Densities, Speeds of Sound, and Viscosities of Binary Mixtures of an n

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

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Densities, Speeds of Sound, and Viscosities of Binary Mixtures of an n-Alkylcyclohexane (n-Propyl‑, n-Pentyl‑, n-Hexyl‑, n-Heptyl, n-Octyl‑, n-Nonyl‑, n-Decyl‑, and n-Dodecyl‑) with n‑Hexadecane Dianne J. Luning Prak,*,† Brian H. Morrow,† Sabina Maskey,† Judith A. Harrison,† 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

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‡

S Supporting Information *

ABSTRACT: This work reports densities, speeds of sound, and viscosities of binary mixtures of n-alkylcyclohexanes (propyl- to dodecylcyclohexane) in n-hexadecane as a function of temperature. Isentropic bulk moduli for these mixtures were calculated from these speed of sound and density data. Mixture densities increased with increasing alkylcyclohexane concentration. As the alkyl-chain length on the alkylcyclohexane increased, the excess molar volume decreased, with n-propylcyclohexane and n-dodecylcyclohexane mixtures having positive and negative excess molar volumes, respectively. Molecular dynamics simulations accurately predict densities and isentropic bulk moduli of n-propylcyclohexane and n-dodecylcyclohexane mixtures, and suggest that the differences in excess molar volumes for different alkyl-chain lengths are related to changes in molecular packing. The speed of sound as a function of mole fraction was modeled using a second-order polynomial, and viscosities were modeled using the McAllister three-body equation. Excess speeds of sound and excess molar Gibbs energies of activation for viscous flow at 293.15 K were not statistically different from zero, which suggest ideal behavior. Many of these mixtures have densities similar to those of petroleum-based diesel and jet fuel and viscosities comparable to diesel fuel. The isentropic bulk modulus of jet fuel is best matched by mixtures of n-propylcyclohexane, while that of diesel fuel is matched by mixtures of n-decylcyclohexane or n-dodecylcyclohexane. n-decylcyclohexane, have also been the focus of smog studies.37 The importance of cycloalkanes as fuel components has also stimulated research into producing them from biomass.38,39 Because n-hexadecane and n-alkylcylohexanes are important for the development of surrogate fuels and can contribute to the understanding of fuel combustion and its modeling, the physical properties (density, viscosity, and speed of sound) of binary mixtures n-hexadecane with n-alkylcyclohexanes ranging from n-propylcyclohexane to n-dodecylcylohexane were measured. Molecular dynamics (MD) simulations can be used to predict properties of hydrocarbon mixtures; in addition, they can model high temperatures and pressures and can give an atomic-level picture of fuel behavior that is difficult or impossible to obtain experimentally. Previous studies calculated the densities, bulk moduli, and heats of vaporization of 12 pure hydrocarbons, as well as densities and bulk moduli of multicomponent fuel surrogates containing up to 12 components, and showed how molecular structure and composition affected the properties of binary mixtures of n-hexadecane and n-alkylbenzenes.40,41

1. INTRODUCTION Petroleum-based and biobased fuels contain linear alkanes (0.3 to 40%), cycloparaffins (0.02 to 40%), branched alkanes, and aromatic components.1−11 Researchers who study the combustion of fuels and rocket propellants often formulate mixtures with a few compounds (surrogate mixtures) as a way to represent the more complex fuel mixtures.12−16 With simpler mixtures, it is easier to model the physical properties and chemical kinetics that contribute to the combustion in engines. Surrogates commonly contain n-hexadecane, n-dodecane, or n-decane for the linear alkane category of components. This class of hydrocarbons has the added benefit of having well characterized chemical kinetics of combustion.17 Compounds from the cycloparaffin category have included methylcyclohexane, n-propylcyclohexane, n-pentylcyclohexane, n-hexylcyclohexane, and n-heptylcyclohexane.12,13,16,18−21 While many studies into the combustion of alkylcyclohexanes have focused on the smaller alkyl-side chains (methyl-, ethyl-, propyl-, and butylcyclohexane), Lai and Song investigated the products formed from the pyrolysis of alkylcyclohexanes with both short and long alkyl chains (methyl-, n-ethyl-, n-propyl-, n-butyl-, n-hexyl-, n-octyl-, and n-decylcyclohexane).15,22−36 Alkylcyclohexanes with longer side chains, such as n-pentyl- and This article not subject to U.S. Copyright. Published XXXX by the American Chemical Society

Received: August 6, 2018 Accepted: October 24, 2018

A

DOI: 10.1021/acs.jced.8b00692 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 1. Summary of Studies that Measure the Densities, Speeds of Sound, and Viscosities of Binary Mixtures n-Alkylcyclohexanes with Other Compounds48−53 n-alkyl-cyclohexane

positive excess molar volumes based on density measurements

cyclo-hexane

n-C6H14, 303.15 K n-C7H16, 298.15 K, 303.15 K n-C8H18, 303.15 K n-C8H18, (298.15 to 308.15) K n-C9H20,(298.15 to 308.15) K

methyl-

ethyln-propyln-butyl-

negative excess molar volumes based on density measurements

n-C6H14, (298.15 to 308.15) K

n-C10H22, (298.15 to 308.15) K n-C12H26, (293.15 to 333.15) K n-C16H34, (293.15 to 333.15) K C2H3Cl3, 298.15 K

n-C7H16, (298.15 to 308.15) K

n-C12H26 (293.15 to 333.15) K n-C16H34 (293.15 to 333.15) K C2H3Cl3, 298.15 K C2H3Cl3, 298.15 K C2H3Cl3, 298.15 K

n-C7H16, 298.15 K

speed of sound literature studies n-C6H14, 303.15 K n-C7H16, 303.15 K n-C8H18, 303.15 K n-C6H14, 298.15 K n-C7H16, 298.15 K n-C8H18, 298.15 K n-C9H20,298.15 K n-C10H22, 298.15 K n-C12H26, (293.15 to 333.15) K n-C16H34, (293.15 to 333.15) K n-C12H26(293.15 to 333.15) K n-C16H34(293.15 to 333.15) K

viscosity literature studies n-C7H16

n-C6H14, (298.15 to 308.15) K n-C7H16, (298.15 to 308.15) K n-C8H18, (298.15 to 308.15) K n-C9H20,(298.15 to 308.15) K n-C10H22, (293.15 to 333.15) K n-C12H26, (293.15 to 333.15) K n-C16H34

n-C12H26 (293.15 to 333.15) K n-C16H34(293.15 to 333.15) K

n-C7H16, 298.15 K n-C7H16, 298.15 K

(1)

n-alkylcyclohexanes. In this study, the density, viscosity, and speed of sound were measured for n-hexadecane with n-propylcyclohexane, n-pentylcyclohexane, n-hexylcyclohexane, n-heptylcyclohexane, n-octylcyclohexane, n-nonylcyclohexane, n-decylcyclohexane, and n-dodecylcyclohexane. Molecular dynamics simulations gave accurate predictions for densities and bulk moduli at 293.15 K, and gave insight into the origins of the nonideal mixing behavior. These measurements and simulations, when combined with chemical kinetic studies, can contribute to the understanding of fuel combustion in engines.

Some of these physical properties have been reported in the literature for mixtures of alkylcyclohexanes with other compounds at various temperatures (Table 1). In the systems studied, the excess molar volumes of the alkylcyclohexane tended to be negative when mixed with small linear alkanes such as n-hexane and n-heptane and positive when mixed with longer linear alkanes and with 1,1,1-tricholoethane.48−53 The exception is for cyclohexane, which has small positive excess molar volumes with n-hexane, n-heptane, and n-octane.48,49 Table 1 also shows that the excess molar volume, speed of sound, and viscosity have been determined for mostly short-chain alkyl-cyclohexanes.48,51,52 From their speed of sound measurements, Oswal and Maisuria48 calculated positive excess isentropic compressibilities for mixtures of cyclohexane with octane, but negative excess isentropic compressibilities for mixtures of cyclohexane with hexane and heptane as well as mixtures of methylcyclohexane in hexane. Excess speeds of sound, calculated in a manner similar to the one in this current work, for methylcyclohexane and ethylcyclohexane in either dodecane or hexadecane were not statistically different from zero.51 For viscosity, Lorenzi et al.52 reported small positive viscosity deviations ( −0.045 mm2·s−1) for 1,1,1,-trichlomethane mixed with cyclohexane, methylcyclohexane, and ethylcyclohexane. In our laboratory, we determined that the Gibbs energies of activation for viscous flow for binary mixtures of methyl- and ethylcyclohexane in dodecane and hexadecane were smaller than the error in the values themselves. Both papers used a similar functional form of viscosity, which is described later in the paper.51 No studies, however, have been conducted to determine the physical properties of n-hexadecane mixed with longer chain

2. MATERIALS AND METHODS 2.1. Materials. The n-hexadecane, n-propylcyclohexane, n-pentylcyclohexane, n-hexylcyclohexane, n-heptylcyclohexane, n-octylcyclohexane, n-nonylcyclohexane, n-decylcyclohexane, n-dodecylcyclohexane were used as received from the supplier and had a mole fraction purity of 0.988 or higher (Table 2). Each compound was sequentially pipetted into a clean vial and weighed on a Mettler Toledo AG204 analytical balance that has an error of less than 0.0004 g. The vial was sealed with a cap fitted with a Teflon septum, and 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 2 to be 0.0001 unless otherwise indicated in the results. 2.2. Laboratory Methods. The density and speed of sound were measured using an Anton Paar DSA 5000 M density and sound analyzer for temperatures ranging from (293.15 to 333.15) K. This instrument 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.53 It measures density using a vibrating tube densimeter as described in Fortin et al.53 Each day, the speed of sound and density were checked using degassed ultrapure water, and periodically, the density measurement was also checked using a NIST-certified density standard (Certificate Standard Reference Material 211d, toluene liquid density-extended range). During the time period of this study, the average speed of sound for degassed ultrapure water at 293.15 K was 1482.7 ± 0.4 m·s−1, which compares favorably with the literature values provided by the instrument vendor, 1482.66 m·s−1.54 The error reported is the expanded uncertainty

The properties tested in the current study are those that affect the transport and injection of a fuel into a combustion chamber (bulk modulus, density, viscosity). Both the American Society for Testing and Materials and the military specify ranges of values for density and viscosity.42−44 Isentropic bulk modulus is an important fuel metric that has been found to influence fuel injection timing.45−47 Isentropic bulk modulus, Ev, is calculated from density, ρ, and speed of sound, c, as Ev = ρ × c 2

B

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Table 2. Chemical Information chemicalname

CASRN

molar mass(g/mol)a

source/lot number

mole fraction purityb

analysis methodb

n-propylcyclohexane (C9H18) n-pentylcyclohexane (C11H22) n-hexylcyclohexane (C12H24) n-heptylcyclohexane (C13H26) n-octylcyclohexane (C14H28) n-nonylcyclohexane (C15H30) n-decylcyclohexane (C16H32) n-dodecylcyclohexane (C18H36) n-hexadecane (C16H34)

