Article pubs.acs.org/jced
Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension, and Flash Point of Binary Mixtures of 2,2,4,6,6-Pentamethylheptane and 2,2,4,4,6,8,8-Heptamethylnonane at (293.15 to 373.15) K and 0.1 MPa and Comparisons with Alcohol-to-Jet Fuel Dianne J. Luning Prak,*,† M. Hope Jones,† Jim S. Cowart,‡ and Paul C. Trulove† †
Chemistry Department, United States Naval Academy, 572M Holloway Road, Annapolis, Maryland 21402, United States Mechanical Engineering Department, United States Naval Academy, 590 Holloway Road, Annapolis, Maryland 21402, United States
‡
S Supporting Information *
ABSTRACT: In this work, the physical properties of binary mixtures of 2,2,4,6,6pentamethylheptane and 2,2,4,4,6,8,8-heptamethylnonane were measured and compared with those of alcohol-to-jet fuel. Density and viscosity were measured at temperatures ranging from (293.15 to 373.15) K, and speed of sound was measured at temperatures ranging from (293.15 to 343.15) K. At 293.15 K, pure component values for 2,2,4,4,6,8,8heptamethylnonane of 784.48 kg·m−3, 3.71 mPa·s, and 1285.8 m·s−1 for density, viscosity, and speed of sound, respectively, agree with literature values. Similarly for 2,2,4,6,6pentamethylheptane, the values of 745.21 kg·m−3, 1.31 mPa·s, and 1203.7 m·s−1 for density, viscosity, and speed of sound, respectively agree with literature values. Density and mole fraction data were fit to a second-order polynomial at each temperature. Values for bulk modulus ranged from (732 to 1297) MPa over (293.15 to 343.15) K. Viscosity mole fraction data were fit using the threebody McAllister model, whereas the viscosity deviations were fit to a Redlich−Kister type equation. For the mixtures, an increase in mole fraction of 2,2,4,4,6,8,8-heptamethylnonane resulted in an increase in density, viscosity, speed of sound, bulk modulus, surface tension, and flash point. Increases in temperature decreased density, viscosity, speed of sound, and bulk modulus. At room temperature, the surface tension values ranged from (21.4 to 24.0) mN·m−1, and the flash points ranged from (318.15 to 367.15) K. Comparison of mixture properties with those of an alcohol-to-jet (ATJ) fuel showed that mixtures containing mass fractions of 2,2,4,4,6,8,8-heptamethylnonane around 0.3001 had properties that best matched the ATJ fuel.
1. INTRODUCTION Recently, the United States Army tested a mixture of petroleum-based jet fuel with a biobased jet fuel made from isobutanol (Gevo) in their UH-60 Black Hawk helicopter.1 These fuels mixtures are also being tested for use in Navy diesel engines2 because jet fuel is used in diesel engines as part of “one fuel forward policy” and for emergency conditions.3,4 Biobased jet fuel from isobutanol, sometimes referred to as alcohol-to-jet (ATJ) synthetic paraffinic kerosene, is commonly composed of a mixture of branched alkanes containing 12 to 16 carbons.2 In order to improve the overall understanding of ATJ combustion, numerical models simulating the combustion of this fuel are needed. Toward that end, detailed physical and chemical characterization of this fuel is required. In a model developed by Lawrence Livermore Laboratories, simulations of the combustion of linear alkanes with chains containing up to 16 carbons required over 10,000 reactions.5 To simplify the modeling process, surrogate mixtures with fewer components can be prepared that match the properties of the fuel of interest. Then the modeling and combustion of the fuel of interest can be compared with those of the surrogate mixtures. The goal of this work was to determine the composition of a surrogate mixture containing a branched alkane with 12 carbons, 2,2,4,6,6-pentamethylheptane, and a branched alkane with 16 © 2015 American Chemical Society
carbons, 2,2,4,4,6,8,8-heptamethylnonane, that best matched the physical properties reported for an ATJ fuel. The physical properties measured in this study for matching the surrogate mixture with that of the ATJ fuel are those that impact the delivery of the fuel and the combustion process. These properties include density, viscosity, speed of sound, surface tension, and flash point. The viscosity, surface tension, and density have been used as input parameters in the simulation of the vaporization of multicomponent fuel droplets.6−9 The bulk modulus directly affects fuel injection time and can be calculated from density and speed of sound measurements.10−12 Other properties, such as flash point, are part of the specifications for military diesel fuel.13 Flash point is also an indicator of the combustibility of the fuel.14−18 These properties have been used in the development of surrogate mixtures for other alternative fuels such as hydrotreated renewable diesel fuel from algae, direct sugar to hydrocarbon diesel fuel, and hydrotreated renewable jet fuel from camelina and tallow.12,14−16 In this work, the density, viscosity, surface Received: Revised: Accepted: Published: 1157
December 16, 2014 February 9, 2015 February 28, 2015 March 10, 2015 DOI: 10.1021/je501141e J. Chem. Eng. Data 2015, 60, 1157−1165
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Table 1. Sample Information molar massa
chemical name
source/lot number
mole fraction purity
analysis method
Aldrich/STBD6660 V STBF0890 V TCI Chemicals/S5P2B
0.998, 0.992 0.992
GCb GCb
g/mol 2,2,4,4,6,8,8-heptamethylnonane 2,2,4,6,6-pentamethylheptane a
226.44116 ± 0.007517 170.33484 ± 0.005641
Calculated using values in ref 26. bGas−liquid chromatography.
