Viscometric Studies of Molecular Interactions in Binary Liquid Mixtures

Apr 16, 2018 - Department of Chemistry, Faculty of Science, University of Chittagong, Chittagong 4331, Bangladesh. §. Graduate School of Natural Scie...
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Viscometric Studies of Molecular Interactions in Binary Liquid Mixtures of Isomeric Xylenes with Methanol M. K. Mohammad Ziaul Hyder,† Muhammad A. Saleh,‡,∇ Faisal Hossain,§ Sajjad Husain Mir,∥ Koichi Iwakabe,⊥,¶ and Ismail M. M. Rahman*,#,¶ †

Department of Chemistry, Faculty of Engineering and Technology, Chittagong University of Engineering and Technology, Chittagong 4349, Bangladesh ‡ Department of Chemistry, Faculty of Science, University of Chittagong, Chittagong 4331, Bangladesh § Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan ∥ Department of Nanosystem Science, Graduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama, Kanagawa 236-0027, Japan ⊥ Chemical Process Department, Process Technology Laboratory, R&D Center, Mitsui Chemicals, Inc., 1-2, Waki 6-chome, Waki-cho, Kuga-gun, Yamaguchi 740-0061, Japan # Institute of Environmental Radioactivity, Fukushima University, 1 Kanayagawa, Fukushima City, Fukushima 960-1296, Japan ABSTRACT: Dynamic viscosities (ηexp) for the binary mixtures of methanol with isomeric (o-, m-, and p-derivatives) xylenes were measured at T = (303.15, 308.15, 313.15, 318.15, and 323.15) K and atmospheric pressure (p = 101 kPa). The viscosity deviation (Δη) that has been derived from the ηexp was correlated using a Redlich− Kister-type equation. The ηexp values were compared with the calculated viscosities (ηcal) obtained using generalized correlation models, such as Bingham, Arrhenius, Kendall−Monroe, Grunberg−Nissan, and Andrade/DIPPR. The changes in the ηexp of solvent mixtures rather than in the pure fluids, or deviations from ηcal, have been discussed in terms of the molecular interactions and structural effects due to the component molecules. Furthermore, the quantum chemical density-functional theory calculations were used to predict the optimized geometry and total energies of the pure fluids and their binary mixtures.

1. INTRODUCTION The viscosities of organic fluids, either pure or in mixtures, are required to be estimated precisely for the application in process simulation calculations.1−4 The experimental determination of fluid-mixture viscosities at different ratios of the components has, thus, become a research issue in recent years.5−14 The alkanols, an amphiphilic material having both biological and industrial significance, have been acclaimed for their exceptional solvation ability.15 The transport properties of mixtures containing alkanols and other hydrocarbons having a strong proton-donating group, i.e., CH3 in xylenes, are interesting due to the presence of H-bonding as the dominant contributor to the intermolecular interaction. The association between the alkanol molecules occurs through the formation of linear chains, while the extent of such associations depends upon the concentration of alkanol, temperature, and pressure. Accurate information on the viscosity of alkanols mixed with apolar hydrocarbons is useful for engineering designs of transport equipment or pipelines.16 The current work, which is a continuation of our previous research on the binary mixtures of organic fluids,17−25 reports experimental viscosities (ηexp) of methanol with isomeric xylenes both for the pure species and for a number of mixtures covering the entire miscibility range of 303.15 to 323.15 K (interval 5 K) and at atmospheric pressure (p = 101 kPa). In © XXXX American Chemical Society

the binary blends of an alkanol with isomeric xylenes, the aliphatic polar liquid (methanol) has been considered to be the solute, while the apolar hydrocarbon (o-, m-, or p-xylene) has been considered to be the solvent. A favorable interaction between the hydroxyl group in the monohydric alkanol and the delocalized π-electrons in the aromatic ring of isomeric xylenes can be assumed during the mixing26 followed by fragmentation of the H-bonding. The ηexp values for the binary systems were compared with the calculated viscosities (ηcal) obtained using the correlations proposed by Bingham,27 Arrhenius,28 Kendall− Monroe,29 Grunberg−Nissan,30 and Andrade/DIPPR.31−33 The viscosities of binary mixtures of methanol + o-xylene34 and + p-xylene35,36 have been reported in the literature at different temperatures. However, we are not aware of any viscometric data in the literature for the systems of m-xylene with methanol as presented in this study or the comparison with o- or p-xylenes under similar experimental conditions covering a wide temperature range. The objectives of the current work were, therefore, to characterize the composition− temperature-dependent molecular interactions in the entirely miscible mixtures of methanol with isomeric xylenes, study the Received: November 8, 2017 Accepted: April 16, 2018

A

DOI: 10.1021/acs.jced.7b00971 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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effect of CH3 unit positions in o-, m-, or p-xylene, and assess the capability of correlative models in assuming the viscosities of binary mixtures containing isomers. The density-functional theory (DFT) calculation, which employs quantum-mechanical considerations for the prediction of component behavior in a system, was used to describe intermolecular interactions such as van der Waals forces and so forth.

liquids were stored over molecular sieves for several weeks before use to reduce the absorption of water, and a similar handling protocol was followed for the binary mixtures after preparation. The ηexp of binary systems was measured, covering the range of 0.0−1.0 mole fraction at T = 303.15 to 323.15 K using a precalibrated A-type Ostwald viscometer. The efflux time, as measured using an electronic digital stopwatch, was varied within the range of 80 to 760 s, which would be sufficient to exclude the kinetic energy correction. A thermostatically controlled water bath equipped with a Thermo Haake DC10 controller (Thermo Fisher Scientific; Waltham, MA) and a minimum−maximum thermometer (Brannan Thermometers; Cumberland, U.K.) was used to attain the desired temperatures. The uncertainties in flow-time measurements and temperatures were ±0.10 s and ±0.05 K, respectively, while the overall uncertainty for ηexp was ±0.0083 mPa·s. Triplicate measurements were performed for the pure liquids and all mixture compositions, and averaged values were considered in all calculations.

