Excess Properties and Spectroscopic Studies for Binary System of

Article pubs.acs.org/jced

Excess Properties and Spectroscopic Studies for Binary System of Polyethylene Glycol 200 (1) + Dimethyl Sulfoxide (2) at T = (298.15 to 318.15) K Tianxiang Zhao,† Qiang Xu,‡ Jianbai Xiao,‡ and Xionghui Wei*,†,‡ †

College of Chemical Engineering, Inner Mongolia University of Technology, Huhhot 010051, China Department of Applied Chemistry, College of Chemistry & Molecular Engineering, Peking University, Beijing 100871, China

‡

S Supporting Information *

ABSTRACT: This work reports density and viscosity data for binary system of polyethylene glycol 200 (PEG) (1) + dimethyl sulfoxide (DMSO) (2) over the whole concentration range at T = (298.15, 303.15, 308.15, 313.15, and 318.15) K as a function of composition under atmospheric pressure. From experimental density and viscosity data, the excess molar volume (VEm), viscosity deviation (Δη), the excess Gibbs free energies of activation for viscous flow (Δ(G*)E), and the apparent molar volumes (Vφ,i) were calculated. The VEm, Δη, and Δ(G*)E were fitted to a Redlich−Kister equation to obtain the coefficients and to estimate the standard deviations between the experimental and calculated quantities; meanwhile, based on the kinematic viscosity data, the viscous flow thermodynamic parameters were also calculated. In addition, based on FTIR and UV−vis spectra for the binary system of PEG (1) + DMSO (2) with various concentrations, the intermolecular interaction of PEG with DMSO was discussed.

1. INTRODUCTION Sulfur dioxide (SO2) is one of the most significant atmospheric pollutants in the environment.1 Its major source is flue gas from the burning of fuels with high sulfur content in industrial processes. Therefore, the necessity to remove of SO2 from industrial gas is an increasingly important environmental challenge and demand.2,3 The existing flue gas desulfurization (FGD) processes, that is, the most widespread lime/limestone scrubbing procedure, have a drawback of producing large volumes of solid waste.4 An alternative has been found in regenerative processes among which organic solvents are often used as absorbents because of their favorable properties. Some of the studied substances have already found industrial application, while the others have been investigated as a more suitable alternative to fluids conventionally used in regenerative processes for SO2 removal. Polyethylene glycol 2005,6 (PEG) and its similar compounds have many favorable properties which make it suitable for various industrial applications. The main advantages of PEG for desulfurization processes are the high solubility of SO2 and excellent ability of desorption, which decrease energy demands during absorption and regeneration stages of the process. Simultaneously, dimethyl sulfoxide (DMSO) was chosen because of its wide range of applicability as a solvent in FGD. It is a highly polar aprotic solvent because of its SO group and has a large dipole moment and relative permittivity (μ = 3.9 D and k = 46.6 at 298.15 K).7 Therefore, based on the principle of dissolution in a similar material structure, the great solubility for SO2 in DMSO was obtained.8 In our recent work,6 DMSO was © XXXX American Chemical Society

added into PEG to improve selective absorption performance of SO2, because DMSO shows excellent solubility to absorb SO2 with about 0.73 g of SO2 per 1.00 g of DMSO. In systematic research, the study of SO2 absorption processes in the system PEG (1) + DMSO (2) includes the following four steps: (i) density, viscosity, and excess properties for PEG (1) + DMSO (2) solutions, (ii) gas−liquid equilibrium data for the mixture gas of SO2 + N2 in various concentrations of PEG (1) + DMSO (2), (iii) SO2 absorption and desorption properties in the system PEG (1) + DMSO (2), and (iv) spectral properties of the system PEG (1) + DMSO (2) + SO2 (3) and intermolecular interaction. However, the physical chemistry and thermodynamics properties of the binary system PEG (1) + DMSO (2) such as density (ρ), viscosity (η), and VEm data, over a wide experimental temperature range are extremely important, but it is a pity the ρ, η, and thermodynamics data are very lacking as the basic data. Therefore, the present works are mainly focused on investigating density and viscosity data at T = (298.15, 303.15, 308.15, 313.15, and 318.15) K for the whole composition range. In this study, mainly works were focused on investigating density and viscosity data at T = (298.15 to 318.15) K for the whole composition range. Based on the preceding experimental results, VEm, Δη, Δ(G*)E, Vφ,i, enthalpy of activation for viscous flow (ΔH*), the entropy of activation for viscous flow (ΔS*), and the Gibbs energies of activation for viscous flow (ΔG*) were Received: March 9, 2015 Accepted: June 10, 2015

A

DOI: 10.1021/acs.jced.5b00209 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Specification of Chemical Samples initial mass fraction purity

a

chemical name

sourceb

%

purification method

PEG 200 DMSO ethanola

Beijing Reagent Co., Ltd., China Tianjin Reagent Co., Ltd., China Beijing Reagent Co., Ltd., China

≥ 99.0 ≥ 99.0 ≥ 99.8

desiccationc and degasificationd desiccationc and degasificationd desiccationc and degasificationd

Chromatographic grade. bDeclared by the supplier. cMolecular sieve type 4A. dUltrasound.

