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Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension, and Flash Point of Binary Mixtures of n-Hexylbenzene (1) or nButylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8-Heptamethylnonane (2) at 0.1 MPa Dianne J. Luning Prak,*,† Sahara L. Graft,† Theodore R. Johnson,† 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

J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF KENTUCKY on 08/22/18. For personal use only.

‡

S Supporting Information *

ABSTRACT: This work reports physical property measurements of binary mixtures of n-hexylbenzene (1) and n-butylbenzene (1) in 2,2,4,6,6pentamethylheptane (2) and 2,2,4,4,6,8,8-heptamethylnonane (2) at temperatures within the range 253.15−333.15 K. Mixture densities, speeds of sound, and calculated bulk moduli increased with increasing aromatic compound concentration. Excess molar volumes were positive for 2,2,4,4,6,8,8-heptamethylnonane mixtures, negative for hexylbenzene/ 2,2,4,6,6-pentamethylheptane mixtures, and close to zero for butylbenzene/2,2,4,6,6-pentamethylheptane mixtures at 293.15 K. Excess speeds of sound were positive for all mixtures at 298.15 K, except for n-butylbenzene/ 2,2,4,4,6,8,8-heptamethylnonane mixtures, which were close to zero. These results show that compressibility as well as volume change is important for excess speeds of sound. Kinematic viscosities decreased as the aromatic concentration increased at 293.15 K, except for hexylbenzene (x1) in 2,2,4,6,6-pentamethylheptane, where increasing hexylbenzene caused a slight viscosity decline before increasing to the value for hexylbenzene. Viscosities were successfully modeled using the McAllister equation. The excess molar Gibbs energy of activation for viscous flow at 293.15 K was not statistically different from zero, which suggests ideal behavior for viscosity. Mixture surface tensions at room temperature and flash points fell within the values of the pure components. Many of these mixtures have property values similar to those of petroleum-based diesel and jet fuel.

1.0. INTRODUCTION

engine were measured for binary mixtures of an aromatic compound (n-butylbenzene or n-hexylbenzene) with a branched alkane (2,2,4,4,6,8,8-heptamethylnonane or 2,2,4,6,6-pentamethylheptane). These isoparaffins and aromatic compounds were studied because they have been found in petroleum-based and bio-based fuels and they are less reactive in diesel engines than other fuel components such as linear alkanes. If these mixtures are used as blending components for fuels, it is important to know their properties to enable prediction of their impact on fuel delivery and spray patterns in an engine. The importance of 2,2,4,4,6,8,8-heptamethylnonane (isocetane), 2,2,4,6,6-pentamethylheptane (isododecane), n-butylbenzene, and n-hexylbenzene in fuel research is demonstrated by studies of their combustion behavior individually and in mixtures with other components11−17 and their use in surrogate

Isoparaffins and aromatic compounds are components of petroleum-based and biobased fuels.1−3 Their presence influences a fuel’s physical properties, chemical kinetics, and engine performance. In an effort to link engine combustion performance with physical properties and chemical kinetics, researchers have studied the behavior of simple mixtures containing up to 10 components, called surrogate mixtures, as model systems to represent petroleum-based and bio-based fuels, which can contain thousands of compounds. In other cases, researchers alter fuel properties by adding organic compounds to determine how the additions alter fuel properties or performance. For example, aromatic compounds have been added to bio-based fuels to enhance their performance in terms of seal swelling, thermal-oxidative stability, and emissions.4−7 Branched alkanes have been investigated as components to be used in partially premixed combustion scenarios to reduce emissions and enhance engine performance.8−10 In the current study, several properties used in assessing fuel behavior in an This article not subject to U.S. Copyright. Published XXXX by the American Chemical Society

Received: May 11, 2018 Accepted: August 3, 2018

A

DOI: 10.1021/acs.jced.8b00387 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Information CAS number

molar massa (g·mol−1)

source/lot number

mole fraction purityb

analysis methodb

2,2,4,6,6-pentamethylheptane (C12H26)

13475-82-6

170.335 ± 0.007

4390-04-9

226.44 ± 0.02

n-hexylbenzene (C12H18)

1077-16-3

162.271 ± 0.008

n-butylbenzene (C10H14)

104-51-8

134.22 ± 0.01

0.995 0.992 0.992 0.983 0.996 0.992 0.994 0.986 0.990 0.999 0.992

GC

2,2,4,4,6,8,8-heptamethylnonane (C16H34)

TCI/ZDS2M TCI/EJW6L TCI/S5P2B TCI/7EDMJ Aldrich/STBD1267V Aldrich/STBF0890V Aldrich/STBF1816V Alfa Aesar/10201705c Alfa Aesar/10206925d TCI/Y3XBD Acros/A03865455

chemical name

GC

GC GC

a

Calculated using values in ref 73. bGas−liquid chromatography, as specified in the Certificates of Analysis provided by the chemical suppliers. Used in mixtures with 2,2,4,6,6-pentamethylheptane. dUsed in mixtures with 2,2,4,4,6,8,8-heptamethylnonane.

c

from 1.00 to 1.37 cm3·mol−1 and for equimolar mixtures with chlorobenzenes that were 0.076 and 0.238 cm3·mol−1 for isododecane and isocetane, respectively.33 Negative excess molar volumes have been found for mixtures of heptane with isododecane (−0.112 cm3·mol−1 at 0.5021 mole fraction of heptane) and with isocetane (−0.253 cm3·mol−1 at 0.4815 mole fraction of heptane).34 Wang et al.35 measured the densities and viscosities of ternary mixtures of hexylbenzene (mole fraction ranging from 0.0571 to 0.0914) with linear alkanes (heptane, octane, and nonane). They found positive excess molar volumes at all temperatures studied. Work in the authors’ laboratory has investigated the density, viscosity, speed of sound, surface tension, and flash point of binary mixtures of isocetane, isododecane, butylbenzene, and hexylbenzene with linear alkanes, and isocetane with isododecane, and ternary mixtures of butyl- or hexylbenzene with butylcyclohexane and nalkanes.36−43 No studies have been done on the physical property measurements of isododecane with hexylbenzene and isocetane with butylbenzene. In this study, the density, viscosity, speed of sound, and surface tension were measured for these mixtures. The measurements of these physical properties provide data to those who model the combustion process by enabling them to include the physical factors that impact fuel behavior in an engine along with the chemical kinetic mechanisms.

mixtures for various fuels.18−24 Detailed chemical kinetic mechanisms have been developed by Lawrence Livermore Laboratories for isocetane.11,12 Pyrolysis models have been published for isododecane.13 Won et al.14 compared the combustion characteristics of 2,2,4-trimethylpentane (isooctane), isododecane, and isocetane using reflected shock ignition delay times and diffusion flame extinction strain rates and concluded that chemical kinetic potentials of the three compounds and mixtures of isocetane and isooctane were the same. Kang et al.15 created jet fuel surrogates containing isocetane whose physical and chemical ignition delay matched those of a jet fuel. Tekawade and Oehlschlaeger16 conducted spray ignition experiments with blends containing butylbenzene and other alkylbenzenes. In the authors’ laboratories, surrogate mixtures containing butylbenzene and hexylbenzene formulated for alternative jet and diesel fuels had combustion metrics that matched those of their respective fuels.23,24 Zhang et al.17 showed that n-butylbenzene had pyrolysis characteristics that differed from small alkylbenzenes in the dominance of certain reaction pathways and in the products formed. The properties tested in the current study are those that affect the injection of a fuel into a combustion chamber (bulk modulus) and the formation of the fuel droplets (density, viscosity, and surface tension). The isentropic bulk modulus, Ev, is calculated from the density, ρ, and speed of sound, c, as Ev = ρ × c 2

2.0. MATERIALS The 2,2,4,6,6-pentamethylheptane, 2,2,4,4,6,8,8-heptamethylnonane, n-hexylbenzene, and n-butylbenzene were used as received from the supplier and had a mole fraction purity of 0.983 or higher (Table 1). Mixtures were prepared at room temperature by sequentially pipetting each compound into a clean vial and weighing on a Mettler Toledo AG204 analytical balance that has an error of 0.0004 g. After sealing the vial with a cap fitted with a Teflon septum, the two components were mixed. The combined expanded uncertainties (level of confidence = 0.95, k = 2) in mole fractions were calculated from the mass and molar mass in Table 1 to 0.0001 unless otherwise indicated in the results.

(1)

The bulk modulus has been found to change fuel injection timing.25,26 The spray pattern of fuel droplets formed in a combustion cylinder has been modeled using dimensionless numbers (e.g., Reynolds, Ohnesorge, and Weber numbers) calculated using density, viscosity, and surface tension.27 The importance of density and viscosity is emphasized by their presence in fuel specifications given by American Society for Testing and Materials and by the military.28−30 Flash point is a combustion property that is also part of these specifications.28−30 In this study, density, viscosity, flash point, speed of sound, and surface tension were measured for the binary mixtures. Some of these physical properties have been reported in the literature for mixtures of isocetane, isododecane, butylbenzene, and hexylbenzene with other compounds. The speed of sound for mixtures of isocetane with chlorobenzene and 1chloronaphthalene has been shown to exhibit nonlinear behavior.31 Excess molar volumes of isododecane and isocetane have been reported for mixtures with oxaalkanes32 that ranged

3.0. METHODS The density and speed of sound were measured using an Anton Paar DSA 5000M density and sound analyzer. This instrument measures the 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 B

DOI: 10.1021/acs.jced.8b00387 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 2. Comparison of the Density ρ, Viscosity η, and Speed of Sound c of 2,2,4,4,6,8,8-Heptamethylnonane, 2,2,4,6,6Pentamethylheptane, n-Butylbenzene, and n-Hexylbenzene with Literature Values at Pressure p = 0.1 MPaa density (kg·m−3) T (K)

this study

viscosity (mPa·s)

literature

this study

literature

speed of sound (m·s−1) this study

literature

2,2,4,4,6,8,8-Heptamethylnonane 14.09

253.15 288.15 293.15 303.15 313.15

811.4 787.76 784.41 777.73 770.99

788.5 ± 1.5q 784,l 784.46 ± 0.5,c 785.1 ± 1.5q 777.76 ± 0.5,c 778,l 778.3 ± 1.5q 771,l 771.04 ± 0.5,c 771.5 ± 1.4q

