Experimental Data and Modeling for Viscosity and Refractive Index of

Jul 30, 2019 - In the present study, the viscosity and refractive index of pure and aqueous 2-(methylamino)ethanol (MAE) and aminoethylethanolamine ...
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Experimental Data and Modeling for Viscosity and Refractive Index of Aqueous Mixtures with 2‑(Methylamino)ethanol (MAE) and Aminoethylethanolamine (AEEA) Diwakar Pandey and Monoj Kumar Mondal* Department of Chemical Engineering and Technology, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005, Uttar Pradesh, India Downloaded via NOTTINGHAM TRENT UNIV on August 7, 2019 at 03:47:01 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: In the present study, the viscosity and refractive index of pure and aqueous 2-(methylamino)ethanol (MAE) and aminoethylethanolamine (AEEA) and an aqueous blend of MAE and AEEA were measured in the temperature range of 293.15−333.15 K with an interval of 5 K at atmospheric pressure. Amine content in aqueous mixtures varied from 0.05 to 0.30 weight fraction. The viscosity of pure components was correlated by Arrhenius-type equation with average absolute deviation percentage (AAD%) values of 1.87 and 2.42 for MAE and AEEA, respectively. Modified Vogel−Tamman− Fulcher equation with AAD% of 1.343 was proposed to correlate the viscosity of pure AEEA. A new equation with respect to temperature was also proposed to correlate the refractive index data of pure MAE and pure AEEA. Viscosity and refractive index data of aqueous MAE, AEEA, and an aqueous blend of MAE and AEEA were associated by newly proposed correlations and maximum AAD% was found to be 0.11 and 0.001 for viscosity and refractive index, respectively. Deviation in viscosity (Δμ) and deviation in refractive index (ΔnD) from ideal solution of aqueous MAE and AEEA were correlated by the Redlich−Kister equation, and the maximum standard deviation was calculated to be 0.091 and 0.0012 for MAE and 0.114 and 0.0011 for AEEA, respectively.

1. INTRODUCTION Chemical absorption using an aqueous solution of alkanolamines is the most mature and effective method for CO2 capture compared to other available technologies for CO2 removal, such as adsorption, absorption, membrane separation, cryogenic separation, etc.1,2 The physical properties of the solvent are very important for modeling and designing the absorption column.3 Mass transfer resistance is related to viscosity, and viscosity data are also useful in finding diffusivity using the Stoke−Einstein equation. Generally, a low-viscous solvent is required for heat and mass transfer applications because it facilitates easier heat and mass transfer than a highviscous solvent. Moreover, low-viscous solvents require less pumping cost.4 Viscosity data of blend of two solvents are useful to understand the molecular interaction of species, and compositions of blend influence the physicochemical property of the mixed system.5 Refractive index is useful for prediction of molecular arrangement and optical property of solvent.6 The kinematic viscosity of the aqueous ternary mixture of 2(methylamino)ethanol (MAE), diethanolamine (DEA), triethanolamine (TEA), 2-amino-2-methyl-1-propanol (AMP), and methyl diethanolamine (MDEA) in the temperature range of 298.15−323.15 K was studied by Á lvarez et al.7 The thermodynamic properties and CO2 solubility of the blend of monoethanolamine (MEA) and diethylenetriamine (DETA)/ © XXXX American Chemical Society

aminoethylethanolamine (AEEA) were measured in the temperature range of 298.15−308.15 K by Moosavi et al.6 Excess refractive index data and excess molar volume were correlated by the Redlich−Kister equation. 2-(Methylamino)ethanol (MAE) is a sterically hindered secondary amine. MAE has a higher reaction rate than primary amines, but it shows higher absorption capacity than tertiary amines. Some researchers studied MAE and reported it as a potential solvent for CO2 absorption in terms of CO2 loading, heat effect, and reaction kinetics.8−11 AEEA is an unhindered diamine that has one primary amine and one secondary amine group. AEEA can absorb 2 mol of CO2 and shows high CO2 cyclic capacity, high values of second-order reaction rate, and lower regeneration energy. Thus, it has been reported as a very efficient activator in amine blend for CO2 absorption and shows high CO2 absorption capacity.12−16 To the best of our knowledge, viscosity and refractive index data have not been correlated with the composition of aqueous blend of MAE and AEEA and temperature in the published literature. The objective of this paper is to measure the viscosity and refractive index data of pure MAE, pure AEEA, aqueous MAE, Received: February 20, 2019 Accepted: July 18, 2019

A

DOI: 10.1021/acs.jced.9b00171 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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10 (A&D Company, Limited, Japan) with 1% repeatability in the temperature range of 293.15−333.15 K and under atmospheric pressure. The viscometer was calibrated with double-distilled water frequently before sampling. Sample temperature in the range of 293.15−333.15 K was maintained by a water bath. As soon as the temperature of the sample reached the desired value, it was poured into a sample cup for the measurement of its viscosity by a viscometer. Simultaneously, the sample temperature was also measured by the viscometer. Error in temperature measurement was ±1 K. The process was repeated three times and average values were reported. 2.3. Refractive Index Measurement. Refractive index of the sample was measured by Abbe refractometer (Rajdhani Instruments Ltd. New Delhi, India) with an accuracy of ±0.0001. The temperature of the sample was maintained in the same way as described for viscosity measurement in the range of 293.15−333.15 K. Before the measurement of the refractive index, the refractometer was calibrated by double-distilled water. The mirror of the refractometer was washed with distilled water and methanol. Accuracy in temperature was ±1 K. Refractive index of each sample was measured three times and average values were reported. To validate the viscometer, refractometer, and experimental procedures, the viscosity and refractive index of pure and aqueous MAE and AEEA were measured at different temperatures and different weight fractions of amines. Measured values and values available in the literature for pure MAE and for pure AEEA are given in Table 2. Graphical comparisons between experimental data and available literature data are given in the Supporting Information. AAD% between measured values and literature6,17,18,35 values were 4.524 and 0.183 for viscosity and refractive index, respectively. Thus, the obtained viscosity and refractive index data in this study were reliable.

