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Experimental and modeling study of diisopropyl ether and 2-alkanol; PC-SAFT model and free volume theory
J. Chem. Thermodynamics 142 (2020) 106025
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Experimental and modeling study of diisopropyl ether and 2-alkanol; PC-SAFT model and free volume theory Simin Ahmadi a, Mohammad Almasi b,⇑ a b
Department of Chemistry, Science and Research Branch, Islamic Azad University, Tehran, Iran Department of Applied Chemistry, Faculty of Science, Malayer University, Malayer 65174, Iran
a r t i c l e
i n f o
Article history: Received 24 August 2019 Received in revised form 5 December 2019 Accepted 7 December 2019 Available online 14 December 2019 Keywords: Diisopropyl ether 2-Alkanols PC-SAFT model Free volume theory
a b s t r a c t In the present study, with the aim to discover the governing interactions in binary mixtures containing diisopropyl ether and short-range 2-alkanol (from 2-propanol to 2-hexanol), experimental values of density and viscosity at temperature range 293.15 K–323.15 K were reported. From these data, values of excess molar volume, partial molar volume, and viscosity deviation for mentioned systems were calculated. Findings show that strong interactions occur among unlike molecules while increasing in the carbon chain length of 2-alkanol, reinforces the interactions. Also, the perturbed-chain SAFT (PC-SAFT) equation of state was implemented to study the density and partial molar volume of binary mixtures. Combination of this model with Free Volume Theory was applied for prediction of binary viscosities. Maximum deviation in AAD for density correlation regarding PC-SAFT model was 1.21%, and for viscosity calculation was 2.19%. Ó 2019 Elsevier Ltd.
1. Introduction Diisopropyl ether (DIPE) is a colorless liquid and soluble in organic solvents. It is used as an extracting solvent to remove polar organic compounds from aqueous solutions such as phenols and acetic acid. Oil-based materials are dissolved in it, so it is the base of many dyes and resins. Oxygenated compounds like ethers and alcohols are becoming ever more crucial in fuel industries. The addition of fuel oxygenates to gasoline increases combustion temperature and promotes engine efficiencies, So that lower levels of carbon monoxide and unburned hydrocarbons are released in the air. Presently Ethyl tert-butyl ether governs the market. Nevertheless, due to the problems such as insufficient supply, tendencies have increased toward the heavier ethers such as DIPE. Therefore, from the industrial point of view, mixtures containing ethers and alkanols are of great significance since they are involved in the gasoline production process, improving the combustion and reducing emissions [1,2]. Accordingly, the study of molecular interactions and structural arrangements such as hydrogen bonds, nonspecific or dispersive forces in these binary mixtures has great importance. For this reason, in the present study, as a continuation of our previous work focusing on interactions between alcohols and different functional groups [3–10], binary mixtures containing
⇑ Corresponding author. E-mail address: [email protected] (M. Almasi). https://doi.org/10.1016/j.jct.2019.106025 0021-9614/Ó 2019 Elsevier Ltd.
DIPE with 2-alkanol were selected. A survey in scientific literature demonstrates that previously, values of densities for binary mixtures of DIPE with 2-propanol and 2-butanol were published [2,11–16]. But no reports are available for binary viscosities or some binary densities. Also, the capability of PC-SAFT theory to correlate densities and partial molar volume of binary mixtures was investigated. Then, combination of this model with free volume theory (FVT) was used to correlate and predict binary viscosities.
2. Experimental section All materials, except 2-hexanol, were purchased from Merck with purities higher than 99% and used as purchased. 2-Hexanol was obtained from Sigma-Aldrich Company and used without further purifications. Pure component specifications are presented in SI, Table S1, and comparison of experimental densities and viscosities with literature are shown in [14–33] Table 1. Maximum of deviation between our densities and literature values was 0.2% and for viscosity data was 5%. An automatic viscometer, namely SVM 3000, was used for measuring the density and viscosity. A thermoelectric thermostat controls the dependency of density and viscosity to temperature. Before measuring, the distilled water and dry air were used to calibrate the apparatus. Stabinger viscometer measures viscosity with the highest accuracy over the wide range of temperature and pressure while corrects the viscos-
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S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025
Table 1 Densities, q and viscosities, g for pure components at various temperatures and pressure 0.1 MPaa. Compound
T (K)
DIPE
293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 T (K)
2-propanol
2-butanol
2-pentanol
Compound 2-hexanol
293.15 298.15 303.15 308.15 313.15 318.15 323.15
q (g.cm3)
g (mPas)
expt.
Lit.
expt.
Lit.
0.7233 0.7183 0.7130 0.7076 0.7025 0.6968 0.6919 0.7854 [18–24] 0.7811[18–24] 0.7768 [18–24] 0.7724 [18–24] 0.7680 [18–24] 0.7634 [18–24] 0.7588 [18–24] 0.8067 [18–24] 0.8027 [18–24] 0.7984 [18–24] 0.7941 [18–24] 0.7898 [18–24] 0.7852 [18–24] 0.7806 [18–24] 0.8093 [18–24] 0.8053 [18–24] 0.8012 [18–24] 0.7970 [18–24] 0.7927 [18–24] 0.7884 [18–24] 0.7840 [18–24] q (g.cm3) expt. 0.8142 0.8101 0.8061 0.8021 0.7984 0.7945 0.7901
0.71789 [14], 0.7235 [16], 0.723509 [17] 0.7183 [16], 0.718289 [17] 0.713032 [17] 0.707727 [17] 0.7024 [16], 0.702378 [17]
0.332 0.319 0.304 0.290 0.274 0.261 0.246 2.42 [18–24] 2.08 [18–24] 1.80 [18–24] 1.56 [18–24] 1.36 [18–24] 1.19 [18–24] 1.05 [18–24] 3.67 [18–24] 3.04 [18–24] 2.54 [18–24] 2.13 [18–24] 1.80 [18–24] 1.54 [18–24] 1.33 [18–24] 3.97 [18–24] 3.32 [33,10] 2.81 [33,10] 2.37 [33,10] 1.99 [33,10] 1.66 [33,10] 1.39 [33,10] g (mPas) expt. 5.15 4.10 3.29 2.71 2.28 1.93 1.64
0.3340 0.3178 0.3001 0.2857 0.2723
0.78535 [25], 0.78525 0.77950 [14], 0.78110 0.77712 [25], 0.77678 0.77232 [25] 0.76879 [25], 0.76897 0.76397 [25] 0.75882 [25] 0.8067 [16], 0.8026 [16], 0.802682 0.798374 [26], 0.7993 0.793881 [26] 0.7896 [16], 0.789487 0.784988 [26] 0.80938 [32] 0.8055 [27], 0.80535 0.8010 [27], 0.80124 0.7969 [27], 0.79705 0.7926 [27], 0.79278
lit. 0.8142 [28] 0.8102 [28] 0.8062 [28] 0.80221 [28] 0.7980 [28] 0.7901 [29]
[30] [25] [30] [30]
[26] [31] [26]
[32] [32] [32] [32]
[17] [17] [17] [17] [17]
2.414 [25], 2.3621[30] 2.070 [25] 1.785 [25], 1.7694 [30] 1.546 [25] 1.347 [25], 1.3297 [30] 1.76 [25] 1.033 [25] 3.074 2.552 2.144 1.818 1.558
[26] [26], 2.527 [31] [26] [26], 1.801 [31] [26]
4.174 [32] 3.45 [27], 3.398 2.77 [27], 2.820 2.32 [27], 2.336 1.92 [27], 1.990
[32] [32] [32] [32]
lit.
3.23 [29] 2.29 [29] 1.64 [29]
Standard uncertainties are u(T) = 0.02 K, u(x) = 0.001, u(p) = 10 kPa, expanded uncertainty for density is U(q) = 0.001 gcm3 and relative expanded uncertainty for viscosity is Ur(g) = 5%. a
ity errors on density. To measure the density and viscosity, mixtures are provided precisely before use on an analytical balance (Mettler AE 163) with the precision 0.01 mg. The expanded uncertainty for density is 1 103 g·cm3, and the relative expanded uncertainty for viscosity is 5%. The uncertainty in the mole fraction is 1 103. Effect of impurity was considered in the mole fraction uncertainty. 3. Results and discussion
Experimental densities and viscosities for studied systems are reported in Table 2. Excess molar volume, V Em was calculated by
X
ð1Þ
xi V i
i
where V is volume of the mixture, Vi and xi are the volume and mole fraction of component i respectively. V Em data were correlated as a function of mole fraction employing Redlich–Kister polynomial [34]
V Em ¼ x1 ð1 x1 Þ
N X
Ak ð1 2x1 Þk
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u 1 X r¼t V Eexp V Ecal 2 n p i¼1
ð3Þ
The subscripts exp and cal indicate experimental and calculated values. Standard deviations are reported in SI, Table S2. Fig. 1 states V Em for all binary mixtures at T = 298.15 K along with solid lines cal-
3.1. Density and excess molar volume
V Em ¼ V
reported in SI, Table S2. Standard deviation was calculated as follows
ð2Þ
k¼0
Ak represents adjustable coefficients, and x1 is the DIPE mole fraction. Excess molar volumes are shown in Table 3, and Ak were