3.75 2.97 2.40

323.15 333.15

764.27 757.53

764,l 764.31 ± 0.5,c 764.7 ± 1.4q 757,l 757.57 ± 0.5,c 757.9 ± 1.6q

1.97 1.65

253.15 288.15 293.15

774.5 748.8 745.2

303.15 313.15 323.15 333.15

737.9 730.6 723.2 715.8

253.15 288.15 293.15

892.6 864.47 860.17

303.15

852.13

851.3,d 852.16 ± 0.10,g 852.23,e 852.428,f 852.43 ± 0.50,g 852.47 ± 0.40q

0.880

313.15

844.07

844.6,d 844.82 ± 0.51,g 845.172f

0.775

0.787,d 0.781,j 0.79j

1276.1

323.15 333.15

835.98 827.86

836.34,i 837.00 ± 0.67,g 838.509f 828.21,i 829.52 ± 0.76m

0.687 0.615

0.684,j 0.7015j 0.614,j 0.6237,j 0.63j

1238.4 1201.5

253.15

889.1,u 888.9v 862.4,u 862.3v 858.6,u 858.5v 851.0,u 850.9v 843.4,u 843.3v 835.8,u 845.7v 828.2,u 828.1v

4.56,u 4.63v

5.11,j 5.17j

3.64,l 3.70 ± 0.008c 2.92,l 2.92 ± 0.008c 2.37 ± 0.008,c 2.383,j 2.43l 1.95 ± 0.008,c 2.01l 1.63 ± 0.008,c 1.658,j 1.69l

1305.1 1285.9 1248.3 1211.7

1285.7 ± 0.3c 1248.5 ± 0.3c 1211.8 ± 0.3c

1175.9 1141.3

1176.0 ± 0.3c 1140.8 ± 0.3c

2,2,4,6,6-Pentamethylheptane 3.08

3.25j

1.31

1.29b

1223.7 1203.8

1203.6 ± 0.3b

1.13 0.955 0.849 0.744

1.10b 0.941b 0.825,j 0.827b 0.726b

1164.7 1126.5 1089.1 1052.7

1164.8 ± 0.3b 1126.7 ± 0.3b 1089.3 ± 0.3b 1052.5 ± 0.3b

2.21

2.22,j 2.23j

1.00

1.032,j 1.034,e 1.035,j 1.050,j 1.07j 0.893,e 0.894,j 0.895,j 0.9035,j 0.901d

749.5 ± 0.90 745.5,b 746.02 ± 0.90q 746.3,s 747.4t 738.2,b 739.06 ± 0.13q 730.9,b 731.5,r 732.10 ± 0.26q 723.5,b 725.13 ± 0.68q 716.1b q

n-Butylbenzene 863.95 ± 0.28,m 864.73 ± 0.60g 859.50 ± 0.60,g 860.052,f 860.15 ± 0.35,g 860.25 ± 0.30,g 861.26e

1373.7 1353.2 1314.3

1341.31,f 1353.4h 1302.11,f 1308,d 1314.3h 1264.92,f 1275.7,h 1276d 1228.70f 1201.4i

n-Hexylbenzene

288.15 293.15 303.15 313.15 323.15 333.15

861.91 ± 0.76,m 863.92 ± 2.0l 851.6,o 857.68,k 858.00 ± 0.40,m 858.02 ± 0.40,m 858.28 ± 0.40,m 859.20 ± 1.00,p 860.0 ± 2.0,l 862.4 ± 0.8n 850.10,k 852.40 ± 0.60m 842.50,k 844.6 ± 1,m 846.8 ± 0.8n 834.88,k 837.7 ± 1.5m 827.24,k 830.8 ± 1.9,m 831.7 ± 0.8n

1.64,u 1.66v 1.39,u 1.41v 1.17,u 1.19v 1.03,u 1.04v 0.902u,v

1.655,j 1.67,j 1.68,k 1.70j 1.40,k 1.403,j 1.409j 1.19,k 1.196,j 1.20 1.03,k 1.035,j 1.07j 0.901,k 0.909j

1395.8,u 1395.6v 1376.0,u 1376.5v 1338.1,u 1338.7v 1301.1,u 1301.6v 1264.7,u 1265.3v 1229.4,u 1229.8v

1376.1 ± 0.8 1338.7 ± 1.0k 1301.7 ± 0.8k 1265.3 ± 0.8k 1229.4 ± 0.8k

a

The average pressure for these measurements was 0.102 MPa. Standard uncertainties u are u(T) = 0.01 K and Uc(ρ) = 0.001 MPa, and expanded uncertainties Uc are T > 288 K Uc(ρ) = 0.7 kg·m−3, Uc(c) = 1 m·s−1, and Uc (η) = 0.02 mPa·s and at T = 253.15 K Uc(η) = 2.0 kg·m−3, Uc(η) = 0.06 mPa·s for the aromatic compounds, Uc(η) = 0.18 mPa·s for 2,2,4,4,6,8,8-heptamethylnonane, and Uc(η) = 0.12 mPa·s for 2,2,4,6,6pentamethylheptane (level of confidence = 0.95, k = 2). bReference 39. cReference 38. dReference 74. eReference 75. fReference 76. gReference 77. h Reference 78. iReference 43. jReference 54. kReference 42. lReference 79. mReference 80. Best fits for butylbenzene: ρ/kg·m3 = 1084.37 − 0.764957*T/K; hexylbenzene: ρ/kg·m3 = 1060.96 − 0.690758*T/K. nReference 81. oReference 82. pReference 83. qReference 84. Best fits for 2,2,4,4,6,8,8-heptamethylnonane: ρ/kg·m3 = 984.48 − 0.68*T/K; 2,2,4,6,6-pentamethylheptane: ρ/kg·m3 = 950.179 − 0.696415*T/K. rReference 85. sReference 86. tReference 87. uHexylbenzene lot 10201705 used for 2,2,4,6,6-pentamethylheptane mixtures. vHexylbenzene lot 10206925 used for 2,2,4,4,6,8,8-heptamethylnonane mixtures.

waves.44 Its measurement of the speed of sound and density was checked daily using degassed ultrapure water, and its density measurement was also checked using a NIST-certified density standard (Certificate Standard Reference Material 211d, toluene liquid density-extended range). The average speed of sound for

degassed ultrapure water at 293.15 K measured during the time period of this study was 1482.9 ± 0.3 m·s−1 for one instrument and 1482.7 ± 0.3 m·s−1 for a second instrument, which compares favorably with the literature values provided by the instrument vendor, 1482.66 m·s−1.45 The error reported is the C

DOI: 10.1021/acs.jced.8b00387 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 3. Experimental Values of Density ρ, in kg·m−3, at Temperature T and Mole Fraction x1, for the Systems n-Hexylbenzene (1) or n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8-Heptamethylnonane (2) at Pressure p = 0.1 MPaa n-Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) x1 0.6998

0.7997b

0.8999b

850.5 824.00 820.27 812.80 805.33 797.82 790.29

863.5 836.31 832.57 825.06 817.55 810.01 802.45

875.7 849.13 845.36 837.82 830.26 822.68 815.08

0.5997

0.7001

0.7998b

0.8992b

820.7 796.54 793.11 786.24 779.36 772.47 765.57

826.1 832.1 838.8 846.5 801.59 807.31 813.73 820.89 798.11 803.78 810.17 817.24 791.16 796.72 803.00 809.95 784.19 789.65 795.81 802.64 777.21 782.56 788.61 795.31 770.20 775.45 781.38 787.95 n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2)

855.7 829.45 825.74 818.29 810.83 803.34 795.82

865.8 839.17 835.37 827.77 820.15 812.49 804.80

878.5 850.51 846.62 838.82 831.01 823.15 815.26

0.1001

0.2000

0.3001

0.6999

0.8009b

0.9000b

782.1 756.92 753.25 745.91 738.55 731.16 723.71

791.5 765.57 761.88 754.49 747.07 739.61 732.11

846.8 819.87 816.01 808.28 800.51 792.72 784.88

860.0 833.77 829.80 821.96 814.10 806.20 798.16

876.1 848.29 844.33 836.41 828.46 820.47 812.44

T (K)

0.1000

0.2065

253.15 288.15 293.15 303.15 313.15 323.15 333.15

784.1 758.47 754.83 747.53 740.20 732.84 725.44

795.0 769.17 765.51 758.19 750.84 743.45 736.04

T (K)

0.1007

0.2007

0.3000

253.15 288.15 293.15 303.15 313.15 323.15 333.15

815.9 791.93 788.54 781.75 774.96 768.15 761.33

T (K) 253.15 288.15 293.15 303.15 313.15 323.15 333.15

0.3009

0.3968

0.5001

0.6000

804.9 815.2 826.8 838.5 778.97 789.42 800.56 812.08 775.30 785.50 796.87 808.37 767.96 778.14 789.48 800.94 760.60 770.75 782.06 793.50 753.21 763.34 774.63 786.03 745.77 755.89 767.15 778.54 n-Butylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2) x1 0.3999

0.4998

x1 0.4006

0.5000

0.6002

801.0 811.2 822.2 834.1 774.88 784.92 795.63 807.34 771.17 781.17 791.85 803.52 763.72 773.66 784.27 795.86 756.25 766.12 776.66 788.17 748.74 758.55 769.02 780.45 741.19 750.94 761.34 772.69 n-Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2) x1

T (K)

0.1015

0.2005

0.2999

0.4001

0.4996

0.6000

0.6999

0.8000b

0.9000b

253.15 288.15 293.15 303.15 313.15 323.15 333.15

816.6 792.77 789.39 782.63 775.87 769.09 762.29

822.2 798.05 794.63 787.80 780.97 774.12 767.25

828.0 803.73 800.29 793.41 786.51 779.61 772.68

834.5 810.02 806.56 799.59 792.62 785.63 778.62

841.5 816.74 813.23 806.19 799.14 792.08 784.99

849.4 824.16 820.65 813.53 806.39 799.24 792.06

857.7 832.36 828.75 821.53 814.29 807.04 799.77

867.1 841.37 837.70 830.36 823.01 815.65 808.26

877.1 851.27 847.55 840.10 832.64 825.16 817.65

a

x1 is the mole fraction of the alkylbenzene in the branched alkane. The average pressure for these measurements was 0.102 MPa. Standard uncertainties u are u(T) = 0.01 K and Uc(p) = 0.001 MPa; expanded uncertainties Uc are Uc(ρ) = 0.7 kg·m−3 for T > 288 K and Uc(ρ) = 2.0 kg·m−3 at T = 253.15 K; and combined expanded uncertainties of Uc(x1) = 0.0001 unless otherwise indicated by the superscript b (level of confidence = 0.95, k = 2). bThe combined expanded uncertainty is Uc(x1) = 0.0002.