Table 2. Comparison of the Measured Density, Speed of Sound, and Viscosity of 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6pentamethylheptane with Literature Valuesa compound
T
density
K 2,2,4,4,6,8,8-heptamethylnonane
2,2,4,6,6-pentamethylheptane
kg·m
speed of sound
−3
viscosity
−1
m·s
this studya
literature
this studya
293.15
784.48
1285.8
303.15
777.78
784.46 ± 0.5b 784.5 ± 0.3c 777.76 ± 0.5b
313.15
771.07
1212.0
323.15
764.34
771.04 ± 0.5b 771.0 ± 0.3c 764.32 ± 0.5b
333.15
757.59
1141.0
343.15 353.15
750.83 743.9
363.15 373.15
737.0 730.2
293.15
745.21
303.15
737.93
757.57 ± 0.5b 757.4 ± 0.3c 750.7 ± 0.5b 743.8 ± 0.5b 743.8 ± 0.3c 736.8 ± 0.5b 729.9 ± 0.5b 730.3 ± 0.3c 745.0 ± 0.3d 745.5 ± 0.2c 746.3 ± 1d 738.2 ± 0.2c
313.15
730.61
730.9 ± 0.2c
1126.7
323.15
723.26
723.5 ± 0.2c
1089.3
333.15 343.15 353.15 363.15 373.15
715.86 708.42 700.7 693.1 685.4
716.1 708.6 700.9 693.2 685.5
± ± ± ± ±
1052.6 1016.5
0.2c 0.2c 0.2c 0.2c 0.2c
1248.6
1176.2
mPa·s literature
1285.7 1285.9 1248.5 1248.6 1211.8 1211.9 1176.0 1176.0 1140.8
± ± ± ± ± ± ± ± ±
0.3b 0.3c 0.3b 0.3c 0.3b 0.3c 0.3b 0.3c 0.3b
1106.5
1203.7
1203.6 ± 0.3b 1204.0 ± 0.3c
1164.9
1164.8 1164.9 1126.7 1126.7 1089.3 1089.3 1052.5
± ± ± ± ± ± ±
0.3b 0.3c 0.3b 0.3c 0.3b 0.3c 0.3b
this studya
literature
3.71
3.70 ± 0.008b
2.93
2.92 ± 0.008b
2.37
2.37 ± 0.008b
1.95
1.95 ± 0.008b
1.64
1.63 ± 0.008b
1.39 1.19
1.39 ± 0.008b 1.19 ± 0.008b
1.04 0.91(3)
1.04 ± 0.008b 0.914 ± 0.008b
1.31
1.29 ± 0.01c
1.11
1.10 ± 0.01c
0.94(8)
0.94(1) ± 0.01c
0.82(0)
0.82(7) 0.825e 0.72(6) 0.64(3) 0.57(3) 0.51(5) 0.46(7)
0.71(5) 0.63(2) 0.56(2) 0.50(5) 0.45(9)
± 0.01c ± ± ± ± ±
0.01c 0.01c 0.01c 0.01c 0.01c
a Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc are Uc(ρ) = 0.06 kg·m−3 for T < 353.15 K and Uc(ρ) = 0.2 kg· m−3 for T ≥ 353.15 K, Uc(c) = 0.5 m·s−1, Uc(μ)= 0.02 mPa·s, (level of confidence = 0.95, k ≈ 2). bRef 16. cRef 15. dRef 20. eRef 21.
tension, speed of sound, and flash point were measured for binary mixtures of 2,2,4,6,6-pentamethylheptane or 2,2,4,4,6,8,8-heptamethylnonane. These properties and calculated bulk modulus were then compared with values for ATJ. The goal of this work was to determine which surrogate mixture best matches these properties. This information can then be used for numerical simulations of the combustion process. Two-component mixture properties can also be used by numerical modelers who are trying to predict mixture properties using numerical simulations.
temperature a Mettler Toledo AG204 analytical balance with an error of 0.0004 g. The error in mass fraction and mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in 2,2,4,6,6-pentamethylheptane as given by the combined expanded uncertainty are 0.0001 and 0.0001, respectively.
