Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension

Article pubs.acs.org/jced

Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension, and Flash Point of Selected Ternary Mixtures of n-Butylcyclohexane + a Linear Alkane (n-Hexadcane or n-Dodecane) + an Aromatic Compound (Toluene, n-Butylbenzene, or n-Hexylbenzene) Dianne J. Luning Prak,*,† Sonya Ye,† Margaret McLaughlin,† Jim S. Cowart,‡ and Paul C. Trulove† †

Chemistry Department, United States Naval Academy 572M Holloway Road Annapolis, Maryland 21402, United States Mechanical Engineering Department, United States Naval Academy 590 Holloway Road Annapolis, Maryland 21402, United States

‡

S Supporting Information *

ABSTRACT: Researchers seek to understand the combustion of petroleum fuel, which contains hundreds of compounds, by studying properties and oxidation behavior of less complex mixtures (surrogates) containing fuel components. In this study, viscosities and densities (293.15 to 343.15 K), speeds of sound (293.15 to 333.15 K), surface tensions (∼314 K) and flash points were measured for ternary mixtures of representative fuel components: n-alkanes, aromatic compounds, and n-butylcyclohexane. Mixture surface tensions and flashpoints fell between the pure component values. The speeds of sound for ternary mixtures containing n-dodecane and n-butylcyclohexane increased with increasing aromatic compound concentration. As the aromatic compound concentration in mixtures with n--hexadecane and n--butylcyclohexane increased, the mixtures’ speeds of sound remained level or decreased to a minimum before increasing to the value of the aromatic compound. The isentropic bulk moduli increased with increasing aromatic compound concentration, except for toluene for which a minimum was found. Excess molar volumes were positive, viscosity deviations were negative, and a McAllister three-body equation successfully modeled viscosity. Positive excess molar volumes and negative dynamic viscosities suggest that dispersion forces dominate the molecular interactions in these mixtures.

1. INTRODUCTION Many physical property measurements are required as part of the ASTM qualification process for jet fuel and the military specifications for diesel and jet fuels.1−3 These requirements find their basis in the performance of petroleum-based fuels, which contain hundreds of compounds. Property prediction is very complex when so many compounds are present, so researchers will often try to formulate less complex mixtures which match key properties of the fuel. These formulations contain either chemical components in the fuel or model compounds from the general categories of hydrocarbons found in the fuel. Cost, safety, availability, and purity of compounds, and availability of chemical kinetic−oxidation mechanisms are also considered when selecting compounds.4,5 The exact composition of the mixture is often determined by matching fuel properties with mixture properties predicted by empirical models.6−14 The validation of empirical models requires comparison with experimental data. Pitz and Mueller state that aromatic compounds, cycloalkanes, n-alkanes, and isoalkanes have been used in the formulation of less complex mixtures to represent diesel fuel.15 The goal of this study was to measure the physical properties of three-component mixtures containing an n-alkane (n-dodecane or n-hexadecane), an aromatic compound (toluene, n-butylbenzene, or n-hexylbenzene), and n-butylcyclohexane and compare them to diesel and jet fuel. This article not subject to U.S. Copyright. Published 2017 by the American Chemical Society

The properties measured in this study include density, viscosity, and flash point because they are part of the specifications for military fuel.2,3 Surface tension is also measured because the primary spray breakup characteristics for injectors are represented by dimensionless numbers (Ohnesorge, Weber, and Reynolds numbers) that include surface tension along with density and viscosity.16 Fuel injection timing has been found to depend on fuel bulk modulus, which is calculated from speed of sound and density, so speed of sound is also measured herein.17,18 Since comparisons of property measurements are often used in the formulation of simple mixtures for fuels, the values from the petroleum-based diesel and jet fuel are compared to those of the mixtures measured herein to assess their potential usefulness. Previous studies have investigated the physical properties of mixtures containing these compounds. The density and viscosity have been measured for two-component mixtures of butylcylclohexane with n-alkanes ranging from n-heptane to n-hexadecane,19−21 two-component mixtures of toluene with n-alkanes ranging from n-octane to n-hexadecane,22−27 and twocomponent mixtures of butylbenzene with n-alkanes ranging Received: May 23, 2017 Accepted: August 11, 2017 Published: August 29, 2017 3452

DOI: 10.1021/acs.jced.7b00466 J. Chem. Eng. Data 2017, 62, 3452−3472

Journal of Chemical & Engineering Data

Article

Table 1. Sample Information

a

chemical name

CASRN

molar mass (g/mol)a

source/lot number

mole fraction purity

analysis method

toluene (C7H8) n-butylcyclohexane (C10H20) n-hexadecane (C16H34) n-butylbenzene (C12H14) n-hexylbenzene (C12H18) n-dodecane (C12H26)

108-88-3 1678-93-9 544-76-3 104-51-8 1077-16-3 112-40-3

92.138 ± 0.007 140.27 ± 0.01 226.44 ± 0.02 134.218 ± 0.005 162.27 ± 0.01 170.335 ± 0.006

Pharmco-Aaeper/C14F12BLK-0000TOL TCI/ZMU4G Acros Organics/A0360424 TCI/Y3XBD Alfa Aesar/10185885 TCI/MHGKM

0.9989 0.999 0.998 0.999 0.996 0.991

GCb GCb GCb GCb GCb GCb

Calculated using values in ref 47. bGas−liquid chromatography, as specified in the Certificates of Analysis provided by the chemical suppliers.

Table 2. Comparison of the Measured Densities ρ of n-Hexadecane, n-Dodecane, n-Butylcyclohexane, Toluene, n-Butylbenzene, and n-Hexylbenzene with Literature Valuesa kg·m−3 T/K

this studya

this studya

lit.

293.15 303.15 313.15 323.15 333.15 343.15

773.42 766.47 759.55 752.63 745.71 738.8

293.15 303.15 313.15 323.15 333.15 343.15

748.79 741.54 734.25 726.94 719.59 712.2

293.15

857.69

303.15

850.09

n-Hexadecane 773.43 ± 0.06b, 773.69d, 773.7 ± 0.2c 766.59 ± 0.05b, 766.75d, 766.8 ± 0.2c 759.55d, 759.83d, 759.9 ± 0.2c, 759.71 ± 0.07b 752.64d, 752.80 ± 0.12b, 752.9 ± 0.2c, 752.91d 745.73d, 745.86 ± 0.18b, 745.99d, 746.0 ± 0.2c 738.90 ± 0.25b, 739.0 ± 0.2c, 739.07d n-Dodecane 749.09 ± 0.28i, 749.37 ± 0.2%m, 749.89 ± 0.5h 741.64 ± 0.5h, 741.70 ± 0.29i, 741.96 ± 0.2%g 734.34 ± 0.30i, 734.35 ± 0.5h, 734.58 ± 0.2%g 726.99 ± 0.32i, 727.04 ± 0.5h, 727.18 ± 0.2%g 719.64 ± 0.33i, 719.69 ± 0.5h, 719.78 ± 0.2%g 712.2 ± 0.5h, 712.27 ± 0.34i, 712.37 ± 0.2%g n-Hexylbenzene 851.6,u 858.00 ± 0.40s, 858.02 ± 0.40s, 858.28 ± 0.40s, 859.20 ± 1.00v, 860.0 ± 2.0w 862.4 ± 0.8t 852.40 ± 0.60s

313.15 323.15 333.15 343.15

842.49 834.87 827.48 819.5

846.8 ± 0.8t 834.88e 831.7 ± 0.8t 821.7 ± 2.0w

799.33 791.82 784.28 776.70 769.09 761.4 866.84 857.52 848.14 838.68 829.15 819.6 860.60 852.56 844.50 836.41 828.29 820.3

lit. n-Butylcyclohexane 799.35 ± 0.39j, 779.37q,799.44,k 799.60l 791.75 ± 0.26j, 791.88q,791.95,k 792.10l 784.35q, 784.38 ± 0.63j, 784.41,k 784.56l 776.70q, 777.17r, 777.25 ± 0.95j 769.09q,769.55r, 769.80 ± 0.60j, 770.36 ± 0.80j 761.43q, 761.88r Toluene 866.84 ± 0.05n, 866.89 ± 0.05%p 857.54 ± 0.05n, 857.57 ± 0.05%p 848.17 ± 0.05n, 848.20 ± 0.05%p 838.73 ± 0.05n, 838.76 ± 0.05%p 829.20 ± 0.05n, 829.23 ± 0.05%p 819.56 ± 0.09n, 819.61 ± 0.05%p n-Butylbenzene 859.50 ± 0.60x, 860.052z, 860.15 ± 0.35x, 860.25 ± 0.30x, 861.26o 851.3y, 852.16 ± 0.10x, 852.23o, 852.428z, 852.43 ± 0.50x 844.6y, 844.82 ± 0.51x, 845.172z 837.00 ± 0.67x, 838.509z 828.21f 819.9f

a Standard uncertainties u are u(T) = 0.01 K. The high uncertainties are not due to instrument issues but are caused by impurities in the samples. The expanded uncertainties Uc are for hexadecane: Uc(ρ) = 0.30 kg·m−3 for T < 343.15 K and Uc(ρ) = 0.86 kg·m−3 for T ≥ 343.15 K; for n-butylcyclohexane, Uc(ρ) = 0.17 kg·m−3 for T < 343.15 K and Uc(ρ) = 0.5 kg·m−3 for T ≥ 343.15 K; for n-dodecane, Uc(ρ) = 1.5 kg·m−3 for T < 343.15 K and Uc(ρ) = 4.3 kg·m−3 for T ≥ 343.15 K; for toluene, Uc(ρ) = 0.17 kg·m−3 for T < 343.15 K and Uc(ρ) = 0.5 kg·m−3 for T ≥ 343.15 K; n-hexylbenzene, Uc(ρ) = 0.5 kg·m−3 for T ≥ 343.15 K. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2). Uc(ρ) = 0.69 kg·m−3 for T < 343.15 K and Uc(ρ) = 2.0 kg·m−3 for T ≥ 343.15 K; n-butylbenzene, Uc(ρ) = 0.17 kg·m−3 for T < 343.15 K and bReference 71: Equation for best of density of n-hexadecane is ρ/kg·m3 = 956.848 − [0.557634 × T/K] + [2.68578 × 10−4 × (T/K)2] − [1.24436 × 10−7 × (T/K)3]. cReference 72. dReference 73. eReference 29. fReference 28. g Reference 74. hReference 75. iReference 71. jReference 76. Equation for best of density of butylcyclohexane is ρ/kg·m3 = 1127.02 − [1.46341 × T/K] + [1.17912 × 10−3 × (T/K)2]. kReference 19. lReference 77. mReference 74. nReference 79. Equation for best of density of toluene is ρ/kg·m3 = 1.18621 × 103 − [1.47573 × T/K] + 2.08566 × 10−3 × (T/K)2 − 2.61945 × 10−6 (T/K)3. oReference 61. pReference 74. qReference 80. r Reference 78. sReference 81. tReference 82. uReference 83. vReference 84. wReferences 81 and 85 for error. xReference 86. yReference 87. z Reference 88.

from n-decane to n-heptadecane,28 and two-component mixtures of hexylbenzene with hexadecane.29 The density and speed of sound have been measured for two-component mixtures of toluene with cyclohexane, methylcyclohexane, and butylcyclohexane.21,30 These studies have reported excess molar volumes that deviate from zero in either a positive or negative direction depending on the study. Density and viscosity have also been measured for ternary mixtures containing n-hexylbenzene with two alkanes (heptane, octane, or nonane)31 and for ternary mixtures containing three of the following: toluene, ethylbenzene, octane, tetradecane, and hexadecane.32 These researchers found

negative viscosity deviations in the three-component systems. Speeds of sound have been reported for two-component mixtures of toluene with n-alkanes, cyclohexanes and alkylcyclohexane.21,22,25−27,30 No work has been reported on the density, viscosity, surface tension, speed of sound, and flashpoint of ternary mixtures containing the n-alkanes (n-dodecane or n-hexadecane), aromatic compounds (toluene, n-butylbenzene, or n-hexylbenzene) and the cycloalkane (n-butylcyclohexane) used in the current study. The mixtures studied herein were selected because they contain components from the categories of compounds found 3453



Article

Table 3. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν as a Function of Mole Fraction of n-Butylbenzene x1 in Mixtures with n-Butylcyclohexane (Mole Fraction x2) and n-Hexadecane (Mole Fraction x3) from Temperature T = (293.15 to 343.15) K and Pressure P = 0.1 MPaa ρ