aqueous AEEA with different concentrations (5, 10, 15, 20, 25, and 30 wt %), and aqueous blend of MAE and AEEA (25 + 5, 20 + 10, 15 + 15, 10 + 20, and 05 + 25 wt % MAE and AEEA) in the temperature range of 293.15−333.15 K. MAE and AEEA weight ratio was selected based on the literature data. Intervals of 5 wt % were selected randomly to measure experimental data and develop empirical correlation. New correlations were developed to predict the viscosity and refractive index of pure solvents, aqueous solvents, as well as aqueous blend in the experimental temperature range of this study. Deviations in viscosity and refractive index from ideal solution of aqueous MAE and aqueous AEEA was also calculated, and the deviated values were fitted to the Redlich−Kister equation.

2. EXPERIMENTAL SECTION 2.1. Materials. MAE (98% pure) was purchased from Sigma-Aldrich, St. Louis, USA, and AEEA (98% pure) was purchased from S D Fine Chem Limited, Mumbai, India. Both chemicals, MAE and AEEA, were used without further purification. Double-distilled water was used to prepare aqueous mixtures. A description of MAE, AEEA, and water used in the experiment is given in Table 1. Throughout the Table 1. Chemical Sample Information chemical name

CAS number

MAEa

109-83-1

AEEAb

111-41-1

water

7732-18-5

source Sigma-Aldrich, St. Louis, USA S D Fine Chem Limited, Mumbai, India Our Laboratory

initial purity (%)

purification method

≥98c

none

98c

none

99.9c

double distillation

a

2-(Methylamino)ethanol. bAminoethylethanolamine. cMass fraction.

experiments, the weight of samples was measured by an electronic balance (Sartorius BP221S) with error of ±0.1 mg. Aqueous solutions of 0.05−0.30 weight fractions were prepared by mixing double-distilled water with MAE and AEEA in appropriate proportions. 2.2. Viscosity Measurement. Viscosity values of pure and aqueous MAE, AEEA, and aqueous blend of MAE and AEEA solutions were measured by Sine-wave Vibro Viscometer SV-

3. RESULTS AND DISCUSSION Viscosities and refractive indexes of pure and aqueous MAE, AEEA, and aqueous blend of MAE and AEEA were measured in the temperature range of 293.15−333.15 K (at 293.15, 298.15, 303.15, 308.15, 313.15, 318.15, 323.15, 328.15, and 333.15 K). Weight fraction of amine in the aqueous mixtures was varied from 0.05 to 0.30 (0.05, 0.10, 0.15, 0.20, 0.25, and

Table 2. Experimental Values of Viscosity and Refractive Index of Pure MAE and Pure AEEA at 101.325 kPa Pressure for T = (293.15−318.15) K with Interval of 5 K and Comparison with Data Available in the Literaturea μ/(mPa s) T/(K)

pure MAE

nD pure AEEA

293.15 298.15

13.12 10.28

10.5106b

153.62 99.27

303.15

8.42

8.5221b

71.31

308.15 313.15 318.15 323.15 328.15 333.15

6.78 5.54 4.61 3.82 3.13 2.42

5.8331

b

4.1774b

52.94 37.67 28.23 21.55 16.43 12.74

pure MAE 98.62c 98.6d 70.57c 70.5d 53.11c 39.4d 23.4d 14.8d

pure AEEA b

1.4386 1.4370

1.4393 1.4375b

1.4856 1.4842

1.4352

1.4356b

1.4827

1.4331 1.4310 1.4288 1.4265 1.4242 1.4218

1.4339b 1.4318b 1.4298b 1.4278b

1.4810 1.4792 1.4772 1.475 1.4727 1.4702

1.4843c 1.48454d 1.4827c 1.48269d 1.4811c 1.47884d 1.47519d 1.47128d

Standard uncertainties u are u(T) = 1 K and u(P) = 1 kPa, and expanded uncertainties at 95% confidence level are U(μ) = 0.08 μ mPa s and U(nD) = 0.02nD. bLi et al. (2007). cMoosavi et al. (2017). dMundhwa et al. (2006). a

B

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Table 3. Experimental Values of Viscosity, Deviation in Viscosity, Refractive Index, and Deviation in Refractive Index of Binary Aqueous System of MAE(1) + H2O(2) and AEEA(1) + H2O(2) at 101.325 kPa Pressure, T = (293.15−318.15) K with Interval of 5 K and w1 = (0.05−0.30)a MAE(1) + H2O(2) T/(K)

μ/(mPa s)

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

1.31 1.1 0.99 0.88 0.79 0.72 0.65 0.58 0.52

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

1.68 1.42 1.22 1.05 0.94 0.84 0.75 0.67 0.6

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

2.38 2.02 1.74 1.42 1.22 1.04 0.93 0.83 0.74

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

2.66 2.17 1.83 1.52 1.32 1.19 1.06 0.94 0.83

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

3.4 2.74 2.32 1.96 1.71 1.49 1.29 1.12 0.99

293.15 298.15 303.15 308.15 313.15 318.15

4.22 3.52 2.96 2.52 2.2 1.92

Δμ/(mPa s) w1 = 0.16 0.09 0.09 0.08 0.08 0.07 0.06 0.04 0.03 w1 = 0.36 0.29 0.22 0.17 0.16 0.14 0.19 0.1 0.08 w1 = 0.60 0.51 0.45 0.30 0.25 0.19 0.18 0.16 0.14 w1 = 0.97 0.75 0.6 0.46 0.39 0.36 0.33 0.29 0.25 w1 = 1.5 1.16 0.96 0.79 0.7 0.6 0.5 0.42 0.38 w1 = 2.09 1.75 1.45 1.23 1.09 0.95