1678-92-8 4292-92-6 4292-75-5 5617-41-4 1795-15-9 2883-02-5 1795-16-0 1795-17-1 544-76-3

126.24 ± 0.01 154.29 ± 0.01 168.32 ± 0.01 182.35 ± 0.01 196.37 ± 0.01 210.40 ± 0.02 224.42 ± 0.02 252.48 ± 0.02 226.44 ± 0.02

TCI/J2BQG TCI/FCV01 TCI/X5F4O TCI/FIB01 TCI/BT8CD TCI/INHUB TCI/FCQ01 TCI/FCQ01 AcrosA0370819

0.999 0.992 0.988 0.995 0.993 0.986 0.994 0.994 0.998

GC GC GC GC GC GC 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.

thermostat and barostat.56 Bonds involving hydrogen were constrained via the SHAKE algorithm57 enabling the use of a 2.0 fs time step. Short-range Lennard-Jones and Coulombic interactions were truncated at 13 Å, with long-range electrostatic interactions calculated using the particle−particle particle− mesh (PPPM) method.58 Standard long-range corrections were applied to the energy and pressure.59 The all-atom optimized potential for liquid simulations (OPLS-AA)60 was used to model the cyclohexane rings, with the L-OPLS parameters for linear alkanes61 used for both alkylcyclohexane alkyl chains and n-hexadecane. For each configuration, the initial 2.0 ns of the NPT simulation were considered equilibrium, and results were averaged over the final 8.0 ns, giving a total of 40 ns of sampling time for each composition. Densities, excess molar volumes, and isentropic bulk moduli were calculated and compared to experiment. Isentropic bulk modulus can be calculated from volume and potential energy fluctuations in NPT simulations; for details see Morrow et al.41

of the measurement (k = 2). The average density of water at 293.15 K measured during the time period of this study was 998.19 ± 0.08 kg·m−3, which compares favorably with the literature values provided by the instrument vendor, 998.203 kg·m−3.54 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 5000 M was cleaned with hexane between samples and with ethanol after checking with water and then dried. At least two samples were measured for each mixture that was tested. The viscosity and density were measured using an Anton Paar SVM 3001 for temperatures ranging from (293.15 to 373.15) K. The density values from the SVM 3001 agreed with those of the DSA 5000 M within the error of the measurements. Since the values from the DSA 5000 are more precise, its values are reported for the lower temperatures. 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. To determine the expanded uncertainty of all 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 the coverage factor of 2. 2.3. Computational Methods. Molecular dynamics simulations were performed for mixtures of n-hexadecane with n-propylcyclohexane or n-dodecylcyclohexane, using the same mole fractions as used in the experiments. Simulation cells were built by randomly placing a total of 500 molecules in a cube using the program Packmol.55 Initial dimensions were chosen by calculating the volume necessary to match the experimental density, then adding an additional 5 Å to each side length to make packing easier. For each composition, five different random configurations were generated to increase sampling. The energy of each system was minimized via 10 000 steps of the conjugate gradient algorithm. This was followed by 100 ps of NVT dynamics at 293.15 K, where the number of atoms N, system volume V, and system temperature T are held constant. Subsequently, each system underwent 10 ns of NPT dynamics, where the system temperature and pressure, P, were maintained at 293.15 K and 1 bar, respectively, using a Nose-Hoover

3. RESULTS 3.1. Density. The measured densities as a function of temperature of pure n-hexadecane, n-propylcyclohexane, n-pentylcyclohexane, n-hexylcyclohexane, n-heptylcyclohexane, n-octylcyclohexane, n-nonylcyclohexane, n-decylcyclohexane, n-dodecylcyclohexane agree with the reported values within the combined expanded uncertainty of the measurements as shown in Table 3. As the mole fraction of the n-alkylcyclohexanes in n-hexadecane increases, the density of the binary mixtures increases (Tables 4−9). Fuel density specifications are (755 to 840) kg·m−3 for Jet A, (751 to 802) kg·m−3 for military JP-4, (788 to 845) kg·m−3 for military JP-5, and (800 to 876) kg·m−3 for military diesel fuel.42−44 Extrapolation of the current data suggests that all mixtures can meet the Jet A and JP-4 specifications. JP-5 specifications were only met by the mixtures of all the longer alkyl-chain alkylcyclohexanes, and by mixtures with high concentrations of the short-chain n-alkyclcohexanes (x1 > 0.83 propylcyclohexane, x1 > 0.5 pentylcyclohexane). The diesel fuel specifications would not be met by n-propylcyclohexane mixtures, but could be met by pentylcyclohexane at mole fractions great than 0.8 and by the longer chain alkylcyclohexanes at mole fractions equal to or greater than 0.2. In a modeling effort, Kim et al.62 determined how the ignition delay and penetration depth of direct injection sprays changed as various fuel properties were varied over a minimum and maximum property range. They found that liquid fuel density had a major influence on both ignition delay and liquid penetration length at low and high temperatures. They concluded that density should be considered in the formulation of surrogate fuel mixtures. C

DOI: 10.1021/acs.jced.8b00692 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 3. Comparison of the Measured Densities ρ, kg·m−3, with Literature Values at Pressure p = 0.1 MPaa this studya

T/K 293.15

793.54

298.15 303.15

789.64 785.73

313.15 323.15 333.15 343.15

777.90 770.04 762.12 754.2

293.15 303.15 313.15 323.15 333.15 343.15 353.15

810.99 803.96 796.93 789.89 782.83 775.8 768.7

293.15 298.15 303.15 333.15

818.55 815.16 811.78 791.50

293.15

822.31

this studya

T/K

lit n-Propylcyclohexane 793.00 ± 0.30b, 793.27 ± 0.20b, 793.47 ± 0.05b, 793.54 ± 0.20b, 793.58 ± 0.15b, 793.7c 789.56 ± 0.20b, 789.58 ± 0.05b, 789.75 ± 0.15b, 789.74 ± 0.20b 785.79 ± 0.15b, 785.9c

298.15

293.15 313.15 333.15

814.14 800.29 786.42

293.15

293.15

777.70 ± 0.30b, 778.1c 770.2c 762.3c 754.4c n-Heptylcyclohexane 810.1f, 810.2 ± 2.00b, 810.6d, 812.4 ± 0.50d, 812.4 ± 0.50b, 803.6d 796.5d 789.4d 782.3d 775.3d 768.2d n-Decylcyclohexane 818.57 ± 0.15b, 818.60 ± 0.50b, 819.10 ± 0.50b 815.17 ± 0.06b 811.83 ± 0.06b 791.80 ± 0.50b n-Dodecylcyclohexane 822.8i, 824.7 ± 0.9b

lit

n-Pentylcyclohexane 804.11 801.8 ± 2.00b, 802.0 ± 2.00b, 802.6 ± 2.00b, 804.4 ± 3.00b, 804.5f n-Hexylcyclohexane 807.71 806.0 ± 2.00b, 808.2 ± 0.60b, 808.1 ± 0.30b, 808.17g 804.13 804.5 ± 0.60b, 804.5 ± 0.30b, 804.52g

293.15

n-Octylcyclohexane 814.31b, 813.9 ± 0.5b 800.4 ± 0.8b 786.40 ± 0.50e, 786.5 ± 0.8b n-Nonylcyclohexane 816.41 817.0 ± 2.00b, 817.2f

293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

773.37 766.43 759.51 752.61 745.69 738.8 731.8 724.9 717.8

n-Hexadecane 773.43 ± 0.06h 766.59 ± 0.05h 759.71 ± 0.07h 752.80 ± 0.12h 745.86 ± 0.18h 738.90 ± 0.25h 731.90 ± 0.31h 724.88 ± 0.38h 717.84 ± 0.44h

Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, and expanded uncertainties Uc are Uc(ρ) = 0.8 kg·m−3 (level of confidence = 0.95, k = 2). Instrumental error is small in comparison to the error introduced by sample purity. The average pressure for these measurements was 0.102 MPa. bReference 74. cReference 64. dReference 75. eReference 76. fReference 77. gReference 78. hReference 79 with the following correlations: Hexadecane: ρ/kg·m3 = 956.848 − [0.557634 × T/K] + [2.68578 × 10−4 (T/K)2] − [1.24436 × 10−7 (T/K)3]. iReference.80 a

Table 4. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν of Mixtures of n-Propylcyclohexane (1) + n-Hexadecane (2), n-Pentylcyclohexane (1) + n-Hexadecane (2), and n-Hexylcyclohexane (1) + n-Hexadecane (2) from Temperature T = (293 to 363) K and Pressure p = 0.1 MPaa

x1

ρ

η

ν

ρ

η

ν

ρ

η

ν

ρ

η

ν

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

kg·m−3

mPa·s

mm2·s−1

n-Propylcyclohexane (1) + n-Hexadecane (2) T = 293.15 K

T = 303.15 K

T = 313.15 K

T = 323.15 K

0.0000

773.37

3.47

4.49

766.43

2.76

3.61

759.51

2.24

2.95

752.61

1.86

2.47

0.2001

775.57

2.90

3.74

768.58

2.34

3.04

761.59

1.93

2.53

754.61

1.61

2.14

c

c

0.4008

778.35

2.35

3.01

771.27

1.94

2.51

764.18

1.61

2.10

757.08

1.37

1.81

0.5001

779.98

2.11

2.70

772.84

1.74

2.25

765.69

1.46

1.91

758.53

1.25

1.65

0.6009

781.97

1.85

2.36

774.74

1.55

2.00

767.50

1.31

1.70

760.24

1.13

1.49

0.8301c

787.65

1.34

1.71

780.16

1.14

1.46

772.64

0.975

1.26

765.09

0.858

1.12

793.54

0.996

1.25

785.73

0.860

1.09

777.90

0.750

0.964

770.04

0.663

0.861

1.000

T = 333.15 K

T = 343.15 K

T = 353.15 K

T = 363.15 K

0.0000

745.69

1.56

2.09

738.78

1.35

1.82

731.9

1.15

1.57

724.9

1.02

1.41

0.2001

747.61

1.37

1.83

740.6

1.19

1.61

733.6

1.02

1.39

726.5

0.918

1.26

0.4008

749.96

1.18

1.57

742.9

1.03

1.39

735.7

0.905

1.23

728.5

0.805

1.11

0.5001

751.33

1.07

1.42

744.1

0.946

1.27

736.9

0.834

1.13

729.5

0.746

1.02

0.6009

752.95

0.970

1.29

745.6

0.863

1.16

738.3

0.764

1.035

730.8

0.685

0.937

c

c

0.8301

757.51

0.747

0.986

749.8

0.673

0.897

742.2

0.594

0.800

734.6

0.503

0.685c

1.000

762.12

0.584

0.766

754.2

0.544

0.721

746.1

0.477

0.639

738.0

0.452

0.613

n-Pentylcyclohexane (1) + n-Hexadecane (2) T = 293.15 K 0.2004 0.4000

T = 303.15 K

T = 313.15 K

T = 323.15 K

777.53

3.10c

3.99c

770.57

2.49

3.23

763.62

2.04

2.67

756.66

1.70

2.24

782.39

c

c

775.39

2.22

2.87

768.39

1.83

2.39

761.38

1.54

2.02

2.74

3.50

D

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Table 4. continued ρ x1 0.4999 0.5999 0.8006c 1.0000 0.2004 0.4000 0.4999 0.5999 0.8006c 1.0000

