Experimental Investigation of Interactions and Thermodynamic

Article pubs.acs.org/jced

Experimental Investigation of Interactions and Thermodynamic Properties of Poly(ethylene glycol) 200/400 + Dimethyl Adipate/ Dimethyl Phthalate Binary Mixtures Jelena M. Vuksanović, Ivona R. Radović, Slobodan P. Šerbanović, and Mirjana Lj. Kijevčanin* Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, 11120 Belgrade, Serbia ABSTRACT: Density ρ, viscosity η, and refractive index nD have been experimentally measured for four binary mixtures dimethyl adipate + poly(ethylene glycol) 200, dimethyl adipate + poly(ethylene glycol) 400, dimethyl phthalate + poly(ethylene glycol) 200, and dimethyl phthalate + poly(ethylene glycol) 400 in the temperature range T = (288.15 to 323.15) K with a temperature step of 5 K and at atmospheric pressure. Excess molar volumes VE, viscosity deviations Δη, and deviations of refractive index ΔnD were calculated from experimental data and fitted using Redlich−Kister polynomial. Fourier-transform infrared analysis of binary mixtures and corresponding pure components was performed at 298.15 K in order to gain insight into the molecular structure of mixtures and possible intra- and intermolecular interactions. Performed IR analysis confirms an absence of intermolecular interactions between unlike compounds. Consequently, the nonideal behavior of mixtures is contributed to geometrical packing or dispersion forces of different species.

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reactions.8−11 PEG has also found widespread application in food, pharmaceutical, biomedical, cosmetic, membrane, and chemical industries as solvent, carrier, humectant, lubricant, binder, and coupling agent.12,13 An interesting fact is that, in the presence of practically nonpolar solvents such as benzene and toluene, PEG adjusts its polarity and exhibits very good or complete miscibility with these important industrial chemicals.14 This work presents continuation of our previous research in the field of experimental determination of thermodynamic properties of binary mixtures in a wide range of temperatures and at atmospheric pressure.15−19 Four binary mixtures, dimethyl adipate (1) + PEG 200 (2), dimethyl adipate (1) + PEG 400 (2), dimethyl phthalate (1) + PEG 200 (2), and dimethyl phthalate (1) + PEG 400 (2), were investigated in the temperature range T = (288.15 to 323.15) K with a temperature step of 5 K, at atmospheric pressure. Thermodynamic properties, such as density ρ, viscosity η, and refractive index nD were experimentally measured. From these experimental data excess molar volumes VE, viscosity deviations Δη, and deviations in refractive index ΔnD were calculated and fitted using a Redlich−Kister polynomial.20 Excess properties calculated from the experimental results give an interpretation of the molecular interactions between the components of the mixtures, as well as the explanation of the effects of temperature and molecular structure on the mixture’s

INTRODUCTION Sustainable processes in the future have to be oriented to the usage of less toxic and less volatile substances in order to reduce air, water and ground pollution. Solvents are fundamental for every industrial process. When the choice of the appropriate industrial solvent has to be made, it is important to define its thermodynamic properties such as density, viscosity, and refractive index in a wide range of temperatures, and in some cases pressures. In certain applications when dissolving power or other solvent properties are not satisfactory, mixing of two or more solvents can lead to desirable performances of a resulting mixture due to their synergistic effect. Very often, in industry, the so-called binary solvent mixtures or mixed solvents are used. Theoretical explanations of the effects caused by mixing the organic substances are extensively described in the literature.1,2 The chemicals used in this work were selected primarily because of their harmless nature and potential usage as solvent mixtures. Esters, dimethyl adipate (DMA) and dimethyl phthalate (DMP), are nonvolatile and low toxicity solvents. Dimethyl adipate is used for gear oils, grease, metal working and for biodegradable hydraulic fluids.3 Dimethyl phthalate has many uses, including in solid rocket propellants, plastics, and insect repellants. Poly(ethylene glycols) 200 and 400 (PEG 200 and PEG 400) are nonvolatile, nontoxic, highly biodegradable polymers.4 PEG is both good proton donor and proton acceptor,5 thus forms strong intra- and intermolecular hydrogen bonds.6,7 Because of its favorable properties, PEG has also been used as an environmentally benign solvent to replace volatile organic solvents in different processes, such as chemical © 2015 American Chemical Society

Received: February 17, 2015 Accepted: May 2, 2015 Published: May 7, 2015 1910

DOI: 10.1021/acs.jced.5b00156 J. Chem. Eng. Data 2015, 60, 1910−1925

Journal of Chemical & Engineering Data

Article

Measurements. Density ρ was measured with an Anton Paar DMA 5000 digital vibrating U-tube densimeter, refractive index n D using an automatic Anton Paar RXA 156 refractometer, and viscosity η using a digital Stabinger viscometer (model SVM 3000/G2). A description of the apparatus is explained in detail in our previous work.17 For the mass composition determination, a Mettler AG 204 balance with a precision 1·10−7 kg was used for all binary mixtures with the measurement procedure described previously.32 The uncertainty of the mole fraction calculation was less than ± 1·10−4. Density measurements were performed with the experimental uncertainty ± 4·10−2 kg·m−3, while the excess molar volume was calculated with the average uncertainty ± 4· 10−6 m3·kmol−1. The uncertainty of the refractive index data measurements is ± 0.00005. The relative uncertainty in dynamic viscosity measurements was estimated to be ± 1 %. The uncertainties for refractive index and viscosity deviations are ± 0.00005 and ± 0.4 %, respectively. FT-IR spectrophotometer (Bomem MB-102) was used for recording IR spectra of the investigated pure components and their binary mixtures, within a range of 400−4000 cm−1, at a resolution of 4 cm−1. All spectroscopic measurements were performed at 298.15 K.

behavior on the molecular level. For more detailed explanation of possible intermolecular interactions, Fourier-transform infrared spectroscopy (FTIR) studies of the binary mixtures (DMA (1) + PEG 200 (2), DMA (1) + PEG 400 (2), DMP (1) + PEG 200 (2), DMP (1) + PEG400 (2)) are performed at 298.15 K. To the best of our knowledge there are no experimental data of thermodynamic properties and spectral analysis for the investigated binary mixtures citied elsewhere in literature.

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EXPERIMENTAL METHODS Chemicals. Dimethyl adipate (w ≥ 0.99) was purchased from Merck, dimethyl phthalate from Fluka (w ∼ 0.99), while PEG 200 (w ≥ 0.999) and PEG 400 (w ≥ 0.999) were supplied by Sigma-Aldrich and Acros Organics, respectively (Table 1). Table 1. Sample Description initial mass fraction purity

purification method

Merck Fluka

≥ 0.99 ∼ 0.99

none none

SigmaAldrich Acros organics

≥ 0.999

none

≥ 0.999

none

chemical name dimethyl adipate dimethyl phthalate PEG 200a PEG 400a a

source

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RESULTS AND DISCUSSION Table 3 reports experimental density, viscosity, and refractive index, as well as the calculated values of excess molar volume, viscosity deviation and deviation in refractive index for the investigated binary mixtures in the temperature range T = (288.15 to 323.15) K. The excess molar volumes VE were calculated from the density data using the following equation:

PEG = poly(ethylene glycol).

Chemicals were kept in dark bottles, in an inert atmosphere and ultrasonically degassed before a sample preparation. In Table 2 densities, dynamic viscosities, and refractive indices of pure substances are compared with literature values at several temperatures.21−31 The agreement for density measurements was within 0.30 kg·m−3 for DMA and DMP and within 0.50 kg· m−3 for PEG. The agreement with literature values for viscosity measurements of less viscous fluids was in most cases 0.17 mPa· s, up to 3.38 mPa·s for PEG, and within 7.26·10−3 for refractive indices of all components.

⎡⎛ ⎞ ⎛ ⎞⎤ 1 1 ⎟ − ⎜⎜ ⎟⎟⎥ ⎢⎣⎝ ρ ⎠ ⎝ ρi ⎠⎥⎦

n

VE =

∑ xiMi⎢⎜ i=1

(1)

where xi is the mole fraction of component i in the mixture; Mi its molecular weight, and ρ and ρi are the measured densities of a mixture and a pure component i, respectively.

