.546 40.492 40.390 40.313 40.266 40.241 40.210 40.158 40.087 40.046

−1

V m2 =cm3 mol

−1

56.086 56.073 56.075 56.098 56.140 56.178 56.207 56.271 56.438 56.870 57.757

Standard uncertainties are u(T) = 0.01 K, u(p) = 10 kPa, u(x1) = 0.0002; relative standard uncertainties are ur(ρ) = 0.002; ur(η) = 0.1, u(VEm)=0.002, uðV i Þ = 0.001 and u(αP) = 5 × 10−5.


2.2. Apparatus All binary solutions were prepared by mass using a single pan Matter balance with an accuracy of ±0.1 mg. The mixtures were freshly prepared and retained at desired temperature for some hours to ensure complete miscibility. Densities of pure liquids and their mixtures were measured using an Anton Paar vibrating U-tube densitometer (model: DMA 500) with the standard uncertainty claimed by the manufacture of ±0.001 g·cm−3 and temperature standard uncertainly of 0.1 K, calibrated at T = 293.15 K with pure water. The densitometer was checked by using dry air and demonized water under atmospheric pressure. Dynamic viscosities, η, were obtained using an Anton Paar viscometer Lovis 2000 M rolling-ball automated viscometer with temperature standard uncertainty of 0.02 K. Different capillaries with different diameters (1.59 mm, 1.8 mm and 2.5 mm) with a standard uncertainty claimed by the manufacture up to 0.5% were selected to allow measurement of viscosities from 0.7 to 1700 mPa·s. The calibration was carried out using the pure water and different references standard of known viscosity correspond to the core range of the capillaries and adjusting the instrument constants in a way that the known correct results are

225

found by the instrument including the level adjustment, adjustment of capillary configuration and temperature adjustment. Refractive indices n, measurements of pure components and mixtures were carried out using an automatic critical-angle refractometer ATR-ST (SN: 33598 - SCHMIDT + HAENSCH Co) with measuring range of 1.33200–1.53200 and standard uncertainly claimed by manufacture of 0.0001. The relative standard uncertainties of measured density, refractive index and viscosity are 0.02, 0.01 and 0.1, respectively, were estimated using the Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results [15–17]. Moreover, the experimental densities, refractive indices and viscosities of pure liquids are compared with the available literature values at all studied temperature is reported in Table 1. Densities data in Table 1 show that the average absolute deviation percent (AAD%) between experimental and literature values are between AAD% = 0.00 for FA at T = 298.15 K [13] and PEG 200 at T = 293.15 K [18] to maximum AAD% = 0.117 for 1,2-ED at T = 303.15 K [19]. The maximum AAD% = 6.598 was found for viscosity from data reported by George and Sastry [20] for 1,3-PD at T = 298.15 K. However, the viscosity data of Nain [11] for FA at T = 298.15 K with AAD% = 0.060 and T = 303.15 K with AAD% = 0.076 show the good satisfactory with

Table 3 E Densities ρ, viscosities η, refractive indices nD, coefficient of thermal expansion αP, excess molar volume Vm , and partial molar volume V mi , of formamide (x1) + 1,3-propanediol binary mixture at T = (293.15, 298.15 or 303.15) K and pressure of (0.1 MPa).

T = 293.15 K x1

ρ/g·cm−3

η/mPa·s

αP ×104/K−1

VEm/cm3 · mol−1

V m1 =cm3 mol

0.0000 0.1034 0.2038 0.3016 0.4021 0.5014 0.5969 0.7026 0.7996 0.8975 1.0000

1.0527 1.0561 1.0604 1.0652 1.0708 1.0773 1.0843 1.0937 1.1046 1.1173 1.1325

54.53 38.53 28.29 19.85 14.09 10.47 8.232 6.233 5.198 4.415 3.734

5.69 6.62 6.08 6.05 6.02 5.98 0.95 0.64 6.25 17.23 25.83

0.0000 0.0888 0.1332 0.1654 0.1908 0.1987 0.2060 0.1853 0.1225 0.0572 0.0000

40.899 40.411 40.189 40.116 40.083 40.022 39.942 39.837 39.757 39.752 39.770

−1

V m2 =cm3 mol

−1

72.290 72.315 72.350 72.378 72.399 72.436 72.547 72.755 72.956 73.012 72.467

T = 298.15 K x1

ρ/g·cm−3

η/mPa·s

αP ×104/K−1

VEm/cm3 · mol−1

V m1 =cm3 mol

0.0000 0.1034 0.2038 0.3016 0.4021 0.5014 0.5969 0.7026 0.7996 0.8975 1.0000

1.0495 1.0528 1.0571 1.0618 1.0673 1.0737 1.0807 1.0901 1.1009 1.1138 1.1290

42.89 29.44 21.08 14.33 9.719 7.266 6.123 5.094 4.135 3.811 3.320

5.71 6.64 6.86 6.82 6.79 7.68 1.39 0.32 7.72 20.81 29.45

0.0000 0.0948 0.1379 0.1749 0.2043 0.2154 0.2204 0.1971 0.1358 0.0596 0.0000

41.105 40.559 40.334 40.271 40.240 40.170 40.077 39.962 39.884 39.872 39.894

−1

V m2 =cm3 mol

−1

n

72.511 72.540 72.571 72.598 72.620 72.664 72.786 73.012 73.229 73.280 72.735

1.4372 1.4376 1.4381 1.4386 1.4392 1.4399 1.4407 1.4418 1.4430 1.4443 1.4459

T = 303.15 K x1

ρ/g·cm−3

η/mPa·s

αP ×104/K−1

VEm/cm3 · mol−1

V m1 =cm3 mol

0.0000 0.1034 0.2038 0.3016 0.4021 0.5014 0.5969 0.7026 0.7996 0.8975 1.0000

1.0463 1.0495 1.0536 1.0582 1.0636 1.0699 1.0767 1.0859 1.0968 1.1095 1.1247

34.62 23.41 16.76 11.34 7.417 5.776 4.679 4.163 3.336 3.213 2.964

5.73 6.66 6.88 6.85 6.81 7.71 1.71 0.64 7.75 20.95 29.57

0.0000 0.0979 0.1495 0.1878 0.2177 0.2285 0.2378 0.2165 0.1434 0.0677 0.0000

41.254 40.773 40.534 40.448 40.410 40.342 40.251 40.130 40.032 40.024 40.046

−1

V m2 =cm3 mol

−1

72.732 72.758 72.796 72.828 72.852 72.893 73.019 73.264 73.505 73.584 72.940


226


Table 4 Densities ρ, viscosities η, refractive indices nD, coefficient of thermal expansion αP, excess molar volume VEm, and Partial molar volume V mi, of formamide (x1) + PEG 200 binary mixture at T = (293.15, 298.15 or 303.15) K and pressure of (0.1 MPa). T = 293.15 K x1

ρ/g · cm−3

η/mPa · s

αP ×104/K−1

VEm/cm3·mol−1

V m1 =cm3 mol

0.0000 0.1213 0.2011 0.3096 0.4003 0.5095 0.6019 0.7030 0.7978 0.9001 1.0000

1.1248 1.1260 1.1267 1.1277 1.1286 1.1296 1.1304 1.1312 1.1319 1.1324 1.1325

64.74 62.52 61.83 59.88 56.31 49.22 41.21 30.71 20.88 11.19 3.734

7.11 7.10 7.10 7.09 6.84 6.59 5.95 5.94 6.09 6.58 25.83

0.0000 −0.1305 −0.1867 −0.2478 −0.2864 −0.3004 −0.2890 −0.2520 −0.1977 −0.1102 0.0000

