Thermophysical Properties of Binary Mixtures of n-Dodecane with n

Article pubs.acs.org/jced

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

Thermophysical Properties of Binary Mixtures of n‑Dodecane with n‑Alkylcyclohexanes: Experimental Measurements and Molecular Dynamics Simulations Dianne J. Luning Prak,*,† Brian H. Morrow,† Jim S. Cowart,‡ Paul C. Trulove,† and Judith A. Harrison† J. Chem. Eng. Data Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 03/27/19. For personal use only.

†

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

‡

S Supporting Information *

ABSTRACT: Thermophysical properties (densities, speeds of sound, bulk moduli, and viscosities) of binary mixtures of n-dodecane with n-alkylcyclohexanes (propyl- to dodecylcyclohexane) were examined at various compositions and temperatures (293.15−333.15 K). Viscosities were analyzed using the McAllister three-body equation, and excess molar Gibbs energies of activation for viscous flow (ΔG*E) at 293.15 K were calculated. Because the ΔG*E values did not differ significantly from zero, the mixtures appear to behave ideally. In contrast, nonzero excess molar volume values obtained both experimentally and using molecular dynamics (MD) simulations suggest nonideal behavior. Excess molar volumes were the most negative for n-dodecylcyclohexane mixtures and increased with decreasing alkyl side-chain length eventually becoming slightly positive for mixtures containing n-propylcyclohexane. MD simulations were able to predict density, isentropic bulk modulus, and dynamic viscosity values, but the accuracy of the calculated densities decreased slightly with increasing temperature. Voronoi tessellation was used to calculate histograms of molecular volumes in the mixtures. The most probable volume of n-dodecane increases or decreases when mixed with n-propylcyclohexane or n-dodecylcyclohexane, respectively. These shifts in molar volume are responsible for the expansion and contraction upon mixing observed in the excess molar volume data. Volume contraction (negative excess molar volume) produces mixture speeds of sound that are faster than ideal (positive excess speed of sound) unless confounded by opposing compressibility differences. Excess speeds of sound were positive for n-dodecylcyclohexane mixtures, decreased as the alkyl side-chain length increased, and were negative for n-propylcyclohexane mixtures.

1. INTRODUCTION Current trends in new energy technology for transportation have focused on either electric energy or bio-based liquid fuels for automotive and jet engine applications. In the area of liquid fuels, some bio-based fuels are mixed with petroleum-based fuels for successful engine operation. These fuels include hydroprocessed esters and fatty acids, which contain mostly linear and branched alkanes, synthetic paraffinic kerosene or isoparaffinic kerosene, which contains branched alkanes, and celluloseor lignin-based fuels, which contain mostly aromatic and alicyclic compounds.1−8 More recently, newer technologies have produced fuels that are drop-in replacements for petroleum-based fuels, such as ReadiJet and ReadiDiesel, which are complex mixtures of organic compounds. These two fuels contain cycloalkanes, linear alkanes, branched alkanes, and aromatic compounds, which are also the classes of compounds found in petroleum-based fuels.9−15 Cycloparaffins made up approximately 42% of a sample of ReadiDiesel and ranged from 20 to 42% in kerosene fuels.9,14 This article not subject to U.S. Copyright. Published XXXX by the American Chemical Society

The combustion of these fuels is a complicated process because of the large number of hydrocarbon components. To simplify the modeling of combustion, researchers prepare hydrocarbon blends containing a few compounds, called surrogate mixtures, which match the fuel’s physical and chemical kinetic properties.16−19 One way to guide the process of component selection for these mixtures is to understand the interaction of the fuel components. In this work, two-component mixtures were prepared from n-alkylcyclohexanes and n-dodecane, which are components of ReadiJet, ReadiDiesel, and petroleumbased fuels, and tested for properties that crucial to the combustion process in engines. Combustion in engines is influenced by chemical kinetics and the physical processes that occur before these reactions Received: November 27, 2018 Accepted: March 14, 2019

A

DOI: 10.1021/acs.jced.8b01135 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Information

a

chemical name

CAS number

n-propylcyclohexane (C9H18) n-pentylcyclohexane (C11H22) n-hexylcyclohexane (C12H24) n-heptylcyclohexane (C13H26) n-octylcyclohexane (C14H28) n-decylcyclohexane (C16H32) n-dodecylcyclohexane (C18H36) n-dodecane (C12H26)

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

Calculated using values in ref 72. suppliers.

b

molar mass (g/mol)a 126.24 154.29 168.32 182.35 196.37 224.42 252.48 170.33

± ± ± ± ± ± ± ±

0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.01

source/lot number

mole fraction purityb

analysis methodb

TCI/J2BQG TCI/FCV01 TCI/X5F4O TCI/FIB01 TCI/BT8CD TCI/FCQ01 TCI/FCQ01 Alfa Aesar 10201309

0.999 0.992 0.988 0.995 0.993 0.994 0.994 0.996

GC GC GC GC GC GC GC GC

Gas−liquid chromatography, as specified in the Certificates of Analysis provided by the chemical

2. MATERIALS The n-dodecane and n-alkylcyclohexanes were used as received from the supplier (Table 1). The mixtures were prepared in ultraclean vials that had caps with Teflon septums. A pipette was used to deliver each component to a clean vial, which was weighed on an analytical balance (Mettler Toledo AG204 analytical balance) after each addition. The masses varied by less than 0.0004 g. After mixing the compounds, the measurements described below were conducted. The molar masses (Table 1) and measured masses were used to calculate the mole fraction, and the combined expanded uncertainty of the mole fraction (level of confidence = 0.95, k = 2) was 0.0001 for most samples. Values that are greater than this are designated as such in the data tables.

begin. Many studies have focused on combustion kinetics of alkylcyclohexanes.20−34 In the current work, some of the properties that influence the processes prior to combustion, such as density, viscosity, and bulk modulus, which are important for fuel pumping and the formation of droplets in an engine’s combustion chamber, are measured. Both the U. S. military and the American Society for Testing and Materials specify the range of acceptable values for density and viscosity.35−37 Bulk modulus is calculated from measured data because engine studies have shown it to impact the time of fuel injection.38−40 Molecular dynamics (MD) simulations have been shown to accurately predict thermophysical properties of hydrocarbon mixtures.41,42 This is particularly useful in cases where properties are problematic to measure or where time and equipment constraints limit the number of properties that can be examined. Previous MD simulations have demonstrated some of the ways the structure of molecules in mixtures that gives rise to observed trends in physical properties. The accuracy of the MD simulation output is linked to the potential energy function, which determines interatomic interactions. A wide variety of potentials exist, each with their own strengths and weaknesses.44 Additionally, potentials might not be transferrable to molecule types, or temperatures and pressures, which were not included in their original parameterization data set. In this work, the accuracy of density, bulk modulus, and dynamic viscosity values predicted using MD simulations for several n-dodecane binary mixtures are assessed. The molecular-level causes of measured and simulated trends in excess molar volume of the binary mixtures examined here are elucidated. Densities, viscosities, and speeds of sound have been measured for some mixtures of cyclohexane and alkylcyclohexanes in linear alkanes (see complete summary in ref 42).42,45−50 Viscosities have been reported for two-component mixtures of cyclohexane with n-alkanes from n-pentane to n-hexadecane; methylcyclohexane in n-hexane, n-dodecane, and n-hexadecane; and n-ethylcyclohexane with n-dodecane and n-hexadecane.47−50 Some speeds of sound data for two-component mixtures of (1) cyclohexane with n-octane, n-heptane, and n-hexane; (2) for methylcyclohexane with n-hexane, n-dodecane, and n-hexadecane; and (3) for n-ethylcyclohexane in n-dodecane and n-hexadecane have also been reported.45,48 Experimental measurements (density, speed of sound, and viscosity) are needed for n-dodecane binary mixtures with alkylcyclohexanes that have a longer alkyl chain. In this study, these properties were measured for n-dodecane with alkylcyclohexanes with several different alkyl chains (dodecyl, decyl, octyl, heptyl, hexyl, pentyl, and propyl). These measurements can help direct the development of surrogate mixtures for bio-based and petroleum-based fuels.

3. METHODS The density and speed of sound were measured at temperatures ranging from (293.15−333.15) K using an Anton Paar DSA 5000M density and sound analyzer. The DSA 5000 M contains two transducers, one emitting and one receiving 3 MHz sound waves, that are used with a time propagation technique to quantify the speed of sound.51 The density and speed of sound of degassed ultrapure water were checked daily, and the density of a NIST-certified density standard (Certificate Standard Reference Material 211d, toluene liquid density-extended range) was measured periodically. For ultrapure (degassed) water, the average speed of sound was 1482.64 ± 0.15 m·s−1 at 293.15 K during the time of this study, which is consistent with 1482.66 m·s−1 provided by the vendor of the DSA 5000M.52 The 0.15 m·s−1 is the expanded uncertainty of the speed of sound (k = 2). For ultrapure (degassed) water, the average density was 998.19 ± 0.01 kg·m−3 during this study, which is consistent with the literature values provided by the instrument vendor, 998.203 kg·m−3.48 The vendor does not provide an error for this value. Density measurements for toluene are compared in the Supporting Information. Hexane and ethanol were used to clean the DSA 5000 M between measurements. Two or more samples of each mixture were measured. The viscosity was measured using an Anton Paar SVM 3001 for temperatures ranging from (293.15−333.15) K. A Paragon Scientific Viscosity reference Standard APS3 was used to check the instrument daily. A comparison of the measured values and the standard values, which is given in the Supporting Information, shows that the measurements are good. Acetone was used to clean the SVM 3001. Two or more samples of each mixture were measured. The expanded uncertainties of density, speed of sound, and viscosity were calculated by multiplying two times the standard B



Article

Table 2. Comparison of the Measured Densities ρ with Literature Values at Pressure p = 0.1 MPaa T/K

measured (kg·m−3)

288.15 293.15

797.42 793.53

298.15

789.63

303.15 313.15 323.15 333.15

785.72 777.88 770.00 762.09

288.15 293.15

807.78 804.13

298.15

800.48

288.15 293.15 298.15

811.34 807.76 804.19

293.15

811.00

303.15 313.15 323.15 333.15

803.99 796.95 789.91 782.85

288.15 293.15

817.58 814.13

literature values (kg·m−3) n-Propylcyclohexane 797.44 ± 0.15h 793.00 ± 0.30b, 793.27 ± 0.20b, 793.47 ± 0.05b, 793.54 ± 0.20b, 793.51 ± 0.13h, 793.58 ± 0.15b, 793.7c 789.56 ± 0.20b, 789.58 ± 0.05b, 789.60 ± 0.17h, 789.75 ± 0.15b, 789.74 ± 0.20b 785.73 ± 0.20h, 785.79 ± 0.15b, 785.9c 777.70 ± 0.30b, 778.06 ± 0.24h, 778.1c 770.2c 762.3c n-Pentylcyclohexane 807.07 ± 5b 801.8 ± 2.00b, 802.0 ± 2.00b, 802.6 ± 2.00b, 804.4 ± 3.00b, 804.5f 798.6 ± 3.00b n-Hexylcyclohexane 812.3 ± 1b 806.0 ± 2.00b, 808.2 ± 0.60b, 808.1 ± 0.30b, 808.17g 804.5 ± 0.60b, 804.5 ± 0.30b, 804.52g 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 n-Octylcyclohexane 817.80 ± 0.74b 814.31 ± 0.76b, 813.9 ± 0.5b

T/K

measured (kg·m−3)

