Density, Viscosity, Speed of Sound, Bulk Modulus ... - ACS Publications

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Density, Viscosity, Speed of Sound, Bulk Modulus, Surface Tension, and Flash Point of Binary Mixtures of Butylcyclohexane with Toluene or n‑Hexadecane Dianne J. Luning Prak* Chemistry Department, United States Naval Academy, 572M Holloway Road, Annapolis, Maryland 21402, United States S Supporting Information *

ABSTRACT: The viscosities and densities ((293.15 to 353.15) K), speeds of sound ((293.15 to 333.15) K), surface tensions (room temperature), and flash points were measured for binary mixtures of n-butylcyclohexane with either toluene or n-hexadecane. Increasing the temperature decreased the densities, and the excess molar volumes of the mixtures were generally positive, suggesting increased spacing due to differences in packing and intermolecular forces. Increasing the temperature also decreased the viscosities, and the McAllister three-body model successfully modeled the viscosity with the larger fitting term corresponding to two molecules of the more viscous substance. The mixture surface tensions and flash points fell between the pure-component values, which ranged from (26.7 to 28.6) mN·m−1 and (324.7 to 406.2) K, respectively. The speed of sound decreased with increasing mole fraction of n-butylcycylohexane in nhexadecane, but several speed of sound values for mixtures of n-butylcyclohexane and toluene were lower than those of either component. For both sets of mixtures, the isentropic bulk moduli of several mixtures were lower than those of their components. These results show that simple blending rules cannot be used to predict the speed of sound and bulk modulus of these mixtures.

1. INTRODUCTION Petroleum researchers often formulate surrogate fuel mixtures in an effort to understand the combustion behavior of fuels containing a large number of components. Surrogates containing from one to 14 components have been formulated for petroleum-based and renewable diesel fuel and jet fuel and for rocket propellants.1−18 Components of the fuel are used to develop formulations whose properties match those of the fuel of interest. Pitz and Mueller1 reported that the primary components that have been used in preparing diesel fuel surrogates are aromatic compounds, cycloalkanes, n-hexadecane (to represent n-alkanes), and isoalkanes. For cycloalkanes, they state that compounds can have up to 22 carbons, but most kinetic studies have focused only on the shorter-chain alkyl groups from lower molecular weight compounds such as methyl-, ethyl-, and propylcyclohexane.1,14,15,19−21 Ristori et al.20 measured the reaction kinetics of propylcyclohexane in a jet-stirred reactor at high temperatures and modeled the reaction kinetics using 1369 reactions with 176 species. Vanderover and Oehlschlaeger19 measured the ignition time in high-pressure shock tubes and found that methylcyclohexane had longer ignition times than ethylcyclohexane under the conditions tested, which suggested a greater reactivity of the longer-chain hydrocarbon. More recent studies have examined the kinetic behavior of butylcyclohexane,22−24 and Mueller et al.3 recently included butylcyclohexane as part of eight- and nine-component diesel fuel surrogates. Liu et al.24 reported ignition temperatures in counterflow configurations at atmospheric pressures that were the same for methyl-, ethyl-, propyl-, and butylcyclohexane. In contrast, Hong et al.23 reported This article not subject to U.S. Copyright. Published XXXX by the American Chemical Society

ignition delay times in shock tubes that were greater for methylcyclohexane than for n-butylcyclohexane, and Natelson et al. 22 found that the low-temperature reactivity of butylcyclohexane oxidized in a flow reactor was similar to that of linear alkanes under conditions where there was no reactivity for methylcyclohexane or n-butylbenzene. Natelson et al.22 developed a model for n-butylcyclohexane kinetics consisting of 80 reactions involving 42 species that was used to model the high-temperature reaction behavior of jet fuel surrogates. All of these shorter-chain cycloalkanes are also found in jet fuel and can be used in jet fuel surrogate mixtures. As these higher-molecular-weight cycloalkanes are used in surrogate mixtures, more information on their properties in mixtures is needed. The current study measured the properties of binary mixtures of butylcyclohexane with two other components commonly found in fuel surrogate mixtures, nhexadecane and toluene.10−13 The fuel properties that have been used in surrogate development are those that are important for the physical process of fuel delivery to the engine and the chemical process of combustion. These properties include ignition quality, boiling point, melting point, speed of sound, viscosity, density, advanced distillation curve, derived cetane number, total sooting index, flash point, lower heating value, surface tension, and smoke point.3,4,7,8,12 Additional factors that have been considered in surrogate formulations are cost, safety, Received: June 22, 2016 Accepted: September 16, 2016

A

DOI: 10.1021/acs.jced.6b00516 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Sample Information

a

chemical

CAS number

molar mass (g/mol)a

source/lot number

mole-fraction purity

analysis method

toluene (C7H8) n-butylcyclohexane (C10H20) n-hexadecane (C16H34)

108-88-3 1678-93-9 544-76-3

92.138 ± 0.007 140.27 ± 0.01 226.44 ± 0.02

Pharmco-Aaper/C100817-Tol TCI/ZMU4G Acros Organics/A0360424

0.9997 0.999 0.998

GCb GCb GCb

Calculated using values in ref 29. bGas−liquid chromatography, as specified in the Certificates of Analysis provided by the chemical suppliers.

Table 2. Comparison of the Measured Densities and Speeds of Sound of n-Hexadecane, n-Butylcyclohexane, and Toluene with Literature Valuesa density/kg·m−3 T/K

this studya

speed of sound/m·s−1 lit.

this studya

lit.

1357.2 1319.5 1283.3 1247.3 1212.0

1357.0 ± 0.3,e 1357.1,d 1357.7,g 1319.5 ± 0.3,e 1319.6,d 1320.0,f 1320.2g 1282.8,i 1282.8 ± 0.3,e 1283,h 1283.4,d 1283.4g 1246.8 ± 0.3,e 1246.9,d 1247.4,g 1248h 1211.2,i 1211.4,f 1211.6,d 1212,h 1212.3g

1328.4 1288.7 1249.5 1210.8 1172.8

1328.7m 1289.0m 1247.7m 1210.4m 1169.8m

1326.6 1283.6 1241.1 1199.2 1157.7

1326.9o 1324.3 ± 1%p 1281.6 ± 1%p 1240.9,o 1239.7 ± 1%p 1198.9o 1198.5 ± 1%p 1157.7,o 1158.0 ± 1%p

n-Hexadecane 293.15 303.15 313.15 323.15 333.15 343.15 353.15

773.41 766.47 759.55 752.63 745.71 738.8 731.9

293.15 303.15 313.15 323.15 333.15 343.15 353.15

799.33 791.82 784.28 776.70 769.09 761.4 753.7

293.15 303.15 313.15 323.15 333.15 343.15 353.15

866.84 857.52 848.14 838.68 829.15 819.6 809.8

773.43 ± 0.06,b 773.69,d 773.7 ± 0.2c 766.59 ± 0.05,b 766.75,d 766.8 ± 0.2c 759.55,d 759.83,d 759.9 ± 0.2,c 759.71 ± 0.07b 752.64,d 752.80 ± 0.12,b 752.9 ± 0.2,c 752.91d 745.73,d 745.86 ± 0.18,b 745.99,d 746.0 ± 0.2c 738.90 ± 0.25,b 739.0 ± 0.2,c 739.07d 731.9 ± 0.2,c 731.90 ± 0.31b n-Butylcyclohexane 799.35 ± 0.39,j 779.37,q799.44,k 799.60l 791.75 ± 0.26j 791.88q 791.95,k 792.10l 784.35,q 784.38 ± 0.63,j 784.41,k 784.56l 776.70,q 777.17,r 777.25 ± 0.95j 769.09,q769.55,r 769.80 ± 0.60,j 770.36 ± 0.80j 761.43,q 761.88r 754.16r Toluene 866.84 ± 0.05,n 866.89 ± 0.05%p 857.54 ± 0.05,n 857.57 ± 0.05%p 848.17 ± 0.05,n 848.20 ± 0.05%p 838.73 ± 0.05,n 838.76 ± 0.05%p 829.20 ± 0.05,n 829.23 ± 0.05%p 819.56 ± 0.09,n 819.61 ± 0.05%p 809.80 ± 0.19,n 809.86 ± 0.05%p