expanded uncertainty of the measurement (k = 2). The average density of water at 293.15 K measured during the time period of this study for both instruments was 998.19 ± 0.01 kg·m−3, which compares favorably with the literature values provided by the instrument vendor, 998.203 kg·m−3.45 No error was provided by the vendor for its value. A comparison of toluene density data with the toluene standard is given in the Supporting Information. The DSA 5000M was cleaned with hexane between samples and with ethanol after checking with water and dried. At least two samples were measured for each mixture that was tested. The density at 253.15 K and the viscosity over the whole temperature range 253.15−333.15 K were measured using an

Anton Paar SVM 3001. This temperature range encompasses the diesel and jet fuel temperature specifications.28−30 This instrument was checked periodically with either the Cannon Certified Viscosity Reference Standard S3 or the Paragon Scientific Viscosity Reference Standard APS3. A comparison of measured viscosity data for the standard with reported values is given in the Supporting Information. The instrument was cleaned between samples with hexane and dried. At least two samples of each compound or mixture were measured using each instrument. The surface tension was measured using a Kruss DS100 drop shape analyzer. This instrument determines surface tension by fitting the shape of a droplet formed on the tip of a needle to the D

DOI: 10.1021/acs.jced.8b00387 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 4. Correlation of ln ρ to Temperature T (T = 288.15−303.15 K), Thermal Expansion Coefficients α, Excess Molar Volume VmE, and Excess Free Energy for the Activation of Flow ΔG*E at Temperature T = 293.15 K and Excess Speeds of Sound cE at T = 298.15 K for the Systems n-Hexylbenzene (1) or n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8-Heptamethylnonane (2), at Pressure p = 0.1 MPaa x1

A0

0.00 0.1000 0.2065 0.3009 0.3968 0.5001 0.6000 0.6998 0.7997 0.8999 1.00

6.90 6.91 6.92 6.93 6.95 6.95 6.97 6.98 6.99 7.00 7.02

± ± ± ± ± ± ± ± ± ± ±

0.01 0.01 0.01 0.01 0.01d 0.01 0.01 0.01 0.01 0.01 0.01

0.0000 0.1007 0.2007 0.3000 0.3999 0.4998 0.5997 0.7001 0.7998 0.8992 1.0000

6.92 6.92 6.93 6.94 6.95 6.96 6.97 6.98 7.00 7.01 7.04

± ± ± ± ± ± ± ± ± ± ±

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01d

0.00 0.1001 0.2000 0.3001 0.4006 0.5000 0.6002 0.6999 0.8009 0.9000 1.00

6.90 6.91 6.92 6.93 6.94 6.96 6.97 6.98 7.00 7.01 7.04

± ± ± ± ± ± ± ± ± ± ±

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01d

0.0000 0.1015 0.2005 0.2999 0.4001 0.4996 0.6000 0.6999 0.8000 0.9000 1.0

6.92 6.92 6.93 6.94 6.95 6.96 6.96 6.98 6.99 7.00 7.02

± ± ± ± ± ± ± ± ± ± ±

0.01 0.01 0.00 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01

103 × A1 (Κ−1)

R2

105 × σ

103 × α (Κ−1)

ΔG*E (kJ·mol−1)

n-Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2): ln ρ = A1T + Ao −0.98 ± 0.03 0.9999 2.3 0.98 −0.97 ± 0.03 0.9999 2.2 0.97 −0.1b −0.96 ± 0.03 0.9999 2.4 0.96 −0.1b −0.95 ± 0.02 0.9999 2.1 0.95 −0.1b −0.95 ± 0.02d 0.9996 10 0.95d −0.1b −0.93 ± 0.03 0.9999 2.2 0.93 −0.2b −0.92 ± 0.02 0.9999 2.0 0.92 −0.2b −0.91 ± 0.02 0.9999 1.8 0.91 −0.1b −0.90 ± 0.02 0.9999 1.7 0.90 −0.1b −0.89 ± 0.02 0.9999 1.8 0.89 −0.1b −0.89 ± 0.02 0.9999 1.3 0.89 n-Butylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2): ln ρ = A1T + Ao −0.86 ± 0.02 0.9999 1.5 0.86 −0.86 ± 0.02 0.9999 1.6 0.86 0.0b −0.87 ± 0.02 0.9999 1.6 0.87 0.0b −0.87 ± 0.02 0.9999 1.6 0.87 0.0b −0.88 ± 0.02 0.9999 1.5 0.88 0.0b −0.89 ± 0.03 0.9999 2.6 0.89 0.0b −0.90 ± 0.02 0.9999 1.8 0.90 0.0b −0.90 ± 0.02 0.9999 1.9 0.90 0.0b −0.91 ± 0.02 0.9999 1.8 0.91 0.0b −0.92 ± 0.02 0.9999 1.9 0.92 0.1b −0.95 ± 0.03d 0.9998d 12d 0.95d n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2): ln ρ = A1T + Ao −0.98 ± 0.03 0.9999 2.3 0.98 −0.98 ± 0.03 0.9999 2.1 0.98 0.0b −0.97 ± 0.03 0.9999 2.2 0.97 −0.1b −0.97 ± 0.03 0.9999 2.6 0.97 −0.1b −0.96 ± 0.03 0.9999 2.4 0.96 −0.1b −0.96 ± 0.03 0.9999 2.4 0.96 −0.2b −0.96 ± 0.03 0.9999 2.7 0.96 −0.1b −0.95 ± 0.03 0.9999 2.3 0.95 −0.1b −0.95 ± 0.02 0.9999 1.9 0.95 −0.1b −0.94 ± 0.02 0.9999 2.1 0.94 0.0b −0.95 ± 0.03d 0.9999d 12d 0.95d n-Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2): ln ρ = A1T + Ao −0.86 ± 0.02 0.9999 1.5 0.86 −0.86 ± 0.02 0.9999 1.6 0.86 0.0b −0.86 ± 0.02 0.9999 1.4 0.86 −0.1b −0.86 ± 0.02 0.9999 1.7 0.86 −0.1b −0.86 ± 0.04 0.9999 3.3 0.86 −0.1b −0.87 ± 0.02 0.9999 1.6 0.87 −0.2b −0.87 ± 0.06 0.9999 4.5 0.87 −0.2b −0.87 ± 0.02 0.9999 1.5 0.87 −0.1b −0.88 ± 0.02 0.9999 1.9 0.88 −0.1b −0.88 ± 0.02 0.9999 1.8 0.88 −0.1b −0.89 ± 0.02 0.9999 1.3 0.89

VmΕ (cm3·mol−1)

−0.03b −0.07 −0.09 −0.09 −0.09 −0.10 −0.10 −0.07b −0.04b

0.07b 0.12 0.17 0.20 0.22 0.27 0.22 0.18 0.11

cE (m·s−1)

6 11 15 18 20 20 19 16 9

0.4b 0.5b 0.6b 0.7b 0.7b 0.9b 1.1b 0.9b 0.6b

0.02b 0.02b 0.02b 0.01b 0.00b −0.03b −0.04b −0.07b −0.05b

3 7 9 11 13 15 14 12 8

0.04b 0.08b 0.11 0.12 0.14 0.13 0.12 0.08b 0.05b

2,c 3,c 4,c 5,c 6,c 7,c 6,c 6,c 4,c

1 2 3 4 5 5 5 4 2

The “±” for the coefficients A0 and A1 are the 95% confidence interval. The σ is the standard error of the fit. The x1 is the mole fraction of butylbenzene or hexylbenzene in mixtures with either 2,2,4,6,6-pentamethylheptane or 2,2,4,4,6,8,8-heptamethylnonane. The combined expanded uncertainties of Uc(x1) = 0.0001 for mole fractions less than 0.7002 and Uc(x1) = 0.0002 for the higher mole fractions. The combined expanded uncertainties of Uc(VmE) are between 0.06 and 0.08 cm3·mol−1, Uc(cE) = 1.5 m·s−1, Uc(ΔG*E ) are between 0.8 and 1.0 kJ·mol−1 (level of confidence = 0.95, k = 2). All excess values are greater than the combined expanded uncertainty except for those with a “b” superscript. The Δc values for all mixtures were based on values of the speed of sound and density at 298.15 K that were interpolated from the measured data. Also included are values at 293.15 K for hexylbenzene and 2,2,4,4,6,8,8-heptamethylnonane that were not based on interpolated speed of sound and density. See footnote c. The heat capacities used for these calculations were 303.19, 350.98, 458.8, and 243.5 J·mol−1·K−1 for hexylbenzene, 2,2,4,6,6-pentamethylheptane, 2,2,4,4,6,8,8-heptamethylnonane, and butylbenzene, respectively, at 298.15 K.64,65,68 Note using a lower value for hexylbenzene that would be more consistent with data from Tschamler,67 251 J·mol−1·K−1, results in Δc values that differ from the values in the a

E

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Table 4. continued table by at most 1 m·s−1. bThese excess values are less than the combined expanded uncertainty of the value. cThe heat capacities used for this calculation were 248 and 447.8 J·mol−1·K−1 for hexylbenzene and 2,2,4,4,6,8,8-heptamethylnonane, respectively, at 293.15 K.66,67 The value for 2,2,4,4,6,8,8-heptamethylnonane came from an extrapolation of data given in Bessieres.66 dThis fit was for temperatures between 288.15 and 313.15 K.