η

ν

ρ

η

ν

ρ

η

ν

x3/x2

x1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

0.3333

0.0000 0.2004 0.4004 0.6003 0.8002 0.0000 0.2009 0.4003 0.6002 0.8000 0.0000 0.2010 0.4009 0.6010 0.8005

789.50 800.34 812.49 826.28 842.18 782.68 793.17 805.49 820.19 838.22 777.44 787.52 799.77 815.10 834.69

0.0000 0.2004 0.4004 0.6003 0.8002 0.0000 0.2009 0.4003 0.6002 0.8000 0.0000 0.2010 0.4009 0.6010 0.8005

767.73 778.18 789.91 803.23 818.60 761.41 771.51 783.37 797.52 814.87 756.48 766.20 778.00 792.73 811.54

0.9992

3.0006

0.3333

0.9992

3.0006

T = 293.15 K 1.78 2.26 1.56 1.95 1.38 1.70 1.25 1.51 1.14 1.35 2.29 2.92 1.93 ± 0.02 2.44 ± 0.03 1.65 2.05 1.41 1.72 1.22 1.45 2.84 3.66 2.35 2.98 1.93 2.41 1.58 1.94 1.29 1.55 T = 323.15 K 1.08 1.41 0.977 1.25 0.887 1.12 0.815 1.01 0.755 0.922 1.33 1.74 1.16 ± 0.02 1.51 ± 0.03 1.03 1.31 0.905 1.13 0.799 0.981 1.58 2.08 1.36 1.78 1.17 1.50 0.994 1.25 0.842 1.04

782.27 792.98 804.99 818.63 834.35 775.60 785.97 798.14 812.66 830.46 770.45 780.42 792.53 807.66 827.00 760.42 770.74 782.32 795.49 810.68 754.28 764.26 775.95 789.91 807.03 749.49 759.07 770.71 785.23 803.77

T = 303.15 K 1.50 1.90 1.32 1.66 1.18 1.46 1.07 1.31 0.983 1.18 1.87 2.42 1.61 ± 0.03 2.04 ± 0.03 1.39 1.74 1.20 1.48 1.05 1.26 2.29 2.97 1.92 2.46 1.61 2.03 1.34 1.65 1.11 1.34 T = 333.15 K 0.942 1.24 0.855 1.11 0.780 1.00 0.720 0.905 0.670 0.827 1.14 1.51 1.01 ± 0.02 1.32 ± 0.03 0.898 1.16 0.797 1.01 0.708 0.878 1.34 1.79 1.17 1.54 1.01 1.31 0.872 1.11 0.744 0.926

775.01 785.59 797.46 810.94 826.49 768.51 778.75 790.77 805.10 822.68 763.47 773.32 785.27 800.21 819.28 753.1 763.2 774.7 787.8 802.7 747.2 756.9 768.5 782.3 799.1 742.5 751.9 763.4 777.7 796.0

T = 313.15 K 1.26 1.63 1.13 1.44 1.02 1.28 0.928 1.14 0.857 1.04 1.56 2.04 1.36 ± 0.02 1.74 ± 0.03 1.19 1.50 1.04 1.29 0.909 1.11 1.88 2.47 1.60 2.08 1.36 1.73 1.15 1.43 0.960 1.17 T = 343.15 K 0.827 1.10 0.756 0.990 0.693 0.895 0.643 0.816 0.600 0.748 0.991 1.33 0.882 ± 0.02 1.17 ± 0.02 0.793 1.03 0.708 0.905 0.633 0.792 1.16 1.56 1.02 1.35 0.889 1.17 0.772 0.992 0.663 0.833

a

x1 is the mole fraction of n-butylbenzene, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-hexadecane. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, Uc(ρ) = 0.30 kg·m−3 for T < 343.15 K and Uc(ρ) = 0.86 kg·m−3 for T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

DeWitt et al.43 examined the swelling behavior of nitrile rubber, fluorosilicone, and fluorocarbon o-rings when aromatic compounds were added to alternative fuels that contained no aromatic compounds. They were able to produce the amount of seal swelling found in petroleum-based fuel by adding 10% by volume or more of an aromatic mixture to the aromatic-free alternative fuel. Graham et al.44 also found that the addition of 10% of aromatic compounds, including toluene, enhanced the swelling of nitrile rubber in contact with a synthetic fuel, S-5, which contained no aromatic compounds. Detailed combustion kinetic models have been developed for toluene and butylbenzene,45,46 and the model of Metcalf et al.45 for toluene included 329 species and 1888 reversible reactions.

in conventional fuels and some information already exists on the combustion behavior of each compound. A three-component mixture was selected because many surrogates contain three compounds.33−36 The alkanes were chosen because n-dodecane and n-hexadecane are often the model alkanes used for jet and diesel fuel, respectively, and their combustion kinetic mechanisms have been developed.37,38 The n-butylcyclohexane was chosen because it falls within the range of cycloalkanes reported in fuels (usually less than 22 carbons), has been used in some preliminary investigations into its kinetic behavior, and is much less expensive than the longer chain cycloalkanes. Natelson et al.39 has modeled n-butylcyclohexane kinetics using 80 reactions involving 42 species to simulate jet fuel reaction behavior at high temperatures. The combustion of butylcyclohexane has also been measured in shock tubes and flow reactors.39−41 An aromatic compound was included in the mixture because the presence of aromatic compounds in fuel is important to maintain the swelling of engine seals. The lack of aromatic compounds, which is found in some alternative fuels, can cause leaks in aircraft fuel systems.42

2. MATERIALS All chemicals were used as received from the supplier (Table 1). The mixtures were prepared by first making a two-component mixture of the n-alkane and n-butylcyclohexane by weighing each component on a Mettler Toledo AG204 analytical balance and 3454



Article

Table 4. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν as a Function of Mole Fraction n-Hexylbenzene (1) x1 in Mixtures with n-Butylcyclohexane (Mole Fraction x2) and n-Hexadecane (mole fraction x3) from Temperature T = (293.15 to 343.15) K and Pressure P = 0.1 MPaa ρ

η

ν

ρ

η

ν

ρ

η

ν

x3/x2

x1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

0.3335

0.0000 0.2004 0.4006 0.6003 0.7997 0.0000 0.2004 0.4008 0.6008 0.8003 0.0000 0.2005 0.4025 0.6007 0.8004

789.61 801.97 814.90 828.48 842.72 782.68 794.83 808.23 823.01 839.39 777.44 789.28 802.98 818.08 836.26

0.0000 0.2004 0.4006 0.6003 0.7997 0.0000 0.2004 0.4008 0.6008 0.8003 0.0000 0.2005 0.4025 0.6007 0.8004

767.83 780.00 792.73 806.09 820.12 761.41 773.32 786.44 800.91 816.95 756.48 767.97 781.46 796.22 813.97

0.9997

2.9967

0.3335

0.9997

2.9967

T = 293.15 K 1.78 1.71 1.66 1.65 1.64 2.29 2.10 1.95 1.82 1.74 2.84 2.52 2.25 2.02 1.83 T = 323.15 K 1.08 1.05 1.03 1.02 1.02 1.33 1.25 1.17 1.11 1.07 1.58 1.44 1.31 1.21 1.11

2.26 2.13 2.04 1.99 1.95 2.92 2.65 2.42 2.22 2.07 3.66 3.20 2.80 2.47 2.19

782.37 794.67 807.53 821.03 835.20 775.60 787.67 800.98 815.66 831.93 770.54 782.11 795.81 810.81 828.84

1.41 1.34 1.30 1.26 1.24 1.74 1.61 1.49 1.39 1.31 2.08 1.87 1.68 1.51 1.36

760.52 772.63 785.29 798.60 812.56 754.28 766.11 779.14 793.51 809.44 749.48 760.87 774.27 788.90 806.50

T = 303.15 K 1.49 1.43 1.40 1.38 1.38 1.87 1.74 1.62 1.53 1.46 2.29 2.05 1.85 1.68 1.53 T = 333.15 K 0.942 0.913 0.897 0.888 0.889 1.14 1.08 1.02 0.970 0.930 1.34 1.23 1.13 1.05 0.966

1.90 1.80 1.73 1.68 1.65 2.42 2.21 2.02 1.87 1.75 2.97 2.63 2.32 2.07 1.84

775.12 787.34 800.14 813.57 827.67 768.51 780.50 793.72 808.29 824.45 763.47 775.05 788.65 803.52 821.41

1.23 1.18 1.14 1.11 1.09 1.51 1.40 1.31 1.22 1.15 1.79 1.62 1.46 1.32 1.20

753.2 765.2 777.7 791.0 804.9 747.2 758.9 771.9 786.1 802.0 742.5 753.8 767.0 781.5 798.9

T = 313.15 K 1.26 1.22 1.19 1.18 1.18 1.56 1.46 1.37 1.30 1.24 1.88 1.70 1.54 1.41 1.29 T = 343.15 K 0.821 0.803 0.791 0.784 0.785 0.991 0.939 0.891 0.853 0.820 1.16 1.07 0.986 0.915 0.849

1.63 1.55 1.49 1.45 1.42 2.04 1.87 1.72 1.60 1.50 2.47 2.20 1.96 1.76 1.57 1.09 1.05 1.02 0.994 0.975 1.33 1.24 1.15 1.08 1.02 1.56 1.41 1.29 1.17 1.06

a

x1 is the mole fraction of n-hexylbenzene, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-hexadecane. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, Uc(ρ) = 0.69 kg·m−3 for T < 343.15 K and Uc(ρ) = 2.0 kg·m−3 for T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

density were measured using Anton Paar SVM 3000 Stabinger Viscometer at temperatures between (293.15 and 343.15) K. The accuracy of the SVM 3000 Stabinger Viscometer was tested using a certified viscosity reference standard (Standard S3, Cannon Instrument Company). If the density deviated by more than 0.1% from the reference value and if the viscosity deviated by more than 1% from the reference value, then the instrument was cleaned and retested. The density values from the viscometer are less precise than from the speed of sound instrument, so the density values at the lower temperatures are reported by the DSA 5000. The accuracy of the DSA 5000 analyzer was checked before use with degassed distilled water. If it failed the check, it was recalibrated as specified by the manufacturer. A Kruss DS100 drop shape analyzer was used to measure surface tension at room temperature. Prior to analysis, the air and organic liquid density and the needle diameter, which was measured by a micrometer (Mitutoyo), were entered into the

mixing. A sample of this mixture was then weighed on the balance to which was added the aromatic compound, which was also weighed. The combined expanded uncertainty (level of confidence = 0.95, k = 2) for the mole fraction of each component was 0.0001, as determined through error propagation of the masses and molar masses. The molar mass errors were based on molar masses and errors calculated using atomic masses in Harris47 (see Table 1) and an analytical balance error of 0.0004 g.

3. METHODS All methods have been described previously.48,49 Density and speed of sound were measured using an Anton Paar DSA 5000 Density and Sound Analyzer at temperatures between (293.15 and 333.15) K. The DSA 5000 measures speed of sound using a propagation time technique with one transducer emitting sound waves at a frequency of approximately 3 MHz and a second transducer receiving those waves.50 The viscosity and 3455



Article

Table 5. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν as a Function of Mole Fraction n-Butylbenzene x1 in Mixtures with n-Butylcyclohexane (Mole Fraction x2) and n-Dodecane (Mole Fraction x3) from Temperature T = (293.15 to 343.15) K and Pressure P = 0.1 MPaa ρ

η

ν

ρ

η

ν

ρ

η

ν

x3/x2

x1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

0.3332

0.0000 0.2001 0.4003 0.6003 0.8000 0.0000 0.2005 0.4007 0.6008 0.8005 0.0000 0.2007 0.4011 0.6013 0.8007

783.9 796.4 810.2 825.4 842.1 770.6 784.6 800.3 817.9 838.0 759.0 774.0 791.1 810.8 833.6

0.0000 0.2001 0.4003 0.6003 0.8000 0.0000 0.2005 0.4007 0.6008 0.8005 0.0000 0.2007 0.4011 0.6013 0.8007

761.6 773.8 787.2 802.0 818.3 748.5 762.2 777.5 794.7 814.3 737.1 751.7 768.5 787.7 810.1

1.0002

3.0005

0.3332

1.0002

3.0005

T = 293.15 K 1.34 1.71 1.23 1.55 1.15 1.42 ± 0.02 1.10 1.34 1.07 1.27 1.38 1.79 1.27 1.62 1.19 1.48 1.12 1.37 1.08 1.29 1.42 1.87 1.29 ± 0.02 1.67 ± 0.03 1.21 1.53 1.14 1.40 1.08 1.30 T = 323.15 K 0.846 1.11 0.796 1.03 0.755 0.959 0.731 0.912 0.713 0.872 0.865 1.16 0.813 1.07 0.769 0.99 0.739 0.93 0.717 0.88 0.883 1.20 0.821 1.09 ± 0.02 0.782 1.02 0.746 0.95 0.719 0.89