The standard uncertainty u is u(T) = 0.01 K, and the expanded uncertainties Uc are Uc(c) = 0.5 m·s−1 and Uc(ρ) = 0.07 kg·m−3 for T < 353.15 K and Uc(ρ) = 0.2 kg·m−3 for T ≥ 353.15 K (level of confidence = 0.9545, k = 2). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty of Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2). bReference 37. The equation for the best fit of the density of nhexadecane is ρ/kg·m−3 = 956.848 − [0.557634 × T/K] + [2.68578 × 10−4 × (T/K)2] − [1.24436 × 10−7 × (T/K)3]. cReference 16. dReference 38. e Reference 39. fReference 40. gReference 41. hReference 42. iReference 43. jReference 44. The equation for the best fit of the density of nbutylcyclohexane is ρ/kg·m−3 = 1127.02 − [1.46341 × T/K] + [1.17912 × 10−3 × (T/K)2]. kReference 33. lReference 45. mReference 46. n Reference 47. The equation for the best fit of the density of toluene is ρ/kg·m−3 = 1.18621 × 103 − [1.47573 × T/K] + [2.08566 × 10−3 × (T/K)2] − [2.61945 × 10−6 (T/K)3]. oReference 48. pReference 49. qReference 50. rReference 51. a

availability, and purity of compounds and availability of chemical kinetic oxidation mechanisms.3,4 In this paper are reported the surface tensions, densities, flash points, viscosities, and speeds of sound of binary mixtures of butylcyclohexane with toluene or n-hexadecane along with calculations of their bulk moduli. Surface tension, density, and viscosity were chosen in this study because they are used in the modeling of spray breakup in the form of Reynolds and Weber numbers.25 Kim et al.25 recently included density, viscosity, and surface tension in their computer simulations of spray properties and ignition behavior. At lower temperatures, they found that the liquid penetration depth had a similar sensitivity to changes in viscosity and surface tension and a greater sensitivity to density changes. At higher temperatures, they found that the sensitivity to viscosity was greater than the sensitivity to surface tension but less than the sensitivity to density. The speed of sound and density were measured herein because they are used to

calculate the bulk modulus, which can impact the timing involved in fuel injection.2,26 The flash point was measured in this study because it is used as a safety metric in the specification of military fuels to avoid fire hazards on ships.27 Since comparisons of property measurements are often used in surrogate development for fuels, the values from petroleumbased diesel and jet fuel are compared to those of the mixtures measured herein to assess their potential usefulness in surrogate development. These measurement can also be useful as test sets for models that seek to predict a mixture’s properties from its chemical composition.

2. MATERIALS Toluene, n-hexadecane, and n-butylcyclohexane were used as received from their suppliers (Table 1). The mixture preparation procedure using a Mettler Toledo AG204 analytical balance can be found in the paper by Luning Prak and Lee.28 B



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Table 3. Densities (in kg·m−3) of Binary Mixtures of n-Butylcyclohexane (1) + Toluene or n-Hexadecane (2) from T = (293.15 to 353.15) K at 0.1 MPa density/kg·m−3 at T/K = w1

x1

293.15

0.1002 0.2175 0.3001 0.3999 0.5000 0.6001 0.6995 0.8001 0.8996

0.0681 0.1544 0.2197 0.3045 0.3964 0.4964 0.6046 0.7244 0.8548

858.58 849.42 843.23 835.97 829.25 822.67 816.44 810.43 804.75

0.1002 0.2000 0.3001 0.3998 0.4998 0.6001 0.7000 0.7999 0.8998

0.1524 0.2876 0.4091 0.5182 0.6173 0.7078 0.7902 0.8658 0.9355

773.41 775.85 778.23 780.67 783.16 785.72 788.34 791.01 793.72

303.15

313.15

323.15

n-Butylcyclohexane (1) + Toluene (2) 849.47 840.29 831.04 840.53 831.58 822.57 834.50 825.72 816.86 827.42 818.82 810.17 820.88 812.46 803.99 814.48 806.25 797.96 808.43 800.37 792.27 802.58 794.70 786.78 797.08 789.37 781.62 n-Butylcyclohexane (1) + n-Hexadecane (2) 766.47 759.55 752.63 768.90 761.94 754.99 771.24 764.25 757.24 773.65 766.60 759.55 776.08 768.99 761.87 778.59 771.43 764.25 781.15 773.92 766.67 783.74 776.44 769.12 786.38 779.00 771.60

333.15

343.15

353.15

821.72 813.48 807.94 801.44 795.45 789.62 784.11 778.81 773.83

812.2 804.3 798.8 792.6 786.8 781.3 775.9 770.7 765.9

802.7 795.1 789.7 783.7 778.1 772.8 767.5 762.6 758.0

745.71 748.02 750.22 752.47 754.73 757.04 759.39 761.76 764.16

738.81 741.10 743.20 745.35 747.50 749.80 752.10 754.35 756.6 ± 0.7

731.9 734.1 736.1 738.3 740.3 742.5 744.7 746.9 749.1 ± 0.6

a

w1 and x1 are the mass fraction and mole fraction, respectively, of n-butylcyclohexane in mixtures with toluene or n-hexadecane. The standard uncertainty u is u(T) = 0.01 K. The expanded uncertainty Uc is Uc(ρ) = 0.07 kg·m−3 for T < 343.15 K and Uc(ρ) = 0.2 kg·m−3 for T ≥ 343.15 K (level of confidence = 0.95, k = 2), unless otherwise indicated by “±”. The combined expanded uncertainties are Uc(x1) = 0.0001 and Uc(w1) = 0.0001, except for x1 = 0.1542 (n-butylcyclohexane + n-hexadecane) and x1 = 0.0681, 0.1544, and 0.2297 (n-butylcyclohexane + toluene), where Uc(x1) = 0.0002. The differences in uncertainty for different temperatures arise from differences in the level of precision for the two instruments. The DSA 5000 analyzer is more precise. The average pressure for these measurements was 0.102 MPa with an expanded uncertainty of Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2).

viscosity ranges. The viscometer is the less precise device, so the reported density values at the lower temperatures are those measured using the DSA 5000 analyzer. The accuracy of the DSA 5000 analyzer was checked before use with degassed distilled water. If it failed the check, it was recalibrated as specified by the manufacturer. Analysis of NIST-certified toluene standards using the DSA 5000 analyzer showed that the density values were within the accepted error reported for the standards. These results are given in Table S1 in the Supporting Information. Surface tension was measured at room temperature using a Kruss DS100 drop shape analyzer, which requires inputs of air and organic liquid density as well as needle size, which was measured by a micrometer (Mitutoyo). The flash point was measured using a Setaflash Series 8 closed-cup flash point tester (model 82000-0, Stanhope-Seta) that conforms to ASTM D3828 (gas ignition option), ASTM D1655 (gas ignition option), ASTM D3278, ASTM D7236, and ASTM E502. For each instrument, two or more measurements were taken to determine the average and standard deviation. For the bulk modulus, the standard deviation was determined by propagating the errors for density and speed of sound. The expanded uncertainty and combined expanded uncertainty were determined by multiplying the standard deviation by 2. When a normal distribution is assumed, multiplying by a coverage factor of 2 produces a 95% confidence interval.

