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Thermophysical and Thermochemical PropertiesSeptember 3, 2025

Binary Mixtures of n-Alkylbenzenes and Pentadecane: Densities, Speeds of Sound, and Viscosities within the Range of 288.15 and 333.15 K and at 0.1 MPa
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Dianne J. Luning Prak*
Dianne J. Luning Prak
Department of Chemistry, U.S. Naval Academy, 572 M Holloway Road, Annapolis, Maryland 21402, United States
*Email: [email protected]Phone: 410-293-6339. Fax: 410-293-2218.
More by Dianne J. Luning Prak
https://orcid.org/0000-0002-5589-7287
Jim S. Cowart
Jim S. Cowart
Department of Mechanical and Nuclear Engineering, U.S. Naval Academy, 590 Holloway Rd, Annapolis, Maryland 21402, United States
More by Jim S. Cowart

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Journal of Chemical & Engineering Data

Cite this: J. Chem. Eng. Data 2025, 70, 9, 3527–3544

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https://doi.org/10.1021/acs.jced.5c00217

Published September 3, 2025

Not subject to U.S. Copyright. Published 2025 by American Chemical Society. This publication is licensed under

CC-BY 4.0 .

Abstract

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The physical properties of mixtures of alkanes and aromatic compounds can aid in the understanding and modeling of their combustion in engines. Herein, densities, viscosities, and speeds of sound of binary mixtures of n-alkylbenzenes with pentadecane and their corresponding excess molar volumes (V_m^E), excess speeds of sound (c^E), excess isentropic compressibilities (Κ_s^E), and viscosity deviations (Δη) are reported. In general, mixture densities, viscosities, and speeds of sound increased monotonically with changing mole fractions, except for the speeds of sound of toluene, ethylbenzene, propylbenzene, and butylbenzene mixtures. These properties can be used for fuel modeling purposes. V_m^E’s, Δη’s, c^E’s, and K_s^E’s ranged from 0.04 to 0.56 cm·mol^–1, −0.14 to 0.09 mPa·s, −14.8 to 2.5 m·s^–1, and −2.2 to 18.1 TPa^–1, respectively. Increasing the n-alkylbenzene size (up to decylbenzene) caused the equimolar mixture’s V_m^E’s, Δη’s, and K_s^E’s to decrease and c^E’s to increase at 293.15 K. The properties of smaller n-alkylbenzene molecules were more affected by the aromatic group. In comparison with n-alkylcyclohexane/pentadecane mixtures, n-alkylbenzene/pentadecane mixture Δη trends were similar, but V_m^E’s, c^E’s, and K_s^E’s trends were different, suggesting that molecular interactions of the benzyl and cyclohexyl groups affect volume and compressibility more than they affect viscosity.

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You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:
- Creative Commons (CC): This is a Creative Commons license.
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Not subject to U.S. Copyright. Published 2025 by American Chemical Society

Subjects

1. Introduction

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Aromatic hydrocarbons and linear alkanes are compounds commonly found in petroleum-based and biobased fuels. (1,2) Physical property measurements and combustion characteristics of these compounds alone and in mixtures can aid in the understanding and modeling of more complex combustion processes. Detailed chemical kinetic reaction mechanisms have been formulated for the combustion of linear alkanes ranging from octane to hexadecane. (3) Droplet autoignition of binary mixtures of alkanes (heptane through eicosane) and n-alkylbenzenes (toluene through n-octylbenzene) has also been quantified. (4) Physical properties, such as viscosity and density, can affect the movement of fuel through the engine’s fuel system as well as the fuel’s injected spray pattern into the engine cylinder air. (5) The densities, viscosities, and speeds of sound of some binary mixtures consisting of an alkane with an n-alkylbenzene have been published, (6−16) but only one study has reported on mixtures containing pentadecane with an n-alkylbenzene, namely n-dodecylbenzene. (16) Pentadecane is found in petroleum-based and biobased fuels and has been included in surrogate mixtures for fuels. (2,17−22) The goal of this study was to measure density, viscosity, and speed of sound for mixtures of pentadecane with n-alkylbenzenes shorter than n-dodecylbenzene and to compare the derived properties with those of other systems containing linear alkanes, n-alkylbenzenes, and n-alkylcyclohexanes.