0.0000 0.1003 0.2002 0.2996 0.4192 0.5004 0.6030 0.8003b 1.000 0.0000 0.1003 0.2002 0.2996 0.4192 0.5004 0.6030 0.8003c 1.000

η −3

ν

kg·m

mPa·s

T = 293.15 785.18 788.23 795.35 804.11 T = 333.15 749.70 754.35 757.00 759.88 766.57 774.74

K 2.56 2.38c 2.03 1.70 K 1.44 1.31 1.24 1.18 1.03 0.895

T = 293.15 773.37 775.83 778.43 781.19 784.77 787.39 790.94 798.59 807.71 T = 333.15 745.69 748.09 750.65 753.35 756.86 759.41 762.86 770.24 779.02

K 3.47 3.35c 3.21 3.09 2.93 2.82 2.70 2.44 2.20 K 1.56 1.51 1.47 1.42 1.37 1.33 1.29 1.20 1.09

ρ

2 −1

mm ·s

3.26 3.02b 2.55 2.11 1.92 1.74 1.64 1.55 1.35 1.16

4.49 4.31c 4.13 3.96 3.74 3.58c 3.41 3.06 2.72 2.09 2.01 1.96 1.88 1.81 1.76 1.70 1.55 1.40

η −3

kg·m

ν

mPa·s

ρ

2 −1

mm ·s

η −3

kg·m

mPa·s

T = 303.15 K T = 313.15 K 778.15 2.08 2.68 771.11 1.73 781.16 1.95 2.50 774.09 1.61 788.18 1.68 2.14 781.00 1.41 796.80 1.42 1.78 789.47 1.21 T = 343.15 K T = 353.15 K 742.8 1.24 1.68 735.8 1.07 747.4 1.14 1.53 740.3 0.985 749.9 1.08 1.45 742.8 0.937 752.9 1.03 1.37 745.7 0.903 759.4 0.916 1.21 752.2 0.809 767.3 0.799 1.04 759.9 0.709 n-Hexylcyclohexane (1) + n-Hexadecane (2) T = 303.15 K T = 313.15 K 766.43 2.76 3.61 759.51 2.24 768.88 2.66 3.47 761.95 2.17 771.48 2.57 3.33 764.54 2.10 774.23 2.47 3.20 767.28 2.02 777.80 2.36 3.03 770.83 1.94 780.41 2.28 2.92 773.42 1.87 783.93 2.19 2.80 776.92 1.80 791.52 2.00 2.52 784.45 1.65 800.56 1.81 2.26 793.40 1.51 T = 343.15 K T = 353.15 K 738.8 1.35 1.82 731.9 1.15 741.2 1.29 1.75 734.2 1.12 743.7 1.27 1.71 736.7 1.09 746.5 1.22 1.64 739.5 1.06 749.9 1.18 1.57 742.9 1.02 752.4 1.15 1.53 745.4 1.00 755.9 1.13 1.49 748.8 0.971 763.1 1.05 1.37 756.0 0.919 771.8 0.964 1.25 764.6 0.847

ν

ρ

2 −1

mm ·s 2.24 2.09 1.80 1.53

1.45 1.33 1.26 1.21 1.08 0.933

2.95 2.84 2.75 2.64 2.51 2.42 2.31 2.10 1.90 1.57 1.53 1.49 1.44 1.38 1.34 1.30 1.22 1.11

−3

kg·m

η

ν

mPa·s

mm2·s−1

T = 323.15 764.07 766.99 773.80 782.12 T = 363.15 728.7 733.2 735.6 738.5 744.8 752.4

K 1.46 1.37 1.21 1.04 K 0.955 0.884 0.843 0.805 0.724 0.637

T = 323.15 752.61 755.02 757.60 760.32 763.85 766.42 769.89 777.35 786.22 T = 363.15 724.9 727.3 729.7 732.5 735.9 738.3 741.7 748.8 757.3

K 1.86 1.80 1.75 1.68 1.62 1.57 1.52 1.40 1.29 K 1.02 0.981 0.977 0.931 0.901 0.880 0.873 0.817 0.758

1.90 1.79 1.57 1.33 1.31 1.21 1.15 1.09 0.971 0.847

2.47 2.38 2.31 2.22 2.12 2.05 1.97 1.80 1.64 1.41 1.35 1.34 1.27 1.22 1.19 1.18 1.09 1.00

a

x1 is the mole fraction of n-propylcyclohexane, n-pentylcyclohexane, or n-hexylcyclohexane in the n-hexadecane. Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa and expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, Uc(ρ)= 0.8 kg·m−3 and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001,unless indicated by a superscript “b”, “c”, or “d” (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bUc(ν) = 0.03 mm2·s−1. cUc(x1) = 0.0002, Uc(η) = 0.02 mPa·s, Uc(ν) = 0.02 mm2·s−1.

Table 5. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν, of Mixtures of n-Heptylcyclohexane (1) + n-Hexadecane (2) from Temperature T = (293 to 373) K and Pressure p = 0.1 MPaa x1

T

x1

K

0.0000 0.1997 0.4002 0.5001 0.6006 0.7998b 1.0000 0.0000 0.1997 0.4002 0.5001 0.6006 0.7998b 1.0000 0.0000 0.1997 0.4002 0.5001

293.15 293.15 293.15 293.15 293.15 293.15 293.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15

ρ

η −3

ν 2 −1

kg·m

mPa·s

mm ·s

773.37 779.33 785.92 789.55 793.34 801.63 810.99 766.43 772.40 778.99 782.60 786.39 794.64 803.96 759.51 765.47 772.06 775.66

3.47 3.34b 3.20 3.13 3.05 2.92 2.80 2.76 2.66 2.56 2.51 2.45 2.35 2.26 2.24 2.17 2.08 2.05

4.49 4.29 4.07 3.97 3.85 3.64 3.46 3.61 3.45 3.28 3.21 3.11 2.96 2.81 2.95 2.83 2.70 2.65

ρ

T K 323.15 323.15 323.15 323.15 323.15 323.15 323.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 343.15 343.15 343.15 343.15

kg·m

η −3

752.61 758.54 765.13 768.71 772.48 780.65 789.89 745.69 751.62 758.19 761.75 765.51 773.64 782.83 738.8 744.7 751.3 754.8 E

mPa·s 1.86 1.80 1.73 1.71 1.67 1.61 1.56 1.56 1.52 1.46 1.45 1.42 1.37 1.33 1.35 1.31 1.25 1.25

ν 2 −1

mm ·s 2.47 2.37 2.26 2.23 2.16 2.06 1.97 2.09 2.02 1.93 1.90 1.85 1.77 1.69 1.82 1.76 1.67 1.66

T K 353.15 353.15 353.15 353.15 353.15 353.15 353.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 373.15 373.15 373.15 373.15

ρ

η

ν

kg·m

mPa·s

mm2·s−1

731.9 737.7 744.3 747.8 751.6 759.6 768.7 724.9 730.8 737.3 740.7 744.5 752.6 761.6 717.9 723.7 730.3 733.7

1.15 1.12 1.09 1.07 1.06 1.03 0.993 1.02 1.00 0.954 0.962 0.932 0.903 0.892 0.885 0.866 0.845 0.834

1.57 1.52 1.46 1.44 1.41 1.35 1.29 1.41 1.37 1.29 1.30 1.25 1.20 1.17 1.23 1.20 1.16 1.14

−3

DOI: 10.1021/acs.jced.8b00692 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 5. continued x1

T

x1

K

0.6006 0.7998b 1.0000

313.15 313.15 313.15

ρ

η −3

kg·m

mPa·s

779.44 787.98 796.93

2.01 1.93 1.86

ν 2 −1

mm ·s 2.57 2.45 2.34

ρ

T

η −3

K

kg·m

343.15 343.15 343.15

758.6 766.7 775.8

mPa·s 1.22 1.18 1.15

ν 2 −1

mm ·s 1.61 1.53 1.48

T K 373.15 373.15 373.15

ρ

η

ν

kg·m

mPa·s

mm2·s−1

737.5 745.4 754.4

0.827 0.803 0.776

1.12 1.08 1.03

−3

a

x1 is the mole fraction of n-heptylcyclohexane in the n-hexadecane. Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, expanded uncertainties Uc are Uc(η) = 0.01 mPa·s and Uc(ρ) = 0.8 kg m−3, and combined expanded uncertainties of Uc(ν) = 0.01 mm·s−1, Uc(x1) = 0.0001, unless indicated by superscript “b” (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bUc(x1) = 0.0002, Uc(η) = 0.02 mPa·s, and Uc(ν) = 0.02 mm2·s−1.

Table 6. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν, of n-Octylcyclohexane (1) + n-Hexadecane (2) from Temperature T = (293 to 373) K and Pressure p = 0.1 MPaa x1

T

ρ

η

ν

T

ρ

η

ν

T

ρ

η

ν

x1

K

kg·m−3

mPa·s

mm2·s−1

K

kg·m−3

mPa·s

mm2·s−1

K

kg·m−3

mPa·s

mm2·s−1

0.0000 0.2001 0.3999 0.5002 0.6009 0.8006b 1.000 0.000 0.2001 0.3999 0.5002 0.6009 0.8006b 1.0000 0.000 0.2001 0.3999 0.5002 0.6009 0.8006b 1.0000

293.15 293.15 293.15 293.15 293.15 293.15 293.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15

773.37 780.29 787.74 791.67 795.83 804.62 814.14 766.43 773.36 780.82 784.77 788.93 797.71 807.22 759.51 766.44 773.91 777.87 782.03 790.79 800.29

3.47 3.46 3.46 3.46 3.44 3.46 3.52 2.76 2.75 2.74 2.75 2.74 2.76 2.79 2.24 2.24 2.23 2.24 2.23 2.24 2.27

4.49 4.43 4.39 4.37 4.32 4.30 4.33 3.61 3.56 3.52 3.51 3.48 3.45 3.46 2.95 2.92 2.88 2.88 2.85 2.83 2.83

323.15 323.15 323.15 323.15 323.15 323.15 323.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

752.61 759.53 767.00 770.97 775.12 783.86 793.36 745.69 752.62 760.08 764.05 768.20 776.93 786.42 738.8 745.7 753.2 757.2 761.3 770.0 779.5

1.86 1.85 1.84 1.85 1.85 1.85 1.88 1.56 1.56 1.55 1.56 1.56 1.56 1.58 1.35 1.34 1.33 1.35 1.33 1.34 1.36

2.47 2.44 2.40 2.40 2.38 2.37 2.36 2.09 2.07 2.04 2.05 2.03 2.01 2.01 1.82 1.80 1.76 1.78 1.75 1.74 1.75

353.15 353.15 353.15 353.15 353.15 353.15 353.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

731.9 738.8 746.3 750.2 754.3 763.1 772.5 724.9 731.8 739.3 743.3 747.4 756.1 765.5 717.9 724.8 732.3 736.3 740.4 749.1 758.5

1.15 1.15 1.15 1.15 1.15 1.16 1.16 1.02 1.02 1.00 1.03 1.01 1.01 1.04 0.885 0.887 0.889 0.890 0.895 0.897 0.899

1.57 1.55 1.54 1.54 1.53 1.52 1.50 1.41 1.40 1.36 1.39 1.35 1.34 1.36 1.23 1.22 1.21 1.21 1.21 1.20 1.18

a x1 is the mole fraction of n-octylcyclohexane in the n-hexadecane. Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, and Uc(ρ)= 0.8 kg·m−3 and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, unless indicated by superscript “b” or “c” (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bUc(x1) = 0.0001, Uc(η) = 0.02 mPa·s, Uc(ν) = 0.02 mm·s−1.