The combined expanded uncertainty (level of confidence = 0.95, k = 2) for the mass fraction of n-butylcyclohexane in toluene or n-hexadecane was determined to be 0.0001. The combined expanded uncertainty for the mole fraction of nbutylcyclohexane in toluene or n-hexadecane was determined to be 0.0001 for most samples, except for x1 = 0.1542 (butylbenzene in n-hexadecane) and x1 = 0.0688, 0.1544, and 0.2297 (butylbenzene in toluene), where the combined expanded uncertainty was 0.0002. These calculations are based on molar masses and errors calculated using atomic masses in Harris29 (see Table 1) and an analytical balance error of 0.0004 g.

3. METHODS All of the methods have been described previously.28,30 Speed of sound and density were measured using an Anton Paar DSA 5000 density and sound analyzer at temperatures between (293.15 and 333.15) K. The DSA 5000 analyzer measures the speed of sound using a propagation time technique with one transducer emitting sound waves at a frequency of approximately 3 MHz and a second transducer receiving those waves.48 The viscosity and density were measured using an Anton Paar SVM 3000 Stabinger viscometer at temperatures between (293.15 and 353.15) K. The accuracy of the viscometer was tested using a certified viscosity reference standard (standard S3, Cannon Instrument Company). If the density deviated by more than 0.1% from the reference value and if the viscosity deviated by more than 1% from the reference value, then the instrument was cleaned and retested. Octane and decane were used to test lower density and

4. RESULTS 4.1. Density. Most of the measured densities of each compound agree with the reported values within the standard C



Article

Figure 2. Excess molar volumes of mixtures of butylcyclohexane (1) and toluene (2) (■, 293.15 K; ▲,313.15 K; ◆, 333.15 K) and of butylcyclohexane (1) and n-hexadecane (2) (□, 293.15 K; △, 313.15 K; ◇,333.15 K). Error bars for the data shown here at 293.15 K are the combined expanded uncertainties at the 0.95 level of confidence (k = 2). Lines shown here are fits using eq 4 with the coefficients given in the Supporting Information.

Figure 1. Densities of n-butylcyclohexane (1) + n-hexadecane (2) (□, 293.15 K; △, 313.15 K; ◇, 333.15 K; ○, 353.15 K) and nbutylcyclohexane (1) + toluene (2) (■, 293.15 K; ▲, 313.15 K; ◆, 333.15 K; ●, 353.15 K). The error bars, which are the combined uncertainties with 0.95 level of confidence (k = 2), are smaller than the symbols. Lines shown are fits using equations and coefficients given in Table 4.

∑ (Pmeasured − Pm ,calc)2

σ=

uncertainty of the measurements, as shown in Table 2. The density of the binary mixtures of n-butylcyclohexane with nhexadecane increases with increasing mole fraction of nbutylcyclohexane, x1, while the density of mixtures of nbutylcyclohexane with toluene decreases with increasing x1 (Table 3). The changes in density are not linear for either set of mixtures, as shown in Figure 1. To capture the trend in the data and to provide an equation for determining the composition at which a binary mixture could match the density of a fuel of interest, eq 1 was used to fit the density−mole fraction data using Microsoft Excel 2010:

∑ A nx1n

(1)

n=0

(2)

In these equations, the An are the fitting parameters, x1 is the mole fraction of n-butylcyclohexane in the mixture, Pmeasured is the measured density, Pm,calc is the fitted density, N is the number of experimental data, and np is the number of parameters in the fitting equation. The maximum exponent in eq 1, m, was increased until the standard error as calculated by eq 2 was less than the combined expanded uncertainty of the measurements. Terms of order lower than the highest order were removed if their 95% confidence interval straddled zero, and the equation was fit again. The fits with the smallest standard error are reported in Table 4 and shown in Figure 1. The reported density values for petroleum-based jet and diesel fuel at 293.15 K are (800.9 and 848) kg·m−3, respectively.9,31 Only the toluene/butylcyclohexane mixtures would adequately

m

ρ /kg·m−3 =

N − np

Table 4. Correlations of the Density to the Mole Fraction of n-Butylcyclohexane, x1, in Binary Mixtures with n-Hexadecane or Toluene and Excess Molar Volumes (VEm) at Specified x1 Values from T = (293.15 to 353.15) K at 0.1 MPa T/K

A4

A3

A2 −3

293.15 303.15 313.15 323.15 333.15 343.15 353.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15

17 17 16 16 16 23 20

± ± ± ± ± ± ±

5 5 5 5 4 9 10

A1

Toluene: ρ/kg·m = A4x1 + ± 10 104 ± 6 ± 10 101 ± 6 ± 10 99 ± 6 ±9 97 ± 6 ±9 95 ± 6 ± 19 102 ± 12 ± 20 96 ± 13 n-Hexadecane: ρ/kg·m−3 9.7 ± 0.2 9.3 ± 0.2 8.9 ± 0.1 8.5 ± 0.1 8.1 ± 0.1 7.9 ± 0.3 7.6 ± 0.2

−61 −59 −58 −57 −55 −70 −62

4

Ao

A3x13

R2

σ

2

+ A2x1 + A1x1 + A0 −128 ± 1 866.83 −124 ± 1 857.51 −121 ± 1 848.13 −118 ± 1 838.68 −115 ± 1 829.14 −114 ± 3 819.5 −109 ± 3 809.8 = A3x13 + A1x1 + A0 16.3 ± 0.2 773.36 16.1 ± 0.2 766.43 15.9 ± 0.2 759.51 15.6 ± 0.1 752.60 15.3 ± 0.1 745.68 14.7 ± 0.3 738.8 14.3 ± 0.2 731.9

± ± ± ± ± ± ±

0.09 0.09 0.09 0.08 0.08 0.1 0.2

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

0.04 0.04 0.04 0.04 0.04 0.08 0.08

± ± ± ± ± ± ±

0.06 0.06 0.05 0.05 0.05 0.1 0.1

0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999

0.03 0.03 0.03 0.03 0.03 0.06 0.04

x1 and VEm/cm3·mol−1 x1 = 0.4964 0.40 0.41 0.42 0.44 0.45 0.44 0.45 x1 = 0.5293 0.12 0.10 0.08 0.06 0.05 NRb NRb

a The “±” for the coefficients A0, A1, A2, A3, and A4 represent the 95% confidence interval. σ is the standard error of the fit as given by eq 2. bNot reported. The errors in these values are greater than the values themselves.