Table 5. Experimental Values of Speed of Sound c, in m·s−1, at Temperature T and Mole Fraction x1 for the Systems nHexylbenzene (1) or n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8-Heptamethylnonane (2) at Pressure p = 0.1 MPaa n-Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) x1 0.6998

0.7997b

0.8999b

1338.0 1318.6 1280.3 1243.0 1206.4 1170.8

1356.4 1337.1 1299.0 1261.7 1225.2 1189.6

1375.5 1356.2 1318.2 1281.0 1244.6 1209.1

0.5997

0.7001

0.7998b

0.8992b

1311.6 1292.7 1255.2 1218.4 1182.3 1147.0

1315.6 1320.4 1325.5 1331.9 1296.6 1301.1 1306.3 1312.5 1258.9 1263.3 1268.3 1274.4 1222.0 1226.2 1231.1 1237.0 1185.8 1189.8 1194.5 1200.2 1150.3 1154.1 1158.8 1164.2 n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2)

1339.5 1320.1 1281.9 1244.2 1207.2 1170.9

1348.9 1329.1 1290.3 1252.3 1215.1 1178.9

1359.8 1340.0 1300.9 1262.7 1225.2 1188.7

0.1001

0.2000

0.3001

0.6999

0.8009b

0.9000b

1234.1 1214.1 1175.0 1136.7 1099.4 1063.0

1245.3 1225.4 1186.5 1148.4 1111.0 1074.5

1315.0 1295.0 1255.8 1217.5 1179.9 1143.2

1332.9 1312.9 1274.1 1235.9 1198.3 1161.4

1352.1 1332.1 1292.8 1254.4 1216.8 1180.0

T (K)

0.1000

0.2065

288.15 293.15 303.15 313.15 323.15 333.15

1238.9 1219.0 1180.0 1141.9 1104.7 1068.5

1255.2 1235.7 1197.2 1159.3 1122.2 1085.8

T (K)

0.1007

0.2007

0.3000

288.15 293.15 303.15 313.15 323.15 333.15

1308.2 1289.3 1251.9 1215.2 1179.3 1144.1

T (K) 288.15 293.15 303.15 313.15 323.15 333.15

0.3009

0.3968

0.5004

0.6000

1270.3 1286.2 1302.9 1320.1 1250.6 1266.0 1283.3 1300.6 1211.8 1227.4 1244.8 1262.2 1174.0 1189.7 1207.2 1224.7 1136.9 1152.8 1170.4 1188.1 1101.0 1117.0 1134.6 1152.5 n-Butylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2) x1 0.3999

0.4998

x1 0.4006

0.5000

0.6002

1257.1 1270.0 1283.8 1298.7 1237.2 1250.0 1263.8 1278.9 1198.0 1210.8 1224.6 1240.1 1159.8 1172.6 1186.3 1201.9 1122.4 1135.1 1148.8 1164.4 1086.1 1098.7 1112.3 1127.7 n-Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2) x1

T (K)

0.1015

0.2005

0.2999

0.4001

0.4996

0.6000

0.6999

0.8000b

0.9000b

288.15 293.15 303.15 313.15 323.15 333.15

1311.3 1292.1 1254.4 1217.8 1181.9 1147.1

1317.6 1298.5 1261.2 1224.6 1188.7 1153.6

1324.6 1305.4 1267.7 1231.0 1195.1 1160.3

1332.0 1313.0 1275.6 1238.9 1203.0 1167.9

1340.4 1321.1 1283.4 1246.6 1210.5 1175.5

1349.4 1330.2 1292.4 1255.5 1219.5 1184.4

1359.3 1340.1 1302.3 1265.4 1229.4 1194.3

1370.0 1350.9 1313.5 1276.7 1240.5 1205.1

1382.2 1363.0 1325.2 1288.3 1252.0 1216.8

a

x1 is the mole fraction of the alkylbenzene in the branched alkane. The average pressure for these measurements was 0.102 MPa. Standard uncertainties u are u(T) = 0.01 K and Uc(p) = 0.001 MPa; expanded uncertainties Uc are Uc(c) = 0.6 m·s−3; and combined expanded uncertainties of Uc(x1) = 0.0001 unless otherwise indicated by the superscript b (level of confidence = 0.95, k = 2). bThe combined expanded uncertainty is Uc(x1) = 0.0002.

Young−LaPlace equation. The fitting software requires the input of air density, organic liquid density, and the needle diameter, which was measured using a Mitutoyo micrometer. At least three samples of each liquid were tested, and at least 20 surface tension measurements for each sample were recorded. The flash point was measured using a Setaflash Series 8 closed cup flash point tester model 82000-0 (Stanhope-Seta) in ramping mode. The 82000-0 model conforms to ASTM D3278 and other standards, as given in the manufacturer’s literature. This instrument was tested with a Cannon certified

flash point reference standard to ensure it was working correctly. The Cannon standard was not tested using the same ASTM standard to which the instrument conforms. The flash point reference standard value of 324.1 ± 2.4 K (ASTM method D56) is the same value given by NIST46 of 324.1 ± 0.8 K. It was assumed that the NIST reference value for D3278 (322.9 ± 1.2 K) could be used for comparison. The flash point of Cannon standard (decane) measured herein of 323 ± 2 K agrees with this value of 322.9 ± 1.2 K within the error of the measurement. It also falls within other reported values for decane (319.3, 321, F

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324, and 325 K).47−50 For each liquid, at least two measurements of flash point were taken. To determine the expanded uncertainty of all of these measurements, the standard deviation of the measurement as described previously was multiplied by 2. When a normal distribution is assumed, multiplying by a coverage factor of 2 is related to a 95% confidence interval. In determining the combined expanded uncertainty of the derived values, the error for the factors that contributed to these values was propagated (positive square root of the sum of the variances). The result of this value was multiplied by a coverage factor of 2.

4.0. RESULTS 4.1. Density. The measured densities of 2,2,4,6,6-pentamethylheptane, 2,2,4,4,6,8,8-heptamethylnonane, n-hexylbenzene, and n-butylbenzene agree with the reported values within the combined expanded uncertainty of the measurements, as shown in Table 2. The densities of the binary mixtures increase with an increase in the mole fraction of the aromatic compound (Table 3). The thermal expansion coefficients, α, were determined from density values, ρ, and temperature, T, from 288.15, 293.15 to 303.15 or 313.15 K on the basis of α=−

∂(ln ρ) ∂T

Figure 1. Speed of sound data for (●) hexylbenzene (x1) in 2,2,4,4,6,8,8-heptamethylnonane; ( ■ ) butylbenzene (x 1 ) in 2,2,4,4,6,8,8-heptamethylnonane; (□) hexylbenzene (x1) in 2,2,4,6,6pentamethylheptane; and (○) butylbenzene (x1) in 2,2,4,6,6pentamethylheptane at 293.15 K. The lines are polynomial regressions of the results of the regression with the coefficients given in Table 6.

mPa·s, are approximately 10% lower than the 5.11 and 5.17 mPa· s values reported in the literature.63 This reference does not state the purity of the chemicals, so the variation in purities may have produced differences in the viscosity values. For the binary mixtures, the viscosities decrease with increasing mole fraction of the aromatic compound, except for mixtures of hexylbenzene (x1) with 2,2,4,6,6-pentamethylheptane (Figure 2, Table 8). For those mixtures, the viscosity either remains constant or decreases slightly, depending on the temperature, and then increases as the mole fraction of hexylbenzene increases. The McAllister three-body model55 was used to fit the kinematic viscosity−mole fraction data.

(2)

and are given in Table 4. A linear equation fit the data well, so the negative of the slope of the linear equation is the thermal expansion coefficient for that range of temperatures. The value for 2,2,4,4,6,8,8-heptamethylnonane of (0.86 ± 0.02) × 10−3 K−1 agrees with 0.853 × 10−3 and 0.854 × 10−3 K−1 reported at 298 K,51,52 and (0.98 ± 0.03) × 10−3 K−1 for 2,2,4,6,6pentamethylheptane agrees with 0.977 × 10−3 K−1 reported at 298.01 K. 52 The thermal expansion coefficient for nhexylbenzene of (0.89 ± 0.02) × 10−3 K−1 agrees with values determined in the authors’ laboratories using a different lot of nhexybenzene,42 0.882 × 10−3 K−1, and the value for nbutylbenzene of (0.95 ± 0.03) × 10−3 K−1 agrees with 9.224 × 10−4 K−1 at 298.15 K53 within the error of the measurements. 4.2. Speed of Sound. The measured speeds of sound for 2,2,4,6,6-pentamethylheptane, 2,2,4,4,6,8,8-heptamethylnonane, n-hexylbenzene, and n-butylbenzene agree with the reported values within the standard uncertainty of the measurements (Table 2). The speeds of sound increase with an increase in the mole fraction of the aromatic compound (Table 5, Figure 1). The speed of sound−mole fraction data were fit to polynomials by increasing the order of the polynomial until the standard error of the fit was less than the combined expanded uncertainty of the measurements. The coefficients of the polynomial equations along with their standard error are given in Table 6. Figure 1 shows that the fits are excellent. The isentropic bulk modulus at ambient pressure, Ev, was calculated from eq 1 with the values given in Table 7. As the mole fraction of the aromatic compound increases, the bulk modulus increases. 4.3. Viscosity. The measured viscosities of 2,2,4,6,6pentamethylheptane, 2,2,4,4,6,8,8-heptamethylnonane, n-hexylbenzene, and n-butylbenzene agree with most of the reported values within the standard uncertainty of the measurements, as shown in Table 2. The viscosity of 2,2,4,6,6-pentamethylheptane at 253.15 K, 3.08 ± 0.12 mPa·s, is 5% lower than the 3.25 mPa·s value reported in the literature,63 and the viscosities of the two lots of n-hexylbenzene at 253.15 K, 4.56 ± 0.06 and 4.63 ± 0.06

ln vm = x13 ln v1 + 3x12x 2 ln v1,2 + 3x1x 2 2 ln v2,1 + x 2 3 ln v2 ij 1 ij ij M yz M yzyz − lnjjjx1 + x 2 2 zzz + 3x12x 2 lnjjjj jjj2 + 2 zzzzzzz j j z M1 { M1 z{{ k k3k ij 1 ij ij M yz M yzyz + 3x1x 2 2 lnjjjj jjj1 + 2 2 zzzzzzz + x 2 3 lnjjj 2 zzz j M1 z j M1 z{{ k { k3k

(3)

In this equation, νm is the kinematic viscosity of the binary mixture, x1 and x2 are the mole fractions, ν1 and ν2 are the kinematic viscosities, and M1 and M2 are the molar masses of the pure components with the aromatic compound as component 1 and a branched alkane as component 2. The interaction parameters ν2,1 and ν1,2 were determined by minimizing the sum of the square of the difference between the value calculated by the model in eq 3 and the measured kinematic viscosity of the binary mixture. The interaction parameters and the standard error of the fit are given in Table 9. The model fits the data well, as shown in Figure 2, for values at 293.15 K, with the remaining fits shown in the Supporting Information. 4.4. Flash Point and Surface Tension. The measured surface tensions and flash points of 2,2,4,6,6-pentamethylheptane, 2,2,4,4,6,8,8-heptamethylnonane, n-hexylbenzene, and nbutylbenzene agree with the reported values within the standard uncertainty of the measurements, as shown in Table 10. The surface tension for the hexylbenzene is lower than those reported by other researchers,56,57 but it is similar to other lots of these chemicals tested in the authors’ laboratories.42 The slightly smaller value may be caused by differences in the purity of the hexylbenzene. The flashpoint for the hexylbenzene is slightly G