Table 2. Comparison of Experimental Density and Viscosity Values of Pure PEG and DMSO with Literature Values at Different Temperature PEG 200

DMSO

ρ −3

T K

η

(g·cm ) expt

298.15

1.1213

303.15

1.1171

308.15

1.1133

313.15

1.1090

318.15

1.1054

ρ

(mPa·s) lit.

expt 9

η −3

(g·cm ) lit.

expt 12

1.120348 1.1211210 1.1163729 1.1171810

58.8

49.465

1.0968

45.3

38.7009

1.0914

1.1123969 1.1132110 1.1084209 1.1092310

34.2

30.8299

1.0861

26.2

24.9549

1.0812

1.1044399

19.8

20.4909

1.0753

(mPa·s) lit. 11

1.09629 1.0963712 1.0914411 1.0914212 1.0903713 1.0864111 1.0864712 1.0864111 1.0815112 1.0805813 1.0764611 1.0765512

expt

lit.

2.01

1.996012

1.82

1.996012 1.78613

1.65

1.668912

1.54

1.535112 1.50613

1.37

1.393512

mixed solution. UV−vis spectra were recorded on a Shimadzu (UV-2450) UV−vis spectrometer with a resolution of 1 nm at room temperature in the region of (190 to 500) nm. All spectral experiments of PEG (1) + DMSO (2) were performed at room temperature and atmospheric pressure. 2.2. Measurements. The density data of pure liquids and their mixtures were determined with a 25 cm3 capillary pycnometer. The volume of pycnometer was calibrated as a function of temperature using doubly distilled water at T = (298.15, 303.15, 308.15, 313.15, and 318.15) K, respectively. A thermostatically controlled and well-stirred water bath, which was controlled to ±0.01 K, was used to measure all the density and viscosity data. The pycnometer filled with liquid was kept in a water bath for 25 min to attain thermal equilibrium. Each experimental density value was an average of at least three measurements. The relative uncertainty of the density measurements was estimated to be ± 0.02 %. The kinematic viscosity (v) values in both the pure liquids and their mixtures were performed using the Ubbelohde type capillary viscometer. The Ubbelohde was calibrated using doubly distilled water and ethanol (HPLC grade) at T = (298.15, 303.15, 308.15, 313.15, and 318.15) K, respectively. After thermal stability was attained, the flow time was determined with a handheld digital stopwatch capable of measuring time within ± 0.01 s. The average of 12 sets of flow times for each fluid was taken for the calculation of viscosity values. The flow times were reproducible to ± 0.06 s. The relative uncertainty of the viscosity measurements was estimated to be ± 2 %.

calculated. These results can be used to provide important basic data for potential industrial application. Moreover, the possible intermolecular interaction of PEG with DMSO was investigated using FTIR and UV−vis spectroscopic techniques.

2. EXPERIMENTAL SECTION 2.1. Materials. The analytical grade PEG with the average molecular weight of 200 (190−210) was purchased from Beijing Reagent Co. (Beijing, China; content ≥ 99.0 %). The analytical grade DMSO was purchased from Tianjin Reagent Co. (Tianjin, China; content ≥ 99.0 %). It was used after drying over 0.4 nm molecular sieves and decompression filtration before measurements, and the samples were degassed by ultrasound just before the experiment. The mass purity of final PEG and DMSO, as found by gas chromatograph (GC), were better than 99.3 % and 99.5 %. The ethanol (HPLC grade) with a purity of minimum mass fraction of 99.8 % was purchased from Beijing Reagent Co. Doubly distilled water with its conductivity lower than 0.1 Ms·cm−1 (25 °C) was used. All specifications of the chemical samples are listed in Table 1. All measurements of mass were performed on an electronic balance with an accuracy of ± 0.1 mg (Sartorius BS224S), and the uncertainty of mole fraction was estimated to be ± 0.0001. Then for each ratio, the different unit concentration solutions were made; meanwhile, doubly distilled water and ethanol (HPLC grade) were used to calibrate the pycnometer and Ubbelohde viscometer. FTIR spectra were recorded on a Nicolet (Nexus 670) FTIR spectrometer with a resolution of 1 cm−1 in the range from (4000 to 1000) cm−1. The spectrometer possesses autoalign energy optimization and a dynamically aligned interferometer and is fitted with two constringent BaF2 pellets for the measurement of

3. RESULTS AND DISCUSSION 3.1. Density and Viscosity. The comparison of density and viscosity values of PEG and DMSO with the literature values9−13 B



Article

Table 3. Density Data for Binary Mixture of PEG (1) + DMSO (2) as a Function of PEG Mole Fraction (x1) at T = (298.15 to 318.15) K and Atmospheric Pressurea a

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

T/K = 318.15

0.0000 0.0201 0.0416 0.0645 0.0890 0.1152 0.1434 0.1738 0.2066 0.2462 0.2809 0.3231 0.3694 0.4204 0.4768 0.5395 0.6097 0.6888 0.7785 0.8812 1.0000

1.0968 1.0979 1.0993 1.1009 1.1024 1.1039 1.1054 1.1070 1.1085 1.1101 1.1114 1.1128 1.1141 1.1153 1.1164 1.1175 1.1184 1.1193 1.1201 1.1208 1.1213

1.0914 1.0931 1.0947 1.0963 1.0979 1.0995 1.1011 1.1026 1.1042 1.1059 1.1072 1.1086 1.1099 1.1111 1.1123 1.1133 1.1143 1.1151 1.1159 1.1167 1.1171