D



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Table 5. Speeds of Sound (in m·s−1) of Binary Mixtures of nButylcyclohexane (1) + Toluene or n-Hexadecane (2) from T = (293.15 to 333.15) K at 0.1 MPa

the molecules to have densities above or below what is found under ideal mixing conditions. The excess molar volume of nbutylcyclohexane in each mixture was calculated using the following equation:

speed of sound/m·s−1 at T/K = x1 0.0681 0.1544 0.2197 0.3045 0.3964 0.4964 0.6046 0.7244 0.8548 0.1524 0.2876 0.4091 0.5182 0.6173 0.7078 0.7902 0.8658 0.9355

293.15

303.15

313.15

323.15

n-Butylcyclohexane (1) + Toluene (2) 1321.1 1278.6 1236.5 1194.9 1316.7 ± 1.0 1274.6 ± 0.9 1232.9 1191.8 1314.5 1272.7 1231.4 1190.6 1313.0 1271.6 1230.6 1190.1 1312.8 1271.6 1230.9 1190.7 1313.5 1272.7 1232.3 1192.5 1315.6 1275.0 1234.9 1195.4 1318.9 1278.6 1238.8 1199.6 1323.3 1283.3 1243.7 1204.8 n-Butylcyclohexane (1) + n-Hexadecane (2) 1353.6 1316.4 1279.7 1243.6 1349.9 1312.6 1275.8 1239.6 1346.4 1309.0 1272.0 1235.5 1343.3 1305.6 1268.5 1231.8 1340.4 1302.5 1265.1 1228.2 1337.4 1299.2 1261.5 1224.3 1334.9 1296.4 1258.3 1220.8 1332.7 1293.8 1255.3 1217.6 1330.4 1291.2 1252.3 1214.1

333.15

VmE =

1153.9 1151.2 1150.3 1150.2 1151.1 1153.2 1156.5 1161.0 1166.5

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

(3)

in which ρm is the mixture density and ρ1 and ρ2 are the purecomponent densities, M1 and M2 are the molar masses, and x1 and x2 are the mole fractions of n-butylcyclohexane as component 1 and either toluene or n-hexadecane as component 2. Values at selected temperatures are shown in Figure 2 and are given in Table 4 for mole fractions close to 0.5 (see Tables S2 and S3 for all of the values). The calculated excess molar volume of 0.12(1) cm3·mol−1 for n-butylcyclohexane in nhexadecane at x1 = 0.5182 is close to the reported value of 0.123 cm3·mol−1 at x1 = 0.50502 at 293.15 K.32 These values are higher than those found for mixtures of n-butylcyclohexane with linear alkanes of lower molar mass and follow the trend of increasing excess molar volume with increasing alkane chain length. Liu and Zhu33 reported excess molar volume values of (−0.311, −0.163, −0.018, 0.064, and 0.115) cm3·mol−1 for butylcyclohexane in mixtures with heptane, octane, decane, dodecane, and tetradecane, respectively, at mole fractions close to 0.50 at 293.15 K. As the chain length on a linear alkane increases, its intermolecular attraction for itself increases. Mixing with butylcyclohexane disrupts this attraction and causes an increase in excess molar volume. Counteracting this increase is a packing effect, which Liu and Zhu say can cause the butylcyclohexane to aggregrate with the n-alkane.33 In their work, they found the packing effect to dominate with butylcyclohexane and n-heptane or n-octane, causing their excess molar volumes to be negative, while what they call the “repulsive force” dominated for butylcyclohexane with decane, dodecane, or tetradecane, causing their excess molar volumes to be positive. This latter behavior is also found for the nhexadecane/n-butylcyclohexane system studied herein. Liu and Zhu33 also showed that the butylcyclohexane excess molar volume decreased as the temperature increased, which is the same trend seen here in Table 4. No studies reporting the excess molar volume of nbutylcyclohexane in toluene were found. Gonzalez et al.34 reported the excess molar volume of cyclohexane in toluene (0.566 cm3·mol−1) to be larger than that of methylcyclohexane in toluene (0.396 cm3·mol−1), with both at mole fractions close to 0.50 at 298.15 K. The vlaues are larger than those at 283.15 K. The excess molar volume of n-butylcyclohexane in toluene at a mole fraction close to 0.50 is 0.40 cm3·mol−1 at 293.15 K and 0.41 cm3·mol−1 at 303.15 K, indicating that its excess molar volume is similar to that for methylcyclohexane. Following the logic given in the previous paragraph, it appears that the relative dominance of the packing effect relative to intermolecular interactions appears to be same for mixing of n-butylcyclohexane with toluene as it is for mixing of methylcyclohexane with toluene. The values found herein also follow the same trend as seen by Gonzalez et al.,34 with the excess molar volume increasing with increasing temperature (Table 4 and Figure 2). The excess molar volumes were fit with a Redlich−Kistertype expression:

1208.1 1203.9 1199.7 1195.7 1191.8 1187.6 1183.9 1180.3 1176.4

a x1 is the mole fraction of n-butylcyclohexane in mixtures with toluene or n-hexadecane. The standard uncertainty u is u(T) = 0.01 K. The expanded uncertainty Uc is Uc(c) = 0.8 m·s−1 (level of confidence = 0.95, k = 2), unless otherwise indicated. The combined expanded uncertainty is Uc(x1) = 0.0001 except for x1 = 0.1542 (nbutylcyclohexane + n-hexadecane) and x1 = 0.0681, 0.1544, and 0.2297 (n-butylcyclohexane + toluene), where Uc(x1) = 0.0002. The average pressure for these measurements was 0.102 MPa with an expanded uncertainty of Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2).

Figure 3. Speeds of sound of mixtures of butylcyclohexane (1) and toluene (2) (■, 293.15 K; ▲, 313.15 K; ◆, 333.15 K) and of butylcyclohexane (1) and n-hexadecane (2) (□, 293.15 K; △, 313.15 K; ◇, 333.15 K). The error bars, which are the combined uncertainties at the 0.95 level of confidence (k = 2), are smaller than the symbols. Lines shown are fits with equations and coefficients given in Table 6.

match the density of the diesel fuel. The density of the jet fuel falls between those of these mixtures and could possibly be matched by a mixture containing all three components. A commonly used parameter for examining the interaction and packing of molecules in multicomponent systems is the excess molar volume (VEm). Interactions and packing can cause E



Article

Table 6. Correlation of the Speed of Sound to the Mole Fraction of n-Butylcyclohexane, x1, in Binary Mixtures with Toluene or n-Hexadecane from T = (293.15 to 333.15) K at 0.1 MPa T/K

A3

A2

A1 −1

−53.3 −51.0 −49.5 −48.4 −46.9

293.15 303.15 313.15 323.15 333.15

± ± ± ± ±

A0

R2

σ

A2x12

+ A1x1 + A0 Toluene: c/m·s = A3x1 + 135 ± 12 −80.0 ± 4.9 130 ± 11 −73.6 ± 4.6 126 ± 11 −67.5 ± 4.4 122 ± 10 −61.7 ± 4.2 118 ± 10 −55.5 ± 4.1 n-Hexadecane: c/m·s−1 = A2x12 + A1x1 + A0 −3.9 ± 1.1 −25.2 ± 1.1 −8.3 ± 1.4 −22.8 ± 1.5 −10.7 ± 0.7 −23.1 ± 0.8 −13.5 ± 1.0 −22.9 ± 1.1 −16.0 ± 1.2 −23.0 ± 1.3

7.9 7.4 7.1 6.8 6.6

293.15 303.15 313.15 323.15 333.15 a

3

1326.2 1283.3 1240.8 1198.9 1157.4

± ± ± ± ±

0.5 0.5 0.5 0.4 0.4

0.998 0.999 0.999 0.999 0.999

0.26 0.25 0.24 0.23 0.22

1357.3 1319.7 1283.3 1247.3 1211.9

± ± ± ± ±

0.3 0.3 0.2 0.2 0.3

0.999 0.999 0.999 0.999 0.999

0.13 0.18 0.09 0.13 0.16

The “±” for the coefficients A0 , A1, A2, and A3 represent the 95% confidence interval. σ is the standard error of the fit as given by eq 2.