culated by Redlich–Kister polynomial. Values of V Em are negative over the entire concentration range and demonstrate that strong interactions occur in mixtures. Looking to the structure of DIPE, figured out that, this molecule has a small dipole due to the difference of electronegativity between carbon and oxygen. The dipole moment of carbon and oxygen do not cancel out each other, so the molecule has a net dipole moment and is therefore weakly polar. Dispersion forces as London type, result from short dipoles induced by fluctuations in the electron shell of molecules, are also present in the mixtures and are responsible for the weak interactions between the alkyl chain of 2-alkanol and the weakly polar ether molecules. Furthermore, hydrogen bonding between OH groups of 2-alkanol and oxygen of ether is possible. Because the ether oxygen can act as hydrogen bond acceptor facing with the hydrogen bond donors like OH of alcohols. This behavior also explains that DIPE is soluble in alkanol despite its low polarity. The values of V Em for DIPE + 2-alkanol mixtures are becoming more
3
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025 Table 2 Densities, q and viscosities, g for the binary mixtures of DIPE with 2-alkanol at various temperatures and pressure 0.1 MPa a. DIPE (1) + 2-Propanol (2)
q (g·cm3) x1 T/K = 293.15 0 0.7854 [18–24] 0.0797 0.7783 0.1607 0.7716 0.2387 0.7656 0.3497 0.7579 0.4359 0.7523 0.5553 0.7452 0.6498 0.7400 0.7351 0.7355 0.8480 0.7300 0.9369 0.7260 1 0.7233 g (mPas) 0 2.42 [18–24] 0.0797 1.78 0.1607 1.32 0.2387 1.02 0.3497 0.755 0.4359 0.635 0.5553 0.52 0.6498 0.458 0.7351 0.418 0.8480 0.38 0.9369 0.35 1 0.332 DIPE (1) + 2-Butanol (2) q (g.cm3) x1 T/K = 293.15 0 0.8067 [18–24] 0.0813 0.7983 0.1604 0.7906 0.2406 0.7830 0.3410 0.7739 0.4470 0.7651 0.5582 0.7557 0.6505 0.7485 0.7374 0.7419 0.8465 0.7340 0.9346 0.7278 1 0.7233 g (mPas) 0 3.67 [18–24] 0.0813 3.00 0.1604 2.51 0.2406 2.10 0.3410 1.653 0.4470 1.304 0.5582 0.976 0.6505 0.772 0.7374 0.623 0.8465 0.473 0.9346 0.384 1 0.332 DIPE (1) + 2-Pentanol (2) q (g·cm3) x1 T/K = 293.15 0 0.8093 [18–24] 0.0801 0.8021 0.1597 0.7950 0.2402 0.7878 0.3503 0.7782 0.4399 0.7704 0.5598 0.7600 0.6493 0.7524 0.7372 0.7450 0.8487 0.7356 0.9379 0.7282 1 0.7233 g (mPas) 0 3.97 [18–24] 0.0801 3.43 0.1597 2.94
T/K = 298.15 0.7811 [18–24] 0.7737 0.7668 0.7607 0.7528 0.7472 0.7400 0.7348 0.7304 0.7249 0.7209 0.7183
T/K = 303.15 0.7768 [18–24] 0.7691 0.7620 0.7557 0.7476 0.7419 0.7346 0.7294 0.7250 0.7195 0.7156 0.7130
T/K = 308.15 0.7724 [18–24] 0.7645 0.7572 0.7507 0.7424 0.7366 0.7293 0.7240 0.7195 0.7140 0.7101 0.7076
T/K = 313.15 0.7680 [18–24] 0.7599 0.7524 0.7459 0.7374 0.7314 0.7240 0.7187 0.7143 0.7089 0.7050 0.7025
T/K = 318.15 0.7634 [18–24] 0.7550 0.7473 0.7405 0.7319 0.7258 0.7183 0.7130 0.7085 0.7032 0.6993 0.6968
T/K = 323.15 0.7588 [18–24] 0.7502 0.7423 0.7355 0.7267 0.7207 0.7132 0.7078 0.7034 0.6982 0.6944 0.6919
2.08 [18–24] 1.55 1.18 0.92 0.68 0.572 0.48 0.43 0.395 0.36 0.332 0.319
1.80 [18–24] 1.39 1.05 0.84 0.63 0.53 0.45 0.404 0.375 0.344 0.318 0.304
1.56 [18–24] 1.21 0.94 0.75 0.56 0.48 0.417 0.379 0.356 0.328 0.305 0.290
1.36 [18–24] 1.05 0.83 0.67 0.51 0.44 0.383 0.356 0.334 0.311 0.29 0.274
1.19 [18–24] 0.93 0.74 0.60 0.465 0.40 0.354 0.331 0.313 0.293 0.276 0.261
1.05 [18–24] 0.82 0.647 0.522 0.410 0.361 0.327 0.309 0.295 0.276 0.26 0.246
T/K = 298.15 0.8027 [18–24] 0.7941 0.7861 0.7784 0.7692 0.7603 0.7507 0.7435 0.7369 0.7290 0.7228 0.7183
T/K = 303.15 0.7984 [18–24] 0.7896 0.7815 0.7735 0.7641 0.7551 0.7455 0.7382 0.7316 0.7236 0.7175 0.7130
T/K = 308.15 0.7941 [18–24] 0.7850 0.7767 0.7686 0.7590 0.7495 0.7401 0.7328 0.7261 0.7182 0.7121 0.7076
T/K = 313.15 0.7898 [18–24] 0.7805 0.7719 0.7637 0.7540 0.7448 0.735 0.7276 0.7209 0.7130 0.7069 0.7025
T/K = 318.15 0.7852 [18–24] 0.7756 0.7668 0.7584 0.7486 0.7393 0.7293 0.7219 0.7152 0.7073 0.7012 0.6968
T/K = 323.15 0.7806 [18–24] 0.7708 0.7619 0.7534 0.7434 0.7339 0.7242 0.7168 0.7102 0.7023 0.6963 0.6919
3.04 [18–24] 2.51 2.09 1.75 1.395 1.122 0.846 0.678 0.56 0.44 0.365 0.319
2.54 [18–24] 2.11 1.742 1.453 1.16 0.95 0.75 0.619 0.522 0.414 0.344 0.304
2.13 [18–24] 1.76 1.48 1.241 1.004 0.834 0.67 0.558 0.473 0.388 0.325 0.29
1.80 [18–24] 1.49 1.25 1.06 0.87 0.73 0.596 0.51 0.44 0.361 0.307 0.274
1.54 [18–24] 1.28 1.074 0.92 0.769 0.65 0.535 0.46 0.40 0.333 0.29 0.261
1.33 [18–24] 1.10 0.931 0.801 0.67 0.575 0.48 0.416 0.367 0.31 0.27 0.246
T/K = 298.15 0.8053 [18–24] 0.7978 0.7905 0.7832 0.7736 0.7656 0.7551 0.7474 0.7400 0.7305 0.7232 0.7183
T/K = 303.15 0.8012 [18–24] 0.7934 0.7859 0.7785 0.7686 0.7606 0.7499 0.7421 0.7345 0.7251 0.7179 0.7130
T/K = 308.15 0.7970 [18–24] 0.7889 0.7812 0.7736 0.7636 0.7554 0.7446 0.7367 0.7291 0.7197 0.7125 0.7076
T/K = 313.15 0.7927 [18–24] 0.7844 0.7765 0.7688 0.7587 0.7504 0.7396 0.7317 0.7240 0.7146 0.7074 0.7025
T/K = 318.15 0.7884 [18–24] 0.7798 0.7717 0.7638 0.7534 0.7449 0.7340 0.7260 0.7183 0.7089 0.7017 0.6968
T/K = 323.15 0.7840 [18–24] 0.7753 0.7671 0.7590 0.7484 0.7399 0.7289 0.7209 0.7133 0.7039 0.6967 0.6919
3.32 [33,10] 2.87 2.44
2.81 [33,10] 2.42 2.06
2.37 [33,10] 2.04 1.74
1.99 [33,10] 1.71 1.45
1.66 [33,10] 1.42 1.20
1.39 [33,10] 1.19 1.02 (continued on next page)
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Table 2 (continued) 0.2402 2.52 0.3503 2.08 0.4399 1.76 0.5598 1.386 0.6493 1.13 0.7372 0.90 0.8487 0.64 0.9379 0.45 1 0.332 DIPE (1) + 2-Hexanol (2) q (g.cm3) x1 T/K = 293.15 0 0.8142 0.0806 0.8076 0.1592 0.8010 0.2412 0.7940 0.3508 0.7844 0.4391 0.7764 0.5594 0.7653 0.6497 0.7569 0.7378 0.7485 0.8483 0.7380 0.9386 0.7293 1 0.7233 g (mPas) 0 5.15 0.0806 4.51 0.1592 3.97 0.2412 3.48 0.3508 2.91 0.4391 2.49 0.5594 1.97 0.6497 1.60 0.7378 1.26 0.8483 0.84 0.9386 0.531 1 0.332
2.10 1.74 1.48 1.176 0.969 0.783 0.57 0.42 0.319
1.78 1.49 1.286 1.04 0.864 0.705 0.518 0.389 0.304
1.50 1.26 1.09 0.89 0.75 0.62 0.47 0.36 0.290
1.26 1.06 0.922 0.755 0.64 0.536 0.414 0.33 0.274
1.05 0.89 0.78 0.642 0.547 0.467 0.375 0.306 0.261
0.89 0.76 0.667 0.554 0.477 0.41 0.33 0.28 0.246
T/K = 298.15 0.8101 0.8033 0.7965 0.7893 0.7795 0.7715 0.7603 0.7519 0.7435 0.7329 0.7242 0.7183
T/K = 303.15 0.8061 0.7990 0.7920 0.7846 0.7746 0.7664 0.7551 0.7466 0.7381 0.7276 0.7189 0.7130
T/K = 308.15 0.8021 0.7948 0.7876 0.7800 0.7698 0.7614 0.7499 0.7413 0.7328 0.7221 0.7134 0.7076
T/K = 313.15 0.7984 0.7908 0.7834 0.7756 0.7652 0.7567 0.7450 0.7363 0.7278 0.7170 0.7083 0.7025
T/K = 318.15 0.7945 0.7866 0.7790 0.7709 0.7602 0.7516 0.7397 0.7308 0.7222 0.7113 0.7026 0.6968
T/K = 323.15 0.7901 0.7821 0.7743 0.7662 0.7553 0.7466 0.7346 0.7258 0.7171 0.7064 0.6977 0.6919
4.10 3.61 3.16 2.76 2.30 1.97 1.56 1.275 1.02 0.706 0.465 0.319
3.29 2.89 2.53 2.20 1.83 1.567 1.25 1.034 0.84 0.60 0.42 0.304
2.71 2.38 2.08 1.825 1.53 1.32 1.06 0.88 0.715 0.52 0.38 0.290
2.28 2.00 1.75 1.54 1.29 1.115 0.906 0.756 0.62 0.46 0.35 0.274
1.93 1.69 1.49 1.31 1.11 0.962 0.783 0.66 0.55 0.416 0.32 0.261
1.64 1.44 1.27 1.12 0.95 0.83 0.68 0.58 0.49 0.38 0.295 0.246
a x1 is the mole fraction of DIPE in binary mixtures. Standard uncertainties u are u (T) = 0.02 K, u(x) = 0.001, u(p) = 10 kPa, the expanded uncertainty is U(q) = 0.001 gcm3 for density and for viscosity the relative expanded uncertainty Ur(g) = 5% (0.95 level of confidence).
negative, going from 2-propanol to 2-hexanol. The dipole moment of DIPE is 1.3 D (at 20C) and is a weak polar molecule. For 2alkanol, from 2-propanol up to 2-hexanol, with an increase in the nonpolar hydrocarbon chain, the polarity of mixtures decreases. So, in the mixing of the ether with 2-alkanol, London dispersion forces get stronger with increasing molecular size. Therefore, we expect that the absolute values of V Em will increase. Similar behavior was observed for DIPE + 1-alkanol mixtures [1]. In SI, Figs. S1 to S4, values of excess molar volumes and experimental densities are compared with literature for corresponding binary mixtures. Maximum deviation between our data and scientific literature is 0.3%. This difference is due to differences in measuring experimental densities for pure material or binary mixtures. The origins of errors for measuring experimental data are the wide range of materials sources (Fluka, Merck, and so forth) and the variation in the amount of impurities (purity percent). Also, different measurement techniques are another factor that makes the differences in measuring density values. When the temperature of mixtures increases, molecular forces such as dipole–dipole interactions or London dispersion forces fall off rapidly. Also, rising in temperature, probably increases the difficulty of accommodation of ether molecules in an ordered structure of alcohols. So, created steric hindrances in binary mixtures, weakens molecular interactions among unlike molecules, resulting into the formation of less rigid liquid solutions. Therefore, values of excess molar volumes increase with temperature. As an example, V Em for binary mixtures DIPE + 2-hexanol at various temperatures are depicted in Fig. 2.