Table 2. Densities ρ, Refractive Indices nD, and Viscosities η of the Pure Components at Temperature T and at Atmospheric Pressurea 10−3·ρ/kg·m−3

η/mPa·s

nD

T/K

exp.

lit.

exp

lit.

exp

dimethyl adipate

293.15

1.061920

1.06190b

1.42876

3.3132

dimethyl phthalate

298.15

1.186865

1.18657d

1.51286

PEG 200

298.15 303.15 298.15

1.120856 1.116876 1.122120

1.45832 1.46508

303.15

1.118024

1.46328

313.15

1.109835

1.12098h 1.11701h 1.12249h 1.12230i 1.1218j 1.12162k 1.11831h 1.1180i 1.1097i 1.1102l

1.4215b 1.4283c 1.5137e 1.513f 1.4585h

component

PEG 400

lit. 3.36g

13.928

13.76169d

1.4650h

49.610 38.801 91.024

48.157h 37.682h 92.797h 94.4j

1.4638h

70.444

71.776h 69.1i 44.4i

44.624

Standard uncertainties u for each variables are u(T) = 0.01 K; u(p) = 5 %; and the combined expanded uncertainties Uc are Uc(ρ) = 4·10−2 kg·m−3, Uc(nD) = 9·10−5, and Uc(η) = 1.0 %, with a 0.95 level of confidence (k ≈ 2). bInce.21 cLide.22 dRostami et al.23 eSvirbely at al.24 fPearce.25 gComuñas et al.26 hOttani et al.27 iMueller et al.28 jHan et al.29 kAucouturier et al.30 lEliassi and Modarress.31 a

1911



Article

Table 3. Densities ρ, Excess Molar Volumes VE, Refractive Indices nD, Refractive Index Deviations ΔnD, Viscosities η, and Viscosity Deviations Δη of the Dimethyl Adipate (1) + PEG 200/400 (2) and Dimethyl Phthalate (1) + PEG 200/400 (2) Systems at T = (288.15 to 323.15) K and at Atmospheric Pressurea x1

10−3·ρ/kg·m−3

0 0.1001 0.2001 0.2997 0.4001 0.4999 0.6000 0.6999 0.7999 0.8996 1

1.128814 1.122666 1.116544 1.110369 1.104079 1.097779 1.091466 1.085135 1.078887 1.072764 1.066790

0 0.1001 0.2001 0.2997 0.4001 0.4999 0.6000 0.6999 0.7999 0.8996 1

1.124834 1.118599 1.112382 1.106108 1.099737 1.093335 1.086927 1.080508 1.074151 1.067945 1.061920

0 0.1001 0.2001 0.2997 0.4001 0.4999 0.6000 0.6999 0.7999 0.8996 1

1.120856 1.114529 1.108212 1.101847 1.095388 1.088886 1.082388 1.075880 1.069422 1.063141 1.057047

0 0.1001 0.2001 0.2997 0.4001 0.4999 0.6000 0.6999 0.7999 0.8996 1

1.116876 1.110454 1.104043 1.097588 1.091037 1.084441 1.077849 1.071250 1.064704 1.058336 1.052176

0 0.1001 0.2001 0.2997 0.4001 0.4999 0.6000 0.6999 0.7999

1.112888 1.106383 1.099875 1.093325 1.086673 1.079989 1.073305 1.066617 1.059988

106·VE/m3·mol−1

nD

ΔnD

Dimethyl Adipate (1) + PEG 200 (2) 288.15 K 1.46180 0.0596 1.45877 0.0001 0.1014 1.45612 0.0005 0.1404 1.45296 0.0004 0.1746 1.44946 0.0001 0.2006 1.44660 0.0003 0.2100 1.44334 0.0001 0.2081 1.44041 0.0003 0.1761 1.43686 −0.0002 0.1114 1.43378 −0.0002 1.43082 293.15 K 1.46007 0.0598 1.45702 0.0001 0.1030 1.45428 0.0005 0.1440 1.45111 0.0004 0.1772 1.44757 0.0000 0.2055 1.44466 0.0002 0.2159 1.44139 0.0001 0.2138 1.43841 0.0003 0.1846 1.43485 −0.0002 0.1184 1.43175 −0.0002 1.42876 298.15 K 1.45832 0.0608 1.45530 0.0001 0.1060 1.45246 0.0005 0.1476 1.44924 0.0004 0.1808 1.44567 0.0000 0.2111 1.44276 0.0002 0.2217 1.43943 0.0001 0.2195 1.43642 0.0002 0.1918 1.43284 −0.0002 0.1228 1.42969 −0.0002 1.42669 303.15 K 1.45661 0.0622 1.45359 0.0002 0.1086 1.45063 0.0004 0.1508 1.44735 0.0003 0.1848 1.44380 0.0000 0.2160 1.44082 0.0002 0.2275 1.43745 0.0000 0.2256 1.43444 0.0002 0.1975 1.43083 −0.0002 0.1276 1.42764 −0.0002 1.42463 308.15 K 1.45488 0.0616 1.45188 0.0002 0.1097 1.44881 0.0004 0.1532 1.44548 0.0003 0.1893 1.44199 0.0000 0.2206 1.43888 0.0002 0.2326 1.43543 0.0000 0.2307 1.43241 0.0002 0.2014 1.42877 −0.0003 1912

η/mPa·s

Δη/mPa·s

86.351 63.529 45.940 33.206 23.649 17.170 12.388 8.9998 6.5240 4.9204 3.7777

−14.556 −23.888 −28.398 −29.640 −27.903 −24.419 −19.558 −13.785 −7.1477

64.712 48.239 35.438 26.003 18.843 13.899 10.198 7.5248 5.5600 4.2592 3.3132

−10.327 −16.988 −20.308 −21.285 −20.120 −17.675 −14.214 −10.045 −5.2184

49.610 37.480 27.843 20.630 15.225 11.409 8.5350 6.3903 4.7929 3.7272 2.9370

−7.4580 −12.428 −14.992 −15.697 −14.869 −13.071 −10.553 −7.4880 −3.8958

38.801 29.639 22.370 16.794 12.561 9.5311 7.3267 5.5314 4.1813 3.2997 2.6289

−5.5412 −9.1930 −11.1662 −11.757 −11.187 −9.7710 −7.9528 −5.6893 −2.9609

30.902 23.870 18.249 13.880 10.501 8.0862 6.2903 4.8220 3.6785

−4.1756 −6.9430 −8.4698 −8.9752 −8.5507 −7.4901 −6.1077 −4.4004



Article

Table 3. continued x1

10−3·ρ/kg·m−3

0.8996 1

1.053543 1.047295

0 0.1001 0.2001 0.2997 0.4001 0.4999 0.6000 0.6999 0.7999 0.8996 1

1.108901 1.102306 1.095704 1.089063 1.082314 1.075539 1.068760 1.061981 1.055277 1.048743 1.042410

0 0.1001 0.2001 0.2997 0.4001 0.4999 0.6000 0.6999 0.7999 0.8996 1

1.104912 1.098224 1.091531 1.084795 1.077943 1.071086 1.064214 1.057344 1.050569 1.043951 1.037519

0 0.1001 0.2001 0.2997 0.4001 0.4999 0.6000 0.6999 0.7999 0.8996 1

1.100921 1.094140 1.087354 1.080526 1.073605 1.066624 1.059661 1.052697 1.045861 1.039096 1.032622

0 0.1005 0.2005 0.3001 0.4002 0.5002 0.6000 0.7001 0.7999 0.8992 1

1.130306 1.127155 1.123646 1.119697 1.115171 1.109974 1.103969 1.096911 1.088655 1.078846 1.066790