2. MATERIALS AND METHODS Methanol, o-xylene, m-xylene, and p-xylene, as procured from Merck KGaA (Darmstadt, Germany), were used without any additional purification. The corresponding characteristics of component liquids in the binary mixtures are summarized in Table 1. The ηexp of pure fluids was compared with the literature values to ascertain the purity of the components in the mixtures (Table 2). Table 1. Specifications of the Components in Binary Mixtures component methanol o-xylene m-xylene p-xylene

source Merck Merck Merck Merck

KGaA KGaA KGaA KGaA

CAS no.

initial purity (mass fraction)

purification

67-56-1 95-47-6 108-38-3 106-42-3

0.99 0.99 0.99 0.99

none none none none

3. RESULTS AND DISCUSSION 3.1. Experimental Observations. The experimental viscosities (ηexp) and viscosity deviations (Δη) of binary systems methanol + o-xylene, + m-xylene, and + p-xylene over the temperature range of (303.15−323.15) K are listed in Table 3. The Δη values were computed from the ηexp data using the relation shown in eq 1, while a Redlich−Kister type smoothing equation (eq 2)37 was used to represent the composition dependence of Δη

Table 2. Comparison of Experimental Viscosity Values (ηexp) of Pure Liquids with Literature Values at T = (303.15, 308.15, 313.15, 318.15, and 323.15) K and p = 101 kPaa ηexp/mPa·s component methanol

o-xylene

m-xylene

p-xylene

T/K 303.15 308.15 313.15 318.15 323.15 303.15 308.15 313.15 318.15 323.15 303.15 308.15 313.15 318.15 323.15 303.15 308.15 313.15 318.15 323.15

exp 0.513 0.480 0.450 0.422 0.397 0.710 0.666 0.628 0.591 0.560 0.554 0.524 0.498 0.472 0.452 0.574 0.542 0.514 0.486 0.461

lit 0.5154 0.4799 0.448 0.4216 0.406 0.709 0.665 0.6261 0.589 0.558 0.5531 0.5201 0.4970 0.471 0.4488 0.5756 0.541 0.5140 0.484 0.4641

Δη = ηexp − (x1η1 + x 2η2)

ref

(1)

n

48 49 50 49 50 51 52 51 52 51 51 53 51 52 51 51 52 51 52 51

Y = x1x 2 ∑ Ai (1 − 2x1)i i=0

(2)

In eqs 1 and 2, x1 and η1 represent the mole fraction and viscosity of methanol, respectively, while x2 and η2 are the corresponding quantities of o-, m-, and p-xylenes. It should be noted that the data points for pure components were excluded in the correlation to the Redlich−Kister equation. In eq 2, Y = Δη and a least-squares regression approach were used to obtain the equation coefficient (Ai) with the standard deviation at each of the temperatures (as calculated using eq 3) by fitting the equation to the experimental values (Table 4) ⎡ (Y − Y )2 ⎤1/2 exp cal ⎥ σ (Y ) = ⎢Σ ⎢⎣ ⎥⎦ n−p

(3)

In eq 3, n and p represent the number of experimental points and the number of coefficients of eq 2, respectively, while the experimental and calculated values of the property (Y = Δη) were denoted using Yexp and Ycal. The distribution of Δη values over the whole range of compositions showed minima at x1 ≈ 0.1, and the maxima appeared at x1 ≈ 0.7 in all three systems (Figure 1). The observed trend in Δη distributions was in the following order of binary combinations of methanol with the isomeric xylenes, oxylene > p-xylene > m-xylene, while the magnitudes of Δη decrease with the rise in temperature in the range of 303.15 to 323.15 K (i.e., ∂Δη/∂T > 0). The Δη values decreased to the negative region in the small concentration range of methanol in the binary mixtures with xylenes, which indicates that the

a Standard uncertainties (u): u(t) = 0.10 s, u(T) = 0.05 K, u(p) = 10 kPa, and u(η) = 0.0083 mPa·s.

Binary mixtures of methanol + o-xylene, + m-xylene, or + pxylene were prepared by mass on a B 204-S analytical balance (Mettler Toledo; Columbus, OH) with an uncertainty of ±0.0001 g. The mole fractions of binary systems, which were completely miscible over the whole composition range, were obtained from the measured masses of components in mixtures with an estimated uncertainty of ± 1.0 × 10−4. All of the pure B