38.363 38.916 39.062 39.196 39.311 39.464 39.577 39.666 39.715 39.755 39.770

−1

V m2 =cm3 mol

−1

169.106 169.075 169.050 169.004 168.935 168.812 168.672 168.505 168.345 168.145 167.766

T = 298.15 K x1

ρ/g · cm−3

η/mPa ·s

αP ×104/K−1

VEm/cm3·mol−1

V m1 =cm3 mol

0.0000 0.1213 0.2011 0.3096 0.4003 0.5095 0.6019 0.7030 0.7978 0.9001 1.0000

1.1207 1.1220 1.1228 1.1239 1.1249 1.1260 1.1268 1.1276 1.1284 1.1287 1.1290

49.45 48.31 47.75 46.73 44.26 39.11 32.58 24.49 16.66 9.049 3.320

7.13 713 7.12 7.11 7.04 6.97 6.14 6.14 6.82 6.95 27.68

0.0000 −0.1426 −0.2093 −0.2776 −0.3218 −0.3377 −0.3189 −0.2736 −0.2173 −0.1106 0.0000

38.471 38.909 39.071 39.250 39.388 39.559 39.690 39.793 39.843 39.888 39.894

−1

V m2 =cm3 mol

−1

n

169.724 169.698 169.669 169.611 169.525 169.383 169.232 169.041 168.849 168.672 168.463

1.4582 1.4583 1.4586 1.4588 1.4589 1.4581 1.4569 1.4552 1.4529 1.4500 1.4459

T = 303.15 K x1

ρ/g · cm−3

η/mPa · s

αP ×104/K−1

VEm/cm3·mol−1

V m1 =cm3 mol

0.0000 0.1213 0.2011 0.3096 0.4003 0.5095 0.6019 0.7030 0.7978 0.9001 1.0000

1.1166 1.1180 1.1189 1.1201 1.1211 1.1222 1.1231 1.1239 1.1245 1.1248 1.1247

37.65 37.18 36.85 36.14 34.36 30.53 25.86 19.57 13.44 7.431 2.964

7.16 7.15 7.14 7.14 7.24 7.35 6.34 6.34 7.56 7.33 29.57

0.0000 −0.1583 −0.2380 −0.3166 −0.3586 −0.3715 −0.3581 −0.3086 −0.2363 −0.1273 0.0000

38.554 38.904 39.100 39.334 39.504 39.687 39.813 39.926 39.996 40.037 40.046

−1

V m2 =cm3 mol

−1

170.347 170.325 170.288 170.208 170.112 169.964 169.800 169.594 169.378 169.155 168.994


Fig. 1. Comparison between the experimental and theoretical density values obtained from Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) models for binary mixtures of formamide (FA) + 1,2-ED, 1,3-PD and PEG 200 at T = 298.15 K.


227

Table 5 The required critical parameters and acentric factors ω, for cubic equation of state as well as the obtained adjustable parameters kij, and average absolute deviation percent AAD%, from PR and SRK CEoS for studied mixtures at T = 298.15 K.

FA [56] 1,2-ED [56] 1,3-PD [56] PEG 200 [57]

Mw

Tc (K)

Pc (bar)

Vc (cm3·mol−1)

Zc

ω

45.041 62.067 76.094 200

771 645 658 759

78 75.3 59.2 23.1

163 191 217

0.198 0.268 0.235

0.453 1.137 1.152 1.96

FA + 1,2-ED

FA + 1,3-PD

SRK

PR

FA + PEG 200

SRK

PR

SRK

PR

kij

AAD%

kij

AAD%

kij

AAD%

kij

AAD%

kij

AAD%

kij

AAD%

6.21

28.8

2.22

20.06

8.60

26.92

8.63

18.55

11.56

35.00

11.51

26.45

the viscosities reported in this work. Moreover, good agreement was observed in comparison of the experimental refractive indices with the literature values, only refractive index data reported by Zhao [21] with AAD% = 1.042 indicated the considerable deviation with this work. Generally, these differences are most probably related to the purity of the components and the measuring method. Moreover, it should be mention that the molecular weight of PEG 200 reported by manufacture are rather uncertain between 190 and 210 g·mol−1 and in this work, the average values of 200 g·mol− 1 (like other researches) are considered as the molecular weight of PEG which cause to the considerable uncertainly in reported volumetric properties. 3. Results and discussion The measured experimental values of densities, viscosities and refractive indices of FA (x1) + 1,2-ED, 1,3-PD or PEG 200 binary mixtures

at temperatures of 293.15, 298.15 and 303.15 K over the whole composition range and atmospheric pressure are listed in Tables 2 to 4. Thermodynamic properties The variations of densities of studied mixtures against FA mole fraction at T = 298.15 K are shown in Fig. 1 along with data obtained from literatures and models. From the Fig. 1, the densities reported by Nain [11] for FA + 1,2-ED binary mixtures are close with data reported in this work. The data reported in Tables 2 to 4 and Fig. 1 indicated that the densities of studied binary mixtures increase with increase of FA mole fraction and decrease linearly with increase of temperature. The density of pure components varies in the order FA N PEG 200 N 1,2ED N 1,3-PD. High polarity of FA molecules and strong inter-intra molecule H-bonding along with small size of FA molecules that cause to the well packing, could be considered as the main reason of high density values of FA. The densities of studied binary mixtures were correlated and predicted with well-known Soave-Redlich-Kwong (SRK) [54] and

Fig. 2. Dependence of excess coefficient of thermal expansion αE, as function of formamide mole fraction (x1), for binary mixtures of formamide + a: 1,2-ethanediol, b: 1,3-propanediol and c: PEG 200 at different temperature.

228


Fig. 3. Dependence of excess molar volume VEm, as function of formamide mole fraction (x1) for binary mixtures of formamide + a: 1,2-ethanediol, b: 1,3-propanediol and c; PEG 200 at different temperature. Dash lines represent the results obtained by Redlich-Kister equation.

Peng-Robinson (PR) [55] equation of state. The general two parameter form of CEOS can be given as; P¼

RT aðT Þ − V m −b ðV m þ δ1 bÞðV m þ δ2 bÞ

ð2Þ

where a(T) and b are the attractive and repulsive terms, respectively, Vm is the molar volume, P represents the pressure of system, and δ1 and δ2 are two parameters which have the following values: (δ1 = 1, δ2 = 0) for the SRK, and (δ1 = 1 + 2, δ2 = 1–2) for the PR equation. The detailed information for calculation of parameters are given elsewhere [54,55].

Table 6 Coefficients (A0 ,A1 ,A2 ,A3 ,A4) of Redlich-Kister equation for excess molar volume VEm, excess viscosity ηE, and excess refractive index nE along with their standard deviations σ.