0 0.1005 0.2005 0.3001 0.4002 0.5002 0.6000 0.7001

1.126215 1.123020 1.119454 1.115440 1.110844 1.105571 1.099507 1.092366

106·VE/m3·mol−1

nD

308.15 K 0.1290 1.42559 1.42255 313.15 K 1.45317 0.0621 1.45013 0.1112 1.44700 0.1553 1.44365 0.1927 1.44020 0.2246 1.43693 0.2375 1.43356 0.2359 1.43038 0.2040 1.42681 0.1309 1.42354 1.42048 318.15 K 1.45150 0.0630 1.44836 0.1125 1.44521 0.1578 1.44184 0.1976 1.43833 0.2284 1.43502 0.2419 1.43162 0.2405 1.42833 0.2053 1.42482 0.1306 1.42146 1.41835 323.15 K 1.44985 0.0637 1.44662 0.1140 1.44340 0.1598 1.44002 0.1963 1.43640 0.2330 1.43312 0.2467 1.42961 0.2459 1.42634 0.2056 1.42278 0.1398 1.41940 1.41631 Dimethyl Adipate (1) + PEG 400 (2) 288.15 K 1.46869 0.0110 1.46646 0.0205 1.46430 0.0313 1.46202 0.0458 1.45933 0.0622 1.45633 0.0776 1.45291 0.0920 1.44871 0.0860 1.44391 0.0608 1.43800 1.43082 293.15 K 1.46687 0.0120 1.46467 0.0246 1.46251 0.0393 1.46018 0.0566 1.45745 0.0752 1.45440 0.0865 1.45094 0.0998 1.44674 1913

ΔnD −0.0002

η/mPa·s 2.9430 2.3660

Δη/mPa·s −2.2880

0.0002 0.0004 0.0003 0.0001 0.0001 0.0000 0.0001 −0.0002 −0.0002

25.011 19.518 15.116 11.593 8.8956 6.9251 5.4610 4.2019 3.2679 2.6439 2.1434

−3.2040 −5.3192 −6.5646 −6.9592 −6.6544 −5.8294 −4.8041 −3.4536 −1.7954

0.0002 0.0003 0.0003 0.0001 0.0001 0.0000 0.0000 −0.0002 −0.0002

20.532 16.184 12.661 9.8187 7.6175 5.9922 4.8432 3.7171 2.9248 2.3917 1.9532

−2.4883 −4.1534 −5.1452 −5.4756 −5.2523 −4.5415 −3.8116 −2.7479 −1.4268

0.0001 0.0003 0.0002 0.0000 0.0000 −0.0001 0.0000 −0.0002 −0.0003

17.079 13.598 10.700 8.4067 6.5895 5.2343 4.2747 3.3135 2.6369 2.1771 1.7939

−1.9510 −3.3205 −4.0914 −4.3694 −4.2037 −3.6332 −3.0675 −2.2171 −1.1514

0.0016 0.0032 0.0047 0.0058 0.0066 0.0069 0.0065 0.0055 0.0034 0.0016 0.0032

162.62 135.70 110.84 84.741 65.206 47.197 32.588 21.523 13.041 7.3661 3.7777

0.0016 0.0033 0.0048 0.0058 0.0066 0.0069 0.0066

120.17 100.42 81.760 65.402 49.690 36.639 25.681 17.310

−10.955 −19.932 −30.210 −33.845 −35.970 −34.727 −29.892 −22.521 −12.423

−8.0072 −14.9802 −19.699 −23.713 −25.079 −24.375 −21.049



Article


10−3·ρ/kg·m−3

106·VE/m3·mol−1

0.7999 0.8992 1

1.084009 1.074101 1.061920

0.0934 0.0642

0 0.1005 0.2005 0.3001 0.4002 0.5002 0.6000 0.7001 0.7999 0.8992 1

1.122120 1.118876 1.115260 1.111192 1.106537 1.101198 1.095057 1.087829 1.079379 1.069359 1.057047

0.0145 0.0285 0.0439 0.0615 0.0802 0.0919 0.1053 0.0973 0.0669

0 0.1005 0.2005 0.3001 0.4002 0.5002 0.6000 0.7001 0.7999 0.8992 1

1.118024 1.114742 1.111080 1.106958 1.102241 1.096834 1.090621 1.083311 1.074760 1.064628 1.052176

0.0137 0.0280 0.0447 0.0634 0.0830 0.0943 0.1070 0.0992 0.0676

0 0.1005 0.2005 0.3001 0.4002 0.5002 0.6000 0.7001 0.7999 0.8992 1

1.113925 1.110605 1.106899 1.102729 1.097958 1.092488 1.086198 1.078801 1.070151 1.059897 1.047295

0.0127 0.0265 0.0424 0.0608 0.0802 0.0924 0.1056 0.0977 0.0668

0 0.1005 0.2005 0.3001 0.4002 0.5002 0.6000 0.7001 0.7999 0.8992 1

1.109835 1.106478 1.102730 1.098511 1.093684 1.088150 1.081787 1.074304 1.065552 1.055172 1.042410

0.0112 0.0239 0.0392 0.0572 0.0763 0.0883 0.1017 0.0942 0.0647

0 0.1005 0.2005 0.3001 0.4002 0.5002 0.6000 0.7001

1.105750 1.102352 1.098564 1.094302 1.089424 1.083831 1.077387 1.069814

0.0107 0.0213 0.0343 0.0503 0.0681 0.0817 0.0959

nD 293.15 K 1.44192 1.43597 1.42876 298.15 K 1.46508 1.46287 1.46079 1.45838 1.45559 1.45250 1.44896 1.44473 1.43992 1.43395 1.42669 303.15 K 1.46328 1.46111 1.45896 1.45658 1.45375 1.45064 1.44705 1.44273 1.43788 1.43188 1.42463 308.15 K 1.46150 1.45938 1.45714 1.45480 1.45194 1.44880 1.44518 1.44080 1.43585 1.42984 1.42255 313.15 K 1.45971 1.45764 1.45540 1.45300 1.45009 1.44693 1.44332 1.43891 1.43391 1.42786 1.42048 318.15 K 1.45791 1.45591 1.45364 1.45115 1.44822 1.44504 1.44142 1.43697 1914

ΔnD 0.0055 0.0034

η/mPa·s

Δη/mPa·s

10.802 6.2675 3.3132

−15.894 −8.8249

0.0017 0.0034 0.0048 0.0059 0.0066 0.0069 0.0065 0.0055 0.0034

91.024 76.538 62.869 50.938 38.971 29.113 20.882 14.296 9.0848 5.4022 2.9370

−5.6331 −10.494 −13.651 −16.801 −17.850 −17.290 −15.058 −11.478 −6.4140

0.0017 0.0034 0.0049 0.0059 0.0067 0.0070 0.0065 0.0055 0.0034

70.444 59.655 49.350 40.000 31.281 23.682 17.154 11.935 7.7343 4.7000 2.6289

−3.9733 −7.4971 −10.093 −12.023 −12.841 −12.601 −11.032 −8.4644 −4.7647

0.0018 0.0035 0.0050 0.0060 0.0068 0.0071 0.0066 0.0055 0.0034

55.592 47.386 39.464 32.269 25.442 19.480 14.300 10.094 6.7244 4.1310 2.3660

−2.8571 −5.4562 −7.3499 −8.8488 −9.4884 −9.3564 −8.2345 −6.2921 −3.6002

0.0019 0.0036 0.0051 0.0061 0.0068 0.0072 0.0067 0.0056 0.0034

44.624 38.228 32.061 26.458 21.000 16.248 12.074 8.6454 5.8537 3.6645 2.1434

−2.1268 −4.0456 −5.4176 −6.6234 −7.1272 −7.0616 −6.2379 −4.7901 −2.7609

0.0020 0.0037 0.0051 0.0061 0.0069 0.0073 0.0068

36.381 31.310 26.438 22.142 17.582 13.738 10.317 7.4853

−1.6109 −3.0402 −3.9072 −5.0208 −5.4222 −5.4073 −4.7928



Article


10−3·ρ/kg·m−3

0.7999 0.8992 1

1.060961 1.050448 1.037519

0 0.1005 0.2005 0.3001 0.4002 0.5002 0.6000 0.7001 0.7999 0.8992 1

1.101669 1.098231 1.094406 1.090104 1.085179 1.079526 1.072997 1.065337 1.056375 1.045717 1.032622

0 0.1001 0.2002 0.3000 0.4000 0.5000 0.5993 0.7000 0.7995 0.8997 1

1.128814 1.135357 1.141982 1.148514 1.154946 1.161309 1.167663 1.174282 1.181134 1.188452 1.196234

0 0.1001 0.2002 0.3000 0.4000 0.5000 0.5993 0.7000 0.7995 0.8997 1

1.124834 1.131282 1.137815 1.144264 1.15062 1.156914 1.163203 1.169758 1.176541 1.183806 1.191543