298.15 303.15 313.15 323.15 333.15

810.67 807.21 800.28 793.35 786.41

288.15 293.15 298.15 303.15 333.15

821.93 818.54 815.16 811.78 791.49

293.15

822.36

288.15 293.15 298.15 303.15 313.15 323.15 333.15

752.35 748.72 745.09 741.46 734.18 726.88 719.53

literature values (kg·m−3) n-Octylcyclohexane 810.84 ± 0.76b 807.36 ± 0.78b 800.40 ± 0.78b 793.45 ± 0.82b 786.40 ± 0.05b, 786.49 ± 0.86b n-Decylcyclohexane 821.90 ± 0.3b 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 n-Dodecane 752.80 ± 0.28h, 753.15 ± 0.5%i 749.09 ± 0.28h, 749.44 ± 0.2%i 745.39 ± 0.28h, 745.45e, 745.73 ± 0.2%i 741.70 ± 0.29h, 742.03 ± 0.2%i 734.33 ± 0.30h, 734.64 ± 0.2 %i 726.99 ± 0.32h, 727.26 ± 0.2 %i 719.64 ± 0.33h, 719.86 ± 0.2 %i

Standard uncertainties u are u(T) = 0.05 K and u(p) = 0.001 MPa, and expanded uncertainties Uc are Uc(ρ) = 0.7 kg·m−3. Instrumental precision is small in comparison to the error introduced by sample purity. The average pressure for these measurements was 0.102 MPa. bReference 73 and its correlations: n-propylcyclohexane: ρ/kg·m3 = 1070.63 − [1.10742 × T/K] + [ 5.52915 × 10−4 (T/K)2]; n-hexylcyclohexane: ρ/kg·m3 = 1042.85 − [0.800 × T/K]; n-octylcyclohexane: ρ/kg·m3 = 1018.27 − [0.695723 × T/K]. cReference 64. dReference 74. eReference 79. f Reference 75. gReference 76. hReference 77 with the following correlations: n-dodecane: ρ/kg·m3 = 1046.13 − [1.49513 × T/K] + [2.35839 × 10−3 (T/K)2] − [2.43796 × 10−6 (T/K)3]. iReference 78. a

developed for n-alkanes were used to model n-dodecane, as well as the alkyl chains of the n-alkylcyclohexanes.55 The conjugate gradient algorithm was used to minimize the energy of each simulation cell at the start of each simulation. Minimization was followed by a 100 ps equilibration stage using an ensemble where the temperature T, number of atoms N, and volume V are all held constant, known as the NVT ensemble. Temperature was held constant at the target value using a Nosé−Hoover thermostat.56 After equilibration, the system T and pressure P were held constant using a Nosé−Hoover thermostat and barostat, respectively, so that each system could be subjected to 10 ns of NPT dynamics.56 The pressure for all simulations was set to 1.0 bar, and simulations were performed at temperatures of 293.15, 313.15, and 333.15 K. All bonds between carbon and hydrogen were held to their equilibrium length using the SHAKE algorithm.57 This allowed a 2.0 fs time step to be used in the simulations. Long-range electrostatic interactions were calculated using the particle− particle particle-mesh method.58 Coulombic and short-range Lennard−Jones interactions were truncated at 13 Å. Standard long-range corrections were applied to the system energy and pressure to account for the truncated Lennard−Jones interactions.59 Results were averaged over the final 8 ns of each NPT simulation for each configuration and temperature, and the

deviation of each measurement. This calculation produces the 95% confidence intervals for substances that follow a normal distribution. Error propagation was used for values derived in this work. The variances of each contributing factor were added; the square root was taken of the sum; and the resulting standard deviation was multiplied by 2. Binary mixtures of n-dodecane with either n-dodecylcyclohexane or n-propylcyclohexane at alkylcyclohexane mole fractions of 0, 0.2, 0.4, 0.5, 0.6, 0.8, and 1.0 were examined using MD simulations. Initial configurations were generated by randomly placing 500 total molecules within a cubic simulation box using the program Packmol.53 Simulation cells were constructed by using the volume needed to match the experimental density, then increasing the length of each side by 5 Å to facilitate the packing process. For each composition, 5 different random initial configurations were generated. These configurations were used to run independent simulations for each composition, temperature, and pressure examined. The ring portion of the n-alkylcyclohexanes was modeled using the all-atom optimized potential for liquid simulation54 (OPLS-AA) force field. Previous studies have shown that for long-chain n-alkanes (10 carbon atoms or more), the OPLSAA parameters can give inaccurate results for density and other properties.55 With that in mind, the L-OPLS parameters C



Article

Table 3. Density ρ of n-Alkylcyclohexanes (1) in n-Dodecane (2) from Temperature T = (288.15−333.15) K and Pressure p = 0.1 MPaa T/K

x1

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 752.35 748.72 745.09 741.46 734.19 726.88 719.53

0.1007 755.55 751.91 748.27 744.62 737.32 729.98 722.61

0.2001 758.92 755.26 751.61 747.95 740.61 733.24 725.82

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 752.35 748.72 745.09 741.46 734.19 726.88 719.53

0.1009 757.14 753.52 749.90 746.27 738.99 731.68 724.33

0.2001 761.98 758.36 754.73 751.10 743.83 736.51 729.17

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 752.35 748.72 745.09 741.46 734.19 726.88 719.53

0.1009 757.85 754.24 750.61 746.99 739.73 732.44 725.11

0.1998 763.33 759.72 756.11 752.50 745.25 737.97 730.66

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 752.35 748.72 745.09 741.46 734.19 726.88 719.53

0.1002 758.60 754.98 751.36 747.74 740.48 733.20 725.89

0.2010 764.82 761.22 757.61 754.01 746.79 739.54 732.26

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 752.35 748.72 745.09 741.46 734.19 726.88 719.53

0.1000 759.33 755.72 752.11 748.50 741.26 734.00 726.70

0.1998 766.24 762.65 759.06 755.45 748.26 741.03 733.78

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 752.35 748.72 745.09 741.46 734.19 726.88 719.53

0.1003 760.76 757.16 753.56 749.96 742.75 735.51 728.24

0.2194 770.26 766.69 763.13 759.57 752.43 745.28 738.08

288.15 293.15 298.15 303.15 313.15

0.000 752.35 748.72 745.09 741.46 734.19

0.1005 762.18 758.60 755.01 751.42 744.23

0.2001 771.24 767.69 764.14 760.58 753.48

n-Propylcyclohexane (1) in n-Dodecane (2) 0.3001 0.4011 0.5000 0.6004 762.54 766.49 770.63 775.15 758.87 762.80 766.92 771.42 755.20 759.11 763.20 767.68 751.53 755.41 759.48 763.93 744.15 747.98 752.01 756.42 736.75 740.52 744.50 748.86 729.30 733.02 736.95 741.26 n-Pentylcyclohexane (1) in n-Dodecane (2) 0.3003 0.4009 0.5001 0.6000 767.03 772.26 777.64 783.17 763.41 768.64 774.02 779.55 759.79 765.01 770.39 775.92 756.16 761.38 766.76 772.28 748.88 754.10 759.47 764.99 741.57 746.79 752.16 757.67 734.22 739.44 744.80 750.31 n-Hexylcyclohexane (1) in n-Dodecane (2) 0.3001 0.4001 0.5004 0.5996 768.99 774.72 780.57 786.46 765.39 771.13 776.99 782.88 761.78 767.53 773.39 779.29 758.17 763.92 769.79 775.70 750.94 756.70 762.59 768.50 743.68 749.46 755.35 761.28 736.38 742.18 748.09 754.02 n-Heptylcyclohexane (1) in n-Dodecane (2) 0.3000 0.3998 0.5002 0.5999 771.01 777.16 783.44 789.63 767.42 773.59 779.88 786.08 763.84 770.01 776.32 782.53 760.25 766.42 772.75 778.98 753.05 759.25 765.60 771.86 745.82 752.06 758.43 764.71 738.56 744.84 751.23 757.54 n-Octylcyclohexane (1) in n-Dodecane (2) 0.3002 0.3998 0.4948 0.5997 772.95 779.63 785.90 792.69 769.38 776.08 782.36 789.17 765.81 772.53 778.83 785.65 762.24 768.97 775.29 782.13 755.08 761.84 768.19 775.07 747.89 754.69 761.08 768.00 740.68 747.52 753.94 760.90 n-Decylcyclohexane (1) in n-Dodecane (2) 0.3002 0.4004 0.4999 0.5993 776.43 783.80 790.80 797.51 772.89 780.28 787.31 794.05 769.34 776.76 783.81 790.58 765.80 773.24 780.31 787.10 758.71 766.19 773.32 780.16 751.59 759.13 766.31 773.20 744.46 752.05 759.29 766.23 n-Dodecylcyclohexane (1) in n-Dodecane (2) 0.2980 0.4031 0.5001 0.6005 779.52 787.80 794.95 801.89 776.00 784.32 791.49 798.47 772.48 780.84 788.04 795.04 768.97 777.36 784.59 791.62 761.93 770.40 777.69 784.77 D

0.6995 780.00 776.23 772.46 768.68 761.11 753.49 745.82

0.7998 785.31 781.51 777.71 773.89 766.24 758.55 750.81

0.8997 791.13 787.31 783.46 779.60 771.86 764.09 756.27

1.0000 797.42 793.53 789.63 785.72 777.88 770.00 762.09

0.7003 789.00 785.37 781.74 778.10 770.80 763.48 756.11

0.8136 795.88 792.25 788.61 784.97 777.66 770.33 762.96

0.9082 801.77 798.13 794.48 790.84 783.52 776.17 768.80

1.0000 807.78 804.13 800.48 796.82 789.49 782.14 774.75

0.7005 792.54 788.97 785.38 781.79 774.60 767.39 760.16

0.7996 798.63 795.06 791.48 787.89 780.72 773.52 766.29

0.8997 804.88 801.31 797.74 794.16 786.99 779.80 772.58

1.0000 811.34 807.76 804.19 800.61 793.43 786.25 779.05

0.6998 795.81 792.27 788.73 785.18 778.09 770.98 763.84

0.8001 802.09 798.57 795.04 791.51 784.43 777.34 770.22

0.8998 808.24 804.73 801.21 797.69 790.64 783.57 776.49

1.0000 814.51 811.00 807.49 803.98 796.95 789.91 782.85

0.6996 798.98 795.48 791.98 788.47 781.45 774.42 767.37

0.7999 805.34 801.86 798.37 794.88 787.89 780.88 773.86

0.9000 811.48 808.01 804.53 801.06 794.10 787.14 780.16

1.0000 817.58 814.13 810.67 807.20 800.28 793.35 786.41

0.7001 804.03 800.58 797.13 793.68 786.78 779.88 772.96

0.8005 810.28 806.85 803.42 799.99 793.13 786.28 779.42

0.8991 816.18 812.78 809.36 805.95 799.14 792.33 785.51

1.0000 821.93 818.54 815.16 811.78 805.02 798.26 791.49

0.7003 808.42 805.01 801.61 798.20 791.40

0.7997 814.50 811.11 807.73 804.35 797.60

0.8994 820.23 816.87 813.51 810.15 803.45

1.0000 825.71 822.36 819.02 815.68 809.03



Article

Table 3. continued T/K 323.15 333.15

x1 726.88 719.53

737.02 729.78

746.35 739.20

n-Dodecylcyclohexane (1) in n-Dodecane (2) 754.88 763.43 770.78 777.93 747.81 756.44 763.86 771.08

784.61 777.81

790.86 784.13

796.76 790.08

802.38 795.75

Standard uncertainties u are u(T) = 0.05 K and u(p) = 0.001 MPa, expanded uncertainties Uc are Uc(ρ) = 0.7 kg·m−3, and combined expanded uncertainties Uc are Uc(x1) = 0.0001 for mole fractions less than 0.71 and Uc(x1) = 0.0002 for the higher mole fractions. Instrumental precision is small in comparison to the error introduced by sample purity. The average pressure for these measurements was 0.102 MPa. x1 is the mole fraction of alkylcyclohexane in the n-dodecane mixture. a

total sampling time for each mixture was 40 ns. Isentropic bulk modulus and density values were calculated from the simulations and compared to the experimentally measured values. Isentropic bulk modulus was calculated from volume and energy fluctuations in NPT simulations, as described in Morrow et al.43 Uncertainties were estimated from the standard deviation of the values obtained from each of the five independent trajectories. Molecular volumes were calculated via the Voronoi tessellation method using Voro+ +.60 All NPT simulations were conducted using the LAMMPS MD package.61 Dynamic viscosities were calculated from NVT simulations via the Green−Kubo method, from the integration of the pressure tensor autocorrelation function η=

V kBT

∫0

Only the cyclohexanes with alkyl chains longer than pentylcyclohexane can form mixtures that would meet the military specification for military diesel fuel F-76 (800−876) kg·m−3.37 Mixtures of n-dodecane with the longer chain alkylcyclohexanes had densities similar to that of one lot of ReadiDiesel (819.4 kg·m−3) but not another (830.5 kg·m−3).10,11 The excess molar volumes (VEm) for binary mixtures of n-dodecane with each alkylcyclohexane were computed by VmE =

(2)

The variables are density of the mixture ρm, pure component densities ρ1 and ρ2, pure component molar masses M1 and M2, and the mole fractions x1 and x2 with component 1 being an alkylcyclohexane and component 2 being n-dodecane. The excess molar volumes at 293.15 K are shown in Figure 1 and tabulated in Table 4.