Table 7. Bulk Moduli (in MPa) of Binary Mixtures of nButylcyclohexane (1) + Toluene or n-Hexadecane (2) from T = (293.15 to 333.15) K at 0.1 MPa

where the Aj are adjustable parameters, j is the order of the polynomial, x1 is the mole fraction of n-butylcyclohexane, and x2 is the mole fraction of either toluene or n-hexadecane. The adjustable parameters Aj were determined by minimizing the sum of the squares of the differences between the calculated excess molar volumes of the binary mixture and the values calculated by the model in eq 4. The standard error for the fit (σ) was determined using eq 2, in which Pmeasured is the experimental excess molar volume and Pm,calc is the fitted excess molar volume. The values of A0, A1, A2, and the standard errors of the fits are given in Table S4. The model fits the data well, as shown in Figure 2. 4.2. Speed of Sound and Bulk Modulus. Most of the measured speeds of sound of each compound agree with the reported values within the standard uncertainty of the measurements, as shown in Table 2. The speeds of sound of binary mixtures of n-butylcyclohexane with n-hexadecane decrease with increasing mole fraction of n-butylcyclohexane, x1 (Table 5). For mixtures with toluene, however, as the mole fraction of butylcyclohexane increases, the speed of sound decreases to values below that of either individual component before increasing to that of n-butylcyclohexane, as shown in Figure 3. No literature values for these mixtures are available for comparison. Gonzalez et al.34 reported a similar dip in the speed of sound for mixtures of cyclohexane with toluene but not for mixtures of methylcyclohexane with toluene. The experimental data for the mixtures were fit using the same approach as was used for density in eq 1. The fitting parameters along with the standard error for the fit (σ) as determined by eq 2, where Pmeasured is the measured speed of sound and Pm,calc is the fitted speed of sound, can be found in Table 6. The model fits the data well (with R2 > 0.999), as shown in Figure 3. The isentropic bulk modulus at ambient pressure, KS, was calculated for each mixture at each temperature using

bulk modulus/MPa at T/K = x1

293.15

0.000 0.0681 0.1544 0.2197 0.3045 0.3964 0.4964 0.6046 0.7244 0.8548 1.000 0.000 0.1524 0.2876 0.4091 0.5182 0.6173 0.7078 0.7902 0.8658 0.9355 1.000

303.15

313.15

323.15

n-Butylcyclohexane (1) + Toluene (2) 1526 1413 1306 1206 1498 1389 1285 1187 1473 1366 1264 1168 1457 1352 1252 1158 1441 1338 1240 1148 1429 1327 1231 1140 1419 1319 1224 1135 1413 1314 1221 1132 1410 1312 1220 1132 1409 1313 1221 1135 1411 1315 1224 1139 n-Butylcyclohexane (1) + n-Hexadecane (2) 1425 1334 1251 1171 1422 1332 1248 1168 1418 1329 1244 1164 1415 1326 1240 1159 1413 1323 1237 1156 1412 1321 1235 1153 1410 1319 1232 1149 1409 1317 1229 1146 1410 1316 1228 1144 1410 1315 1226 1141 1411 1315 1224 1139

333.15 1111 1094 1078 1069 1060 1054 1050 1049 1050 1053 1058 1095 1092 1087 1083 1079 1075 1071 1068 1065 1061 1058

a x1 is the mole fraction of n-butylcyclohexane in mixtures with toluene or n-hexadecane. The standard uncertainty u is u(T) = 0.01 K, and the combined expanded uncertainties Uc are Uc(bulk modulus) = 1 MPa (level of confidence = 0.95, k = 2), unless otherwise indicated, and Uc(x1) = 0.0001, except for x1 = 0.1542 (n-butylcyclohexane + nhexadecane) and x1 = 0.0681, 0.1544, and 0.2297 (n-butylcyclohexane + toluene), where Uc(x1) = 0.0002. The average pressure for these measurements was 0.102 MPa with an expanded uncertainty of Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2).

KS /Pa = (c 2/m 2·s−2)(ρ /kg·m−3)

where c is the speed of sound and ρ is the density, and the calculated values are given in Table 7. At 293.15 K, the bulk modulus declines to values slightly below that of either individual component before increasing again to that for nbutylcyclohexane. At higher temperatures, this is seen only for the toluene mixtures. When the combined expanded uncertainty of the values is taken into consideration, the bulk modulus could be considered level at all high mole fractions of n-butylcyclohexane. The bulk modulus and speed of sound for

n

VmE = x1x 2 ∑ Aj (x1 − x 2) j j=0

= x1x 2[A 0 + A1(x1 − x 2) + A 2 (x1 − x 2)2 ]

(5)

(4)

F



Article

Table 8. Comparison of the Measured Viscosity Values, mPa·s, of Toluene, Butylcyclohexane, and n-Hexadecane with Literature Values n-butylcyclohexane

toluene T/K

this work

lit.

this work

293.15

0.60(7) ± 0.01

0.5859,b 0.5866,c 0.5887,d 0.5882e

1.31 ± 0.01

303.15

0.54(0) ± 0.01

1.12 ± 0.01

313.15

0.48(3) ± 0.01

0.517,f 0.519,g 0.5204,h0.5203,c 0.521,i 0.5224,j 0.5226,d 0.524,k 0.5372l 0.4659,d 0.465,c,g 0.470,k 0.474,o 0.4851l

323.15

0.43(4) ± 0.01

333.15

0.96(1) ± 0.01 0.83(7) ± 0.01

0.39(1) ± 0.01

0.4189,c 0.420,g 0.4211,m 0.4215,n 0.4221,h 0.4222,j 0.4272l 0.380,c 0.381,g 0.390,o 0.3905l

343.15

0.34(9) ± 0.02(7)

0.346,c 0.347g

0.64(8) ± 0.01

353.15

0.30(7) ± 0.01

0.317,c 0.326o

0.57(6) ± 0.02

0.73(5) ± 0.01

lit. 1.296,p 1.300,q 1.304,u 1.314c 1.105,c 1.107,p 1.109,q,u 1.114c 0.958,p 0.960,q 0.961,q 0.955c 0.828,c 0.830,c 0.835,v 0.844u 0.7249,c 0.734,c 0.741,v 0.749u 0.658,c 0.663,v 0.671u 0.5795,c 0.60,c 0.601v

n-hexadecane this work 3.44 ± 0.01 2.72 ± 0.01 2.21 ± 0.01 1.83 ± 0.01 1.54 ± 0.01 1.31 ± 0.01 1.14 ± 0.01