Further, the partial molar volumes V m;i for mentioned systems were calculated [35] using
V m;1 ¼ V Em þ V m;1 þ ð1 x1 Þð@V Em =@x1 ÞT;p
V m;2 ¼ V Em þ V m;2 x1 ð@V Em =@x1 ÞT;p
ð4Þ ð5Þ
where V m;i is the pure molar volume. V m;1 for binary systems DIPE + 2alkanol at T = 298.15 K are depicted in Fig. 3 and Table 4. Rise of temperature causes the weakening of DIPE -alcohol bindings, which makes a significant increase in the partial molar volume of mixtures. 3.2. Dynamic viscosities For binary mixtures, the values of viscosity are presented in Table 2. It is clear that binary viscosities increase with the number of the carbon atom of alcohols and decreases with temperature. Deviation in the viscosity was calculated by the following equation
Dg ¼ g x1 g1 x2 g2
ð6Þ
In the above equation,g shows mixture viscosity whilegi is the pure viscosity. Viscosity deviation for binary systems DIPE + 2alkanol is shown in Fig. 4. Rising in the alkyl chain of the alcohols makes an increase in the viscosity deviations, which can be attributed to the strengthening of interactions in solutions. Dgvalues were correlated by Redlich–Kister and binary parameters along with the standard deviations are presented in SI, Table S2 (Fig 5). 3.3. PC-SAFT model One of the most famous methods for calculating thermodynamic properties of pure substances and mixtures is PC-SAFT
5
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025 Table 3 Excess molar volumes, V Em and viscosity deviations, D g for binary mixtures at various temperatures and pressure 0.1 MPa a. DIPE (1) + 2-Propanol (2) V Em (cm3·mol1) T/K = 293.15 x1 0.0797 0.150 0.1607 0.270 0.2387 0.360 0.3497 0.450 0.4359 0.477 0.5553 0.470 0.6498 0.430 0.7351 0.350 0.8480 0.220 0.9369 0.090 D g (mPas) 0.0797 0.474 0.1607 0.764 0.2387 0.902 0.3497 0.935 0.4359 0.875 0.5553 0.741 0.6498 0.605 0.7351 0.467 0.8480 0.269 0.9369 0.114 DIPE (1) + 2-Butanol (2)
T/K = 298.15 0.130 0.240 0.320 0.400 0.430 0.420 0.380 0.315 0.183 0.076
T/K = 303.15 0.120 0.220 0.292 0.356 0.377 0.371 0.338 0.276 0.160 0.063
T/K = 308.15 0.120 0.208 0.270 0.326 0.345 0.340 0.300 0.241 0.137 0.054
T/K = 313.15 0.091 0.169 0.218 0.252 0.259 0.246 0.218 0.171 0.100 0.037
T/K = 318.15 0.106 0.191 0.249 0.289 0.297 0.285 0.254 0.207 0.116 0.044
T/K = 323.15 0.077 0.134 0.174 0.20 0.204 0.191 0.165 0.130 0.076 0.03
0.390 0.617 0.740 0.784 0.740 0.622 0.506 0.390 0.227 0.098
0.291 0.510 0.603 0.647 0.618 0.519 0.424 0.325 0.187 0.080
0.249 0.416 0.507 0.556 0.526 0.438 0.356 0.270 0.155 0.065
0.223 0.355 0.431 0.470 0.447 0.374 0.298 0.228 0.128 0.053
0.186 0.301 0.368 0.395 0.385 0.320 0.255 0.194 0.109 0.044
0.166 0.274 0.336 0.356 0.339 0.277 0.219 0.164 0.092 0.037
T/K = 298.15 0.186 0.336 0.451 0.553 0.608 0.606 0.565 0.486 0.327 0.161
T/K = 303.15 0.178 0.324 0.426 0.527 0.582 0.580 0.542 0.460 0.311 0.156
T/K = 308.15 0.166 0.303 0.400 0.488 0.530 0.535 0.496 0.426 0.292 0.153
T/K = 313.15 0.156 0.273 0.365 0.456 0.495 0.497 0.458 0.391 0.271 0.133
T/K = 318.15 0.139 0.247 0.333 0.412 0.453 0.455 0.420 0.362 0.253 0.129
T/K = 323.15 0.116 0.213 0.294 0.362 0.402 0.407 0.386 0.330 0.224 0.118
0.309 0.514 0.635 0.717 0.722 0.675 0.592 0.474 0.297 0.132
0.248 0.439 0.549 0.618 0.607 0.542 0.466 0.369 0.233 0.106
0.220 0.355 0.446 0.499 0.487 0.433 0.375 0.300 0.184 0.085
0.186 0.305 0.373 0.410 0.399 0.352 0.297 0.235 0.147 0.067
0.156 0.261 0.312 0.335 0.328 0.291 0.248 0.197 0.124 0.055
0.142 0.225 0.268 0.290 0.278 0.245 0.209 0.164 0.102 0.047
T/K = 293.15 0.210 0.384 0.526 0.670 0.720 0.710 0.663 0.565 0.355 0.140
T/K = 298.15 0.188 0.350 0.487 0.642 0.689 0.677 0.627 0.540 0.322 0.130
T/K = 303.15 0.169 0.322 0.452 0.602 0.653 0.631 0.573 0.465 0.287 0.120
T/K = 308.15 0.152 0.294 0.421 0.561 0.612 0.595 0.537 0.434 0.263 0.110
T/K = 313.15 0.140 0.266 0.385 0.530 0.581 0.570 0.512 0.403 0.246 0.105
T/K = 318.15 0.121 0.240 0.358 0.478 0.514 0.504 0.452 0.369 0.227 0.093
T/K = 323.15 0.110 0.224 0.328 0.431 0.460 0.454 0.413 0.331 0.200 0.080
0.249 0.449 0.576 0.616 0.610 0.547 0.478 0.388 0.242 0.108
0.210 0.401 0.499 0.529 0.520 0.464 0.402 0.325 0.203 0.085
0.189 0.350 0.428 0.442 0.422 0.367 0.319 0.258 0.165 0.071
0.163 0.298 0.370 0.381 0.365 0.316 0.269 0.217 0.135 0.059
0.143 0.266 0.318 0.329 0.313 0.274 0.236 0.189 0.120 0.051
0.128 0.237 0.274 0.280 0.265 0.235 0.205 0.162 0.098 0.042
0.108 0.187 0.225 0.229 0.220 0.196 0.170 0.137 0.089 0.037
V Em (cm3·mol1) x1 T/K = 293.15 0.0813 0.191 0.1604 0.360 0.2406 0.476 0.3410 0.590 0.4397 0.655 0.5582 0.648 0.6505 0.598 0.7374 0.511 0.8465 0.352 0.9346 0.165 D g (mPas) 0.0813 0.399 0.1604 0.625 0.2406 0.767 0.3410 0.879 0.4397 0.898 0.5582 0.831 0.6505 0.727 0.7374 0.586 0.8465 0.371 0.9346 0.166 DIPE (1) + 2-Pentanol (2) V Em (cm3·mol1) x1 0.0801 0.1597 0.2402 0.3503 0.4399 0.5598 0.6493 0.7372 0.8487 0.9379 D g (mPas) 0.0801 0.1597 0.2402 0.3503 0.4399 0.5598 0.6493 0.7372 0.8487 0.9379
(continued on next page)
6
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025
Table 3 (continued) DIPE (1) + 2-Hexanol (2) V Em (cm3·mol1) x1 0.0806 0.1592 0.2412 0.3508 0.4391 0.5594 0.6497 0.7378 0.8483 0.9386 D g (mPas) 0.0806 0.1592 0.2412 0.3508 0.4391 0.5594 0.6497 0.7378 0.8483 0.9386
T/K = 293.15 0.244 0.440 0.606 0.757 0.810 0.800 0.746 0.630 0.413 0.194
T/K = 298.15 0.233 0.410 0.558 0.700 0.760 0.756 0.702 0.589 0.391 0.172
T/K = 303.15 0.214 0.380 0.525 0.660 0.710 0.700 0.649 0.542 0.357 0.154
T/K = 308.15 0.197 0.360 0.488 0.617 0.664 0.651 0.603 0.500 0.324 0.133
T/K = 313.15 0.180 0.333 0.458 0.570 0.618 0.609 0.558 0.467 0.294 0.12
T/K = 318.15 0.166 0.306 0.421 0.527 0.572 0.555 0.507 0.421 0.264 0.105
T/K = 323.15 0.153 0.276 0.385 0.489 0.526 0.505 0.459 0.385 0.242 0.093
0.252 0.413 0.508 0.550 0.544 0.485 0.420 0.335 0.223 0.097
0.185 0.338 0.428 0.474 0.470 0.425 0.368 0.290 0.187 0.086
0.159 0.285 0.370 0.413 0.412 0.370 0.316 0.247 0.157 0.067
0.135 0.245 0.301 0.331 0.327 0.296 0.258 0.210 0.137 0.059
0.118 0.211 0.256 0.286 0.284 0.252 0.221 0.180 0.118 0.047
0.105 0.174 0.217 0.235 0.235 0.213 0.186 0.149 0.098 0.043
0.088 0.148 0.184 0.201 0.198 0.180 0.154 0.122 0.077 0.037
a x1 is the mole fraction of Diisopropyl ether in the binary mixtures. Standard uncertainties u are u(T) = 0.02 K, u(x) = 0.001, u(p) = 10 kPa, the expanded uncertainty is U (q) = 0.001 gcm3 for density and for viscosity the relative expanded uncertainty Ur(g) = 5% (0.95 level of confidence).
Fig. 3. Partial molar volumes V m;1 versus mole fraction of DIPE with (r) 2-propanol, (D) 2-butanol, (d) 2-pentanol, (*) 2-hexanol at T = 298.15 K. (—) PC-SAFT model. Fig. 1. Excess molar volume V Em , versus the mole fraction x1 of DIPE with (▲) 2propanol (d) 2-butanol, (j) 2-pentanol, (*) 2-hexanol T = 298.15 K. (—) RedlichKister equation.
model [36,37]. In this theory, hard chains are used as reference fluid and chain–chain interactions are computed, which improves the thermodynamic description of fluid mixtures. This model is explained by the sum of all residual Helmholtz free energy.
ares ¼ ahc þ adisp þ aassoc
ð7Þ
The hard-chain reference fluid is made up of spherical segments that have not any attractive interactions. This part is defined by two parameters namely the number of segments m and the diameter of segments r
ahc ¼ m ahs
X
xi ðmi 1Þlng ij hs
ð8Þ
i
In the above equation, m is the mean segment number, andg hs ij the pair distribution function Fig. 2. Excess molar volumes V Em for DIPE + 2-hexanol at temperatures: 293.15 K (h), 298.15 K (d), 303.15 K (j), 308.15 K (▲), 313.15 K (D), 318.15 K (r), 323.15 K (s). (—) Redlich-Kister equation.