FA + 1,2-ED VEm

ηE

nE FA + 1,3-PD VEm

ηE

nE FA + PEG200 VEm

ηE

nE

A4

A3

A2

A1

A0

σ

T T T T T T T

= 293.15 K = 298.15 K = 303.15 K = 293.15 K = 298.15 K = 303.15 K = 298.15 K

0.1021 −0.0659 −0.0176 −1.0416 7.4688 2.6512 −0.0025

0.3806 0.3879 0.4423 6.6281 3.1563 2.0571 0.0001

0.2911 0.3753 0.3674 −6.6725 −9.5713 −3.5083 −0.0010

0.2150 0.2205 0.2014 8.4319 7.9812 6.8489 −0.0063

0.5647 0.6329 0.6786 −17.8609 −15.3200 −13.3348 −0.0074

0.0015 0.0044 0.0014 0.0699 0.1014 0.1199 0.0001

T T T T T T T

= 293.15 K = 298.15 K = 303.15 K = 293.15 K = 298.15 K = 303.15 K = 298.15 K

−0.2564 −0.2007 −0.3578 −15.1144 −21.0813 −23.5619 −0.0022

−0.6902 −0.7453 −0.7753 0.9137 −4.8750 −2.7838 0.0010

0.0962 0.0436 0.1310 −1.6450 3.0375 4.7725 0.0020

0.2143 0.2516 0.2753 38.7413 38.7800 31.8788 −0.0006

0.8131 0.8749 0.9344 −74.7556 −63.3113 −52.6456 −0.0019

0.0043 0.0035 0.0052 0.3232 0.3385 0.3437 0.0001

T T T T T T T

= 293.15 K = 298.15 K = 303.15 K = 293.15 K = 298.15 K = 303.15 K = 298.15 K

−0.3173 −0.1554 0.0184 9.2338 18.3988 12.9175 0.0039

0.1111 0.1263 0.0803 17.6625 11.2813 2.5587 0.0024

0.1459 0.1552 0.0501 −56.9533 −53.4963 −39.8363 −0.0129

−0.0769 −0.0452 −0.0108 −30.3205 −23.5698 −15.5813 −0.0031

−1.2022 −1.3419 −1.4916 63.0385 52.8450 42.6433 0.0094

0.0020 0.0047 0.0011 0.0585 0.0913 0.0435 0.0001


The following mixing rules were used to calculate the attraction and repulsion terms of SRK and PR CEoS of mixtures; n n 1=2 a ¼ ∑ ∑ xi x j 1−kij ai a j

ð3Þ

i¼1 j¼1 n

b ¼ ∑ xi i

bi þ b j 2

ð4Þ

where xi and xj are mole fraction of components i and j, respectively, and k ij is the adjustable interaction parameters. The calculated values of densities for studied binary mixtures in comparison with the experimental data are shown in Fig. 1. Moreover, the required pure critical parameters and calculated average absolute percentage deviation (AAD % ) and the obtained interaction parameters of used cubic equation of state are listed in Table 5. The results show the deficiently of PR and SRK cubic equation of state in density reproduction of FA + diols binary mixtures with AAD% between 26.9–35.0 and 18.55–26.4 for SRK and PR, respectively. As it seen,

−1

229

the PR equation represents the better prediction to SRK model for both pure and binaries. Moreover, the weakest results were found for FA + PEG 200 binary mixtures. Furthermore, between used pure components, the largest deviation was found for FA with AAD% = 48.4 and 48.2 for PR and SRK. These results indicated that the prediction accuracy of SRK and PR models decrease with increase of component's inter-intra molecules association. Figs. S1 to S3 show the slop of density variation against temperature for FA (x 1 ) + 1,2-ED, 1,3-PD or PEG 200 binary mixtures varies from − 0.00078 to − 0.00071, − 0.00078 to − 0.00064 and, − 0.00078 to − 0.00082, respectively. These results are shown the resistant of volume expansion to temperatures. Based on the temperature dependence of density, the experimental values of densities were fitted to the following equation: ρðT Þ ¼ aT 2 þ bT þ c

ð5Þ

This density temperature dependence relation enabled us to calculate the thermal expansion coefficient αP, and excess values αEP, by the

Fig. 4. Dependence of partial molar volume, V m;i =cm3 mol , of (a): formamide (FA), (b):1,2-ethanediol (1,2-ED), (c):1,3-propanediol (1,3-PD) and (d): poly (ethylene glycol) 200 (PEG) as a function of FA mole fraction (x1) for binary mixtures of FA + 1,2-ED, 1,3-PD and PEG 200 at different temperatures.

230


Eq. (8): φ1 ¼ 1−φ2 ¼

Fig. 5. Dependence of excess refractive indices nE, as a function of formamide mole fraction (x1) for binary mixtures of formamide (FA) + 1,2-ethanediol (1,2-ED), 1,3-propanediol (1,3-PD) and PEG 200 at T = 298.15 K.

x1 V 1 x1 V 1 þ x2 V 2

ð8Þ

The calculated values of thermal expansion coefficients are listed in Tables 2 to 4. From the reported αP data, it seems that the thermal expansion coefficients show less dependency to temperature and are positive for all studied mixtures. The positive values of αP reveal the tendency of these solutions for expansion when temperature increases. Fig. 2 shows the variation of αEP against the FA mole fraction for studied binary mixtures. Accordingly, the values of excess thermal expansion coefficient are negative for all studied mixtures with the extremum values around 0.9 FA mole fraction for FA + 1,2-ED or PEG 200 binaries and with minimum values at 0.7 FA mole fraction for FA + 1,3-PD mixtures. Less flexibility against temperature than an ideal solution can be explained as the negative values of αEp. The values of excess molar volumes, VEm, were calculated by the following equation: V Em ¼

x1 M 1 þ x2 M 2 x1 M1 x2 M 2 − þ ρ ρ1 ρ2

ð9Þ

following equations: " −1

∂ρ ∂T ! E

α P ¼ −ρ 2 1 4 ∂V m ¼ V ∂T

# 1 ∂V m ¼ V m ∂T P;x P;x ! 3 2 ∂ 5 þ ∑ xi V i ∂T i¼1

p;x

α EP ¼ ½α P −ðφ1 α 1 þ φ2 α 2 Þ

ð6Þ

p;x

ð7Þ

where φ1, α1, φ2 and α2 are volume fraction and the thermal expansion coefficient of components 1 and 2, respectively, and Vm is the molar volume of system. The volume fraction of mixtures φi, is calculated using

where ρ is density of binary mixtures, and x1, M1, ρ1, x2, M2, ρ2 are the mole fraction, molar mass, and densities of components 1 and 2, respectively. The calculated values of excess molar volumes for all studied mixtures at different temperatures are listed in Tables 2 to 4, and graphically shown in Fig. 3. Fig. 3 reveals that the VEm values are positive for FA + 1,2-ED or 1,3-PD mixtures with maximum values around the 0.7 FA mole fraction and are negative over the entire composition range with extremum at 0.5 FA mole fractions for FA + PEG 200 binary mixtures. The magnitude of VEm values follows the sequence FA + PEG b FA + 1,2-ED b FA + 1,3-PD. The VEm values can be explained in terms of positive contributions due to breaking of like interactions of the pure liquids and negative contributions due to the formation of

Fig. 6. Comparison between the experimental and theoretical viscosity values of formamide + A: 1,2-ethanediol, B: 1,3-propanediol and C: PEG 200 binary mixtures at T = 293.15 K.