3. METHODS The speed of sound and density of the 2,2,4,4,6,8,8heptamethylnonane in 2,2,4,6,6-pentamethylheptane and their mixtures were measured using an Anton Paar DSA 5000 density and sound analyzer, and their viscosity and density were measured using an Anton Paar SVM 3000 Stabinger viscometer. The methods for cleaning, calibrating, and checking the accuracy of these instruments have been described previously.15,16 A NIST toluene density reference standard
2. MATERIALS The 2,2,4,6,6-pentamethylheptane or 2,2,4,4,6,8,8-heptamethylnonane were used as received from the supplier (Table 1). To prepare the mixtures, each component was weighed at room 1158
DOI: 10.1021/je501141e J. Chem. Eng. Data 2015, 60, 1157−1165
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was used to test the accuracy of the density measurements. For the DSA 5000, samples of each individual liquid or liquid mixture were measured at six temperatures between (293.15 and 343.15) K, and replicate samples were used to determine the precision of the measurement. The highest temperature that this instrument can attain is 343.15 K. Using the SVM 3000, two or more samples of each individual liquid or liquid mixture were measured at eight temperatures between (293.15 and 373.15) K, and these replicate measurements were used to determine the precision of the measurement. Because this instrument can reach 373.15 K, it was also used to measure density at three temperatures from (353.15 to 373.15) K. The surface tension of each organic liquid was measured using a Kruss DS100 drop shape analyzer.14−16 This instrument records the magnified image of an organic liquid droplet formed in air on the tip of a needle. The surface tension is then determined using software that fits the shape of the recorded drop to the Young−LaPlace equation using input parameters of air density, organic liquid density, and the needle diameter that has been measured using a micrometer (Mitutoyo). Using this instrument, more than 15 surface tension measurements were taken for a minimum of three droplets of each liquid, and these values were used to calculate the standard deviation of each measurement. To determine the flash points of the organic liquids, a Setaflash Series 8 closed cup flash point tester model 82000-0 (Stanhope-Seta) was used in temperature ramping mode. The manufacturer’s literature specifies that this flash point tester conforms to ASTM D3828 (gas ignition option), ASTM D1655 (gas ignition option), ASTM D3278, ASTM D7236, and ASTM E502. Two measurements were taken for each mixture from which the average and standard deviation were determined. The combined expanded uncertainty of density, viscosity, speed of sound, surface tension, and flash point was determined by multiplying the standard deviation of the measurements (taken at each temperature as described above) by 2. When a normal distribution is assumed, multiplying by a coverage factor of 2 produces a 95% confidence interval. The purity of a sample also impacts the precision of the measurements, and this was taken into account when determining the combined expanded uncertainty.19
Table 3. Comparison of the Measured Density of NISTCertified Toluene with Certified Values compound
density kg·m−3 this study
NIST certified toluene standard
293.15 303.15 313.15 323.15 333.15 343.15
866.803 857.484 848.105 838.657 829.125 819.497
literature 866.828 857.507 848.131 838.684 829.152 819.516
± ± ± ± ± ±
0.031a 0.032a 0.033a 0.034a 0.035a 0.037a
Ref 22. Values for liquid density of SRM 211d “as shipped”. Error bars are the reported standard uncertainties.
a
In this equation, X1 is the mole fraction of the 2,2,4,4,6,8,8heptamethylnonane and A, B, and C are fitting parameters, which are given in Table 5. The standard error of the fit was calculated using σ=
∑ (Pmeasured − Pm,cal)2 N−n
(2)
in which Pmeasured is the measured density, Pm,cal is the fitted density, N is the number of experimental data, and n is the number of parameters in the fitting equation. The fitting procedure was conducted using Microsoft Excel 2010, and the results are given in Table 5. The fits are good with R2 > 0.9999 as shown in Figure 1. The excess molar volumes (VmE) of 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6-pentamethylheptane mixtures were calculated using the following equation: VmE =
M1X1 + M 2X 2 MX MX − 1 1 − 2 2 ρm ρ1 ρ2
(3)
in which ρm is the density of the mixture, ρ1 and ρ2 are the pure component densities, M1 and M2 are the molar masses, and X1 and X2 are the mole fractions of the 2,2,4,4,6,8,8-heptamethylnonane as component 1 and 2,2,4,6,6-pentamethylheptane as component 2. The calculated excess molar volumes for the 0.4293 mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in 2,2,4,6,6-pentamethylheptane (weight fraction = 0.5000) are given in Table 5. The excess molar volumes are negative values that change very little over the temperature range studied. The negative values indicate that the molecules are more closely packed in the mixture than they are as pure liquids, and this packing does not change much with temperature. In contrast, previous work with mixtures of these branched alkanes with nhexadecane have positive values of excess molar volume of 0.03 and 0.126 cm3·mol−1 for 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6-pentamethylheptane, respectively, at 293.15 K.14,15 As the temperature increased, the excess molar volume of the 2,2,4,6,6-pentamethylheptane and n-hexadecane mixtures decreased to a value of −0.39 cm3·mol−1 at 373.15 K. The packing of these molecules was enhanced by increases in temperature, unlike the mixtures reported herein. Reported values of excess molar volume for mixtures of these branched alkanes with ndodecane do not differ significantly from zero over the temperature range tested, (293.15 to 373.15) K,16 suggesting no significant change in packing, which differs the mixture behavior of the branched alkanes reported herein.