g hs ij ¼
2 1 di dj 3f2 di dj 2f2 2 þ þ 2 1 f3 di þ dj ð1 f3 Þ di þ dj ð1 f3 Þ3
ð9Þ
7
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025 Table 4 Partial molar volumes, V m;1 for Binary Mixtures DIPE with 2-Alkanol at T = 298.15 K and pressure 0.1 MPa. DIPE + 2-Propanol
DIPE + 2-Butanol
DIPE + 2-Pentanol
x1
1 V m;1 cm3 :mol
x1
V m;1 ðcm3 :mol
0 0.0797 0.1607 0.2387 0.3497 0.4359 0.5553 0.6498 0.7351 0.848 0.9369 1
139.36 139.73 140.14 140.49 140.95 141.28 141.66 141.88 142.04 142.19 142.24 142.26
0 0.0813 0.1604 0.2406 0.341 0.4397 0.5582 0.6505 0.7374 0.8465 0.9346 1
139.81 140.17 140.52 140.84 141.19 141.48 141.76 141.96 142.09 142.21 142.24 142.25
1
Þ
DIPE + 2-Hexanol
x1
V m;1 ðcm3 :mol
0 0.0801 0.1597 0.2402 0.3503 0.4399 0.5598 0.6493 0.7372 0.8487 0.9379 1
140.19 140.51 140.79 141.06 141.38 141.61 141.86 142.02 142.13 142.23 142.26 142.26
1
Þ
x1
V m;1 ðcm3 :mol
0 0.0806 0.1592 0.2412 0.3508 0.4391 0.5594 0.6497 0.7378 0.8483 0.9386 1
140.5 140.76 141.01 141.24 141.52 141.73 141.97 142.1 142.19 142.26 142.26 142.26
1
Þ
fn is defined as n p X q xi mi dni
fn ¼
6
ð11Þ
i¼1
di is the segment diameter. For determination of dispersive attraction contribution in Helmholtz energy, PC-SAFT uses the Barker and Henderson perturbation theory [38] to the hard-chain reference system. Therefore, the effect of the non-spherical shape of molecules on attractive dispersions is considered.
ð12Þ
adis ¼ 2pqI1 m2 er3 pq m C 1 I2 m2 e2 r3 The C1 coefficient is calculated as
"
C1 ¼ 1 þ m Fig. 4. Comparisons of calculated and experimental densities for DIPE + 2-pentanol at (r) 293.15 K, (D) 303.15 K, (d) 313.15 K, (s) 323.15 K. (—) PC-SAFT model.
8g 2g2 ð1 gÞ4
þ ð1 mÞ
20g 27g2 þ 12g3 2g4 ½ð1 gÞð2 gÞ2
#1 ð13Þ
where g is the reduced density, I1 and I2 are perturbation integrals. The association interactions such as hydrogen bonding are also regarded in this theory. It is assumed that a molecule has one or more association sites and forms hydrogen bonds. If the molecule has two association sites A and B, two parameters, namely the association energy eAiBi/k and the effective association volume jAiBi is considered. The number of association sites and possible interactions among them has profound effect on the structure of fluids and their phase behavior. aassoc is written as:
aassoc ¼
X
x i¼1 i
" X
Ai
lnX Ai
X Ai 2
!
1 þ Mi 2
#
ð14Þ
The mole fraction of molecules not bonded at site A is presented by XAi and the association sites on a molecule with Mi. Cross association parameters are determined using combining rules of the pure parameters without introducing binary parameters.
eAi Bj ¼ Fig. 5. Viscosity deviation D g versus the mole fraction x1 of DIPE with (▲) 2propanol (d) 2-butanol, (j) 2-pentanol, (*) 2-hexanol at T = 298.15 K. (—) RedlichKister equation.
j
Ai Bj
"
ahs ¼
f32
1 3f1 f2 þ þ f0 1 f3 f3 ð1 f3 Þ2
f32 f23
!
eij ¼
#
f0 lnð1 f3 Þ
ð10Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j j Ai Bi
Aj Bj
pffiffiffiffiffiffiffiffiffiffiffi !3 rr ii jj 0:5 rii þ rjj
ð15Þ
ð16Þ
Cross parameters for non-associated compounds are obtained by
Hard sphere contribution ahs is given by
¼
1 Ai Bi e þ eAi Bi 2
rij ¼
pffiffiffiffiffiffiffi
ei ej 1 kij
ri þ rj 2
ð17Þ ð18Þ
8
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025
Table 5 Pure Component Parameters Obtained for PC-SAFT Model at pressure 0.1 MPa. Component
mi
ri
ei /k
jAi Bi
eAi Bi/k
T Range (K)
DIPE 2-Propanol 2-Butanol 2-Pentanol 2-Hexanol
3.72 3.098 2.851 3.763 3.632
3.451 3.206 3.546 3.362 3.595
220.7 205.32 237.11 220.76 238.21
– 0.0251 0.0075 0.0189 0.00702
– 2251.9 2481 2225 2476
293–323 293–323 293–323 293–323 293–323
dij ¼
di dj di þ dj
ð19Þ
Eq. (17) contains an adjustable parameterkij , which corrects the dispersion energy in the mixture and obtained by the iteration method when predicted values have the closest amount to experimental data. Values of pure parameters for DIPE and 2-alkanols were obtained by adjusting their saturated vapor pressure and liquid densities with PC-SAFT model. DIPE was investigated as a nonassociated component, and three parameters for the pure state were obtained. For 2-alkanol, two association sites were considered per each molecule as type 2B, and five parameters were calculated. Obtained values are reported in Table 5 along with the deviation and temperature range. Maximum of deviation in vapor pressure was 5.18% and in liquid densities was 1.36%. Using the combining rules mentioned in Eqs. (15) to (19), values of densities were obtained for all binary mixtures. The parameter kij was obtained by the iteration method when predicted values have the closest amount to experimental data. By defining an objective function, densities were obtained.
OF ¼
2 N exp X q qcalc i
i¼1
qexp i
ð20Þ
i
Then, from the output densities of the PC-SAFT model, values of partial molar volumes were calculated. Adjusting parameter kij is presented in Table 6. For calculation of densities, AAD for binary mixtures DIPE + 2-propanol is 1.14%, for DIPE + 2-butanol is 1.06%, for DIPE + 2-pentanol is 1.21% and for DIPE + 2-hexanol is 1.16%. Fig. 4 demonstrates experimental and calculated densities for DIPE + 2-pentanol at various temperatures. Also results of partial molar volumes obtained by this model indicate that deviation in AAD for DIPE + 2-propanol is 1.89%, for DIPE + 2-butanol 2.34%, for DIPE + 2-pentanol 1.76%, and for DIPE + 2-hexanol 1.46%. Calculated partial molar volumes by this model along with experimental data for DIPE + 2-alkanol at T = 298.15 K are depicted in Fig.3. 3.4. Free volume theory In recent years, among several theoretical or semi-empirical approaches for calculation of dense fluid viscosities, free volume theory, and friction theory are further developed. In FVT [39,40] viscosity is related to the structure of fluid and dense or dilute state of fluids is precisely described. In this approach, viscosity is shown by two parts:
g ¼ g0 þ Dg
ð21Þ
res
Table 6 Binary Interaction Parameter kij for PC-SAFT model. Binary Systems DIPE DIPE DIPE DIPE
+ + + +
2-Propanol 2-Butanol 2-Pentanol 2-Hexanol
kij 0.027 0.023 0.031 0.018
AAD (%) Pressure
Density
5.18 4.76 5.14 4.19 3.85
1.36 1.17 1.23 1.16 1.09
Viscosity in the dilute gas limit is presented by g0 and its deviation from dilute gas by residual viscosityDgres . The dilute gas term explains the fluid viscosity in gaseous or low-density state. The modified form of this equation is as follow:
g0 ¼ 40:785
pffiffiffiffiffiffiffiffiffiffiffi MW T v 2=3 c X
ð22Þ
Fc
X is reduced collision integral, molecular weight and F c is
vc
the critical volume, MW the
F c ¼ 1 0:275x þ 0:059035l4r þ v
ð23Þ
v is correction factor for hydrogen bonds, x the acentric factor and lr is dimensionless dipole moment. Combination of the residual part of viscosity with exponential relation [41] leads to the following equation
B Dgres ¼ 1014 qNa L2 f0 exp fV
ð24Þ
B is a parameter related to the overlap of free-volume among molecules [42] f0 the friction coefficient, q the density, Na Avogadro’s number, f V free volume fraction, and L2 is average quadratic length. f0 could be obtained from the energy of dissipation E by the relation
f0 ¼ 1010
E Na bf
103 M W 3RT
!0:5
ð25Þ
bf is dissipation of energy length. Combination of Eqs. (24) to (25) results in
Dgres
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
103 RTMW 2=3 B ¼ 10 qLV f V exp fV 3 4
ð26Þ
Above equation contains three adjustable coefficients: (i) a length parameter named Lv which is connected to the molecules structure and relaxation time; (ii) a proportion parameter namely a which related to the barrier of energy and density; (iii) B parameter corresponds to the free-volume overlap. Three parameters were calculated by the fitting of Eq. (26) to pure viscosities. Also, accurate and reliable thermodynamic properties such as density and pressure are needed obtaining true values of viscosity. In the present study, density and pressure are the output of the PCSAFT model. For calculation of binary viscosities, mixing rules of Lorentz type were applied without further adjustable parameters.
amix ¼
n X
ai xi
ð27Þ
Bi xi
ð28Þ
i¼1
Bmix ¼
n X i¼1
LV;mix ¼
n X
Lv ;i xi
ð29Þ
i¼1
Average absolute deviation for viscosity of DIPE + 2-propanol is 1.89%, for DIPE + 2-butanol is 2.19%, for DIPE + 2-pentanol is 1.64% and finally for DIPE + 2-hexanol is 1.92%. Fig. 6 demonstrates
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025
Fig. 6. Binary viscosities g versus the mole fraction x1 of DIPE with (r) 2-propanol, (D) 2-butanol, (d) 2-pentanol, (*) 2-hexanol at T = 298.15 K. at T = 298.15 K. (—) FVT.
experimental viscosities along with calculated values with free volume theory at 298.15 K. 4. Conclusions Experimental values of density and viscosity for mixtures DIPE + 2-propanol up to 2-hexanol at various temperatures have been reported, and for interpretation of interactions in the mixtures, values of V Em andDg were calculated. The negative values of the mentioned parameters display that stronger interactions in the mixtures occur relative to the pure state. Rising in the number of the carbon atom of alcohols increases the dispersion forces and leads to an increase in the V Em values. The PC-SAFT model was used to model the densities and partial molar volumes. Calculated density in the binary mixture shows the maximum of 1.21% deviation from experimental data. Maximum of deviation between experimental and calculated partial molar volumes was 2.34%. For correlation and prediction of viscosities, the combination of PC-SAFT model with FVT was implemented. Maximum of deviation from experimental viscosities was 2.19% and belonged to the binary mixtures of DIPE + 2-butanol. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jct.2019.106025. References [1] Á. Piñeiro, Excess volumes and isobaric heat capacities of diisopropyl ether with several alkanols at 298.15K Application of the symmetrical extended real associated solution model, Fluid Phase Equilib. 216 (2004) 245–256. [2] K. Kammerer, R.N. Lichtenthaler, Excess properties of binary alkanol–ether mixtures and the application of the ERAS model, Thermochim. Acta 310 (1998) 61–67. [3] M. Almasi, Thermodynamic study of interactions between 1-alkanol and butanone, Chem. Phys. 527 (2019), 110474.