DOI: 10.1021/acs.jced.7b00971 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Composition, Viscosities (η) and Viscosity Deviations (Δη) for the Binary Systems of Methanol (1) + o-Xylene (2), + m-Xylene (2), and + p-Xylene (2) at T = (303.15, 308.15, 313.15, 318.15, and 323.15) K (x1, Mole Fraction of Methanol in Methanol + Xylenes Mixtures; ηexp, Experimental Viscosities; ηcal, Calculated Viscosities) at p = 101 kPaa measured ηexp/mPa·s

x1

Δηexp/mPa·s

Bingham

Arrhenius

Kendell−Munroe

Grunberg−Nissan

Andrade/DIPPR

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

0.710 0.688 0.667 0.647 0.625 0.606 0.587 0.567 0.549 0.531 0.513

0.710 0.710 0.706 0.697 0.681 0.663 0.639 0.611 0.581 0.548 0.513

0.709 0.686 0.675 0.669 0.666 0.663 0.654 0.636 0.608 0.567 0.513

0.666 0.646 0.625 0.607 0.586 0.568 0.549 0.531 0.514 0.496 0.480

0.666 0.665 0.660 0.650 0.635 0.617 0.595 0.569 0.542 0.511 0.480

0.666 0.643 0.631 0.625 0.621 0.617 0.609 0.593 0.567 0.529 0.480

0.628 0.608 0.589 0.571 0.551 0.534 0.516 0.499 0.483 0.466 0.450

0.628 0.625 0.619 0.609 0.594 0.577 0.556 0.532 0.507 0.479 0.450

0.627 0.604 0.591 0.585 0.581 0.577 0.569 0.553 0.530 0.495 0.450

0.591 0.572 0.554 0.537 0.518 0.501 0.485 0.468 0.452 0.437 0.422

0.591 0.587 0.579 0.569 0.554 0.538 0.518 0.496 0.473 0.448 0.422

0.592 0.568 0.555 0.548 0.544 0.540 0.532 0.518 0.496 0.464 0.422

0.560 0.542 0.524 0.508 0.490 0.474 0.458

0.560 0.555 0.547 0.536 0.522 0.506 0.487

0.559 0.535 0.522 0.515 0.511 0.506 0.499

0.0000 0.1007 0.2013 0.2961 0.4030 0.5003 0.6010 0.7025 0.8006 0.9013 1.0000

0.710 0.684 0.674 0.671 0.666 0.663 0.655 0.638 0.610 0.567 0.513

0.000 −0.005 0.004 0.019 0.036 0.051 0.064 0.067 0.057 0.035 0.000

0.710 0.690 0.670 0.651 0.630 0.611 0.592 0.572 0.552 0.533 0.513

0.0000 0.1007 0.2013 0.2961 0.4030 0.5003 0.6010 0.7025 0.8006 0.9013 1.0000

0.666 0.641 0.631 0.626 0.621 0.617 0.607 0.595 0.567 0.530 0.480

0.000 −0.007 0.002 0.015 0.030 0.044 0.053 0.059 0.050 0.032 0.000

0.666 0.648 0.629 0.611 0.591 0.573 0.554 0.535 0.517 0.498 0.480

0.0000 0.1007 0.2013 0.2961 0.4030 0.5003 0.6010 0.7025 0.8006 0.9013 1.0000

0.628 0.603 0.591 0.587 0.582 0.577 0.569 0.554 0.531 0.495 0.450

0.000 −0.007 0.000 0.012 0.026 0.038 0.048 0.051 0.045 0.027 0.000

0.628 0.610 0.592 0.575 0.556 0.539 0.521 0.503 0.486 0.468 0.450

0.0000 0.1007 0.2013 0.2961 0.4030 0.5003 0.6010 0.7025 0.8006 0.9013 1.0000

0.591 0.566 0.555 0.550 0.543 0.538 0.531 0.516 0.494 0.462 0.422

0.000 −0.008 −0.002 0.009 0.021 0.032 0.042 0.044 0.039 0.024 0.000

0.591 0.574 0.557 0.541 0.523 0.506 0.489 0.472 0.455 0.438 0.422

0.0000 0.1007 0.2013 0.2961 0.4030 0.5003 0.6010

0.560 0.535 0.523 0.517 0.511 0.506 0.496

0.000 −0.008 −0.004 0.006 0.017 0.027 0.034

0.560 0.543 0.527 0.512 0.494 0.479 0.462

Methanol (1) + o-Xylene (2) T/K = 303.15 0.710 0.687 0.665 0.645 0.623 0.603 0.584 0.565 0.548 0.530 0.513 T/K = 308.15 0.666 0.645 0.624 0.605 0.584 0.565 0.547 0.529 0.512 0.496 0.480 T/K = 313.15 0.628 0.607 0.587 0.569 0.549 0.532 0.514 0.497 0.481 0.465 0.450 T/K = 318.15 0.591 0.571 0.552 0.535 0.516 0.499 0.482 0.466 0.451 0.436 0.422 T/K = 323.15 0.560 0.541 0.522 0.506 0.488 0.472 0.456 C

DOI: 10.1021/acs.jced.7b00971 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. continued measured ηexp/mPa·s