4. RESULTS 4.1. Density. The density values of 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6-pentamethylheptane are given as a function of temperature in Table 2 along with literature values. The densities of the pure components match most of the reported values within the error of the measurements. The measured density values of the NIST-certified toluene standard match the certified values within the error of the measurements (Table 3), demonstrating the accuracy of the instrument. The density values of the 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6-pentamethylheptane mixtures are given in Table 4 as a function of the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane (X1). For the mixtures, the density increased as mole fraction of the 2,2,4,4,6,8,8-heptamethylnonane increased, but the increase was not linear as shown in Figure 1. A second order polynomial was used to fit the density and mole fraction data ρ /kg·m−3 = AX12 + BX1 + C
T K
(1) 1159
DOI: 10.1021/je501141e J. Chem. Eng. Data 2015, 60, 1157−1165
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Table 4. Density, in kg·m−3, of Mixtures 2,2,4,4,6,8,8-Heptamethylnonane, X1, in 2,2,4,6,6-Pentamethylheptane from T = (293.15 to 373.15) K and 0.1 MPaa W1
X1
Temperature K
0.8998 0.8000 0.7000 0.6000 0.5000 0.4000 0.3001 0.2001 0.1000
0.8711 0.7506 0.6371 0.5302 0.4293 0.3340 0.2439 0.1584 0.0772
293.15
303.15
313.15
323.15
333.15
343.15
353.15
363.15
373.15
780.52 776.56 772.47 768.56 764.68 760.65 756.76 752.89 749.05
773.76 769.74 765.59 761.62 757.69 753.60 749.65 745.73 741.82
766.98 762.90 758.69 754.66 750.67 746.52 742.51 738.53 734.56
760.19 756.05 751.78 747.69 743.63 739.41 735.34 731.30 727.27
753.38 749.18 744.84 740.68 736.56 732.28 728.14 724.04 719.94
746.55 742.28 737.87 733.65 729.46 725.11 720.90 716.73 712.57
739.5 735.1 730.8 726.4 722.1 717.7 713.4 709.3 705.0
732.5 728.1 723.7 719.2 714.8 710.4 706.1 701.8 697.5
725.6 721.1 716.7 712.1 707.5 703.1 698.6 694.2 689.9
a
W1 is the mass fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane) and X1 is the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane). Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc is Uc(ρ) = 0.06 kg·m−3 at T < 353.15 K and Uc(ρ) = 0.2 kg·m−3 at T ≥ 353.15 K (level of confidence = 0.95, k ≈ 2).
The density value of ATJ has been reported to be 756.7 kg· m−3 at 293.15 K.2 This density value is very close to the density value of 756.76 kg·m−3 for the 0.3001 mass fraction of 2,2,4,4,6,8,8-heptamethylnonane in 2,2,4,6,6-pentamethylheptane. 4.2. Speed of Sound and Bulk Modulus. The speed of sound values of 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6pentamethylheptane measured herein are given as a function of temperature in Table 2 along with literature values. The values measured herein agree with the reported values within the error of their measurement. The speed of sound values of the 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6-pentamethylheptane mixtures are given in Table 6 as a function of the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane (X1). As the mole fraction of the 2,2,4,4,6,8,8-heptamethylnonane increased, the speed of sound increased as shown in Figure 2. The experimental data were fit with a linear model
Figure 1. Density of 2,2,4,4,6,8,8-heptamethylnonane (X1) + 2,2,4,6,6pentamethylheptane mixtures at: □, 293.15 K; ■, 303.15 K; △, 313.15 K; ▲, 323.15 K; ◇, 333.15 K; ◆, 343.15 K; ○, 353.15 K; ●, 363.15 K; ×, 373.15 K. Error bars, which are the combined expanded uncertainties with 0.95 level of confidence (k ≈ 2), are smaller than the symbols. Lines shown are second order fits using eq 1 with the coefficients in Table 5
c /m·s−1 = AX1 + B
(4)