∞

⟨Pαβ(t ) ·Pαβ(0)⟩dt

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

(1)

where kB is the Boltzmann constant, Pαβ is the αβ element of the pressure tensor, and the angled brackets represent the ensemble average. Because of the difficulty of obtaining converged viscosities from equilibrium MD simulations, we follow the time decomposition method proposed by Zhang et al.62 Briefly, many independent NVT trajectories are run, with the integral of the pressure tensor autocorrelation function calculated for each trajectory. The integral as a function of time is averaged over all of the trajectories and is then fit to a double-exponential function. The viscosity is then determined from the plateau region of this fitted function. For full details of the procedure, see Zhang et al.62 The viscosity simulations were performed with system sizes equal to the average values obtained from the NPT simulations. Independent trajectories were initiated by using different random initial velocities. For each composition and temperature, 20 independent 10 ns NVT runs were performed. Pressure tensor components were saved every 10 time steps (20 fs), and viscosities were calculated using the final 9.0 ns of each trajectory, with the Green−Kubo relation applied to the three off-diagonal components of the pressure tensor. Uncertainties were estimated by the standard deviation of four viscosities calculated using five trajectories each. All NVT simulations were performed using Gromacs, version 2016.63

Figure 1. Excess molar volumes for binary mixtures of n-dodecane with blue ○ n-dodecylcyclohexane (x1), Δ n-decylcyclohexane (x1), green ■ n-octylcyclohexane (x1), □ n-heptylcyclohexane (x1), pink ⧫ n-hexylcyclohexane (x1), ◊ n-pentylcyclohexane (x1), and yellow ▲ n-propylcycohexane (x1) from the current study and with × n-ethylcyclohexane (x1), and red ● n-methylcyclohexane (x1) from ref 48 (to show they follow the same trend) at 293.15 K. The lines are fits using the Redlich−Kister expression with values of the coefficients given in Table 6.

The excess molar volumes of n-dodecane/n-propylcyclohexane mixtures were positive and small, indicating an expansion upon mixing. When considering the error as the propagated standard deviation, the values differ from zero. If the combined expanded uncertainty is used, then the values do not differ statistically from zero. Excess molar volumes decrease with increasing n-alkyl chain length on the cycloalkane until negative values are found for mixtures with alkyl chain lengths equal to or longer than n-heptylcyclohexane. To show that smaller n-akylcyclohexanes also follow this trend, excess more volumes for methyl- and n-ethylcyclohexane are included in Figure 1.48 Binary mixtures of n-heptane with methyl-, n-ethyl-, n-propyl-, and n-butylcyclohexane have also been shown to also have declining excess molar volumes of −0.017,

4. RESULTS 4.1. Density. A comparison of the measured and literature values of density shows agreement within their combined expanded uncertainties (Table 2). The densities of the twocomponent mixtures increase as the mole fraction of the alkylcyclohexane increases (Table 3). This table also shows that mixtures of each alkylcyclohexane with n-dodecane can be found to fall within the fuel density specifications set at 288.15 K: 755−840 kg·m−3 for commercial Jet A, 788−845 kg·m−3 for military JP-5, and 751−802 kg·m−3 for military JP-4.35,36 E



Article

Table 4. Excess Molar Volumes, VE, Excess Speed of Sound cE, and Excess Free Energies of Activation of Flow ΔG*E at Temperature T = 293.15 K for Binary Mixtures of n-Alkylcyclohexane (1) and n-Dodecane (2) at p = 0.1 MPaa x1

Vem (cm3·mol−1)

ΔG*E (kJ·mol−1)

cE (m·s−1)

n-Propylcyclohexane (1) + n-Dodecane (2) 0.1007 0.02 ± 0.18 0.0 0 0.2001 0.04 ± 0.10 0.0 0 0.3001 0.05 ± 0.07 0.1 −1 0.4011 0.06 ± 0.06 0.1 −1 0.5000 0.06 ± 0.06 0.1 −1 0.6004 0.06 ± 0.06 0.1 −1 0.6995 0.05 ± 0.08 0.1 −1 0.7998 0.04 ± 0.10 0.1 −1 0.8997 0.01 ± 0.17 0.0 0 n-Heptylcyclohexane (1) + n-Dodecane (2) 0.1002 −0.03 ± 0.22 0.0 1 0.2010 −0.03 ± 0.11 0.0 2 0.3000 −0.05 ± 0.09 −0.1 3 0.3998 −0.04 ± 0.07 −0.1 3 0.5002 −0.05 ± 0.07 −0.1 4 0.5999 −0.05 ± 0.07 −0.1 4 0.6998 −0.03 ± 0.09 −0.1 3 0.8001 −0.04 ± 0.12 −0.1 3 0.8998 −0.01 ± 0.24 0.0 1 0.1005 0.2001 0.2980

−0.07 ± 0.23 −0.12 ± 0.13 −0.15 ± 0.11

0.1 0.1 0.1

4 7 8

Vem (cm3·mol−1)

x1

ΔG*E (kJ·mol−1)

cE (m·s−1)

n-Pentylcyclohexane (1) + n-Dodecane (2) 0.1009 0.00 ± 0.21 0.0 1 0.2001 0.04 ± 0.10 0.0 0 0.3001 0.05 ± 0.07 0.1 −1 0.4011 0.06 ± 0.06 0.1 −1 0.5000 0.06 ± 0.06 0.1 −1 0.6004 0.06 ± 0.06 0.1 −1 0.6995 0.05 ± 0.08 0.1 −1 0.8136 0.01 ± 0.12 0.0 1 0.9082 0.02 ± 0.24 0.0 0 n-Octylcyclohexane (1) + n-Dodecane (2) 0.1000 −0.03 ± 0.13 0.0 2 0.1998 −0.07 ± 0.12 0.0 3 0.3002 −0.07 ± 0.09 0.0 5 0.3998 −0.09 ± 0.08 −0.1 5 0.4948 −0.10 ± 0.07 −0.1 6 0.5997 −0.09 ± 0.08 −0.1 5 0.6996 −0.06 ± 0.09 −0.1 5 0.7999 −0.06 ± 0.12 0.0 4 0.9000 −0.03 ± 0.24 0.0 2 n-Dodecyclohexane (1) + n-Dodecane (2) 0.4031 −0.16 ± 0.09 0.1 9 0.5001 −0.16 ± 0.08 0.1 9 0.6005 −0.15 ± 0.08 0.1 9

x1

Vem (cm3·mol−1)

ΔG*E (kJ·mol−1)

cE (m·s−1)

n-Hexylcyclohexane (1) + n-Dodecane (2) 0.1009 0.00 ± 0.22 0.0 1 0.1998 0.00 ± 0.11 0.0 2 0.3001 −0.01 ± 0.09 0.0 2 0.4001 0.00 ± 0.07 −0.1 2 0.5004 0.00 ± 0.07 −0.1 3 0.5996 0.00 ± 0.07 −0.1 3 0.7005 0.00 ± 0.09 0.0 2 0.7996 0.01 ± 0.12 0.0 2 0.8997 0.01 ± 0.24 0.0 1 n-Decyclohexane (1) + n-Dodecane (2) 0.1003 −0.05 ± 0.23 0.0 3 0.2194 −0.09 ± 0.12 0.0 5 0.3002 −0.11 ± 0.10 0.0 6 0.4004 −0.13 ± 0.09 0.0 7 0.4999 −0.14 ± 0.08 0.0 7 0.5993 −0.14 ± 0.09 0.0 7 0.7001 −0.11 ± 0.09 0.0 6 0.8005 −0.09 ± 0.13 0.0 4 0.8991 −0.06 ± 0.23 0.0 3 0.7003 0.7997 0.8994

−0.13 ± 0.10 −0.10 ± 0.15 −0.05 ± 0.23

0.1 0.1 0.1

8 6 3

a

x1 is the mole fraction of alkylcyclohexane in the n-dodecane 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 0.71 and Uc(x1) = 0.0002 for the higher mole fractions, Uc(Δc) = 2 m·s−1, and Uc(ΔG*E) are between 0.8 and 1.0 kJ·mol−1 (level of confidence = 0.95, k = 2).

Table 5. Comparison of Excess Molar Volumes, VE in cm3·mol−1 at Equal Mole Fractions of n-Alkycyclohexane (1) in n-Dodecane (2) from Temperature T = (288.15−333.15) K and Pressure p = 0.1 MPaa T/K

propyl-cyclohexane x1 = 0.5000

pentyl-cyclohexane x1 = 0.5001

hexyl-cyclohexane x1 = 0.5004

heptyl-cyclohexane x1 = 0.5002

octyl-cyclohexane x1 = 0.4948

decyl-cyclohexane x1 = 0.4999

dodecyl-cyclohexane x1 = 0.5001

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.07 0.06 0.06 0.05 0.04 0.04 0.03

0.02 0.02 0.01 0.01 0.00 0.00 −0.01

0.00 0.00 −0.01 −0.01 −0.02 −0.03 −0.04

−0.05 −0.05 −0.06 −0.06 −0.07 −0.08 −0.09

−0.09 −0.10 −0.10 −0.11 −0.12 −0.13 −0.14

−0.13 −0.14 −0.14 −0.15 −0.16 −0.17 −0.19

−0.15 −0.16 −0.17 −0.18 −0.20 −0.22 −0.25

a x1 is the mole fraction of alkylcyclohexane in the n-dodecane mixture. The combined expanded uncertainties Uc are Uc(x1) = 0.0001 for mole fractions less than 0.71 and Uc(x1) = 0.0002 for the higher mole fractions, and Uc(VE) are between 0.06 and 0.08 m·s−1 cm3·mol−1 (level of confidence = 0.95, k = 2).

−0.143, −0.237, and −0.301 cm3·mol−1, respectively, as the number of alkyl carbons in the alkylcyclohexanes increased (methyl-, n-ethyl-, n-propyl-, and n-butylcyclohexane).46 Temperature had a small effect on excess molar volume. As the temperature increased from 288.15 to 333.15 K, the excess molar volumes at x1 = 0.5 decrease steadily (Table 5). If the propagated standard deviations are used for comparison, then the decline is significant, but if the combined expanded uncertainties are used, then the decline is only significant for the n-dodecylcyclohexane. It may be that the higher temperatures allow more movement of the molecules so that they can pack more closely together. A Redlich−Kister type expression was fit to the excess molar volume VmE = x1x 2(Ao + A1(x1 − x 2))

The variables are adjustable parameters Ao and A1 and mole fractions x1 and x2 of the alkylcyclohexane and n-dodecane, respectively. The fits are good as shown in Figure 1 with the adjustable parameters given in Table 6 for 293.15 K. 4.2. Speed of Sound. Only the speeds of sound of n-dodecane and n-propylcyclohexane could be compared to literature values because the values for other compounds were not available (Table 7). The speeds of sound of n-dodecane match those in the literature within the error of the measurements. The values for propylcyclohexane, however, are greater than the speeds of sound published by Laesecke et al.64 The purity differences may be the reason for the discrepancy. In the current study, the purity is 99.5%, which is greater than the 96.68% reported by Laesecke et al.64 There is also a small difference in atmospheric pressure between the two systems (101 kPa in the current study and 88 kPa in their study).