AEEA(1) + H2O(2) nD

ΔnD

μ/(mPa s)

0.05 1.3421 1.3414 1.3405 1.3396 1.3386 1.3375 1.3364 1.3352 1.334

0.0077 0.0072 0.007 0.0067 0.0063 0.006 0.0056 0.0056 0.0054

1.2 1.11 0.95 0.85 0.76 0.69 0.64 0.59 0.55

1.3452 1.3444 1.3435 1.3426 1.3416 1.3405 1.3394 1.3381 1.3368

0.0094 0.0088 0.0086 0.0083 0.008 0.0077 0.0073 0.0072 0.0069

1.6 1.36 1.18 1.06 0.94 0.84 0.77 0.7 0.64

1.3484 1.3476 1.3467 1.3456 1.3445 1.3434 1.3421 1.3406 1.3391

0.0111 0.0106 0.0103 0.0099 0.0095 0.0092 0.0087 0.0083 0.0079

2.02 1.74 1.48 1.32 1.17 1.03 0.92 0.82 0.74

1.3522 1.3513 1.3502 1.349 1.3478 1.3465 1.3451 1.3436 1.342

0.0132 0.0126 0.0121 0.0116 0.0111 0.0107 0.0101 0.0097 0.0092

2.58 2.22 1.89 1.63 1.41 1.24 1.08 0.95 0.87

1.3568 1.3558 1.3547 1.3534 1.352 1.3505 1.349 1.3474 1.3456

0.0159 0.0152 0.0148 0.0142 0.0136 0.013 0.0123 0.0119 0.0112

3.47 2.98 2.37 2.08 1.76 1.53 1.28 1.11 1.02

1.3624 1.3614 1.3602 1.3588 1.3573 1.3558

0.0194 0.0188 0.0183 0.0177 0.0169 0.0164

4.73 3.95 3.32 2.61 2.19 1.86

0.10

0.15

0.20

0.25

0.30

C

Δμ/(mPa s) w1 = 0.05 −1.19 −0.68 −0.48 −0.34 −0.23 −0.16 −0.1 −0.05 −0.02 w1 = 0.10 −2.18 −1.32 −0.89 −0.61 −0.38 −0.26 −0.16 −0.09 −0.04 w1 = 0.15 −3.5 −2.06 −1.4 −0.95 −0.58 −0.39 −0.25 −0.15 −0.08 w1 = 0.20 −4.75 −2.75 −1.83 −1.26 −0.78 −0.51 −0.34 −0.21 −0.1 w1 = 0.25 −5.85 −3.27 −2.26 −1.48 −0.91 −0.58 −0.41 −0.26 −0.11 w1 = 0.30 −6.8 −3.73 −2.34 −1.71 −1.01 −0.65

nD

ΔnD

1.3406 1.3401 1.3394 1.3387 1.3378 1.3368 1.3358 1.3347 1.3335

0.0062 0.0059 0.0058 0.0057 0.0054 0.0052 0.0051 0.0049 0.0048

1.3452 1.3446 1.3438 1.343 1.3421 1.341 1.3398 1.3385 1.3371

0.0094 0.009 0.0088 0.0086 0.0084 0.0081 0.0078 0.0074 0.0071

1.351 1.3504 1.3496 1.3487 1.3476 1.3464 1.3451 1.3436 1.342

0.0134 0.0131 0.0129 0.0126 0.0122 0.0118 0.0114 0.0109 0.0103

1.3582 1.3575 1.3567 1.3558 1.3548 1.3536 1.3523 1.3508 1.3491

0.0188 0.0184 0.0182 0.0179 0.0176 0.0172 0.0169 0.0164 0.0157

1.366 1.3652 1.3643 1.3633 1.3622 1.361 1.3597 1.3582 1.3566

0.0246 0.0241 0.0238 0.0235 0.0231 0.0227 0.0224 0.0219 0.0214

1.3752 1.3744 1.3735 1.3724 1.3712 1.3698

0.0316 0.0311 0.0309 0.0304 0.0299 0.0294

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Table 3. continued MAE(1) + H2O(2) T/(K)

μ/(mPa s)

323.15 328.15 333.15

1.65 1.41 1.2

Δμ/(mPa s) 0.8 0.66 0.55

AEEA(1) + H2O(2) nD

ΔnD

μ/(mPa s)

1.3542 1.3524 1.3504

0.0156 0.015 0.0141

1.59 1.35 1.2

Δμ/(mPa s) −0.41 −0.25 −0.11

nD

ΔnD

1.3682 1.3664 1.3648

0.0288 0.028 0.0275

Standard uncertainties u are u(T) = 1 K, u(P) = 1 kPa, and u(w1) = 0.01, and expanded uncertainties at 95% confidence level are U(μ) = 0.05 μ mPa s and U(nD) = 0.02nD.