and a second order model, c /m·s−1 = CX12 + DX1 + E
(5)
Table 5. Parameters for Equation 1, ρ = AX12 + BX1 + C, That Correlate Density, in kg·m−3, to Mole Fraction of 2,2,4,4,6,8,8Heptamethylnonane, X1, in 2,2,4,6,6-Pentamethylheptane, and the Excess Molar Volumeb, VmE, at X1 = 0.4293, T = (293.15 to 373.15) K, and 0.1 MPaa T
A
B
R2
C
σ
cm3·mol−1
K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15
V mE
−10.2 −10.4 −10.6 −10.7 −10.9 −11.1 −11.3 −11.4 −11.8
± ± ± ± ± ± ± ± ±
0.5 0.5 0.5 0.6 0.6 0.6 0.7 0.7 0.6
49.4 50.1 50.9 51.7 52.5 53.4 54.3 55.1 56.4
± ± ± ± ± ± ± ± ±
0.5 0.5 0.5 0.6 0.6 0.6 0.7 0.7 0.6
745.29 738.01 730.69 723.34 715.95 708.50 700.84 693.26 685.51
± ± ± ± ± ± ± ± ±
0.11 0.11 0.11 0.11 0.12 0.12 0.14 0.15 0.13
0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999
0.07 0.07 0.07 0.07 0.07 0.07 0.09 0.09 0.08
−0.11 −0.12 −0.13 −0.14 −0.15 −0.17 −0.17 −0.16 −0.16
a
X1 is the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane). The errors for the coefficients A, B, and C represent the 95% confidence interval. The σ is the standard error of the fit as given by eq 2. bThe standard deviation in the excess volume was calculated to be 0.02 cm3·mol−1 at T < 353.15 K and 0.04 cm3·mol−1 at T ≥ 353.15 K. 1160
DOI: 10.1021/je501141e J. Chem. Eng. Data 2015, 60, 1157−1165
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Table 6. Speed of Sound, m·s−1, of Mixtures of 2,2,4,4,6,8,8-Heptamethylnonane (X1) in 2,2,4,6,6-Pentamethylheptane from T = (293.15 to 343.15) K and 0.1 MPaa W1
X1
Temperature K
0.8998 0.8000 0.7000 0.6000 0.5000 0.4000 0.3001 0.2001 0.1000
0.8711 0.7506 0.6371 0.5302 0.4293 0.3340 0.2439 0.1584 0.0772
293.15
303.15
313.15
323.15
333.15
343.15
1276.9 1268.2 1259.6 1251.1 1242.9 1234.8 1226.7 1219.4 1211.7
1239.6 1230.8 1221.9 1213.3 1205.0 1196.6 1188.4 1180.9 1173.0
1202.8 1193.9 1184.8 1176.1 1167.6 1159.0 1150.7 1143.0 1135.0
1166.8 1157.7 1148.5 1139.7 1131.0 1122.2 1113.7 1105.9 1097.7
1131.6 1122.3 1112.9 1103.9 1095.1 1086.1 1077.5 1069.5 1061.1
1096.9 1087.5 1077.9 1068.8 1059.8 1050.7 1041.9 1033.7 1025.2
a
W1 is the mass fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane) and X1 is the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane). Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc is Uc(c) = 0.4 m·s−1, (level of confidence = 0.95, k ≈ 2).
eq 4, does not fit the data very well, with standard errors of at least 1.5 m·s−1, which are much greater than the combined expanded uncertainty of the measurements, which is 0.5 m·s−1. The standard errors for the second order fit, which are approximately 0.20 m·s−1, are much closer to the uncertainities found in the measurements themselves. These second order fits have R2 > 0.999 and are shown in Figure 2. The isentropic bulk modulus of the 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6-pentamethylheptane mixtures, Ev, was calculated at each temperature and ambient pressure from the speed of sound (c) and density (ρ) by12,14−18 Ev /Pa = (c 2/m 2·s−2)(ρ /kg·m−3)
(6)
The calculated values are given Table 8. The bulk modulus increases with decreasing temperature and increasing mole fraction of 2,2,4,4,6,8,8-heptamethylnonane. The bulk modulus value for an ATJ was reported to be 1143 MPa at 293.15 K.2 This bulk modulus value falls between (1139 and 1160) MPa for the 0.3001 and 0.4000 mass fraction of 2,2,4,4,6,8,8heptamethylnonane in 2,2,4,6,6-pentamethylheptane, respectively. 4.3. Viscosity. The viscosity values of 2,2,4,4,6,8,8heptamethylnonane and 2,2,4,6,6-pentamethylheptane are given as a function of temperature in Table 2 along with literature values. The viscosities of the pure components match reported values within the error of the measurements. The dynamic and kinematic viscosity values of 2,2,4,4,6,8,8heptamethylnonane, 2,2,4,6,6-pentamethylheptane and their