363.15

0.99(4) ± 0.01

373.15

0.87(8) ± 0.01

lit. 3.44 ± 0.01,r 3.447,s 3.484,c 3.505c 2.72 ± 0.01,r 2.748,c 2.766,c 2.21 ± 0.01,r 2.223,c 2.23 ± 1%,t 2.243s 1.82 ± 0.01,r 1.840,c 1.866c 1.53 ± 0.01,r 1.550,c 1.56 ± 1%,t 1.573c 1.31 ± 0.01,r 1.326,c 1.346c 1.13 ± 0.01,r 1.152,c 1.16 ± 1%,t 1.166c 0.99(0) ± 0.01,r 1.010,c 1.021c 0.87(6) ± 0.01,r, 0.896 ± 1%t

a

x1 is the mole fraction of n-butylcyclohexane in mixtures with toluene or n-hexadecane. The standard uncertainty u is u(T) = 0.01 K, and the expanded uncertainties for viscosity are indicated by “±” symbols (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty of Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2). bReference 52. cReference 53. dReference 54. eReference 55. fReference 56. gReference 57. hReference 58. iReference 59. jReference 60. kReference 61. lReference 62. mReference 63. n Reference 64. oReference 65. pReference 33. qReference 45. rReference 16. sReference 66. tReference 67. uReference 50. vReference 51.

where νm is the kinematic viscosity of the binary mixture and 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 n-butylcyclohexane as component 1 and either toluene or n-hexadecane as component 2. The interaction parameters ν2,1 and ν1,2, were determined by minimizing the sum of the squares of the differences between the measured kinematic viscosities of the binary mixture, νmeasured, and the values calculated by the model in eq 6, νm,calc. The standard error for the fit (σ) was determined using eq 2, in which Pmeasured is the measured viscosity and Pm,calc is the fitted viscosity. The fitted interaction parameters and the standard errors of the fits are given in Table 10. Figure 4 shows that the model fits the data well. In this three-body model, the free energy impacts on the viscosity are broken into two parts.35 In the first part, the ν1,2 fitting term accounts for interactions occurring with two n-butylcyclohexane molecules and one molecule of the other compound in the mixture. In the second part, the ν2,1 term accounts for interactions occurring with two molecules of the other substance and one molecule of nbutylcyclohexane. For the mixtures studied herein, the term corresponding to two molecules of the substance with a higher pure-component viscosity had a larger value, suggesting a greater contribution to the overall viscosity of the mixture. Specifically, the ν1,2 term was larger for the toluene mixtures, while the ν2,1 term was larger for the n-hexadecane mixtures. Viscosity deviation has been calculated by researchers using both kinematic and dynamic viscosity. To aid in comparison with the work of Liu and Zhu33 with butylcyclohexane and nalkanes from heptane to tetradecane, the viscosity deviation used herein is

the mixtures measured herein do not follow simple blending rules. The reported speeds of sound for petroleum-based jet and diesel fuel at 293.15 K are (1316.9 and 1378.6) m·s−1, respectively.9,31 Only the toluene + n-butylcyclohexane mixtures could adequately match the values for the jet fuel. For the bulk modulus, values of (1389 and 1612) MPa have been found for petroleum-based jet and diesel fuel, respectively, at 293.15 K.9,31 The values for mixtures reported herein are too high for the jet fuel and too low for the diesel fuel. 4.3. Viscosity. Most of the measured viscosities of each compound agree with the reported values within the standard uncertainty of the measurements, as shown in Table 8. The dynamic and kinematic viscosities of the n-butylcyclohexane mixtures are given in Table 9 as functions of the mole fraction of n-butylcyclohexane, x1, and selected values are shown in Figure 4. The viscosity of the binary mixtures of nbutylcyclohexane with n-hexadecane decreases with increasing x1 , while the viscosity of the binary mixtures of nbutylcyclohexane with toluene increases with increasing x1. The reported viscosities for petroleum-based jet and diesel fuel at 293.15 K are (1.88 and 3.65) mm2·s−1, respectively.9,36 Only the n-hexadecane + n-butylcyclohexane mixtures could match the properties of the jet fuel and diesel fuel. The McAllister three-body model35 was used to fit the kinematic viscosity data: ln νm = x13 ln ν1 + 3x12x 2 ln ν1,2 + 3x1x 2 2 ln ν2,1 ⎛ M ⎞ + x 2 3 ln ν2 − ln⎜x1 + x 2 2 ⎟ + 3x12 M1 ⎠ ⎝ ⎤ ⎡1⎛ ⎡1⎛ M ⎞ M ⎞⎤ x 2 ln⎢ ⎜2 + 2 ⎟⎥ + 3x1x 2 2 ln⎢ ⎜1 + 2 2 ⎟⎥ ⎢⎣ 3 ⎝ ⎢⎣ 3 ⎝ M1 ⎠⎥⎦ M1 ⎠⎥⎦ ⎛M ⎞ + x 2 3 ln⎜ 2 ⎟ ⎝ M1 ⎠

Δη = ηmixture − (x1η1 + x 2η2)

(7)

where η1 and η2 are the dynamic viscosities and x1 and x2 are the mole fractions of the pure components and ηmixture is the dynamic viscosity of the mixture. The calculated values are

(6) G



Article

Table 9. Viscosities of Binary Mixtures of n-Butylcyclohexane (1) + Toluene or n-Hexadecane (2) from T = (293.15 to 353.15) K at 0.1 MPa x1

viscosity

T/K = 293.15

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

0.60(7) 0.70(1) 0.62(2) 0.72(4) 0.64(9) 0.76(4) 0.67(8) 0.80(4) 0.72(1) 0.86(2) 0.77(4) 0.93(4) 0.83(8) 1.02 0.91(6) 1.12 1.02 1.26 1.16 ± 0.02 1.44 ± 0.02 1.31 1.64

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

3.44 4.44 3.07 3.96 2.76 3.54 2.48 3.18 2.25 2.87 2.04 2.60 1.86 2.36 1.70 2.15 1.55 1.96 1.42 1.79 1.31 1.64

0.0681 0.1544 0.2197 0.3045 0.3964 0.4964 0.6046 0.7244 0.8548 1.000

0.000 0.1524 0.2876 0.4091 0.5182 0.6173 0.7078 0.7902 0.8658 0.9355 1.000

T/K = 303.15

T/K = 313.15

T/K = 323.15

n-Butylcyclohexane (1) + Toluene (2) 0.54(0) 0.48(3) 0.43(4) 0.63(0) 0.57(0) 0.51(8) 0.55(2) 0.49(5) 0.44(6) 0.65(0) 0.58(9) 0.53(7) 0.57(8) 0.51(8) 0.46(6) 0.68(8) 0.62(3) 0.56(7) 0.60(3) 0.53(8) 0.48(4) 0.72(2) 0.65(2) 0.59(3) 0.63(8) 0.56(8) 0.51(0) 0.77(1) 0.69(4) 0.62(9) 0.68(3) 0.60(7) 0.54(1) 0.83(2) 0.74(7) 0.67(3) 0.73(5) 0.65(1) 0.58(0) 0.90(2) 0.80(7) 0.72(6) 0.80(0) 0.70(4) 0.62(5) 0.99(0) 0.88(0) 0.78(9) 0.88(5) 0.77(5) 0.68(3) 1.10 0.97(5) 0.86(8) 0.99(1) ± 0.02 0.86(2) ± 0.02 0.75(4) ± 0.02 1.24 ± 0.02 1.09 ± 0.02 0.96(4) ± 0.02 1.12 0.96(1) 0.83(7) 1.41 1.22 1.08 n-Butylcyclohexane (1) + n-Hexadecane (2) 2.72 2.21 1.83 3.55 2.91 2.43 2.46 2.01 1.68 3.20 2.64 2.22 2.23 1.84 1.54 2.89 2.40 2.03 2.03 1.68 1.42 2.62 2.19 1.87 1.85 1.54 1.31 2.38 2.01 1.72 1.69 1.42 1.21 2.17 1.84 1.585 1.55 1.31 1.12 1.98 1.69 1.463 1.42 1.21 1.04 1.81 1.56 1.35 1.31 1.12 0.966 1.66 1.43 1.25 1.21 1.03 0.897 1.53 1.32 1.16 1.12 0.96(1) 0.83(7) 1.41 1.22 1.08