Researchers have reported on densities, viscosities, and speeds of sound of some binary mixtures consisting of an alkane (hexane through heptadecane) with an n-alkylbenzene (methylbenzene through dodecylbenzene). (6−16) Table 1 shows the temperature ranges over which these studies have been conducted. Some researchers have focused on one temperature, while others have explored a range of temperatures. This table reveals that very little work has been done with pentadecane. These properties are important for understanding combustion in engines. Further, density and viscosity are included in specifications for jet and diesel fuel. (23−25)

Table 1. Temperature Ranges for Previous Studies Exploring the Density, Viscosity, and Speed of Sound of Binary Mixtures of Alkanes with n-Alkylbenzenes

linear alkane	n-alkyl-benzene	density temperatures (K)	viscosity temperatures (K)	speed of sound temperatures (K)
hexane	methyl-	298.15 and 323.15 (15)		313.15 (12)
		313.15 (12)
hexane	ethyl-	298.15 and 323.15 (15)		313.15 (12)
		313.15 (12)
hexane	propyl-	298.15 and 323.15 (15)
hexane	butyl-	298.15 and 323.15 (15)
heptane	methyl-	313.15 (12)		313.15 (12)
heptane	ethyl	313.15 (12)		313.15 (12)
heptane	nonyl-		313.15–353.15 (13)
octane	methyl-	293.15–313.15 (9)
		313.15 (12)
octane	ethyl-	293.15–313.15 (9)		313.15 (12)
		313.15 (12)
nonane	methyl-	313.15 (12)		313.15 (12)
nonane	ethyl-	313.15 (12)		313.15 (12)
decane	methyl-	293.15–313.15 (9)	298.15 (11)
		298.15 (11)
decane	butyl-	293.15–373.15 (6)	293.15–373.15 (6)	293.15–333.15 (6)
decane	dodecyl-	288.15–333.15 (16)	288.15–323.15 (16)	288.15–333.15 (16)
dodecane	methyl-	293.15–313.15 (9)
dodecane	butyl-	293.15–373.15 (6)	293.15–373.15 (6)	293.15–333.15 (6)
dodecane	nonyl-	288.15–333.15 (10)	293.15–333.15 (10)	288.15–333.15 (10)
dodecane	dodecyl-	288.15–333.15 (16)	288.15–333.15 (16)	288.15–333.15 (16)
tridecane	dodecyl-	288.15–333.15 (16)	288.15–333.15 (16)	288.15–333.15 (16)
tetradecane	methyl-	293.15–313.15 (9)	298.15 (11)
		298.15 (11)
tetradecane	ethyl-	293.15–313.15 (9)
tetradecane	butyl-	293.15–373.15 (6)	293.15–373.15 (6)	293.15–333.15 (6)
tetradecane	dodecyl-	288.15–333.15 (16)	288.15–333.15 (16)	288.15–333.15 (16)
pentadecane	dodecyl-	288.15–333.15 (16)	288.15–333.15 (16)	288.15–333.15 (16)
hexadecane	methyl-	293.15–313.15 (9)	293.15–373.15 (7,26)	293.15–333.15 (7,26)
		293.15–373.15 (7,26)
hexadecane	ethyl-	293.15–313.15 (9)	293.15–373.15 (7,26)	293.15–333.15 (7,26)
		293.15–373.15 (7,26)
hexadecane	propyl-	298.15–318.15 (14)	298.15–318.15 (14)	298.15–318.15 (14)
hexadecane	butyl-	293.15–373.15 (6)	293.15–373.15 (6)	293.15–333.15 (6)
hexadecane	hexyl-	293.15–373.15 (8)	293.15–373.15 (8)	293.15–333.15 (8)
hexadecane	octyl-	293.15–373.15 (8)	293.15–373.15 (8)	293.15–333.15 (8)
hexadecane	nonyl-	293.15–333.15 (10)	293.15–333.15 (10)	293.15–333.15 (10)
hexadecane	dodecyl-	293.15–373.15 (8)	293.15–373.15 (8)	293.15–333.15 (8)
heptadecane	butyl-	303.15–373.15 (6)	303.15–373.15 (6)	303.15–333.15 (6)

The delivery of fuel into an engine depends on the bulk modulus, which is calculated from the density and speed of sound. The start of injection (SOI) results from the engine’s fuel pump creating a high-pressure pulse. This pulse is transmitted faster and is injected sooner into the engine when the fuel has a higher bulk modulus associated with a higher speed of sound. (27) Tat and Van Gerpen calculated a 1° timing advance (injected earlier) when the bulk modulus was changed from 1398.2 to 1566.9 MPa. (28) After injection, fuel forms into ligaments and droplets, whose shape depends on their density and viscosity. The sensitivity of spray formation to these parameters was explored by Kim et al., who concluded that liquid density, specific heat, viscosity, and vapor pressure are important parameters to use when formulating surrogate fuel mixtures that will properly capture the liquid penetration and ignition delay characteristics of the fuel being studied. (5)

The effect of the compound structure on fuel mixtures can be explored using derived properties such as excess molar volume (V_m^E) and viscosity deviation (Δη). V_m^E is calculated from mixture density (ρ_mix), component densities (ρ_i), molar masses (M_i), and mole fractions (x_i), using eq 1.