(3) F



Article

Douheret et al.68 provide a series of equations that calculate excess speed of sound, cE using and the speed of sound of an ideal mixture, cID, and the measured value for the mixture, cmix

Table 6. Parameters for Redlich−Kister Equation, Eq 3, for Excess Molar Volume Vm E for the Systems for Binary Mixtures of n-Alkylcyclohexane (1) and n-Dodecane (2) at Temperature T = 293.15 K and Pressure p = 0.1 MPaa −1

−1

−1

Ao (cm ·mol ) A1 (cm ·mol ) σ (cm ·mol ) 3

cycloalkane n-propylcyclohexane n-pentylcyclohexane n-hexylcyclohexane n-heptylyclohexane n-octylcyclohexane n-decylcyclohexane n-dodecylcyclohexane

0.246 0.087 −0.005 −0.202 −0.362 −0.556 −0.658

3

0.024 0.000 0.061 0.028 0.027 −0.020 0.115

3

0.005 0.010 0.004 0.008 0.010 0.005 0.006

288.15 293.15 298.15 303.15 313.15 323.15 333.15

ID

ÉÑ ÅÄÅ ÅÅ ϕ1V1α12 ϕ2V2α2 2 VmID(α ID)2 ÑÑÑÑ Å ÑÑ = ϕ1κ1 + ϕ2κ2 + T ÅÅÅ + − ÅÅ C p,1 C p,2 C pID ÑÑÑÑ ÅÇ Ö

(7)

(8)

The variables are temperature T, thermal expansion coefficient αi, isobaric heat capacity Cpi, density ρ, isentropic compressibility κ, volume fraction ϕi, molar volume Vi, ideal therID mal expansion coefficient CID p , ideal heat capacity Cp , and ID ideal molar volume Vm where “i” is the specific component value. The Supporting Information contains the complete set of equations used to calculate these variables. The excess speeds of sound are small negative values for propylcyclohexane mixtures that do not differ from zero when considering the combined expanded uncertainty (Table 4). The speed of sound deviations increase as the alkyl chain length on the cycloalkane increases until values of 9 m·s−1 are found for n-dodecylcyclohexane in mixtures with x1 = 0.5. Two factors have been reported to contribute to excess speed of sound: excess molar volume and liquid compressibility, which can depend on intermolecular forces and molecular shape and orientation.69 If compressibility is not a confounding factor, then the sign of excess molar volume will differ from that of excess speed of sound. For example, it would be expected that volume contraction (negative excess molar volume) would be expected to produce faster speeds of sound (positive excess speed of sound) because the closer molecules would transmit sound more quickly than those farther apart. All mixtures studied herein show this difference in sign, except n-hexylcyclohexane in n-dodecane mixtures where the excess molar volumes are zero. 4.3. Viscosity. A comparison of the viscosities of n-dodecane and the n-alkylcylohexanes with literature values shows that agreement is found for many of the compounds within their combined expanded uncertainties (Table 11). For the n-pentylcyclohexane, n-decylcyclohexane, n-dodecylcyclohexane viscosities that do not agree, the largest percentage deviations from literature values are 2%. For the two-component mixtures, increasing the mole fraction of the n-propylcyclohexane produces a decrease in viscosity, whereas increasing the mole fractions of the other alkycylcohexanes produces an increase of viscosity in the mixtures (Figure 3, Table 12). The military diesel fuel specification requires viscosity to be in the range of 1.4 and 4.3 mm2·s−1 at 313.15 K.36 Mixtures could be prepared from any of the alkylcyclohexanes with n-dodecane to meet this specification. Two ReadiDiesels prepared for different applications had viscosities of 2.096 and 2.67 mm2·s−1.10,11 Only mixtures of n-dodecane with n-octylcyclohexane, n-decylcyclohexane, or n-dodecylcyclohexane could be used for the higher viscosity sample, whereas those mixtures and the mixture of n-heptylcyclohexane with n-dodecane could be used for the lower viscosity sample.

literature

n-Propylcyclohexane 1307.7 1307.1b 1266.6 1265.5b 1226.2 1224.7b 1186.5 1184.7b 1147.7 1145.4b n-Dodecane 1317.2 1321.7 ± 0.5%c 1297.7 1297d, 1298.25e, 1301.2 ± 0.5%c 1278.2 1280.9 ± 0.5%c 1259.0 1259d, 1260.9 ± 0.5 %c, 1261.2f 1221.1 1221.9 ± 0.5%c 1184.0 1183.8 ± 0.5%c 1147.8 1146.6 ± 0.5%c, 1147.7f

a

Standard uncertainties u are u(T) = 0.05 K and u(p) = 0.001 MPa, and expanded uncertainties Uc are Uc(c) = 0.8 m·s−1 The average pressure for these measurements was 0.102 MPa, which the values for n-propylcyclohexane were taken at 88 kPa. bReference 64. cReference 78. d Reference 80. eReference 81. fReference 79.

As the alkylcyclohexane mole fraction increases, the speed of sound increases, except for n-propylcyclohexane at higher temperatures (Table 8, Figure 2). The speed of sound-mole fraction data were fit to polynomials of increasing order until the error of the fits was smaller than the error in the measurements, and the polynomials are given in Table 9. Figure 2 shows that the data at 298.15 K are fit well by the polynomials. The isentropic bulk modulus of the mixtures, Bs, was calculated from density, ρ, and speed of sound, c, from Bs = ρ × c 2

(6)

κ

Table 7. Comparison of the Measured Speeds of Sound c, m·s−1, of with Literature Valuesa

293.15 303.15 313.15 323.15 333.15

c ID = (ρ ID κ ID)

κ ID = ϕ1ρ1 + ϕ2ρ2

The σ is the standard error of the fit.

this studya

(5)

The ideal density, ρID, and ideal isentropic compressibility, κID, are given by

a

T/K

c E = cmix − c ID

(4)

with the results given in Table 10. The values of bulk modulus increase with increasing concentration of the n-alkylcyclohexanes in n-dodecane. This table also shows that mixtures of each alkylcyclohexane with n-dodecane can be prepared to match the reported bulk moduli of petroleum-based jet fuel (1389 MPa) and ARA jet fuel (1393 MPa) at 293.15 K, but only mixtures containing n-dodecylcyclohexane have bulk moduli that match that reported for diesel fuel (1590 and 1612 MPa).11,65−67 Mixtures of n-dodecane with alkylcycylohexanes with alkyl groups of six carbons or longer can be made that have bulk modulus values that match that of a ReadiDiesel (1532 MPa).12 G



Article

Table 8. Speeds of Sound c, m·s−1, of n-Alkylcyclohexanes (1) in n-Dodecane (2) from Temperature T = (288.15−333.15) K and Pressure p = 0.1 MPaa T/K

x1

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.0000 1317.2 1297.7 1278.2 1259.0 1221.1 1184.0 1147.8

0.1007 1317.5 1297.9 1278.4 1259.1 1221.1 1183.9 1147.6

0.2001 1317.8 1298.2 1278.6 1259.2 1221.1 1183.7 1147.3

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.0000 1317.2 1297.7 1278.2 1259.0 1221.1 1184.0 1147.8

0.1009 1321.1 1301.6 1282.5 1263.2 1225.5 1188.3 1151.9

0.2001 1324.9 1305.5 1286.2 1267.1 1229.3 1192.1 1155.8

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.0000 1317.2 1297.7 1278.2 1259.0 1221.1 1184.0 1147.8

0.1009 1322.7 1303.2 1283.8 1264.6 1226.8 1189.7 1153.6

0.1998 1328.2 1308.8 1289.4 1270.2 1232.4 1195.4 1159.3

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 1317.2 1297.7 1278.2 1259.0 1221.1 1184.0 1147.8

0.1002 1324.4 1304.9 1285.5 1266.3 1228.4 1191.3 1155.3

0.2010 1331.8 1312.4 1293.1 1273.9 1236.2 1199.2 1163.2

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 1317.2 1297.7 1278.2 1259.0 1221.1 1184.0 1147.8

0.1000 1326.2 1306.9 1287.6 1268.4 1230.7 1193.7 1157.6

0.1998 1335.1 1315.8 1296.5 1277.3 1239.6 1202.7 1166.9

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 1317.2 1297.7 1278.2 1259.0 1221.1 1184.0 1147.8

0.1003 1329.7 1310.3 1290.9 1271.8 1234.1 1197.2 1161.3

0.2194 1344.0 1324.7 1305.4 1286.4 1248.9 1212.3 1176.5

288.15 293.15 298.15

0.000 1317.2 1297.7 1278.2

0.1005 1333.2 1313.7 1294.4

0.2001 1348.0 1328.7 1309.5

n-Propylcycylohexane (1) in n-Dodecane (2) 0.3001 0.4011 0.5000 0.6004 1318.2 1319.3 1320.1 1320.9 1298.6 1299.8 1300.2 1300.8 1279.0 1280.3 1280.8 1280.8 1259.5 1260.9 1261.1 1261.0 1221.3 1222.3 1222.6 1222.1 1183.8 1184.5 1184.6 1183.9 1147.3 1147.5 1147.3 1146.7 n-Pentylcyclohexane (1) in n-Dodecane (2) 0.3003 0.4009 0.5001 0.6000 1329.1 1333.4 1338.1 1343.0 1309.6 1313.9 1318.6 1323.4 1290.3 1294.6 1299.2 1304.0 1271.2 1275.4 1280.0 1284.8 1233.4 1237.6 1242.1 1246.8 1196.2 1200.3 1204.8 1209.6 1159.8 1163.9 1168.3 1172.9 n-Hexylcyclohexane (1) in n-Dodecane (2) 0.3001 0.4001 0.5004 0.5996 1334.2 1340.2 1346.3 1352.5 1314.7 1320.7 1326.9 1333.2 1295.3 1301.3 1307.5 1313.8 1276.1 1282.1 1288.3 1294.6 1238.3 1244.3 1250.5 1256.8 1201.3 1207.4 1213.6 1219.8 1165.3 1171.3 1177.6 1183.9 n-Heptylcyclohexane (1) in n-Dodecane (2) 0.3000 0.3998 0.5002 0.5999 1339.3 1346.8 1354.4 1362.0 1319.9 1327.3 1335.1 1342.8 1300.8 1308.0 1316.0 1323.6 1281.8 1288.8 1297.0 1304.7 1244.2 1251.2 1259.6 1267.3 1207.3 1214.3 1222.8 1230.6 1171.2 1178.5 1186.8 1194.6 n-Octylcyclohexane (1) in n-Dodecane (2) 0.3002 0.3998 0.4948 0.5997 1344.1 1353.1 1361.6 1370.8 1324.8 1333.9 1342.3 1351.6 1305.5 1314.8 1323.4 1332.6 1286.4 1295.9 1304.4 1313.8 1248.9 1258.6 1267.1 1276.7 1212.2 1221.9 1230.5 1240.1 1176.4 1186.0 1194.8 1204.5 n-Decylcyclohexane (1) in n-Dodecane (2) 0.3002 0.4004 0.4999 0.5993 1353.5 1364.7 1375.6 1386.2 1334.2 1345.7 1356.6 1367.1 1315.0 1326.8 1337.8 1348.6 1296.0 1308.1 1319.1 1329.7 1258.7 1271.0 1282.2 1292.0 1222.1 1234.7 1246.0 1257.0 1186.5 1199.1 1210.6 1221.8 n-Dodecylcyclohexane (1) in n-Dodecane (2) 0.2980 0.4031 0.5001 0.6005 1361.9 1375.7 1387.9 1400.0 1342.6 1356.6 1368.9 1381.0 1323.5 1337.6 1350.0 1362.1 H