x1

Δηexp/mPa·s

Bingham

Arrhenius

Kendell−Munroe

Grunberg−Nissan

Andrade/DIPPR

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

0.442 0.427 0.412 0.398

0.467 0.445 0.422 0.397

0.486 0.465 0.436 0.397

0.554 0.549 0.545 0.541 0.537 0.533 0.529 0.525 0.521 0.517 0.513

0.554 0.559 0.563 0.564 0.563 0.560 0.555 0.548 0.538 0.526 0.513

0.555 0.543 0.542 0.547 0.556 0.563 0.568 0.567 0.558 0.540 0.513

0.524 0.520 0.515 0.511 0.506 0.502 0.497 0.493 0.488 0.484 0.480

0.524 0.528 0.531 0.531 0.529 0.526 0.520 0.512 0.503 0.492 0.480

0.524 0.513 0.511 0.514 0.520 0.526 0.530 0.530 0.522 0.506 0.480

0.498 0.493 0.488 0.483 0.478 0.474 0.469 0.464 0.460 0.455 0.450

0.498 0.500 0.501 0.500 0.497 0.493 0.487 0.480 0.471 0.461 0.450

0.496 0.486 0.483 0.484 0.488 0.493 0.496 0.496 0.490 0.475 0.450

0.472 0.467 0.462 0.457 0.451 0.446 0.441 0.436 0.431 0.426 0.422

0.472 0.473 0.472 0.470 0.467 0.462 0.456 0.449 0.441 0.432 0.422

0.470 0.461 0.457 0.456 0.459 0.462 0.466 0.466 0.461 0.447 0.422

0.452 0.446 0.441 0.435

0.452 0.451 0.449 0.446

0.447 0.438 0.433 0.431

0.7025 0.8006 0.9013 1.0000

0.484 0.462 0.434 0.397

0.039 0.032 0.020 0.000

0.446 0.430 0.414 0.398

0.0000 0.1008 0.2003 0.2999 0.4000 0.4997 0.6003 0.7001 0.8001 0.9012 1.0000

0.554 0.539 0.542 0.548 0.553 0.560 0.566 0.570 0.565 0.546 0.513

0.000 −0.010 −0.003 0.006 0.016 0.027 0.037 0.045 0.044 0.028 0.000

0.554 0.549 0.545 0.541 0.537 0.533 0.529 0.525 0.521 0.517 0.513

0.0000 0.1008 0.2003 0.2999 0.4000 0.4997 0.6003 0.7001 0.8001 0.9012 1.0000

0.524 0.510 0.510 0.514 0.519 0.526 0.530 0.532 0.526 0.509 0.480

0.000 −0.010 −0.005 0.003 0.013 0.024 0.032 0.039 0.037 0.025 0.000

0.524 0.520 0.515 0.511 0.506 0.502 0.498 0.493 0.489 0.484 0.480

0.0000 0.1008 0.2003 0.2999 0.4000 0.4997 0.6003 0.7001 0.8001 0.9012 1.0000

0.498 0.483 0.483 0.485 0.488 0.493 0.496 0.497 0.492 0.477 0.450

0.000 −0.010 −0.006 0.002 0.009 0.019 0.027 0.033 0.032 0.022 0.000

0.498 0.493 0.488 0.484 0.479 0.474 0.469 0.465 0.460 0.455 0.450

0.0000 0.1008 0.2003 0.2999 0.4000 0.4997 0.6003 0.7001 0.8001 0.9012 1.0000

0.472 0.456 0.456 0.457 0.460 0.462 0.465 0.466 0.460 0.445 0.422

0.000 −0.011 −0.006 0.000 0.008 0.015 0.023 0.029 0.028 0.018 0.000

0.472 0.467 0.462 0.457 0.452 0.447 0.442 0.437 0.432 0.427 0.422

0.0000 0.1008 0.2003 0.2999

0.452 0.435 0.433 0.433

0.000 −0.011 −0.008 −0.002

0.452 0.446 0.441 0.436

T/K = 323.15 0.440 0.426 0.411 0.398 methanol (1) + m-xylene (2) T/K = 303.15 0.554 0.549 0.545 0.541 0.537 0.533 0.529 0.525 0.521 0.517 0.513 T/K = 308.15 0.524 0.519 0.515 0.510 0.506 0.501 0.497 0.493 0.488 0.484 0.480 T/K = 313.15 0.498 0.493 0.488 0.483 0.478 0.474 0.469 0.464 0.459 0.455 0.450 T/K = 318.15 0.472 0.467 0.462 0.456 0.451 0.446 0.441 0.436 0.431 0.426 0.422 T/K = 323.15 0.452 0.446 0.440 0.435

D

DOI: 10.1021/acs.jced.7b00971 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 3. continued measured ηexp/mPa·s