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Table 6. Correlation of Speed of Sound c to Mole Fraction x1 for the Systems n-Hexylbenzene (1) or n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8-Heptamethylnonane (2) at Temperature T and Pressure p = 0.1 MPa along with Associate Error σa T (K)

A3

A2

A1

A0 −1

288.15 293.15 303.15 313.15 323.15 333.15 288.15 293.15 303.15 313.15 323.15 333.15 288.15 293.15 303.15 313.15 323.15 333.15 288.15 293.15 303.15 313.15 323.15 333.15

R2

σ

0.999 0.999 0.999 0.999 0.999 0.999

0.38 0.26 0.33 0.36 0.35 0.30

0.999 0.999 0.999 0.999 0.999 0.999

0.25 0.10 0.22 0.27 0.27 0.22

0.999 0.999 0.999 0.999 0.999 0.999

0.09 0.10 0.21 0.29 0.29 0.22

0.999 0.999 0.999 0.999 0.999 0.999

0.52 0.54 0.57 0.60 0.57 0.51

2

n-Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2): c (m·s ) = A2x1 + A1x1 + A0 26.8 ± 3.0 144.4 ± 3.1 1224.1 ± 0.7 26.3 ± 2.1 145.3 ± 2.2 1204.2 ± 0.5 26.2 ± 2.6 146.6 ± 2.7 1165.1 ± 0.6 26.0 ± 2.8 148.0 ± 2.9 1126.9 ± 0.6 25.6 ± 2.7 149.3 ± 2.8 1089.5 ± 0.6 25.3 ± 2.4 150.6 ± 3.1 1053.1 ± 0.5 n-Butylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2): c (m·s−1) = A3x13 + A2x12 + A1x1 + A0 37.0 ± 1.3 31.2 ± 1.3 1305.2 ± 0.4 41.2 ± 3.3 −8.6 ± 5.0 34.7 ± 2.1 1258.9 ± 0.4 44.8 ± 6.6 −15.4 ± 4.2 36.5 ± 4.2 1248.3 ± 0.5 46.1 ± 8.1 −18.3 ± 12.4 36.4 ± 5.2 1211.6 ± 0.5 45.4 ± 8.1 −18.0 ± 12.3 34.8 ± 5.2 1175.8 ± 0.6 42.0 ± 6.7 −12.6 ± 10.1 30.6 ± 5.2 1141.2 ± 0.5 n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2): c (m·s−1) = A3x13 + A2x12 + A1x1 + A0 25.7 ± 2.8 21.4 ± 4.2 103 ± 2 1223.7 ± 0.2 22.6 ± 4.7 25.2 ± 4.7 102 ± 2 1203.8 ± 0.2 23.4 ± 6.5 24.2 ± 9.9 102 ± 4 1164.6 ± 0.5 23.6 ± 8.7 23.7 ± 4.2 102 ± 6 1126.4 ± 0.6 24.0 ± 8.6 22.8 ± 13 102 ± 6 1089.1 ± 0.6 25.1 ± 6.8 20.8 ± 10 103 ± 4 1052.6 ± 0.5 n-Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2): c (m·s−1) = A2x12 + A1x1 + A0 40.0 ± 4.1 49.1 ± 4.3 1305.8 ± 0.9 40.0 ± 4.2 49.0 ± 4.4 1286.6 ± 0.9 39.8 ± 4.1 49.2 ± 4.7 1249.0 ± 1.0 39.5 ± 4.7 49.1 ± 4.9 1212.4 ± 1.1 39.2 ± 4.5 48.8 ± 4.6 1176.6 ± 1.0 39.3 ± 4.0 48.0 ± 4.1 1141.9 ± 0.9

The “±” for the coefficients A0, A1, A2, A3, and A4 represent the 95% confidence interval. The σ is the standard error of the fit. The x1 is the mole fraction of the aromatic compound in mixtures in the branched alkane.

a

heptamethylnonane),38 and negative values have also been found in mixtures of small alkylbenzenes (toluene and ethylbenzene) and small linear alkanes.60,61 The excess molar volume is positive when molecules pack together more loosely in mixtures than they do as pure liquids. Such packing may result from a disruption of the intermolecular attraction of the pure components, which allowed them to pack closely together, or by the presence of molecules that interfere with the ordered structure of the pure components. Positive excess molar volumes have been found for longer chain linear alkanes with longer chain alkylbenzenes.42,43,60,61 They have also been found for chlorobenzene with 2,2,4,6,6-pentamethylheptane (0.076 cm3·mol−1 at 0.5 mole fraction of chlorobenzene), 2,2,4,4,6,8,8-heptamethylnonane (0.238 cm3·mol−1 at 0.5 mole fraction of chlorobenzene),33 and several oxaalkanes with both branched compounds studied herein at 298.15 K.32 In the authors’ previous work, very small positive excess molar volumes have been found for binary mixtures of 2,2,4,6,6-pentamethylheptane with dodecane or hexadecane (in some cases not significantly different from zero) and slightly larger positive values for binary mixtures of 2,2,4,4,6,8,8-heptamethylnonane with dodecane or hexadecane at 293.15 K.38−40 The excess molar volumes (VmE) for binary mixtures of each aromatic compound with each branched alkane were calculated using the following equation

higher than those reported by other researchers but is similar to other lots of these chemicals tested in the authors’ laboratories. The possible cause of the difference has been discussed previously and may be due to different measurement techniques.42 In the binary mixtures, increasing the concentration of the aromatic species increased the surface tension (Table 11). Increasing the aromatic compound concentration in 2,2,4,6,6-pentamethylheptane caused the flash point to increase and in 2,2,4,4,6,8,8-heptamethylnonane caused the flash point to decrease. 4.5. Excess Molar Volume, Excess Molar Gibbs Energy of Activation for Viscous Flow (ΔG*E ). Excess molar properties and property deviations from ideal mixing can provide some insight into the packing and intermolecular forces between compounds in mixtures. 4.5.1. Excess Molar Volume. The excess molar volume is negative when molecules pack together more closely in mixtures than they do as pure liquids. Such packing may result when one type of molecule can fit in the voids of another molecule (interstitial accommodation).58 Negative excess molar volumes have been found for heptane in 2,2,4,6,6-pentamethylheptane (−0.112 cm3·mol−1 at 0.5021 mole fraction of heptane) and 2,2,4,4,6,8,8-heptamethylnonane (−0.253 cm3·mol−1 at 0.4815 mole fraction of heptane)59 at 298.15 K. Also, excess molar volumes have been found to be negative in mixtures of 2,2,4,6,6pentamethylheptane and 2,2,4,4,6,8,8-heptamethylnonane (−0.11 cm3·mol−1 at 0.4293 mole fraction of 2,2,4,4,6,8,8H

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Table 7. Experimental Values of Bulk Modulus Ev, in MPa, at Temperature T and Mole Fraction x1 for the Systems nHexylbenzene (1) or n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8-Heptamethylnonane (2) at Pressure p = 0.1 MPaa n-Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) x1 T (K)

0.00

0.1000

0.2065

288.15 293.15 303.15 313.15 323.15 333.15

1121 1080 1001 927 858 793

1164 1122 1041 965 894 828

1212 1169 1087 1009 936 868

T (K)

0.00

0.1007

0.2007

288.15 293.15 303.15 313.15 323.15 333.15

1342 1297 1212 1132 1057 987

1355 1311 1225 1144 1068 996

1370 1325 1239 1157 1080 1007

0.3009

0.3968

0.5004

0.6000

1257 1306 1359 1415 1212 1259 1312 1367 1128 1172 1223 1276 1048 1091 1140 1190 974 1015 1061 1110 904 943 988 1034 n-Butylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2)

0.6998

0.7997b

0.8999b

1.00

1475 1426 1332 1244 1161 1083

1539 1488 1392 1301 1216 1136

1607 1555 1456 1363 1274 1192

1680 1626 1524 1428 1337 1252

0.7001

0.7998b

0.8992b

1.00

1488 1439 1345 1255 1171 1091

1527 1476 1378 1286 1200 1119

1573 1520 1420 1325 1236 1152

1631 1575 1472 1374 1282 1195

0.6999

0.8009b

0.9000b

1.00

1418 1369 1275 1187 1104 1026

1481 1430 1334 1243 1158 1077

1551 1498 1398 1304 1215 1131

1631 1575 1472 1374 1282 1195

x1 0.3000

0.3999

0.4998

0.5997

1387 1408 1430 1456 1342 1361 1382 1408 1254 1271 1292 1315 1171 1187 1206 1228 1093 1108 1125 1146 1019 1033 1049 1068 n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) x1

T (K)

0.00

0.100

0.2000

288.15 293.15 303.15 313.15 323.15 333.15

1121 1080 1001 927 858 793

1153 1110 1030 954 884 818

1187 1144 1062 985 913 845

T (K)

0.00

0.1015

0.2005

0.2999

0.4001

0.4996

0.6000

0.6999

0.8000b

0.9000b

1.00

288.15 293.15 303.15 313.15 323.15 333.15

1342 1297 1212 1132 1057 987

1363 1318 1232 1151 1074 1003

1385 1340 1253 1171 1094 1021

1410 1364 1275 1192 1114 1040

1437 1390 1301 1217 1137 1062

1467 1419 1328 1242 1161 1085

1501 1452 1359 1271 1189 1111

1538 1488 1393 1304 1220 1141

1579 1529 1433 1341 1255 1174

1626 1575 1475 1382 1293 1211

1680 1626 1524 1428 1337 1252

0.3001

0.4006

0.5000

0.6002

1225 1266 1311 1362 1180 1221 1265 1314 1096 1134 1176 1224 1017 1053 1093 1139 943 977 1015 1058 874 907 942 983 n-Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2) x1

a

x1 is the mole fraction of the alkylbenzene in the branched alkane. The average pressure for these measurements was 0.102 MPa. Standard uncertainties u are u(T) = 0.01 K and Uc(p) = 0.001 MPa, expanded uncertainties Uc are Uc(Ev) = 1 MPa, and combined expanded uncertainties of Uc(x1) = 0.0001 unless otherwise indicated by the superscript b (level of confidence = 0.95, k = 2). bThe combined expanded uncertainty is Uc(x1) = 0.0002.