a

0.30). The weight fraction of amines in an aqueous blend of MAE and AEEA was kept constant at 0.30. Contribution of MAE and AEEA in the blend was varied in different proportions as 0.25 + 0.05, 0.20 + 0.10, 0.15 + 0.15, 0.10 + 0.20, and 0.05 + 0.25. 3.1. Viscosity. From the results, it was found that viscosities of pure amines, aqueous amines, and aqueous blend decreased with increasing temperature. Liquid molecules are bonded by intermolecular forces, and at a low temperature, intermolecular attraction is strong. Increasing the temperature of pure and aqueous MAE, AEEA, and the aqueous blend of MAE and AEEA provides additional energy to their molecules to overcome intermolecular forces, and the distance between molecules increases, thereby decreasing the viscosity. The viscosity of pure MAE was lower than the viscosity of pure AEEA. This may be due to more hydrogen bonding in AEEA molecules than in MAE molecules. Viscosity data with temperature for pure MAE and AEEA are presented in Table 2. Viscosity data of aqueous MAE, aqueous AEEA, and an aqueous blend of MAE and AEEA with different weight fractions and at different temperatures are listed in Tables 3 and 4, respectively, and depicted in Figures 1 and 2, Table 4. Experimental Values of Viscosity of Aqueous Blend MAE(1) + AEEA(2) + H2O(3) at 101.325 kPa Pressurea

Figure 1. Viscosity versus temperature of aqueous MAE and aqueous AEEA for different weight fractions of (a) MAE and (b) AEEA, w1: ⧫ 0.05; ▲ 0.10; * 0.15; + 0.20; − 0.25; ■ 0.30; calculated values with eq 6.

μ/(mPa s) w1/w2

w1/w2

w1/w2

w1/w2

w1/w2

T/(K)

0.25/0.05

0.20/0.10

0.15/0.15

0.10/0.20

0.05/0.25

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

5.58 4.52 3.66 3.10 2.65 2.24 1.92 1.65 1.44

5.80 4.72 3.82 3.23 2.78 2.36 2.03 1.77 1.52

6.05 4.96 4.05 3.45 2.96 2.49 2.13 1.83 1.58

6.27 5.18 4.25 3.64 3.10 2.60 2.21 1.88 1.62

6.48 5.39 4.46 3.86 3.28 2.71 2.30 1.95 1.67

a

Standard uncertainties u are u(T) = 1 K, u(P) = 1 kPa, u(w1) = 0.01, and u(w2) = 0.01, and expanded uncertainties at 95% confidence level are U(μ) = 0.05 μ mPa s.

respectively. Increase in weight fraction of amine in aqueous mixture results in increasing viscosity. This was due to the increase in adhesive forces between amine molecules and water molecules. In the aqueous blend of MAE and AEEA, varying the weight proportion of MAE and AEEA did not significantly affect the viscosity of the blend, however, increasing the weight fraction of AEEA increased viscosity values slightly. 3.1.1. Correlations for Viscosity. Many correlations for estimating dynamic viscosity of binary and multicomponent liquid mixtures have been made in the literature. However, there is a lack of theoretical description of the viscosity of

Figure 2. Viscosity of aqueous blend of MAE and AEEA versus temperature for different weight fractions of MAE + AEEA, w1 + w2: ⧫ 0.25 + 0.05; ▲ 0.20 + 0.10; * 0.15 + 0.15; + 0.10 + 0.20; − 0.05 + 0.25; calculated values with eq 7.

liquid mixtures. For the prediction of the viscosity of hydrocarbons and their mixtures, some viscosity models have been given in the literature based on the quantitative structure−property relation and structural additive orthochor D

DOI: 10.1021/acs.jced.9b00171 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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value.19,20 Zhelezny et al.21 suggested a model to predict the viscosity of refrigerant oil solutions (ROS), where the pseudocritical temperature of ROS was used. This model is not well applicable for aqueous amine mixtures. The Grunberg−Nissan approach is used to calculate the liquid viscosity for a multicomponent system at low temperatures. But this method is not suitable for aqueous mixtures.22 The correlation proposed by Hartono et al.23 for the MEA system performs satisfactorily only for the amine content between 0.3 and 0.4 weight fractions. Similarly, the model suggested by Weiland et al.24 for the MEA system works correctly in the range of 0.2−0.4 weight fraction.25 To calculate the viscosity of binary solvent at different temperatures, the following Jouyban−Acree model can be used26 ÄÅ É Å X X ÑÑ ln μm , T − X1 ln μ1, T + X 2 ln μ2, T + A 0ÅÅÅÅ 1 2 ÑÑÑÑ ÅÅÇ T ÑÑÖ É ÄÅ ÅÄÅ X X (X − X ) ÑÉÑ ÅÅ X X (X − X )2 ÑÑÑ ÅÅ 1 2 1 2 Ñ 1 2 1 2 ÑÑ Å Ñ ÑÑ + A 2 ÅÅÅ + A1ÅÅ ÑÑ ÅÅÅ ÑÑÑ ÑÑÖ Å T T Å (1) Ç Ö Ç

AEEA with temperature in the range of 293.15−333.15 K, which can be presented as eq 4 μ=A+

ln μ = A +

100 × n

(2)

n

∑ i=1

(5)

j=4

μm , T = exp[w1 ln μ1, T + w1 ln μ2, T ] +

∑ Cj w1 j j=0

(6)

where w1 and w2 are weight fractions of MAE/AEEA and water, respectively; μ1,T and μ2,T are viscosities of pure MAE/ AEEA and water at temperature T, respectively; and C0, C1, C2, C3, and C4 are newly introduced Redlich−Kister-type coefficients,31 which can be called mass interaction parameters. Values of coefficients Cj were found out by multiple regressions using the least-squares method and are listed in Table 5. For viscosity of aqueous MAE, third-order polynomial was sufficient for best fit, while for aqueous AEEA, fourth-order polynomial was used. For this correlation, AAD% = 0.63 and 0.40 for aqueous MAE and aqueous AEEA, respectively. An aqueous blend of MAE and AEEA shows very less change in viscosity with respect to the composition of the blend at a particular temperature, but for a particular composition, the viscosity decreased with increasing temperature. A new correlation for the tertiary mixture, similar to eq 6, given by eq 7, was used to fit the experimental data of viscosity.