x1

Δηexp/mPa·s

Bingham

Arrhenius

Kendell−Munroe

Grunberg−Nissan

Andrade/DIPPR

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

0.430 0.424 0.419 0.413 0.408 0.403 0.397

0.442 0.437 0.430 0.423 0.416 0.407 0.397

0.432 0.435 0.438 0.438 0.434 0.421 0.397

0.574 0.567 0.561 0.555 0.549 0.543 0.537 0.531 0.525 0.519 0.513

0.574 0.587 0.596 0.600 0.600 0.596 0.587 0.574 0.557 0.537 0.513

0.574 0.559 0.556 0.560 0.567 0.573 0.576 0.572 0.561 0.541 0.513

0.542 0.536 0.529 0.523 0.517 0.510 0.504 0.498 0.492 0.486 0.480

0.542 0.553 0.559 0.562 0.561 0.556 0.548 0.535 0.520 0.501 0.480

0.542 0.528 0.524 0.526 0.531 0.536 0.538 0.535 0.525 0.508 0.480

0.514 0.507 0.501 0.494 0.488 0.481 0.475 0.469 0.463 0.457 0.450

0.514 0.514 0.514 0.511 0.507 0.501 0.494 0.485 0.475 0.463 0.450

0.513 0.500 0.494 0.494 0.497 0.501 0.503 0.501 0.493 0.477 0.450

0.486 0.479 0.472 0.466 0.459 0.453 0.447 0.440 0.434 0.428 0.422

0.486 0.492 0.495 0.496 0.493 0.488 0.479 0.468 0.455 0.440 0.422

0.486 0.474 0.467 0.466 0.467 0.470 0.472 0.471 0.464 0.449 0.422

0.4000 0.4997 0.6003 0.7001 0.8001 0.9012 1.0000

0.434 0.437 0.437 0.437 0.432 0.419 0.397

0.004 0.012 0.018 0.024 0.024 0.016 0.000

0.430 0.425 0.419 0.414 0.408 0.403 0.397

0.0000 0.1001 0.1998 0.3015 0.4005 0.5000 0.5999 0.7005 0.8000 0.8984 1.0000

0.574 0.559 0.556 0.563 0.567 0.573 0.576 0.577 0.568 0.549 0.513

0.000 −0.009 −0.005 0.007 0.018 0.030 0.039 0.045 0.043 0.029 0.000

0.574 0.568 0.562 0.556 0.550 0.544 0.537 0.531 0.525 0.519 0.513

0.0000 0.1001 0.1998 0.3015 0.4005 0.5000 0.5999 0.7005 0.8000 0.8984 1.0000

0.542 0.527 0.524 0.527 0.529 0.533 0.536 0.536 0.529 0.512 0.480

0.000 −0.009 −0.006 0.003 0.012 0.022 0.032 0.038 0.036 0.026 0.000

0.542 0.536 0.530 0.523 0.517 0.511 0.505 0.498 0.492 0.486 0.480

0.0000 0.1001 0.1998 0.3015 0.4005 0.5000 0.5999 0.7005 0.8000 0.8984 1.0000

0.514 0.498 0.494 0.496 0.498 0.501 0.504 0.502 0.495 0.479 0.450

0.000 −0.009 −0.007 0.002 0.010 0.019 0.028 0.032 0.032 0.022 0.000

0.514 0.507 0.501 0.495 0.488 0.482 0.476 0.469 0.463 0.457 0.450

0.0000 0.1001 0.1998 0.3015 0.4005 0.5000 0.5999 0.7005 0.8000 0.8984 1.0000

0.486 0.469 0.465 0.466 0.467 0.469 0.469 0.469 0.462 0.447 0.422

0.000 −0.010 −0.008 0.000 0.007 0.015 0.022 0.028 0.028 0.019 0.000

0.486 0.479 0.473 0.466 0.460 0.454 0.447 0.441 0.434 0.428 0.422

T/K = 323.15 0.429 0.424 0.418 0.413 0.408 0.403 0.397 Methanol (1) + p-Xylene (2) T/K = 303.15 0.574 0.567 0.561 0.555 0.549 0.543 0.537 0.531 0.525 0.519 0.513 T/K = 308.15 0.542 0.536 0.529 0.523 0.516 0.510 0.504 0.498 0.492 0.486 0.480 T/K = 313.15 0.514 0.507 0.500 0.494 0.487 0.481 0.475 0.468 0.462 0.456 0.450 T/K = 318.15 0.486 0.479 0.472 0.465 0.459 0.453 0.446 0.440 0.434 0.428 0.422

E

DOI: 10.1021/acs.jced.7b00971 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 3. continued measured x1

Bingham

Arrhenius

Kendell−Munroe

Grunberg−Nissan

Andrade/DIPPR

ηexp/mPa·s

Δηexp/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

ηcal/mPa·s

0.461 0.445 0.439 0.440 0.440 0.443 0.443 0.441 0.434 0.420 0.397

0.000 −0.010 −0.010 −0.002 0.004 0.013 0.020 0.024 0.024 0.016 0.000

0.461 0.455 0.449 0.442 0.436 0.429 0.423 0.417 0.410 0.404 0.397

0.461 0.455 0.448 0.442 0.435 0.429 0.422 0.416 0.410 0.404 0.397

0.461 0.460 0.458 0.454 0.449 0.443 0.436 0.427 0.418 0.409 0.397

0.461 0.450 0.443 0.440 0.440 0.442 0.444 0.443 0.437 0.423 0.397

0.0000 0.1001 0.1998 0.3015 0.4005 0.5000 0.5999 0.7005 0.8000 0.8984 1.0000 a

T/K = 323.15 0.461 0.455 0.448 0.441 0.435 0.428 0.422 0.416 0.410 0.404 0.397

Standard uncertainties (u): u(t) = 0.10 s, u(T) = 0.05 K, u(p) = 10 kPa, u(x1) = 0.0001, and u(η) = 0.0083 mPa·s.

resulting in much less resistance to flow and a negative deviation in viscosity. The Δη values became positive in the increased mole fraction of methanol, as attributable to the selfassociation of methanol molecules through the H-bonding with the increase in methanol concentration in the mixtures. A similar pattern for Δη distributions has been observed for the mixtures of chloroform and methanol.38 In the literature, there are reports on the viscosities of methanol + o-xylene34 and methanol + p-xylene.35,36 A comparison of the ηexp values from the current work with those reported in the literature, as illustrated in Figure 2,

Table 4. Coefficients (Ai) of the Redlich−Kister Equation (eq 2), Expressing Viscosity Deviations (Δη /mPa·s) and Standard Deviation (σ) for the Binary Systems of Methanol (1) + o-Xylene (2), + m-Xylene (2), and + p-Xylene (2) at T = (303.15, 308.15, 313.15, 318.15 and 323.15) K T/K