Table 7. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν, of Mixtures of n-Nonylcyclohexane (1) + n-Hexadecane (2) from Temperature T = (293 to 373) K and Pressure p = 0.1 MPaa x1

T

ρ

η

ν

T

ρ

η

ν

T

ρ

η

ν

x1

K

kg·m−3

mPa·s

mm2·s−1

K

kg·m−3

mPa·s

mm2·s−1

K

kg·m−3

mPa·s

mm2·s−1

0.0000 0.2005 0.4001 0.5002 0.5998 0.8002b 1.0000 0.0000 0.2005 0.4001 0.5002 0.5998 0.8002b 1.0000 0.0000 0.2005 0.4001

293.15 293.15 293.15 293.15 293.15 293.15 293.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15

773.37 781.15 789.28 793.52 797.86 806.91 816.41 766.43 774.24 782.39 786.64 790.99 800.06 809.57 759.51 767.33 775.51

3.47 3.58 3.72 3.79 3.89 4.07b 4.34 2.76 2.84 2.95 3.00 3.06 3.20 3.39 2.24 2.30 2.38

4.49 4.59 4.72 4.78 4.87 5.05b 5.32 3.61 3.67 3.77 3.82 3.87 4.00 4.19 2.95 3.00 3.07

323.15 323.15 323.15 323.15 323.15 323.15 323.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 343.15 343.15 343.15

752.61 760.43 768.63 772.90 777.25 786.35 795.80 745.69 753.54 761.74 766.02 770.38 779.49 789.05 738.8 746.6 754.9

1.86 1.90 1.96 2.00 2.03 2.12 2.22 1.56 1.60 1.65 1.68 1.70 1.77 1.85 1.35 1.38 1.40

2.47 2.50 2.55 2.59 2.61 2.69 2.79 2.09 2.13 2.16 2.20 2.21 2.27 2.35 1.82 1.84 1.86

353.15 353.15 353.15 353.15 353.15 353.15 353.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 373.15 373.15 373.15

731.9 739.7 748.0 752.3 756.8 765.8 775.4 724.9 732.7 741.1 745.4 749.8 758.9 768.5 717.9 725.7 734.2

1.15 1.18 1.21 1.23 1.25 1.30 1.35 1.02 1.05 1.06 1.09 1.09 1.13 1.20 0.885 0.908 0.931

1.57 1.59 1.62 1.64 1.65 1.69 1.74 1.41 1.43 1.42 1.47 1.45 1.49 1.56 1.23 1.25 1.27

F

DOI: 10.1021/acs.jced.8b00692 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 7. continued x1

T

x1

K

0.5002 0.5998 0.8002b 1.0000

313.15 313.15 313.15 313.15

ρ

η −3

ν 2 −1

ρ

T

η −3

kg·m

mPa·s

mm ·s

K

kg·m

779.77 784.12 793.21 802.74

2.43 2.47 2.58 2.72

3.12 3.15 3.25 3.38

343.15 343.15 343.15 343.15

759.2 763.6 772.7 782.2

mPa·s 1.44 1.45 1.50 1.57

ν 2 −1

mm ·s 1.90 1.90 1.95 2.01

T K 373.15 373.15 373.15 373.15

ρ

η

ν

kg·m

mPa·s

mm2·s−1

738.5 742.9 752.0 761.6

0.944 0.960 1.00 1.03

1.28 1.29 1.33 1.35

−3

a

x1 is the mole fraction of n-nonylcyclohexane in the n-hexadecane. Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, and Uc(ρ)= 0.8 kg·m−3 and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, unless indicated by superscript “b” (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bUc(x1) = 0.0002, Uc(η) = 0.02 mPa·s, Uc(ν) = 0.02 mm2·s−1

Table 8. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν, of Mixtures of n-Decylcyclohexane (1) + n-Hexadecane (2) from Temperature T = (293 to 373) K and Pressure p = 0.1 MPaa x1

T

x1

K

0.0000 0.2000 0.4000 0.4999 0.6008 0.7237b 1.0000 0.0000 0.2000 0.4000 0.4999 0.6008 0.7237b 1.0000 0.0000 0.2000 0.4000 0.4999 0.6008 0.7237b 1.0000

293.15 293.15 293.15 293.15 293.15 293.15 293.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15

ρ

η −3

ν 2 −1

kg·m

mPa·s

mm ·s

773.37 781.98 790.75 795.26 799.82 805.48 818.55 766.43 775.08 783.89 788.42 792.99 798.67 811.78 759.51 768.19 777.04 781.59 786.18 791.88 805.02

3.47 3.73b 4.03 4.19 4.36b 4.63 5.32 2.76 2.95 3.16 3.29 3.41 3.60 4.09 2.24 2.39 2.54 2.64 2.73 2.87 3.23

4.49 4.77b 5.10 5.27 5.45b 5.75 6.50 3.61 3.81 4.03 4.17 4.30 4.51 5.04 2.95 3.10 3.27 3.38 3.47 3.62 4.02

ρ

T K 323.15 323.15 323.15 323.15 323.15 323.15 323.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

η

kg·m

−3

752.61 761.30 770.20 774.76 779.37 785.08 798.27 745.69 754.42 763.35 767.92 772.55 778.28 791.50 738.8 747.5 756.5 761.3 765.8 771.6 784.8

mPa·s 1.86 1.97 2.09 2.18 2.24 2.34 2.62 1.56 1.65 1.75 1.81 1.87 1.95 2.16 1.35 1.42 1.48 1.54 1.58 1.64 1.82

ν 2 −1

mm ·s 2.47 2.59 2.71 2.81 2.87 2.98 3.28 2.09 2.19 2.29 2.36 2.42 2.50 2.73 1.82 1.90 1.96 2.02 2.07 2.13 2.32

T K 353.15 353.15 353.15 353.15 353.15 353.15 353.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

ρ

η

ν

kg·m

mPa·s

mm2·s−1

731.9 740.7 749.7 754.4 759.0 764.8 778.0 724.9 733.7 742.8 747.6 752.1 758.0 771.2 717.9 726.8 735.9 740.7 745.2 751.1 764.4

1.15 1.21 1.28 1.32 1.36 1.41 1.55 1.02 1.08 1.10 1.17 1.18 1.22 1.34 0.885 0.926 0.979 1.01 1.04 1.07 1.17

1.57 1.63 1.70 1.75 1.79 1.84 1.99 1.41 1.47 1.48 1.57 1.57 1.61 1.74 1.23 1.27 1.33 1.36 1.40 1.43 1.53

−3

a x1 is the mole fraction of n-decylcyclohexane in the n-hexadecane. Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, expanded uncertainties Uc are Uc(η) = 0.01 mPa·s, and Uc(ρ)= 0.8 kg·m−3 and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, unless indicated by superscript “b” (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bUc(x1) = 0.0002, Uc(η) = 0.02 mPa·s, Uc(ν) = 0.02 mm2·s−1.

Table 9. Experimental Densities ρ, Dynamic Viscosities η, and Kinematic Viscosities ν, of Mixtures of n-Dodecylcyclohexane (1) + n-Hexadecane (2) from Temperature T = (293 to 373) K and Pressure p = 0.1 MPaa T x1

K

0.0000 0.2002 0.4001 0.5001 0.6003 0.8001c 1.0000 0.0000 0.2002 0.4001 0.5001 0.6003 0.8001c 1.0000 0.0000 0.2002 0.4001

293.15 293.15 293.15 293.15 293.15 293.15 293.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 313.15 313.15 313.15

ρ kg·m

η −3

773.37 783.66 793.67 798.59 803.47 812.98 822.31 766.43 776.77 786.84 791.79 796.69 806.26 815.65 759.51 769.91 780.03

ν 2 −1

mPa·s

mm ·s

3.47 4.02 4.72 5.11 5.49b 6.49 7.76 2.76 3.17 3.66 3.95 4.23 4.93 5.81 2.24 2.56 2.92

4.49 5.13 5.94 6.40 6.84b 7.98c 9.43 3.61 4.08 4.66 4.98 5.30 6.12 7.12 2.95 3.32 3.74

ρ

T K 323.15 323.15 323.15 323.15 323.15 323.15 323.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 343.15 343.15 343.15

η −3

kg·m

752.61 763.05 773.23 778.23 783.19 792.89 802.37 745.69 756.19 766.43 771.46 776.44 786.20 795.74 738.8 749.3 759.7 G

mPa·s 1.86 2.10 2.38 2.54 2.70 3.09 3.55 1.56 1.76 1.97 2.10 2.23 2.53 2.88 1.35 1.49 1.67

ν 2 −1

mm ·s 2.47 2.76 3.07 3.27 3.45 3.90 4.43 2.09 2.33 2.58 2.73 2.88 3.22 3.63 1.82 1.99 2.19

T K 353.15 353.15 353.15 353.15 353.15 353.15 353.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 373.15 373.15 373.15

ρ

η

ν

kg·m

mPa·s

mm2·s−1

731.9 742.4 752.9 757.9 763.0 772.9 782.5 724.9 735.6 746.1 751.1 756.2 766.2 775.9 717.9 728.7 739.3

1.15 1.28 1.43 1.51 1.60 1.79 2.01 1.02 1.14 1.24 1.31 1.38 1.54 1.72 0.885 0.978 1.08

1.57 1.73 1.90 1.99 2.10 2.32 2.56 1.41 1.55 1.66 1.74 1.83 2.01 2.22 1.23 1.34 1.47

−3

DOI: 10.1021/acs.jced.8b00692 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 9. continued ρ

T x1

K

0.5001 0.6003 0.8001c 1.0000

313.15 313.15 313.15 313.15

η

kg·m

−3

785.01 789.93 799.57 809.01

ν 2 −1

ρ

T

η −3

mPa·s

mm ·s

K

kg·m

mPa·s

3.13 3.34 3.85 4.48

3.99 4.23 4.82 5.54

343.15 343.15 343.15 343.15

764.7 769.7 779.6 789.1

1.77 1.88 2.11 2.39

ν

T

2 −1

mm ·s

K

2.32 2.44 2.71 3.03

373.15 373.15 373.15 373.15

ρ

η

ν

kg·m

mPa·s

mm2·s−1

744.3 749.4 759.5 769.2

1.14 1.21 1.34 1.48

1.53 1.61 1.77 1.93

−3

a x1 is the mole fraction of n-dodecylcyclohexane in the n-hexadecane. Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, expanded uncertainties Uc are Uc(η) = 0.01 mPa·s and Uc(ρ)= 0.8 kg·m−3 and combined expanded uncertainties of Uc(ν) = 0.01 mm2·s−1, Uc(x1) = 0.0001, unless indicated by superscript “b” or “c” (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bUc(η) = 0.04 mPa·s, Uc(ν) = 0.05 mm2·s−1. cUc(x1) = 0.0001, Uc(ν) = 0.02 mm2·s−1.