|Yexperimental − Ycalculated | Yexperimental

B (T − C )

where A = −6.342, B = 1642.000, and C = 148.500, and AAD% is 1.27. Low value of AAD% indicates good correlation for experimental values of viscosity. To predict the viscosities of aqueous MAE and aqueous AEEA at different weight fractions and temperatures, a Jouyban−Acree model-type modified correlation was developed using experimental data obtained in the temperature range of 293.15−333.15 K and weight fractions of 0.05 and 0.30 for MAE and AEEA, respectively. The developed correlation is presented in eq 6. It would be a very appropriate model for the calculation of viscosity of aqueous amine solutions because it covers a wide range of amine weight fractions and temperatures that may be used in carbon dioxide capture applications.

where μ, A0, R, and T are viscosity, a preexponential factor, gas constant, and temperature, respectively. Eav is interpreted as activation energy for viscous flow. Values of A0 and Eav for MAE were found to be 1.542 × 10−5 and 33 280.94 kJ/mol K, respectively, and values of A0 and Eav for AEEA were 1.874 × 10−7 and 49 850.74 kJ/mol K, respectively. Here, activation energy for viscous flow of AEEA is higher than for MAE, which signifies higher viscosity of pure AEEA than pure MAE at the same temperature. In the Arrhenius equation, the value of activation energy is used with a negative sign, but in eq 2, the value of activation energy for flow (Eav) is used with a positive sign because the reaction rate constant increases with increasing temperature while viscosity decreases with increasing temperature. Average absolute deviation percentage (AAD %) was calculated using eq 328,29 AAD% =

(4)

where A, B, and C are the equation parameters. For MAE, A = −4.90, B = 502.00, and C = 265.20, and AAD% for this correlation is 1.05. For pure AEEA fitted in eq 3, A = −31.88, B = 2281.00, and C = 280.80, and the corresponding AAD% was 2.46. A low value of AAD% shows good agreement of correlated values with experimental data of viscosity. The viscosity data of pure AEEA in the temperature range of 293.15−333.15 K were also fitted to the new correlation in terms of modified Vogel−Tamman−Fulcher (VTF) eq 5. A modified VTF equation has already been used to correlate viscosity of aqueous alkali salts of α-alanine,30 and the same type of equation was used to correlate the viscosity data of the present study

where X1 and X2 are the mole fractions of liquids 1 and 2, respectively; μ1,T and μ2,T are the viscosities of pure liquids; μm,T is the viscosity of binary mixture at temperature T; and A0, A1, and A2 are the model constants. The merit of this model over other proposed mixing rules for the liquid’s physicochemical properties is that it can be used for both aqueous and nonaqueous mixtures, and it requires the properties of pure components and the experimental data for the property of mixture. Pure MAE and pure AEEA viscosity data were correlated with temperature using the well-known Arrhenius-type equation and a newly proposed equation (eq 4). The Arrhenius-like equation is27 shown below μ = A 0 e Eav / RT

B (T − C )

(3)

where Yexperimental and Ycalculated are the experimental and calculated values of viscosity and refractive index, respectively, based on the given empirical correlation at the same operating conditions and n is the number of data points. Fitting data of viscosities were obtained by eq 2, and the corresponding experimental AAD% values were 1.87 and 2.42 for MAE and AEEA, respectively. A new correlation has also been developed for the viscosities of pure MAE and pure

μm , T = exp[w1 ln μ1, T + w2 ln μ2, T + w3 ln μ3, T ] j=3

+

∑ Cjw1 j j=0

E

(7) DOI: 10.1021/acs.jced.9b00171 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 5. Regressed Coefficients (C0, C1, C2, C3, and C4) for Equations 6 and 7 T/(K) 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

C0

C1

C2

C3

For Viscosity of Aqueous MAE 0.0479 2.0571 9.9831 18.473 −0.1925 6.9748 −30.489 92.942 −0.1093 4.7616 −20.986 70.694 −0.0395 2.8844 −15.547 62.431 −0.0363 2.7566 −16.669 62.146 0.0236 0.8782 −5.5509 38.043 −0.0125 1.5021 −8.2653 36.092 −0.0362 1.5525 −7.4898 28.922 −0.0293 0.8999 −1.9204 13.61 For Viscosity of Aqueous AEEA −0.4173 11.045 −105.59 351.93 −0.0458 1.8556 −33.554 156.43 0.3117 −12.806 148.89 −706.58 −0.1412 3.5738 −40.174 165.93 −0.0658 0.8214 −5.393 5.6094 −0.0705 1.1967 −13.595 56.26 0.0296 −2.0357 27.415 −149.81 0.0181 −0.9885 14.438 −88.884 0.0015 0.365 −6.2818 26.383 For Viscosity of Aqueous Blend of MAE and AEEA 2.1091 8.5499 −26.468 34.467 1.8837 5.8372 −24.017 38.413 1.5317 4.2522 −22.756 43.64 1.5006 −0.1534 3.8179 −10.548 1.2712 0.4061 −3.482 8.6057 0.8951 1.8215 −7.1829 8.1094 0.7535 0.6879 1.8879 −12.236 0.6546 −1.2541 18.937 −52.484 0.4788 0.4706 5.0216 −19.25

C4

−332.47 −175.82 1169.8 −222.01 18.183 −77.574 258.7 160.91 −37.537

Figure 3. Refractive index versus temperature of aqueous MAE and of aqueous AEEA for different weight fractions of (a) MAE and (b) AEEA w1: ⧫ 0.05; ▲ 0.10; * 0.15; + 0.20; − 0.25; ■ 0.30; and calculated values for eq 9 in (a) and for eq 10 in (b).