A0

303.15 308.15 313.15 318.15 323.15

0.2091 0.1767 0.1551 0.1319 0.1100

303.15 308.15 313.15 318.15 323.15

0.1124 0.0961 0.0779 0.0666 0.0493

303.15 308.15 313.15 318.15 323.15

0.1201 0.0918 0.0786 0.0628 0.0533

A1

A2

Methanol (1) + o-Xylene (2) −0.2822 −0.0532 −0.2496 −0.0417 −0.2307 −0.0522 −0.2115 −0.0522 −0.1863 −0.0559 Methanol (1) + m-Xylene (2) −0.2153 0.0181 −0.2000 0.0021 −0.1744 −0.0003 −0.1595 −0.0123 −0.1431 −0.0144 Methanol (1) + p-Xylene (2) −0.2182 −0.0037 −0.1991 0.0077 −0.1774 −0.0048 −0.1572 −0.0042 −0.1558 −0.0261

A3

σ

0.0070 −0.0254 −0.0133 −0.0124 −0.0184

0.0012 0.0015 0.0008 0.0013 0.0010

−0.0861 −0.0667 −0.0696 −0.0632 −0.0677

0.0018 0.0011 0.0012 0.0014 0.0012

−0.0744 −0.0608 −0.0634 −0.0718 −0.0451

0.0010 0.0008 0.0007 0.0010 0.0007

Figure 2. Comparison between the experimental viscosities (ηexp) against the mole fraction of methanol (x1) for the binary systems of (a) methanol (1) + o-xylene (2) and (b, c) methanol (1) + p-xylene (2) with the data from the present work (●, 303.15 K; ▼, 308.15 K; ▲, 313.15 K; ⧫, 318.15 K; and ■, 323.15 K) and the work of (a) Prasad et al.34 (b) Wanchoo and Narayan,35 and (c) Prasad et al.,36 (○, 303.15 K; ▽, 308.15 K; Δ, 313.15 K; ◊, 318.15 K; and □, 323.15 K).

species formed upon mixing methanol with xylene flow more easily than was expected ideally. Methanol remained highly associated in the pure state, and it was dissociated into monomers or smaller multimers when added to xylenes,

Figure 1. Viscosity deviations (Δη) against the mole fraction of methanol (x1) for the binary systems of methanol (1) + (a) o-xylene (2), + (b) mxylene (2), and + (c) p-xylene (2) at different temperatures: ●, 303.15 K; ○, 308.15 K; ▲, 313.15 K; □, 318.15 K; and ■, 323.15 K. The solid lines represent the computed values obtained from the Redlich−Kister equation (eq 3) using the parameters listed in Table 4. F

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Table 5. Parameters for the Grunberg−Nissan and Andrade/DIPPR Viscosity Models Used to Correlate the Experimental (ηexp) and Calculated (ηcal) Data for the Binary Systems of Methanol (1) + o-Xylene (2), + m-Xylene (2), and + p-Xylene (2) at T = (303.15, 308.15, 313.15, 318.15, and 323.15) K G12

Grunberg−Nissan T/K → methanol (1) + o-xylene (2) methanol (1) + m-xylene (2) methanol (1) + p-xylene (2) Andrade/DIPPR methanol (1) + o-xylene (2)

methanol (1) + m-xylene (2)

methanol (1) + p-xylene (2)

i

303.15 0.3736 0.1998 0.3736 j

308.15 0.3487 0.1877 0.3487

313.15 0.3282 0.1606 0.1635

318.15 0.2989 0.1422 0.2989

323.15 0.2808 0.1178 0.1334

aij

bij

cij

dij

1 1 2 2 1 1 2 2 1 1 2 2

1 2 1 2 1 2 1 2 1 2 1 2

−11.2753 −12.2535 −12.2535 −11.1366 −11.2753 −10.4837 −10.4837 −10.7509 −11.2753 −10.3825 −10.3825 −10.9532

1252.4283 1464.6909 1464.6909 1165.7513 1252.4283 842.6918 842.6918 998.1673 1252.4283 813.0075 813.0075 1068.3854

−0.4308 0.7244 0.7244 0.0398 −0.4308 −7.0956 −7.0956 −0.2548 −0.4308 −7.2082 −7.2082 −0.0344

0.0010 −159.5922 −159.5922 −0.0010 0.0010 2273.3180 2273.3180 65.5231 0.0010 2327.7306 2327.7306 0.0012

Table 6. Root-Mean-Square-Deviation (RMSD) Values for the Viscosities When the Experimental (ηexp) Data are Correlated with Calculated (ηcal) Data from the Viscosity Models for the Binary Systems of Methanol (1) + o-Xylene (2), + m-Xylene (2), and + p-Xylene (2) at T = (303.15, 308.15, 313.15, 318.15, and 323.15) K Bingham

T/K →

303.15

308.15

313.15

318.15

323.15

methanol (1) + o-xylene (2) methanol (1) + m-xylene (2) methanol (1) + p-xylene (2) Arrhenius

mPa·s mPa·s mPa·s T/K →

0.0438 0.0284 0.0291 303.15

0.0379 0.0246 0.0240 308.15

0.0332 0.0208 0.0209 313.15

0.0287 0.0181 0.0179 318.15

0.0242 0.0151 0.0157 323.15

methanol (1) + o-xylene (2) methanol (1) + m-xylene (2) methanol (1) + p-xylene (2) Kendell−Munroe

mPa·s mPa·s mPa·s T/K →

0.0492 0.0286 0.0296 303.15

0.0430 0.0249 0.0246 308.15

0.0381 0.0211 0.0214 313.15

0.0333 0.0185 0.0184 318.15

0.0286 0.0155 0.0163 323.15

methanol (1) + o-xylene (2) methanol (1) + m-xylene (2) methanol (1) + p-xylene (2) Grunberg−Nissan