Table 10. Excess Molar Volumes, VEm, Excess Speeds of sound cE Δc, and Excess Molar Gibbs Energies of Activation for Viscous Flow ΔG*E at Temperature T = 293.15 K for Binary Mixtures of an Alkylcyclohexane (1) and n-Hexadecane (2) at 0.1 MPaa ΔG*E

VEm −1

cm ·mol 3

x1 0.2001 0.4008 0.5001 0.6009 0.8301 0.2004 0.4000 0.4999 0.5999 0.8006 0.1003 0.2002 0.2996 0.4192 0.5004 0.6063 0.8003 0.1997 0.4002 0.5001 0.6006 0.7998

−1

kJ·mol

n-Propylcyclohexane (1) + n-Hexadecane (2) 0.07 ± 0.06 0.2 0.12 ± 0.04 0.4 0.14 ± 0.04 0.4 0.13 ± 0.04 0.4 0.09 ± 0.03 0.3 n-Pentylcyclohexane (1) + n-Hexadecane (2) 0.06 ± 0.06 0.1 0.11 ± 0.04 0.2 0.11 ± 0.04 0.2 0.11 ± 0.04 0.2 0.08 ± 0.04 0.1 n-Hexylcyclohexane (1) + n-Hexadecane (2) 0.03 ± 0.06 0.0 0.05 ± 0.06 0.1 0.07 ± 0.05 0.1 0.08 ± 0.04 0.1 0.09 ± 0.04 0.1 0.08 ± 0.04 0.1 0.06 ± 0.04 0.1 n-Heptylcyclohexane (1) + n-Hexadecane (2) 0.03 ± 0.06 0.0 0.06 ± 0.05 0.0 0.05 ± 0.04 0.0 0.06 ± 0.04 0.0 0.03 ± 0.05 0.0

cE m·s

ΔG*E

VEm

−1

x1

−1 −1 −1 −1 −1

0.2001 0.3999 0.5002 0.6009 0.8006

−1 −2 −2 −2 −2

0.2005 0.4001 0.5002 0.5998 0.8002

0 −1 −1 −1 −1 −2 −1

0.2000 0.4000 0.4999 0.6008 0.7237 0.2002 0.4001 0.5001 0.6003 0.8001

−1 −1 −1 −1 −1

−1

cm ·mol 3

−1

kJ·mol

n-Octylcyclohexane (1) + n-Hexadecane (2) 0.02 ± 0.05 0.0 0.03 ± 0.04 0.0 0.04 ± 0.04 0.0 0.05 ± 0.04 0.0 0.04 ± 0.04 0.0 n-Nonylcyclohexane (1) + n-Hexadecane (2) 0.00 ± 0.05 0.0 0.00 ± 0.04 0.0 0.00 ± 0.04 −0.1 0.00 ± 0.04 0.0 0.00 ± 0.04 0.0 n-Decyclohexane (1) + n-Hexadecane (2) −0.02 ± 0.05 0.0 −0.01 ± 0.04 −0.1 −0.02 ± 0.04 −0.1 −0.01 ± 0.04 −0.1 −0.01 ± 0.05 0.0 n-Dodecyclohexane (1) + n-Hexadecane (2) −0.04 ± 0.05 0.0 −0.06 ± 0.04 0.0 −0.06 ± 0.04 0.0 −0.1 −0.06 ± 0.04 −0.03 ± 0.05 0.0

cE m·s−1 0 0 0 0 −1 0 1 1 1 0 1 1 1 1 1 1 2 3 2 2

a x1 is the mole fraction of alkylcyclohexane in n-hexadecane mixture. The combined standard uncertainty of excess molar volume is given by the “ ± ” symbol. The combined expanded uncertainties Uc are Uc(x1) = 0.0001 for mole fractions less than 0.72 and Uc(x1) = 0.0002 for the higher mole fractions, Uc(cE) = 2 m·s−1, and Uc(ΔG*E) values are between 0.8 and 1.0 kJ·mol−1 (level of confidence = 0.95, k = 2).

The excess molar volumes (VEm) of the n-alkylcyclohexane with n-hexadecane mixtures were calculated using the following equation: VmE =

M1x1 + M 2 x2 Mx M x − 11 − 2 2 ρm ρ1 ρ2

where A0 is Aj are adjustable parameters, and x1 and x2 are the mole fraction of n-alkylcyclohexane and n-hexadecane, respectively. Parameters were added to the model until the standard error of the fit was less than the error in the excess molar volumes themselves. With only a one parameter fit, the largest error was 7.4 × 10−3 cm3·mol−1, which is smaller than the error in the excess molar volumes themselves. Results for fitting with one, two, and three adjustable parameters can be found in the Supporting Information. The successful fits are shown in Figure 1 with the coefficients given in the caption of that figure. Small, positive values of excess molar volumes are obtained for mixtures of n-hexadecane with propylcyclohexane. As the chain length on the n-alkylcylohexanes increases, VEm decreases and becomes negative for mixtures with n-dodecylcylohexane. Previously reported values for binary mixtures with shortchain alkylcyclohexanes adhere to this trend. Reported values of VEm at equal mole fractions for n-hexadecane mixtures with

(2)

where 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 n-alkylcyclohexane as component 1 and n-hexadecane as component 2. The calculated VEm values are given in Table 10 at 293.15 K and shown in Figure 1. A Redlich−Kister type expression was used to fit to the excess molar volume data: n

VmE = x1x 2 ∑ Aj (x1 − x 2) j j=0

(3) H

DOI: 10.1021/acs.jced.8b00692 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 11. Comparison of the Measured Speeds of Sound c, m· s−1, of with Literature Values from Temperature T = (293 to 333) and Pressure p = 0.1 MPaa

Figure 1. Excess molar volumes for binary mixtures of n-hexadecane with (□) n-propylcycohexane (x1), (red ■) n-pentylcyclohexane, (△) n-hexylcyclohexane, (blue ▲) n-heptylcyclohexane, (green ○) n-octylcyclohexane, (yellow ●) n-nonylcyclohexane, (◇) n-decylcyclohexane, (red ⧫) n-dodecylcyclohexane at 293.15 K. Error bars at each mole fraction are of similar size for each alkylcyclohexane mixture. Only two are shown for clarity purposes. The lines are fits using the Redlich−Kister expression: VEm(n-propylcycohexane) = 0.536 x1 x2; VEm(n-pentylcycohexane) = 0.445 x1 x2; VEm(n-hexylcycohexane) = 0.337 x1 x2; VEm(n-heptycycohexane) = 0.238 x1 x2; VEm(n-octylcycohexane) = 0.137 x1 x2; VEm(n-nonylcycohexane) = 0.004 x1 x2; VEm(n-decylcycohexane) = −0.043 x1 x2; VEm(n-dodecylcycohexane) = −0.242 x1 x2. The standard error for the fits was at most 0.01 cm3·mol−1.

T/K

this studya

293.15 303.15 313.15 323.15 333.15

1307.8 1266.2 1225.6 1185.9 1147.3

293.15 303.15 313.15 323.15 333.15

1357.4 1319.6 1282.9 1247.0 1212.1

lit. n-Propylcyclohexane 1307.1b 1265.5b 1224.7b 1184.7b 1145.4b n-Hexadecane 1357.1c, 1357.7d 1319.6c, 1320.0f, 1320.2d 1282.8e, 1283g, 1283.4c, 1283.4d 1246.9c, 1247.4d 1211.2e, 1211.4f, 1211.6c, 1212g, 1212.3d

a Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, and expanded uncertainties Uc are Uc(c) = 0.6 m·s−1 (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bThese values are measured at 83 kPa, Reference 64. c Reference 81. dReference 82. eReference 83. fReference 84. g Reference 85.

For n-hexylcyclohexane mixtures, the speed of sound remains fairly constant at low mole fractions of n-hexylcyclohexane and only increases at higher mole fractions. These speed of sound data were fit to a second-order polynomial, and the coefficients are given in Table 13. The polynomials fit the data well as shown at 293.15 K in Figure 2. The bulk modulus of each mixture was calculated using eq 1 (Table 14). The bulk modulus for diesel fuel has been reported to be between 1590 and 1612 MPa, while a value for jet fuel has been reported to be 1389 MPa at 293.15 K.65−67 The propylcyclohexane mixtures have values that are reasonable for jet fuel, and the n-decylcyclohexane and n-dodecylcyclohexane mixtures have values that are reasonable for diesel fuel. Bulk modulus influences the injection time. Higher values can cause the start of injection time in mechanical injection diesel engines to occur sooner, which will impact the time of combustion.45,46,68 Tat and van Gerpen68 compared the combustion behavior of a biobased to a petroleum-based fuel. They calculated that a timing advance in the pressure pulse of 0.45 to 0.65 degrees was caused by a 169 MPa difference in the bulk modulus.68 Boehman et al.46 found similar behavior in their work with biodiesel. The excess speed of sound, cE, were calculated at 293.15 K using the measured mixture speed of sound, cmix, and an ideal mixture speed of sound cID determined from equations given by Douheret et al.69 which have been summarized in Luning Prak et al.51

methyl- and ethylcyclohexane51 are higher than those for n-propylcyclohexane and values for butylcyclohexane in n-hexadecane are lower.63 Binary mixtures of n-heptane with alkylcyclohexanes mixtures also have decreasing values of VEm (−0.017, −0.143, −0.237, −0.301 cm3·mol−1) as the chain length on the n-alkylcyclohexanes increased (methyl-, n-ethyl-, n-propyl-, and n-butylcyclohexane).49 Excess molar volume, which is the difference between the molar volume of the real mixture and the molar volume that would be obtained with ideal mixing, is one way to quantify the degree of nonideality of a solution. Thus, positive and negative excess molar volumes correspond to an expansion and contraction of volume upon mixing, respectively. Differences between the strength of intermolecular interactions between dissimilar molecules compared to the intermolecular interactions in the pure components gives rise to nonideal behavior. For the molecules studied here, London dispersion is the dominant intermolecular force between all molecules because they are all nonpolar, indicating that differences in the arrangement of molecules in the mixtures results in changes in the strength of these interactions. This is also supported by the MD simulations, which are discussed later in the paper. 3.2. Speed of Sound. A comparison of speeds of sound with literature values was only possible for n-hexadecane and n-propylcyclohexane (Table 11). The speeds of sound of n-hexadecane match those in the literature within the error of the measurements. The measured speeds of sound for propylcyclohexane are higher than those reported by Laesecke et al.64 The differences may be caused by differences in the purity of the compounds or the ambient pressure. Laesecke et al.64 reported a mole fraction purity of 96.68%, which is less than the 99.5% purity reported herein. Their measurements were taken at a pressure of 83 kPa, which is lower than the 0.1 MPa for the current experiments. Increasing the concentration of the alkylcyclohexane in the n-hexadecane mixtures results in a decrease in speed of sound for n-propylcyclohexane and n-pentylcylohexane mixtures and an increase in speed of sound for n-heptyl-, n-octyl-, n-nonyl, n-decyl-, and n-dodecylcylohexane mixtures. (Table 12, Figure 2).