T/K = 333.15

T/K = 343.15

T/K = 353.15

0.39(1) 0.47(2) 0.40(5) 0.49(2) 0.42(2) 0.51(8) 0.43(7) 0.54(1) 0.46(0) 0.57(4) 0.48(6) 0.61(1) 0.51(9) 0.65(7) 0.55(8) 0.71(1) 0.60(4) 0.77(6) 0.66(3) ± 0.02 0.85(7) ± 0.02 0.73(5) 0.95(6)

0.34(9) 0.42(5) 0.37(0) 0.45(6) 0.37(9) 0.47(1) 0.39(7) 0.49(7) 0.41(8) 0.52(7) 0.43(8) 0.55(7) 0.46(9) 0.60(0) 0.50(2) 0.64(6) 0.53(5) 0.69(4) 0.58(6) ± 0.02 0.76(5) ± 0.02 0.64(8) 0.85(1)

0.30(7) 0.37(9) 0.32(5) 0.40(5) 0.34(5) 0.43(4) 0.35(6) 0.45(1) 0.37(3) 0.47(7) 0.39(5) 0.50(8) 0.42(6) 0.55(1) 0.45(1) 0.58(8) 0.49(0) 0.64(2) 0.53(2) 0.70(2) 0.57(6) 0.76(5)

1.54 2.06 1.42 1.90 1.31 1.75 1.21 1.61 1.13 1.49 1.05 1.38 0.97(2) 1.28 0.90(6) 1.19 0.84(4) 1.10 0.78(3) 1.02 0.73(5) 0.95(6)

1.31 1.78 1.22 1.64 1.13 1.52 1.05 1.41 0.97(7) 1.31 0.91(2) 1.22 0.85(1) 1.13 0.79(7) 1.06 0.74(5) 0.98(5) 0.694 0.91(5) 0.64(8) 0.85(1)

1.14 1.55 1.06 1.44 0.98(7) 1.34 0.92(1) 1.25 0.86(0) 1.16 0.80(5) 1.08 0.75(3) 1.01 0.706 0.94(6) 0.662 0.88(4) 0.619 0.82(4) 0.57(6) 0.76(4)

± ± ± ± ± ±

0.02 0.02 0.03 0.03 0.03 0.04

± 0.02 ± 0.03

± 0.02 ± 0.02 ± 0.02

a x1 is the mole fraction of n-butylcyclohexane in mixtures with toluene or n-hexadecane. The standard uncertainty u is u(T) = 0.01 K. The expanded uncertainties Uc are Uc(μ) = 0.01 mPa·s and Uc(ν) = 0.01 mm2·s−1, unless otherwise indicated by a “±” symbol. The combined expanded uncertainty is Uc(x1) = 0.0001, except for x1 = 0.1542 (n-butylcyclohexane + n-hexadecane) and x1 = 0.0681, 0.1544, and 0.2297 (butylcyclohexane + toluene), where Uc(x1) = 0.0002 (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty of Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2).

listed in the Tables S5 and S6. The viscosity deviations for the binary mixtures of n-butylcyclohexane and n-hexadecane shown in Figure 5 are positive. Liu and Zhu33 showed that the viscosity deviations for butylcyclohexane in n-heptane, n-octane, n-nonane, and n-decane were negative and increased as the carbon chain length increased. For binary mixtures of butylcyclohexane in n-dodecane and n-tetradecane, the viscosity

deviations were positive and increased as the carbon chain length increased.33 The viscosity deviations of n-butylcyclohexane in n-hexadecane in the current study follow this trend in that they are larger than those reported for dodecane and ntetradecane. For these molecules, the positive viscosity deviations indicate that the molecules in the mixtures do not move past each other as well as would be predicted for an ideal H



Article

Figure 4. Viscosities of mixtures of n-butylcyclohexane (1) and toluene (2) (■, 293.15 K; ▲, 313.15 K; ◆, 333.15 K) and of nbutylcyclohexane (1) and n-hexadecane (2) (□, 293.15 K; △, 313.15 K; ◇, 333.15 K). The error bars, which are the combined uncertainties at the 0.95 level of confidence (k = 2), are smaller than the symbols. Lines shown are fits using eq 6 with the coefficients in Table 10.

Figure 5. Viscosity deviations of binary mixtures of n-butylcyclohexane (1) and toluene (2) (■, 293.15 K; ▲, 313.15 K; ◆, 333.15 K) and of butylcyclohexane (1) and n-hexadecane (2) (□, 293.15 K; △, 313.15 K; ◇, 333.15 K). The error bars for the data shown here at 293.15 K are the combined expanded uncertainties at the 0.95 level of confidence (k = 2). Lines shown here are fits using eq 8 with the coefficients given in the Supporting Information.

Table 10. Values of the Coefficients of the McAllister Equation (eq 6) and Associated Standard Errors (eq 2) for Binary Mixtures of n-Butylcyclohexane (1) + Toluene or nHexadecane (2) from T = (293.15 to 353.15) K at 0.1 MPa T/K 293.15 303.15 313.15 323.15 333.15 343.15 353.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15

ν12/mm2·s−1

ν21/mm2·s−1

Table 11. Comparison of the Measured Flash Points and Surface Tensions of n-Butylcyclohexane, Toluene, and nHexadecane with Literature Values

103·σ/mm2·s−1

n-Butylcyclohexane (1) + Toluene (2) 1.23 0.838 1.07 0.759 0.950 0.687 0.844 0.629 0.750 0.582 0.663 0.553 0.627 0.501 n-Butylcyclohexane (1) + n-Hexadecane (2) 2.64 3.50 2.21 2.86 1.88 2.38 1.63 2.02 1.42 1.74 1.26 1.51 1.13 1.32

flash point/K

4.1 2.3 1.9 0.90 0.60 3.8 3.5

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

1.8 1.4 1.8 1.5 2.1 2.2 2.6

surface tension/mN·m−1

n-Hexadecane 406.2 ± 2 27.1 ± 0.3 @ 294.0 ± 1 K 407 ± 2,b 408,c,d 409e 27.3 @ 294.0 K,d 27.4 @ 294.0 Kj Toluene 280.7 ± 2 28.6 ± 0.2 @ 294.2 ± 1 K 275.2,e 277,g 279.15,h 280f 28.4 @ 294.2 Kj n-Butylcyclohexane 324.7 ± 2 26.7 ± 0.2 @ 294.0 ± 1 K 321,g 324.8,f 325.65h 26.9 @ 294.0 K,j 26.6 @ 294.0 Kk