776.5 788.9 802.6 817.6 834.2 763.3 777.2 792.7 810.2 830.1 751.7 766.6 783.6 803.2 825.8 754.1 766.2 779.5 794.2 810.4 741.1 754.6 769.8 786.9 806.3 729.7 744.2 760.8 780.0 802.1

T = 303.15 K 1.13 1.46 1.05 1.34 0.990 1.23 0.952 1.16 0.925 1.11 1.17 1.53 1.08 1.39 1.01 1.28 0.965 1.19 0.932 1.12 1.20 1.59 1.10 ± 0.02 1.43 ± 0.03 1.03 1.32 0.976 1.21 0.934 1.13 T = 333.15 K 0.743 0.985 0.701 0.915 0.668 0.857 0.649 0.817 0.635 0.783 0.757 1.02 0.715 0.948 0.680 0.883 0.656 0.834 0.639 0.792 0.770 1.06 0.721 0.968 0.690 0.907 0.660 0.847 0.639 0.797

769.1 781.4 794.9 809.8 826.3 755.9 769.7 785.1 802.5 822.2 744.4 759.2 776.0 795.5 817.9 746.5 758.4 771.7 786.2 802.3 733.6 747.0 762.1 779.1 798.3 722.2 736.1 753.1 772.1 794.1

T = 313.15 K 0.974 1.27 0.910 1.17 0.860 1.08 0.830 1.03 0.809 0.978 1.00 1.32 0.933 1.21 0.879 1.12 0.841 1.05 0.814 0.990 1.02 1.37 0.944 ± 0.02 1.24 ± 0.02 0.894 1.15 0.848 1.07 0.816 1.00 T = 343.15 K 0.656 0.879 0.623 0.821 0.596 0.773 0.581 0.739 0.569 0.710 0.668 0.911 0.635 0.850 0.607 0.796 0.586 0.752 0.572 0.716 0.678 0.939 0.639 0.868 0.614 0.816 0.589 0.763 0.573 0.721

a x1 is the mole fraction of n-butylbenzene, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-dodecane. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, Uc(ρ) = 1.5 kg·m−3 for T < 343.15 K and Uc(ρ) = 4.3 kg·m−3 for T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

4. RESULTS 4.1. Density. The densities for each component match the literature values within the error of the measurement, except for n-hexylbenzene (Table 2). The unknown or low purities of n-hexylbenzene from those studies account for the discrepancies as discussed in Luning Prak et al.29 The ternary mixture densities increased with increasing mole fraction of the aromatic compound and an increasing amount of n-butylcyclohexane (smaller x3/x2) (Tables 3−7). When the density values for petroleum-based jet and diesel fuel of 800.9 and 848 kg·m−3 at 293.15 K, respectively,51,52 are compared, the density of jet fuel could be matched by those of mixtures containing a variety of combinations of an aromatic compound, n-butylcyclohexane, and n-alkane tested. In general lower mole fractions of the aromatic compound would be needed for density matching of the jet fuel. The mixtures would have to contain a large amount of the aromatic compound to match the density of the diesel fuel.

software. An organic liquid droplet was then formed on the tip of the needle, magnified, and analyzed using the Young LaPlace equation by the computer software to obtain the surface tension. Setaflash Series 8 closed cup flash point tester model 82000-0 (Stanhope-Seta) was used to measure flashpoint. The flash/no flash setting was used. The manufacturer’s literature specifies that this flash point tester conforms to ASTM D3828 (gas ignition option), ASTM D1655 (gas ignition option), ASTM D3278, ASTM D7236, and ASTM E502. For each instrument two or more measurements (60 in the case of the surface tension) were taken to determine the average and standard deviation. For bulk modulus, the standard deviation was determined by propagating the error for density and speed of sound. The expanded uncertainty and combined expanded uncertainty was determined by multiplying the standard deviation by 2. When a normal distribution is assumed, multiplying by a coverage factor of 2 produces a 95% confidence interval. 3456



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Table 6. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν as a Function of Mole Fraction n-Hexylbenzene x1 in Mixtures with n-Butylcyclohexane (Mole Fraction x2) and n-Dodecane (Mole Fraction x3) from Temperature T = (293.15 to 343.15) K and Pressure P = 0.1 MPaa ρ

η −3

x3/x2

x1

0.3332

0.0000 0.2008 0.4002 0.6001 0.8004 0.0000 0.2002 0.3999 0.5973 0.8000 0.0000 0.2008 0.3999 0.5999 0.8002

783.9 798.4 812.9 827.7 842.6 770.6 786.8 803.5 820.7 839.0 759.0 776.5 794.9 814.6 835.5

0.0000 0.2008 0.4002 0.6001 0.8004 0.0000 0.2002 0.3999 0.5973 0.8000 0.0000 0.2008 0.3999 0.5999 0.8002

761.6 775.9 790.4 805.0 819.9 748.5 764.5 781.1 798.2 816.3 737.1 754.4 772.7 792.1 812.9

1.0001

2.9949

0.3332

1.0001

2.9949

kg·m

mPa·s

ν

ρ

2 −1

mm ·s

T = 293.15 K 1.34 1.36 1.41 1.48 1.56 1.38 1.39 1.43 1.48 1.55 1.44 1.44 1.45 1.49 1.57 T = 323.15 K 0.845 0.862 0.889 0.925 0.972 0.880 0.888 0.893 0.920 0.972 0.896 0.897 0.917 0.936 0.969

kg·m

η −3

1.70 1.70 1.73 1.78 1.85 1.79 1.77 1.77 1.80 1.85 1.90 1.85 1.83 1.84 1.87

776.5 790.9 805.4 820.1 835.1 763.3 779.4 796.1 813.2 831.4 751.7 769.2 787.5 807.1 828.0

1.11 1.11 1.13 1.15 1.18 1.18 1.16 1.15 1.15 1.19 1.22 1.19 1.19 1.18 1.19

754.1 768.4 782.8 797.5 812.3 741.1 757.1 773.6 790.6 808.7 729.7 747.0 765.2 784.6 805.3

mPa·s T = 303.15 K 1.13 1.15 1.19 1.24 1.31 1.17 1.18 1.21 1.25 1.31 1.22 1.22 1.23 1.26 1.32 T = 333.15 K 0.741 0.757 0.780 0.811 0.850 0.774 0.782 0.788 0.811 0.854 0.788 0.790 0.808 0.824 0.853

ν 2 −1

mm ·s

ρ −3

kg·m

1.46 1.46 1.48 1.52 1.57 1.54 1.52 1.52 1.53 1.58 1.62 1.58 1.56 1.56 1.59

769.1 783.4 797.9 812.6 827.5 755.9 772.0 788.6 805.7 823.9 744.4 761.8 780.1 799.6 820.4

0.982 0.985 1.00 1.02 1.05 1.04 1.03 1.02 1.03 1.06 1.08 1.06 1.06 1.05 1.06

746.5 760.7 775.2 789.8 804.6 733.7 749.7 766.3 783.2 801.2 722.5 739.7 757.8 777.3 797.9

η

ν

mPa·s

mm2·s−1

T = 313.15 K 0.972 0.992 1.02 1.07 1.12 1.01 1.02 1.03 1.07 1.12 1.04 1.04 1.05 1.08 1.12 T = 343.15 K 0.656 0.671 0.691 0.718 0.751 0.686 0.695 0.701 0.722 0.759 0.699 0.703 0.717 0.733 0.759

1.26 1.27 1.28 1.31 1.36 1.33 1.32 1.31 1.33 1.36 1.40 1.37 1.35 1.35 1.37 0.878 0.881 0.891 0.910 0.934 0.935 0.927 0.915 0.922 0.947 0.967 0.950 0.946 0.943 0.951

a

x1 is the mole fraction of n-hexylbenzene, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-dodecane. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, Uc(ρ) = 1.5 kg·m−3 for T < 343.15 K and Uc(ρ) = 4.3 kg·m−3 for T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

interaction, while negative values can be caused by interstitial accommodation and can indicate specific interactions such as hydrogen-bonding or dipole−induced dipole interactions.53 All of the excess molar volumes in this work are positive and change very little with temperature (Table 8 and Supporting Information, Tables S1−S3) indicating the dominance of dispersion forces as would be expected with nonpolar compounds. The excess molar volumes of mixtures containing n-hexadecane are slightly larger than those with n-dodecane when the aromatic compound is the same (Table 8). As the alkyl portion on the aromatic chain increases, the excess molar volumes decrease (toluene > n-butylbenzene > n-hexylbenzene) in ternary mixtures with n-hexadecane and n-butylcyclohexane as shown in Figure 1 for 293.15 K. These results are consistent with the authors’ recently published work that showed that in binary mixtures with n-hexadecane, the excess molar volumes with the aromatic constituents were positive and fell in the order of n-hexylbenzene > n-octylbenzene > n-dodecylbenzene.29 In that study it was hypothesized that as the alkyl chain length increases on the

All the values in Tables 3−7 are below that of the diesel fuel, but the aromatic compounds themselves have densities above that of the diesel fuel. Excess molar volume can be used to assess the interaction and packing of molecules in multicomponent systems. The excess molar volume (VmE) in each mixture was calculated using the following equation: VmE =

M1x1 + M 2x 2 + M3x3 Mx Mx Mx − 11 − 2 2 − 3 3 ρm ρ1 ρ2 ρ3

(1)

in which the mixture density is ρm; the pure component densities are ρ1, ρ2, and ρ3; the molar masses are M1, M2, and M3; and the mole fractions are x1, x2, and x3 with the aromatic compound as component 1, n-butylcyclohexane as component 2, and the n-alkane as component 3. Structural properties and intermolecular interactions can cause the molecules to have densities above or below what is found under ideal mixing conditions, which is represented by the first term in eq 1. Positive values of excess molar volume indicate that dispersion forces dominate the 3457



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Table 7. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν as a Function of Mole Fraction Toluene x1 in Mixtures with n-Butylcyclohexane (Mole Fraction x2) and n-Hexadecane (Mole Fraction x3) from Temperature T = (293.15 to 343.15) K and Pressure P = 0.1 MPaa ρ

η −3

x3/x2

x1

0.2500

0.0000 0.2318 0.3996 0.5993 0.7999 0.0000 0.2003 0.4007 0.6000 0.7999 0.0000 0.2010 0.4008 0.6013 0.8015 0.0000 0.2012 0.4013 0.6031 0.8012

791.29 800.59 809.16 822.36 840.42 785.19 792.94 803.09 816.75 836.15 780.35 787.94 797.83 811.59 832.44 776.54 783.79 793.46 807.75 828.85

0.0000 0.2318 0.3996 0.5993 0.7999 0.0000 0.2003 0.4007 0.6000 0.7999 0.0000 0.2010 0.4008 0.6013 0.8015 0.0000 0.2012 0.4013 0.6031 0.8012

769.38 777.83 785.66 797.73 814.33 763.75 770.83 780.11 792.63 810.44 759.24 766.20 775.28 787.90 807.06 755.63 762.32 771.23 784.36 803.77

0.6666

1.5000

3.9977

0.2500

0.6667

1.5000

3.9977

kg·m

mPa·s T = 293.15 K 1.68 1.31 1.10 0.892 0.725 2.08 1.65 1.30 1.01 0.778 2.50 1.97 1.51 1.13 0.831 2.96 2.30 1.73 1.26 0.889 T = 323.15 K 1.03 0.846 0.730 0.612 0.512 1.23 1.02 0.844 0.684 0.544 1.42 1.18 0.961 ± 0.02 0.750 0.577 1.62 1.34 1.07 0.827 0.614

ν 2 −1

mm ·s

ρ

η −3

kg·m

2.12 1.64 1.36 1.09 0.862 2.65 2.08 1.62 1.24 0.931 3.21 2.50 1.89 1.39 0.998 3.81 2.93 2.18 1.56 1.07

784.02 793.04 801.37 814.20 831.79 778.07 785.60 795.47 808.75 827.63 773.33 780.72 790.35 803.73 824.04 769.57 776.65 786.07 799.99 820.54

1.34 1.09 0.929 0.767 0.629 1.61 1.33 1.08 0.863 0.672 1.88 1.54 1.24 ± 0.03 0.952 0.716 2.15 1.75 1.39 1.05 0.764