c E = cmix − c ID

(4)

c ID = (ρ ID c ID)−0.5

(5)

Here, the ideal density, ρID, and ideal isentropic compressibility, κID, are ÄÅ ÉÑ ÅÅ ϕ V α 2 ϕ2V2α22 VmID(α ID)2 ÑÑÑÑ ÅÅ 1 1 1 ID ÑÑ κ = ϕ1κ1 + ϕ2κ2 + T ÅÅÅ + − ID ÑÑ ÅÅ Cp ,1 Cp ,2 C ÑÑÖ p ÅÇ ρ ID = ϕ1ρ1 + ϕ2ρ2

(6)

(7)

In these equations Vi, ϕi, κ, ρ, Cpi, and αi are component molar volume, volume fraction, isentropic compressibility, density, I

DOI: 10.1021/acs.jced.8b00692 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 12. Speed of Sound c in m·s−1 of Alkylcylcohexanes (1) + n-Hexadecane (2) from Temperature T = (293.15 to 333.15) K and Pressure p = 0.1 MPaa x1

T/K = 293.15

0.0000 0.2001 0.4008 0.5001 0.6009 0.8301b 1.000

1357.4 1349.9 1341.6 1336.9 1331.7 1318.8 1307.8

0.1003 0.2002 0.2996 0.4192 0.5004 0.6030 0.8003b 1.000

1357.1 1356.8 1356.9 1357.0 1357.1 1357.4 1358.6 1361.0

0.2001 0.3999 0.5002 0.6009 0.8006b 1.000

1361.6 1366.8 1369.7 1372.6 1378.6 1387.0

0.2000 0.4000 0.4999 0.6008 0.7237b 1.0000

1366.2 1375.8 1380.7 1385.6 1392.0 1406.7

T/K = 303.15

T/K = 313.15

T/K = 323.15

n-Propylcyclohexane (1) + n-Hexadecane (2) 1319.6 1282.9 1247.0 1312.1 1275.2 1239.0 1303.8 1266.6 1230.0 1298.4 1260.8 1224.0 1293.3 1255.6 1218.5 1279.2 1240.3 1202.0 1266.2 1225.6 1185.9 n-Hexylcyclohexane (1) + n-Hexadecane (2) 1319.8 1283.2 1247.3 1319.5 1282.8 1246.9 1319.6 1282.9 1246.9 1319.6 1282.8 1246.7 1319.7 1282.9 1246.7 1319.8 1282.9 1246.6 1320.7 1283.5 1246.9 1322.1 1284.2 1247.1 n-Octylcyclohexane (1) + n-Hexadecane (2) 1324.4 1287.9 1252.0 1329.6 1293.0 1257.2 1332.1 1295.4 1259.5 1335.0 1298.3 1262.4 1341.3 1304.6 1268.6 1349.1 1312.1 1275.9 n-Decylcyclohexane (1) + n-Hexadecane (2) 1329.0 1292.6 1256.8 1338.4 1301.9 1266.2 1343.3 1306.8 1271.1 1348.3 1311.8 1276.2 1354.7 1318.3 1282.7 1369.4 1333.0 1297.5

T/K = 333.15

x1

T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

T/K = 333.15

n-Pentylcyclohexane (1) + n-Hexadecane (2) 1212.1 1203.8 1194.3 1188.0 1182.1 1164.5 1147.3

0.2004 0.4000 0.4999 0.5999 0.8006b 1.0000

1354.6 1351.9 1350.6 1349.4 1347.2 1345.9

1212.3 1211.9 1211.7 1211.5 1211.4 1211.2 1211.1 1211.0

0.1997 0.4002 0.5001 0.6006 0.7998b 1.0000

1358.9 1362.0 1363.4 1365.3 1368.8b 1374.4

1217.1 1222.1 1224.6 1227.3 1233.7 1240.5

0.2005 0.4001 0.5002 0.5998 0.8002b 1.0000

1363.9 1371.3 1375.2 1379.1 1387.3 1397.2

1221.9 1231.6 1236.3 1241.5 1248.2 1262.9

0.2002 0.4001 0.5001 0.6003 0.8001b 1.0000

1370.4 1384.0 1390.6 1396.7 1410.4 1423.3

1317.2 1280.5 1244.5 1314.4 1277.6 1241.4 1313.0 1276.0 1239.7 1311.6 1274.5 1237.9 1309.0 1271.3 1234.3 1306.4 1267.8 1230.1 n-Heptylcyclohexane (1) + n-Hexadecane (2) 1321.7 1285.1 1249.3 1324.4 1287.5 1251.5 1326.1 1289.4 1253.4 1327.5 1290.6 1254.5 1331.3b 1294.3b 1258.1b 1336.1 1298.7 1262.1

n-Nonylcyclohexane (1) + n-Hexadecane (2) 1326.7 1290.2 1254.4 1334.2 1297.7 1261.9 1338.1 1301.6 1265.8 1342.0 1305.6 1269.8 1350.2 1313.8 1278.1 1359.6 1322.9 1287.1 n-Dodecylcyclohexane (1) + n-Hexadecane (2) 1333.2 1296.9 1261.2 1347.0 1310.8 1275.3 1353.7 1317.6 1282.1 1359.9 1323.8 1288.5 1373.4 1337.3 1302.0 1386.3 1350.4 1315.2

1209.3 1206.0 1204.2 1202.3 1198.0 1193.4 1214.4 1216.7 1218.2 1219.4 1222.8b 1226.5

1219.5 1226.9 1230.9 1234.9 1243.4 1252.2 1226.5 1240.6 1247.5 1254.3 1267.8 1281.1

a

x1is the mole fraction of the alkylcyclohexane in n-hexadecane. Standard uncertainties u are u(T) = 0.01 K and u(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). The average pressure for these measurements was 0.102 MPa. bUc(x1) = 0.0002 or Uc(c) = 1 m·s−1.

the combined expanded uncertainty of the excess speed of sound. This suggests the mixtures are behaving ideally for speed of sound (Table 10). 3.3. Viscosity. The measured viscosities of n-hexadecane, n-propylcyclohexane, n-pentylcyclohexane, n-hexylcyclohexane, n-heptylcyclohexane, n-octylcyclohexane, n-nonylcyclohexane, n-decylcyclohexane, n-dodecylcyclohexane agree with many of the reported values within the combined expanded uncertainty of the measurements as shown in Table 15. For those measurements that do not agree, the largest percentage deviations from reported values are 1% (n-pentylcyclohexane), 1% (n-hexylcyclohexane), 3% (n-heptylcyclohexane), 1% (n-octylcyclohexane), 4% (n-nonylcyclohexane), 5% (n-decylcyclohexane), and 6% (n-dodecylcyclohexane). For the binary mixtures, the viscosities decrease with increasing mole fraction of the n-propylcyclohexane, n-pentylcyclohexane, n-hexylcyclohexane, n-heptylcyclohexane, and n-octylcyclohexane, and the viscosities increase with increasing mole fraction of n-nonylcyclohexane, n-decylcyclohexane, n-dodecylcyclohexane (Figure 3, Tables 4−9). The military specifies that its diesel fuel must have a viscosity between 1.4 and 4.3 mm2·s−1 at 313.15 K.43 All the mixtures studied herein have viscosities that fall within this specification, except for the higher concentrations of n-dodecylcyclohexane in n-hexadecane. In a modeling effort, Kim et al.62 found that liquid

Figure 2. Speeds of sound for binary mixtures of n-hexadecane with (□) n-propylcycohexane (x 1 ), (red ■ ) n-pentylcyclohexane, ( △) n-hexylcyclohexane, (blue ▲) n-heptylcyclohexane, (green ○) n-octylcyclohexane, (yellow ●) n-nonylcyclohexane, (◇) n-decylcyclohexane, (red ◆) n-dodecylcyclohexane at 293.15 K. The lines are second-order polynomial fits with coefficients given in Table 13.

isobaric heat capacity, and thermal expansion coefficient, resID ID pectively, and T is the temperature in Kelvin. VID m , Cp , α are the ideal molar volume, heat capacity, and thermal expansion coefficient, respectively. The remaining equations used to compute these variables can be found in the Supporting Information. The excess speeds of sound are small, and most are smaller than J

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Table 13. Polynomial Equation (c/m·s−1 = A2x12 + A1x1 + Ao) that Relates Speed of Sound c to Mole Fraction of an Alkylcyclohexane x1, in n-Hexadecane (2) at Temperature T = 293.15 and 333.15 K and Pressure p = 0.1 MPaa T/K

A2 m·s−1

A1 m·s−1

n-Propylcyclohexane (1) + n-Hexadecane (2) 293.15 −16.9 ± 1.3 −32.5 ± 1.4 333.15 −34.6 ± 7.6 −29.0 ± 8.0 n-Pentylcyclohexane (1) + n-Hexadecane (2) 293.15 4.3 ± 1.6 −16.0 ± 1.7 333.15 −5.8 ± 0.4 −12.9 ± 0.4 n-Hexylcyclohexane (1) + n-Hexadecane (2) 293.15 8.3 ± 1.4 −5.0 ± 1.5 333.15 0.9 ± 1.1 −2.2 ± 1.1 n-Heptylcyclohexane (1) + n-Hexadecane (2) 293.15 9.9 ± 3.2 7.0 ± 3.4 333.15 5.0 ± 1.7 9.3 ± 1.8 n-Octylcyclohexane (1) + n-Hexadecane (2) 293.15 10.4 ± 3.9 18.9 ± 4.1 333.15 6.8 ± 2.6 21.4 ± 2.8 n-Nonylcyclohexane (1) + n-Hexadecane (2) 293.15 8.7 ± 2.4 30.9 ± 2.5 333.15 5.1 ± 0.8 35.0 ± 0.8 n-Decylcyclohexane (1) + n-Hexadecane (2) 293.15 5.6 ± 0.8 43.8 ± 0.8 333.15 4.1 ± 2.2 46.5 ± 2.3 n-Dodecylcyclohexane (1) + n-Hexadecane (2) 293.15 −0.3 ± 2.9 66.3 ± 3.0 333.15 −3.6 ± 0.6 72.5 ± 0.7