1.0861 1.0876 1.0894 1.0912 1.0930 1.0947 1.0965 1.0982 1.0999 1.1016 1.1030 1.1045 1.1058 1.1071 1.1083 1.1094 1.1104 1.1113 1.1122 1.1129 1.1133

1.0812 1.0831 1.0849 1.0868 1.0887 1.0905 1.0923 1.0940 1.0957 1.0975 1.0989 1.1003 1.1017 1.1030 1.1041 1.1052 1.1062 1.1071 1.1080 1.1087 1.1090

1.0753 1.0773 1.0794 1.0814 1.0834 1.0854 1.0873 1.0892 1.0910 1.0929 1.0944 1.0959 1.0974 1.0987 1.1000 1.1012 1.1023 1.1034 1.1043 1.1051 1.1054

a Standard uncertainties u for each variable are u(T) = 0.01 K, u(p) = 5 %, u(x1) = 0.0001, and the combined expanded uncertainty is uc(ρ) = ± 0.02 %, with a 0.95 level of confidence (k ≈ 2)

where ν is kinematic viscosity, A and B are viscometer contents, and t is its flow time in the viscometer. A and B are determined from measurements with the calibration fluids of ethanol (HPLC grade) and doubly distilled water, respectively. The absolute viscosity (η) data were calculated from the following eq 2:

at the studied temperature is given in Table 2. The agreement between the experimental and literature values was found to be satisfactory. Experimental density data under atmospheric pressure for the binary system of PEG (1) + DMSO (2) at T = (298.15 to 318.15) K was obtained throughout the whole concentration range. The measured density data are listed in Table 3 and plotted in Figure 1.

η = ρv

(2)

where ρ is density data and v is kinematic viscosity data. Experimentally acquired η data for binary system PEG (1) + DMSO (2) at T = (298.15 to 318.15) K are listed in Table 4, and the dependence of η values has been plotted in Figure 2. As shown in Figure 2, the viscosity values augment with the increasing mole fraction of PEG in the binary system over the whole concentration range; meanwhile, the viscosity values decrease with the increasing of temperature at the same composition, and this is possibly caused by the weak hydrogen bonding interaction. The density calculated value (ρcalc) and viscosity calculated value (ηcalc) were correlated by following eqs 3 and 4,13,14 respectively: ρ= Figure 1. Experimental density values with mole fraction for PEG (1) + DMSO (2) at T = (298.15 to 318.15) K and atmospheric pressure.

x1M1 + x 2M 2 n V1 + V2 + x1x 2 ∑i = 0 Ai (2x1 − 1)i n

η = x1η1 + x 2η2 + x1x 2 ∑ Ai (2x1 − 1)i i=0

As shown in Figure 1, the density values augment with the increasing mole fraction of PEG in the binary system over the whole concentration range; meanwhile, density values at the same concentration decrease with increasing temperature. Kinematic viscosity (v) data were calculated from the following eq 1: v = At − B/t

(3)

(4)

where x1, M1, x2, and M2 denote the mole fractions and relative molecular masses of pure PEG and pure DMSO, V1 and V2 are the molar volumes of pure PEG and DMSO, and the coefficients of Ai are parameters which are obtained by fitting the Redich− Kister equation to the experimental values with a least-squares method. η is the viscosity of mixtures, and η1 and η2 represent the viscosity values of pure PEG and pure DMSO, respectively.

(1) C



Article

Table 4. Viscosity Data for Binary Mixture of PEG (1) + DMSO (2) as a Function of PEG Mole Fraction (x1) at T = (298.15 to 318.15) K and Atmospheric Pressurea η/(mPa·s) x1

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

T/K = 318.15

0.0000 0.0201 0.0416 0.0645 0.0890 0.1152 0.1434 0.1738 0.2066 0.2462 0.2809 0.3231 0.3694 0.4204 0.4768 0.5395 0.6097 0.6888 0.7785 0.8812 1.0000

2.01 2.82 3.44 4.26 5.30 6.60 8.17 10.1 12.3 15.2 18.0 21.5 25.5 29.6 34.0 38.5 43.4 48.6 52.7 56.3 58.8

1.82 2.34 2.85 3.51 4.34 5.37 6.61 8.08 9.81 12.1 14.1 16.7 19.7 23.0 26.6 30.1 33.7 37.1 39.7 42.5 45.3

1.65 2.01 2.47 3.04 3.73 4.56 5.54 6.68 8.01 9.71 11.3 13.2 15.4 17.9 20.5 23.5 26.1 28.4 30.4 32.1 34.2

1.54 1.76 2.16 2.64 3.20 3.87 4.64 5.53 6.54 7.84 9.01 10.5 12.1 13.9 15.9 18.0 20.0 21.8 23.4 24.8 26.2

1.37 1.59 1.99 2.44 2.96 3.54 4.21 4.95 5.79 6.82 7.55 8.69 9.85 11.1 12.5 14.2 15.6 16.7 17.9 18.8 19.8

Standard uncertainties u for each variable are u(T) = ± 0.01 K, u(p) = 5 %, and u(x1) = 0.0001, and the combined expanded uncertainty is uc(η) = ± 2 %, with a 0.95 level of confidence (k ≈ 2). a

are shown in Supporting Information (SI) Figures S1 and S2, respectively. It can be see from the SI Figure S1 that the relative deviation values of the density for binary system PEG (1) + DMSO (2) were within ± 0.02 %, and from SI Figure S2 that the relative deviation of the viscosity was within ± 2 %. Furthermore, the average absolute deviations of density and viscosity for the binary system of PEG (1) + DMSO (2) are given in Table 5. Table 5. Average Absolute Deviations of Density and Viscosity for Binary System PEG (1) + DMSO (2) at T = (298.15 to 318.15) K and Atmospheric Pressure