mPa·s mPa·s mPa·s T/K →

0.0474 0.0285 0.0294 303.15

0.0413 0.0248 0.0244 308.15

0.0364 0.0210 0.0212 313.15

0.0318 0.0184 0.0183 318.15

0.0271 0.0154 0.0161 323.15

methanol (1) + o-xylene (2) methanol (1) + m-xylene (2) methanol (1) + p-xylene (2) Andrade/DIPPR

mPa·s mPa·s mPa·s T/K →

0.0231 0.0182 0.0251 303.15

0.0212 0.0165 0.0238 308.15

0.0192 0.0147 0.0148 313.15

0.0176 0.0135 0.0198 318.15

0.0158 0.0123 0.0128 323.15

methanol (1) + o-xylene (2) methanol (1) + m-xylene (2) methanol (1) + p-xylene (2)

mPa·s mPa·s mPa·s

0.0014 0.0039 0.0039

0.0013 0.0023 0.0021

0.0010 0.0016 0.0013

0.0016 0.0020 0.0021

0.0019 0.0027 0.0026

indicated a similar ηexp pattern with the change in the xylene component in mixtures and the variation in trends with increasing temperature. However, the discrepancies between the newly measured data and those taken from the literature (Figure 2) were up to 0.05 mPa·s. It should be noted that the source or composition of solvents (methanol or xylenes), as used by other researchers to formulate the binary mixtures, was either not mentioned or procured from local producers. Hence, the disagreement could be attributable to the variations in solvent purity as used in the current work compared to those of others. 3.2. Correlation and Prediction. The generalized correlations for the viscosity prediction of liquid mixtures consider the interaction between component molecules to be negligible, assuming them to be additives, and model it using

the ideal viscosity data.39 In this study, the ηcal values obtained using Bingham (eq 4),27 Arrhenius (eq 5),28 and Kendall− Monroe (eq 6)29 equations, which predict the solution viscosity of binary blends without using any adjustable parameter, were compared with ηexp (Table 3)

ηcal = η1x1 + η2x 2

(4)

ηcal = e(x1ln η1+ x2 ln η2)

(5)

ηcal = (x1η11/3 + x 2η21/3)3

(6)

An inverse mixing law is proposed in the Bingham model; the logarithmic-scale average of the viscosities is computed in the Arrhenius model, and the viscosity as a cubic average of the G

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Table 7. Comparison of the Experimental, ηexp, and Calculated, ηcal, Viscosities in Terms of the Average Absolute Deviation, AAD, and the Maximum Deviation of the Viscosity, |Eη|max, for the Binary Systems of Methanol (1) + o-Xylene (2), + m-Xylene (2), and + p-Xylene (2) at T = (303.15, 308.15, 313.15, 318.15, and 323.15) K Bingham T/K

AAD/%

Arrhenius

|Eη|max/%

AAD/%

303.15 308.15 313.15 318.15 323.15

4.82 4.46 4.16 3.88 3.51

10.44 9.99 9.15 8.61 7.98

5.47 5.14 4.83 4.53 4.12

303.15 308.15 313.15 318.15 323.15

3.52 3.27 2.95 2.75 2.50

7.84 7.36 6.59 6.26 5.54

3.55 3.31 3.00 2.82 2.55

303.15 308.15 313.15 318.15 323.15

3.60 3.16 2.94 2.69 2.58

7.87 7.08 6.45 6.06 5.54

3.66 3.24 3.03 2.79 2.65

Kendell−Munroe

|Eη|max/%

AAD/%

2

ln ηcal =

kij = aij + mij = cij +

AAD =

Eη =

(7)

|Eη|max/%

AAD/%

|Eη|max/%

2.68 2.63 2.55 2.49 2.35

4.71 4.61 4.63 4.41 4.43

0.15 0.14 0.12 0.23 0.27

0.38 0.36 0.34 0.41 0.69

2.43 2.38 2.25 2.19 2.12

4.83 4.28 4.15 4.00 3.87

0.48 0.29 0.21 0.27 0.43

1.34 0.72 0.69 1.04 1.19

3.17 3.18 2.25 2.98 2.17

7.04 6.84 4.03 6.49 4.32

0.37 0.28 0.18 0.31 0.39

1.34 0.81 0.53 0.87 1.04

Np

1 Np

(11)

Np

∑ |E η , j |

ηexp − ηcal ηexp

(12)

j

× 100 (13)

In eqs 11 and 12, Np stands for the number of total data points, while the other notations have the same significance as mentioned before. The RMSDs, AADs, and |Eη|max decreased with the system temperature increase for the Bingham, Arrhenius, Kendall−Monroe, and Grunberg−Nissan models. However, the corresponding values for the correlations with Andrade/DIPPR had no definite pattern. The RMSDs and AADs for the Bingham, Arrhenius, and Kendall−Monroe equations were larger than those obtained for the Grunberg− Nissan or Andrade/DIPPR equations. The lowest values were obtained for Andrade/DIPPR, and those were at least 10 times lower than those of Grunberg−Nissan. The differences in the RMSDs or AADs pattern might be attributable to the number of fitting parameters involved in the model. The Bingham, Arrhenius, and Kendall−Monroe models quantitatively analyze the interactions to predict the viscosity, while the accuracy has frequently been questioned due to the absence of interaction parameters.43 The Grunberg−Nissan model has one binary interaction parameter to be obtained at each temperature, while the Andrade/DIPPR model has a total of six parameters. Although the appropriate model for viscosity prediction cannot be decided only by the number of parameters,18 the Andrade/ DIPPR model that has more parameters than the other models checked in the current study provided the best prediction results for the viscosities of the methanol−xylene binary