0 0.1001 0.2002 0.3000 0.4000 0.5000 0.5993 0.7000 0.7995 0.8997 1

1.120856 1.127203 1.133649 1.140019 1.146300 1.152521 1.158740 1.165226 1.171953 1.179164 1.186865

0 0.1001 0.2002 0.3000 0.4000 0.5000 0.5993

1.116876 1.123134 1.129492 1.135780 1.141985 1.148135 1.154287

106·VE/m3·mol−1

nD

ΔnD

318.15 K 0.0885 1.43192 0.0057 0.0615 1.42581 0.0035 1.41835 323.15 K 1.45612 0.0096 1.45412 0.0020 0.0172 1.45185 0.0037 0.0267 1.44933 0.0052 0.0397 1.44635 0.0062 0.0563 1.44315 0.0069 0.0724 1.43944 0.0072 0.0869 1.43497 0.0067 0.0811 1.42989 0.0056 0.0587 1.42377 0.0035 1.41631 Dimethyl Phthalate (1) + PEG 200 (2) 288.15 K 1.46180 −0.0476 1.46734 0.0000 −0.0901 1.47275 −0.0001 −0.1039 1.47807 −0.0003 −0.0840 1.48341 −0.0005 −0.0378 1.48869 −0.0008 0.0184 1.49403 −0.0009 0.0661 1.49957 −0.0009 0.0857 1.50518 −0.0008 0.0646 1.51101 −0.0005 1.51708 293.15 K 1.46007 −0.0430 1.46554 −0.0000 −0.0817 1.47091 −0.0001 −0.0933 1.4762 −0.0003 −0.0723 1.48151 −0.0005 −0.0261 1.48676 −0.0007 0.02951 1.49207 −0.0009 0.0761 1.49756 −0.0009 0.0947 1.50312 −0.0008 0.0699 1.50891 −0.0005 1.51494 298.15 K 1.45832 −0.0373 1.46376 −0.0000 −0.0729 1.46910 −0.0001 −0.0826 1.47436 −0.0003 −0.0604 1.47963 −0.0005 −0.0134 1.48487 −0.0007 0.0424 1.49014 −0.0009 0.0886 1.49558 −0.0009 0.1046 1.50110 −0.0008 0.0764 1.50685 −0.0005 1.51286 303.15 K 1.45661 −0.0331 1.46200 −0.0000 −0.0651 1.46731 −0.0002 −0.0723 1.47256 −0.0003 −0.0485 1.47778 −0.0005 −0.0007 1.48302 −0.0007 0.0551 1.48825 −0.0009 1915

η/mPa·s 5.1430 3.2728 1.9532

Δη/mPa·s −3.6992 −2.1507

30.073 25.993 22.084 18.374 14.935 11.826 8.9738 6.5914 4.6047 2.9652 1.7939

−1.2378 −2.3190 −3.2124 −3.8202 −4.1018 −4.1317 −3.6834 −2.8479 −1.6792

86.351 83.525 77.094 69.131 60.797 52.717 45.174 38.091 31.562 26.607 23.526

3.4631 3.3206 1.6278 −0.4242 −2.2213 −3.5260 −4.2823 −4.5604 −3.2204

64.712 62.132 57.014 50.897 44.643 38.701 33.258 28.210 23.520 20.033 17.704

2.1252 1.7130 0.2877 −1.2659 −2.5067 −3.2821 −3.5965 −3.6091 −2.3859

49.610 46.722 42.768 38.315 33.724 29.255 25.104 21.311 18.080 15.545 13.928

0.6834 0.30154 −0.5903 −1.6137 −2.5140 −3.1218 −3.3213 −3.0022 −1.9619

38.801 36.774 33.472 29.762 26.113 22.738 19.694

0.7408 0.2063 −0.7448 −1.6285 −2.2383 −2.5370



Article


10−3·ρ/kg·m−3

0.7000 0.7995 0.8997 1

1.160709 1.167373 1.174535 1.182202

0 0.1001 0.2002 0.3000 0.4000 0.5000 0.5993 0.7000 0.7995 0.8997 1

1.112888 1.119066 1.125339 1.131544 1.13767 1.143748 1.149835 1.156197 1.162800 1.169918 1.177547

0 0.1001 0.2002 0.3000 0.4000 0.5000 0.5993 0.7000 0.7995 0.8997 1

1.108901 1.114997 1.121187 1.127312 1.133364 1.139372 1.145394 1.151692 1.158235 1.165308 1.172909

0 0.1001 0.2002 0.3000 0.4000 0.5000 0.5993 0.7000 0.7995 0.8997 1

1.104912 1.110939 1.117044 1.123084 1.129058 1.134997 1.140957 1.147197 1.153674 1.160707 1.168277

0 0.1001 0.2002 0.3000 0.4000 0.5000 0.5993 0.7000 0.7995 0.8997 1

1.100921 1.106873 1.112901 1.118864 1.124761 1.130627 1.13652 1.142701 1.149123 1.156121 1.163654

0 0.1000 0.2005 0.2997 0.4004 0.5000

1.130306 1.134035 1.138020 1.142420 1.147300 1.152786

106·VE/m3·mol−1

nD

ΔnD

303.15 K 0.1004 1.49366 −0.0009 0.1151 1.49914 −0.0008 0.0830 1.50485 −0.0005 1.51083 308.15 K 1.45488 −0.0301 1.46023 −0.0001 −0.0586 1.46551 −0.0002 −0.0627 1.47074 −0.0003 −0.0367 1.47599 −0.0005 0.0122 1.48116 −0.0007 0.0680 1.48638 −0.0008 0.1122 1.49177 −0.0009 0.1255 1.49722 −0.0008 0.0888 1.50290 −0.0005 1.50885 313.15 K 1.45317 −0.0265 1.45844 −0.0001 −0.0517 1.46369 −0.0002 −0.0530 1.46890 −0.0004 −0.0251 1.47415 −0.0005 0.0248 1.47931 −0.0007 0.0810 1.48451 −0.0009 0.1247 1.48986 −0.0009 0.1367 1.49528 −0.0008 0.0960 1.50095 −0.0006 1.50693 318.15 K 1.45150 −0.0250 1.45667 −0.0002 −0.0461 1.46187 −0.0004 −0.0436 1.46705 −0.0005 −0.0131 1.47225 −0.0007 0.0379 1.47739 −0.0009 0.0939 1.48254 −0.0011 0.1365 1.48785 −0.0012 0.1482 1.49326 −0.0011 0.1026 1.49896 −0.0007 1.50507 323.15 K 1.44985 −0.0222 1.45491 −0.0003 −0.0405 1.46006 −0.0004 −0.0351 1.46521 −0.0006 −0.0021 1.47038 −0.0007 0.0509 1.47549 −0.0009 0.1076 1.48062 −0.0011 0.1494 1.48588 −0.0012 0.1593 1.49123 −0.0011 0.1083 1.49692 −0.0008 1.50303 Dimethyl Phthalate (1) + PEG 400 (2) 288.15 K 1.46869 −0.1568 1.47114 −0.0024 −0.2529 1.47427 −0.0041 −0.3362 1.47739 −0.0058 −0.3707 1.48094 −0.0071 −0.3915 1.48515 −0.0077 1916

η/mPa·s

Δη/mPa·s

16.892 14.261 12.370 11.152

−2.5549 −2.4346 −1.5552

30.902 29.207 26.485 23.508 20.645 18.053 15.744 13.603 11.498 10.057 9.1230

0.48468 −0.0568 −0.8604 −1.5454 −1.9595 −2.1059 −2.0538 −1.9917 −1.2504

25.001 23.536 21.351 18.974 16.667 14.562 12.693 11.000 9.4493 8.3302 7.6118

0.2761 −0.1687 −0.8105 −1.3780 −1.7444 −1.8867 −1.8282 −1.6490 −1.0257

20.532 19.424 17.591 15.572 13.652 11.947 10.472 9.1460 7.8928 7.0109 6.4530

0.3015 −0.1224 −0.7360 −1.2488 −1.5457 −1.6225 −1.5308 −1.3830 −0.8542

17.079 15.901 14.449 12.926 11.447 10.073 8.8346 7.7150 6.7412 6.0286 5.5783

−0.0269 −0.3276 −0.7029 −1.0315 −1.2554 −1.3520 −1.3135 −1.1430 −0.7032

162.62 155.51 149.57 142.52 132.55 119.05

6.7992 14.835 21.586 25.623 25.978



Article


10−3·ρ/kg·m−3

106·VE/m3·mol−1 −0.3743 −0.3282 −0.2108 −0.0959

0.5997 0.7002 0.7999 0.8999 1

1.158974 1.166147 1.174202 1.183993 1.196234

0 0.1000 0.2005 0.2997 0.4004 0.5000 0.5997 0.7002 0.7999 0.8999 1

1.126215 1.129891 1.133831 1.138186 1.143020 1.148482 1.154571 1.161686 1.169677 1.179338 1.191543