The relative deviations of the density and viscosity were calculated by following eq 5:13

∑ |100(Yexpt − Ycalc)/Yexpt| n

av absolute deviations of density av absolute deviations of viscosity

0.08 1.12

105 105

(7)

where ρm represents the density of mixtures, x1, ρ1, M1, x2, ρ2, and M2 denote the mole fractions, density values, and relative molecular masses of pure PEG and pure DMSO, respectively. The results of VEm are given in Table 6. 3.2.2. Viscosity Deviation and Excess Gibbs Free Energy of Activation of Viscous Flow. The Δη and Δ(G*)E values were calculated from experimental data of viscosity according to the following eqs 8 and 9,17−19 respectively:

(5)

where Y = ρ or η, Yexpt is the experimental value, and Ycalc is the calculated value obtained with eqs 3 and 4, respectively. The average absolute deviations were calculated following eq 6:13 AAD% =

no. of points

VmE = (x1M1 + x 2M 2)/ρm − (x1M1/ρ1 + x 2M 2 /ρ2 )

100(Yexpt − Ycalc) Ycalc

AAD%

The average absolute deviation of density is 0.08 %, while average absolute deviation of viscosity is 1.12 %. 3.2. Excess Properties. 3.2.1. Excess Molar Volume. The VmE values were calculated from the experimental results according to the following eq 7:15,16

Figure 2. Experimental viscosity values with mole fraction for PEG (1) + DMSO (2) at T = (298.15 to 318.15) K and atmospheric pressure.

RD% =

type

(6)

The relative deviation of the density and viscosity at T = (298.15 to 318.15) K for binary system PEG (1) + DMSO (2)

Δη = η − (x1η1 + x 2η2) D

(8) DOI: 10.1021/acs.jced.5b00209 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 6. Excess Molar Volumes (VEm) for Binary System PEG (1) + DMSO (2) at T = (298.15 to 318.15) Ka VEm/(cm3·mol−1)

a

x1

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

T/K = 318.15

0.0201 0.0416 0.0645 0.0890 0.1152 0.1434 0.1738 0.2066 0.2462 0.2809 0.3231 0.3694 0.4204 0.4768 0.5395 0.6097 0.6888 0.7785 0.8812

−0.1427 −0.3470 −0.5446 −0.7339 −0.9126 −1.0781 −1.2278 −1.3585 −1.4771 −1.5489 −1.6008 −1.6185 −1.5976 −1.5343 −1.4247 −1.2653 −1.0524 −0.7806 −0.4381

−0.2556 −0.4712 −0.6786 −0.8758 −1.0607 −1.2306 −1.3827 −1.5140 −1.6309 −1.6998 −1.7466 −1.7573 −1.7278 −1.6540 −1.5321 −1.3582 −1.1283 −0.8359 −0.4684

−0.2148 −0.4697 −0.7119 −0.9394 −1.1497 −1.3402 −1.5081 −1.6505 −1.7744 −1.8451 −1.8905 −1.8965 −1.8596 −1.7764 −1.6434 −1.4569 −1.2117 −0.8997 −0.5054

−0.2799 −0.5475 −0.8006 −1.0371 −1.2547 −1.4506 −1.6219 −1.7658 −1.8892 −1.9579 −1.9995 −2.0002 −1.9567 −1.8659 −1.7243 −1.5281 −1.2719 −0.9467 −0.5351

−0.2991 −0.5994 −0.8814 −1.1429 −1.3814 −1.5942 −1.7784 −1.9314 −2.0607 −2.1311 −2.1718 −2.1690 −2.1196 −2.0207 −1.8685 −1.6583 −1.3831 −1.0309 −0.5810

Standard uncertainties u for each variable are u(T) = 0.01 K, u(p) = 5 %, and u(x1) = 0.0001

Δ(G*)E = RT[ln(ηV ) − x1 ln(η1V1) − x 2 ln(η2V2)]

giving more compact structure of mixtures, and (iii) strong intermolecular interactions attributed to the charge-transfer, hydrogen bonding between unlike molecules finally leading to the more efficient packing in the mixture than in the pure liquids. The DMSO molecules enter into the space among PEG molecules when these two kinds of solutions are mixed; it is worth noting that the minimum is about x1 ≈ 0.37, which indicates that the PEG molecule could combine the DMSO molecule and the intermolecular binding most closely when the molar ratio of PEG and DMSO is about 1:2 in the mixtures. The reason may be related to the intermolecular interactions between PEG and DMSO, and the reason has been proved by FTIR and UV−vis in the next section. Meanwhile, the VEm values become less negative with the increasing temperature, and it may be because the molecular kinetic energy augments with the increasing temperature and causes the mixed volume expansion.23 Figure 4 shows the dependence of viscosity deviations on composition and temperature. It can be seen from each Δη curve of PEG (1) + DMSO (2) that the value of the viscosity deviation is not always negative but also shows a positive maximum and negative minimum at around x1 ≈ 0.69 and x1 ≈ 0.14, respectively. The curves become more and more flat, and the absolute values decrease with elevated temperatures. As shown in Figure 5, the Δ(G*)E values are positive over the whole fraction range for binary system PEG (1) + DMSO (2) at all temperature points. The sign of Δ(G*)E values can be considered as a reliable criterion for detecting or excluding the presence of interaction between different molecules, and the Δ(G*)E values are the indicatively strong molecular interaction of PEG with DMSO. 3.2.3. Apparent Molar Volume. In the binary mixture of PEG (1) + DMSO (2), the apparent molar volumes Vφ,1 and Vφ,2 are defined by following eqs 12 and 13,16 respectively:

(9)

where R is the universal constant of gases, T is the absolute temperature, V, V1, and V2 are the molar volumes of the binary mixtures and pure PEG and DMSO, and η, η1, and η2 are the absolute viscosity of the binary mixtures, pure PEG, and pure DMSO. The results of the Δη and Δ(G*)E values are given in Table 7. The values of VEm, Δη, and Δ(G*)E can be correlated using the following eq 10:20 n

Q = x1(1 − x1) ∑ Ai (2x1 − 1)i i=0

(10)

where Q denotes VEm, Δη, or Δ(G*)E, x1 represents the mole fraction of PEG, n is the polynomial degree, and the coefficients of Ai are parameters which are obtained by fitting the equations to the experimental values with a least-squares method and given in Table 8. In order to investigate the fitting efficiency for VEm, Δη, and Δ(G*)E, the standard deviations between the calculated and experimental values are obtained by the following eq 11,21,22 and the calculation results are given in Table 7: N

σ=

E E 2 [∑ (Ycalc, i − Yexpt, i) /(N − m)] i=1

(11)

where Y refers to VEm, Δη, or Δ(G*)E and N and m are the number of experimental points and number of parameters retained in the respective equations. From Figure 3, the VEm values for the binary system of PEG (1) + DMSO (2) at T = (298.15 to 318.15) K are negative for all of the mixtures over the entire mole fraction range. The negative contributions are a consequence of the following effects: (i) from a macroscopic point of view, the negative VEm indicate that there is a volume contraction on mixing, and considering the physical interactions important in these mixtures, (ii) structural effects which arise from suitable interstitial accommodation

Vφ ,1 = E

x 2M 2 ρ2 − ρm M + 1 x1 ρ2 ρm ρm


a

F

−0.35 −0.78 −1.11 −1.35 −1.45 −1.44 −1.29 −0.98 −0.46 0.10 0.89 1.83 2.89 4.05 4.84 5.38 5.36 4.04 2.36

−0.32 −0.92 −1.40 −1.75 −1.94 −1.97 −1.81 −1.44 −0.75 0.01 1.12 2.49 3.70 4.92 5.86 6.78 7.45 6.49 4.30

−0.29 −0.53 −0.71 −0.81 −0.84 −0.77 −0.62 −0.36 0.05 0.48 1.06 1.75 2.53 3.37 4.26 4.60 4.36 3.44 1.79

T/K = 308.15 −0.28 −0.41 −0.49 −0.54 −0.51 −0.44 −0.30 −0.10 0.22 0.54 0.96 1.45 2.00 2.59 3.19 3.37 3.28 2.68 1.55

T/K = 313.15 −0.15 −0.15 −0.12 −0.05 0.05 0.20 0.38 0.62 0.92 1.01 1.37 1.68 2.02 2.38 2.85 2.97 2.67 2.21 1.22

T/K = 318.15

Standard uncertainties u for each variable are u(T) = ± 0.01 K, u(p) = 5 %, and u(x1) = 0.0001

T/K = 303.15

T/K = 298.15

x1

0.0201 0.0416 0.0645 0.0890 0.1152 0.1434 0.1738 0.2066 0.2462 0.2809 0.3231 0.3694 0.4204 0.4768 0.5395 0.6097 0.6888 0.7785 0.8812

Δη/(mPa·s) 0.713 1.05 1.42 1.78 2.14 2.45 2.74 2.98 3.20 3.33 3.43 3.48 3.42 3.29 3.07 2.76 2.34 1.74 0.981

T/K = 298.15 0.501 0.853 1.22 1.59 1.94 2.26 2.54 2.79 3.01 3.14 3.24 3.28 3.26 3.17 2.96 2.66 2.23 1.62 0.893

T/K = 303.15 0.380 0.772 1.16 1.52 1.86 2.16 2.43 2.66 2.87 2.99 3.09 3.13 3.12 3.03 2.88 2.58 2.15 1.58 0.856

T/K = 308.15

Δ(G*)E/(kJ·mol−1) 0.231 0.636 1.02 1.37 1.70 1.99 2.24 2.46 2.66 2.78 2.88 2.92 2.91 2.84 2.69 2.42 2.03 1.51 0.831

T/K = 313.15

0.284 0.757 1.16 1.53 1.85 2.13 2.37 2.58 2.75 2.79 2.88 2.89 2.86 2.77 2.64 2.37 1.97 1.47 0.802

T/K = 318.15

Table 7. Viscosity Deviation (Δη) and Excess Gibbs Free Energy of Activation of Viscous Flow (Δ(G*)E) for Binary System PEG (1) + DMSO (2) at T = (298.15 to 318.15) Ka

Journal of Chemical & Engineering Data Article



Article

Table 8. Coefficients of Redlich−Kister Equation and Standard Deviations for Excess Molar Volumes (VEm), Viscosity Deviation (Δη), and Excess Gibbs Free Energy of Activation (Δ(G*)E) for Binary System PEG (1) + DMSO (2) at T = (298.15 to 318.15) K property VEm/(cm3·mol−1)