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JCT 2019-675
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
Experimental and modeling study of diisopropyl ether and 2-alkanol; PC-SAFT model and free volume theory Simin Ahmadi a, Mohammad Almasi b,⇑ a b
Department of Chemistry, Science and Research Branch, Islamic Azad University, Tehran, Iran Department of Applied Chemistry, Faculty of Science, Malayer University, Malayer 65174, Iran
a r t i c l e
i n f o
Article history: Received 24 August 2019 Received in revised form 5 December 2019 Accepted 7 December 2019 Available online 14 December 2019 Keywords: Diisopropyl ether 2-Alkanols PC-SAFT model Free volume theory
a b s t r a c t In the present study, with the aim to discover the governing interactions in binary mixtures containing diisopropyl ether and short-range 2-alkanol (from 2-propanol to 2-hexanol), experimental values of density and viscosity at temperature range 293.15 K–323.15 K were reported. From these data, values of excess molar volume, partial molar volume, and viscosity deviation for mentioned systems were calculated. Findings show that strong interactions occur among unlike molecules while increasing in the carbon chain length of 2-alkanol, reinforces the interactions. Also, the perturbed-chain SAFT (PC-SAFT) equation of state was implemented to study the density and partial molar volume of binary mixtures. Combination of this model with Free Volume Theory was applied for prediction of binary viscosities. Maximum deviation in AAD for density correlation regarding PC-SAFT model was 1.21%, and for viscosity calculation was 2.19%. Ó 2019 Elsevier Ltd.
1. Introduction Diisopropyl ether (DIPE) is a colorless liquid and soluble in organic solvents. It is used as an extracting solvent to remove polar organic compounds from aqueous solutions such as phenols and acetic acid. Oil-based materials are dissolved in it, so it is the base of many dyes and resins. Oxygenated compounds like ethers and alcohols are becoming ever more crucial in fuel industries. The addition of fuel oxygenates to gasoline increases combustion temperature and promotes engine efficiencies, So that lower levels of carbon monoxide and unburned hydrocarbons are released in the air. Presently Ethyl tert-butyl ether governs the market. Nevertheless, due to the problems such as insufficient supply, tendencies have increased toward the heavier ethers such as DIPE. Therefore, from the industrial point of view, mixtures containing ethers and alkanols are of great significance since they are involved in the gasoline production process, improving the combustion and reducing emissions [1,2]. Accordingly, the study of molecular interactions and structural arrangements such as hydrogen bonds, nonspecific or dispersive forces in these binary mixtures has great importance. For this reason, in the present study, as a continuation of our previous work focusing on interactions between alcohols and different functional groups [3–10], binary mixtures containing
⇑ Corresponding author. E-mail address: [email protected] (M. Almasi). https://doi.org/10.1016/j.jct.2019.106025 0021-9614/Ó 2019 Elsevier Ltd.
DIPE with 2-alkanol were selected. A survey in scientific literature demonstrates that previously, values of densities for binary mixtures of DIPE with 2-propanol and 2-butanol were published [2,11–16]. But no reports are available for binary viscosities or some binary densities. Also, the capability of PC-SAFT theory to correlate densities and partial molar volume of binary mixtures was investigated. Then, combination of this model with free volume theory (FVT) was used to correlate and predict binary viscosities.
2. Experimental section All materials, except 2-hexanol, were purchased from Merck with purities higher than 99% and used as purchased. 2-Hexanol was obtained from Sigma-Aldrich Company and used without further purifications. Pure component specifications are presented in SI, Table S1, and comparison of experimental densities and viscosities with literature are shown in [14–33] Table 1. Maximum of deviation between our densities and literature values was 0.2% and for viscosity data was 5%. An automatic viscometer, namely SVM 3000, was used for measuring the density and viscosity. A thermoelectric thermostat controls the dependency of density and viscosity to temperature. Before measuring, the distilled water and dry air were used to calibrate the apparatus. Stabinger viscometer measures viscosity with the highest accuracy over the wide range of temperature and pressure while corrects the viscos-
2
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025
Table 1 Densities, q and viscosities, g for pure components at various temperatures and pressure 0.1 MPaa. Compound
T (K)
DIPE
293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 T (K)
2-propanol
2-butanol
2-pentanol
Compound 2-hexanol
293.15 298.15 303.15 308.15 313.15 318.15 323.15
q (g.cm3)
g (mPas)
expt.
Lit.
expt.
Lit.
0.7233 0.7183 0.7130 0.7076 0.7025 0.6968 0.6919 0.7854 [18–24] 0.7811[18–24] 0.7768 [18–24] 0.7724 [18–24] 0.7680 [18–24] 0.7634 [18–24] 0.7588 [18–24] 0.8067 [18–24] 0.8027 [18–24] 0.7984 [18–24] 0.7941 [18–24] 0.7898 [18–24] 0.7852 [18–24] 0.7806 [18–24] 0.8093 [18–24] 0.8053 [18–24] 0.8012 [18–24] 0.7970 [18–24] 0.7927 [18–24] 0.7884 [18–24] 0.7840 [18–24] q (g.cm3) expt. 0.8142 0.8101 0.8061 0.8021 0.7984 0.7945 0.7901
0.71789 [14], 0.7235 [16], 0.723509 [17] 0.7183 [16], 0.718289 [17] 0.713032 [17] 0.707727 [17] 0.7024 [16], 0.702378 [17]
0.332 0.319 0.304 0.290 0.274 0.261 0.246 2.42 [18–24] 2.08 [18–24] 1.80 [18–24] 1.56 [18–24] 1.36 [18–24] 1.19 [18–24] 1.05 [18–24] 3.67 [18–24] 3.04 [18–24] 2.54 [18–24] 2.13 [18–24] 1.80 [18–24] 1.54 [18–24] 1.33 [18–24] 3.97 [18–24] 3.32 [33,10] 2.81 [33,10] 2.37 [33,10] 1.99 [33,10] 1.66 [33,10] 1.39 [33,10] g (mPas) expt. 5.15 4.10 3.29 2.71 2.28 1.93 1.64
0.3340 0.3178 0.3001 0.2857 0.2723
0.78535 [25], 0.78525 0.77950 [14], 0.78110 0.77712 [25], 0.77678 0.77232 [25] 0.76879 [25], 0.76897 0.76397 [25] 0.75882 [25] 0.8067 [16], 0.8026 [16], 0.802682 0.798374 [26], 0.7993 0.793881 [26] 0.7896 [16], 0.789487 0.784988 [26] 0.80938 [32] 0.8055 [27], 0.80535 0.8010 [27], 0.80124 0.7969 [27], 0.79705 0.7926 [27], 0.79278
lit. 0.8142 [28] 0.8102 [28] 0.8062 [28] 0.80221 [28] 0.7980 [28] 0.7901 [29]
[30] [25] [30] [30]
[26] [31] [26]
[32] [32] [32] [32]
[17] [17] [17] [17] [17]
2.414 [25], 2.3621[30] 2.070 [25] 1.785 [25], 1.7694 [30] 1.546 [25] 1.347 [25], 1.3297 [30] 1.76 [25] 1.033 [25] 3.074 2.552 2.144 1.818 1.558
[26] [26], 2.527 [31] [26] [26], 1.801 [31] [26]
4.174 [32] 3.45 [27], 3.398 2.77 [27], 2.820 2.32 [27], 2.336 1.92 [27], 1.990
[32] [32] [32] [32]
lit.
3.23 [29] 2.29 [29] 1.64 [29]
Standard uncertainties are u(T) = 0.02 K, u(x) = 0.001, u(p) = 10 kPa, expanded uncertainty for density is U(q) = 0.001 gcm3 and relative expanded uncertainty for viscosity is Ur(g) = 5%. a
ity errors on density. To measure the density and viscosity, mixtures are provided precisely before use on an analytical balance (Mettler AE 163) with the precision 0.01 mg. The expanded uncertainty for density is 1 103 g·cm3, and the relative expanded uncertainty for viscosity is 5%. The uncertainty in the mole fraction is 1 103. Effect of impurity was considered in the mole fraction uncertainty. 3. Results and discussion
Experimental densities and viscosities for studied systems are reported in Table 2. Excess molar volume, V Em was calculated by
X
ð1Þ
xi V i
i
where V is volume of the mixture, Vi and xi are the volume and mole fraction of component i respectively. V Em data were correlated as a function of mole fraction employing Redlich–Kister polynomial [34]
V Em ¼ x1 ð1 x1 Þ
N X
Ak ð1 2x1 Þk
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u 1 X r¼t V Eexp V Ecal 2 n p i¼1
ð3Þ
The subscripts exp and cal indicate experimental and calculated values. Standard deviations are reported in SI, Table S2. Fig. 1 states V Em for all binary mixtures at T = 298.15 K along with solid lines cal-
3.1. Density and excess molar volume
V Em ¼ V
reported in SI, Table S2. Standard deviation was calculated as follows
ð2Þ
k¼0
Ak represents adjustable coefficients, and x1 is the DIPE mole fraction. Excess molar volumes are shown in Table 3, and Ak were