unlike FA − diols H-bonding structure and accommodation of FA molecules in the voids provided by the diols (packing effect). For FA + 1,2-ED or 1,3-PD systems, the VEm values increase (become more positive) whereas for FA + PEG systems, VEm values decrease (shift to more negative values) with increase in temperature. In the case of FA + PEG mixtures, the expansion in volume due to increase in temperature of the systems seems to be dominated by more favorable fitting of smaller FA molecules into the larger voids created by PEG molecules at higher temperatures, leading to a contraction in volume, hence, resulting in more negative VEm values with rise in temperature. On the other hand, in case of FA + 1,2-ED and 1,3-PD mixtures, the increase in VEm is attributed to the breaking of associates presents between unlike molecules with rise in temperature, leading to an expansion in volume. The calculated values of VEm were fitted to the Redlich–Kister polynomial equation [58]. The Redlich-Kister expansion provides a flexible algebraic expression for representing the excess properties of a liquid mixture using the following formula, N

V Em ¼ x1 x2 ∑ Ai ðx1 −x2 Þi−1

defined as the sum of absolute standard deviations σ, which were calculated using the following expression,

σ ðY Þ ¼

1 = 2 2 V Emexp −V Emcal =ðN−nÞ

ð11Þ

where, N is the number of data points and n is the order of fitting polynomial. The calculated values of Ai along with their standard deviations are listed in Table 6. As it can be seen, good fitting of VEm to Redlich-Kister equation was found with σ b 0.0052 for studied mixtures at all temperatures. The partial molar volume V m;i , of components were calculated using the following relations, E

m;1 ¼V E þ V þ ð1−x1 Þ ∂V m V m 1 ∂x1

ð10Þ

i¼1

231

E

m;2 ¼V E þ V −x1 ∂V m V m 2 ∂x1

Here x1 and x2 are mole fractions of components 1 and 2, respectively and, Ai values are adjustable parameters which the nature of various classes of solutions is expressed in the magnitude of these parameters [58]. This correlation was carried out minimizing an objective function

! ð12Þ T;P

! ð13Þ T;P

where V∗1 and V∗2 are molar volumes of pure components 1 and 2, respec∂V

E

tively. The derivative, ð ∂xm Þ 1

T;P

could be obtained by differentiation of the

Table 7 Adjustable parameters of investigated viscosity models along with their average absolute deviation percent (AAD%) for formamide + 1,2-ethanediol, 1,3-propanediol or PEG 200 binary mixtures. Formamide + 1,2-ED x1 Andrads

0.00 0.22 4.72 1.89 0.35

A B × 10−2 C × −10−2 AAD%

0.10 0.21 4.42 1.92 0.31

0.20 2.76 0.48 2.63 0.18

0.30 1.59 0.67 2.58 0.19

McAllister

T = 293.15 K T = 298.15 K T = 308.15 K

0.40 0.14 3.72 2.06 0.5

0.50 0.14 3.622 2.04 0.91

0.60 0.07 4.88 1.87 0.31

0.70 1.05 0.61 2.57 0.06

Eyring-Margules

0.80 1.4 0.39 2.62 0.14

0.90 1.19 0.53 2.53 0.04

1.00 0.15 4.15 1.64 0.1

Grunberg-Nissan

ν12

ν21

AAD%

A12

A21

AAD%

D12

AAD%

1.74 1.52 1.30

2.13 1.89 1.70

0.78 1.44 3.09

−0.04 −0.38 −0.51

−0.66 −0.86 −1.00

0.98 1.49 1.04

−0.46 −0.69 −0.77

1.75 1.90 1.74

Formamide + 1,3-PD x1 Andrads

0.00 0.85 3.40 2.11 0.09

A B × 10−2 C × −10−2 AAD%

0.10 0.001 23.25 0.72 1.44

0.20 0.11 5.55 1.93 2.23

0.30 0.14 4.01 2.12 1.34

McAllister

T = 293.15 K T = 298.15 K T = 308.15 K

0.40 0.04 5.41 2.01 7.27

0.50 0.04 5.33 1.98 7.1

0.60 0.02 7.48 1.73 8.77

0.70 0.06 5.65 1.74 6.24

Eyring-Margules

0.80 0.08 3.76 2.04 2.38

0.90 0.09 4.51 1.78 0.84

1.00 0.15 4.15 0.02 0.10

Grunberg-Nissan

ν12

ν21

AAD%

A12

A21

AAD%

D12

AAD%

1.59 1.70 0.93

2.77 2.44 2.20

2.12 2.34 3.20

−1.41 −1.01 −2.35

−0.64 −0.85 −1.61

1.43 2.21 3.37

−1.09 −1.07 −1.97

2.49 2.14 4.03

Formamide + PEG 200 x1 Andrads

0.00 0.62 35.8 2.16 0.77

A B × 10−2 C × −10−2 AAD%

0.12 0.60 37.4 2.12 0.62

0.20 0.42 43.6 2.06 0.29

McAllister

T = 293.15 K T = 298.15 K T = 308.15 K

0.31 1.40 24.1 2.28 0.15

0.40 2.51 16.5 2.40 0.20

0.51 1.29 24.1 2.27 0.21

0.60 0.91 27.4 2.21 0.19

0.70 0.57 31.5 2.14 0.37

Eyring-Margules

0.80 0.18 47.1 1.94 0.22

0.90 0.28 29.9 2.12 0.19

1.00 0.15 41.6 1.64 0.10

Grunberg-Nissan

ν12

ν21

AAD%

A12

A21

AAD%

D12

AAD%

4.85 4.59 4.30

3.68 3.46 3.32

4.37 2.81 2.04

8.96 8.69 8.39

2.45 2.33 2.29

2.94 2.77 2.23

0.63 0.58 0.51

18.04 16.55 14.57

232


Eq. (10), and leads to the following expanded equations, n

n

i¼0

i¼1

n

n

i¼0

i¼1

V m;1 ¼ V 1 þ x22 ∑ Ai ð1−2x1 Þi −2x1 x22 ∑ Ai ð1−2x1 Þi−1

V m;2 ¼ V 2 þ x21 ∑ Ai ð1−2x1 Þi −2x2 x21 ∑ Ai ð1−2x1 Þi−1

introduce the molar refraction,

ð14Þ

ð15Þ

The calculated values of partial molar volumes are listed in columns 6 and 7 of Tables 2–4 and are plotted in Fig. 4. From Fig. 4, the partial molar volume of 1,2-ED and 1,3-PD increase and partial molar volume of PEG 200 decrease with increase of FA mole fraction. Moreover, partial molar volume of FA shows the opposite behavior at all mixtures. This behavior is dominated for other partial molar properties. Based on the Gibbs-Duhem equation, the partial molar quantities of a mixture cannot change independently of the other components. In a binary mixture, if one partial molar quantity increases, then the other must decrease. 3.1. Optical properties The experimental values of refractive indices nD are summarized in Tables 2–4for binary mixtures of FA + 1,2-ED, 1,3-PD or PEG 200 as a function of FA mole fraction at temperatures of 298.15 K and 0.1 MPa pressure. The reported refractive indices for FA + 1,2-ED or 1,3-PD show that the refractive indices increase linearly with increase of FA mole fraction while for FA + PEG 200 binaries the refractive indices decrease non-lineally with increase of FA mole fraction. Base on the definition of refractive index, this optical property give the information about the free volume available in the systems. The correlation between density and refractive index is reflected in Lorentz-Lorenz equation by