Figure 2. Speed of sound of 2,2,4,4,6,8,8-heptamethylnonane (X1) + 2,2,4,6,6-pentamethylheptane mixtures at: □, 293.15 K; ■, 303.15 K; △, 313.15 K; ▲, 323.15 K; ◇, 333.15 K; ◆, 343.15 K. Error bars, which are the combined expanded uncertainties with 0.95 level of confidence (k ≈ 2), are smaller than the symbols. Lines shown are polynomial fits using eq 5 with the coefficients in Table 7
In these equations, X1 is the mole fraction of the 2,2,4,4,6,8,8heptamethylnonane, and A, B, C, D, and E are fitting parameters, which are given in Table 7. The standard error for the fit (σ) was determined by eq 2 for the first order and the second order models, where Pmeasured is the measured speed of sound and Pm,cal is the fitted speed of sound. The linear model,
Table 7. Parameters for Equation 4, c = AX1 + B, and Equation 5, c = CX12 + DX1 + E, That Correlates Speed of Sound, c in m· s−1, to the Mole Fraction of 2,2,4,4,6,8,8-Heptamethylnonane (X1) in 2,2,4,6,6-Pentamethylheptane and Associated Standard Error, Equation 2 Over Temperature Range T = (293.15 to 343.15) Ka T
A
σ
C
−1
K 293.15 303.15 313.15 323.15 333.15 343.15
R2
B m·s
82.0 83.6 85.2 86.8 88.4 90.0
± ± ± ± ± ±
3.3 3.4 3.5 3.6 3.7 3.8
1206.2 1167.5 1129.4 1092.0 1055.3 1019.3
± ± ± ± ± ±
D
−1
m·s 1.8 1.9 2.0 2.0 2.1 2.1
0.997 0.997 0.997 0.997 0.997 0.997
1.5 1.6 1.6 1.7 1.7 1.8
−15.4 −16.0 −16.6 −17.0 −17.5 −17.9
± ± ± ± ± ±
E m·s
1.6 1.6 1.6 1.5 1.5 1.5
97.1 ± 1.7 99.3 ± 1.6 101.4 ± 1.6 103.5 ± 1.6 105.6 ± 1.5 107.6 ± 1.5
1204.0 1165.2 1127.1 1089.6 1052.9 1016.8
R2
σ
0.999 0.999 0.999 0.999 0.999 0.999
0.21 0.20 0.20 0.20 0.19 0.19
−1
± ± ± ± ± ±
0.2 0.3 0.3 0.3 0.3 0.3
a
X1 is the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane). The errors for the coefficients A, B, C, D, and E are the 95% confidence interval. 1161
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ln νm = X13 ln ν1 + 3X12X 2 ln ν1,2 + 3X1X 22 ln ν2,1 + X 23 ln ν2
Table 8. Bulk Modulus, in MPa, of Mixtures of 2,2,4,4,6,8,8Heptamethylnonane, X1, in 2,2,4,6,6-Pentamethylheptane from T = (293.15 to 343.15) K and 0.1 MPaa W1
X1
⎛1⎛ ⎛ M ⎞ M ⎞⎞ − ln⎜X1 + X 2 2 ⎟ + 3X12X 2 ln⎜⎜ ⎜2 + 2 ⎟⎟⎟ M1 ⎠ M1 ⎠⎠ ⎝ ⎝3⎝
temperature
⎛1⎛ ⎛M ⎞ M ⎞⎞ + 3X1X 22 ln⎜⎜ ⎜1 + 2 2 ⎟⎟⎟ + X 23 ln⎜ 2 ⎟ M1 ⎠⎠ ⎝ M1 ⎠ ⎝3⎝
K 1.000 0.8998 0.8000 0.7000 0.6000 0.5000 0.4000 0.3001 0.2001 0.1000 0.000
293.15
303.15
313.15
323.15
333.15
343.15
1297 1273 1249 1226 1203 1181 1160 1139 1119 1100 1080
1213 1189 1166 1143 1121 1100 1079 1059 1040 1021 1001
1133 1110 1087 1065 1044 1023 1003 983 965 946 928
1057 1035 1013 992 971 951 931 912 894 876 858
986 965 944 922 903 883 864 845 828 811 793
919 898 878 857 838 819 800 783 766 749 732
1.000 0.8711 0.7506 0.6371 0.5302 0.4293 0.3340 0.2439 0.1584 0.0772 0.000
(7)
Here, νm is the kinematic viscosity of the binary mixture, X1 and X2 are the mole fractions, ν1 and ν2 are the kinematic viscosities of the pure components, and M1 and M2 are the molar masses of 2,2,4,4,6,8,8-heptamethylnonane as component 1 and 2,2,4,6,6-pentamethylheptane as component 2. To determine the interaction parameters ν2,1 and ν1,2, the GRG nonlinear engine of the SOLVER function in Microsoft Excel 2010 was used to minimize the sum of the square of the difference between the value calculated by the model in eq 7, νm,calc, and the measured kinematic viscosity of the binary mixture, νmeasured15−18
a
W1 is the mass fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane) and X1 is the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane). Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc is Uc(bulk modulus) = 0.5 MPa, (level of confidence = 0.95, k ≈ 2).