762.02 770.17 777.74 789.42 805.51 756.56 763.40 772.37 784.49 801.74 752.17 758.91 767.69 779.92 798.48 748.65 755.13 763.76 776.49 795.30

mPa·s T = 303.15 K 1.40 1.12 0.950 0.780 0.640 1.71 1.39 1.11 0.881 0.687 2.04 1.63 1.28 ± 0.02 0.977 0.731 2.37 1.88 1.45 1.08 0.779 T = 333.15 K 0.898 0.746 0.649 0.548 0.463 1.06 0.894 0.743 0.609 0.491 1.22 1.02 0.835 0.667 0.517 1.38 1.15 0.929 0.731 0.550

ν 2 −1

mm ·s

ρ kg·m

−3

1.79 1.41 1.19 0.958 0.770 2.20 1.77 1.40 1.09 0.830 2.64 2.09 1.62 ± 0.02 1.22 0.887 3.08 2.42 1.85 1.36 0.950

776.71 785.45 793.53 805.99 823.09 770.92 778.23 787.81 800.71 819.06 766.29 773.47 782.83 795.84 815.58 762.61 769.49 778.66 792.20 812.18

1.18 0.969 0.835 0.694 0.574 1.40 1.17 0.963 0.776 0.612 1.62 1.35 1.09 0.855 0.648 1.84 1.52 1.22 0.94 0.691

754.6 762.4 769.7 780.9 796.6 749.4 755.9 764.5 776.3 792.9 745.1 751.5 760.1 771.8 789.8 741.4 747.9 756.2 768.5 786.7

η

ν

mPa·s

mm2·s−1

T = 313.15 K 1.19 0.968 0.829 0.689 0.571 1.44 1.18 0.965 0.773 0.610 1.69 1.38 1.10 ± 0.02 0.852 0.647 1.95 1.57 1.24 0.943 0.689 T = 343.15 K 0.789 0.663 0.581 0.492 0.421 0.926 0.788 0.663 0.547 0.446 1.06 0.895 0.737 0.594 0.463 1.19 1.00 0.819 0.652 0.497

1.54 1.23 1.05 0.854 0.694 1.87 1.52 1.22 0.965 0.744 2.20 1.78 1.41 ± 0.02 1.07 0.793 2.55 2.05 1.59 1.19 0.848 1.05 0.869 0.755 0.630 0.529 1.24 1.04 0.868 0.705 0.563 1.42 1.19 0.969 0.769 ± 0.02 0.586 1.60 1.34 1.08 0.849 0.632

a

x1 is the mole fraction of toluene, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-hexadecane. Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, Uc(ρ) = 0.30 kg·m−3 for T < 343.15 K and Uc(ρ) = 0.86 kg·m−3 for T ≥ 343.15 K, and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001 unless indicated by “ ± ”. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2).

n-butylbenzene increase with increasing aromatic concentration (Tables 10−12). In contrast, the addition of toluene to twocomponent mixtures of n-hexadecane and n-butylcyclohexane causes the speed of sound to decrease to values lower than either toluene or the two component mixture (Figure 2, Table 12). The addition of n-butylbenzene to these two-component mixtures results in a fairly constant value of the speed of sound until higher levels of n-butylbenzene are reached where the speed of sound increases (Table 10). The addition of hexylbenzene at a small

alkylbenzene, the molecule can stack in a way that is similar to that of n-hexadecane, resulting in a smaller excess molar volume.29 Such could also be the case in the ternary mixtures studied herein. 4.2. Speed of Sound and Bulk Modulus. Most of the measured speeds of sound of each compound agree with the reported values within the standard uncertainty of the measurements as shown in Table 9. The speeds of sound of ternary mixtures of n-dodecane, n-butylcyclohexane, and n-hexylbenzene, or 3458



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Table 8. Excess Molar Volumes VmE in cm3·mol−1, Viscosity Deviations Δη in mPa·s, and Speeds of Sound Δc Deviations for Ternary Mixtures of n-Butylbenzene or n-Hexylbenzene (Mole Fraction x1), + n-Butylcyclohexane (Mole Fraction x2), + n-Hexadecane (Mole Fraction x3), at Temperature T = 293.15 K and Pressure P = 0.1 MPaa x1

V mE

Δη1

Δη2

Δc

n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) x3/x2 = 0.3333 0.0000 0.15 0.12 −0.05 −1 0.2004 0.25 0.04 −0.12 −4 0.4004 0.31 0.00 −0.14 −5 0.6003 0.30 −0.02 −0.12 −5 0.8002 0.20 −0.02 −0.07 −4 x3/x2 = 0.9992 0.0000 0.14 0.17 −0.08 −2 0.2009 0.30 0.09 −0.17 −4 0.4003 0.37 0.05 −0.19 −6 0.6002 0.38 0.02 −0.17 −6 0.8000 0.26 0.00 −0.10 −5 x3/x2 = 3.0006 0.0000 0.10 0.15 −0.06 −1 0.2010 0.29 0.12 −0.18 −4 0.4009 0.41 0.08 −0.23 −6 0.6010 0.41 0.05 −0.21 −7 0.8005 0.29 0.02 −0.13 −6 n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) x3/x2 = 0.3332 0.0000 0.04 −0.01 −0.01 0 0.2001 0.18 −0.05 −0.06 −2 0.4003 0.24 −0.07 −0.08 −3 0.6003 0.23 −0.06 −0.07 −3 0.8000 0.15 −0.04 −0.05 −2 x3/x2 = 1.0002 0.0000 0.05 −0.01 −0.01 0 0.2005 0.19 −0.05 −0.06 −2 0.4007 0.26 −0.06 −0.07 −3 0.6008 0.26 −0.06 −0.07 −3 0.8005 0.15 −0.04 −0.05 −2 x3/x2 = 3.0005 0.0000 0.04 −0.01 −0.01 0 0.2007 0.21 −0.05 −0.07 −2 0.4011 0.30 −0.06 −0.07 −2 0.6013 0.31 −0.06 −0.07 −3 0.8007 0.22 −0.04 −0.05 −2

x1

VmE

Δη1

Δη2

Δc

n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) x3/x2 = 0.3335 0.0000 0.12 0.12 −0.05 −2 0.2004 0.20 0.04 −0.10 −2 0.4006 0.24 −0.01 −0.11 −2 0.6003 0.21 −0.03 −0.10 −2 0.7997 0.13 −0.03 −0.07 −2 x3/x2 = 0.9997 0.0000 0.14 0.17 −0.08 −2 0.2004 0.24 0.08 −0.13 −3 0.4008 0.28 0.02 −0.14 −3 0.6008 0.26 −0.02 −0.13 −3 0.8003 0.17 −0.02 −0.08 −2 x3/x2 = 2.9967 0.0000 0.10 0.15 −0.05 −1 0.2005 0.24 0.07 −0.13 −3 0.4025 0.24 0.02 −0.16 −4 0.6007 0.31 0.00 −0.14 −4 0.8004 0.20 −0.01 −0.09 −3 n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) x3/x2 = 0.3332 0.0000 0.05 −0.01 −0.01 0 0.2008 0.13 −0.05 −0.05 0 0.4002 0.17 −0.06 −0.07 0 0.6001 0.15 −0.06 −0.07 0 0.8004 0.10 −0.05 −0.05 0 x3/x2 = 1.0001 0.0000 0.05 −0.01 −0.01 0 0.2002 0.14 −0.05 −0.06 1 0.3999 0.18 −0.07 −0.08 1 0.5973 0.17 −0.08 −0.08 1 0.8000 0.11 −0.06 −0.07 1 x3/x2 = 2.9949 0.0000 0.04 0.01 0.01 0 0.2008 0.14 −0.04 −0.04 1 0.3999 0.18 −0.07 −0.08 1 0.5999 0.17 −0.08 −0.08 2 0.8002 0.11 −0.06 −0.06 2

x1

V mE

Δη1

Δη2

Δc

Toluene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) x3/x2 = 0.2500 0.0000 0.10 0.09 −0.06 −1 0.2318 0.34 0.04 −0.16 −8 0.3996 0.45 0.02 −0.18 −11 0.5993 0.47 0.01 −0.16 −14 0.7999 0.37 0.00 −0.10 −12 x3/x2 = 0.6667 0.0000 0.14 0.15 −0.08 −2 0.2003 0.36 0.12 −0.20 −8 0.4007 0.49 0.10 −0.23 −12 0.6000 0.53 0.06 −0.21 −15 0.7999 0.43 0.02 −0.13 −13 x3/x2 = 1.5000 0.0000 0.14 0.17 −0.07 −2 0.2010 0.36 0.19 −0.21 −7 0.4008 0.54 0.15 −0.28 −12 0.6013 0.64 0.10 −0.26 −15 0.8015 0.49 0.05 −0.16 −14 Toluene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) (continued) x3/x2 = 3.9977 0.0000 0.09 0.13 −0.05 −1 0.2012 0.34 0.23 −0.22 −6 0.4013 0.56 0.21 −0.31 −11 0.6031 0.59 0.15 −0.29 −14 0.8012 0.54 0.07 −0.19 −14

Calculations: VEm is given by eq 1, Δη1 is given by eq 19, Δη2 is given by eq 20, and Δc is given by eqs 2 to 11, where x1, x2 , and x3 are the mole fractions of the aromatic compound, linear alkane, and n-butylcylohexane, respectively. The combined expanded uncertainties of Uc(VmE) = 0.04 cm3·mol−1, Uc(Δη1) = 0.03 mPa·s, Uc(Δη2) = 0.05 mPa·s, Uc(Δc) = 1 m·s−1, Standard uncertainties u are u(T) = 0.01 K, and the average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.001 MPa (level of confidence = 0.95, k = 2). a

The speed of sound deviation, Δc, can be calculated using

mole fraction, 0.2005, to the system with a high mole fraction of n-hexadecane (x3/x2 = 2.9967) also shows only a slight increase in the speed of sound. At higher mole fractions of hexylbenzene or in systems with more butylcyclohexane (lower x3/x2), the speed of sound increases steadily with increasing n-hexylbenzene. Researchers have reported other aromatic mixtures whose speed of sound is lower than that of the individual components. These include binary mixtures of toluene or ethylbenzene with n-hexadecane, cyclohexane, and butylcyclohexane, ethyoxyethanols, ethylbenzene with 1-nonanol and 2-decanol, and n-butylbenzene with n-tetradecane, n-hexadecane, or n-heptadecane.26,28,54−56

Δc = cmix − c ID

(2)

where the mixture speed of sound is cmix, and the ideal mixture cID is given by Douheret et al.:57 c ID = (ρ ID κ ID)−0.5

(3)

The ideal density, ρID, and ideal isentropic compressibility, κID, are defined by ρ ID = ϕ1ρ1 + ϕ2ρ2 + ϕ3ρ3 3459

(4) DOI: 10.1021/acs.jced.7b00466 J. Chem. Eng. Data 2017, 62, 3452−3472


Article

Table 9. Comparison of the Speeds of Sound c of n-Hexadecane, n-Dodecane, n-Butylcyclohexane, Toluene, n-Butylbenzene, and n-Hexylbenzene with Literature Values at Pressure P = 0.1 MPaa m·s−1 T/K

this studya

293.15

1356.4

303.15

1319.0

313.15

1282.6

323.15

1246.9

333.15

1212.0

293.15

1297.3

303.15

1259.1

313.15

1221.5

n-Hexadecane 1357.0 ± 0.3e, 1357.1d, 1357.7g 1319.5 ± 0.3e, 1319.6d, 1320.0f, 1320.2g 1282.8i, 1282.8 ± 0.3e, 1283h, 1283.4d, 1283.4g 1246.8 ± 0.3e, 1246.9d, 1247.4g, 1248h 1211.2i, 1211.4f, 1211.6d, 1212h, 1212.3g n-Dodecane 1297s, 1297.6 ± 0.3p, 1298.25t, 1301.2 ± 0.5%r 1259s, 1259.3 ± 0.3p, 1260.9 ± 0.5%r, 1261.2q 1221.4 ± 0.3p, 1221.8 ± 0.5%r

323.15

1184.4

1183.8 ± 0.5%r, 1184.2 ± 0.3p

333.15

1148.0

293.15

1374.7

1146.6 ± 0.5%r, 1147.3 ± 0.3p, 1147.4q n-Hexylbenzene 1376.1b

303.15

1337.3

1338.7b

313.15

1300.5

1301.7b

323.15 333.15

1264.3 1228.8

1265.3b 1229.4b

E

Figure 1. Excess molar volumes Vm of ternary mixtures of n-hexadecane (mole fraction x3), n-butylcylohexane (mole fraction x2), and ■, toluene at mole fraction x1 with x3/x2 = 0.2500; red □, toluene at mole fraction x1, with x3/x2 = 0.6667; green △, n-butylbenzene at mole fraction x1 with x3/x2 = 0.3334; and blue ○, n-hexylbenzene at mole fraction x1 with x3/x2 = 0.3335 at 293.15 K. The error bars are the combined expanded uncertainty (level of confidence = 0.95, k = 2).