Δη/(mPa·s)

Δ(G*)E/(kJ·mol−1)

T/K

A0

A1

A2

A3

A4

σ

298.15 303.15 308.15 313.15 318.15 298.15 303.15 308.15 313.15 318.15 298.15 303.15 308.15 313.15 318.15

−10.1507 −11.9250 −13.2783 −14.5780 −16.2964 −38.20 −24.94 −13.20 −9.31 −0.52 20.05 21.67 21.83 23.62 23.24

18.1368 27.1201 30.0763 36.1326 42.1146 191.85 108.89 53.45 49.18 17.35 −47.05 −53.92 −51.20 −59.78 −68.25

−5.4526 −24.4477 −25.5842 −37.5348 −47.1976 −224.60 −36.03 44.01 −13.39 12.91 51.99 66.73 55.90 71.05 100.30

−7.2869 11.1899 9.2580 20.2046 28.0537 67.70 −143.49 −187.61 −72.58 −66.51 −35.72 −51.73 −38.57 −49.76 −82.49

4.7258 −1.9242 −0.4920 −4.2239 −6.6802 3.03 95.55 103.41 46.18 36.87 10.81 17.28 12.02 14.75 27.28

0.0297 0.0138 0.0217 0.0107 0.0060 0.23 0.06 0.05 0.07 0.11 0.08 0.02 0.03 0.12 0.07

Figure 5. Excess Gibbs free energies of activation for viscous flow (Δ(G*)E) with mole fraction for PEG (1) + DMSO (2) at T = (298.15 to 318.15) K. The symbols represent experimental values, and the solid curves represent the values calculated from eq 11.

Figure 3. Excess molar volumes (VEm) with mole fraction for PEG (1) + DMSO (2) at T = (298.15 to 318.15) K. The symbols represent experimental values, and the solid curves represent the values calculated from eq 11.

Vφ ,2 =

ρ − ρm x1M1 M × 1 + 2 x2 ρ1ρm ρm

(13)

where ρm represents the density of mixtures, x1, ρ1, M1, x2, ρ2, and M2 denote the mole fractions, density values, and relative molecular masses of pure PEG and pure DMSO, respectively. Vφ,1 and Vφ,2 values of PEG and DMSO at T = (298.15 to 318.15) K are listed in Table 9 as a function of mole fraction, respectively. Excess properties for the binary system of PEG (1) + DMSO (2) indicated that the intermolecular interaction between PEG and DMSO is existent; meanwhile, this kind of interaction is affected by temperature, and the temperature effect on viscosity is sharper than that on density. 3.3. Thermodynamic Parameters. The activation thermodynamic parameters of viscous flow, such as ΔG*, ΔH*, and ΔS*, were evaluated on the basis of Eyring’s approach to Andrade’s theory with the viscosity expressed in the following form:24,25

Figure 4. Viscosity deviations (Δη) with mole fraction for PEG (1) + DMSO (2) at T = (298.15 to 318.15) K. The symbols represent experimental values, and the solid curves represent the values calculated from eq 11.

v= G

⎛ ΔG* ⎞ hNA ⎟ exp⎜ ⎝ RT ⎠ M


T/K = 298.15

178.76 178.28 177.91 177.80 177.73 177.69 177.62 177.60 177.61 177.61 177.63 177.67 177.73 177.80 177.87 177.97 178.05 178.14 178.24 178.36

x1

0.0000 0.0201 0.0416 0.0645 0.0890 0.1152 0.1434 0.1738 0.2066 0.2462 0.2809 0.3231 0.3694 0.4204 0.4768 0.5395 0.6097 0.6888 0.7785 0.8812 1.0000

182.97 179.18 177.99 177.46 177.18 177.04 177.04 177.02 177.07 177.15 177.27 177.42 177.60 177.76 177.97 178.17 178.39 178.60 178.79 179.04

T/K = 303.15 183.89 180.92 179.93 179.43 179.20 179.00 178.90 178.82 178.82 178.82 178.83 178.89 178.95 179.02 179.10 179.19 179.29 179.38 179.50 179.65

T/K = 308.15

Vφ,1(PEG)/(cm3·mol−1)

184.66 181.69 180.59 180.04 179.77 179.60 179.52 179.46 179.43 179.44 179.49 179.53 179.59 179.69 179.77 179.87 179.97 180.06 180.17 180.34

T/K = 313.15 185.65 182.18 181.13 180.60 180.28 180.12 180.01 179.96 179.96 179.96 180.02 180.07 180.16 180.24 180.33 180.43 180.51 180.63 180.74 180.93

T/K = 318.15 71.23 71.24 71.23 71.20 71.18 71.15 71.12 71.07 71.03 70.98 70.93 70.87 70.82 70.76 70.71 70.64 70.60 70.52 70.44 70.31

T/K = 298.15

Table 9. Apparent Molar Volumes Vφ,1 and Vφ,2 for Mixtures of PEG with DMSO at T = (298.15 to 318.15) K

71.59 71.56 71.53 71.51 71.48 71.44 71.40 71.37 71.31 71.25 71.20 71.15 71.09 71.03 70.96 70.91 70.83 70.79 70.71 70.45