Vm E =

M1x1 + M 2x 2 Mx Mx − 11 − 2 2 ρm ρ1 ρ2

compound and branched alkane, respectively. The fitted values of Α0, A1, A2, and A3 and the standard errors of the fits are given in Table 12. The model fits the data well, as shown in Figure 3. The excess molar volumes for the binary mixtures containing 2,2,4,4,6,8,8-heptamethylnonane are positive at all mole fractions tested at 293.15 K. The 2,2,4,4,6,8,8-heptamethylnonane mixtures with n-butylbenzene mixtures have higher excess molar volumes than those with n-hexylbenzene. For these mixtures, the packing arrangement of each individual component is disrupted in such a manner so as to expand the volume. The lack of symmetry of the molar volume−mole fraction plot for n-butylbenzene (e.g., VmE for x1 = 0.8 being greater than VmE for x1 = 0.2) suggests that the 2,2,4,4,6,8,8heptamethylnonane disrupts n-butylbenzene packing more than its packing is disrupted by n-butylbenzene. Using molecular dynamics simulations, Morrow et al.62 evaluated the differences

(4)

in which ρm is the density of the mixture, ρ1 and ρ2 are the pure component densities, M1 and M2 are the molar masses, and x1 and x2 are the mole fractions of the aromatic compound as component 1 and the branched compound as component 2. The calculated excess molar volumes are given in Table 4 at 293.15 K and shown in Figure 3. A Redlich−Kister type expression was fit to the excess molar volume j=n

Vm E = x1x 2∑ Aj (x1 − x 2) j j=0

(5)

where Aj are adjustable parameters, j is the order of the polynomial, and x1 and x2 are the mole fraction of the aromatic I

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lower, respectively, than their values at 293.15 K. These declines are very small and close to the uncertainty in the excess molar volumes themselves. 4.5.2. Excess Speeds of Sound. The excess speed of sound, cE, can be calculated using the measured mixture speed of sound, cmix, and an ideal mixture speed of sound cID using the equations given by Douheret et al.:63 c E = cmix − c ID

(6)

c ID = (ρ ID κ ID)−0.5

(7)

Additional equations used to calculate the excess speed of sound include71 ideal density:

Figure 2. Viscosity data for (●) hexylbenzene (x1) in 2,2,4,4,6,8,8heptamethylnonane; (■) butylbenzene (x1) in 2,2,4,4,6,8,8-heptamethylnonane; (□) hexylbenzene (x1) in 2,2,4,6,6-pentamethylheptane; and (○) butylbenzene (x1) in 2,2,4,6,6-pentamethylheptane at 293.15 K. The lines are fits using the McAllister equation with the fitted parameters given in Table 9.

ρ ID = ϕ1ρ1 + ϕ2ρ2

(8)

ideal isentropic compressibility: ÉÑ ÄÅ ÅÅ ϕ V α 2 ϕ2V2α2 2 Vm ID(α ID)2 ÑÑÑÑ ÅÅ 1 1 1 ID ÑÑ + − κ = ϕ1κ1 + ϕ2κ2 + T ÅÅÅ ÅÅ Cp ,1 Cp ,2 Cp ID ÑÑÑÑ ÅÇ Ö

in the intermolecular interactions between aromatic compounds (alkylbenzenes) and n-hexadecane. They found that the benzene ring in an alkylbenzene molecule can lie parallel or perpendicular to the benzene ring in another alkylbenzene molecule.62 The alkylbenzenes with the shorter alkyl chain length had a larger number of molecules with the perpendicular orientation. When mixed with n-hexadecane, the alkylbenzenes with the shorter alkyl chain length (toluene and benzene) showed a greater increase in the number of molecules that changed from perpendicular to parallel than those with longer chains (e.g., butylbenzene). These shorter alkyl chain length alkylbenzenes also had a higher excess molar volume. This suggests that the orientation of the benzene ring impacts the excess molar volume, which may be the case in the current study. The current study also gives results that have the excess molar volume of the shorter alkyl chain aromatic butylbenzene having a higher excess molar volume than the longer alkyl chain aromatic hexylbenzene. At 333.15 K and x1 = 0.5, the excess molar volumes for the n-butylbenzene and n-hexylbenzene mixtures in 2,2,4,4,6,8,8heptamethylnonane are 0.035 and 0.002 cm3·mol−1 lower, respectively, than their values at 293.15 K. These declines are smaller than the uncertainty in the excess molar volumes themselves. The excess molar volumes for the binary mixtures containing 2,2,4,6,6-pentamethylheptane are negative at all mole fractions for mixtures with hexylbenzene at 293.15 K. The 2,2,4,6,6pentamethylheptane packs together more closely with hexylbenzene than either of the two compounds pack alone. This may be caused by interstitial accommodation. Its excess molar volume of −0.09 cm3·mol−1 around 0.5 mole fraction is similar to −0.10 cm3·mol−1 found for 2,2,4,6,6-pentamethylheptane and 2,2,4,6,6-pentamethylheptane mixtures at the same temperature and a similar mole fraction. For mixtures of butylbenzene with 2,2,4,6,6-pentamethylheptane, the excess molar volumes transition from being positive at low mole fractions of butylbenzene to negative values at mole fractions greater than 0.5. It is important to note that these values are very small and some are less than the combined expanded uncertainty of 0.06 cm3·mol−1, which could suggest that many of these mixtures are behaving ideally. At 333.15 K and x1 = 0.5, the excess molar volumes for the n-butylbenzene and n-hexylbenzene mixtures in 2,2,4,6,6-pentamethylheptane are 0.02 and 0.08 cm3·mol−1

(9)

volume fraction: ϕι = xιVi /Vm ID

(10)

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

(11)

component isentropic compressibility: 1 κi = ρi ci 2 1 i ∂ρ y = − jjjj i zzzz ρi k ∂T { P

(12)

component thermal expansion coefficient: αi = −

∂(ln ρi ) ∂T

(13)

ideal mixture thermal expansion coefficient: α ID = ϕ1α1 + ϕ2α2

(14)

ideal mixture heat capacity: Cp ID = x1Cp ,1 + x 2Cp ,2

(15)

In these equations, 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 heat capacity of 2,2,4,6,6-pentamethylheptane, 350.98 J·mol−1·K−1, was only available at 298.15 K.64 Messerly et al.65 provided a correlation for butylbenzene heat capacity, which gave a value of 243.4 J·mol−1·K−1 at 298.15 K. The heat capacity of 2,2,4,4,6,8,8-heptamethylnonane was reported to be 458.8 J·mol−1 ·K −1 at 298.15 K, 64 which is similar to extrapolating data from Bessieres et al.66 to 298.15 K to give a value of 453 J·mol−1·K−1. Tschamler67 reported the heat capacity of hexylbenzene to be 248 J·mol−1·K−1 at 293 K, which is much less than the value reported by Paramo et al.,68 300.14 J·mol−1·K−1, at the same temperature. Paramo et al.68 also report a value of 303.08 J·mol−1·K−1 at 298.15 K. The excess speeds of sound were calculated using eqs 6−15 at 298.15 K for all mixtures and also at 293.15 K for mixtures of hexylbenzene and 2,2,4,4,6,8,8-heptamethylnonane (Table 4). J

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Table 8. Experimental Values of Dynamic Viscosity η in mPa·s and Kinematic Viscosity ν in mm2·s−1 at Temperature T and Mole Fraction x1 for the Systems n-Hexylbenzene (1) or n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8-Heptamethylnonane (2) at Pressure p = 0.1 MPaa n-Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) x1 T (K) 253.15 293.15 303.15 313.15 323.15 333.15

0.1000 ν η ν η ν η ν η ν η ν η

(mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s)

3.83e 3.00e 1.73 1.31 1.50 1.12 1.29 0.957 1.16 0.848 1.03 0.749

0.2065 3.82f 3.03f 1.72 1.31 1.49 1.13 1.28 0.962 1.15 0.853 1.02 0.753 n-Butylbenzene

0.6000

0.6998

0.7997b

0.8999b

3.83 3.92 4.00 4.14 3.08 3.19 3.31 3.47 1.69 1.71 1.70 1.73 1.31 1.35 1.36 1.40 1.48 1.48 1.48 1.50 1.14 1.15 1.17 1.20 1.27 1.27 1.28 1.29 0.967 0.979 1.00 1.02 1.14 1.14 1.15 1.16 0.861 0.873 0.889 0.911 1.02 1.02 1.02 1.03 0.758 0.768 0.783 0.803 (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2)

4.35 3.70 1.78 1.46 1.54 1.25 1.32 1.06 1.18 0.943 1.05 0.828

4.55 3.93 1.81c 1.51c 1.56 1.29 1.33 1.09 1.19 0.964 1.05 0.844

4.79 4.20 1.85 1.56 1.59 1.33 1.35 1.12 1.21 0.992 1.07 0.870

0.3009

0.3968

0.5004

x1 T (K) 253.15 293.15 303.15 313.15 323.15 333.15

ν η ν η ν η ν η ν η ν η

2 −1

(mm ·s ) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s)

0.1007

0.2007

0.5997

0.7001

0.7998b

0.8992b

13.56 11.06 4.08 3.22 3.31 2.58 2.73 2.11 2.29 1.76 1.95 1.49

10.89 8.83 7.17 5.88 4.87 8.94 7.29 5.97 4.93 4.12 3.50 3.02 2.60 2.26 1.96 2.77 2.41 2.09 1.83 1.60 2.86 2.49 2.18 1.93 1.70 2.25 1.97 1.73 1.55 1.37 2.39 2.09 1.85 1.63 1.44 1.86 1.64 1.46 1.30 1.16 2.03 1.79 1.63 1.45 1.29 1.56 1.39 1.27 1.14 1.03 1.74 1.55 1.42 1.28 1.14 1.33 1.20 1.10 1.00 0.900 n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2)

4.05 3.46 1.70 1.41 1.48 1.21 1.27 1.03 1.15 0.920 1.02 0.812

3.42 2.96 1.54 1.29 1.33 1.10 1.17 0.957 1.02 0.831 0.916 0.736

2.94 2.59d 1.36 1.15 1.18 0.993 1.03 0.855 0.918 0.754 0.822 0.670

0.6000

0.6999

0.8000b

0.9000b

3.11 2.92 2.77 2.68 2.49 2.37 2.28 2.24 1.46 1.39 1.33 1.28 1.13 1.08 1.05 1.02 1.29 1.23 1.18 1.14 0.989 0.951 0.924 0.904 1.14 1.09 1.05 1.01 0.862 0.837 0.814 0.798 1.02 0.969 0.934 0.900 0.762 0.735 0.718 0.703 0.911 0.870 0.836 0.811 0.675 0.653 0.636 0.627 (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2)