κ

ID

= ϕ1κ1 + ϕ2κ2 + ϕ1κ3 ⎡ ϕ Vα 2 ϕ V3α32 ϕ V2α22 V ID(α ID)2 ⎤ 1 1 + T⎢ 1 + 2 + 3 − m ID ⎥ ⎢⎣ Cp ,1 ⎥⎦ Cp ,2 Cp ,3 Cp (5)

with the parameters in these equations defined by the following:

this studya

lit.

volume fraction:

ϕi = xiVi /Vm ID

(6)

ideal molar volume: Vm ID = x1V1 + x 2V2 + x3V3

(7)

component isentropic compressibility: κi =

1287.9

1289.0j

1248.7

1247.7j

1210.3

1210.4j

1172.6

1169.8j

1326.6u 1283.6u

Toluene 1326.9k, 1324.3 ± 1%l 1281.6 ± 1%l

1241.1u

1240.9k, 1239.7 ± 1%l 1199.2u 1198.9k, 1198.5 ± 1%l u 1157.7 1157.7k, 1158.0 ± 1%l n-Butylbenzene 1352.8 1341.31o, 1353.4n 1314.0 1302.11o, 1308m, 1314.3n 1275.8 1264.92o, 1275.7n, 1276m 1238.2 1228.70o 1201.4 1201.4c

a

1 ρi ci2

Standard uncertainties u are u(T) = 0.01 K, and expanded uncertainties Uc are Uc(c) = 0.8 m·s−1. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2). bReference 29. c Reference 28. dReference 73. eReference 89. fReference 90. g Reference 91. hReference 92. iReference 93. jReference 94. k Reference 50. lReference 74. mReference 87. nReference 88. o Reference 95. pReference 75. qReference 90. rReference 74. s Reference 96. tReference 97. uReference 20.

(8)

component thermal expansion coefficient: αi = −

lit.

n-Butylcyclohexane 1327.7 1328.7j

∂(ln ρi ) ∂T

1 ⎛ ∂ρ ⎞ = − ⎜ i⎟ ρi ⎝ ∂T ⎠ P

(9)

ideal mixture thermal expansion coefficient: α ID = ϕf1 α1 + ϕ2α2 + ϕ3α3

sound deviations match with positive excess molar volumes, except for hexylbenzene, butylcyclohexane, and dodecane mixtures, the values of which are positive but very close to zero. It may be that the influence on packing that expands the molar volume may cause the speed of sound to be lower than predicted by ideal behavior. The isentropic bulk modulus at ambient pressure, Ks, was calculated for each mixture at each temperature using

(10)

ideal mixture isentropic compressibility: Cp ID = x1Cp ,1 + x 2Cp ,2 + x3Cp ,3

(11)

where Vi, xi, ρi, ci,, Cp,i are the molar volume, mole fraction, density, speed of sound, and isobaric heat capacity, respectively, of each component, and T is the temperature in Kelvin. The thermal expansion coefficients derived from data reported herein and the heat capacity values are provided in the Supporting Information (Table S4). The excess speed of sound values estimated by eq 2 are given in Table 8. The greatest speed of sound deviations are found for the toluene mixtures and the smallest deviations for the hexylbenzene mixtures. Such a result would be expected based on the modest reduction in speeds of sound found for toluene mixtures and less uniform increase in speed of sound for butylbenzene. Most of the negative speed of

K s/Pa = (c 2/m 2·s−2)(ρ /kg·m−3)

(12)

where c is speed of sound and ρ is density, and the calculated values are given in Tables 13−15. For ternary mixtures with n-butylbenzene and n-hexylbenzene, the bulk modulus increases with an increasing amount of the aromatic compound (Tables 13, 14). For toluene in mixtures with n-hexadecane and n-butylcyclohexane, the bulk modulus declines to values slightly below either toluene or the binary mixture of n-hexadecane and 3460



Article

Table 10. Experimental Speeds of Sound c, m·s−1, of Ternary Mixtures of n-Butylbenzene or n-Hexylbenzene (Mole Fraction x1) + n-Butylcyclohexane (Mole Fraction x2) + n-Hexadecane (Mole Fraction x3) from Temperature T = (293.15 to 333.15) K and Pressure P = 0.1 MPaa x3/x2

x1

0.3333

0.0000 0.2004 0.4004 0.6003 0.8002 0.0000 0.2009 0.4003 0.6002 0.8000 0.0000 0.2010 0.4009 0.6010 0.8005

0.9992

3.0006

0.3335

0.9997

2.9967

0.3335

0.0000 0.2004 0.4006 0.6003 0.7997 0.0000 0.2004 0.4008 0.6008 0.8003 0.0000 0.2005 0.4025 0.6007 0.0000

T/K = 293.15

T/K = 303.15

T/K = 313.15

n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1335.5 1297.1 1259.3 1334.5 1296.1 1258.3 1335.4 1297.0 1259.2 1338.4 1299.9 ± 0.9 1262.1 1343.7 1305.2 1267.1 1342.9 1305.2 1268.2 1340.5 1302.8 1265.7 ± 0.9 1339.3 1301.6 1264.3 1340.5 ± 1.2 1302.5 ± 1.3 1265.2 ± 1.3 1343.9 1305.6 1268.0 1350.0 1312.7 1276.0 1345.9 1308.6 1272.0 1343.3 1305.9 1269.1 1342.4 1304.8 1267.8 1344.4 1306.4 1269.0 n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1335.2 1296.8 1259.1 1340.3 1302.1 1264.5 1346.7 1308.8 1271.5 1354.5 ± 0.9 1316.8 ± 1.0 1279.6 ± 1.0 1363.3 1325.7 1288.6 1342.9 1305.2 1268.2 1345.5 1307.9 1270.9 1349.7 1312.2 1275.4 1355.7 1318.4 1281.6 1363.8 1326.5 1289.7 1349.7 1312.4 1275.9 1350.7 1313.6 1277.1 1353.1 1316.0 1279.5 1357.1 1320.0 1283.6 1364.0 1326.8 1290.2

T/K = 323.15

T/K = 333.15

1222.1 1221.1 1222.0 1224.8 1229.8 1231.8 1229.2 1227.7 1228.4 ± 1.2 1230.8 1240.1 1235.9 1232.9 1231.4 1232.2

1185.7 1184.8 1185.6 1188.3 ± 0.9 1193.2 1196.2 1193.6 1191.9 1192.0 1194.5 1205.0 1200.7 1197.5 1195.8 1196.1

1222.0 1227.7 1234.8 1243.2 ± 1.0 1252.3 1231.8 1234.6 1239.2 1245.5 1253.5 1239.9 1241.2 1243.6 1247.6 1254.2

1185.6 1191.5 1198.8 1207.5 ± 1.2 1217.0 1196.2 1199.1 1203.7 1210.1 1218.0 1204.7 1206.1 1208.5 1212.5 1218.9

a

x1 is the mole fraction of the aromatic compound, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-hexadecane. Standard uncertainties u are u(T) = 0.01 K, expanded uncertainties Uc are Uc(c) = 0.8 m·s−1 unless otherwise indicated by “ ± ” and combined expanded uncertainty is Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 (level of confidence = 0.95, k = 2).

n-butylcyclohexane (Table 15). These results show that simple blending rules result in an underestimation of bulk modulus. Reported speeds of sound for petroleum-based jet and diesel fuel at 293.15 K are 1316.9 and 1378.6 m·s−1, respectively.51,52 The speed of sound of jet-fuel can be matched by ternary mixtures of toluene, n-hexadecane, and n-butylcylohexane and also by ternary mixtures of n-dodecane, n-butylcyclohexane, with either n-butylbenzene or n-hexylbenzene. None of the mixtures match the speed of sound of the diesel fuel. For bulk modulus, values of 1389 and 1612 MPa have been found for petroleum-based jet and diesel fuel, respectively, at 293.15 K.51,52 The bulk modulus of jet-fuel can be matched by ternary mixtures of n-dodecane, n-butylcyclohexane, with either n-butylbenzene or n-hexylbenzene. None of the mixtures match the bulk modulus of the diesel fuel, and the bulk modulus of pure n-hexylbenzene, 1621 MPa, is slightly higher than that of the diesel fuel. Higher values of bulk modulus can cause the start of injection time in mechanical injection diesel engines to occur sooner (advance relative to piston Top Dead Center), which can further impact the timing of combustion.17,58 Tat and van Gerpen58 attributed a 0.45 to

0.68 degree timing advance in pressure pulse to the difference of 169 MPa in bulk modulus between a petroleum-based and biobased fuel. 4.3. Viscosity. Most of the measured viscosities of each compound agree with the reported values within the standard uncertainty of the measurements as shown in Table 16. The dynamic and kinematic viscosities of the mixture studied herein are given in Tables 3−7. The viscosities of ternary mixtures of n-hexadecane, n-butylcyclohexane, and the aromatic compounds studied herein decrease as the aromatic concentration increases. Similar behavior is found for ternary mixtures of n-dodecane, n-butylcyclohexane, and the butylbenzene. In contrast, the viscosity increases with increased hexylbenzene in mixtures with n-dodecane and n-butylcyclohexane. Reported viscosities for petroleumbased jet and diesel fuel at 293.15 K are 1.88 and 3.65 mm2·s−1, respectively.51,59 The military specifications for diesel fuel require the viscosity at 313.15 K to be between 1.4 and 4.3 mm2·s−1.3 Only ternary mixtures with n-hexadecane/n-butylcyclohexane and an aromatic could match the properties of the jet fuel and diesel fuel and fall within the specifications for the diesel fuel. 3461



Article

Table 11. Experimental Speeds of Sound c, of m·s−1, Ternary Mixtures of n-Butylbenzene or n-Hexylbenzene (Mole Fraction x1) + n-Butylcyclohexane (Mole Fraction x2) + n-Dodecane (Mole Fraction x3) from Temperature T = (293.15 to 333.15) K and Pressure P = 0.1 MPaa x3/x2

x1

0.3332

0.0000 0.2001 0.4003 0.6003 0.8000 0.0000 0.2005 0.4007 0.6008 0.8005 0.0000 0.2007 0.4011 0.6013 0.8007

1.0002

3.0005

0.3332

1.0001

2.9949

0.0000 0.2008 0.4002 0.6001 0.8004 0.0000 0.2002 0.3999 0.5973 0.8000 0.0000 0.2008 0.3999 0.5999 0.8002

T/K = 293.15

T/K = 303.15

T/K = 313.15

n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) 1317.5 1278.4 1239.9 1319.8 1280.9 1242.5 1324.5 1285.6 1247.3 1331.0 1292.3 1254.0 1340.2 1301.4 1263.2 1308.8 1270.1 1232.0 1312.2 1273.7 1235.7 1317.6 1279.2 1241.3 1325.7 1287.2 1249.3 1337.1 1298.5 1260.4 1302.6 1264.3 1226.5 1306.3 1268.0 1230.4 1312.3 1274.1 1236.4 1321.3 1283.0 1245.3 1334.3 1295.8 1257.9 n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) 1317.3 1278.1 1239.7 1326.5 1287.8 1249.7 1337.1 1298.7 1261.0 1348.5 1310.5 1273.1 1361.1 1323.4 1286.3 ± 0.9 1309.0 1270.4 1232.3 1319.1 1280.8 1243.1 1330.3 1292.2 1254.8 1343.3 1305.5 1268.2 1358.3 1320.6 1283.6 1302.4 1264.0 1226.2 1312.9 1274.8 1237.3 1325.0 1287.1 1249.9 1339.2 1301.5 1264.5 1355.8 1318.4 1281.4

T/K = 323.15

T/K = 333.15

1202.0 1204.8 1209.7 1216.4 1225.7 1194.6 1198.4 1203.9 1211.9 1223.1 1189.3 1193.3 1199.3 1208.1 1220.6

1164.8 1167.8 1172.9 1179.6 1189.1 1157.9 1161.7 1167.3 1175.3 1186.5 1152.9 1156.9 1162.9 1171.7 1184.1

1201.8 1212.3 1223.9 1236.3 1249.8 ± 0.9 1194.8 1206.0 1217.9 1231.6 1247.1 1189.0 1200.4 1213.2 1228.0 1245.1

1164.7 1175.6 1187.5 1200.4 1214.2 1158.1 1169.6 1181.9 1195.9 1211.6 1152.5 1164.2 1177.3 1192.2 1209.5

a x1 is the mole fraction of the aromatic compound, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-dodecane. Standard uncertainties u are u(T) = 0.01 K, expanded uncertainties Uc are Uc(c) = 0.8 m·s−1 unless otherwise indicated by “ ± ” and combined expanded uncertainty is Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 (level of confidence = 0.95, k = 2).