Rm ¼

n2 −1 M 4π ¼ NA α e 3 n2 þ 2 ρ

ð16Þ

where, Rm is the molar refraction in mol−1, NA is the Avogadro's number in mol−1 and αe is electronic polarizability cm3·mol−1. The polarizability is obtained from sum of four contributions; electronic, atomic, orientationally and space charge polarization. Electron polarizability (optical polarization) αe, is the deformation or translation of the originally symmetrical distribution electron clouds of atoms or molecules under the electric field and gives information about the molecular shape and the electronic charge distribution. The obtained values of molar refraction Rm, and polarizability αe, for the studied binary mixtures are shown in Fig. S2 in Supporting information. From the Fig. S2, it can be observed that the opposite of density and viscosity behavior, the molar refraction of studied mixtures decrease with increase of FA mole fraction. This decrement could be ascribed to that with the molecular size decrements, the electronic clouds cannot be easily displaced from the nuclei in response to the field seen by molecules and so the electron polarizability and molar refraction decrease. Using the volume-fraction mixing rule to indicating the ideal liquid mixtures [59], the excess refractive index calculated by the following equation and results are represented in Fig. 5, h 2 2 i12 nED ¼ nD − φ1 nD1 þ φ2 nD2

ð12Þ

Fig. 5 shows that the excess refractive indices are negative for FA + 1,2-ED or 1,3-PD binary mixtures with extremum values at 0.7 FA mole fraction and are positive for FA + PEG 200 binary mixtures with maximum at 0.5 FA mole fractions. When VEm is negative, the free

Fig. 7. Dependence of excess viscosity ηE, as function of formamide mole fraction (x1) for binary mixtures of formamide + a: 1,2-ethanediol, b: 1,3-propanediol and c: PEG 200 at different temperatures.


volume is less available than in the ideal solution and so light photons travel at lower velocity in the medium concerned and its refractive index would be higher in an ideal solution; thus, the excess refractive index becomes positive. These results are in agreements with VEm values. It should be noticed that this is not a general rule because diverse factors can be contributed to excess molar volume and excess refractive index. 3.2. Transport properties The measured viscosities values of FA + 1,2-ED, 1,3-PD or PEG 200 binary mixtures at all studied temperatures are listed in Tables 2 to 4, and graphically shown in Fig. 6 at T = 298.15 K along with data obtained by models and literature. Accordingly, viscosities of mixtures decrease nonlinearly with increasing FA mole fraction in mixtures. For all studied mixtures, the degree of self-association among the moving layer of FAs less than the degree of hetero-association between moving layers of FA and diols mixtures and so the viscosities of mixtures decrease with increase of FA composition. Moreover, the viscosities decrease with increase of temperature and the slop of η against T decrease with increase of FA mole fraction and vary from non-linear to linear shape. Based on the dependency of viscosity to temperature and composition, several semi-empirical relations have been proposed to estimate the viscosity of liquid mixtures. Herein, the Andrade (Eq. (13)) [60] temperature – dependence model and different composition – dependence models including the Grunberg-Nissan (Eq. (14)) [61], Eyring-Margules (Eq. (15)) [62] and McAllister (Eq. (16)) [63] were used to reproduce the viscosities of studied binary mixture at T = 293.15, 298.15 and 303.15 K and p = 0.1 MPa. B η ¼ A: exp T þC

ð13Þ

ln η ¼ x1 ln η1 þ x2 ln η2 þ x1 x2 D12

ð14Þ

ln ðηV Þ ¼ x1 ln η1 V 1 þ x2 ln η2 V 2 þ x1 x2 ½x1 A12 þ x2 A21

ð15Þ

ln υ ¼ x31 ln υ1 þ 3x21 x2 ln υ12 þ 3x 1 x22 ln υ21 M2 2 þ ðM 2 =M1 Þ þ3x21 x2 ln þ x32 ln υ2 − ln x1 þ x2 M1 3 1 þ ð2M2 =M1 Þ M2 2 3 þ x2 ln þ 3x1 x2 ln M1 3

ð16Þ

The results compared with experimental values in terms of average absolute deviation percent (AAD%). The average absolute deviation percent AAD% between measurements and calculated thermophysical values is obtained by the Eq. (17),

exp cal 100 N

Ai −Ai

∑

AAD% ¼

N i¼1 Aexp i

ð17Þ

233

where ηmix, η1 and η2are the viscosity of mixtures, pure components 1 and 2, respectively. The calculated values of ηE, against FA mole fraction for all studied binary mixtures at T = 293.15, 298.15 and 303.15 K are plotted in Fig. 7. The obtained ηE values for FA + 1,2-ED and FA + 1,3PD are negative over the entire range of composition with extremum values around the 0.3–0.4 formamide mole fraction. The breakup of self-associations in the pure component would make the mixture to flow more easily, at the same time, the hydrogen bonds between different molecules could increase the viscosity during the mixing process, but the effect is not as important as the breakup of self-associations, thus the excess viscosity are negative. For FA + PEG 200 binary mixtures, the maximum positive value was achieved at the 0.4 FA mole fractions. The positive values of ηE are due to the hydrogen bonds between FA and PEG 200 molecules formatted in the mixing process, which are greater than the breakup of self-associations. Kauzmann and Eyring [64] addressed the issue that the viscosity of a mixture strongly depends on the entropy of the mixture, which is closely related to the liquid structure and molecular interactions between the components of the mixture. As it can be seen, the sign of VEm and ηE are conflicting implies that the specific interactions between unlike molecules dominate in FA + PEG 200 binary mixtures. Moreover, for all studied mixture, ηE values shift to zero point with increasing temperature. 4. Conclusion The experimental values of densities, viscosities and refractive indices of formamide + 1,2-ethanediol, 1,3-propanediol and poly (ethylene glycol) 200 binary liquid mixtures were measured at T = 293.15, 298.15 and 303.15 K. The reported experimental values of the pure components generally agreed with the available literature data. The calculated values of VEm for FA + 1,2-ED or 1,3-PD binary mixtures were positive and for FA + PEG 200 binary mixtures were negative over the entire composition range at all studied temperature. Moreover, negative values of ηE for FA + 1,2-ED or 1,3-PD binaries and positive values of ηE for binary mixtures of FA + PEG 200 was obtained. The negative values of VEm and positive values of ηE indicated the present of strong interaction between unlike molecules in the mixtures. Moreover, the calculated excess properties were well correlated with the Redlich-Kister polynomial equation for all binary mixtures. Furthermore, the partial molar volumes of component were calculated and it was observed that with increasing the partial molar volume of one component, the partial molar volume of the other component decreases. Acknowledgment The instrumental support from Shomal University is gratefully acknowledged. Appendix A. Supplementary data

where N is the number of experimental data points. The subscripts “exp” and “calc” represent the values of the experimental and calculated property, respectively. The obtained adjustable parameters of viscosity models along with the absolute average deviation percent values are reported in Table 7. Moreover, Fig. 6 graphically illustrates the comparison between calculated and experimental viscosity values at T = 298.15 K. From Fig. 6 and data reported in Table 7, the experimental viscosities of studied mixtures are well correlated to temperature dependence Andrade equation with AAD% b 1.44. For all used models, good fitting was seen with experimental values and only large values of AAD% = 18.04 was observed in viscosity correlation with Grunberg Nissan for FA + PEG 200 binary mixtures at T = 293.15. The excess viscosity was also calculated to discuss the molecular interactions existing in the studied solutions using the following equation, ηE ¼ ηmix −x1 η1 −x2 η2