culated by Redlich–Kister polynomial. Values of V Em are negative over the entire concentration range and demonstrate that strong interactions occur in mixtures. Looking to the structure of DIPE, figured out that, this molecule has a small dipole due to the difference of electronegativity between carbon and oxygen. The dipole moment of carbon and oxygen do not cancel out each other, so the molecule has a net dipole moment and is therefore weakly polar. Dispersion forces as London type, result from short dipoles induced by fluctuations in the electron shell of molecules, are also present in the mixtures and are responsible for the weak interactions between the alkyl chain of 2-alkanol and the weakly polar ether molecules. Furthermore, hydrogen bonding between OH groups of 2-alkanol and oxygen of ether is possible. Because the ether oxygen can act as hydrogen bond acceptor facing with the hydrogen bond donors like OH of alcohols. This behavior also explains that DIPE is soluble in alkanol despite its low polarity. The values of V Em for DIPE + 2-alkanol mixtures are becoming more
3
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025 Table 2 Densities, q and viscosities, g for the binary mixtures of DIPE with 2-alkanol at various temperatures and pressure 0.1 MPa a. DIPE (1) + 2-Propanol (2)
q (g·cm3) x1 T/K = 293.15 0 0.7854 [18–24] 0.0797 0.7783 0.1607 0.7716 0.2387 0.7656 0.3497 0.7579 0.4359 0.7523 0.5553 0.7452 0.6498 0.7400 0.7351 0.7355 0.8480 0.7300 0.9369 0.7260 1 0.7233 g (mPas) 0 2.42 [18–24] 0.0797 1.78 0.1607 1.32 0.2387 1.02 0.3497 0.755 0.4359 0.635 0.5553 0.52 0.6498 0.458 0.7351 0.418 0.8480 0.38 0.9369 0.35 1 0.332 DIPE (1) + 2-Butanol (2) q (g.cm3) x1 T/K = 293.15 0 0.8067 [18–24] 0.0813 0.7983 0.1604 0.7906 0.2406 0.7830 0.3410 0.7739 0.4470 0.7651 0.5582 0.7557 0.6505 0.7485 0.7374 0.7419 0.8465 0.7340 0.9346 0.7278 1 0.7233 g (mPas) 0 3.67 [18–24] 0.0813 3.00 0.1604 2.51 0.2406 2.10 0.3410 1.653 0.4470 1.304 0.5582 0.976 0.6505 0.772 0.7374 0.623 0.8465 0.473 0.9346 0.384 1 0.332 DIPE (1) + 2-Pentanol (2) q (g·cm3) x1 T/K = 293.15 0 0.8093 [18–24] 0.0801 0.8021 0.1597 0.7950 0.2402 0.7878 0.3503 0.7782 0.4399 0.7704 0.5598 0.7600 0.6493 0.7524 0.7372 0.7450 0.8487 0.7356 0.9379 0.7282 1 0.7233 g (mPas) 0 3.97 [18–24] 0.0801 3.43 0.1597 2.94
T/K = 298.15 0.7811 [18–24] 0.7737 0.7668 0.7607 0.7528 0.7472 0.7400 0.7348 0.7304 0.7249 0.7209 0.7183
T/K = 303.15 0.7768 [18–24] 0.7691 0.7620 0.7557 0.7476 0.7419 0.7346 0.7294 0.7250 0.7195 0.7156 0.7130
T/K = 308.15 0.7724 [18–24] 0.7645 0.7572 0.7507 0.7424 0.7366 0.7293 0.7240 0.7195 0.7140 0.7101 0.7076
T/K = 313.15 0.7680 [18–24] 0.7599 0.7524 0.7459 0.7374 0.7314 0.7240 0.7187 0.7143 0.7089 0.7050 0.7025
T/K = 318.15 0.7634 [18–24] 0.7550 0.7473 0.7405 0.7319 0.7258 0.7183 0.7130 0.7085 0.7032 0.6993 0.6968
T/K = 323.15 0.7588 [18–24] 0.7502 0.7423 0.7355 0.7267 0.7207 0.7132 0.7078 0.7034 0.6982 0.6944 0.6919
2.08 [18–24] 1.55 1.18 0.92 0.68 0.572 0.48 0.43 0.395 0.36 0.332 0.319
1.80 [18–24] 1.39 1.05 0.84 0.63 0.53 0.45 0.404 0.375 0.344 0.318 0.304
1.56 [18–24] 1.21 0.94 0.75 0.56 0.48 0.417 0.379 0.356 0.328 0.305 0.290
1.36 [18–24] 1.05 0.83 0.67 0.51 0.44 0.383 0.356 0.334 0.311 0.29 0.274
1.19 [18–24] 0.93 0.74 0.60 0.465 0.40 0.354 0.331 0.313 0.293 0.276 0.261
1.05 [18–24] 0.82 0.647 0.522 0.410 0.361 0.327 0.309 0.295 0.276 0.26 0.246
T/K = 298.15 0.8027 [18–24] 0.7941 0.7861 0.7784 0.7692 0.7603 0.7507 0.7435 0.7369 0.7290 0.7228 0.7183
T/K = 303.15 0.7984 [18–24] 0.7896 0.7815 0.7735 0.7641 0.7551 0.7455 0.7382 0.7316 0.7236 0.7175 0.7130
T/K = 308.15 0.7941 [18–24] 0.7850 0.7767 0.7686 0.7590 0.7495 0.7401 0.7328 0.7261 0.7182 0.7121 0.7076
T/K = 313.15 0.7898 [18–24] 0.7805 0.7719 0.7637 0.7540 0.7448 0.735 0.7276 0.7209 0.7130 0.7069 0.7025
T/K = 318.15 0.7852 [18–24] 0.7756 0.7668 0.7584 0.7486 0.7393 0.7293 0.7219 0.7152 0.7073 0.7012 0.6968
T/K = 323.15 0.7806 [18–24] 0.7708 0.7619 0.7534 0.7434 0.7339 0.7242 0.7168 0.7102 0.7023 0.6963 0.6919
3.04 [18–24] 2.51 2.09 1.75 1.395 1.122 0.846 0.678 0.56 0.44 0.365 0.319
2.54 [18–24] 2.11 1.742 1.453 1.16 0.95 0.75 0.619 0.522 0.414 0.344 0.304
2.13 [18–24] 1.76 1.48 1.241 1.004 0.834 0.67 0.558 0.473 0.388 0.325 0.29
1.80 [18–24] 1.49 1.25 1.06 0.87 0.73 0.596 0.51 0.44 0.361 0.307 0.274
1.54 [18–24] 1.28 1.074 0.92 0.769 0.65 0.535 0.46 0.40 0.333 0.29 0.261
1.33 [18–24] 1.10 0.931 0.801 0.67 0.575 0.48 0.416 0.367 0.31 0.27 0.246
T/K = 298.15 0.8053 [18–24] 0.7978 0.7905 0.7832 0.7736 0.7656 0.7551 0.7474 0.7400 0.7305 0.7232 0.7183
T/K = 303.15 0.8012 [18–24] 0.7934 0.7859 0.7785 0.7686 0.7606 0.7499 0.7421 0.7345 0.7251 0.7179 0.7130
T/K = 308.15 0.7970 [18–24] 0.7889 0.7812 0.7736 0.7636 0.7554 0.7446 0.7367 0.7291 0.7197 0.7125 0.7076
T/K = 313.15 0.7927 [18–24] 0.7844 0.7765 0.7688 0.7587 0.7504 0.7396 0.7317 0.7240 0.7146 0.7074 0.7025
T/K = 318.15 0.7884 [18–24] 0.7798 0.7717 0.7638 0.7534 0.7449 0.7340 0.7260 0.7183 0.7089 0.7017 0.6968
T/K = 323.15 0.7840 [18–24] 0.7753 0.7671 0.7590 0.7484 0.7399 0.7289 0.7209 0.7133 0.7039 0.6967 0.6919
3.32 [33,10] 2.87 2.44
2.81 [33,10] 2.42 2.06
2.37 [33,10] 2.04 1.74
1.99 [33,10] 1.71 1.45
1.66 [33,10] 1.42 1.20
1.39 [33,10] 1.19 1.02 (continued on next page)
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Table 2 (continued) 0.2402 2.52 0.3503 2.08 0.4399 1.76 0.5598 1.386 0.6493 1.13 0.7372 0.90 0.8487 0.64 0.9379 0.45 1 0.332 DIPE (1) + 2-Hexanol (2) q (g.cm3) x1 T/K = 293.15 0 0.8142 0.0806 0.8076 0.1592 0.8010 0.2412 0.7940 0.3508 0.7844 0.4391 0.7764 0.5594 0.7653 0.6497 0.7569 0.7378 0.7485 0.8483 0.7380 0.9386 0.7293 1 0.7233 g (mPas) 0 5.15 0.0806 4.51 0.1592 3.97 0.2412 3.48 0.3508 2.91 0.4391 2.49 0.5594 1.97 0.6497 1.60 0.7378 1.26 0.8483 0.84 0.9386 0.531 1 0.332
2.10 1.74 1.48 1.176 0.969 0.783 0.57 0.42 0.319
1.78 1.49 1.286 1.04 0.864 0.705 0.518 0.389 0.304
1.50 1.26 1.09 0.89 0.75 0.62 0.47 0.36 0.290
1.26 1.06 0.922 0.755 0.64 0.536 0.414 0.33 0.274
1.05 0.89 0.78 0.642 0.547 0.467 0.375 0.306 0.261
0.89 0.76 0.667 0.554 0.477 0.41 0.33 0.28 0.246
T/K = 298.15 0.8101 0.8033 0.7965 0.7893 0.7795 0.7715 0.7603 0.7519 0.7435 0.7329 0.7242 0.7183
T/K = 303.15 0.8061 0.7990 0.7920 0.7846 0.7746 0.7664 0.7551 0.7466 0.7381 0.7276 0.7189 0.7130
T/K = 308.15 0.8021 0.7948 0.7876 0.7800 0.7698 0.7614 0.7499 0.7413 0.7328 0.7221 0.7134 0.7076
T/K = 313.15 0.7984 0.7908 0.7834 0.7756 0.7652 0.7567 0.7450 0.7363 0.7278 0.7170 0.7083 0.7025
T/K = 318.15 0.7945 0.7866 0.7790 0.7709 0.7602 0.7516 0.7397 0.7308 0.7222 0.7113 0.7026 0.6968
T/K = 323.15 0.7901 0.7821 0.7743 0.7662 0.7553 0.7466 0.7346 0.7258 0.7171 0.7064 0.6977 0.6919
4.10 3.61 3.16 2.76 2.30 1.97 1.56 1.275 1.02 0.706 0.465 0.319
3.29 2.89 2.53 2.20 1.83 1.567 1.25 1.034 0.84 0.60 0.42 0.304
2.71 2.38 2.08 1.825 1.53 1.32 1.06 0.88 0.715 0.52 0.38 0.290
2.28 2.00 1.75 1.54 1.29 1.115 0.906 0.756 0.62 0.46 0.35 0.274
1.93 1.69 1.49 1.31 1.11 0.962 0.783 0.66 0.55 0.416 0.32 0.261
1.64 1.44 1.27 1.12 0.95 0.83 0.68 0.58 0.49 0.38 0.295 0.246
a x1 is the mole fraction of DIPE in binary mixtures. Standard uncertainties u are u (T) = 0.02 K, u(x) = 0.001, u(p) = 10 kPa, the expanded uncertainty is U(q) = 0.001 gcm3 for density and for viscosity the relative expanded uncertainty Ur(g) = 5% (0.95 level of confidence).
negative, going from 2-propanol to 2-hexanol. The dipole moment of DIPE is 1.3 D (at 20C) and is a weak polar molecule. For 2alkanol, from 2-propanol up to 2-hexanol, with an increase in the nonpolar hydrocarbon chain, the polarity of mixtures decreases. So, in the mixing of the ether with 2-alkanol, London dispersion forces get stronger with increasing molecular size. Therefore, we expect that the absolute values of V Em will increase. Similar behavior was observed for DIPE + 1-alkanol mixtures [1]. In SI, Figs. S1 to S4, values of excess molar volumes and experimental densities are compared with literature for corresponding binary mixtures. Maximum deviation between our data and scientific literature is 0.3%. This difference is due to differences in measuring experimental densities for pure material or binary mixtures. The origins of errors for measuring experimental data are the wide range of materials sources (Fluka, Merck, and so forth) and the variation in the amount of impurities (purity percent). Also, different measurement techniques are another factor that makes the differences in measuring density values. When the temperature of mixtures increases, molecular forces such as dipole–dipole interactions or London dispersion forces fall off rapidly. Also, rising in temperature, probably increases the difficulty of accommodation of ether molecules in an ordered structure of alcohols. So, created steric hindrances in binary mixtures, weakens molecular interactions among unlike molecules, resulting into the formation of less rigid liquid solutions. Therefore, values of excess molar volumes increase with temperature. As an example, V Em for binary mixtures DIPE + 2-hexanol at various temperatures are depicted in Fig. 2.