0.6995 1322.1 1301.9 1281.8 1261.8 1222.6 1184.1 1146.7

0.7998 1323.8 1303.4 1283.1 1262.9 1223.3 1184.6 1146.8

0.8997 1326.1 1305.3 1284.7 1264.3 1224.3 1185.1 1146.9

1.0000 1328.6 1307.7 1287.1 1266.6 1226.2 1186.5 1147.7

0.7003 1348.1 1328.5 1309.1 1289.8 1251.7 1214.3 1177.6

0.8136 1354.4 1334.7 1315.2 1295.8 1257.6 1220.1 1183.4

0.9082 1359.9 1340.2 1320.6 1301.1 1262.8 1225.1 1188.4

1.0000 1365.8 1346.0 1326.4 1306.7 1268.2 1230.5 1193.5

0.7005 1359.2 1339.8 1320.4 1301.2 1263.4 1226.4 1190.5

0.7996 1365.9 1346.5 1327.1 1307.8 1270.1 1233.1 1197.1

0.8997 1373.0 1353.4 1334.0 1314.7 1276.9 1239.8 1203.6

1.0000 1380.4 1360.9 1341.4 1322.1 1284.2 1247.1 1211.0

0.6998 1369.8 1350.4 1331.1 1312.1 1274.6 1238.0 1202.4

0.8001 1377.6 1358.3 1339.3 1320.3 1283.0 1246.3 1210.5

0.8998 1385.6 1366.2 1346.9 1327.9 1290.5 1253.9 1218.5

1.0000 1393.6 1374.2 1355.1 1336.1 1298.8 1262.2 1226.7

0.6996 1379.4 1360.3 1341.2 1322.2 1285.1 1248.7 1213.3

0.7999 1388.2 1369.1 1350.2 1331.4 1294.4 1258.1 1222.7

0.9000 1396.9 1377.8 1358.7 1339.9 1302.8 1266.6 1231.5

1.0000 1405.5 1386.4 1367.4 1348.6 1311.6 1275.5 1240.3

0.7001 1396.3 1377.5 1358.8 1340.2 1303.7 1267.7 1232.7

0.8005 1406.3 1387.5 1368.8 1350.4 1313.9 1278.1 1243.2

0.8991 1415.8 1397.1 1378.5 1360.1 1323.7 1288.0 1253.2

1.0000 1425.2 1406.4 1387.7 1369.1 1332.8 1297.2 1262.7

0.7003 1411.3 1392.4 1374.0

0.7997 1421.8 1403.1 1384.7

0.8994 1432.1 1413.3 1395.1

1.0000 1441.5 1422.9 1404.8



Article

Table 8. continued T/K 303.15 313.15 323.15 333.15

x1 1259.0 1221.1 1184.0 1147.8

1275.3 1237.7 1200.9 1165.1

n-Dodecylcyclohexane (1) in n-Dodecane (2) 1304.6 1318.8 1331.3 1343.5 1267.5 1281.9 1294.6 1307.0 1231.1 1245.9 1258.7 1271.3 1195.8 1210.7 1223.8 1236.5

1290.5 1253.1 1216.6 1181.0

1355.4 1319.2 1283.6 1248.9

1366.3 1330.2 1294.8 1260.3

1376.6 1340.7 1305.4 1271.0

1386.3 1350.5 1315.4 1281.4

Standard uncertainties u are u(T) = 0.05 K and u(p) = 0.001 MPa, expanded uncertainties Uc are Uc(c) = 0.9 m·s−1, and combined expanded uncertainties Uc are Uc(x1) = 0.0001 for mole fractions less than 0.71 and Uc(x1) = 0.0002 for the higher mole fractions. The average pressure for these measurements was 0.102 MPa. x1 is the mole fraction of alkylcyclohexane in the n-dodecane mixture. a

The kinematic viscosity-mole fraction data were fit to the McAllister three-body model70 ln νm = x13 ln ν1 + 3x12x 2 ln ν1,2 + 3x1x 2 2 ln ν2,1 + x 2 3 ij M yz ln ν2 − lnjjjx1 + x 2 2 zzz + 3x12x 2 j M1 z{ k M yzzy M yzzy ji 1 ij ji 1 ij lnjjjj jjj2 + 2 zzzzzzz + 3x1x 2 2 lnjjjj jjj1 + 2 2 zzzzzzz j z j M1 {{ M1 z{{ k3k k3k ij M yz + x 2 3 lnjjj 2 zzz jM z k 1{

Figure 2. Speeds of sound for binary mixtures of n-dodecane with blue ○ n-dodecylcyclohexane (x1), Δ n-decylcyclohexane (x1), green ■ n-octylcyclohexane (x1), □ n-heptylcyclohexane (x1), pink ⧫ n-hexylcyclohexane (x1), ◊ n-pentylcyclohexane (x1), and yellow ▲ n-propylcycohexane (x1) at 293.15 K. The lines are first- and second-order polynomial fits with coefficients given in Table 9.

(9)

The variables are the kinematic viscosity of the binary mixture νm, mole fractions x1 and x2, kinematic viscosities ν1

Table 9. Correlation of Speed of Sound c to Mole Fraction x1 for Mixtures of n-Alkylcyclohexanes (1) in n-Dodecane (2) at Temperature T and Pressure p = 0.1 MPa along with the Associated Error σa c/m·s−1 = A2x12 + A1x1 + Ao T/K 288.15 293.15 298.15 303.15 313.15 323.15 288.15 293.15 298.15 303.15 313.15 323.15 333.15 288.15 293.15 298.15 303.15 313.15 323.15 333.15 288.15 293.15 298.15 303.15

A2 (m·s−1)

A1 (m·s−1)

Ao (m·s−1)

n-Propylycylohexane (1) in n-Dodecane (2) 10.9 ± 0.6 1317.2 ± 0.3 9.6 ± 0.6 1297.6 ± 0.3 8.2 ± 0.8 1278.3 ± 0.4 6.9 ± 0.9 1258.9 ± 0.4 4.4 ± 1.0 1221.0 ± 0.5 1.9 ± 0.9 1183.7 ± 0.4 n-Pentylcycylohexane (1) in n-Dodecane (2) 13.9 ± 1.2 34.3 ± 1.3 1317.4 ± 0.3 13.1 ± 1.3 34.7 ± 1.3 1297.9 ± 0.3 12.6 ± 1.7 35.0 ± 1.7 1278.6 ± 0.4 11.4 ± 1.5 35.8 ± 1.6 1259.3 ± 0.3 10.5 ± 1.6 36.0 ± 1.7 1221.5 ± 0.4 9.8 ± 1.5 36.1 ± 1.5 1184.3 ± 0.3 9.5 ± 1.2 35.8 ± 1.3 1148.0 ± 0.3 n-Hexylcycylohexane (1) in n-Dodecane (2) 10.0 ± 1.0 53.0 ± 1.0 1317.2 ± 0.2 9.7 ± 0.7 53.3 ± 0.7 1297.7 ± 0.1 9.4 ± 0.6 53.6 ± 0.7 1278.3 ± 0.1 9.1 ± 0.6 53.8 ± 0.6 1259.0 ± 0.1 8.5 ± 0.6 54.4 ± 0.6 1221.2 ± 0.1 8.0 ± 0.6 54.9 ± 0.6 1184.1 ± 0.1 7.2 ± 1.0 55.8 ± 1.0 1147.8 ± 0.2 n-Heptylcycylohexane (1) in n-Dodecane (2) 76.4 ± 0.8 1316.5 ± 0.5 76.6 ± 0.8 1297.1 ± 0.5 76.8 ± 0.7 1277.7 ± 0.4 77.1 ± 0.7 1258.5 ± 0.4

c/m·s−1 = A2x12 + A1x1 + Ao σ

T/K

0.27 0.28 0.40 0.41 0.46 0.30

313.15 323.15 333.15 288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.15 0.16 0.21 0.19 0.21 0.19 0.16

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.12 0.09 0.08 0.08 0.07 0.07 0.12

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.39 0.35 0.32 0.33

A2 (m·s−1)

A1 (m·s−1)

Ao (m·s−1)

n-Heptylcycylohexane (1) in n-Dodecane (2) 77.7 ± 0.7 1220.7 ± 0.4 78.2 ± 0.7 1183.6 ± 0.4 78.9 ± 0.6 1147.4 ± 0.3 n-Octylcycylohexane (1) in n-Dodecane (2) 88.4 ± 0.5 1317.5 ± 0.3 88.8 ± 0.6 1298.1 ± 0.6 89.2 ± 0.8 1278.7 ± 0.5 89.6 ± 0.9 1259.5 ± 0.5 90.5 ± 1.1 1221.8 ± 0.6 91.5 ± 1.1 1184.7 ± 0.6 92.5 ± 1.0 1148.5 ± 0.6 n-Decylcycylohexane (1) in n-Dodecane (2) −17.8 ± 0.8 125.6 ± 0.2 1317.3 ± 0.2 −18.2 ± 0.6 126.8 ± 0.6 1297.7 ± 0.1 −19.3 ± 0.9 128.8 ± 0.9 1278.2 ± 0.2 −19.8 ± 1.2 130.2 ± 1.2 1258.9 ± 0.2 −19.7 ± 2.9 131.5 ± 3.1 1221.1 ± 0.7 −21.1 ± 1.4 134.5 ± 1.4 1183.9 ± 0.3 −21.3 ± 0.8 136.3 ± 1.0 1147.7 ± 0.2 n-Dodecylcycylohexane (1) in n-Dodecane (2) −34.4 ± 1.8 158.3 ± 1.8 1317.5 ± 0.4 −34.6 ± 1.7 159.3 ± 1.7 1298.0 ± 0.4 −34.1 ± 1.8 160.3 ± 1.8 1278.5 ± 0.4 −34.7 ± 1.7 161.6 ± 1.8 1259.3 ± 0.4 −35.3 ± 1.8 164.2 ± 1.9 1221.4 ± 0.4 −36.0 ± 1.8 167.0 ± 1.9 1184.4 ± 0.4 −36.9 ± 2.1 169.8 ± 2.2 1148.2 ± 0.5

σ 0.32 0.30 0.26 0.25 0.27 0.37 0.43 0.50 0.50 0.47 0.11 0.07 0.11 0.15 0.37 0.18 0.13 0.22 0.21 0.22 0.21 0.23 0.23 0.27

The “±” for the coefficients Ao, A1, and A2 represents the 95% confidence interval. The σ is the standard error of the fit. The x1 is the mole fraction of n-alkylcyclohexane in the n-dodecane mixture. The R2 for all equations are >0.999, except n-propylcyclohexane where R2 > 0.922.

a

I



Article

Table 10. Bulk Modulus Bs, MPa, of n-Alkylcyclohexanes (1) in n-Dodecane (2) from Temperature T = (288.15−333.15) K and Pressure p = 0.1 MPaa T/K

x1

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.0000 1305 1261 1217 1175 1095 1019 948

0.1007 1311 1267 1223 1180 1099 1023 952

0.2001 1318 1273 1229 1186 1104 1027 955

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.0000 1305 1261 1217 1175 1095 1019 948

0.1009 1322 1277 1233 1191 1110 1033 961

0.2001 1338 1292 1249 1206 1124 1047 974

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.0000 1305 1261 1217 1175 1095 1019 948

0.1009 1326 1281 1237 1195 1113 1037 965

0.1998 1347 1301 1257 1214 1132 1055 982

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 1305 1261 1217 1175 1095 1019 948

0.1002 1331 1286 1242 1199 1117 1041 969

0.2010 1357 1311 1267 1224 1141 1063 991

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 1305 1261 1217 1175 1095 1019 948