Ao m·s−1

σ m·s−1

1357.3 ± 0.3 1211.6 ± 1.8

0.13 0.73

1357.5 ± 0.4 1212.1 ± 0.1

0.16 0.04

1357.5 ± 0.3 1212.3 ± 0.2

0.16 0.13

1357.5 ± 0.8 1212.2 ± 0.4

0.31 0.16

1357.5 ± 0.9 1212.3 ± 0.6

0.37 0.25

1357.4 ± 0.6 1212.1 ± 0.2

0.23 0.08

1357.4 ± 0.2 1212.2 ± 0.5

0.08 0.21

1357.3 ± 0.7 1212.2 ± 0.2

0.27 0.06

fuel viscosity had a major influence on liquid penetration length of direct injection sprays. In their work, they used dodecane as a model system and then varied various physical parameters to determine their impact on ignition delay and the depth of penetration depth of direct injection sprays. They concluded that viscosity should be considered in the formulation of surrogate fuel mixtures. The McAllister three-body model70 was used to fit the kinematic viscosity-mole fraction data. ln vm = x13 ln v1 + 3x12x 2 ln v1,2 + 3x1x 22 ln v2,1 + x 23 ln v2 ij 1 ji M zy M zyyz ji − lnjjjx1 + x 2 2 zzz + 3x12x 2 lnjjjj jjj2 + 2 zzzzzzz j j M1 z{ M1 z{{ k k3k ij 1 ij ij M yz M yzyz + 3x1x 22 lnjjjj jjj1 + 2 2 zzzzzzz + x 23 lnjjj 2 zzz j jM z M1 z{{ k 1{ k3k

(8)

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 alkylcylohexane as component 1 and n-hexadecane 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 8 and the measured kinematic viscosity of the binary mixture. The interaction parameters and the standard error of the fit are given in Table 16. The model fits the data well, as shown in Figure 3, for values at 293.15 K. The excess molar Gibbs energy of activation for viscous flow (ΔG*E) was calculated from kinematic viscosity data by71 ÄÅ ÉÑ n ÅÅ ÑÑ Å Ñ E Å ΔG* = RT ÅÅln(vmM m) − ∑ xi ln viM i ÑÑÑ ÅÅ ÑÑ ÅÇ ÑÖ (9) i−1

The “ ± ” for the coefficients Ao, A1, andA2, represent the 95% confidence interval. All had R2 > 0.999, except for hexylcyclohexane with R2 = 0.989 for T = 293.15 K and R2 = 0.940 for T = 333.15 K. The σ is the standard error of the fit. Thex1 is the mole fraction of alkylcyclohexane in n-hexadecane. a

Table 14. Bulk Moduli Ev in MPa of Alkylcylcohexanes (1) + n-Hexadecane (2) from Temperature T = (293.15 to 333.15) K and Pressure p = 0.1 MPaa x1 0.0000 0.2001 0.4008 0.5001 0.6009 0.8301 1.0000 0.1003 0.2002 0.2996 0.4192 0.5004 0.6030 0.8003 1.0000 0.2001 0.3999 0.5002 0.6009 0.8006

T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

n-Propylcyclohexane (1) + n-Hexadecane (2) 1425 1335 1250 1170 1413 1323 1238 1158 1401 1311 1226 1145 1394 1303 1217 1136 1387 1296 1210 1129 1370 1277 1189 1105 1357 1260 1169 1083 n-Hexylcyclohexane (1) + n-Hexadecane (2) 1428 1339 1255 1175 1433 1343 1258 1178 1438 1348 1263 1182 1445 1354 1269 1187 1450 1359 1273 1191 1457 1365 1279 1196 1474 1381 1292 1209 1496 1399 1308 1223 n-Octylcyclohexane (1) + n-Hexadecane (2) 1447 1356 1271 1191 1472 1380 1294 1212 1485 1393 1305 1223 1499 1406 1318 1235 1529 1435 1346 1262

T/K = 333.15

x1

1096 1083 1070 1060 1052 1027 1003

0.0000 0.2004 0.4000 0.4999 0.5999 0.8006 1.0000

1099 1102 1106 1111 1114 1119 1130 1142 1115 1135 1146 1157 1183 K

T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

T/K = 333.15

0.1997 0.4002 0.5001 0.6006 0.7998 1.0000

n-Pentylcyclohexane (1) + n-Hexadecane (2) 1425 1335 1250 1170 1427 1337 1252 1172 1430 1340 1254 1173 1432 1341 1256 1174 1435 1344 1257 1175 1444 1350 1262 1179 1457 1360 1269 1183 n-Heptylcyclohexane (1) + n-Hexadecane (2) 1439 1349 1264 1184 1458 1366 1280 1198 1468 1376 1290 1208 1479 1386 1298 1216 1502b 1408b 1320b 1236b 1532 1435 1344 1258

1109 1122 1130 1138 1157 1178

0.2005 0.4001 0.5002 0.5998 0.8002

n-Nonylcyclohexane (1) + n-Hexadecane (2) 1453 1363 1277 1197 1484 1393 1306 1224 1501 1408 1321 1238 1517 1425 1337 1253 1553 1459 1369 1284

1121 1147 1161 1175 1205

1096 1096 1097 1098 1098 1100 1103

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Table 14. continued x1 1.000 0.2000 0.4000 0.4999 0.6008 0.7237 1.0000

T/K = 293.15

T/K = 303.15

T/K = 313.15

T/K = 323.15

n-Octylcyclohexane (1) + n-Hexadecane (2) 1566b 1469b 1378b 1291 n-Decylcyclohexane (1) + n-Hexadecane (2) 1460 1369 1283 1202 1497 1404 1317 1235 1516 1423 1335 1252 1536 1442 1353 1269 1575 1480 1390 1305 1620 1522 1430 1344

T/K = 333.15

x1

T/K = 293.15

1210

1.0000

1126 1158 1174 1191 1226 1262

0.2002 0.4001 0.5001 0.6003 0.8001 1.000

T/K = 303.15

T/K = 313.15

T/K = 323.15

n-Nonylcyclohexane (1) + n-Hexadecane (2) 1594 1496 1405 1318 n-Dodecylcyclohexane (1) + n-Hexadecane (2) 1472 1381 1295 1214 1520 1428 1340 1258 1544 1451 1363 1279 1567 1473 1384 1300 1617 1521 1430 1344 1666 1568 1475 1388

T/K = 333.15 1237 1138 1180 1201 1222 1264 1306

a

x1 is the mole fraction of n-dodecylcyclohexane in the n-hexadecane. Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa and combined expanded uncertainties of Uc(Ev) = 1 MPa unless indicated by “b” superscript, Uc(x1) = 0.0001 for mole fractions less than 0.72 and Uc(x1) = 0.0002 for the higher mole fractions (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. b Uc(Ev) = 1.5 MPa.

Table 15. Comparison of the Measured Dynamic Viscosities η of with Literature Values at Pressure p = 0.1 MPaa T

this studya

lit.

this studya

lit.

this studya

lit.

K

mPa·s

mPa·s

mPa·s

mPa·s

mPa·s

mPa·s

293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

n-Propylcyclohexane 0.996 1.005b, 1.006b 0.860 0.8606b, 0.870b 0.750 0.759b, 0.760b 0.663 0.672b 0.584 0.5784b, 0.601b 0.544 0.542b 0.477 0.4755b, 0.49b 0.452 0.45b n-Heptylcyclohexane 2.80 2.81b, 2.810d 2.26 2.230d, 2.25b 1.86 1.830b,d 1.56 1.540d, 1.544b 1.33 1.320b,d 1.15 1.140b,d 0.993 0.987d, 0.99b 0.892 0.87b 0.776 0.77 n-Decylcyclohexane 5.32c 5.26b, 6.332b 4.09 4.05b 3.23 3.19b 2.62 2.59b 2.16 2.16b, 2.160b 1.82 1.81b 1.55 1.53b 1.34 1.31b 1.17 1.12

n-Pentylcyclohexane 1.70 1.723b 1.42 1.418b 1.21 1.191b 1.04 1.026b 0.895 0.898b 0.799 0.79b 0.709 0.71b 0.637 0.63b n-Octylcyclohexane 3.52 3.51b, 3.52e 2.79 2.77b 2.27 2.24b 1.88 1.86b 1.58 1.571b, 1.58e 1.36 1.34b 1.16 1.16b 1.04 1.00b 0.899 0.88 n-Dodecylcyclohexane 7.76c 7.54b 5.81 5.68b 4.48 4.38b 3.55 3.50b 2.88 2.86b 2.39 2.36b 2.01 1.96b 1.72 1.65b 1.48 1.40b

n-Hexylcyclohexane 2.20 2.22b 1.81 1.80b 1.51 1.492b 1.29 1.268b, 1.30b 1.09 1.097b 0.964 0.96b 0.847 0.84b 0.758 0.75b n-Nonylcyclohexane 4.34 4.32b 3.39 3.37b 2.72 2.68b 2.22 2.20b 1.85 1.85b 1.57 1.57b 1.35 1.34b 1.20 1.15b 1.03 1.00, 1.04 n-Hexadecane 3.47f 3.44b, 3.447b, 3.453b, 3.484b, 3.505b, 3.52b, 3.522b, 3.53b 2.76 2.748b, 2.76b, 2.766b, 2.86b 2.24 2.223b, 2.225b, 2.23b, 2.250b, 1.86 1.829b, 1.84b, 1.862b, 1.866b, 1.888b, 1.89b, 1.905b 1.56 1.550b, 1.56b, 1.570b, 1.573b, 1.35 1.326b, 1.343b, 1.346b, 1.15 1.152b, 1.159b, 1.16b, 1.166b, 1.167b, 1.172b 1.02 1.010b, 1.017b, 1.021b, 0.885 0.875b, 0.8952b, 0.896, 0.900b, 0.9019b, 0.955b, 0.972b

a Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, and expanded uncertainties Ucare Uc(η) = 0.01 mPa·s unless indicated by symbol “c” or “f ” (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bReference 86/ cUc(η) = 0.02 mPa·s. dReference 75. eReference 76. fUc(η) = 0.03 mPa·s.

where R is the gas constant (8.314 J·mol−1·K−1), T is 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 = ∑i2= 1xiMi), M1 and M2 are the pure component molar masses, and x1 and x2 are the mole fractions with the alkylcyclohexane as component 1 and the n-hexadecane as component 2. All of the excess molar Gibbs energies of activation for viscous flow in Table 10 are less than the error in the values themselves, suggesting that the mixtures are behaving as ideal mixtures in their flow properties.