Further, the partial molar volumes V m;i for mentioned systems were calculated [35] using
V m;1 ¼ V Em þ V m;1 þ ð1 x1 Þð@V Em =@x1 ÞT;p
V m;2 ¼ V Em þ V m;2 x1 ð@V Em =@x1 ÞT;p
ð4Þ ð5Þ
where V m;i is the pure molar volume. V m;1 for binary systems DIPE + 2alkanol at T = 298.15 K are depicted in Fig. 3 and Table 4. Rise of temperature causes the weakening of DIPE -alcohol bindings, which makes a significant increase in the partial molar volume of mixtures. 3.2. Dynamic viscosities For binary mixtures, the values of viscosity are presented in Table 2. It is clear that binary viscosities increase with the number of the carbon atom of alcohols and decreases with temperature. Deviation in the viscosity was calculated by the following equation
Dg ¼ g x1 g1 x2 g2
ð6Þ
In the above equation,g shows mixture viscosity whilegi is the pure viscosity. Viscosity deviation for binary systems DIPE + 2alkanol is shown in Fig. 4. Rising in the alkyl chain of the alcohols makes an increase in the viscosity deviations, which can be attributed to the strengthening of interactions in solutions. Dgvalues were correlated by Redlich–Kister and binary parameters along with the standard deviations are presented in SI, Table S2 (Fig 5). 3.3. PC-SAFT model One of the most famous methods for calculating thermodynamic properties of pure substances and mixtures is PC-SAFT
5
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025 Table 3 Excess molar volumes, V Em and viscosity deviations, D g for binary mixtures at various temperatures and pressure 0.1 MPa a. DIPE (1) + 2-Propanol (2) V Em (cm3·mol1) T/K = 293.15 x1 0.0797 0.150 0.1607 0.270 0.2387 0.360 0.3497 0.450 0.4359 0.477 0.5553 0.470 0.6498 0.430 0.7351 0.350 0.8480 0.220 0.9369 0.090 D g (mPas) 0.0797 0.474 0.1607 0.764 0.2387 0.902 0.3497 0.935 0.4359 0.875 0.5553 0.741 0.6498 0.605 0.7351 0.467 0.8480 0.269 0.9369 0.114 DIPE (1) + 2-Butanol (2)
T/K = 298.15 0.130 0.240 0.320 0.400 0.430 0.420 0.380 0.315 0.183 0.076
T/K = 303.15 0.120 0.220 0.292 0.356 0.377 0.371 0.338 0.276 0.160 0.063
T/K = 308.15 0.120 0.208 0.270 0.326 0.345 0.340 0.300 0.241 0.137 0.054
T/K = 313.15 0.091 0.169 0.218 0.252 0.259 0.246 0.218 0.171 0.100 0.037
T/K = 318.15 0.106 0.191 0.249 0.289 0.297 0.285 0.254 0.207 0.116 0.044
T/K = 323.15 0.077 0.134 0.174 0.20 0.204 0.191 0.165 0.130 0.076 0.03
0.390 0.617 0.740 0.784 0.740 0.622 0.506 0.390 0.227 0.098
0.291 0.510 0.603 0.647 0.618 0.519 0.424 0.325 0.187 0.080
0.249 0.416 0.507 0.556 0.526 0.438 0.356 0.270 0.155 0.065
0.223 0.355 0.431 0.470 0.447 0.374 0.298 0.228 0.128 0.053
0.186 0.301 0.368 0.395 0.385 0.320 0.255 0.194 0.109 0.044
0.166 0.274 0.336 0.356 0.339 0.277 0.219 0.164 0.092 0.037
T/K = 298.15 0.186 0.336 0.451 0.553 0.608 0.606 0.565 0.486 0.327 0.161
T/K = 303.15 0.178 0.324 0.426 0.527 0.582 0.580 0.542 0.460 0.311 0.156
T/K = 308.15 0.166 0.303 0.400 0.488 0.530 0.535 0.496 0.426 0.292 0.153
T/K = 313.15 0.156 0.273 0.365 0.456 0.495 0.497 0.458 0.391 0.271 0.133
T/K = 318.15 0.139 0.247 0.333 0.412 0.453 0.455 0.420 0.362 0.253 0.129
T/K = 323.15 0.116 0.213 0.294 0.362 0.402 0.407 0.386 0.330 0.224 0.118
0.309 0.514 0.635 0.717 0.722 0.675 0.592 0.474 0.297 0.132
0.248 0.439 0.549 0.618 0.607 0.542 0.466 0.369 0.233 0.106
0.220 0.355 0.446 0.499 0.487 0.433 0.375 0.300 0.184 0.085
0.186 0.305 0.373 0.410 0.399 0.352 0.297 0.235 0.147 0.067
0.156 0.261 0.312 0.335 0.328 0.291 0.248 0.197 0.124 0.055
0.142 0.225 0.268 0.290 0.278 0.245 0.209 0.164 0.102 0.047
T/K = 293.15 0.210 0.384 0.526 0.670 0.720 0.710 0.663 0.565 0.355 0.140
T/K = 298.15 0.188 0.350 0.487 0.642 0.689 0.677 0.627 0.540 0.322 0.130
T/K = 303.15 0.169 0.322 0.452 0.602 0.653 0.631 0.573 0.465 0.287 0.120
T/K = 308.15 0.152 0.294 0.421 0.561 0.612 0.595 0.537 0.434 0.263 0.110
T/K = 313.15 0.140 0.266 0.385 0.530 0.581 0.570 0.512 0.403 0.246 0.105
T/K = 318.15 0.121 0.240 0.358 0.478 0.514 0.504 0.452 0.369 0.227 0.093
T/K = 323.15 0.110 0.224 0.328 0.431 0.460 0.454 0.413 0.331 0.200 0.080
0.249 0.449 0.576 0.616 0.610 0.547 0.478 0.388 0.242 0.108
0.210 0.401 0.499 0.529 0.520 0.464 0.402 0.325 0.203 0.085
0.189 0.350 0.428 0.442 0.422 0.367 0.319 0.258 0.165 0.071
0.163 0.298 0.370 0.381 0.365 0.316 0.269 0.217 0.135 0.059
0.143 0.266 0.318 0.329 0.313 0.274 0.236 0.189 0.120 0.051
0.128 0.237 0.274 0.280 0.265 0.235 0.205 0.162 0.098 0.042
0.108 0.187 0.225 0.229 0.220 0.196 0.170 0.137 0.089 0.037
V Em (cm3·mol1) x1 T/K = 293.15 0.0813 0.191 0.1604 0.360 0.2406 0.476 0.3410 0.590 0.4397 0.655 0.5582 0.648 0.6505 0.598 0.7374 0.511 0.8465 0.352 0.9346 0.165 D g (mPas) 0.0813 0.399 0.1604 0.625 0.2406 0.767 0.3410 0.879 0.4397 0.898 0.5582 0.831 0.6505 0.727 0.7374 0.586 0.8465 0.371 0.9346 0.166 DIPE (1) + 2-Pentanol (2) V Em (cm3·mol1) x1 0.0801 0.1597 0.2402 0.3503 0.4399 0.5598 0.6493 0.7372 0.8487 0.9379 D g (mPas) 0.0801 0.1597 0.2402 0.3503 0.4399 0.5598 0.6493 0.7372 0.8487 0.9379
(continued on next page)
6
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025
Table 3 (continued) DIPE (1) + 2-Hexanol (2) V Em (cm3·mol1) x1 0.0806 0.1592 0.2412 0.3508 0.4391 0.5594 0.6497 0.7378 0.8483 0.9386 D g (mPas) 0.0806 0.1592 0.2412 0.3508 0.4391 0.5594 0.6497 0.7378 0.8483 0.9386
T/K = 293.15 0.244 0.440 0.606 0.757 0.810 0.800 0.746 0.630 0.413 0.194
T/K = 298.15 0.233 0.410 0.558 0.700 0.760 0.756 0.702 0.589 0.391 0.172
T/K = 303.15 0.214 0.380 0.525 0.660 0.710 0.700 0.649 0.542 0.357 0.154
T/K = 308.15 0.197 0.360 0.488 0.617 0.664 0.651 0.603 0.500 0.324 0.133
T/K = 313.15 0.180 0.333 0.458 0.570 0.618 0.609 0.558 0.467 0.294 0.12
T/K = 318.15 0.166 0.306 0.421 0.527 0.572 0.555 0.507 0.421 0.264 0.105
T/K = 323.15 0.153 0.276 0.385 0.489 0.526 0.505 0.459 0.385 0.242 0.093
0.252 0.413 0.508 0.550 0.544 0.485 0.420 0.335 0.223 0.097
0.185 0.338 0.428 0.474 0.470 0.425 0.368 0.290 0.187 0.086
0.159 0.285 0.370 0.413 0.412 0.370 0.316 0.247 0.157 0.067
0.135 0.245 0.301 0.331 0.327 0.296 0.258 0.210 0.137 0.059
0.118 0.211 0.256 0.286 0.284 0.252 0.221 0.180 0.118 0.047
0.105 0.174 0.217 0.235 0.235 0.213 0.186 0.149 0.098 0.043
0.088 0.148 0.184 0.201 0.198 0.180 0.154 0.122 0.077 0.037
a x1 is the mole fraction of Diisopropyl ether in the binary mixtures. Standard uncertainties u are u(T) = 0.02 K, u(x) = 0.001, u(p) = 10 kPa, the expanded uncertainty is U (q) = 0.001 gcm3 for density and for viscosity the relative expanded uncertainty Ur(g) = 5% (0.95 level of confidence).
Fig. 3. Partial molar volumes V m;1 versus mole fraction of DIPE with (r) 2-propanol, (D) 2-butanol, (d) 2-pentanol, (*) 2-hexanol at T = 298.15 K. (—) PC-SAFT model. Fig. 1. Excess molar volume V Em , versus the mole fraction x1 of DIPE with (▲) 2propanol (d) 2-butanol, (j) 2-pentanol, (*) 2-hexanol T = 298.15 K. (—) RedlichKister equation.
model [36,37]. In this theory, hard chains are used as reference fluid and chain–chain interactions are computed, which improves the thermodynamic description of fluid mixtures. This model is explained by the sum of all residual Helmholtz free energy.
ares ¼ ahc þ adisp þ aassoc
ð7Þ
The hard-chain reference fluid is made up of spherical segments that have not any attractive interactions. This part is defined by two parameters namely the number of segments m and the diameter of segments r
ahc ¼ m ahs
X
xi ðmi 1Þlng ij hs
ð8Þ
i
In the above equation, m is the mean segment number, andg hs ij the pair distribution function Fig. 2. Excess molar volumes V Em for DIPE + 2-hexanol at temperatures: 293.15 K (h), 298.15 K (d), 303.15 K (j), 308.15 K (▲), 313.15 K (D), 318.15 K (r), 323.15 K (s). (—) Redlich-Kister equation.
g hs ij ¼
2 1 di dj 3f2 di dj 2f2 2 þ þ 2 1 f3 di þ dj ð1 f3 Þ di þ dj ð1 f3 Þ3
ð9Þ
7
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025 Table 4 Partial molar volumes, V m;1 for Binary Mixtures DIPE with 2-Alkanol at T = 298.15 K and pressure 0.1 MPa. DIPE + 2-Propanol
DIPE + 2-Butanol
DIPE + 2-Pentanol
x1
1 V m;1 cm3 :mol
x1
V m;1 ðcm3 :mol
0 0.0797 0.1607 0.2387 0.3497 0.4359 0.5553 0.6498 0.7351 0.848 0.9369 1
139.36 139.73 140.14 140.49 140.95 141.28 141.66 141.88 142.04 142.19 142.24 142.26
0 0.0813 0.1604 0.2406 0.341 0.4397 0.5582 0.6505 0.7374 0.8465 0.9346 1
139.81 140.17 140.52 140.84 141.19 141.48 141.76 141.96 142.09 142.21 142.24 142.25
1
Þ
DIPE + 2-Hexanol
x1
V m;1 ðcm3 :mol
0 0.0801 0.1597 0.2402 0.3503 0.4399 0.5598 0.6493 0.7372 0.8487 0.9379 1
140.19 140.51 140.79 141.06 141.38 141.61 141.86 142.02 142.13 142.23 142.26 142.26
1
Þ
x1
V m;1 ðcm3 :mol
0 0.0806 0.1592 0.2412 0.3508 0.4391 0.5594 0.6497 0.7378 0.8483 0.9386 1
140.5 140.76 141.01 141.24 141.52 141.73 141.97 142.1 142.19 142.26 142.26 142.26
1
Þ
fn is defined as n p X q xi mi dni
fn ¼
6
ð11Þ
i¼1
di is the segment diameter. For determination of dispersive attraction contribution in Helmholtz energy, PC-SAFT uses the Barker and Henderson perturbation theory [38] to the hard-chain reference system. Therefore, the effect of the non-spherical shape of molecules on attractive dispersions is considered.