ð18Þ

Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.molliq.2017.03.008. References [1] X. Wang, X. Wang, B. Song, Densities and viscosities of binary mixtures of 2,2,4trimethylpentane + 1-propanol, + 1-pentanol, + 1-hexanol, and + 1-heptanol from (298.15 to 323.15) K, J. Chem. Eng. Data 60 (2015) 1664–1673, http://dx.doi. org/10.1021/je501041r. [2] M.T. Zafarani-Moattar, S. Dehghanian, Intermolecular interactions in mixtures of poly (ethylene glycol) with methoxybenzene and ethoxybenzene: volumetric and viscometric studies, J. Chem. Thermodyn. 71 (2014) 221–230, http://dx.doi.org/10. 1016/j.jct.2013.12.008. [3] E.M. Živković, D.M. Bajić, I.R. Radović, S.P. Šerbanović, M.L. Kijevčanin, Volumetric and viscometric behavior of the binary systems ethyl lactate + 1,2-propanediol, +1,3-propanediol, +tetrahydrofuran and +tetraethylene glycol dimethyl ether. New UNIFAC–VISCO and ASOG–VISCO parameters determination, Fluid Phase Equilib. 373 (2014) 1–19, http://dx.doi.org/10.1016/j.fluid.2014.04.002.

234


[4] H. Zarei, S.A. Golroudbari, M. Behroozi, Experimental studies on volumetric and viscometric properties of binary and ternary mixtures of N,N-dimethylacetamide, Nmethylformamide and propane-1,2-diol at different temperatures, J. Mol. Liq. 187 (2013) 260–265, http://dx.doi.org/10.1016/j.molliq.2013.07.002. [5] A.K. Nain, S. Ansari, A. Ali, Densities, refractive indices, ultrasonic speeds and excess properties of acetonitrile + poly(ethylene glycol) binary mixtures at temperatures from 298.15 to 313.15 K, J. Solut. Chem. 43 (2014) 1032–1054, http://dx.doi.org/ 10.1007/s10953-014-0189-9. [6] A.K. Nain, Densities and volumetric properties of (formamide + ethanol, or 1propanol, or 1,2-ethanediol, or 1,2-propanediol) mixtures at temperatures between 293.15 K and 318.15 K, J. Chem. Thermodyn. 39 (2007) 462–473, http://dx.doi.org/ 10.1016/j.jct.2006.07.021. [7] E.D. Glendening, J.A. Hrabal, Resonance in formamide and its chalcogen replacement analogues: a natural population analysis/natural resonance theory viewpoint, J. Am. Chem. Soc. 119 (1997) 12940–12946, http://dx.doi.org/10.1021/ja970074j. [8] R. Alcalde, G. García, J.L. Trenzado, M. Atilhan, S. Aparicio, Characterization of amidealkanediol intermolecular interactions, J. Phys. Chem. B 119 (2015) 4725–4738, http://dx.doi.org/10.1021/acs.jpcb.5b00936. [9] A. Awasthi, A. Awasthi, Acoustic, volumetric, and spectroscopic studies of formamide with 2-alkoxyethanols at different temperatures, J. Chem. Thermodyn. 53 (2012) 144–151, http://dx.doi.org/10.1016/j.jct.2012.04.024. [10] M. Moosavi, A. Motahari, A. Omrani, A.A. Rostami, Thermodynamic study on some alkanediol solutions: measurement and modeling, Thermochim. Acta 561 (2013) 1–13, http://dx.doi.org/10.1016/j.tca.2013.03.010. [11] A.K. Nain, Ultrasonic and viscometric studies of molecular interactions in binary mixtures of formamide with ethanol, 1-propanol, 1,2-ethanediol and 1,2propanediol at different temperatures, J. Mol. Liq. 140 (2008) 108–116, http://dx. doi.org/10.1016/j.molliq.2008.01.016. [12] M. Rani, S. Maken, Topological studies of molecular interactions of formamide with propanol and butanol at 298.15 K, J. Ind. Eng. Chem. 18 (2012) 1694–1704, http:// dx.doi.org/10.1016/j.jiec.2012.03.011. [13] M. Almasi, Densities and viscosities of the mixtures (formamide + 2-alkanol): experimental and theoretical approaches, J. Chem. Thermodyn. 69 (2014) 101–106, http://dx.doi.org/10.1016/j.jct.2013.09.043. [14] A.K. Nain, Densities and volumetric properties of (acetonitrile + an amide) binary mixtures at temperatures between 293.15 K and 318.15 K, J. Chem. Thermodyn. 38 (2006) 1362–1370, http://dx.doi.org/10.1016/j.jct.2006.01.015. [15] Q. Dong, R.D. Chirico, X. Yan, X. Hong, M. Frenkel, Uncertainty reporting for experimental thermodynamic properties†, J. Chem. Eng. Data 50 (2005) 546–550, http:// dx.doi.org/10.1021/je049673d. [16] B.N. Taylor, C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, https://www.nist.gov/pml/nist-technical-note-1297 1994. [17] R.D. Chirico, M. Frenkel, J.W. Magee, V. Diky, C.D. Muzny, A.F. Kazakov, K. Kroenlein, I. Abdulagatov, G.R. Hardin, W.E. Acree, J.F. Brenneke, P.L. Brown, P.T. Cummings, T.W. de Loos, D.G. Friend, A.R.H. Goodwin, L.D. Hansen, W.M. Haynes, N. Koga, A. Mandelis, K.N. Marsh, P.M. Mathias, C. McCabe, J.P. O'Connell, A. Pádua, V. Rives, C. Schick, J.P.M. Trusler, S. Vyazovkin, R.D. Weir, J. Wu, Improvement of quality in publication of experimental thermophysical property data: challenges, assessment tools, global implementation, and online support, J. Chem. Eng. Data 58 (2013) 2699–2716, http://dx.doi.org/10.1021/je400569s. [18] J.M. Vuksanovic, M.S. Calado, G.R. Ivanis, M.L. Kijevcanin, S.P. Serbanovic, Z.P. Visak, Environmentally friendly solutions of liquid poly(ethylene glycol) and imidazolium based ionic liquids with bistriflamide and triflate anions: volumetric and viscosity studies, Fluid Phase Equilib. 352 (2013) 100–109, http://dx.doi.org/10.1016/j.fluid. 2013.05.013. [19] N.G. Tsierkezos, I.E. Molinou, Thermodynamic properties of water + ethylene glycol at 283.15, 293.15, 303.15, and 313.15 K, J. Chem. Eng. Data 43 (1998) 989–993, http://dx.doi.org/10.1021/je9800914. [20] J. George, N.V. Sastry, Densities, dynamic viscosities, speeds of sound, and relative permittivities for water + alkanediols (propane-1,2- and -1,3-diol and butane-1,2-, -1,3-, -1,4-, and -2,3-diol) at different temperatures, J. Chem. Eng. Data 48 (2003) 1529–1539, http://dx.doi.org/10.1021/je0340755. [21] D. Zhao, S. Li, Q. Zhai, Y. Jiang, M. Hu, Solution behavior of {(formamide/Nmethylformamide/N,N-dimethylformamide) + CsCl + water} ternary systems at multiple temperatures, J. Chem. Thermodyn. 78 (2014) 134–142, http://dx.doi. org/10.1016/j.jct.2014.05.013. [22] R. Singh, M. Yasmin, H. Agarwal, V.K. Shukla, M. Gupta, J.P. Shukla, Study of molecular interactions in binary mixtures of formamide with 2-methoxyethanol and 2ethoxyethanol at varying temperatures, Phys. Chem. Liq. 51 (2013) 606–620, http://dx.doi.org/10.1080/00319104.2013.763941. [23] R.K. Shukla, A. Kumar, U. Srivastava, K. Srivastava, V.S. Gangwar, Density, refractive index and molar refractivity of binary liquid mixture at 293.15, 298.15, 303.15, 308.15 and 313.15 K, Arab. J. Chem. (2012)http://dx.doi.org/10.1016/j.arabjc.2012. 02.013. [24] V.K. Sharma, R. Dua, Topological and thermodynamic investigations of mixtures containing o-chlorotoluene and lower amides, J. Chem. Thermodyn. 71 (2014) 182–195, http://dx.doi.org/10.1016/j.jct.2013.12.006. [25] S. Kumar, A. Maken, S. Agarwal, S. Maken, Topological studies of molecular interactions of 1,4-dioxane with formamides or anilines at 308.15K, J. Mol. Liq. 155 (2010) 115–120, http://dx.doi.org/10.1016/j.molliq.2010.05.023. [26] P.K. Pandey, A. Awasthi, A. Awasthi, Acoustic, volumetric and spectroscopic properties of formamide + N-methylformamide + 2-chloroethanol at different temperatures, Phys. Chem. Liq. 52 (2014) 320–330, http://dx.doi.org/10.1080/00319104. 2013.828211.