−0.1508 −0.2442 −0.3263 −0.3609 −0.3879 −0.3621 −0.3184 −0.2038 −0.0836

0 0.1000 0.2005 0.2997 0.4004 0.5000 0.5997 0.7002 0.7999 0.8999 1

1.12212 1.125741 1.129642 1.133954 1.138735 1.144137 1.150178 1.157229 1.165151 1.174776 1.186865

−0.1435 −0.2360 −0.3172 −0.3497 −0.3746 −0.3512 −0.3084 −0.1953 −0.0843

0 0.1000 0.2005 0.2997 0.4004 0.5000 0.5997 0.7002 0.7999 0.8999 1

1.118024 1.121614 1.125456 1.129724 1.134459 1.139778 1.145793 1.152775 1.160638 1.170223 1.182202

−0.1432 −0.2283 −0.3080 −0.3399 −0.3572 −0.3408 −0.2974 −0.1873 −0.0843

0 0.1000 0.2005 0.2997 0.4004 0.5000 0.5997 0.7002 0.7999 0.8999 1

1.113925 1.117485 1.121285 1.125510 1.130191 1.135456 1.141418 1.148335 1.156133 1.165648 1.177547

−0.1432 −0.2254 −0.3034 −0.3321 −0.3479 −0.3320 −0.2885 −0.1800 −0.0801

0 0.1000 0.2005 0.2997 0.4004 0.5000

1.109835 1.113360 1.117122 1.121301 1.125937 1.131148

−0.1414 −0.2219 −0.2972 −0.3250 −0.3391

nD 288.15 K 1.48969 1.49484 1.50088 1.50805 1.51708 293.15 K 1.46687 1.46930 1.47240 1.47550 1.47904 1.48325 1.48775 1.49288 1.49888 1.50599 1.51494 298.15 K 1.46508 1.46749 1.47055 1.47365 1.47717 1.48129 1.48583 1.49096 1.49692 1.50398 1.51286 303.15 K 1.46328 1.46565 1.46869 1.47178 1.47530 1.47945 1.48393 1.48907 1.49497 1.50202 1.51083 308.15 K 1.46150 1.46382 1.46684 1.46990 1.47344 1.47758 1.48202 1.48720 1.49302 1.50011 1.50885 313.15 K 1.45971 1.46201 1.46497 1.46803 1.47154 1.47563 1917

ΔnD

η/mPa·s

Δη/mPa·s

−0.0080 −0.0077 −0.0065 −0.0042

101.88 81.744 60.849 39.830 23.526

22.675 16.518 9.4903 2.3807

−0.0024 −0.0041 −0.0058 −0.0071 −0.0077 −0.0080 −0.0076 −0.0064 −0.0041

120.17 114.46 109.42 103.61 95.828 85.706 73.182 58.782 44.055 29.141 17.704

4.5336 9.7959 14.149 16.685 16.769 14.461 10.359 5.8476 1.1802

−0.0024 −0.0041 −0.0058 −0.0070 −0.0077 −0.0079 −0.0076 −0.0064 −0.0041

91.024 86.449 82.223 77.421 71.277 63.528 54.001 43.668 32.974 22.181 13.928

3.1348 6.6565 9.5027 11.122 11.052 9.2115 6.6266 3.6191 0.5357

−0.0024 −0.0041 −0.0058 −0.0070 −0.0076 −0.0079 −0.0075 −0.0063 −0.0040

70.444 66.759 63.243 59.267 54.401 48.371 41.280 33.364 25.397 17.462 11.152

2.2444 4.6875 6.5928 7.6975 7.5731 6.3934 4.4363 2.3807 0.3749

−0.0024 −0.0042 −0.0058 −0.0070 −0.0076 −0.0079 −0.0075 −0.0064 −0.0040

55.592 52.581 49.648 46.357 42.482 37.690 32.205 26.121 20.043 13.976 9.1230

1.6356 3.3734 4.6918 5.4962 5.3322 4.4805 3.0666 1.6216 0.2015

−0.0024 −0.0042 −0.0058 −0.0071 −0.0077

44.624 42.101 39.653 36.963 33.815 29.998

1.1782 2.4501 3.4316 4.0107 3.8800



Article

Table 3. continued 10−3·ρ/kg·m−3

x1

106·VE/m3·mol−1 −0.3219 −0.2787 −0.1719 −0.0751

0.5997 0.7002 0.7999 0.8999 1

1.137050 1.143904 1.151639 1.161085 1.172909

0 0.1000 0.2005 0.2997 0.4004 0.5000 0.5997 0.7002 0.7999 0.8999 1

1.10575 1.109255 1.112976 1.117101 1.121689 1.126853 1.132695 1.139484 1.147152 1.156511 1.168277

−0.1442 −0.2218 −0.2920 −0.3179 −0.3320 −0.3134 −0.2698 −0.1640 −0.0676

0 0.1000 0.2005 0.2997 0.4004 0.5000 0.5997 0.7002 0.7999 0.8999 1

1.101669 1.105135 1.108837 1.112919 1.117455 1.122572 1.128348 1.135077 1.142675 1.151958 1.163654

−0.1412 −0.2224 −0.2903 −0.3130 −0.3270 −0.3051 −0.2620 −0.1565 −0.0618

nD 313.15 K 1.48008 1.48530 1.49116 1.49821 1.50693 318.15 K 1.45791 1.46018 1.46314 1.46617 1.46964 1.47372 1.47814 1.48332 1.48916 1.49621 1.50507 323.15 K 1.45612 1.45841 1.46132 1.46433 1.46775 1.47177 1.47620 1.48134 1.48720 1.49418 1.50303

ΔnD

η/mPa·s

−0.0079 −0.0075 −0.0063 −0.0040

25.657 20.885 16.153 11.414 7.6118

Δη/mPa·s 3.2292 2.1769 1.1351 0.0973

−0.0025 −0.0042 −0.0059 −0.0072 −0.0078 −0.0081 −0.0076 −0.0065 −0.0041

36.381 34.260 32.206 29.974 27.404 24.311 20.820 17.011 13.264 9.4857 6.4530

0.8722 1.8257 2.5624 3.0062 2.8936 2.3868 1.5856 0.8224 0.0369

−0.0024 −0.0042 −0.0059 −0.0072 −0.0078 −0.0081 −0.0076 −0.0065 −0.0042

30.073 28.427 26.741 24.859 22.704 20.136 17.282 14.172 11.122 8.0590 5.5783

0.8034 1.5795 2.1271 2.4387 2.3103 1.8985 1.2502 0.6423 0.0288

a x1 is the mole fraction of dimethyl adipate/dimethyl phthalate. Standard uncertainties u for each variables are u(T) = 0.01 K; u(p) = 5 %; u(x1) = 0.0001, and the combined expanded uncertainties Uc are Uc(ρ) = 4·10−2 kg·m−3, Uc(nD) = 9·10−5, and Uc(η) = 1.0 %, with a 0.95 level of confidence (k ≈ 2).