0.1000 1336 1291 1247 1204 1123 1046 974

0.1998 1366 1320 1276 1232 1150 1072 999

288.15 293.15 298.15 303.15 313.15 323.15 333.15

0.000 1305 1261 1217 1175 1095 1019 948

0.1003 1345 1300 1256 1213 1131 1054 982

0.2194 1391 1345 1300 1257 1174 1095 1022

288.15 293.15 298.15 303.15 313.15

0 1305 1261 1217 1175 1095

0.1005 1355 1309 1265 1222 1140

0.2001 1401 1355 1310 1267 1183

n-Propylcycylohexane (1) in n-Dodecane (2) 0.3001 0.4011 0.5000 0.6004 1325 1334 1343 1352 1280 1288 1296 1305 1235 1244 1252 1259 1192 1200 1208 1215 1110 1117 1124 1130 1033 1039 1045 1050 960 965 970 975 n-Pentylcylohexane (1) in n-Dodecane (2) 0.3003 0.4009 0.5001 0.6000 1355 1373 1392 1412 1309 1327 1346 1365 1265 1282 1300 1319 1222 1239 1256 1275 1139 1155 1172 1189 1061 1076 1092 1109 988 1002 1017 1032 n-Hexylcycylohexane (1) in n-Dodecane (2) 0.3001 0.4001 0.5004 0.5996 1369 1391 1415 1439 1323 1345 1368 1391 1278 1300 1322 1345 1235 1256 1278 1300 1151 1172 1193 1214 1073 1092 1112 1133 1000 1018 1037 1057 n-Heptycycylohexane (1) in n-Dodecane (2) 0.3000 0.3998 0.5002 0.5999 1383 1410 1437 1465 1337 1363 1390 1417 1292 1317 1345 1371 1249 1273 1300 1326 1166 1189 1215 1240 1087 1109 1134 1158 1013 1034 1058 1081 n-Octylcycylohexane (1) in n-Dodecane (2) 0.3002 0.3998 0.4948 0.5997 1396 1427 1457 1489 1350 1381 1410 1442 1305 1335 1364 1395 1261 1291 1319 1350 1178 1207 1233 1263 1099 1127 1152 1181 1025 1051 1076 1104 n-Decylcycylohexane (1) in n-Dodecane (2) 0.3002 0.4004 0.4999 0.5993 1422 1460 1496 1532 1376 1413 1449 1484 1330 1367 1403 1437 1286 1323 1358 1391 1202 1238 1271 1303 1123 1157 1190 1220 1048 1081 1113 1143 n-Dodecylcycylohexane (1) in n-Dodecane (2) 0.2980 0.4031 0.5001 0.6005 1446 1491 1531 1572 1399 1444 1483 1523 1353 1397 1436 1475 1309 1352 1391 1429 1224 1266 1303 1340 J

0.6995 1363 1316 1269 1224 1138 1057 981

0.7998 1376 1328 1280 1234 1147 1064 987

0.8997 1391 1341 1293 1246 1157 1073 995

1.0000 1408 1357 1308 1260 1169 1084 1004

0.7003 1434 1386 1340 1294 1208 1126 1049

0.8136 1460 1411 1364 1318 1230 1147 1068

0.9082 1483 1434 1386 1339 1249 1165 1086

1.0000 1507 1457 1408 1361 1270 1184 1104

0.7005 1464 1416 1369 1324 1236 1154 1077

0.7996 1490 1441 1394 1348 1259 1176 1098

0.8997 1517 1468 1420 1373 1283 1199 1119

1.0000 1546 1496 1447 1399 1308 1223 1143

0.6998 1493 1445 1398 1352 1264 1182 1104

0.8001 1522 1473 1426 1380 1291 1207 1129

0.8998 1552 1502 1454 1407 1317 1232 1153

1.0000 1582 1532 1483 1435 1344 1258 1178

0.6996 1520 1472 1425 1378 1291 1208 1130

0.7999 1552 1503 1455 1409 1320 1236 1157

0.9000 1583 1534 1485 1438 1348 1263 1183

1.0000 1615 1565 1516 1468 1377 1291 1210

0.7001 1568 1519 1472 1426 1337 1253 1174

0.8005 1602 1553 1505 1459 1369 1284 1205

0.8991 1636 1586 1538 1491 1400 1315 1234

1.0000 1669 1619 1570 1522 1430 1343 1262

0.7003 1610 1561 1513 1466 1377

0.7997 1647 1597 1549 1502 1411

0.8994 1682 1632 1583 1535 1444

1.0000 1716 1665 1616 1568 1476



Article

Table 10. continued T/K 323.15 333.15

x1 1019 948

1063 991

1105 1031

n-Dodecylcycylohexane (1) in n-Dodecane (2) 1144 1185 1221 1257 1069 1109 1144 1179

1293 1213

1326 1245

1358 1276

1388 1307

a

Standard uncertainties u are u(T) = 0.05 K and u(p) = 0.001 MPa, and combined expanded uncertainties Uc are Uc(Bs) = 1 MPa, Uc(x1) = 0.0001 for mole fractions less than 0.71 and Uc(x1) = 0.0002 for the higher mole fractions. The average pressure for these measurements was 0.102 MPa. x1 is the mole fraction of alkylcyclohexane in the n-dodecane mixture.

and ν2, and molar masses M1 and M2 of the pure components with component 1 being the n-alkylcylohexane and component 2 being n-dodecane. The interaction parameters ν2,1 and ν1,2 were calculated by minimizing the sum of the square of the difference between the model (eq 9) and the experimental kinematic viscosities. Table 13 contains ν2,1 and ν1,2 and the standard error of the fit. Figure 3 shows that the data are fitted well by the model. The kinematic viscosity was also used to determine the excess molar Gibbs energy of activation for viscous flow (ΔG*E)71 ÄÅ ÉÑ n ÅÅÅ ÑÑÑ E ΔG* = RT ÅÅÅln(νmM m) − ∑ xi ln νiMi ÑÑÑ ÅÅ ÑÑ ÅÇ ÑÖ (10) i−1

increase with increasing alkylcyclohexane mole fraction and decrease with increasing temperature; both of these trends are reproduced by the simulations. Unlike the calculated densities, the accuracy of the calculated bulk moduli does not depend on temperature. For example, for the n-propylcyclohexane mixtures, the rmsd relative to the experiment is about 30 MPa at all three temperatures considered here. It is unclear why the predicted densities become less accurate with increasing temperature, whereas the predicted isentropic bulk moduli do not. The isentropic bulk modulus calculation is a complicated function of volume, potential energy, and temperature (see Morrow et al.43). It is possible that the volume inaccuracy that gives rise to incorrect densities is offset in the isentropic bulk modulus calculation. Dynamic viscosities from NVT simulations are compared to the experimental values in Figure 6. For pure n-dodecane at 293.15 K, the predicted viscosity is 1.71 mPa·s, 15% higher than the experimental value of 1.49 mPa·s. This is in good agreement with the results obtained at a slightly different temperature by Siu et al.,55 who reported a dynamic viscosity of 1.668 mPa·s for n-dodecane at 298.15 K using the L-OPLS force field. The trends in viscosity as a function of temperature and composition are reproduced qualitatively by the simulations for mixtures of both PCH and DDCH. The dynamic viscosity decreases and increases with increasing mole fraction of PCH and DDCH, respectively, and decreases with increasing temperature. For all of the systems and temperatures considered here, the calculated viscosity is too large compared to the experiment, with the error decreasing with increasing temperature. For the PCH mixtures, the rmsd values with respect to the experiment are 0.34, 0.17, and 0.09 mPa·s at 293.15, 313.15, and 333.15 K, respectively. For the DDCH mixtures, the rmsd values are 0.50, 0.37, and 0.22 mPa·s at 293.15, 313.15, and 333.15 K, respectively. Previous simulations of binary mixtures of n-hexadecane with either DDCH or PCH found that differences in excess molar volumes between the two mixtures are due to differences in the arrangement of the molecules relative to each other, rather than changes in conformation of individual molecules.42 The arrangement or packing of molecules in a fluid can be assessed by comparing the volume occupied by the individual fluid molecules. The volume occupied by each molecule in a simulation can be calculated using the Voronoi tessellation technique.60 This calculation can be done for every molecule at every step of the trajectory to create a probability distribution of molecular volumes for a given molecule type. That is, the molecular volumes of different molecule types in a mixture can be assessed separately. These distributions can then be used to gain insight into excess molar volume trends. For example, smaller molecular volumes mean that molecules are more tightly packed, which would lead to negative excess molar volumes. Histograms of molecular volumes for DDCH and PCH at 293.15 K are compared in Figure 7. Comparison to the

The variables are the gas constant R (8.314 J·mol−1·K−1), temperature T in Kelvin, mixture kinematic viscosity νm, pure component kinematic viscosities ν1 and ν2, the molar mass of the mixture (Mm = ∑i=12xiMi), the pure component molar masses M1 and M2, and mole fractions x1 and x2 with component 1 being the alkylcyclohexane and component 2 being the n-dodecane. The values for the excess molar Gibbs energies of activation for viscous flow for all of the mixtures are not statistically different from zero. Because a zero value for excess properties indicates ideal behavior, these mixtures appear to be behaving ideally (Table 4). 4.4. Simulations. MD simulations were carried out for binary mixtures of n-dodecane (DD) with either n-dodecylcyclohexane (DDCH) or n-propylcyclohexane (PCH) at temperatures of 293.15, 313.15, and 333.15 K. Figure 4 shows a comparison of the calculated densities and the experimental values. The simulations correctly capture the changes in density as a function of composition and temperature, including the negative and positive deviations from ideality seen in the excess molar volumes of the n-propylcyclohexane and n-dodecylcyclohexane mixtures, respectively. At 293.15 K, densities for both mixtures are under predicted slightly, with a root-mean-square deviation (rmsd) relative to the experimental values of 1.7 and 1.9 kg/m3 for the DDCH and PCH mixtures, respectively. As the temperature increases, the accuracy of the calculated densities decreases. In the n-propylcyclohexane mixtures, the rmsd values are 4.2 and 6.4 kg/m3 at 313.15 and 333.15 K, respectively; rmsd values for the n-dodecylcyclohexane mixtures are similar. These data indicate that although intermolecular interactions are accurately reproduced at lower temperatures, they become weaker relative to reality as the temperature is increased. At 333.15 K, the highest temperature considered here, the calculated densities are still within 1% of the experimental values. However, care should be taken when using the OPLS-AA or L-OPLS force fields to make quantitative density predictions at more extreme temperatures, such as the near- and supercritical conditions relevant to the study of diesel fuel injection. Predicted values for isentropic bulk moduli are compared to the experimental values in Figure 5. Isentropic bulk moduli K



Article

Table 11. Comparison of the Measured Dynamic Viscosities η of with Literature Values at Pressure p = 0.1 MPaa T/K

this studya (mPa·s)

293.15 303.15 313.15 323.15 333.15

0.981 0.856 0.750 0.668 0.594

293.15 303.15 313.15 323.15 333.15

1.69 1.43 1.21 1.05 0.914

293.15 303.15 313.15 323.15 333.15

2.19 1.79 1.52 1.30 1.12

293.15 303.15 313.15 323.15 333.15

2.80 2.25 1.85 1.55 1.31

293.15 303.15 313.15 323.15 333.15

3.52 2.79 2.26 1.87 1.57

293.15 303.15 313.15 323.15 333.15

5.34 4.09 3.23 2.60 2.15

293.15 303.15 313.15 323.15 333.15

7.77 5.81 4.48 3.55 2.87

293.15

1.49

303.15

1.27

313.15

1.08

323.15

0.934

333.15

0.813

literature/mPa·s n-Propylcyclohexane 1.005b, 1.006b 0.8606b, 0.870b 0.759b, 0.760b 0.672b 0.5784b, 0.601b n-Pentylcyclohexane 1.723b 1.418b 1.191b 1.026b 0.898b n-Hexylcyclohexane 2.22b 1.80b 1.492b 1.268b, 1.30b 1.097b n-Heptylcyclohexane 2.81b, 2.810d 2.230d, 2.25b 1.830b,d 1.540d, 1.544b 1.320b,d n-Octylcyclohexane 3.51b, 3.52c 2.77b 2.24b 1.86b 1.571b, 1.58c n-Decylcyclohexane 5.26b, 6.332b 4.05b 3.19b 2.59b 2.16b, 2.160b n-Dodecylcyclohexane 7.54b 5.68b 4.38b 3.50b 2.86b n-Dodecane 1.480b, 1.488b, 1.4885 ± 0.5%e, 1.492b, 1.493b, 1.50b, 1.508b 1.2315b, 1.2328b, 1.248b, 1.2462 ± 0.5%e, 1.252f, 1.265b, 1.267b 1.0610 ± 0.5%e, 1.066b, 1.07b, 1.075c, 1.0915b, 1.150b 0.9100b, 0.9146b, 0.91601 ± 0.5%e, 0.9215b, 0.9290b 0.9321b 0.80022 ± 0.5%e, 0.8026b, 0.8046b, 0.81b, 0.8134b, 0.8147b