3.4. Molecular Dynamics Simulations. MD simulations were performed for two of the binary mixtures containing n-hexadecane. Mixtures with n-propylcyclohexane and n-dodecylcyclohexane were examined to both assess the accuracy of the chosen force field and to attempt to gain insight into the trend in excess molar volume as the alkylcyclohexane chain length is changed. Mixtures of n-hexadecane with n-propylcyclohexane or n-dodecylcyclohexane have positive and negative VEmvalues, respectively. Calculated densities and isentropic bulk moduli for n-propylcyclohexane and n-dodecylcylohexane mixtures L

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The simulations capture the correct trends in bulk modulus as a function of composition, with the bulk modulus of n-propylcyclohexane and n-dodecyclcyclohexane mixtures slightly decreasing and increasing, respectively, with increasing n-alkylcyclohexane content. The RMSD for the bulk modulus is 22.2 and 38.5 MPa for n-propyl- and n-dodecylcyclohexane mixtures, respectively. The accuracy of the density and bulk modulus predictions suggests that the simulations are accurately modeling key aspects of the atomic-level interactions, and thus that the simulations can be used to gain insight into the atomiclevel structure of the fluids. The liquid structures of the n-propyl- and n-dodecylcyclohexane mixtures were probed in various ways, such as calculating radial distribution functions (RDFs) between the centers of the cyclohexane rings and RDFs between alkyl chain and n-hexadecane carbon atoms. No significant differences were seen in RDFs as a function of composition (data not shown), suggesting that differences in intermolecular interactions due to different molecule types are not the cause of the observed excess molar volumes. Angular radial distribution functions between cyclohexane rings also show little difference as a function of composition or alkyl-chain length, suggesting that the orientation of the ring portion of the molecules relative to each other is not significantly impacted by either of those factors.41 In addition, the radius of gyration of n-hexadecane is the same in all of the mixtures, suggesting that the average n-hexadecane conformation does not change regardless of mixture mole fraction or alkyl-chain length.

Figure 3. Viscosities ν for binary mixtures of n-hexadecane (2) with (□) n-propylcycohexane (x1), (■) n-pentylcyclohexane, (△) n-hexylcyclohexane, (▲) n-heptylcyclohexane, (○) n-octylcyclohexane, (●) n-nonylcyclohexane, (◇) n-decylcyclohexane, (◆) n-dodecylcyclohexane at 293.15 K. The lines are fits using the McAllister equation with coefficients given in Table 16.

at 293.15 K and 1 bar are compared to the experimental values in Figure 4. Predicted values for both properties are in good agreement with experiment. The root-mean-squared deviation (RMSD) of the density compared to experiment is only 2.2 and 1.9 kg/m3 for the n-propyl- and n-dodecylcyclohexane mixtures, respectively. This is in agreement with previous work that showed the OPLS-AA and L-OPLS parameters yielded accurate densities at 293.15 K for binary mixtures of n-hexadecane with either benzene, toluene, n-propylbenzene, or n-butylbenzene.41

Table 16. McAllister Equation (eq 14) Coefficient for Mixtures of an Alkycyclohexane (1) from T = (293.15 to 373.15) K and 0.1 MPa T K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15

293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

ν12 2 −1

mm ·s

ν21 2 −1

mm ·s

103·σ 2 −1

mm ·s

n-Propylcyclohexane (1)+ n-Hexadecane (2) 2.43 3.38 14 2.07 2.78 2.8 1.75 2.33 4.1 1.56 1.97 2.2 1.33 1.72 5.1 1.18 1.52 1.9 1.09 1.32 6.4 0.877 1.28 30 n-Heptylcyclohexane (1) + n-Hexadecane (2) 5.4 3.77 4.19 5.4 3.06 3.37 5.5 2.53 2.77 6.7 2.14 2.32 6.8 1.83 1.98 7.0 1.57 1.73 13 1.40 1.48 2.2 1.22 1.35 14 1.12 1.17 1.7 n-Decylcyclohexane (1) + n-Hexadecane (2) 5.51 4.96 15 4.34 3.93 7.7 3.51 3.20 6.6 2.90 2.67 12 2.43 2.25 4.6 2.06 1.94 6.1 1.81 1.67 3.1 1.58 1.48 24 1.42 1.30 4.9

ν12

ν21

2 −1

2 −1

mm ·s

mm ·s

103·σ 2 −1

mm ·s

n-Pentylcyclohexane (1) + n-Hexadecane (2) 2.98 3.75 2.4 2.49 3.04 2.7 2.07 2.55 5.1 1.79 2.13 3.5 1.54 1.84 1.9 1.37 1.61 2.8 1.22 1.38 6.0 1.10 1.26 2.0 n-Octylcyclohexane (1) + n-Hexadecane (2) 4.25 4.44 15 3.44 3.54 7.0 2.82 2.91 5.3 2.36 2.43 6.1 2.01 2.06 5.4 1.72 1.80 14 1.53 1.54 2.4 1.32 1.40 16 1.21 1.21 1.7 n-Dodecylcyclohexane (1) + n-Hexadecane (2) 7.07 5.67 28 5.47 4.46 12 4.35 3.60 6.7 3.55 2.97 5.7 2.96 2.49 4.6 2.52 2.11 4.9 2.17 1.83 2.8 1.87 1.62 11 1.67 1.41 3.0 M

ν12 2 −1

mm ·s

ν21 2 −1

mm ·s

103·σ mm2·s−1

n-Hexylcyclohexane (1) + n-Hexadecane (2) 3.36 3.95 5.1 2.77 3.18 5.4 2.28 2.64 3.4 1.95 2.21 5.9 1.70 1.88 5.0 1.49 1.61 12 1.30 1.43 6.9 1.19 1.24 18 n-Nonylcyclohexane (1) + n-Hexadecane (2) 4.84 3.86 3.15 2.61 2.21 1.90 1.66 1.42 1.30

4.66 3.72 3.03 2.53 2.15 1.86 1.60 1.45 1.25

8.3 6.3 6.7 5.4 5.7 12 1.9 1.6 3.4

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Figure 4. Comparison of calculated densities (A) and isentropic bulk moduli (B) to experimental values. Data for n-propyl- and n-dodecylcyclohexane mixtures are shown in black circles and red squares, respectively. The diagonal lines indicate exact agreement with experiment.

Figure 5. Probability distribution for molecular volume of n-propylcyclohexane (A) and n-dodecylcyclohexane (B) in pure fluids (black) or 50:50 mixtures with n-hexadecane (red, dashed line).

n-dodecylcyclohexane occupy less volume than when they are in pure n-hexadecane. These differences in n-hexadecane molecular volume are reflected in the positive and negative values of excess molar volume for mixtures with n-propylcyclohexane and n-dodecylcyclohexane, respectively. As discussed above, no change in n-hexadecane radius of gyration was observed as a function of composition. Therefore, the differences in molecular volume (and excess molar volume) appear to be due to the relative arrangement of the various molecules within the mixtures. As the alkyl portion of the alkylcyclohexane lengthens, its shape becomes more similar to that of n-hexadecane and the alkyl chains can pack with less disruption. This should lead to a steady decrease in the volume occupied by the n-hexadecane in the mixture. For n-octyl-, n-nonyl- and n-decylcyclohexane the excess molar volumes reach zero within the error of the measurement, which indicates ideal mixing behavior. Negative excess molar volumes indicate a more closely packed structure in the mixtures than in the pure liquids and have been attributed to interstitial accommodation.50 As the alkyl-chain length becomes even longer as in n-dodecylcylohexane, the negative excess molar volume may indicate that the n-alkyl chain portion of the alkylcyclohexane is packing tightly with n-hexadecane, decreasing the average molar volume of the n-hexadecane molecules.

Taken together, these observations indicate that the observed trends in excess molar volume are not due to changing molecular conformations of each molecule type upon mixing. Instead, there are subtle differences in the arrangement of the molecules in mixtures with different n-alkylcyclohexane chain lengths. Voronoi tessellation is a method that calculates the set of points closer to a given atom than any other atom.72 This can be used to calculate the volume occupied by each molecule in a simulation. By calculating the volume of each molecule in each step of the trajectory, a histogram showing the probability of finding a molecule with a given volume can be generated. Figure 5 compares the molecular volumes of pure n-propyl- and n-dodecylcyclohexane in pure liquids to those in 50:50 binary mixtures with n-hexadecane. For both n-alkylcyclohexanes, the probability distributions shift to slightly higher volumes in mixtures compared to the pure components. Similarly, the volume occupied by n-hexadecane depends on whether the molecule is in a pure fluid or a mixture (Figure 6). In 50:50 mixtures with

4. CONCLUSION This work investigates the impact of adding n-alkylcyclohexanes of various alkyl-chain lengths (e.g., n-propylcyclohexane to n-dodecylcyclohexane) to n-hexadecane on mixture density, viscosity, speed of sound, and bulk modulus. Second-order polynomials fit speed of sound data versus mole fraction data, and the McAllister three-body equation successfully modeled viscosities. Excess molar volumes were positive for mixtures of nhexadecane with n-propylcyclohexane and they decreased as the alkyl-chain length on the cyclohexane increased, indicating nonideal behavior for some mixtures. In contrast, ideal behavior was found for speed of sound and viscosity in that excess speeds

Figure 6. Probability distribution for n-hexadecane in pure fluid (black), or in a 50:50 mixture with n-propylcyclohexane (red, long dash line) or n-dodecylcyclohexane (green dashed line).

n-propylcyclohexane, n-hexadecane molecules occupy, on average, more volume than they do in pure n-hexadecane. In contrast, n-hexadecane molecules in a 50:50 mixture with N

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of sound and excess molar Gibbs energies of activation for viscous flow at 293.15 K were not statistically different from zero. A comparison of mixture properties with those of petroleum-based diesel and jet fuel specifications showed that density was fairly well matched by many of the mixtures. Viscosities were comparable to diesel fuel at 313.15 K, and no comparison was done for jet fuel because the temperature used in those specifications is 253.15 K, which is below the freezing point of n-hexadecane. The bulk modulus of jet fuel is best matched by mixtures of n-propylcyclohexane, while that of diesel fuel is matched by mixtures of n-decylcyclohexane or n-dodecylcyclohexane. Molecular dynamics simulations demonstrate that the OPLS-AA and L-OPLS parameters can be used to obtain accurate predictions for density and bulk modulus for n-hexadecane and alkylcyclohexane binary mixtures at 293.15 K. In addition, the simulations provide molecular-level insight into the measured differences in physical properties. They suggest that differences in molecular packing in mixtures with different alkyl chain lengths give rise to different excess molar volumes. These physical properties can be used by researchers studying the combustion of these mixtures as a way to separate the kinetic aspects of combustion from the physical processes involved.

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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.8b00692.

■

A comparison of the measured values of densities of a NISTCertified Toluene Standard with the reported standard values; one, two, and three parameter Redlich− Kister fits to excess molar volume; a comparison of the measured values of an Anton Paar certified viscosity standard APS3 with the reported values; complete set of equations for calculating the excess speed of sound; fits of viscosity using the McCallister equation at all temperatures (PDF)

AUTHOR INFORMATION

Corresponding Author

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

Dianne J. Luning Prak: 0000-0002-5589-7287 Brian H. Morrow: 0000-0002-7462-4540 Paul C. Trulove: 0000-0002-3935-8793 Funding

This work was funded by the Office of Naval Research NEPTUNE program under the direction Maria Medeiros, Grant No. N0001418WX0014. B.H.M. also acknowledges the Research Office at the Naval Academy for partial support. Notes

The authors declare no competing financial interest.

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REFERENCES

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DOI: 10.1021/acs.jced.8b00692 J. Chem. Eng. Data XXXX, XXX, XXX−XXX