The McAllister three-body model was used to fit the kinematic viscosity data32,60

n-butylcyclohexane as component 2, and the n-alkane as component 3. The interaction parameters ν1,2, ν2,1, ν1,3, ν3,1, ν2,3, ν3,2, and ν1,2,3 were determined by minimizing the sum of the square of the difference between the measured kinematic viscosity of the binary mixture, νmeasured and the value calculated by the model in eq 13, νm,calc. The fitted interaction parameters and the standard errors of the fits are given in Table 17. Figure 3 shows that the model fits the data well. Viscosity deviation (Δviscosity) is the difference between the measured value and an “ideal value”:

ln νm,calc = x13 ln ν1 + x 23 ln ν2 + x33 ln ν3 + 3x12x 2 ln ν1,2 + 3x12x3 ln ν1,3 + 3x1x 22 ln ν2,1 + 3x 22x3 ln ν2,3 + 3x1x32 ln ν3,1 + 3x 2x32 ln ν3,2 + 6x1x 2x3 ln ν1,2,3 − ln(x1M1 + x 2M 2 + x3M3) ⎛ 2M + M 2 ⎞ ⎟ + x13 ln M1 + x 23 ln M 2 + x33 ln M3 + 3x12x 2 ln⎜ 1 ⎝ ⎠ 3 ⎛ ⎞ 2 + M M ⎛ ⎞ 2 + M M 3⎟ 1⎟ + 3x12x3 ln⎜ 1 + 3x1x 22 ln⎜ 2 ⎝ ⎠ ⎝ ⎠ 3 3

Δviscosity = viscosity(measured) − viscosity(ideal)

⎛ 2M + M3 ⎞ ⎛ 2M3 + M1 ⎞ ⎟ + 3x x 2 ln⎜ ⎟ + ln⎜ 2 1 3 ⎝ ⎠ ⎝ ⎠ 3 3 ⎛ ⎞ ⎛ ⎞ 2 + + M M M M 2⎟ 2 + M3 ⎟ + 3x 2x32 ln⎜ 3 + 6x1x 2x3 ln⎜ 1 ⎝ ⎠ ⎝ ⎠ 3 3 3x 22x3

(14)

The ideal viscosity can be based on either kinematic viscosity, dynamic viscosity, or natural logarithms of these values.31,53,61−70 The instrument used in this study measures dynamic viscosity, so ideal viscosities (ηideal) were calculated by31,32,53,61,63,69,70 (13)

Here, the calculated kinematic viscosity of the ternary mixture is νm,calc; the pure component kinematic viscosities are ν1, ν2, and ν3; the molar masses are M1, M2, and M3; and the mole fractions are x1, x2, and x3 with the aromatic compound as component 1,

ηideal = x1η1 + x 2η2 + x3η3

(15)

ηideal = exp(x1 ln η1 + x 2 ln η2 + x3 ln η3)

(16)

or

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Table 12. Experimental Speeds of Sound c, m·s−1, of Ternary Mixtures of Toluene (Mole Fraction x1) + n-Butylcyclohexane (Mole Fraction x2) + n-Hexadecane (Mole Fraction x3) from Temperature T = (293.15 to 333.15) K and Pressure P = 0.1 MPaa x3/x2

x1

T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

T/K = 333.15

0.2500

0.0000 0.2318 0.3996 0.5993 0.7999 0.0000 0.2003 0.4007 0.6000 0.7999 0.0000 0.2010 0.4008 0.6013 0.8015 0.0000 0.2012 0.4013 0.6031 0.8012

1334.4 1324.6 1318.7 1313.6 1313.7 1339.5 1330.8 1322.7 1316.1 1314.3 1345.6 1336.6 ± 0.9 1327.4 1319.3 1315.4 ± 0.9 1350.8 1341.4 1331.6 1322.3 1316.4 ± 0.9

1295.9 1285.6 1279.2 1273.5 1272.5 1301.7 1292.7 1284.1 1276.6 1273.5 1308.2 1298.9 ± 0.9 1289.2 1280.4 1275.2 ± 0.9 1313.6 1303.9 1293.8 1283.7 1276.3

1257.8 1247.0 1240.2 1233.7 1231.8 1264.4 1254.9 1245.8 1237.5 1233.2 1271.3 1261.6 1251.4 1241.8 1235.3 ± 1.0 1277.0 1267.0 1256.4 1245.5 1236.8

1220.2 1209.0 1201.7 1194.4 1191.4 1227.5 1217.7 1207.9 1198.9 1193.3 1234.9 1224.8 1214.0 1203.6 1195.8 ± 0.9 1240.9 1230.6 1219.5 1207.7 1197.7

1183.2 1171.4 1163.7 1155.7 1151.6 1191.2 1181.0 1170.6 1160.8 1154.0 1199.1 1188.5 1177.2 1166.0 1156.7 ± 1.0 1205.4 1194.8 1183.1 1170.5 1159.0

0.6667

1.5000

3.9977

a x1 is the mole fraction of toluene, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-hexadecane. Standard uncertainties u are u(T) = 0.01 K, expanded uncertainties Uc are Uc(c) = 0.8 m·s−1 unless otherwise indicated by “ ± ” and combined expanded uncertainty is Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 (level of confidence = 0.95, k = 2).

from ln ηideal = x1 ln η1 + x 2 ln η2 + x3 ln η3

(17)

where η1, η2, and η3 are the dynamic viscosities of the pure components, and x1, x2, and x3 are their mole fractions with the aromatic compound as component 1, n-butylcyclohexane as component 2, and the n-alkane as component 3. The viscosity deviations calculated using eqs 14−16 have been related to the strength of intermolecular interactions between mixing components,68,69 and Grunberg and Nissan68 included an extra term in their prediction of viscosity in a 2-component system (ηmix) to account for these interactions:

Figure 2. Speeds of sound c of ternary mixtures of n-hexadecane (mole fraction x3), n-butylcylohexane (mole fraction x2) and ■, toluene at mole fraction x1, with x3/x2 j= 0.2500; red □, toluene at mole fraction x1, with x3/ x2 = 0.6667; green △, n-butylbenzene at mole fraction x1 with x3/x2 = 0.3334; and blue ○, n-hexylbenzene at mole fraction x1, with x3/x2 = 0.3335 at 293.15 K. Error bars, which are the combined uncertainties with 0.95 level of confidence (k = 2), are smaller than the symbols.

ln ηmix = x1 ln η1 + x 2 ln η2 + x1x 2d

(18)

where d is the “characteristic constant of the system.” 4.3.1. Natural Log Viscosity Deviations. The viscosity deviation based on eqs 14 and 16 is

Table 13. Bulk Moduli, in MPa, of Ternary Mixtures of n-Butylbenzene or n-Hexylbenzene (Mole Fraction x1) + nButylcyclohexane (Mole Fraction x2) + n-Hexadecane (Mole Fraction x3) from Temperature T = (293.15 to 333.15) K and Pressure P = 0.1 MPaa x3/x2 0.3333

0.9992

x1 0.0000 0.2004 0.4004 0.6003 0.8002 0.0000 0.2009 0.4003 0.6002

T/K = 293.15

T/K = 303.15

T/K = 313.15

n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1408 1316 1229 1425 1332 1244 1449 1354 1264 1480 1383 1292 1521 1421 1327 1412 1321 1236 1425 1334 1248 1445 1352 1264 1474 ± 1.9 1379 ± 2.0 1289 ± 1.9 3463

T/K = 323.15 1147 1160 1180 1205 1238 1155 1166 1181 1204 ± 1.7

T/K = 333.15 1069 1082 1100 1123 1154 1079 1089 1102 1122



Article

Table 13. continued x3/x2

x1

0.9992 3.0006

0.8000 0.0000 0.2010 0.4009 0.6010 0.8005

0.3335

0.0000 0.2004 0.4006 0.6003 0.7997 0.0000 0.2004 0.4008 0.6008 0.8003 0.0000 0.2005 0.4025 0.6007 0.8004

0.9997

2.9967

T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1514 1416 1323 1417 1328 1243 1427 1336 1251 1443 1352 1265 1469 1375 1286 1509 1411 1319 n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1408 1316 1229 1441 1347 1259 1478 1383 1294 1520 1424 ± 1.5 1332 ± 1.5 1566 1468 1374 1412 1321 1236 1439 1347 1261 1472 1379 1291 1513 1418 1328 1561 1464 1371 1416 1327 1243 1440 1350 1264 1470 1378 1291 1507 1413 1324 1556 1459 1367

T/K = 333.15

1234 1163 1170 1183 1202 1232

1151 1088 1094 1105 1123 1150

1147 1176 1209 1246 1286 1155 1179 1208 1242 1284 1163 1183 1209 1239 1280

1069 1097 1129 1164 ± 1.6 1203 1079 1102 1129 1162 1201 1088 1107 1131 1160 1198

a

x1 is the mole fraction of the aromatic compound, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-hexadecane. Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc are Uc(bulk modulus) = 1 MPa unless otherwise indicated by “ ± ”, and Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2).

Table 14. Bulk Moduli, in MPa, of Ternary Mixtures of n-Butylbenzene or n-Hexylbenzene (Mole Fraction x1) + n-Butylcyclohexane (Mole Fraction x2) + n-Dodecane (Mole Fraction x3) from Temperature T = (293.15 to 333.15) K and Pressure P = 0.1 MPaa x3/x2 0.3332

1.0002

3.0005

0.3332

1.0001

x1

T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) 0.0000 1361 1269 1182 1100 0.2001 1387 1294 1206 1123 0.4003 1421 1326 1237 1152 0.6003 1462 1365 1274 1187 0.8000 1513 1413 1319 1229 0.0000 1320 1231 1147 1068 0.2005 1351 1261 1175 1095 0.4007 1389 1297 1210 1127 0.6008 1437 1342 1252 1167 0.8005 1498 1400 1306 1218 0.0000 1288 1202 1120 1043 0.2007 1321 1233 1149 1070 0.4011 1362 1272 1186 1105 0.6013 1415 1322 1234 1150 0.8007 1484 1387 1294 1207 n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) 0.0000 1360 1269 1182 1100 0.2008 1405 1312 1224 1140 0.4002 1453 1358 1269 1184 0.6001 1505 1408 1317 1230 0.8004 1561 1463 1369 1281 0.0000 1320 1232 1148 1069 0.2002 1369 1279 1193 1112 0.3999 1422 1329 1242 1159 0.5973 1481 1386 1296 1211 0.8000 1548 1450 1357 1270

Table 14. continued x3/x2 2.9949

T/K = 333.15 1023 1045 1072 1105 1146 994 1018 1049 1087 1135 970 996 1029 1071 1125

x1

T/K = 293.15

T/K = 303.15

T/K = 313.15

n-Hexylbenzene (1) + n-Butylcyclohexane 0.0000 1288 1201 0.2008 1339 1250 0.3999 1396 1305 0.5999 1461 1367 0.8002 1536 1439

T/K = 323.15

(2) + n-Dodecane (3) 1119 1042 1166 1087 1219 1137 1278 1194 1347 1260

T/K = 333.15 969 1013 1061 1115 1178

a

x1 is the mole fraction of the aromatic compound, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-dodecane. Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc are Uc (bulk modulus) = 1 MPa unless otherwise indicated by “ ± ”, and Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2).