where w1, w2, and w3 are the weight fractions of MAE, AEEA, and water, respectively, and μ1,T, μ2,T, and μ3,T are the viscosities of pure MAE, pure AEEA, and water at temperature T, respectively. Values of model coefficients of w1 are presented in Table 5. For this correlation, AAD% was found to be 0.11. 3.2. Refractive Index. Refractive index for pure and aqueous MAE, pure and aqueous AEEA, and an aqueous blend of MAE and AEEA was found out in the temperature range of 293.15−333.15 K. Refractive index values of pure components are given in Table 2. The refractive index increased with increasing temperature in all samples, whereas it increased with increasing weight fraction of amines in aqueous mixtures, as shown in Figure 3. It is clearly shown in Figure 4 and Table 6 that refractive index data of an aqueous blend of MAE and AEEA are significantly varied by changing the fractions of MAE and AEEA in the blend. 3.2.1. Correlations of Refractive Index. Refractive index data for pure MAE and pure AEEA with respect to temperature were correlated by the newly proposed equation given by eq 8 in the temperature range of 293.15−333.15 K. nD = A(ln T )2 + B(ln T ) + C

Figure 4. Refractive index of aqueous blend of MAE and AEEA versus temperature for different weight fractions of MAE + AEEA, w1 + w2: for ⧫ 0.25 + 0.05; ■ 0.20 + 0.10; ▲ 0.15 + 0.15; × 0.10 + 0.20; * 0.05 + 0.25; and calculated values with eq 11.

polynomial of ln T. Negative values of coefficients A and C decrease nD with increasing ln T. The very low value of AAD% showed an excellent correlation equation. A new correlation based on the weight fraction of amines and temperature was introduced for the refractive index of aqueous MAE. j=2

nDm , T = w1nD1, T + w2nD2, T +

∑ Cjw1 j j=0

(8)

(9)

where w1 is the weight fraction of pure MAE and nDm,T, nD1, and nD2 are the refractive indexes of aqueous MAE mixture, pure MAE, and water at temperature T, respectively. Values of equation coefficients of w1 (C0, C1, and C2) were calculated by multiple regression and are reported in Table 7. For this correlation, AAD% = 0.052, which shows a good agreement of

The values of A, B, and C in eq 8 were found out using the MATLAB fitting tool. A = −0.2637, B = 2.8974, C = −6.5108, and AAD% = 0.0062 were found for pure MAE, whereas A = −0.3742, B = 4.1793, C = −10.1802, and AAD% = 0.0019 were calculated for pure AEEA. Equation 8 was a second-order F

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3.3. Deviation in Properties. Deviation in properties from an ideal solution to an aqueous mixture of amines was found by eq 1232 as

Table 6. Experimental Values of Refractive Index of Aqueous Blend MAE(1) + AEEA(2) + H2O(3) at 101.325 kPa Pressurea nD

ΔY = Y − (x1Y1 + x 2Y2)

w1/w2

w1/w2

w1/w2

w1/w2

w1/w2

T/(K)

0.25/0.05

0.20/0.10

0.15/0.15

0.10/0.20

0.05/0.25

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

1.3751 1.3747 1.3742 1.3736 1.373 1.3724 1.3716 1.3709 1.3701

1.3764 1.376 1.3755 1.375 1.3744 1.3738 1.3731 1.3724 1.3716

1.378 1.3775 1.3771 1.3766 1.376 1.3754 1.3747 1.374 1.3732

1.3798 1.3794 1.3789 1.3784 1.3778 1.3772 1.3765 1.3756 1.3748

1.382 1.3815 1.381 1.3804 1.3798 1.3791 1.3784 1.3776 1.3767

where ΔY is the deviation in property, Y is the value of the property of aqueous mixture, x1 and x2 are mol fractions of components 1 and 2, respectively, and Y1 and Y2 are the properties of pure components 1 and 2, respectively, of a binary mixture. Deviations in viscosities of aqueous MAE and aqueous AEEA from ideal solution were calculated by eq 13 and are presented in Table 3. Δμ = μ − (x1Δμ1 + x 2Δμ2 )

Standard uncertainties u are u(T) = 1 K, u(P) = 1 kPa, u(w1) = 0.01, and u(w2) = 0.01, and expanded uncertainties at 95% confidence level are U(nD) = 0.02nD.

correlated and experimental data of refractive index. Refractive index data of aqueous AEEA were fitted in a new correlation similar to eq 6, which can be presented as eq 10 j=2

∑ Cj w1 j j=0

ΔnD = nD − (x1nD1 + x 2nD2)

(10)

(14)

where ΔnD is a deviation in refractive index, nD is the refractive index of the aqueous mixture, and nD1 and nD2 are the refractive indexes of pure MAE/AEEA and water, respectively. Plots between deviations in the property (viscosity/refractive index) versus w1 are shown in the Supporting Information. 3.4. Redlich−Kister Fitting Model. Redlich and Kister studied that excess thermodynamic property (volume, viscosity, refractive index, etc.) of the binary mixture can be fitted as a polynomial function of the difference of mole fraction of two components, which can be represented as eq 1531

where nDm,T is the refractive index of the aqueous mixture, and w1 and w2 are weight fractions of pure AEEA and water, respectively. Values of coefficients of w1 were found using the least-squares method and are shown in Table 7. AAD% for this correlation is 0.01. An aqueous blend of MAE and AEEA has very less difference in refractive index values with respect to amine weight fractions. A new correlation analogous to eq 7 was given to fit experimental refractive index data with the weight fraction of components and temperature. nDm , T = exp[w1 ln nD1, T + w2 ln nD2, T + w2 ln nD3, T ]

i=n

j=2

+

(13)

where Δμ is a deviation in viscosity, μ is the viscosity of the aqueous mixture, μ1 and μ2 are the viscosities of pure MAE/ AEEA and viscosity of water, respectively, and x1 and x2 are mole fractions of MAE/AEEA and water, respectively. MAE shows positive deviation in viscosity, while AEEA shows negative deviation in viscosity, which may be due to strong adhesive forces between pure MAE and water molecules compared to those between pure AEEA and water molecules. Deviations in the refractive index of aqueous MAE and aqueous AEEA were calculated using eq 14 and are reported in Table 3.