Figure 3. Viscosities ν for binary mixtures of n-dodecane with blue ○ n-dodecylcyclohexane (x1), Δ n-decylcyclohexane (x1), green ■ n-octylcyclohexane (x1), □ n-heptylcyclohexane (x1), pink ⧫ n-hexylcyclohexane (x1), ◊ n-pentylcyclohexane (x1), and yellow ▲ n-propylcycohexane (x1) at 293.15 K. The lines are fits using the McAllister equation with coefficients given in Table 13.

for n-propylcyclohexane is about 0.15 nm3 smaller than that of n-dodecylcyclohexane. In addition, the distribution for n-dodecylcyclohexane is much broader than it is for n-propylcyclohexane. The longer alkyl side-chain makes the molecule take up more space and leading to various packing arrangements of the n-dodecylcyclohexane molecules, both of which contribute to the changes in the distribution. Both alkylcyclohexane molecules occupy slightly more volume in 50% mixtures with n-dodecane than the same alkylcyclohexane molecules do in a pure fluid, possibly because the presence of n-dodecane disrupts the arrangement of the cyclohexane rings compared to the pure fluid. Figure 8 compares the molecular volume distribution of pure n-dodecane to that of n-dodecane in the 50% binary mixtures at 293.15 K. Molecules of n-dodecane in mixtures with n-propylcyclohexane and n-dodecylcyclohexane occupy larger and smaller volumes, respectively, compared to that in pure n-dodecane. Figures 7 and 8 give molecular-level insight into the differences in excess molar volume for the two binary mixtures at 293.15 K (Table 4). In binary mixtures of n-propylcyclohexane and n-dodecane, both molecules occupy slightly larger volumes than in their respective pure fluids, leading to positive values of excess molar volume. In contrast, n-dodecylcyclohexane and n-dodecane in binary mixtures occupy larger and smaller volumes compared to their respective pure fluids; the net result is an overall negative excess molar volume for these binary mixtures. The excess molar volumes of both the n-propylcyclohexane and n-dodecylcyclohexane mixtures decrease with increasing temperature (Table 5). However, the excess molar volumes of the binary mixtures of both n-alkycyclohexanes with n-dodecane exhibit opposite trends with respect to ideality; the values for n-propylcyclohexane mixtures become less positive (more ideal) with increasing temperature, whereas the values for n-dodecylcyclohexane become more negative (less ideal). At 333.15 K, the molecular volumes of both pure n-propylcyclohexane and n-dodecylcyclohexane in mixtures with n-dodecane are slightly larger than that in the pure fluids (data not shown), similar to the results at 293.15 K. However, the molecular volume distributions of n-dodecane at 333.15 K (Figure 9) are different from those at 293.15 K. In 50% mixtures with n-dodecylcyclohexane, n-dodecane molecules occupy less volume than those in pure n-dodecane. The magnitude of this decrease is larger than that at 293.15 K (the most probable molecular volume decreases by 1.6 and 2.6% at 293.15 and 333.15 K, respectively), resulting in a lower excess

a Standard uncertainties u are u(T) = 0.05 K and Uc(p) = 0.001 MPa, and expanded uncertainties Uc are Uc(η) = 0.03 mPa·s (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa. bReference 82. cReference 83. dReference 84. e Reference 78. fReference 85.

distributions for pure n-propylcyclohexane and n-dodecylcyclohexane fluids reveals that the most probable molar volume L



Article

Table 12. Kinematic Viscosities ν and Dynamic Viscosities η of n-Alkylcyclohexanes (1) in n-Dodecane (2) from Temperature T = (288.15−333.15) K and Pressure p = 0.1 MPaa kinematic viscosities ν (mm2·s−1) x1

dynamic viscosities η (mPa·s)

T/K

0 0.1007 0.2001 0.3001 0.4011 0.5000 0.6004 0.6995 0.7998 0.8997 1

293.15 1.99 1.91 1.84 1.76 1.68 1.61 1.53 1.46 1.38 1.31 1.24b

303.15 1.71 1.65 1.58 1.52 1.46 1.40 1.33 1.27 1.21 1.15 1.09b

313.15 1.47 1.42 1.37 1.31 1.26 1.22 1.17 1.12 1.07 1.01 0.965b

0.0000 0.1009 0.2001 0.3003 0.4009 0.5001 0.6000 0.7003 0.8136 0.9082 1.0000

293.15 1.99 1.99 1.99 1.99 2.00 2.01 2.02 2.03 2.05 2.08 2.10b

303.15 1.71 1.71 1.71 1.71 1.72 1.73 1.73 1.74 1.76 1.78 1.79b

313.15 1.47 1.47 1.47 1.47 1.48 1.48 1.49 1.49 1.51 1.52 1.54b

0.0000 0.1009 0.1998 0.3001 0.4001 0.5004 0.5996 0.7005 0.7996 0.8997 1.0000

293.15 1.99 2.03 2.08 2.14 2.20 2.26 2.34 2.42 2.50 2.59 2.71b

303.15 1.71 1.75 1.78 1.83 1.87 1.93 1.98 2.04 2.11 2.19 2.24b

313.15 1.47 1.50 1.53 1.56 1.60 1.64 1.69 1.73 1.79 1.85 1.92b

0.0000 0.1002 0.2010 0.3000 0.3998 0.5002 0.5999 0.6998 0.8001 0.8998 1.0000

293.15 1.99 2.08 2.19 2.29 2.42b 2.55 2.69 2.85 3.03 3.24d 3.45

303.15 1.71 1.78 1.86 1.95 2.04 2.15 2.23 2.35 2.49 2.65e 2.80

313.15 1.47 1.52 1.59 1.66 1.73 1.82 1.90 1.97 2.08 2.19 2.32

0.0000 0.1000 0.1998 0.3002

293.15 1.99 2.13 2.29 2.48

303.15 1.71 1.82 1.95 2.10

313.15 1.47 1.56 1.66 1.76

x1 n-Propylcycylohexane (1) in n-Dodecane (2) 323.15 333.15 293.15 1.29 1.13 0.0000 1.49 1.24 1.10 0.1007 1.44 1.20 1.06 0.2001 1.39 1.16 1.03 0.3001 1.34 1.12 0.995 0.4011 1.28 1.08 0.959 0.5000 1.23 1.04 0.924 0.6004 1.18 1.00 0.890 0.6995 1.13 0.95 0.852 0.7998 1.08 0.908 0.817 0.8997 1.03 0.868b 0.780b 1.0000 0.981b n-Pentylcyclohexane (1) in n-Dodecane (2) 323.15 333.15 293.15 1.29 1.13 0.0000 1.49 1.29 1.13 0.1009 1.50 1.29 1.13 0.2001 1.51 1.29 1.14 0.3003 1.52 1.29 1.14 0.4009 1.54 1.30 1.14 0.5001 1.55 1.30 1.15 0.6000 1.57 1.31 1.15 0.7003 1.60 1.32 1.16 0.8136 1.62 1.33 1.17 0.9082 1.66 1.34b 1.18b 1.0000 1.69b n-Hexylcyclohexane (1) in n-Dodecane (2) 323.15 333.15 293.15 1.29 1.13 0.0000 1.49 1.31 1.15 0.1009 1.53 1.34 1.17 0.1998 1.58 1.36 1.20 0.3001 1.64 1.39 1.22 0.4001 1.70 1.43 1.25 0.5004 1.76 1.47 1.28 0.5996 1.83 1.50 1.31 0.7005 1.91 1.55 1.35 0.7996 1.99 1.60 1.39 0.8997 2.08 1.65b 1.43b 1.0000 2.19b n-Heptylcyclohexane (1) in n-Dodecane (2) 323.15 333.15 293.15 1.29 1.13 0.0000 1.49 1.33 1.17 0.1002 1.57 1.39 1.22 0.2010 1.67 1.44 1.26 0.3000 1.76 1.50 1.31 0.3998 1.87 1.57 1.37 0.5002 1.99 1.64 1.42 0.5999 2.12 1.72 1.49 0.6998 2.26 1.77 1.53 0.8001 2.42 1.85b 1.59b 0.8998 2.60c 1.96 1.68 1.0000 2.80 n-Octylcyclohexane (1) in n-Dodecane (2) 323.15 333.15 293.15 1.29 1.13 0.0000 1.49 1.36 1.19 0.1000 1.61 1.44 1.26 0.1998 1.74 1.53 1.33 0.3002 1.91 M

T/K 303.15 1.27 1.23 1.18 1.14 1.10 1.06 1.02 0.977 0.936 0.897 0.856b

313.15 1.08 1.05 1.01 0.979 0.946 0.914 0.882 0.850 0.818 0.783 0.750b

323.15 0.934 0.909 0.882 0.856 0.831 0.802 0.776 0.750 0.721 0.694 0.668b

333.15 0.813 0.792 0.769 0.750 0.729 0.707 0.685 0.663 0.640 0.618 0.594b

303.15 1.27 1.28 1.29 1.30 1.31 1.32 1.34 1.35 1.38 1.40 1.43b

313.15 1.08 1.08 1.09 1.10 1.11 1.12 1.14 1.15 1.17 1.19 1.21b

323.15 0.934 0.941 0.949 0.957 0.967 0.976 0.988 1.00 1.02 1.03 1.05b

333.15 0.813 0.819 0.825 0.833 0.841 0.851 0.861 0.871 0.887 0.897 0.914b

303.15 1.27 1.30 1.34 1.38 1.43 1.48 1.54 1.60 1.66 1.74 1.79b

313.15 1.08 1.11 1.14 1.17 1.21 1.25 1.30 1.34 1.40 1.46 1.52b

323.15 0.934 0.958 0.986 1.01 1.05 1.08 1.12 1.15 1.20 1.25 1.30b

333.15 0.813 0.833 0.855 0.880 0.906 0.935 0.966 1.00 1.04 1.07 1.12b

303.15 1.27 1.33 1.41 1.48 1.57 1.66 1.74 1.85 1.97 2.11d 2.25

313.15 1.08 1.13 1.19 1.25 1.32 1.39 1.47 1.54 1.63 1.73 1.85

323.15 0.934 0.976 1.02 1.08 1.13 1.19 1.25 1.32 1.38 1.45 1.55

333.15 0.813 0.851 0.891 0.933 0.977 1.03 1.08 1.14 1.18 1.23 1.31

303.15 1.27 1.36 1.47 1.60

313.15 1.08 1.16 1.24 1.33

323.15 0.934 1.00 1.07 1.14

333.15 0.813 0.865 0.923 0.984



Article

Table 12. continued kinematic viscosities ν (mm2·s−1) x1

dynamic viscosities η (mPa·s)