The fitting parameters and the corresponding root-meansquare deviations (rmsd) σ, defined by

The viscosity deviations Δη were calculated from the viscosity of the mixture η and pure component i, ηi according to the equation:

m

σ = (∑ (Yexp − Ycal)2 /m)1/2

n

Δη = η −

∑ xiηi

i=1

(2)

i=1

are given in Table 4 for excess molar volume VE, viscosity deviation Δη, and deviation in refractive index ΔnD. In eq 5, m is the number of experimental data points. Excess molar volumes, obtained from experimental data and plotted against the x1 mole fraction along with the results obtained using Redlich−Kister equation are shown in Figure 1. Mixtures of DMA with PEG200 or PEG400 show volume expansion and positive VE values. The curves of both systems are asymmetrical and shifted toward higher DMA mole fractions. For the DMA (1) + PEG 200 (2) system, a maximum of VE vs x1 occurs at x1 = 0.6, while for the system DMA (1) + PEG 400 (2) maximum is located around x1 = 0.7. The system DMP (1) + PEG200 (2) has the S-shaped curve (at x1 = 0.3 and x1 = 0.8 VE exhibits a minimum and maximum, respectively). The system DMP (1) + PEG 400 (2) is characterized with negative VE values; the minimum of the curve lies at equimolar composition, but the curve is slightly Sshaped in the DMP-rich region. With increasing temperature VE values increase for the system DMA (1) + PEG 200 (2). For system containing PEG 400 (Figure 1b) VE values decrease as temperature increases at

The deviations in refractive index ΔnD were calculated from the equation: n

ΔnD = nD −

∑ xinDi

(3)

i=1

where nD and nDi refer to the refractive index of a mixture and a pure component i, respectively. In all the above given equations n denotes the number of components. Excess molar volumes VE, viscosity deviations Δη and deviations in refractive index ΔnD were correlated with the Redlich−Kister (RK) equation:20 k

Y = xixj

∑ A p(2xi − 1)p (4)

p=0

(5)

E

where Y represents the binary excess molar volume V , viscosity deviation Δη or deviation in refractive index ΔnD of the mixture, Ap are fitting parameters, and k + 1 is the number of parameters, which was optimized using the F-test. 1918



Article

Table 4. Parameters Ap of eq 4 and the Corresponding rmsd σ for the Binary Mixtures at Temperature T T/K 106·VE/m3·mol−1

Δη/mPa·s

106·VE/m3·mol−1

ΔnD

Δη/mPa·s

106·VE/m3·mol−1

ΔnD

Δη/mPa·s

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15

A0

A1

Dimethyl Adipate (1) + PEG 200 (2) 0.7974 0.3891 0.8105 0.4151 0.8271 0.4281 0.8473 0.4513 0.8698 0.4651 0.8874 0.4793 0.9106 0.4844 0.9316 0.4756 −111.66 52.735 −80.595 36.366 −59.567 26.005 −44.753 18.623 −34.192 13.682 −26.601 9.9943 −20.978 7.5365 −16.834 5.9330 Dimethyl Adipate (1) + PEG 400 (2) 0.2478 0.3419 0.2999 0.3595 0.3197 0.3599 0.3312 0.3717 0.3199 0.3716 0.3043 0.3678 0.2713 0.3507 0.2240 0.3393 0.0264 0.0119 0.0265 0.0115 0.0265 0.0109 0.0268 0.0106 0.0272 0.0107 0.0274 0.0106 0.0277 0.0104 0.0277 0.0099 −143.77 −9.1248 −100.33 −5.4104 −71.329 −5.1715 −51.360 −5.4082 −37.971 −4.7396 −28.528 −4.1634 −21.683 −3.5087 −16.524 −2.8871 Dimethyl Phthalate (1) + PEG 200 (2) −0.1512 1.0908 −0.1042 1.0834 −0.0535 1.0951 −0.0029 1.1019 0.0487 1.1128 0.0994 1.1267 0.1516 1.1343 0.2035 1.1628 −0.0030 −0.0036 −0.0030 −0.0035 −0.0029 −0.0036 −0.0028 −0.0035 −0.0028 −0.0033 −0.0030 −0.0033 −0.0036 −0.0038 −0.0038 −0.0036 −8.8854 −31.451 −10.027 −20.393 1919

A2

A3

102·σ

0.1950 0.2636 0.2985 0.3199 0.2927 0.2807 0.2328 0.1902 −15.872 −10.041 −6.8603 −4.4319 −3.0782 −1.8959 −1.3177 −0.9809

0.0027 0.0020 0.0026 0.0025 0.0020 0.0017 0.0017 0.0028 0.1147 0.0734 0.0906 0.0772 0.0659 0.0622 0.0720 0.0618

0.2342 0.1894 0.2035 0.1830 0.1875 0.1794 0.1982 0.2384 0.0018 0.0024 0.0035 0.0027 0.0023 0.0031 0.0038 0.0038 23.966 11.646 7.6490 4.8342 4.0388 2.6231 1.6596 0.8211

0.0024 0.0033 0.0030 0.0034 0.0030 0.0030 0.0025 0.0025 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.9118 0.2811 0.3236 0.0625 0.0655 0.0747 0.1513 0.0292

0.3824 0.3957 0.4235 0.4368 0.4323 0.4464 0.4356 0.4280 0.0003 0.0000 −0.0004 −0.0006 −0.0007 −0.0014 −0.0025 −0.0031 16.032 13.429

−0.4904 −0.4701 −0.4783 −0.4640 −0.4509 −0.4336 −0.3906 −0.4034

−23.301 −17.040

0.0001 0.0008 0.0002 0.0006 0.0015 0.0019 0.0034 0.0043 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.2356 0.2290



Article

Table 4. continued T/K 298.15 303.15 308.15 313.15 318.15 323.15 106·VE/m3·mol−1

ΔnD

Δη/mPa·s

288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15

A0

A1

Dimethyl Phthalate (1) + PEG 200 (2) −10.056 −15.558 −8.9534 −9.0338 −7.8379 −5.4597 −6.9976 −5.0438 −6.1828 −3.6441 −5.0215 −3.2450 Dimethyl Phthalate (1) + PEG 400 (2) −1.5658 −0.0337 −1.5516 −0.0738 −1.4985 −0.0443 −1.4290 −0.0400 −1.3918 −0.0235 −1.3566 −0.0006 −1.3281 −0.0028 −1.3078 0.0821 −0.0309 −0.0117 −0.0306 −0.0115 −0.0307 −0.0111 −0.0304 −0.0109 −0.0304 −0.0108 −0.0308 −0.0103 −0.0311 −0.0110 −0.0312 −0.0111 103.91 −30.124 67.076 −22.577 44.210 −17.101 30.292 −12.971 21.329 −9.8629 15.520 −7.4840 11.574 −5.7852 9.2410 −5.2380

A3

102·σ

4.6407 6.8556 5.6217 4.3193 4.9109 1.3792

−4.3594 −10.881 −10.273 −6.1872 −6.7905 −2.4343

0.0132 0.1518 0.1807 0.0796 0.0906 0.0276

0.2534 0.3903 0.3650 0.2587 0.2372 0.2411 0.2374 0.2813 −0.0078 −0.0077 −0.0069 −0.0074 −0.0079 −0.0070 −0.0076 −0.0067 −81.977 −54.318 −36.031 −24.581 −17.259 −13.150 −10.174 −7.0383

0.7149 0.8454 0.7134 0.7025 0.7234 0.7208 0.8367 0.7342

0.0108 0.0104 0.0103 0.0107 0.0110 0.0107 0.0097 0.0101 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.2776 0.2441 0.2197 0.1155 0.0966 0.0799 0.0714 0.0492