a

nDm , T = exp[w1 ln nD1, T + w2 ln nD2, T ] +

(12)

∑ Cj w1

ΔY = x1x 2 ∑ Ai (x1 − x 2)i

j

(15)

i=0

(11)

j=0

where ΔY is a deviation in properties and Ai are the fitting coefficients of the Redlich−Kister model; n can be any positive number for which deviated data fit well. The standard deviation was calculated using eq 1633

where w1, w2, and w3 are the weight fractions of MAE, AEEA, and water, respectively. Values of coefficients of w1 were found using the least-squares method, which are presented in Table 7. AAD% was 0.001 for this equation.

Table 7. Regressed Coefficients (C0, C1, and C2) for Equations 9−11 eq 9

eq 10

eq 11

T/(K)

C0

C1

C2

C0

C1

C2

C0

C1

C2

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

0.0072 0.0068 0.0065 0.0063 0.006 0.0057 0.0054 0.0054 0.0053

−0.0708 −0.0709 −0.0698 −0.0702 −0.0686 −0.0672 −0.0675 −0.0683 −0.0688

0.1293 0.1300 0.1264 0.1257 0.1193 0.1136 0.1129 0.1121 0.1086

0.0039 0.0037 0.0036 0.0036 0.0033 0.0032 0.0031 0.003 0.0031

−0.0833 −0.0838 −0.0839 −0.0844 −0.0842 −0.0842 −0.0847 −0.0865 −0.0922

0.2134 0.2143 0.2151 0.2152 0.2146 0.214 0.2134 0.2157 0.2315

0.0074 0.0074 0.0077 0.0078 0.0082 0.0085 0.0089 0.0094 0.0099

−0.0073 −0.0067 −0.0046 −0.0008 −0.0005 0.0018 0.0033 0.0041 0.0062

0.0564 0.0564 0.0507 0.0393 0.0392 0.0335 0.0278 0.0278 0.0221

G

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Table 8. Regressed Coefficients for the Redlich−Kister Equation in Equations 12−15, R2, and Standard Deviation (s.d.) for the Binary Aqueous System of MAE(1) + H2O(2) and AEEA(1) + H2O(2) T/(K)

A0

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

−40 765 −35 428 3945.7 −10 605 −27 936 −9475.9 17 947 17 048 3792.2

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

1843.34 1790.86 1639.25 1426.38 1285.79 1229.07 984.74 930.84 864.31

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

−836 323.95 −157 040.40 62 962.85 −299 681.09 −209 602.08 −184 571.43 −90 921.32 −72 991.97 −45 958.84

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

5463.76 5516.44 6039.65 6207.59 5320.41 5053.00 5414.70 5297.89 5045.15

A1

A2

A3

For Deviation in Viscosity of MAE(1) + H2O(2) −183 282 −308 084 −229 673 −164 493 −285 346 −219 382 14 951 20 880 12 567 −48 590 −82 789 −62 300 −126 428 −213 705 −160 011 −41 983 −69 128 −50 202 80 479 135 490 101 425 75 746 126 206 93 399 16 184 25 866 18 297 For Deviation in Refractive Index of MAE(1) + H2O(2) 8462.73 14 565.46 11 138.01 8212.84 14 119.86 10 785.35 7519.30 12 931.19 9880.76 6552.67 11 287.10 8639.36 5905.69 10 171.51 7785.15 5634.24 9685.74 7399.93 4523.22 7793.26 5968.74 4285.55 7401.03 5681.64 3984.35 6890.12 5296.83 For Deviation in Viscosity of AEEA(1) + H2O(2) −3 666 148.71 −6 021 760.91 −4 391 982.37 −680 845.88 −1 105 223.89 −795 983.37 255 221.37 386 219.93 258 584.20 −1 310 599.02 −2 147 851.91 −1 563 259.51 −921 114.51 −1 516 890.00 −1 109 406.41 −808 797.65 −1 328 247.21 −968 868.40 −404 476.86 −673 939.08 −498 456.00 −323 152.37 −535 839.50 −394 396.63 199 002.22 −322 703.28 −232 265.12 For Deviation in Refractive Index of AEEA(1) + H2O(2) 24 185.37 40 139.08 29 599.26 24 384.22 40 411.73 29 757.77 26 660.93 44 123.56 32 444.95 27 400.52 45 343.71 33 338.64 23 520.70 38 983.85 28 707.26 22 365.26 37 112.05 27 359.76 23 980.73 39 813.94 29 365.36 23 506.65 39 096.49 28 885.79 22 424.85 37 362.84 27 652.88

ÄÅ n ÉÑ0.5 ÅÅ (ΔYexperimental, i − ΔYcalculated, i)2 ÑÑÑ ÅÅ ÑÑ σ = ÅÅÅ ∑ ÑÑ ÅÅ i = 1 ÑÑ n−p ÅÇ ÑÖ

(16)

s.d.