T/K = 303.15 71.94 71.93 71.89 71.86 71.82 71.78 71.73 71.68 71.62 71.56 71.50 71.44 71.39 71.32 71.25 71.18 71.11 71.04 70.89 70.69

T/K = 308.15

Vφ,2(DMSO)/(cm3·mol−1) 72.26 72.23 72.19 72.15 72.10 72.05 72.00 71.95 71.89 71.82 71.76 71.70 71.63 71.56 71.51 71.44 71.36 71.27 71.10 70.84

T/K = 313.15

72.66 72.62 72.58 72.53 72.48 72.43 72.37 72.31 72.25 72.18 72.12 72.06 71.99 71.93 71.86 71.78 71.69 71.55 71.40 71.07

T/K = 318.15

Journal of Chemical & Engineering Data Article

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Table 10. Enthalpy of Activation (ΔH*) and Entropy of Activation (ΔS*) for the Viscous Flow about PEG (1) + DMSO (2) at Different Concentrations x1

ΔS*/(J·K−1·mol−1)

ΔH*/(kJ·mol−1)

R2

0.0000 0.0201 0.0416 0.0645 0.0890 0.1152 0.1434 0.1738 0.2066 0.2462 0.2809 0.3231 0.3694 0.4204 0.4768 0.5395 0.6097 0.6888 0.7785 0.8812 1.0000

−6.13 ± 0.99 21.56 ± 4.90 16.67 ± 5.23 16.18 ± 5.52 17.88 ± 5.26 21.29 ± 5.16 24.88 ± 4.86 29.09 ± 4.64 33.10 ± 4.16 37.60 ± 2.36 43.55 ± 2.28 46.78 ± 1.53 50.63 ± 0.80 52.59 ± 1.33 53.91 ± 1.77 52.50 ± 1.69 54.32 ± 1.31 57.67 ± 1.01 57.69 ± 1.29 58.92 ± 2.32 57.48 ± 1.94

13.95 ± 0.60 21.87 ± 1.23 20.97 ± 1.51 21.43 ± 1.61 22.56 ± 1.70 24.21 ± 1.62 25.90 ± 1.59 27.77 ± 1.50 29.56 ± 1.43 31.55 ± 1.28 33.84 ± 0.73 35.36 ± 0.70 37.05 ± 0.47 38.14 ± 0.25 39.02 ± 0.41 39.05 ± 0.55 40.03 ± 0.52 41.45 ± 0.40 41.80 ± 0.31 42.51 ± 0.40 42.40 ± 0.71

0.9927 0.9875 0.9796 0.9778 0.9777 0.9823 0.9851 0.9885 0.9907 0.9934 0.9982 0.9984 0.9994 0.9998 0.9996 0.9992 0.9993 0.9996 0.9998 0.9997 0.9989

Figure 6. Gibbs energies of activation of viscous flow (ΔG*) for the viscous flow about PEG (1) + DMSO at T = (298.15 to 318.15) K and atmospheric pressure.

⎛ M ⎞ ΔH * R ln⎜v − ΔS* ⎟= T ⎝ hNA ⎠

According to Erying’s theory, ΔH* and ΔS* can be calculated from eq 16. Plots of the term on the left-hand side of eq 16 against 1/T for each binary mixture are nearly linear (SI Figure S3), and ΔH* and ΔS* were calculated from the slopes and intercepts. The ΔG* values were obtained according to eq 15. The ΔH* and ΔS* values are listed in Table 10, the ΔG* values are listed in Table 11 and shown in Figure 6. The positive ΔH* values decrease with the increasing PEG concentration revealing that the viscous flow in pure DMSO is easier than in pure PEG or the binary system of

where M = ∑xiMi is the average molar mass, h is Planck’s constant, NA is the Avogadro number, R is the gas constant, and T is the absolute temperature. By applying the standard thermodynamic equation, (15)

ΔG* = ΔH * − T ΔS*

(16)

it is possible to write

Table 11. Gibbs Energies of Activation for Viscous Flow (ΔG*) for the Viscous Flow about PEG (1) + DMSO (1) at T = (298.15 to 318.15) K ΔG*/(kJ·mol−1) x1

T/K = 298.15

T/K = 303.15

T/K = 308.15

T/K = 313.15

T/K = 318.15

0.0000 0.0201 0.0416 0.0645 0.0890 0.1152 0.1434 0.1738 0.2066 0.2462 0.2809 0.3231 0.3694 0.4204 0.4768 0.5395 0.6097 0.6888 0.7785 0.8812 1.0000

14.78 15.44 16.00 16.61 17.23 17.86 18.48 19.10 19.69 20.34 20.86 21.41 21.95 22.46 22.95 23.40 23.83 24.26 24.60 24.94 25.26

14.81 15.33 15.92 16.52 17.14 17.75 18.36 18.95 19.53 20.15 20.64 21.18 21.70 22.20 22.68 23.13 23.56 23.97 24.31 24.65 24.97

14.84 15.23 15.83 16.44 17.05 17.65 18.23 18.81 19.36 19.97 20.42 20.94 21.45 21.94 22.41 22.87 23.29 23.68 24.03 24.36 24.69

14.87 15.12 15.75 16.36 16.96 17.54 18.11 18.66 19.20 19.78 20.21 20.71 21.20 21.67 22.14 22.61 23.02 23.39 23.74 24.06 24.40

14.90 15.01 15.67 16.28 16.87 17.44 17.99 18.51 19.03 19.59 19.99 20.48 20.94 21.41 21.87 22.35 22.75 23.10 23.45 23.77 24.11