(8)

bij (9)

dij T

AAD/%

Σ(ηexp − ηcal )2

RMSD =

2

T

Andrade/DIPPR

(eq 12) and the maximum deviation of the dynamic viscosity (| Eη|max) (eq 13) (Table 7) were also calculated

∑ ∑ (kijxixj + mijxi 2xj 2) i=1 j=1

|Eη|max/%

Methanol (1) + o-Xylene (2) 11.46 5.25 11.13 11.04 4.91 10.70 10.23 4.61 9.88 9.74 4.29 9.37 9.15 3.90 8.77 Methanol (1) + m-Xylene (2) 7.90 3.54 7.88 7.43 3.30 7.41 6.69 2.98 6.66 6.39 2.80 6.34 5.67 2.53 5.62 Methanol (1) + p-Xylene (2) 7.99 3.64 7.95 7.23 3.21 7.18 6.62 3.00 6.57 6.26 2.76 6.19 5.76 2.63 5.69

viscosities was estimated by the Kendall−Monroe model.39 The correlative models that use viscosity data of pure fluids, related functional group parameters, and one or more interaction parameters40,41 have been employed to include the interaction between the components in alkanol-containing hydrocarbon mixtures.42 Hence, different from the mentioned mixing rules, the Grunberg−Nissan (eq 7)30 and Andrade/DIPPR (eq 8−10)31−33 models, which use interaction parameters to estimate changes in the viscosities of binary blends due to the mixing of molecules of different characteristics, were applied to predict ηcal and compare it with ηexp ln ηcal = x1 ln η1 + x 2 ln η2 + x1x 2G12

Grunberg−Nissan

(10)

In eqs 4 to 7, x1 and η1 have the same significance as mentioned before. In eq 7, G12 represents the interaction parameter of the Grunberg−Nissan model that has to be determined at each of the temperatures. aij, bij, cij, and dij are the adjustable parameters used in the Andrade/DIPPR model (eqs 9 and 10). A total of six parameters (a11, a12, a22, b11, b12, and b22) were correlated to the experimental data in the Andrade/DIPPR model, while a12 = a21, b12 = b21, and cij, dij are set to zero for simplification in this study. Parameters obtained from the Grunberg−Nissan and Andrade/DIPPR models are listed in Table 5. The deviations between ηexp and ηcal for the Bingham, Arrhenius, Kendall−Monroe, Grunberg−Nissan, and Andrade/ DIPPR models were used in calculating the corresponding root-mean-square-deviation (RMSD) values (eq 11) (Table 6). The average absolute deviation, AAD, of the dynamic viscosity H

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Figure 3. Comparison between the experimental viscosities (ηexp, ○) with the calculated values (ηcal) obtained using correlative models (Bingham, dark red; Arrhenius, black; Kendell−Munroe, bright red; Grunberg−Nissan, green; and Andrade/DIPPR, blue) for the binary systems of methanol (1) + (a) o-xylene (2), + (b) m-xylene (2), and + (c) p-xylene (2) at T = (303.15, 308.15, 313.15, 318.15, and 323.15) K against the mole fraction of methanol (x1).

The computed interaction energies (kJ mol−1) among the components in the binary systems varied as follows: methanol + p-xylene (−0.09) < methanol + o-xylene (−12.25) < methanol + m-xylene (−16.34). The DFT calculations identified moderate H-bonding in the methanol + o-xylene and methanol + m-xylene systems, as evident from the respective bond distances of 2.51 and 2.59 Å. The two H atoms attached to the substituted carbons of o-xylene possessing the highest electropositivity are arranged closer to each other in a symmetric position, which interacts with the O atom in methanol at almost the same strength and at a similar distance (Figure 5a). However, only one H atom in the substituted carbons of m-xylene has the highest atomic charge of 0.123 and, more appositely, is accessible for greater interaction with the O atom in methanol (Figure 5b). Although the substituted carbons in p-xylene have more electropositive H atoms than do the other xylene isomers, they are of the same strength and are symmetrically very far from each other, unlike in the case of o-xylene. Hence, the optimized complex geometries for the methanol + p-xylene system showed negligible interaction and no H-bonding. The quantum-mechanical approach has been used to predict the physicochemical properties of a solvent including viscosity,45 and the B3LYP level of theory was used to discover the correlations between ηexp and ηcal.46 The interaction energy between the components in a mixed solvent system was assumed to control the transport behavior at all temperatures, while H-bonding can outperform the effect for any correlations.47 The findings for the interaction energies and H-bonding between the methanol and isomeric xylenes have been used to explain the corresponding ηexp trends (Table 3 and Figure 3). The ortho isomer of xylene when mixed with methanol in different ratios resulted in a continuous decrease in ηexp as attributable to the better fluidity of the mixture compared to that of the pure state. It might be due to the higher interaction and strong H-bonding with methanol using both side chains of o-xylene. The decrease in ηexp for the mix of methanol and the meta isomer of xylene started after the addition of a certain methanol concentration because only one of the side-chain methyl groups in m-xylene interacts with methanol, yielding a much lower interaction. A nonsignificant variation in ηexp after mixing the para isomer of xylene with methanol, even in an increasing ratio, confirmed a negligible interaction between the two components, as shown by the quantum-mechanical calculation.

mPa·s with average relative errors of