[27] M. Rani, S. Agarwal, P. Lahot, S. Maken, Excess molar enthalpies of binary mixtures of formamide with butanol at 298.15 K: application of Prigogine–Flory–Patterson theory and Treszczanowicz–Benson association model, J. Ind. Eng. Chem. 19 (2013) 1715–1721, http://dx.doi.org/10.1016/j.jiec.2013.02.011. [28] M. Rani, S. Maken, Excess molar enthalpies and excess molar volumes of formamide + 1-propanol or 2-propanol and thermodynamic modeling by Prigogine– Flory–Patterson theory and Treszczanowicz–Benson association model, Thermochim. Acta 559 (2013) 98–106, http://dx.doi.org/10.1016/j.tca.2013.02.010. [29] A. Awasthi, A. Awasthi, Intermolecular interactions in formamide + 2alkoxyethanols: viscometric study, Thermochim. Acta 537 (2012) 57–64, http:// dx.doi.org/10.1016/j.tca.2012.03.001. [30] M. Vraneš, S. Dožić, A. Tot, S. Gadžurić, Viscosity of ammonium nitrate + formamide mixtures, J. Chem. Eng. Data 59 (2014) 3365–3371, http://dx.doi.org/10.1021/ je500284p. [31] A.M. Cases, A.C. Gómez Marigliano, C.M. Bonatti, H.N. Sólimo, Density, viscosity, and refractive index of formamide, three carboxylic acids, and formamide + carboxylic acid binary mixtures, J. Chem. Eng. Data 46 (2001) 712–715, http://dx.doi.org/10. 1021/je000327f. [32] V. Campos, A.C. Gómez Marigliano, H.N. Sólimo, Density, viscosity, refractive index, excess molar volume, viscosity, and refractive index deviations and their correlations for the (formamide + water) system. Isobaric (vapor + liquid) equilibrium at 2.5 kPa, J. Chem. Eng. Data 53 (2008) 211–216, http://dx.doi.org/10.1021/ je700517f. [33] M. Yasmin, M. Gupta, Thermoacoustical analysis of solutions of poly(ethylene glycol) 200 through H-bond complex formation, Thermochim. Acta 518 (2011) 89–100, http://dx.doi.org/10.1016/j.tca.2011.02.011. [34] R. Francesconi, A. Bigi, K. Rubini, F. Comelli, Molar heat capacities, densities, viscosities, and refractive indices of poly(ethylene glycols) + 2-methyltetrahydrofuran at (293.15, 303.15, and 313.15) K, J. Chem. Eng. Data 52 (2007) 2020–2025, http://dx. doi.org/10.1021/je7003066. [35] D.M. Bajić, G.R. Ivaniš, Z.P. Visak, E.M. Živković, S.P. Šerbanović, M.L. Kijevčanin, Densities, viscosities, and refractive indices of the binary systems (PEG200 + 1,2propanediol, + 1,3-propanediol) and (PEG400 + 1,2-propanediol, + 1,3propanediol) at (288.15 to 333.15) K and atmospheric pressure: measurements and modeling, J. Chem. Thermodyn. 57 (2013) 510–529, http://dx.doi.org/10. 1016/j.jct.2012.07.024. [36] S. Ottani, R. Francesconi, F. Comelli, C. Castellari, Excess molar enthalpies of binary mixtures containing poly(ethylene glycol) 200 + four cyclic ethers at (288.15, 298.15 and 313.15) K and at atmospheric pressure, Thermochim. Acta 401 (2003) 87–93, http://dx.doi.org/10.1016/S0040-6031(02)00501-4. [37] M.S. Calado, A.S.H. Branco, J.C.F. Diogo, J.M.N.A. Fareleira, Z.P. Visak, Solubility, volumetric properties and viscosity of the sustainable systems of liquid poly(ethylene glycol) 200 with imidazolium- and phosphonium-based ionic liquids: cation and anion effects, J. Chem. Thermodyn. 80 (2015) 79–91, http://dx.doi.org/10.1016/j. jct.2014.08.018. [38] M. Yasmin, M. Gupta, J.P. Shukla, Experimental and computational study on viscosity and optical dielectric constant of solutions of poly (ethylene glycol) 200, J. Mol. Liq. 160 (2011) 22–29, http://dx.doi.org/10.1016/j.molliq.2011.02.005. [39] D.M. Bajić, J. Jovanović, E.M. Živković, Z.P. Visak, S.P. Šerbanović, M.L. Kijevčanin, Experimental measurement and modelling of viscosity of the binary systems pyridine or nicotine with polyethylene glycols at T = (288.15–333.15)K. New UNIFAC–VISCO and ASOG–VISCO interaction parameters, Fluid Phase Equilib. 338 (2013) 282–293, http://dx.doi.org/10.1016/j.fluid.2012.11.021. [40] F. Comelli, S. Ottani, R. Francesconi, C. Castellari, Excess molar enthalpies of binary mixtures containing glycols or polyglycols + dimethyl sulfoxide at 308.15 K, J. Chem. Eng. Data 48 (2003) 995–998, http://dx.doi.org/10.1021/je034007i. [41] Q.-S. Li, Y.-M. Tian, S. Wang, Densities and excess molar volumes for binary mixtures of 1,4-butanediol + 1,2-propanediol, + 1,3-propanediol, and + ethane-1,2-diol from (293.15 to 328.15) K, J. Chem. Eng. Data 53 (2008) 271–274, http://dx.doi. org/10.1021/je700499d. [42] K. Zemánková, J. Troncoso, L. Romaní, Excess volumes and excess heat capacities for alkanediol + water systems in the temperature interval (283.15313.15)K, Fluid Phase Equilib. 356 (2013) 1–10, http://dx.doi.org/10.1016/j. fluid.2013.06.041. [43] E. Zorębski, B. Lubowiecka-Kostka, Thermodynamic and transport properties of (1,2-ethanediol + 1-nonanol) at temperatures from (298.15 to 313.15)K, J. Chem. Thermodyn. 41 (2009) 197–204, http://dx.doi.org/10.1016/j.jct.2008.09.018. [44] M. Cocchi, A. Marchetti, G. Sanna, L. Tassi, A. Ulrici, G. Vaccari, Kinematic viscosities of ternary mixtures containing ethane-1,2-diol, 2-methoxyethanol and water from −10 °C to 80 °C, Fluid Phase Equilib. 157 (1999) 317–342, http://dx.doi.org/10. 1016/S0378-3812(99)00006-0. [45] C. Yang, P. Ma, F. Jing, D. Tang, Excess molar volumes, viscosities, and heat capacities for the mixtures of ethylene glycol + water from 273.15 K to 353.15 K, J. Chem. Eng. Data 48 (2003) 836–840, http://dx.doi.org/10.1021/je020140j. [46] E. Jiménez, M. Cabanas, L. Segade, S. García-Garabal, H. Casas, Excess volume, changes of refractive index and surface tension of binary 1,2-ethanediol + 1propanol or 1-butanol mixtures at several temperatures, Fluid Phase Equilib. 180 (2001) 151–164, http://dx.doi.org/10.1016/S0378-3812(00)00519-7. [47] T.M. Aminabhavi, K. Banerjee, Density, viscosity, refractive index, and speed of sound in binary mixtures of methyl acetate + ethylene glycol or + poly(ethylene glycol) in the temperature interval (298.15–308.15) K, J. Chem. Eng. Data 43 (1998) 852–855 (doi:S0021-9568(98)00075-2). [48] M.L. Kijevčanin, E.M. Živković, B.D. Djordjević, I.R. Radović, J. Jovanović, S.P. Šerbanović, Experimental determination and modeling of excess molar volumes, viscosities and refractive indices of the binary systems (pyridine + 1-propanol, + 1,2-propanediol, + 1,3-propanediol, and + glycerol). New UNIFAC-VISCO