2.60 2.20 1.24 1.01 1.10 0.887 0.976 0.781 0.872 0.692 0.786 0.617

2.54 2.19 1.20 0.995 1.06 0.874 0.945 0.770 0.846 0.682 0.764 0.610

3.01 2.21 1.18 0.997 1.05 0.874 0.929 0.770 0.832 0.683 0.752 0.611

0.3000

0.3999

0.4998

x1 T (K) 253.15 293.15 303.15 313.15 323.15 333.15

0.1015 ν η ν η ν η ν η ν η ν η

2 −1

(mm ·s ) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s)

3.60 2.82 1.64 1.24 1.43 1.07 1.25 0.92 1.11 0.813 0.989 0.715

0.2005 3.32 2.63 1.54 1.18 1.36 1.03 1.19 0.890 1.06 0.784 0.946 0.692 n-Hexylbenzene

0.2999

0.4001

0.4996

x1 T (K) 253.15 293.15 303.15 313.15 323.15

ν η ν η ν η ν η ν

2 −1

(mm ·s ) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1) (mPa·s) (mm2·s−1)

0.1015

0.2005

0.2999

0.4001

0.4996

0.6000

0.6999

0.8000b

0.9000b

14.48 11.82 4.27 3.37 3.43 2.68 2.82 2.19 2.36

12.38 10.18 3.82 3.04 3.10 2.44 2.57 2.00 2.16

10.92 9.04 3.43 2.75 2.81 2.23 2.34 1.84 1.99

9.53 7.96 3.12 2.51c 2.56 2.05 2.15 1.70 1.83

8.42 7.08 2.83 2.30 2.34 1.89 1.98 1.58 1.73

7.50 6.37 2.59 2.12 2.18 1.78 1.85 1.49 1.60

6.74 5.78 2.39 1.98 2.02 1.66 1.71 1.40 1.49

6.11 5.30 2.21 1.85 1.88 1.56 1.60 1.32 1.40

5.64 4.94 2.05 1.74 1.76 1.48 1.50 1.25 1.32

K

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Table 8. continued n-Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2) x1 T (K) 333.15

η (mPa·s) ν (mm2·s−1) η (mPa·s)

0.1015

0.2005

0.2999

0.4001

0.4996

0.6000

0.6999

0.8000b

0.9000b

1.82 2.01 1.53

1.67 1.85 1.42

1.55 1.71 1.32

1.44 1.58 1.23

1.37 1.50 1.18

1.28 1.40 1.11

1.20 1.31 1.04

1.14 1.23 0.990

1.09 1.16 0.945

a x1 is the mole fraction of n-hexylbenzene in 2,2,4,6,6-pentamethylheptane or n-butylbenzene in 2,2,4,4,6,8,8-heptamethylnonane. The average pressure for these measurements was 0.102 MPa. Standard uncertainties u are u(T) = 0.01 K and Uc(p) = 0.001 MPa; expanded uncertainties Uc are Uc(η) = 0.02 mPa·s at T ≥ 293.15 K and Uc(η) = 0.06 mPa·s at 253.15 K; and combined expanded uncertainties of Uc(ν) = 0.03 mm2·s−1 at T ≥ 293.15 K and Uc(ν) = 0.06 mm2·s−1 at 253.15 K; Uc(x1) = 0.0001 unless otherwise indicated by the superscript b (level of confidence = 0.95, k = 2). bThe combined expanded uncertainty is Uc(x1) = 0.0002. cUc(η) = 0.03 mPa·s and Uc(ν) = 0.04 mm2·s−1. dUc(η) = 0.15 mPa·s and Uc(ν) = 0.2 mm2·s−1. eUc(η) = 0.05 mPa·s and Uc(ν) = 0.06 mm2·s−1. fUc(η) = 0.04 mPa·s and Uc(ν) = 0.05 mm2·s−1.

Table 9. Values of the Coefficients for the McAllister Equation ν12 and ν21 (eq 3) and Associated Standard Error σ for the Systems of Butylbenzene (1) or Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8Heptamethylnonane (2) at Pressure p = 0.1 MPaa Τ (Κ)

2 −1

ν12 (mm ·s )

2 −1

ν21 (mm ·s )

Table 10. Comparison of the Measured Flash Points FP and Surface Tensions γ of Butylbenzene Hexylbenzene, 2,2,4,6,6Pentamethylheptane, and 2,2,4,4,6,8,8-Heptamethylnonane with Literature Valuesa FP (K)

2 −1

10 ·σ (mm ·s ) 3

this study literature

Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) 253.15 4.17 3.53 26 293.15 1.72 1.65 9.7 303.15 1.49 1.43 5.1 313.15 1.28 1.24 4.7 323.15 1.16 1.11 3.9 333.15 1.02 1.00 3.8 Butylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2) 253.15 4.49 7.29 99 293.15 1.83 2.82 30 303.15 1.59 2.34 11 313.15 1.34 2.01 11 323.15 1.22 1.73 9.8 333.15 1.09 1.51 9.5 Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) 253.15 2.56 2.81 9.9 293.15 1.20 1.41 1.6 303.15 1.07 1.25 2.8 313.15 0.948 1.13 2.4 323.15 0.852 0.992 2.6 333.15 0.769 0.890 2.3 Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (2) 252.15 6.88 9.51 83 293.15 2.37 3.26 5.9 303.15 2.02 2.66 7.8 313.15 1.73 2.23 6.4 323.15 1.52 1.89 8.1 333.15 1.34 1.64 7.7

this study literature

this study literature

this study literature

γ (mN·m−1)

n-Butylbenzene 331 ± 2 29.0 ± 0.2 @ 295 ± 1 K 322,m 323,b 330,n 344c 29.0 @ 295 Kj n-Hexylbenzene 360 ± 2 29.2 ± 0.2p @ 295 ± 1 K 29.3 ± 0.2q @ 295 ± 1 K b d i 356, 356.15, 360 29.8 @ 295 Kj,o 29.5 ± 0.3 @ 294.4 ± 1 Ki 2,2,4,6,6-Pentamethylheptane 319 ± 2 22.1 ± 0.3 @ 294 ± 1 K 320 ± 3.5h 21.6 @ 296.7 Kk 21.8 @ 294 Kl 2,2,4,4,6,8,8-Heptamethylnonane 368 ± 2 24.2 ± 0.2 @ 294.7 ± 1 K 368,f 369g 24.2 @ 294.7 ± 1 Ke 24.2 @ 296.7 ± 1 Kk

a Expanded uncertainties Uc are given by the “±” symbol (level of confidence = 0.9545, k = 2). bReference 92. cReference 47. d Reference 95. eUsed a linear regression of the values in ref 88. f Reference 89. gReference 90. hCorrelation in ref 91. iReference 42. j Reference 56. kReference 93. lReference 39. mReference 94. n Reference 95. oReference 57. pHexylbenzene lot 10201705 used for 2,2,4,6,6-pentamethylheptane mixtures. qHexylbenzene lot 10206925 used with 2,2,4,4,6,8,8-heptamethylnonane mixtures.

speeds of sound calculated at 298.15 K were within 2 m·s−1 of values at 293.15 K. The excess speeds of sound for mixtures of n-butylbenzene and 2,2,4,4,6,8,8-heptamethylnonane were not statistically different from zero, suggesting that these mixtures are behaving ideally for speed of sound propagation. For all of the other mixtures, the excess speeds of sound were positive, with the mixtures containing n-hexylbenzene having higher values than those of n-butylbenzene and the mixtures containing 2,2,4,6,6pentamethylheptane having values greater than those of 2,2,4,4,6,8,8-heptamethylnonane. All of these systems have positive excess speeds of sound, but their excess molar volumes have varying signs. It might be expected that faster mixture speeds of sound and positive excess speeds of sound would only result from a contraction of the system, as indicated by a negative excess molar volume, as is seen in the case of n-hexylbenzene and 2,2,4,6,6-pentamethylheptane mixtures. While some studies have shown this connection, others have shown that the excess

The σ is the standard error of the fit.

a

These temperatures were the only temperatures for which heat capacity data were available. The heat capacity of hexylbenzene used for this calculation was 303.19 J·mol−1·K−1. When a lower value of 251 J·mol−1·K−1 was used to be more consistent with data from Tschamler,67 251 J·mol−1·K−1, the resulting Δc values differed from the values in the table by at most 1 m·s−1, which is within the error of the calculated value. The speed of sound and density values used in these calculations at 298.15 K were interpolated from measured values. As is shown for nhexylbenzene and 2,2,4,4,6,8,8-heptamethylnonane, the excess L

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Table 11. Experimental Values of Surface Tension γ at Temperature T and Flash Point FP at Mole Fraction x1 for the Systems n-Hexylbenzene (1) or n-Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (2) or 2,2,4,4,6,8,8Heptamethylnonane (2) at Pressure p = 0.1 MPaa γ (mN·m−2)

x1

FP (K)

Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (T = 294 ± 1 K for γ) 0.1000 21.9 ± 0.2 321 ± 2 0.2065 22.5 ± 0.2 323 ± 2 0.3009 23.1 ± 0.2 324 ± 2 0.3968 23.5 ± 0.2 325 ± 2 0.5001 24.1 ± 0.4 328 ± 2 0.6000 24.7 ± 0.2 331 ± 2 0.6998 25.5 ± 0.2 335 ± 2 0.7997 26.5 ± 0.2 340 ± 2 0.8999 27.7 ± 0.2 348 ± 2 Butylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (T = 295 ± 1 K for γ) 0.1007 24.3 ± 0.2 358 ± 2 0.2007 24.6 ± 0.2 351 ± 2 0.3000 24.8 ± 0.2 346 ± 2 0.3999 25.1 ± 0.2 342 ± 2 0.4998 25.5 ± 0.2 339 ± 2 0.5997 26.0 ± 0.2 337 ± 2 0.7001 26.2 ± 0.2 335 ± 2 0.7998 26.7 ± 0.2 333 ± 2 0.8992 27.3 ± 0.2 331 ± 2 Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane (T = 295 ± 1 K for γ) 0.1015 24.4 ± 0.2 367 ± 2 0.2005 24.5 ± 0.2 366 ± 2 0.2999 24.7 ± 0.2 365 ± 2 0.4001 25.3 ± 0.2 363 ± 2 0.4996 25.6 ± 0.2 363 ± 2 0.6000 25.8 ± 0.2 362 ± 2 0.6999 26.5 ± 0.2 362 ± 2 0.8000 27.2 ± 0.2 362 ± 2 0.9000 27.9 ± 0.2 361 ± 2 Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane (T = 295 ± 1 K for γ) 0.1001 22.0 ± 0.2 319 ± 2 0.2000 22.2 ± 0.2 319 ± 2 0.3001 22.7 ± 0.2 320 ± 2 0.4006 23.1 ± 0.2 321 ± 2 0.5000 23.5 ± 0.2 322 ± 2 0.6002 24.0 ± 0.2 322 ± 2 0.6999 24.8 ± 0.2 323 ± 2 0.8009 25.7 ± 0.2 324 ± 2 0.8985 26.7 ± 0.2 326 ± 2