The expanded uncertainties Uc are given by the “±” symbol (level of confidence = 0.9545, k = 2). bReference 68. cReference 69. dReference 39. eReference 70. fReference 71. gReference 72. hReference 73. j Reference 74. kReference 50. a

standard error. The values of A0, A1, and the standard errors of the fits are given in Table S7. The model fits the data well, as shown in Figure 5. 4.4. Surface Tension and Flash Point. The surface tensions and flash points of the pure components are given in Table 11. These values agree with literature values within the error of the measurements. The surface tensions and flash points for binary mixtures of n-butylcyclohexane and either toluene or n-hexadecane are given in Table 12. No values for mixtures are available in the literature for comparison. As can be seen from the data in Table 12, the surface tensions decrease as the mole fraction of n-butylcyclohexane increases. The flash point increases as the mole fraction of n-butylcyclohexane in toluene increases but decreases as the mole fraction of nbutylcyclohexane in n-hexadecane increases. The reported surface tension values for petroleum-based jet and diesel fuel near 293.15 K are 26.1 and 26.9 mN·m−2, respectively.9,36 Either set of mixtures have surface tension values that can match the diesel fuel. The reported flash points for petroleumbased jet and diesel fuel are 334 and 335 K, respectively.9,31 Only the n-butylcyclohexane + n-hexadecane mixtures have flash points that could match those values.

mixture. In contrast, the viscosity deviations of n-butylcyclohexane in toluene are negative. These molecules appear to move more easily past each other in the mixture than would be expected for ideal behavior. In both sets of mixtures, the deviations from ideality become smaller as the temperature increases. The viscosity deviations were fit with a Redlich−Kister-type expression: n

Δη = x1x 2 ∑ Aj (x1 − x 2) j = x1x 2[A 0 + A1(x1 − x 2)] j=0

(8)

with the parameters described previously for eq 4. Equation 2 was used to determine the standard error for the fit (σ), where Pmeasured is the calculated viscosity deviation and Pm,calc is the fitted viscosity deviation. A one-term fit was not used because the viscosity deviations were not symmetrical about x1 = x2 = 0.5. A two-parameter fit was selected because adding more terms did not significantly improve the fit, as indicated by the I



Article

body model. For the mixtures studied herein, the term including two molecules of the substance with a higher purecomponent viscosity had a larger value, suggesting a greater contribution to the overall viscosity of the mixture. The mixtures prepared herein can be used in conjunction with available kinetic models to understand the combustion of surrogate fuel mixtures. None of mixtures prepared herein, however, matched all of the properties of petroleum jet and diesel fuel. For jet fuel, the speed of sound could be matched by toluene + butylcyclohexane mixtures, while the viscosity and flash point could be matched by n-hexadecane + butylcyclohexane mixtures. The density of jet fuel fell between those of the two sets of mixtures, suggesting that three-component mixtures containing n-hexadecane, toluene, and n-butylcyclohexane might be good surrogates for jet fuel to match the density. For diesel fuel, the density and surface tension could be matched by toluene + butylcyclohexane mixtures, while the surface tension, viscosity, and flash point could be matched by n-hexadecane + butylcyclohexane mixtures. Future work for diesel fuel should test higher-molecular-weight cycloalkanes with n-hexadecane since the range of alkyl chain lengths found in jet fuel can go as high at 16 carbons.

Table 12. Surface Tensions and Flash Points of Binary Mixtures of n-Butylcyclohexane (1) + Toluene or nHexadecane (2) x1 0.0681 0.1544 0.2197 0.3045 0.3964 0.4964 0.6046 0.7244 0.1524 0.2876 0.4091 0.5182 0.6173 0.7078 0.7902 0.8658 0.9355

surface tension/mN·m−1

flash point/K

n-Butylcyclohexane (1) + Toluene (2) 28.1 ± 0.2 27.7 ± 0.2 27.5 ± 0.2 27.3 ± 0.2 27.2 ± 0.2 27.0 ± 0.2 26.9 ± 0.2 26.7 ± 0.2 n-Butylcyclohexane (1) + n-Hexadecane (2) 26.9 ± 0.2 26.9 ± 0.2 26.9 ± 0.2 26.8 ± 0.2 26.8 ± 0.2 26.8 ± 0.2 26.7 ± 0.2 26.7 ± 0.2 26.7 ± 0.2

NM 285 ± NM NM 289 ± 292 ± 295 ± 298 ±

2 2 2 2

± ± ± ± ± ± ± ± ±

2 2 2 3 2 2 3 3 2

366 354 346 340 335 332 330 327 326

2

■

a

x1 is the mole fraction of n-butylcyclohexane in mixtures with toluene or n-hexadecane. The expanded uncertainties Uc for surface tension and flash point are given by the symbol “±”, and the combined expanded uncertainty Uc is Uc(x1) = 0.0001, except for x1 = 0.1542 (nbutylcyclohexane + n-hexadecane) and x1 = 0.0681, 0.1544, and 0.2297 (n-butylcyclohexane + toluene), where Uc(x1) = 0.0002 (level of confidence = 0.9545, k = 2). Surface tension measurements were performed at room temperature (294.4 ± 1 K). The average pressure for these measurements was 0.102 MPa with an expanded uncertainty of Uc(P) = 0.002 MPa (level of confidence = 0.95, k = 2). NM = not measured.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00516. Density and speed of sound measurements for the NISTcertified toluene standard, excess molar volumes of binary mixtures of n-butylcyclohexane (1) + nhexadecane or toluene (2), parameters for the Redlich−Kister equation for the excess molar volumes of binary mixtures of n-butylcyclohexane (1) + toluene or nhexadecane (2), viscosity deviations of binary mixtures of n-butylcyclohexane (1) + n-hexadecane or toluene (2), and parameters for the Redlich−Kister equation for the viscosity deviations of binary mixtures of n-butylcyclohexane (1) + toluene or n-hexadecane (2) (PDF)

5. CONCLUSIONS This study measured the density, viscosity, speed of sound, surface tension, and flash point of mixtures of n-butylcyclohexane with toluene or n-hexadecane. Correlations of density− mole fraction data were fourth-order for toluene mixtures and third-order for n-hexadecane mixtures and can be useful in surrogate development for matching with fuels of interest. The excess molar volumes were higher than those found by other researchers for butylcyclohexane with linear alkanes of lower mass. This result suggests that in mixtures of n-butylcyclohexane and n-hexadecane, the intermolecular interactions contribute more than packing does to the excess molar volume than is the case for mixtures of butylcyclohexane with other linear alkanes of low mass. The excess molar volume of nbutylcyclohexane with toluene was similar to that with methylcyclohexane, suggesting that the two sets of mixtures have a similar balance of packing and intermolecular interactions. The speeds of sound for some of the toluene mixtures fell below those of the individual components at low mole fractions of n-butylcyclohexane, while the bulk moduli for both sets of mixtures dipped to values below those of the individual components at high mole fractions of n-butylcyclohexane. The variation in density, which is the other factor in the calculation of bulk modulus, causes the shift in mole fraction where the minimal value is found. Both the speeds of sound and bulk moduli of these mixtures cannot be predicted by simple blending rules. Viscosity values of the mixtures at each temperature were well-modeled using the McAllister three-

■

AUTHOR INFORMATION

Corresponding Author

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

This work was funded by the Office of Naval Research (Grants N0001415WX01853 and N0001416WX01648). Notes

The author declares no competing financial interest.

■

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