ð12Þ
adis ¼ 2pqI1 m2 er3 pq m C 1 I2 m2 e2 r3 The C1 coefficient is calculated as
"
C1 ¼ 1 þ m Fig. 4. Comparisons of calculated and experimental densities for DIPE + 2-pentanol at (r) 293.15 K, (D) 303.15 K, (d) 313.15 K, (s) 323.15 K. (—) PC-SAFT model.
8g 2g2 ð1 gÞ4
þ ð1 mÞ
20g 27g2 þ 12g3 2g4 ½ð1 gÞð2 gÞ2
#1 ð13Þ
where g is the reduced density, I1 and I2 are perturbation integrals. The association interactions such as hydrogen bonding are also regarded in this theory. It is assumed that a molecule has one or more association sites and forms hydrogen bonds. If the molecule has two association sites A and B, two parameters, namely the association energy eAiBi/k and the effective association volume jAiBi is considered. The number of association sites and possible interactions among them has profound effect on the structure of fluids and their phase behavior. aassoc is written as:
aassoc ¼
X
x i¼1 i
" X
Ai
lnX Ai
X Ai 2
!
1 þ Mi 2
#
ð14Þ
The mole fraction of molecules not bonded at site A is presented by XAi and the association sites on a molecule with Mi. Cross association parameters are determined using combining rules of the pure parameters without introducing binary parameters.
eAi Bj ¼ Fig. 5. Viscosity deviation D g versus the mole fraction x1 of DIPE with (▲) 2propanol (d) 2-butanol, (j) 2-pentanol, (*) 2-hexanol at T = 298.15 K. (—) RedlichKister equation.
j
Ai Bj
"
ahs ¼
f32
1 3f1 f2 þ þ f0 1 f3 f3 ð1 f3 Þ2
f32 f23
!
eij ¼
#
f0 lnð1 f3 Þ
ð10Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
j j Ai Bi
Aj Bj
pffiffiffiffiffiffiffiffiffiffiffi !3 rr ii jj 0:5 rii þ rjj
ð15Þ
ð16Þ
Cross parameters for non-associated compounds are obtained by
Hard sphere contribution ahs is given by
¼
1 Ai Bi e þ eAi Bi 2
rij ¼
pffiffiffiffiffiffiffi
ei ej 1 kij
ri þ rj 2
ð17Þ ð18Þ
8
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025
Table 5 Pure Component Parameters Obtained for PC-SAFT Model at pressure 0.1 MPa. Component
mi
ri
ei /k
jAi Bi
eAi Bi/k
T Range (K)
DIPE 2-Propanol 2-Butanol 2-Pentanol 2-Hexanol
3.72 3.098 2.851 3.763 3.632
3.451 3.206 3.546 3.362 3.595
220.7 205.32 237.11 220.76 238.21
– 0.0251 0.0075 0.0189 0.00702
– 2251.9 2481 2225 2476
293–323 293–323 293–323 293–323 293–323
dij ¼
di dj di þ dj
ð19Þ
Eq. (17) contains an adjustable parameterkij , which corrects the dispersion energy in the mixture and obtained by the iteration method when predicted values have the closest amount to experimental data. Values of pure parameters for DIPE and 2-alkanols were obtained by adjusting their saturated vapor pressure and liquid densities with PC-SAFT model. DIPE was investigated as a nonassociated component, and three parameters for the pure state were obtained. For 2-alkanol, two association sites were considered per each molecule as type 2B, and five parameters were calculated. Obtained values are reported in Table 5 along with the deviation and temperature range. Maximum of deviation in vapor pressure was 5.18% and in liquid densities was 1.36%. Using the combining rules mentioned in Eqs. (15) to (19), values of densities were obtained for all binary mixtures. The parameter kij was obtained by the iteration method when predicted values have the closest amount to experimental data. By defining an objective function, densities were obtained.
OF ¼
2 N exp X q qcalc i
i¼1
qexp i
ð20Þ
i
Then, from the output densities of the PC-SAFT model, values of partial molar volumes were calculated. Adjusting parameter kij is presented in Table 6. For calculation of densities, AAD for binary mixtures DIPE + 2-propanol is 1.14%, for DIPE + 2-butanol is 1.06%, for DIPE + 2-pentanol is 1.21% and for DIPE + 2-hexanol is 1.16%. Fig. 4 demonstrates experimental and calculated densities for DIPE + 2-pentanol at various temperatures. Also results of partial molar volumes obtained by this model indicate that deviation in AAD for DIPE + 2-propanol is 1.89%, for DIPE + 2-butanol 2.34%, for DIPE + 2-pentanol 1.76%, and for DIPE + 2-hexanol 1.46%. Calculated partial molar volumes by this model along with experimental data for DIPE + 2-alkanol at T = 298.15 K are depicted in Fig.3. 3.4. Free volume theory In recent years, among several theoretical or semi-empirical approaches for calculation of dense fluid viscosities, free volume theory, and friction theory are further developed. In FVT [39,40] viscosity is related to the structure of fluid and dense or dilute state of fluids is precisely described. In this approach, viscosity is shown by two parts:
g ¼ g0 þ Dg
ð21Þ
res
Table 6 Binary Interaction Parameter kij for PC-SAFT model. Binary Systems DIPE DIPE DIPE DIPE
+ + + +
2-Propanol 2-Butanol 2-Pentanol 2-Hexanol
kij 0.027 0.023 0.031 0.018
AAD (%) Pressure
Density
5.18 4.76 5.14 4.19 3.85
1.36 1.17 1.23 1.16 1.09
Viscosity in the dilute gas limit is presented by g0 and its deviation from dilute gas by residual viscosityDgres . The dilute gas term explains the fluid viscosity in gaseous or low-density state. The modified form of this equation is as follow:
g0 ¼ 40:785
pffiffiffiffiffiffiffiffiffiffiffi MW T v 2=3 c X
ð22Þ
Fc
X is reduced collision integral, molecular weight and F c is
vc
the critical volume, MW the
F c ¼ 1 0:275x þ 0:059035l4r þ v
ð23Þ
v is correction factor for hydrogen bonds, x the acentric factor and lr is dimensionless dipole moment. Combination of the residual part of viscosity with exponential relation [41] leads to the following equation
B Dgres ¼ 1014 qNa L2 f0 exp fV
ð24Þ
B is a parameter related to the overlap of free-volume among molecules [42] f0 the friction coefficient, q the density, Na Avogadro’s number, f V free volume fraction, and L2 is average quadratic length. f0 could be obtained from the energy of dissipation E by the relation
f0 ¼ 1010
E Na bf
103 M W 3RT
!0:5
ð25Þ
bf is dissipation of energy length. Combination of Eqs. (24) to (25) results in
Dgres
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
103 RTMW 2=3 B ¼ 10 qLV f V exp fV 3 4
ð26Þ
Above equation contains three adjustable coefficients: (i) a length parameter named Lv which is connected to the molecules structure and relaxation time; (ii) a proportion parameter namely a which related to the barrier of energy and density; (iii) B parameter corresponds to the free-volume overlap. Three parameters were calculated by the fitting of Eq. (26) to pure viscosities. Also, accurate and reliable thermodynamic properties such as density and pressure are needed obtaining true values of viscosity. In the present study, density and pressure are the output of the PCSAFT model. For calculation of binary viscosities, mixing rules of Lorentz type were applied without further adjustable parameters.
amix ¼
n X
ai xi
ð27Þ
Bi xi
ð28Þ
i¼1
Bmix ¼
n X i¼1
LV;mix ¼
n X
Lv ;i xi
ð29Þ
i¼1
Average absolute deviation for viscosity of DIPE + 2-propanol is 1.89%, for DIPE + 2-butanol is 2.19%, for DIPE + 2-pentanol is 1.64% and finally for DIPE + 2-hexanol is 1.92%. Fig. 6 demonstrates
S. Ahmadi, M. Almasi / J. Chem. Thermodynamics 142 (2020) 106025
Fig. 6. Binary viscosities g versus the mole fraction x1 of DIPE with (r) 2-propanol, (D) 2-butanol, (d) 2-pentanol, (*) 2-hexanol at T = 298.15 K. at T = 298.15 K. (—) FVT.
experimental viscosities along with calculated values with free volume theory at 298.15 K. 4. Conclusions Experimental values of density and viscosity for mixtures DIPE + 2-propanol up to 2-hexanol at various temperatures have been reported, and for interpretation of interactions in the mixtures, values of V Em andDg were calculated. The negative values of the mentioned parameters display that stronger interactions in the mixtures occur relative to the pure state. Rising in the number of the carbon atom of alcohols increases the dispersion forces and leads to an increase in the V Em values. The PC-SAFT model was used to model the densities and partial molar volumes. Calculated density in the binary mixture shows the maximum of 1.21% deviation from experimental data. Maximum of deviation between experimental and calculated partial molar volumes was 2.34%. For correlation and prediction of viscosities, the combination of PC-SAFT model with FVT was implemented. Maximum of deviation from experimental viscosities was 2.19% and belonged to the binary mixtures of DIPE + 2-butanol. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jct.2019.106025. References [1] Á. Piñeiro, Excess volumes and isobaric heat capacities of diisopropyl ether with several alkanols at 298.15K Application of the symmetrical extended real associated solution model, Fluid Phase Equilib. 216 (2004) 245–256. [2] K. Kammerer, R.N. Lichtenthaler, Excess properties of binary alkanol–ether mixtures and the application of the ERAS model, Thermochim. Acta 310 (1998) 61–67. [3] M. Almasi, Thermodynamic study of interactions between 1-alkanol and butanone, Chem. Phys. 527 (2019), 110474.
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JCT 2019-675