Δη = ηmix − ηideal = ηmix − exp(x1 ln η1 + x 2 ln η2 + x3 ln η3) (19)

The viscosity deviations for the mixtures studied herein are given in Table 8 for 293.15 K and in the Supporting Information for 313.15 and 333.15 K. In the binary mixtures of n-butylcylohexane with n-dodecane, the viscosity deviations calculated by eq 19 are zero within the standard error of the measurements (0.00 ± 0.02 mPa·s). The addition of n-butylbenzene or n-hexylbenzene to these mixtures in the current study causes the deviations to become negative by a small amount (largest deviation is Δη = −0.08 mPa·s) as shown in Table 8. The small deviations suggest that the mixing behavior in these systems is close to ideal. In the binary mixtures of n-butylcylohexane with n-hexadecane, the viscosity deviations calculated by eq 19 are positive and small (greatest is Δη = 0.17 mPa·s) (Tables 8 and 10). The addition of n-butylbenzene or n-hexylbenzene to the binary

1023 1062 1104 1149 1198 994 1036 1081 1131 1187

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mixture causes the viscosity deviations to steadily decline and some cases to become essentially zero within the standard error of the measurements (±0.02 mPa·s). This was also found when toluene was added to binary mixtures of n-butylcylohexane with n-hexadecane with mostly n-butylcyclohexane (small x3/x2), but for mixtures with more n-hexadecane (larger x3/x2), the viscosity deviation increased to a maximum after which it declined. The largest deviation found here was 0.21 mPa·s 4.3.2. Linear Viscosity Deviations. The viscosity deviation based on eqs 14 and 16 is

Table 15. Bulk Modului, in MPa, of Ternary Mixtures of Toluene (Mole Fraction x1) + n-Butylcyclohexane (Mole Fraction x2) + n-Hexadecane (Mole Fraction x3) from Temperature T = (293.15 to 333.15) K and PressureP = 0.1 MPaa x3/x2

x1

T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

T/K = 333.15

0.2500

0.0000 0.2318 0.3996 0.5993 0.7999 0.0000 0.2003 0.4007 0.6000 0.7999 0.0000 0.2010 0.4008 0.6013 0.8015 0.0000 0.2012 0.4013 0.6031 0.8012

1409 1405 1407 1419 1450 1409 1404 1405 1415 1444 1413 1408 1406 1413 1440 1417 1410 1407 1412 1436

1317 1311 1311 1320 1347 1318 1313 1312 1318 1342 1323 1317 1313 1318 1340 1328 1321 1316 1318 1337

1229 1221 1221 1227 1249 1232 1226 1223 1226 1246 1238 1231 1226 1227 1244 1244 1235 1229 1229 1242

1146 1137 1134 1138 1156 1151 1143 1138 1139 1154 1158 1149 1143 1141 1154 1164 1154 1147 1144 1153

1067 1057 1053 1054 1068 1074 1065 1058 1057 1068 1081 1072 1064 1060 1068 1088 1078 1069 1064 1068

0.6667

1.5000

3.9977

3

Δη = ηmix −

∑ xiηi

(20)

i=1

The viscosity deviations for the mixtures studied herein are given in Table 8 for 293.15 K and in the Supporting Information for 313.15 and 333.15 K. In the binary mixtures of n-butylcylohexane with n-dodecane, the viscosity deviations calculated by eq 20 are zero within the standard error of the measurements (0.00 ± 0.02 mPa·s) (Table 8). This result is consistent with Liu and Zhu41 who report a maximum value of viscosity deviation for n-butylcylohexane with n-dodecane at 293.15 K to be 0.016 mPa·s. The addition of n-butylbenzene or n-hexylbenzene to these mixtures causes the deviations to become negative by a small amount (largest deviation is Δη = −0.08 mPa·s). The small deviations calculated suggest that the mixing behavior in these systems is close to ideal. In the binary mixtures of n-butylcylohexane with n-hexadecane, the viscosity deviations are negative and small (greatest deviation is Δη = −0.08 mPa·s) (Table 8). The addition of any of the n-alkylbenzenes to the mixture of n-butylcylohexane with n-hexadecane causes the viscosity deviations to decline to a minimum value around a mole fraction of the n-alkylbenzene

a

x1 is the mole fraction of the toluene, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of n-hexadecane. Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc are Uc(bulk modulus) = 1 MPa unless otherwise indicated by “ ± ”, and Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2).

Table 16. Comparison of the Measured Dynamic Viscosity Values η, mPa·s, of n-Hexadecane, n-Dodecane, n-Butylcyclohexane, Toluene, n-Butylbenzene, and n-Hexylbenzene with Literature Values at Pressure P = 0.1 MPaab T/K

measured

ref aa

measured

ref

ref

0.517e, 0.519f, 0.5204g, 0.5203b, 0.521h, 0.5224i 0.5226c, 0.524j, 0.5372k 0.4659c, 0.465f,b, 0.470j, 0.474n,0.4851k

1.11

1.105b, 1.107o 1.109p,t, 1.114b

n-Hexadecane 3.43 3.44 ± 0.01q, 3.447r, 3.484b, 3.505b 2.72 2.72 ± 0.01q, 2.748b, 2.766b

0.961

0.958o, 0.960p, 0.961p, 0.955b

2.20

0.837

0.828b, 0.830b, 0.835u, 0.844t

1.82

0.391

0.4189b, 0.420f, 0.4211l, 0.4215m, 0.4221g, 0.4222i 0.4272k 0.380b, 0.381f, 0.390n, 0.3905k

0.736

0.7249,b 0.734b, 0.741u, 0.749t

1.54

0.349

0.346b, 0.347f

0.653

293.15

1.47

1.06

303.15

1.23

1.245 ± 0.5%y, 1.25 ± 0.008x

0.915

313.15 323.15 333.15 343.15

1.05 0.902 0.786 0.690

1.06 ± 0.008x, 1.060 ± 0.5%f, 1.062 ± 0.1%r, 1.07 ± 1%s 0.915 ± 0.5%y, 0.916 ± 0.008x 0.799 ± 0.008x, 0.799 ± 0.5%y, 0.81 ± 1%s 0.704 ± 0.008x, 0.705 ± 0.5%y

0.801 0.708 0.631 0.566

0.658b, 0.663u, 0.671t n-Butylbenzene 1.032b, 1.034w 1.035b, 1.050b, 1.07b 0.893w, 0.894b, 0.895b, 0.901v 0.9035b 0.787v, 0.781b, 0.79b 0.684b, 0.7015b 0.614b, 0.6237b 0.63b 0.550b

1.31

n-Dodecane 1.48 ± 0.1%r, 1.487 ± 0.5%y, 1.49 ± 0.008x, 1.50 ± 1%s

293.15

Toluene 0.607 0.5859a, 0.5866b, 0.5887c, 0.5882d

303.15

0.540

313.15

0.483

323.15

0.434

333.15 343.15

n-Butylcyclohexane 1.31 1.296°, 1.300p, 1.304t, 1.314b

measured

2.21 ± 0.01q, 2.223b, 2.23 ± 1%,s 2.243r 1.82 ± 0.01q, 1.840b, 1.866b

1.68

1.53 ± 0.01q, 1.550b, 1.56 ± 1%,s 1.573b 1.31 ± 0.01q, 1.326b, 1.346b n-Hexylbenzene 1.655b, 1.675b,1.70b

1.41

1.403b

1.20 1.03 0.901 0.794

1.196b, 1.20b 1.035b, 1.07b 0.895b, 0.909b 0.804b

a

Reference 98. bReference 99. cReference 100. dReference 101. eReference 102. fReference 103. gReference 104. hReference 105. iReference 106. Reference 107. kReference 108. lReference 109. mReference 110. nReference 111. oReference 19. pReference 77. qReference 72. rReference 112. s Reference 113. tReference 80. uReference 78. vReference 87. wReference 61. xReference 75. yReference 87. zLiterature values for viscosity of hexylbenzene were converted from mm2·s−1 in ref 65 using density values in the current work. aaReference 20. abStandard uncertainties u are u(T) = 0.01 K, expanded uncertainties Uc are Uc(η) = 0.01 mPa·s. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2). j

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Table 17. Values of the Coefficients for McAllister Equation (eq 13) and Associated Standard Error, σ, for Ternary of Mixtures of the Aromatic Compound (Mole Fraction x1), n-Butylcyclohexane (Mole Fraction x2) + Linear Alkane (Mole Fraction x3) from Temperature T = (293.15 to 353.15) K and Pressure P = 0.1 MPa mm2·s−1 T/K

ν12

ν13

293.15 303.15 313.15 323.15 333.15 343.15

1.27 1.11 0.981 0.876 0.787 0.713

2.10 1.80 1.56 1.37 1.21 1.08

293.15 303.15 313.15 323.15 333.15 343.15

1.75 1.50 1.30 1.14 1.01 0.908

2.61 2.19 1.85 1.59 1.40 1.23

293.15 303.15 313.15 323.15 333.15 343.15

1.25 1.10 0.970 0.864 0.779 0.706

1.38 1.12 1.05 0.936 0.838 0.754

293.15 303.15 313.15 323.15 333.15 343.15

1.75 1.50 1.30 1.14 1.00 0.892

1.79 1.52 1.31 1.15 1.04 0.946

293.15 303.15 313.15 323.15 333.15 343.15

0.889 0.789 0.701 0.646 0.588 0.541

1.87 1.64 1.47 1.29 1.15 1.03

ν21

ν23

ν31

n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1.39 2.67 3.14 1.22 2.23 2.60 1.08 1.90 2.19 0.957 1.63 1.88 0.856 1.43 1.63 0.778 1.26 1.43 n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1.66 2.66 3.43 1.41 2.23 2.77 1.21 1.90 2.30 1.06 1.63 1.94 0.943 1.43 1.67 0.846 1.26 1.46 n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1.34 1.73 1.55 1.16 1.48 1.33 1.01 1.28 1.16 0.908 1.12 1.03 0.808 0.996 0.913 0.729 0.887 0.824 n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1.70 1.69 1.94 1.44 1.45 1.64 1.25 1.25 1.41 1.10 1.11 1.26 0.0956 0.976 1.09 0.844 0.864 0.956 Toluene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 1.18 2.63 2.91 1.04 2.21 2.10 0.946 1.87 2.04 0.826 1.62 1.75 0.761 1.42 1.53 0.695 1.26 1.36

ν32

ν123

σ

3.49 2.85 2.37 2.02 1.73 1.51

2.29 1.92 1.65 1.43 1.26 1.12

0.0055 0.0045 0.0036 0.0031 0.0028 0.0025

3.50 2.85 2.38 2.02 1.73 1.51

2.58 2.20 1.88 1.64 1.44 1.27

0.0055 0.0035 0.0027 0.0024 0.0020 0.0019

1.85 1.58 1.36 1.19 1.05 0.934

1.57 1.36 1.20 1.05 0.941 0.848

0.0051 0.0036 0.0031 0.0029 0.0024 0.0020

1.91 1.65 1.43 1.25 1.12 1.02

1.65 1.45 1.26 1.09 1.00 0.916

0.0042 0.0016 0.0019 0.0070 0.0057 0.0043

3.52 2.87 2.40 2.02 1.74 1.52

2.20 1.89 1.60 1.43 1.24 1.09

0.0041 0.0024 0.0033 0.0027 0.0026 0.0041

equal to 0.5 and then to increase again (greatest deviation is Δη= −0.31 mPa·s). On the basis of the data the authors previously published, mixtures of toluene with either n-butylcyclohexane or n-hexadecane have negative viscosity deviations using eq 20.20,26 Negative values of viscosity deviation have been attributed the dominance of dispersion forces in the mixing process, while positive values would indicate more specific interactions such as hydrogen bonding.53,70 The negative viscosity deviations found for the mixtures herein suggest that dispersion forces are dominating, and this result is consistent with the trend found for excess molar volume, which also suggested that dispersion was the major interaction among the molecules. Wang et al.31 reported negative dynamic viscosity deviations using eq 20 for ternary mixtures of n-hexylbenzene with two alkanes: heptane, octane, or nonane with the largest deviation of −0.10051 mPa·s for a mixture of heptane, nonane, and hexylbenzene at 293.15 K. Nhaesi and Asfour32 reported negative dynamic viscosity deviations for ternary mixtures containing three of the following: toluene, ethylbenzene, octane, tetradecane, and hexadecane. The smallest deviations were reported for ternary mixtures of toluene, octane, and ethylbenzene (∼0.03 mPa·s), while the largest

Figure 3. Viscosities η of select ternary mixtures at 293.15 K: purple ■, n-hexylbenzene (x1) in xn‑hexadecane/xn‑butylcyclohexane = 0.3335; □, n-butylbenzene (x1) in xn‑hexadecane/xn‑butylcyclohexane = 0.3334; green ▲, n-butylbenzene (x1) in xn‑dodecane/xn‑butylcyclohexane = 0.3332; red ◆, n-hexylbenzene (x1) in xn‑dodecane/xn‑butylcyclohexane = 0.3332; and ●, toluene (x1) in xn‑hexadecane/xn‑butylcyclohexane = 0.2500. Error bars, which are the combined uncertainties with 0.95 level of confidence (k = 2), are smaller than the symbols. Lines shown are fits to the McAllister eq (eq 13) with the coefficients listed in Table 17. 3466



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deviations were found for ternary mixtures of toluene, octane, and hexadecane (∼0.37 mPa·s). These systems would also have been dominated by dispersion forces because these molecules are nonpolar. 4.4. Surface Tension and Flash Point. The surface tensions and flash points of the pure components are given in Table 18. These values agree with most literature values within the error of the measurements. The surface tensions and flash points for ternary mixtures of n-butylcyclohexane, an n-alkane (n-hexadecane or n-dodecane), and an aromatic compound (n-butylbenzene, n-hexylbenzene, or toluene) are given in Table 19. No values for mixtures are available in the literature for comparison. As can be seen from the data in Table 19, the surface tensions increase as the mole fraction of n-hexadecane or the aromatic compound increases and as mole fraction of n-dodecane decreases. The flash points of n-butylbenzene or toluene mixtures increase as the mole fraction of either n-hexadecane or n-dodecane increases and as the mole fraction the aromatic compound decreases. For n-hexylbenzene mixtures, the flash points increase as the mole fraction of either n-hexadecane or n-dodecane increases and as the mole fraction of n-hexylbenzene decreases. Reported surface tension values for petroleum-based jet and diesel fuel near 293.15 K are 26.1 and 26.9 mN·m−2, respectively.51,52 On the basis of the ternary mixture systems tested, only those mixtures containing n-dodecane could have surface tensions that can match the jet fuel, and all the ternary mixture systems studied herein could have surface tensions that can match the diesel fuel at certain mixture compositions. Reported flash points for petroleum-based jet and diesel fuel are 334 and 335 K, respectively.51,52 The military specification for JP-5 jet fuel and diesel fuel sets a minimum limit of 333.15 K.2,3 The ternary mixtures studied herein have flash points that can match the diesel fuel at certain mixture compositions.