A2

show very small positive or negative deviations from ideal behavior. ΔnD values are not presented for the system DMA (1) + PEG 200 (2) as they almost equal to zero. The system DMA (1) + PEG 400 (2) is positive, while both systems with DMP show negative refractive index deviations. In all cases ΔnD vs x1 curves are shifted toward higher DMA or DMP mole fractions. As it is well-known, positive or negative deviations from ideal behavior can be attributed to hydrogen bonding or dipole− dipole interactions between compounds or to geometrical packing between molecules in a mixture.33 To reveal which of the mentioned factors is dominant FT-IR analysis is performed for the pure components and for the selected compositions of the analyzed binary mixtures (Figure 4). Self-association through hydrogen bonding of the investigated esters (DMA and DMP) is not possible since they only act as proton acceptors.34 On the other hand, one of the hydrogen atoms from polyethylene glycol can be attracted to one of the lone pairs on oxygen atoms in an ester but also can form intra- and intermolecular hydrogen bonds within or between PEG molecules. Besides, all of the analyzed compounds have notable polar nature: the dimethyl phthalate35 and dimethyl adipate36 dipole moments are 9.34·10−30 and 7.34·10−30 C·m, respectively, while those of PEG 200 and PEG 400 are 1.02·10−29 to 1.3·10−29 and 1.23·10−29 to 1.65·10−29 C· m, respectively.37 Consequently, dispersion forces and dipole−

higher temperatures, while that trend is disrupted for (288.15, 293.15, and 298.15) K. For the DMP (1) + PEG 200 (2) system, absolute VE values decrease as temperature increases, in minima region. On the contrary, positive VE values are getting higher as temperature increases in the PEG 200 rich region. For the system DMP (1) + PEG 400 (2) absolute VE values decrease with increasing temperature from (288.15 to 323.15) K. The viscosity deviations are presented in Figure 2. For the systems with DMA (Figure 2a and b), Δη values are negative. Viscosity deviations are positive for the binary DMP (1) + PEG 400 (2) mixture (Figure 2d), while for the system DMP (1) + PEG 200 (2) (Figure 2c) the Δη vs x1 curve changes sign from positive (maximum at x1 = 0.1) to negative (minimum around x1 = 0.7). An exception is obtained for the highest temperature, 323.15 K, where Δη values are negative over the entire concentration range. For two systems containing PEG 400 curves are symmetrical, while for DMA (1) + PEG 200 (2) mixture minimum of the curve is shifted toward lower DMA mole fractions (minimum at x1 = 0.4). The temperature effect for all investigated binary mixtures shows the same trend, with increasing temperature from (288.15 to 323.15) K absolute values of viscosity deviations decrease. The deviations of refractive indices ΔnD for the investigated systems are presented in Figure 3. Bearing in mind that the temperature influence on ΔnD for these systems is negligible, data are given only for the temperature 303.15 K. These values 1920



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Figure 1. Experimental excess molar volumes VE for the systems: (a) DMA (1) + PEG 200 (2); (b) DMA (1) + PEG 400 (2); (c) DMP (1) + PEG 200 (2); (d) DMP (1) + PEG 400 (2); where x1 denotes mole fraction of DMA or DMP at following temperatures: ◇, 288.15 K; ◆, 293.15 K; ○, 298.15 K; ●, 303.15 K; △, 308.15 K; ▲, 313.15 K; □, 318.15 K; ■, 323.15 K; , RK equation.

attached to a carbonyl group; (c) strong CO stretching band ν(CO) (1740 cm−1) absorbs at higher frequencies than in ketones because the −I effect of the oxygen atom from the -OCH3 group increases the electron density of the CO bond as well as ν(CO) frequency; (d) C−O stretching bands νas(C−O) (1173, 1200, and 1252 cm−1) are very intensive. In DMP following bands are characteristic: (a) C−H stretching bands from CH3 groups attached to the carbonyl group νs(CH) (2844 cm−1) and νas(CH) (2955 cm−1) are less intensive comparing to the bands in DMA, especially νs(CH). C−H band from benzene ring ν(CH) (3003 cm−1) has also very poor intensity as well as the CC band ν(CC) (1580 and 1600 cm−1); (b) C−H bending γ(C−H) (747 cm−1) is in a good agreement with frequency values for 1,2-disubstituted aromatic compounds (770−735 cm−1). C−H bending from CH3 groups δs(C−H) (1289 cm−1) and δas(C−H) (1435 cm−1) have lower frequencies because CH3 groups are attached to the carbonyl group; (c) CO stretching band ν(CO) (1731 cm−1) is slightly shifted comparing to DMA spectra because conjugation of ester carbonyl group decreases electron density of the CO bond as well as the ν(CO) frequency; (d) C−O stretching bands νas(C−O) (1076, 1126, and 1193 cm−1) are intensive. Figure 4a compares the infrared spectra for the binary mixture DMA (1) + PEG 200 (2) at x1 = 0.6 (maximum in VE vs x1 curve) with those of the pure components, at 298.15 K. Since DMA acts only as hydrogen bond acceptor selfassociation through hydrogen bonding is excluded. Contrarily,

dipole interactions between ester and polymer molecules are possible. Inspection of Figure 4 shows that for the pure PEG following bands are of greater importance: (a) two C−H stretching bands close to each other νs(CH) (2873 cm−1) and a shoulder νas(CH) (∼2941 cm−1) in CH2 groupfrequencies are slightly higher than it is expected for the C−H bond from CH2 group in saturated compounds because of the presence of electronegative C−O bond; (b) C−H scissoring band δscissoring(CH) (1454 cm−1); (c) C−O stretching band νas(C−O) (∼1123 cm−1 for PEG 200 and 1112 cm−1 for PEG 400) which is very intensive and easy to notice but also influenced by adjacent C− C bond; (d) stretching OH band ν(OH) (3408 cm−1 for PEG 200 and 3443 cm−1 for PEG 400) whose frequency highly depends on hydrogen bonds between or within PEG molecules. Stronger hydrogen bonds lead to lower ν(OH) frequencies and higher band intensity, so from these assumptions one can conclude that stronger hydrogen bonds are present in PEG 200 molecules. Detailed explanation of the influence of the PEG chain length on the IR spectra can be found in the literature.37 For esters, characteristic CO and C−O bands are the most intensive so for DMA following observations are made: (a) C− H stretching bands from CH2 and CH3 groups νs(CH) (2872 cm−1) and νas(CH) (2953 cm−1) have low intensity; (b) scissoring C−H band in CH2 group (1367 cm−1) and C−H bending in CH3 group (1439 cm−1) have slightly lower frequencies than expected because these groups are directly 1921



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Figure 2. Experimental deviations in dynamic viscosities Δη for the systems: (a) DMA (1) + PEG 200 (2); (b) DMA (1) + PEG 400 (2); (c) DMP (1) + PEG 200 (2); (d) DMP (1) + PEG 400 (2), where x1 denotes mole fraction of DMA or DMP at following temperatures: ◊, 288.15 K; ⧫, 293.15 K; ○, 298.15 K; ●, 303.15 K; △, 308.15 K; ▲, 313.15 K; □, 318.15 K; ■, 323.15 K; , RK equation.

wavenumber (3456 cm−1) in the mixture, showing a peak of less intensity, comparing to the pure PEG 200. This is the socalled blueshift indicating contraction of the OH bond confirming absence of new heteromolecular interactions that would cause volume contraction, which is in accordance with positive VE values. Also, stretching corresponding to the CO and C−O−C bonds shows no shift comparing to the pure DMA and PEG 200. Viscosity deviations are negative for this system which corresponds to a binary system where dispersion forces predominate.38 Similar behavior is noticed for the DMA (1) + PEG 400 (2) system. In Figure 4b the infrared spectra for the binary mixture DMA (1) + PEG 400 (2) at x1 = 0.7 with those of the pure components are presented. The OH stretching band (3463 cm−1) is not shifted, but the intensity of the peak is decreased comparing to pure PEG 400. The same can be concluded for the CO and C−O−C stretching (1737 and 1112 cm−1), no shift is present, but the intensity of the peaks decreases comparing to pure components. Taking into account positive excess volumes, negative viscosity deviations, and recorded IR spectra, it can be concluded that dispersion forces between compounds predominate for this mixture. Figure 4c shows a comparison of the IR spectra for the mixture DMP (1) + PEG 200 (2) at x1 = 0.3 and x1 = 0.8 with those of the pure components. Selected compositions correspond to the minimal and maximal VE values. OH stretching for the mixture

Figure 3. Experimental refractive index deviations ΔnD for the systems: ◊, DMA (1) + PEG 400 (2); ⧫, DMP (1) + PEG 200 (2) and △, DMP (1) + PEG 400 (2) where x1 denotes mole fraction of DMA or DMP at 303.15 K and , RK equation.

both intra- and intermolecular hydrogen bonding in a PEG molecules is possible. From the spectra it is obvious that the stretching corresponding to the OH group is shifted to a higher 1922



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Figure 4. Infrared spectra of: (a) pure DMA (blue), pure PEG 200 (yellow), and the mixture DMA + PEG 200 with xDMA = 0.6 (red); (b) pure DMA (blue), pure PEG400 (yellow), and the mixture DMA + PEG 400 with xDMA = 0.7 (red); (c) pure DMF (red), pure PEG 200 (green), the mixture DMF + PEG 200 with xDMA = 0.3 (blue) and xDMA = 0.8 (yellow); (d) pure DMF (blue), pure PEG 400 (yellow), and the mixture DMF + PEG 400 with xDMA = 0.5 (red).