−64 098 −63 102 2696.9 −17 491 −44 793 −13 574 28 474 25 896 4824.2

0.99 0.99 0.97 0.98 0.99 0.99 0.99 0.99 0.99

0.043 0.022 0.091 0.076 0.043 0.054 0.005 0.098 0.014

3193.07 3088.53 2830.61 2479.50 2234.42 2120.19 1714.72 1636.07 1527.48

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.0010 0.0007 0.0012 0.0006 0.0004 0.0006 0.0004 0.0005 0.0002

−1 200 205.62 −214 642.61 64 565.19 −426 374.19 −304 063.01 −264 872.82 −138 088.67 −108 726.61 −62 607.95

0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.94

0.0417 0.0075 0.1145 0.0312 0.0996 0.0182 0.0349 0.1036 0.0655

8182.82 8214.81 8943.65 9188.85 7924.62 7560.85 8118.34 7998.94 7670.61

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

0.00091 0.00024 0.00068 0.00053 0.00017 0.00064 0.00051 0.00025 0.00111

4. CONCLUSIONS Viscosities and refractive indexes of pure and aqueous MAE, AEEA, and an aqueous blend of MAE and AEEA were found in the temperature range of 293.15−333.15 K at a 5 K temperature interval and atmospheric pressure. Both viscosity and refractive index decreased with increasing temperature, whereas they increased with increasing amine weight fraction in aqueous solutions. Several correlations were developed using experimental data of viscosity and refractive index. The experimental viscosity of pure MAE and pure AEEA with temperature was correlated by Arrhenius-type equation, and new correlations were also developed. AAD% for Arrheniustype equation was found to be 1.87 and 2.42 for MAE and

j=n

∑ aj ·T j j=0

R2

Redlich−Kister equation, as shown in the Supporting Information. Interaction parameters for coefficients of the Redlich−Kister equation were calculated and are listed in Table 9.

where n is the number of experimental points and p is the number of adjustable fitting coefficients. Coefficients Ai’s are a function of temperature and can be written as polynomial eq 1734 Ai ’s =

A4

(17)

where aj is the interaction parameter and T is the temperature in Kelvin. To calculate viscosity and refractive index, coefficients of the Redlich−Kister equation were calculated using multiple regressions and are listed in Table 8 for aqueous MAE and aqueous AEEA. Experimental data of viscosity and refractive index were compared to the calculated data obtained by the H

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ORCID

Table 9. Interaction Parameters for Coefficients for the Redlich−Kister Equation a0 A0 A1 A2 A3 A4 A0 A1 A2 A3 A4 A0 A1 A2 A3 A4 A0 A1 A2 A3 A4

a1

a2

For Viscosity of MAE 77.18 × 10 −780.02 × 103 2609.98 371.06 × 106 −3737.64 × 103 12 471.56 422.02 × 106 −4326.78 × 103 14 654.40 530.04 × 106 −5309.11 × 103 17 629.63 157.46 × 106 −1573.43 × 103 5213.93 For Refractive Index of MAE −513.19 × 103 5033.50 −16.31 −2370.54 × 103 23 254.27 −75.35 −4099.99 × 103 40 225.81 −130.36 −3146.73 × 103 30 878.40 −100.09 −904.22 × 103 8874.50 −28.77 For Viscosity of AEEA −2849.28 × 106 27 055.07 × 103 −85 581.16 −13 035.57 × 106 123 769.63 × 103 −391 483.10 −19 697.92 × 106 187 094.95 × 103 −592 000.63 −16 249.75 × 106 154 290.28 × 103 −488 028.50 −3340.49 × 106 31 755.21 × 103 −100 564.67 For Refractive Index of AEEA −2996.81 × 103 28 586.77 −90.58 −13 010.53 × 103 124 157.44 −393.57 −21 171.23 × 103 202 115.85 −640.94 −15 303.49 × 103 146 159.50 −463.68 −4146.13 × 103 39 615.65 −125.73 6

Monoj Kumar Mondal: 0000-0002-4544-7127 Notes

a3

The authors declare no competing financial interest.

■

−2.9 −13.81 −16.43 −19.43 −5.74

ACKNOWLEDGMENTS The authors acknowledge the support and financial assistance provided by the Indian Institute of Technology (Banaras Hindu University), Varanasi, and the Ministry of Human Resource Development, Government of India, to carry out the present work.

0.0175 0.080 0.140 0.110 0.0309

■

90.18 412.50 624.02 514.24 106.10 0.10 0.42 0.68 0.49 0.13

AEEA, respectively. For newly reported correlations, AAD% was 1.05 and 2.46 for MAE and AEEA, respectively. Viscosities of aqueous MAE, aqueous AEEA, and an aqueous blend of MAE and AEEA were measured and correlated by the newly proposed equation; AAD% for these correlations was 0.63, 0.40, and 0.11, respectively. Refractive indexes of pure MAE and pure AEEA were correlated by the newly proposed equation and showed a very low value of AAD%. Experimental refractive index data of aqueous MAE, aqueous AEEA, and an aqueous blend of MAE and AEEA were correlated by newly proposed correlations, and AAD% values were obtained as 0.0527, 0.01, and 0.001, respectively. The Redlich−Kister equation correlated the values of deviation in viscosity (Δμ) and deviation in refractive index (ΔnD) of aqueous MAE and aqueous AEEA, and the maximum standard deviations were calculated to be 0.091, 0.0012, 0.114, and 0.0011, respectively.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00171. Graphical comparisons between experimental data and available literature data; plots between deviations in the property (viscosity/refractive index) versus w1; and comparison plots of experimental data and calculated values obtained by the Redlich−Kister equation (PDF)

■

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +919452196638. Fax: + 91 542 2368092. I

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DOI: 10.1021/acs.jced.9b00171 J. Chem. Eng. Data XXXX, XXX, XXX−XXX