Table 18. Comparison of the Measured Flash Points and Surface Tensions of n-Hexadecane, n-Dodecane, n-Butylcyclohexane, Toluene, n-Butylbenzene, and n-Hexylbenzene with Literature Values at Pressure P = 0.1 MPaa

this study lit. this study lit. this study lit.

this study lit. this study lit. this study lit.

flash point

surface tension

K

mN·m−1

n-Hexadecane 407.2 ± 2 27.2 ± 0.2 @ 294.0 ± 1 K 407 ± 2b, 408c,d, 409e 27.3 @ 294.0 Kd 27.4 @ 294.0 Kj n-Dodecane 354 ± 2 25.0 ± 0.2 @ 293.6 ± 1 K 347e, 352l 25.3 @ 293.6 Kj Toluene 280.7 ± 2reference 28.6 ± 0.2 @ 293 ± 1 K 275.2e, 277g, 279.15h, 28.5 @ 293 Kj f 280 n-Butylbenzene 328.7 ± 2 28.8 ± 0.2 @ 294.4 ± 1 K 322m, 323g, 330n, 344e 29.1@ 293.6 Kj n-Hexylbenzene 362.7 ± 2 29.4 ± 0.2 @ 294.1 ± 1 K 356g, 356.15h 29.9 @ 294.1 Kj,o n-Butylcyclohexane 324.7 ± 2 26.6 ± 0.2 @ 294.5 ± 1 K 321g, 324.8f, 325.65h 26.9@ 294.0 Kj 26.6 @ 294.0 Kk

Expanded uncertainties Uc are given by the “ ± ” symbol (level of confidence = 0.9545, k = 2). bReference 114. cReference 115. d Reference 89. eReference 116. fReference 117. gReference 118. h Reference 119. jReference 120. kReference 80. lReference 121. m Reference 122. nReference 123. oReference 124. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2). a

Table 19. Surface Tensions and Flash Points of Ternary Mixtures of an Aromatic Compound (Mole Fraction x1), and n-Butylcyclohexane (Mole Fraction x2), and a Linear Alkane (Mole Fraction x3) at Pressure P = 0.1 MPaa x3/x2

x1

flash point

surface tension

K

mN·m−1

x3/x2

n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 0.3333 0.0000 331.3 ± 2 26.7 ± 0.2 0.2004 331.3 ± 2 26.7 ± 0.2 0.4004 330.5 ± 2 27.4 ± 0.2 0.6003 329.5 ± 2 27.7 ± 0.2 0.8002 330.5 ± 2 28.2 ± 0.2 0.9992 0.0000 340.0 ± 2 26.9 ± 0.2 0.2009 336.0 ± 2 27.1 ± 0.2 0.4003 334.0 ± 2 27.4 ± 0.2 0.6002 330.0 ± 2 27.8 ± 0.2 0.8000 330.0 ± 2 28.1 ± 0.2 3.0006 0.0000 356.0 ± 2 27.0 ± 0.2 0.2010 350.2 ± 2 27.1 ± 0.4 0.4009 344.5 ± 2 27.3 ± 0.3 0.6010 339.7 ± 2 27.6 ± 0.3 0.8005 333.5 ± 2 28.1 ± 0.2 n-Butylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) 0.3332 0.0000 329.0 ± 2 26.1 ± 0.2 0.2001 328.0 ± 2 26.3 ± 0.3 0.4003 328.0 ± 2 26.7 ± 0.3 0.6003 327.0 ± 2 27.3 ± 0.2 0.8000 328.0 ± 2 27.8 ± 0.2 1.0002 0.0000 335.0 ± 2 25.6 ± 0.2 0.2005 333.0 ± 2 26.0 ± 0.3

x1

flash point

surface tension

K

mN·m−1

n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Hexadecane (3) 0.3335 0.0000 331.3 ± 2 26.9 ± 0.2 0.2004 335.0 ± 2 27.2 ± 0.2 0.4006 338.0 ± 2 27.4 ± 0.2 0.6003 343.0 ± 2 28.2 ± 0.2 0.7997 350.0 ± 2 28.5 ± 0.2 0.9997 0.0000 340.0 ± 2 26.9 ± 0.2 0.2004 343.0 ± 2 27.0 ± 0.2 0.4008 346.0 ± 2 27.7 ± 0.2 0.6008 350.0 ± 2 28.2 ± 0.2 0.8003 355.0 ± 2 28.6 ± 0.2 2.9967 0.0000 356.0 ± 2 27.1 ± 0.2 0.2005 356.0 ± 2 27.4 ± 0.2 0.4025 357.0 ± 2 27.4 ± 0.2 0.6007 358.0 ± 2 27.9 ± 0.2 0.8004 360.0 ± 2 28.6 ± 0.2 n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) 0.3335 0.0000 330.0 ± 2 26.1 ± 0.2 0.2001 333.0 ± 2 26.7 ± 0.2 0.4002 336.0 ± 2 26.9 ± 0.2 0.6000 341.0 ± 2 27.7 ± 0.2 0.7997 348.0 ± 2 28.3 ± 0.2 0.9998 0.0000 336.0 ± 2 25.8 ± 0.3 0.1999 338.0 ± 2 26.3 ± 0.2 3467



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Table 19. continued flash point x3/x2

x1

K

surface tension mN·m

−1

x3/x2

n-Butylbenzene (1) + n-Butylcyclohexane 1.002 0.4007 331.0 ± 0.6008 331.0 ± 0.8005 330.0 ± 3.0005 0.0000 343.0 ± 0.2007 338.0 ± 0.4011 335.0 ± 0.6013 333.0 ± 0.8007 331.0 ± 0.2500

0.6667

0.0000 0.2318 0.3996 0.5993 0.7999 0.0000 0.2003 0.4007 0.6000 0.7999

328 300 295 294 284 335 304 296 291

± ± ± ± ± ± ± ± ±

(2) + n-Dodecane (3) 2 26.5 ± 0.2 2 27.1 ± 0.2 2 27.8 ± 0.2 2 25.3 ± 0.2 2 25.7 ± 0.2 2 26.2 ± 0.2 2 26.8 ± 0.2 2 27.8 ± 0.3 Toluene (1) + n-Butylcyclohexane 2 26.6 ± 0.2 2 26.9 ± 0.2 2 27.0 ± 0.2 2 27.4 ± 0.2 2 27.5 ± 0.2 3 26.9 ± 0.2 2 26.9 ± 0.2 2 26.9 ± 0.2 2 27.0 ± 0.2 27.6 ± 0.2

flash point

surface tension

K

mN·m−1

x1

n-Hexylbenzene (1) + n-Butylcyclohexane (2) + n-Dodecane (3) 0.9998 0.4002 342.0 ± 2 26.9 ± 0.2 0.6001 346.0 ± 2 27.6 ± 0.2 0.7999 352.0 ± 2 28.0 ± 0.2 2.9968 0.0000 343.0 ± 2 25.4 ± 0.2 0.1999 346.0 ± 2 25.9 ± 0.2 0.4002 348.0 ± 2 26.4 ± 0.2 0.5998 351.0 ± 2 27.1 ± 0.3 0.7998 355.0 ± 2 28.1 ± 0.2 (2) + n-Hexadecane (3) 1.5000 0.0000 345 ± 3 26.9 ± 0.2 0.2010 307 ± 3 27.1 ± 0.2 0.4008 296 ± 2 27.2(5) ± 0.2 0.6013 290 ± 2 27.3(1) ± 0.2 0.8015 284 ± 2 27.7 ± 0.2 3.9977 0.0000 359 ± 2 27.0 ± 0.2 0.2012 312 ± 2 27.0 ± 0.2 0.4013 296 ± 2 27.1 ± 0.2 0.6031 290 ± 2 27.3 ± 0.2 0.8012 284 ± 2 27.6 ± 0.2

a x1 is the mole fraction of the aromatic compound, x2 is the mole fraction of n-butylcylohexane, and x3 is the mole fraction of linear alkane. Expanded uncertainties Uc are indicated by the symbol “ ± ”, and combined expanded uncertainties of Uc(x1) = 0.0001, Uc(x2) = 0.0001, and Uc(x3) = 0.0001. Surface tension measurements were taken at room temperature, 294.5 ± 1 K. The average pressure P for these measurements was 0.102 MPa with an expanded uncertainty Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2).

5. CONCLUSIONS This study measured the density, viscosity, speed of sound, viscosity, surface tension, and flashpoint of mixtures of ternary mixtures of n-butylcyclohexane with an alkane (n-dodecane or n-hexadecane) and an aromatic compound (toluene, n-butylbenzene, or n-hexylbenzene). Mixture surface tensions and flashpoints fell between the pure component values. Excess molar volumes calculated from density measurements were positive, which indicates the dominance of dispersion forces between molecules. The speed of sound deviations were negative for most mixtures, which suggest that the interactions that cause the positive excess molar volumes may also be causing the reduction in speeds of sound compared to ideal behavior. Viscosities were modeled well using a McAllister three-body model. Viscosity deviations were calculated using dynamic viscosity and natural log of dynamic viscosity. For the mixtures containing n-dodecane, small deviations that were calculated by both viscosity deviation equations suggest that the mixing behavior in those systems is close to ideal. For the n-hexadecane mixtures, the viscosity deviations that were calculated using dynamic viscosity were negative for all mixtures. This result suggests the dominance of dispersion forces, which is consistent with what was found for excess molar volume. The largest negative deviations were found for toluene and the smallest for n-hexylbenzene, which suggests that the mixing behavior in the n-hexylbenzene cases is closer to ideal than toluene. When the viscosity deviations for the n-hexadecane mixtures were calculated using the natural log of dynamic viscosity, both negative and positive values were found, and in a similar manner, the mixtures with n-hexylbenzene had smaller viscosity deviations than those containing toluene. The usefulness of these mixtures as surrogates was assessed by comparing their values to those reported for diesel and jet fuels and to their specifications. None of mixtures tested in this study

had properties that matched all the properties of petroleum jet and diesel fuel. Jet fuel’s density, speed of sound, bulk modulus, surface tension, and flashpoint fell among the values found for ternary mixtures with n-dodecane. Less success was found for diesel fuel, where only its viscosity, surface tension, and flashpoint fell among the values for ternary mixtures containing n-hexadecane.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00466. Parameters needed for the speed of sound deviation calculations; Excess molar volumes and viscosity deviations for ternary mixtures of (a) n-butylbenzene or n-hexylbenzene (mole fraction x1), + n-butylcyclohexane (mole fraction x2), + n-hexadecane (mole fraction x3); (b) n-butylbenzene or n-hexylbenzene (mole fraction x1), + n-butylcyclohexane (mole fraction x2), + n-dodecane (mole fraction x3); (c) toluene (mole fraction x1), + n-butylcyclohexane (mole fraction x2), + n-hexadecane (mole fraction x3) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (410)293-6399. Fax: (410)2932218. ORCID

Dianne J. Luning Prak: 0000-0002-5589-7287 Funding

This work was funded by the Office of Naval Research, Grant No. N0001416WX01648 and No. N0001417WX00892. 3468



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Notes

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The authors declare no competing financial interest.

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Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension

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