[49]

[50]

[51]

[52]

[53]

[54]

[55] [56]

parameters determination, J. Chem. Thermodyn. 56 (2013) 49–56, http://dx.doi. org/10.1016/j.jct.2012.06.031. D.M. Bajić, E.M. Živković, S.P. Šerbanović, M.L. Kijevčanin, Experimental measurements and modelling of volumetric properties, refractive index and viscosity of selected binary systems with butyl lactate at 288.15–323.15 K and atmospheric pressure. New UNIFAC-VISCO interaction parameters, Thermochim. Acta 562 (2013) 42–55, http://dx.doi.org/10.1016/j.tca.2013.03.025. P. Góralski, M. Tkaczyk, Heat capacities of some liquid α,ω-alkanediols within the temperature range between (293.15 and 353.15) K, J. Chem. Eng. Data 53 (2008) 1932–1934, http://dx.doi.org/10.1021/je800356x. J.-W. Lee, S.-B. Park, H. Lee, Densities, surface tensions, and refractive indices of the water + 1,3-propanediol system, J. Chem. Eng. Data 45 (2000) 166–168, http://dx. doi.org/10.1021/je990196m. M. Moosavi, A. Motahari, A. Omrani, A.A. Rostami, Investigation on some thermophysical properties of poly(ethylene glycol) binary mixtures at different temperatures, J. Chem. Thermodyn. 58 (2013) 340–350, http://dx.doi.org/10.1016/ j.jct.2012.11.016. M.J. Fontao, M. Iglesias, Effect of temperature on the refractive index of aliphatic hydroxilic mixtures (C2–C3), Int. J. Thermophys. 23 (2002) 513–527, http://dx. doi.org/10.1023/A:1015113604024. G. Soave, Equilibrium constants from a modified Redlich-Kwong equation of state, Chem. Eng. Sci. 27 (1972) 1197–1203, http://dx.doi.org/10.1016/00092509(72)80096-4. D. Peng, D.B. Robinson, A new two-constant equation of state, Ind. Eng. Chem. Fundam. 15 (1976) 59–64, http://dx.doi.org/10.1021/i160057a011. C.L. Yaws, Yaws' Handbook of Thermodynamic and Physical Properties of Chemical Compounds, McGraw-Hill, 2003https://books.google.com/books/about/Yaws_ Handbook_of_Thermodynamic_and_Physi.html?id=PjhEYgEACAAJ.

235

[57] M. Hou, S. Liang, Z. Zhang, J. Song, T. Jiang, B. Han, Determination and modeling of solubility of CO2 in PEG200 + 1-pentanol and PEG200 + 1-octanol mixtures, Fluid Phase Equilib. 258 (2007) 108–114, http://dx.doi.org/10.1016/j.fluid.2007.06.002. [58] Y. Yin, C. Zhu, Y. Ma, Volumetric and viscometric properties of binary and ternary mixtures of 1-butyl-3-methylimidazolium tetrafluoroborate, monoethanolamine and water, J. Chem. Thermodyn. 102 (2016) 413–428, http://dx.doi.org/10.1016/j. jct.2016.07.041. [59] J.C.R. Reis, I.M.S. Lampreia, Â.F.S. Santos, M.L.C.J. Moita, G. Douhéret, Refractive index of liquid mixtures: theory and experiment, ChemPhysChem 11 (2010) 3722–3733, http://dx.doi.org/10.1002/cphc.201000566. [60] M. Hemmat, M. Moosavi, A.A. Rostami, Study on volumetric and viscometric properties of 1,4-dioxane and 1,2-ethanediol/1,3-propanediol binary liquid mixtures, measurement and prediction, J. Mol. Liq. 225 (2017) 107–117, http://dx.doi.org/10. 1016/j.molliq.2016.11.052. [61] L. Grunberg, A.H. Nissan, Mixture law for viscosity, Nature 164 (1949) 799–800, http://dx.doi.org/10.1038/164799b0. [62] M. Moosavi, A. Omrani, A. Ali Rostami, A. Motahari, Isobaric, isothermal theoretical investigation and examination of different prediction equations on some physicochemical properties in PEG liquid polymer system, J. Chem. Thermodyn. 68 (2014) 205–215, http://dx.doi.org/10.1016/j.jct.2013.09.006. [63] R.A. McAllister, The viscosity of liquid mixtures, AICHE J. 6 (1960) 427–431, http:// dx.doi.org/10.1002/aic.690060316. [64] W. Kauzmann, H. Eyring, The viscous flow of large molecules, J. Am. Chem. Soc. 62 (1940) 3113–3125, http://dx.doi.org/10.1021/ja01868a059.