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PEG (1) + DMSO (2). The positive ΔS* values reveal that the binding force of self-association of PEG molecules with DMSO molecules are weaker than their cross-association. The ΔG* values are found to be positive for the whole range of composition at all temperatures indicating the specific interaction occurring between the components. 3.4. Spectral Properties. Foregoing results may be related to the intermolecular hydrogen bonding and interactions between PEG and DMSO. Figure 7 shows that the FTIR spectra

Figure 8. UV−vis spectra for binary system of PEG (1) + DMSO (2).

of DMSO, the intermolecular hydrogen bonding and interaction of the hydroxyl hydrogen atom in PEG with the oxygen atom in DMSO easily happened so that the n → σ* electronic transition of the unshared electronic pair of the oxygen atom in DMSO became more easy. The present results showed that the hydrogen bonding and interaction of the oxygen atom in DMSO with the hydroxyl hydrogen atoms in PEG formed as -OCH2CH2O−H··· OS(CH3)2. According to FTIR and UV−vis results, it is expected that the intermolecular interactions in the system PEG (1) + DMSO (2) are due to the hydrogen bonding and interactions between PEG and DMSO as the formation of -OCH2CH2O−H···O S(CH3)2.

Figure 7. FTIR spectra of binary system for PEG (1) + DMSO (2) for the following weight percentages of PEG: (a) 0 %, (b) 20 %, (c) 40 %, (d) 60 %, (e) 80 %, and (f)100 %, respectively.

of pure PEG, pure DMSO, and the binary system of PEG (1) + DMSO (2) with various concentrations were determined. The FTIR spectral results showed that one stretching band is observed at 3421 cm−1, which is due to the stretching vibrational band of the hydroxyl group in PEG.26 The stretching vibrational band of hydroxyl shifted from (3421 to 3353) cm−1 with the increasing mass fraction of DMSO in the binary system of PEG (1) + DMSO (2); meanwhile, the bending vibrational band of the hydroxyl group in PEG shifted to lower frequency from (1129 to 1123) cm−1 with the increasing concentration of DMSO.26 The fact that the intermolecular hydrogen bond in PEG was broken gradually, and the new hydrogen between PEG and DMSO was formed, and the absorption bands of hydroxyl in PEG shifted toward lower frequency were due to the vibrational properties of hydroxyl in PEG. It is also found that the stretching vibrational bond of the SO (1057 cm−1)27 in DMSO splits into two new absorption bands. At least two peaks could be identified: one is at about 1030 cm−1; the other, 1057 cm−1. The former is assigned to that of the SO in interactions with hydroxyl in PEG, while the latter to the free SO groups or SO groups forming cyclic dimmer with another DMSO molecule.28 FTIR results indicated the intermolecular hydrogen bonding and interaction of hydroxyl hydrogen in PEG with oxygen in DMSO, and similar to association hydrogen bonding between DMSO and ethylene glycol.29,30 The recorded UV−vis spectra of PEG (1) + DMSO (2) are shown in Figure 8, and PEG was used as the reference solution. There are a series of absorption bands at nearly 210 nm, which could be due to the n → σ* electronic transition of the unshared electronic pair of the oxygen atom in DMSO.31 It is clearly visible that the absorption band red-shifted from 210 to 217 nm with the increasing concentration of DMSO in the binary system of PEG (1) + DMSO (2). With the increasing concentration

4. CONCLUSIONS This work reports density and viscosity data for the binary system of PEG (1) + DMSO (2) over the whole concentration range at T = (298.15, 303.15, 308.15, 313.15, and 318.15) K under atmospheric pressure. The relative deviation of the density for the binary system is within ± 0.02 %. The relative deviation of the viscosity is within ± 2 %. Simultaneously, the density and viscosity data have been used to compute the parameters of excess properties and viscous flow thermodynamics for the binary system of PEG (1) + DMSO (2). The VEm values were negative, the Δη values was not always negative but also showed a positive maximum and negative minimum at around x1 ≈ 0.69 and x1 ≈ 0.14, the Δ(G*)E values were positive, and Vφ,1 and Vφ,2 were positive at all compositions and temperatures; meanwhile, the ΔH*, ΔS*, and ΔG* values were calculated, and the results show that ΔH* and ΔG* were positive while ΔS* gradually increased from (−6.13 to 57.48) J·K−1·mol−1 with the increasing composition of PEG. In addition, the FTIR and UV−vis spectral results indicated that there are hydrogen bonding and interactions of hydroxyl hydrogen atoms in PEG with oxygen atoms in DMSO with the formation of -OCH2CH2O−H···O S(CH3)2.

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ASSOCIATED CONTENT

S Supporting Information *

Figures showing relative deviations of desnsity deviations and a plot of R ln ν(M)/hNA vs 1/T for the PEG (1) + DMSO (2) system. The Supporting Information is available free of charge on J



Article

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the ACS Publications website at DOI: 10.1021/acs.jced.5b00209.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-10-62751529; Fax: +86-10-62751529. E-mail: [email protected]. Funding

This project was financed by Jiangxi Boyuan Industry Co. Ltd. (Jiangxi Province, China). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Professor Jianbin Zhang (Inner Mongolia University of Technology) for his suggestions on this work. REFERENCES

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Excess Properties and Spectroscopic Studies for Binary System of

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