kinetic energy is increased, and molecules become packed and more chaotic. Since molecules do not fit well, positive VE values increase slightly, while negative VE values become less negative at higher temperatures. Due to increase of kinetic energy, dispersion forces between molecules are weakened leading to decrease of viscosity deviations at higher temperatures.

rich in PEG 200 is shifted toward higher wave numbers (3450 cm−1) comparing to pure PEG 200, with decrease of the peak intensity. CO and C−O−C stretching (1737 and 1112 cm−1) remain unchanged, which indicates that these groups are not participating in chemical interactions. Taking into account negative VE values in PEG rich region (x1 = 0.3) and blueshift of the OH bond (followed by shortening of the OH bond) geometrical packing of DMP molecules (Vm = 163.61·10−6 m3· mol−1) into PEG 200 molecules (Vm = 178.44·10−6 m3·mol−1) is possible explanation for negative VE values. A similar spectroscopic study is obtained for the same mixture in DMP reach region (x1 = 0.8). There is a blueshift of the OH bond (∼3469 cm−1) with a decrease of the peak intensity comparing to the pure PEG 200. CO and C−O−C stretching (1737 and 1112 cm−1) remain unchanged. IR spectra for the mixture DMP (1) + PEG 400 (2) at x1 = 0.5 are presented in Figure 4d. OH (3465 cm−1), CO (1730 cm−1), and C−O−C (1112 cm−1) stretching in the mixture remain unchanged comparing to pure components. One can conclude that, in the absence of the intermolecular dipole−dipole interactions, geometrical packing of DMP (Vm = 163.61·10−6 m3·mol−1) molecules into the PEG 400 (Vm = 356.47·10−6 m3·mol−1) molecules contributes to the negative VE values. In all cases considering VE values, it can be concluded that packing effect is dominant. With increase of temperature,

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CONCLUSIONS In this work density ρ, viscosity η, and refractive index nD of the binary mixtures DMA + PEG 200 or PEG 400 and DMP + PEG 200 or PEG 400 were experimentally determined in the temperature range T = (288.15 to 323.15) K and at atmospheric pressure. From the experimental data excess molar volume VE and deviations Δη and ΔnD were calculated and fitted using RK polynomial. FT-IR analysis was performed at 298.15 K for all binary mixtures in order to determine possible effects of the constituents on the molecular structure of the mixtures. In the case of VE and Δη values, various trends are noticed, from positive to S-shaped curves. ΔnD deviations for all binary mixtures have very small values, especially for the system DMA + PEG 200. Due to reasonable polarity of the components and their ability to form hydrogen bonds, it was assumed that intermolecular hydrogen bonds between unlike molecules are possible. FT-IR studies prove that neither hydrogen bonds nor 1923



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(15) Knežević-Stevanović, A. B.; Smiljanić, J. D.; Šerbanović, S. P.; Radović, I. R.; Kijevčanin, M. Lj. Densities, refractive indices and viscosities of the binary mixtures of dimethyl phthalate or dimethyl adipate with tetrahydrofuran. J. Serbian Chem. Soc. 2014, 79, 77−87. (16) Vuksanović, J. M.; Calado, M. S.; Ivaniš, G. R.; Kijevčanin, M. Lj.; Šerbanović, S. P.; Višak, Z. P. 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. 2013, 352, 100−109. (17) Vuksanović, J. M.; Ž ivković, E. M.; Radović, I. R.; Šerbanović, S. P.; Kijevčanin, M. Lj. Experimental study and modelling of volumetric properties, viscosities and refractive indices of binary liquid mixtures benzene + PEG 200/PEG 400 and toluene + PEG 200/PEG 400. Fluid Phase Equilib. 2013, 345, 28−44. (18) Bajić, D. M.; Jovanović, J.; Ž ivković, E. M.; Višak, Z. P.; Šerbanović, S. P.; Kijevčanin, M. Lj. Experimental measurement and modelling of viscosity of the binary systems pyridine or nicotine with polyethylene glycols at T = (288.15−333.15) K. New UNIFACVISCO and ASOG-VISCO interaction parameters. Fluid Phase Equilib. 2013, 338, 282−293. (19) Knežević-Stevanović, A. B.; Šerbanović, S. P.; Đorđević, B. D.; Grozdanić, D. K.; Smiljanić, J. D.; Kijevčanin, M. Lj. Experimental determination and modeling of densities and refractive indices of the binary mixtures of dimethylphthalate (or dimethyladipate) + 1butanol, or + 2-butanol, or+2-butanone at T = (288.15−323.15) K. Thermochim. Acta 2012, 533, 28−38. (20) Redlich, O.; Kister, A. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (21) Ince, E. Liquid−liquid equilibria of the ternary system water + acetic acid + dimethyl adipate. Fluid Phase Equilib. 2005, 230, 58−63. (22) Lide, D. R. Handbook of Chemistry and Physics; CRC Press Inc.: Boca Raton, FL, 2002 (Section 3). (23) Rostami, A. A.; Chaichi, M. J.; Sharifi, M. Densities viscosities, and excess gibbsenergy of activation for viscous flow, for binary mixtures of dimethyl phthalate (dmp) with 1-pentanol, 1-butanol, and 1-propanol at two temperatures. Monatsh. Chem. 2007, 138, 967−971. (24) Svirbely, W. J.; Eareckson, W. M.; Matsuda, K.; Pickard, H. B.; Solet, I. S.; Tuemmler, W. B. Physical properties of some organic insect repellants. J. Am. Chem. Soc. 1949, 71, 507−509. (25) Pearce, E. M. Kirk-Othmer Encyclopedia of Chemical Technology; Interscience: NewYork, 1978. (26) Comuñas, M. J. P.; Bazile, J.-P.; Lugo, L.; Baylaucq, A.; Fernández, J.; Boned, C. Influence of the molecular structure on the volumetric properties and viscosities of dialkyladipates (dimethyl, diethyl and diisobutyladipates). J. Chem. Eng. Data 2010, 55, 3697− 3703. (27) Ottani, S.; Vitalini, D.; Comelli, F.; Castellari, C. Densities, Viscosities, and Refractive Indices of Poly(ethylene glycol) 200 and 400 + Cyclic Ethers at 303.15 K. J. Chem. Eng. Data 2002, 47, 1197− 1204. (28) Mueller, E. A.; Rasmussen, P. Densities and excess volumes in aqueous poly(ethylene glycol) solutions. J. Chem. Eng. Data 1991, 36, 214−217. (29) Han, F.; Zhang, J.; Chen, G.; Wei, X. Density, Viscosity, and Excess Properties for Aqueous Poly(ethylene glycol) Solutions from (298.15 to 323.15) K. J. Chem. Eng. Data 2008, 53, 2598−2601. (30) Aucouturier, C.; Roux-Desgranges, G.; Roux, A. H. Excess molar volumes and excess molar heat capacities of (polyethylene glycols + water) at temperatures between T = 278 K and T = 328 K. J. Chem. Thermodyn. 1999, 31, 289−300. (31) Eliassi, A.; Modarress, H. Densities of Poly(ethylene glycol) + Water Mixtures in the 298.15−328.15 K Temperature Range. J. Chem. Eng. Data 1998, 43, 719−721. (32) Tasić, A. Z.; Grozdanić, D. K.; Đorđevic, B. D.; Šerbanović, S. P.; Radojković, N. Refractive Indices and Densities of the System Acetone + Benzene + Cyclohexane at 298.15 K. Changes of Refractivity and of Volume on Mixing. J. Chem. Eng. Data 1995, 40, 586−588.

dipole−dipole interactions between unlike molecules exist and that geometrical packing between unlike molecules are the most possible explanation for negative VE values, while positive VE and negative Δη values can be attributed to dispersion forces between unlike molecules.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +381 11 3370523; fax: +381 11 3370387. E-mail address: [email protected]. Funding

The authors gratefully acknowledge the financial support received from the Research Fund of Ministry of Science and Environmental Protection, Serbia and the Faculty of Technology and Metallurgy, University of Belgrade (project no. 172063). Notes

The authors declare no competing financial interest.

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Experimental Investigation of Interactions and Thermodynamic

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