min Σ(νm,calc − νmeasured)2
(8)
The standard error for the fit (σ) was determined by eq 2, in which Pmeasured is the measured viscosity and Pm,cal is the fitted viscosity. Both the fitted values of ν2,1, and ν1,2, and the standard errors of the fits are given in Table 10 at each temperature. Figure 3 shows that the model fits the data well. The viscosity deviation (Δν) was also calculated for the twocomponent systems using
mixtures are given in Table 9 as a function of the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane (X1). The McAllister three-body model23 was used to fit the kinematic viscosity data
Δν = νm − (X1ν1) − (X 2ν2)
(9)
Table 9. Viscosity of Mixtures of 2,2,4,4,6,8,8-Heptamethylnonane, X1, in 2,2,4,6,6-Pentamethylheptane from T = (293.15 to 373.15) K and 0.1 MPaa W1
X1
viscosity
temperature K
1.000
1.000
0.8998
0.8711
0.8000
0.7506
0.7000
0.6371
0.6000
0.5302
0.5000
0.4293
0.4000
0.3340
0.3001
0.2439
0.2001
0.1584
0.1000
0.0772
0.000
0.000
μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1 μ/mPa·s ν/mm2·s−1
293.15
303.15
313.15
323.15
333.15
343.15
353.15
363.15
373.15
3.71 4.73 3.25 4.16 2.86 3.69 2.56 3.31 2.29 2.98 2.08 2.72 1.87 2.46 1.70 2.25 1.55 2.06 1.43 1.90 1.31 1.76
2.93 3.77 2.59 3.35 2.31 3.00 2.08 2.72 1.88 2.46 1.71 2.26 1.55 2.05 1.42 1.89 1.30 1.74 1.20 1.62 1.11 1.50
2.37 3.07 2.12 2.76 1.90 2.49 1.72 2.27 1.56 2.07 1.43 1.91 1.30 1.74 1.20 1.62 1.10 1.49 1.02 1.39 0.948 1.30
1.95 2.55 1.76 2.31 1.59 2.10 1.44 1.92 1.32 1.76 1.21 1.63 1.11 1.50 1.03 1.40 0.947 1.30 0.882 1.21 0.820 1.13
1.64 2.16 1.48 1.96 1.34 1.79 1.23 1.65 1.13 1.52 1.04 1.41 0.956 1.31 0.889 1.22 0.822 1.14 0.768 1.07 0.715 0.999
1.39 1.85 1.26 1.69 1.15 1.55 1.06 1.44 0.975 1.33 0.906 1.24 0.834 1.15 0.778 1.08 0.721 1.01 0.676 0.948 0.632 0.892
1.19 1.61 1.09 1.48 0.998 1.36 0.923 1.26 0.852 1.17 0.794 1.10 0.734 1.02 0.687 0.963 0.638 0.899 0.600 0.851 0.562 0.802
1.04 1.41 0.954 1.30 0.880 1.21 0.813 1.12 0.753 1.05 0.704 0.985 0.653 0.919 0.613 0.869 0.570 0.813 0.538 0.772 0.505 0.729
0.913 1.25 0.841 1.16 0.780 1.08 0.723 1.01 0.673 0.944 0.630 0.890 0.586 0.833 0.553 0.791 0.515 0.741 0.487 0.706 0.459 0.669
a
W1 is the mass fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane) and X1 is the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane). Standard uncertainties u are u(T) = 0.01 K, and combined expanded uncertainties Uc is Uc(μ) = 0.02 mPa·s and Uc(ν) = 0.02 mm2·s−1 (level of confidence = 0.95, k ≈ 2). 1162
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Table 10. Values of the Coefficients for McAllister Equation, Equation 7, and Associated Standard Error, Equation2, for Binary Mixtures of 2,2,4,4,6,8,8-Heptamethylnonane and 2,2,4,6,6-Pentamethylheptane from T = (293.15 to 373.15) K T
ν12
ν21
σ
K
mm2·s−1
mm2·s−1
103·mm2·s−1
293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15
3.40 2.79 2.33 1.97 1.70 1.47 1.29 1.15 1.04
2.50 2.09 1.78 1.53 1.33 1.17 1.04 0.934 0.847
6.5 4.9 3.8 3.1 2.8 2.7 2.5 2.0 2.0
Figure 4. Viscosity deviation of 2,2,4,4,6,8,8-heptamethylnonane (X1) + 2,2,4,6,6-pentamethylheptane mixtures as calculated by eq 9 shown at: □, 293.15 K; ■, 303.15 K; △, 313.15 K; ▲, 323.15 K; ◇, 333.15 K; ◆, 343.15 K; ○, 353.15 K; ●, 363.15 K; ×, 373.15 K. Lines shown are fits to eq 10 with the coefficients in Table 11. Data can be found in the Supporting Information.
deviation and Pfit is the fitted viscosity deviation. The fitted values of A1, A2, and A3, and the standard errors of the fits are given in Table 11 for each temperature. The model fits the data well as shown in Figure 4. Table 11. Parameters for Redlich−Kister Equation, Equation 10, for Excess Viscosity of Mixtures of 2,2,4,4,6,8,8Heptamethylnonane and 2,2,4,6,6-Pentamethylheptane and Associated Standard Error, Equation 2, at 0.1 MPa
Figure 3. Viscosity of 2,2,4,4,6,8,8-heptamethylnonane (X1) + 2,2,4,6,6-pentamethylheptane mixtures at: □, 293.15 K; ■, 298.15 K; △, 303.15 K; ▲, 308.15 K; ◆, 318.15 L; ○, 323.15 K; ●, 328.15 K; ×, 333.15 K. Error bars, which are the combined expanded uncertainties with 0.95 level of confidence (k ≈ 2), are smaller than the symbols. Lines shown are fits using eq 7 with the coefficients in Table 10.