Figure 3. Excess molar volumes for binary mixtures of (●) hexylbenzene (x1) in 2,2,4,4,6,8,8-heptamethylnonane; (■) butylbenzene (x1) in 2,2,4,4,6,8,8-heptamethylnonane; (□) hexylbenzene (x1) in 2,2,4,6,6-pentamethylheptane; and (○) butylbenzene (x1) in 2,2,4,6,6-pentamethylheptane at 293.15 K. The lines are fits used the Redlich−Kister expression with coefficients given in Table 12.

Table 12. Parameters for the Redlich−Kister Equation, eq 5, for Excess Molar Volume VmE for the Systems nHexylbenzene (1) or n-Butylbenzene (1) in 2,2,4,6,6Pentamethylheptane (2) or 2,2,4,4,6,8,8Heptamethylnonane (2) at Temperature T = 293.15 K and Pressure p = 0.1 MPaa A0

A3

σ

Hexylbenzene (1) in 2,2,4,6,6-Pentamethylheptane 0.0096 Butylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane 0.943 0.346 0.013 Hexylbenzene (1) in 2,2,4,4,6,8,8-Heptamethylnonane 0.530 0.0070 Butylbenzene (1) in 2,2,4,6,6-Pentamethylheptane −0.0192 −0.367 −0.295 −0.171 0.0040 a

The σ is the standard error of the fit.

tane > n-butylbenzene/2,2,4,6,6-pentamethylheptane > nhexylbenzene/2,2,4,4,6,8,8-heptamethylnonane > n-butylbenzene/2,2,4,4,6,8,8-heptamethylnonane follows the opposite trend of their respective excess molar volumes. This shows the impact of expansion/compression on excess speeds of sound. 4.5.3. Excess Molar Gibbs Energy of Activation for Viscous Flow. The excess molar Gibbs energy of activation for viscous flow (ΔG*E ) was calculated from kinematic viscosity data by72 ÄÅ ÉÑ n ÅÅÅ ÑÑÑ E ÑÑ ΔG* = RT ÅÅÅln(vmM m) − ∑ xi ln vM i i ÑÑ ÅÅ ÑÑÖ ÅÇ (16) i−1 −1 −1 where R is the gas constant (8.314 J·mol ·K ), T is the temperature in Kelvin, νm is the kinematic viscosity of the mixture, ν1 and ν2 are the pure component kinematic viscosities, Mm is the molar mass of the mixture (Mm = ∑2i=1 xiMi), M1 and M2 are the pure component molar masses, and x1 and x2 are the mole fractions with the aromatic compound as component 1 and the branched alkane as component 2. All of the excess molar Gibbs energies of activation for viscous flow in Table 4 are less than the error in the values themselves. Such results suggest that the mixtures are behaving as ideal mixtures in their flow properties. The nonidealities in packing and compressibility, as

molar volume and excess speeds of sound can have the same sign.69−71 Chorazewski69 showed that positive excess speeds of V κ sound can be found when mID > ID and that the molecular κ

orientation, size, and shape of molecules and intermolecular interactions impact the compressibility of a liquid. This inequality is satisfied for all of the mixtures studied herein with values of VmID ranging from 1.0000 to 1.1037 and κID ranging Vm

A2

−0.408

a Expanded uncertainties Uc are given by the “±” symbol (level of confidence = 0.9545, k = 2).

Vm

A1

κ

from 0.9686 to 0.9995. This suggests that, while a system may expand upon mixing, its compressibility may be great enough to produce an increase in the speed of sound and a positive excess speed of sound. In the systems tested here, the trend in excess speeds of sound of n-hexylbenzene/2,2,4,6,6-pentamethylhepM

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Table 13. Military and ASTM Specifications for Density ρ at 288.15 K, Flash Point FP, and Viscosity ν of Diesel and Jet Fuels along with Reported Values for Speed of Sound c and Bulk Modulus Ev at 293.15 K and Surface Tension γ at Room Temperatureh jet Aa −3

JP-4c military jet fuel

JP-5 military jet fuel

ρ (kg·m ) FP (K) ν (mm2·s−1) c (m·s−1)

755−840 >311.15 ≤8.0 at 253.15 K NA

751−802 >311.15c none given NA

788−845 >333.15c ≤7.0 at 253.15 K 1316.9d

Ev (MPa)

NA

NA

1389d

γ (mN·m−2)

NA

NA

26.1d

c

c

F-76b military diesel fuel 800−876b >333.15b 1.4−4.3 at 313.5 K 1229f 1378.6e 1590g 1612e 26.7f 27.8g

a

Reference 28. bReference 29. cReference 30. dReference 96. eReference 97. fReference 26. gReference 98. hNA is not available.

volumes for butylbenzene/2,2,4,6,6-pentamethylheptane mixtures showed slightly positive values at low aromatic concentrations and slightly negative values at high aromatic concentrations. This may suggest a more complex packing arrangement where the butylbenzene disrupts the packing of the 2,2,4,6,6-pentamethylheptane and makes the volume greater (low butylbenzene concentration) but where the 2,2,4,6,6pentamethylheptane can fit into voids for the butylbenzene (butylbenzene concentration > 2,2,4,6,6-pentamethylheptane concentration). In both cases (high or low butylbenzene), the values are very close to zero and the true impact is minimal; some of the mixtures may be behaving ideally. Ideal behavior was found for viscosity, where the excess molar Gibbs energy of activation for viscous flow at 293.15 K was not statistically different from zero. Only n-butylbenzene/2,2,4,4,6,8,8-heptamethylnonane mixtures demonstrated ideal behavior for speed of sound, with excess speeds of sound close to zero. The other mixtures had positive excess speeds of sound. Both volume change and compressibility impact excess speed of sound. The result that the volumes expanded, contracted, and were close to zero for these mixtures, while all had positive or zero excess speeds of sound, emphasized the importance of compressibility. Mixture surface tensions at room temperature and flash points fell within the values of the pure components. A comparison of the measured property values with those of petroleum-based jet fuels shows that certain properties, such as density, are matched by many of the mixtures. Other properties, such as surface tension, are only matched for a smaller set of mixture compositions. These results can be useful when considering the compounds as additives to fuels, but the mixtures themselves would not be good fuel surrogates because they lack a major category of components found in petroleum-based fuel, linear alkanes.

indicated by excess molar volumes and excess speeds of sound, are not affecting the flow of the molecules past each other. 4.6. Comparison with Petroleum-Based Fuels. The branched and aromatic compounds used in this study were chosen because they have been used as model compounds in surrogate mixtures for petroleum-based fuels; they could be used as additives to bio-based fuels or as a way to enhance combustion performance; and their combustion behavior has been characterized.1−24 The properties of the mixtures measured herein can be compared with those found for petroleum-based fuels to provide a context for surrogate formulation and to predict their impact if added to these fuels. Table 13 shows the viscosity, flash point, and density of fuels that are specified for use in the military and in the aviation community. Most of the mixtures have densities that fall within the range of specified values. All mixtures meet the lower flash point standards of jet A and the military jet fuel, JP-4, but only some meet the higher flash point standard of another military jet fuel, JP-5, and a military diesel fuel, F-76. Most mixtures meet the viscosity specifications for the jet fuels, but only some of the 2,2,4,4,6,8,8-pentamethylheptane mixtures meet the diesel fuel specifications. Table 13 also shows reported values for speed of sound, bulk modulus, and surface tension from military jet and diesel fuels. Some of the mixtures are close to the reported speed of sound and bulk modulus values, and the mixtures with higher concentrations of the aromatic component are closer to the reported surface tension values. Adding these compounds or mixtures to fuels could alter some of their physical properties in a way that would cause them to be out of specification or change their behavior when injected into an engine. Alone, these mixtures would not be suitable as surrogates for jet and diesel fuel because they lack a major class of compounds, linear alkanes, which are present in these fuels.

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5.0. CONCLUSION In this work, the density, viscosity, speed of sound, bulk modulus, surface tension, and flashpoint were measured for binary mixtures of n-hexylbenzene (1) and n-butylbenzene (1) in 2,2,4,6,6-pentamethylheptane (2) and 2,2,4,4,6,8,8-heptamethylnonane (2) at temperatures within the range 253.15−333.15 K. Analysis of mixture densities provides excess molar volumes that were positive and showed volume expansion for mixtures containing the longer chain branched alkane, 2,2,4,4,6,8,8heptamethylnonane, suggesting an interruption in the orderly packing of the molecules. Excess molar volumes were negative and showed volume compression for hexylbenzene/2,2,4,6,6pentamethylheptane mixtures, suggesting that each molecule could fit into void spaces left by the other molecule. Excess molar

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00387. A comparison of the measured values of densities of a NIST-certified toluene standard with the reported standard values; a comparison of the measured values of an Anton Paar certified viscosity standard APS3 with the reported values; plots showing the fits for the McAllister equation to the viscosity data for all temperatures tested (PDF) N

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (410)293-6399. Fax: (410) 293-2218. ORCID

Dianne J. Luning Prak: 0000-0002-5589-7287 Paul C. Trulove: 0000-0002-3935-8793 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the Office of Naval Research NEPTUNE program under the direction of Maria Medeiros, grant no. N0001418WX0014.

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DOI: 10.1021/acs.jced.8b00387 J. Chem. Eng. Data XXXX, XXX, XXX−XXX