T/K

0.3998 0.4948 0.5997 0.6996 0.7999 0.9000 1.0000

2.64 2.85 3.09 3.35 3.63 3.96 4.32

2.20 2.35 2.54 2.73 2.95 3.19 3.45

1.88 1.98 2.12 2.27 2.44 2.62 2.82

0 0.1003 0.2194 0.3002 0.4004 0.4999 0.5993 0.7001 0.8005 0.8991 1.0000

293.15 1.99 2.24 2.58 2.83 3.18 3.58 4.03 4.55b 5.12 5.76e 6.52

303.15 1.71 1.91 2.18 2.34 2.61 2.91 3.25 3.63 4.04 4.51b 5.04

313.15 1.47 1.63 1.84 1.97 2.18 2.41 2.67 2.96 3.27 3.62 4.01

0.0000 0.1005 0.2001 0.2980 0.4031 0.5001 0.6005 0.7003 0.7997 0.8994 1.0000

293.15 1.99 2.39g 2.79 3.26 3.86 4.48 5.23b 6.08 7.06 8.18b 9.43

303.15 1.71 2.04g 2.31 2.67 3.12 3.59 4.14 4.75 5.45 6.23 7.12

313.15 1.47 1.74h 1.94 2.23 2.58 2.94 3.35 3.81 4.32 4.89 5.54

x1

T/K

n-Octylcyclohexane (1) in n-Dodecane (2) 1.63 1.41 0.3998 2.05 1.72 1.49 0.4948 2.23 1.80 1.56 0.5997 2.44 1.92 1.65 0.6996 2.66 2.05 1.75 0.7999 2.91 2.19 1.87 0.9000 3.20 2.36 2.00 1.0000 3.52 n-Decylcycylohexane (1) in n-Dodecane (2) 323.15 333.15 293.15 1.29 1.13 0 1.49 1.42 1.24 0.1003 1.70 1.59 1.39 0.2194 1.98 1.72 1.49 0.3002 2.19 1.85 1.60 0.4004 2.48 2.04 1.74 0.4999 2.82 2.24 1.91 0.5993 3.20 2.46 2.09 0.7001 3.64 2.70 2.28 0.8005 4.13 2.97 2.49 0.8991 4.68d 3.26 2.72 1 5.34 n-Dodecylcycylohexane (1) in n-Dodecane (2) 323.15 333.15 293.15 1.29 1.13 0.0000 1.49 1.48 1.29 0.1005 1.82e 1.70 1.48 0.2001 2.14 1.89 1.63 0.2980 2.53 2.17 1.86 0.4031 3.03 2.45 2.08 0.5001 3.55 2.77 2.33 0.6005 4.17b 3.13 2.62 0.7003 4.90 3.52 2.92 0.7997 5.73 3.94 3.25 0.8994 6.68b 4.43 3.63 1.0000 7.76

1.69 1.82 1.98 2.15 2.34 2.55 2.79

1.43 1.52 1.64 1.77 1.92 2.08 2.26

1.23 1.31 1.38 1.48 1.60 1.73 1.87

1.06 1.12 1.18 1.26 1.36 1.46 1.57

303.15 1.27 1.43 1.65 1.79 2.02 2.27 2.55 2.88 3.23 3.63 4.09

313.15 1.08 1.21 1.39 1.49 1.67 1.87 2.08 2.33 2.60 2.89 3.23

323.15 0.934 1.04 1.19 1.29 1.41 1.56 1.73 1.92 2.13 2.35 2.60

333.15 0.813 0.904 1.02 1.11 1.20 1.32 1.46 1.61 1.78 1.95 2.15

303.15 1.27 1.53e 1.75 2.05 2.43 2.82 3.28 3.79 4.38 5.05 5.81

313.15 1.08 1.29f 1.46 1.70 1.99 2.28 2.63 3.01 3.45 3.93 4.48

323.15 0.934 1.09 1.27 1.43 1.66 1.89 2.16 2.45 2.78 3.14 3.55

333.15 0.813 0.945 1.09 1.22 1.40 1.59 1.80 2.03 2.29 2.57 2.88

a Standard uncertainties u are u(T) = 0.05 K and Uc(p) = 0.001 MPa, expanded uncertainties Uc are Uc(η) = 0.02 mPa·s, and combined expanded uncertainties are Uc(ν) = 0.02 mm2·s−1 unless indicated by a superscript (level of confidence = 0.95, k = 2), Uc(x1) = 0.0001 for mole fractions less than 0.71 and Uc(x1) = 0.0002 for the higher mole fractions. The average pressure for these measurements was 0.102 MPa. x1 is the mole fraction of alkylcyclohexane in the n-dodecane mixture. bUc(ν) = 0.03 mm2·s−1, Uc(η) = 0.03 mPa·s. cUc(ν) = 0.04 mm2·s−1, Uc(η) = 0.04 mPa·s. dUc(ν) = 0.05 mm2·s−1, Uc(η) = 0.05 mPa·s. eUc(ν) = 0.06 mm2·s−1, Uc(η) = 0.06 mPa·s. fUc(ν) = 0.07 mm2·s−1, Uc(η) = 0.07 mPa·s. gUc(ν) = 0.08 mm2·s−1, Uc(η) = 0.08 mPa·s. hUc(ν) = 0.09 mm2·s−1, Uc(η) = 0.09 mPa·s.

Table 13. Values of the Coefficients for McAllister Equation ν12 and ν21 (Eq 9) and Associated Standard Error σ for the Systems of Binary Mixtures of n-Alkylcyclohexane (1) and n-Dodecane (2) at Pressure p = 0.1 MPaa

molar volume at the higher temperature. In contrast to the results at 293.15 K, n-dodecane molecules at 333.15 K occupy slightly less volume in n-propylcyclohexane mixtures than in pure n-dodecane. This results in an excess molar volume for n-dodecane plus n-propylcyclohexane binary mixtures at 333.15 K that is still positive, but has a lower magnitude than that at 293.15 K. A detailed investigation of the atomic level causes of these trends in molecular volume as a function of molecular structure and temperature is beyond the scope of the current work.

T/Κ 293.15 303.15 313.15 323.15 333.15

5. CONCLUSIONS This work explores the effects of the addition of n-alkylcyclohexanes containing a variety of n-alkyl chain lengths (e.g., n-propylcyclohexane to n-dodecylcyclohexane) to n-dodecane on properties, such as density, viscosity, speed of sound, and bulk modulus, as well as excess functions. Negative excess molar volumes were obtained for mixtures at equal mole fractions of n-dodecane with n-dodecylcyclohexane, n-decylcyclohexane, or n-octylcyclohexane, indicating a contraction

293.15 303.15 313.15 323.15 333.15 293.15 303.15 N

ν12/mm2·s−1

ν21/mm2·s−1

n-Propylcyclohexane (1) + n-Dodecane (2) 1.51 1.75 1.31 1.52 1.16 1.31 1.03 1.16 0.92 1.03 n-Pentylcyclohexane (1) + n-Dodecane (2) 2.00 1.99 1.72 1.71 1.48 1.47 1.48 1.36 1.14 1.13 n-Hexylcyclohexane (1) + n-Dodecane (2) 2.35 2.14 2.04 1.81

σ/mm2·s−1 0.002 0.0008 0.001 0.001 0.0009 0.002 0.001 0.001 0.0007 0.001 0.002 0.005



Article

Table 13. continued T/Κ 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15 293.15 303.15 313.15 323.15 333.15

ν12/mm2·s−1

ν21/mm2·s−1

n-Hexylcyclohexane (1) + n-Dodecane (2) 1.70 1.56 1.30 1.29 1.29 1.19 n-Heptylcyclohexane (1) + n-Dodecane (2) 2.75 2.32 2.27 1.98 1.91 1.69 1.66 1.47 1.44 1.29 n-Octylcylohexane (1) + n-Dodecane (2) 3.20 2.52 2.61 2.13 2.18 1.80 1.83 1.58 1.58 1.38 n-Decycylohexane (1) + n-Dodecane (2) 4.35 2.96 3.49 2.44 2.86 2.05 2.37 1.78 2.02 1.54 n-Dodecyclohexane (1) + n-Dodecane (2) 5.87 3.57 4.61 2.91 3.71 2.41 3.05 2.05 2.56 1.76

σ/mm2·s−1 0.001 0.001 0.0007 0.004 0.008 0.006 0.009 0.009 0.007 0.012 0.005 0.008 0.007 0.005 0.009 0.007 0.01 0.009

Figure 5. Isentropic bulk moduli for binary mixtures of n-dodecane with n-propylcyclohexane (a) or n-dodecylcyclohexane (b). Experimental values are filled symbols connected with solid lines; values from MD simulations are shown as open symbols connected by dashed lines.

0.01 0.01 0.01 0.009 0.009

The σ is the standard error of the fit.

a

Figure 6. Dynamic viscosity, η, for binary mixtures of n-dodecane with n-propylcyclohexane (a) or n-dodecylcyclohexane (b). Experimental values are filled symbols connected with solid lines; values from MD simulations are shown as open symbols connected by dashed lines. Figure 4. Densities for binary mixtures of n-dodecane with n-propylcyclohexane (a) or n-dodecylcyclohexane (b). Experimental values are filled symbols connected with solid lines; values from MD simulations are shown as open symbols connected by dashed lines.

expand upon mixing. MD simulations were used to elucidate the trends in excess molar volume. Simulations reveal that the volume that the n-dodecane molecule occupies in solution compared to its volume in pure n-dodecane drives the changes in excess molar volume. Histograms of the molar volume of n-dodecane show that the most probable volume of n-dodecane shifts to a smaller value when mixed with n-dodecylcyclohexane, whereas it shifts to a slightly larger value when mixed with n-propylcyclohexane. This change is not due to changes in the conformations of the n-dodecane molecules but due to

upon mixing. Reducing the length of the n-alkyl side chain causes a steady increase in the excess molar volumes of the equimolar mixtures. Mixtures of n-dodecane with either n-heptylcylohecane, n-hexylcylohecane, n-pentylcyclohexane, or n-propylcyclohexane were close to zero or slightly positive, suggesting that these mixtures behave ideally or slightly O



Article

mixtures examined here. For the mixtures with negative excess molar volume, the volume contraction helps produce speeds of sound that are faster than that predicted by ideal behavior, resulting in positive excess speeds of sound. Volume expansion (positive excess molar volumes) has the opposite effect, producing negative excess speeds of sound. This only occurs when compressibility differences do not counter the trend. A comparison of mixture properties with those of petroleum-based jet and diesel fuel specifications and with bio-based fuels containing cycloalkanes showed that many of the densities fell within the specification, and the mixtures with the longer chain n-alkylcylcohexanes were closer to the values of the bio-based fuel. Mixtures could be prepared with any alkylcyclohexane to match the diesel fuel viscosity standard at 313.15 K, and mixtures would have to contain longer alkyl chain cylohexanes to match the viscosity of the biofuel tested. No measurements were taken at 253.15 K, which is the temperature for jet fuel specifications. The bulk modulus of jet fuel can be matched by mixtures containing any of the alkanes, but only mixtures containing longer chain alkylcylohexanes could be used for petroleum-based and biobased diesel fuel. The physical properties measured herein can help researchers develop surrogate mixtures for petroleumbased and bio-based fuels containing alkylcyclohexanes.

Figure 7. Probability distribution for molecular volume of n-propylcyclohexane (a) and n-dodecylcyclohexane (b) in pure fluids (black) or in 50:50 mixtures with n-dodecane (red). Data from simulations at 293.15 K.

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b01135.

■

Figure 8. Probability distribution for molecular volume of n-dodecane in pure fluid (black), or in 50:50 mixtures with n-propylcyclohexane (red) or n-dodecylcyclohexane (blue). Data from simulations at 293.15 K.

Comparison of the measured values of densities of a NIST-Certified Toluene Standard with the reported standard values; 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; and comparison of speed of sound values determined experimentally to those predicted by the MD simulations (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (410)293-6399. Fax: (410) 293-2218 (D.J.L.P.). 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 #N0001418WX00142 and #N0001419WX00395. B.H.M. and J.A.H. also acknowledge partial support from the Research Office of the US Naval Academy.

Figure 9. Probability distribution for molecular volume of n-dodecane in pure fluid (black), or in 50:50 mixtures with n-propylcyclohexane (red) or n-dodecylcyclohexane (blue). Data from simulations at 333.15 K.

Notes

The authors declare no competing financial interest.

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packing differences brought about by mixing. Ideal behavior was also found for viscosity, where the excess molar Gibbs energies of activation for viscous flow at 293.15 K were not statistically different from zero. Excess speeds of sound had opposite signs from the excess molar volume for most of the

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