νm is the kinematic viscosity of the binary mixture, ν1 and ν2 are the kinematic viscosities of the pure components, and X1 and X2 are the mole fractions of 2,2,4,4,6,8,8-heptamethylnonane as component 1 and 2,2,4,6,6-pentamethylheptane as component 2. The calculated values of the viscosity deviations for all 2component mixtures are given in Table S1 of the Supporting Information. Figure 4 shows that the viscosity deviations for the mixtures are negative. The negative viscosity deviations indicate that the molecules in the mixture are sliding past each other more easily than they do in pure liquids. As the temperature increases, the values deviate less from zero. The viscosity deviations were fit using a Redlich−Kister type expression18,24
A1·10
A2·102
A3·102
σ·103
K
mm2·s−1
mm2·s−1
mm2·s−1
mm2·s−1
293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15
−13.7 −9.41 −6.65 −4.84 −3.58 −2.72 −2.19 −1.65 −1.26
−29.2 −18.1 −11.6 −7.84 −5.32 −3.84 −3.21 −1.72 −1.07
− 17.8 −10.9 −7.32 −5.29 −2.60 −2.82 −2.32 −1.16 −≤1.73
6.1 4.9 3.9 3.2 3.1 2.9 2.8 2.2 2.3
The viscosity value for an ATJ was reported to be 1.52 mm2· s at 313.15 K.2 This viscosity value falls between the viscosity values of (1.49 and 1.62) mm2·s−1 for mass fractions of 2,2,4,4,6,8,8-heptamethylnonane in 2,2,4,6,6-pentamethylheptane of 0.2001 and 0.3001, respectively. 4.4. Surface Tension and Flash Point. The surface tension and flash point values are given in Table 12 for the mixtures studied herein as a function of the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane, X1. The surface tension of 2,2,4,6,6-pentamethylheptane, 21.4 ± 0.2 mN·m−1 at 295.2 K is slightly lower than the previously reported value of 21.8 ± 0.2 mN·m−1 at 294 K.15 Because surface tension decreases as temperature increases, a slightly lower value is expected when the temperature increases by a small amount. As can be seen from the data in Table 12, the surface tension decreases as the mole fraction of the 2,2,4,4,6,8,8-heptamethylnonane decreases. The flash point values also decrease as the mole fraction of the 2,2,4,4,6,8,8-heptamethylnonane decreases, but the decrease is not linear as shown in Figure 5. There is a steeper decrease as −1
j−1
Δν = X1X 2 ∑ Aj (X1 − X 2) j j=0
T
(10)
where Aj are adjustable parameters, j is the order of the polynomial, and X1 and X2 are the mole fraction of the 2,2,4,4,6,8,8-heptamethylnonane and 2,2,4,6,6-pentamethylheptane, respectively. The standard error for the fit (σ) was determined by eq 2, where Pmeasured is the calculated viscosity 1163
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5. CONCLUSIONS In this work, the physical properties of mixtures of 2,2,4,6,6pentamethylheptane and 2,2,4,4,6,8,8-heptamethylnonane were measured and compared with those of ATJ fuel, which contains branched alkanes. Most of the pure component measurements fell within values reported in the literature. The densities of the mixtures as a function of mole fraction of 2,2,4,4,6,8,8heptamethylnonane at each temperature were well modeled using a second-order polynomial function, and the viscosity values of the mixtures at each temperature were well modeled using the McAllister three-body model. A second-order polynomial function best fits the speed of sound and mole fraction data. Comparison of mixture properties with those of an alcohol-to-jet (ATJ) fuel showed that the properties of density, bulk modulus, viscosity, surface tension, and flash point were matched by mixtures containing mass fractions of 2,2,4,4,6,8,8-heptamethylnonane in 2,2,4,6,6-pentamethylheptane between 0.2001 and 0.5000, with a mass fraction of 0.3001 being the best. These results suggest that a mixture containing 0.3001 mass fraction of 2,2,4,4,6,8,8-heptamethylnonane in 2,2,4,6,6-pentamethylheptane would be a good surrogate for combustion testing alongside the ATJ fuel.
Table 12. Surface Tension and Flash Point of Mixtures of 2,2,4,4,6,8,8-Heptamethylnonane (X1) in 2,2,4,6,6Pentamethylheptanea X1 1.000 0.8711 0.7506 0.6371 0.5302 0.4293 0.3340 0.2439 0.1584 0.0772 0.000
surface tension (mN·m−1) c
24.0 23.7 23.3 23.1 22.9 22.6 22.2(3) 22.1(6) 21.9 21.7 21.4
flash point (K) 367b 351 342 336 332 329 326 323 322 321 318b
a
X1 is the mole fraction of 2,2,4,4,6,8,8-heptamethylnonane in (2,2,4,4,6,8,8-heptamethylnonane + 2,2,4,6,6-pentamethylheptane). Combined expanded uncertainties Uc are U(x1) = 0.0001, Uc(surface tension) = 0.2 mN·m−1, Uc(Flash point) = 2 K (level of confidence = 0.95, k ≈ 2). Surface tension measurements were taken at room temperature, 294.9 ± 1 K. bRef 15. cRef 16.
■
ASSOCIATED CONTENT
* Supporting Information S
The values of the viscosity deviation for the mixtures. This material is available free of charge via the Internet at http:// pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: (410) 293-6339. Fax: (410) 293-2218. Funding
This work was funded by the Office of Naval Research. Notes
The authors declare no competing financial interest.
Figure 5. Flash point of 2,2,4,4,6,8,8-heptamethylnonane (X1) + 2,2,4,6,6-pentamethylheptane mixtures. Flash point is nonlinear with X1.
■
REFERENCES
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