V_{m}^{E} = \frac{M_{1} x_{1} + M_{2} x_{2}}{ρ_{m i x}} - \frac{M_{1} x_{1}}{ρ_{1}} - \frac{M_{2} x_{2}}{ρ_{2}}

(1)

Previous studies with other alkanes have shown that V_m^E’s for equimolar mixtures decrease with (1) increasing the size of n-alkylbenzene for a specific alkane and (2) decreasing the size of the alkane on a specific n-alkylbenzene. (6−10) Viscosity deviations are the differences between the measured viscosity and an estimated viscosity based on a mixing rule. The current study calculates dynamic viscosity deviation, Δη, from mixture viscosities (η_mix), component viscosities (η_i), and mole fractions (x_i) using eqs 2 and 3.

Δ η = η_{m i x} - η_{c a l c u l a t e d}

(2)

\ln (η_{c a l c u l a t e d}) = x_{1} \ln (η_{1}) + x_{2} \ln (η_{2})

(3)

The trends in the literature values of Δη as a function of alkane and n-alkylbenzene sizes are not simple monotonically changing functions. For specific alkanes, increasing the n-alkylbenzene size from toluene tends to cause Δη to decrease, and for some alkanes, a minimum is found before Δη increases. For the longer chain hexadecane, increasing the n-alkylbenzene size produced smaller Δη’s. (7,8,10) For decane and tetradecane mixtures, Δη ’s for n-butylbenzene were smaller than those of toluene and n-dodecylbenzene. (11,16) For specific n-alkylbenzenes, differing trends can be found for different alkanes. In toluene and n-butylbenzene mixtures, Δη for tetradecane was higher than that for decane. (11,29) In contrast, Δη of tetradecane was lower than that of decane in n-dodecylbenzene mixtures. (16) Part of this pattern may depend on the actual viscosities of the components in the mixture. When the components are more similar in viscosity, it is more likely that their Δη values will be smaller.

The goal of this study was to measure the densities, viscosities, and speeds of sound of binary mixtures of n-alkylbenzenes with pentadecane and to compare their mixture V_m^E’s and Δη’s with those of other systems containing alkanes and n-alkylbenzenes. Based on the trends discussed above, it was hypothesized that (1) V_m^E’s of the pentadecane mixtures would fall between those of hexadecane and tetradecane, (2) V_m^E’s would decrease as the size of n-alkylbenzenes increased from toluene n-octylbenzene, and (3) Δη’s would decrease as the size of n-alkylbenzenes decreased and a minimum might be found. The measured densities, viscosities, and speeds of sound can complement kinetic studies and provide researchers with information for their modeling efforts.

2. Experimental and/or Computational Methods

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The two-component mixtures were prepared using commercially supplied n-alkylbenzenes and pentadecane without further purification (Table 2). Each component was weighed using a Mettler Toledo MS304TS analytical balance (uncertainty less than 0.0002 g) after its addition to an ultraclean vial. Then, the vial was sealed with a Teflon cap and mixed gently for a brief time, and the first replicate was immediately analyzed. At least two replicates were analyzed for each mixture. The mole fraction uncertainty was 0.0001, which was calculated from the methods described by Harris (30) without inclusion of the uncertainties in atomic mass, and is shown in the Supporting Information.

Table 2. Chemical Information

chemical name	CAS number	molar mass (g/mol)a	source	mole fraction purityb
pentadecane (C₁₅H₃₂)	629-62-9	212.41 ± 0.04	TCI	0.998
n-decylbenzene (C₁₆H₂₆)	2189-60-8	218.38 ± 0.03	TCI	0.994
n-octylbenzene (C₁₄H₂₂)	2189-60-8	190.32 ± 0.03	TCI	0.982
n-heptylbenzene (C₁₃H₂₀)	1078-71-3	176.30 ± 0.03	TCI	0.995
n-hexylbenzene (C₁₂H₁₈)	1077-16-3	162.27 ± 0.02	TCI	0.993
n-pentylbenzene (C₁₁H₁₆)	538-68-1	148.25 ± 0.02	Aldrich	0.999
n-butylbenzene (C₁₀H₁₄)	104-51-8	134.22 ± 0.02	TCI	0.999
n-propylbenzene (C₉H₁₂)	103-65-1	120.20 ± 0.02	TCI	0.999
ethylbenzene (C₈H₁₀)	100-41-4	106.17 ± 0.02	TCI	1.000
toluene (C₇H₈)	108-88-3	92.14 ± 0.01	Pharmco	0.9987

^{^a}

Calculated using values in the work by Harris. (30)

^{^b}

The method of analysis for all the compounds is gas–liquid chromatography, as specified in the Certificates of Analysis provided by the chemical suppliers.

The speed of sound and density were measured using an Anton Paar DSA 5000 M sound and density analyzer, and the dynamic viscosity was measured using an Anton Paar SVM 3001 viscometer using the highest precision setting, as was done in the authors’ previous studies. (31−33) Each instrument continuously measured the properties and reported the values when precision was achieved. The speeds of sound and densities were measured at 288.15, 293.15, 298.15, 303.15, 313.15, 323.15, and 333.15 K, except for toluene, which was measured only at lower temperatures. Dynamic viscosities were measured at a subset of these temperatures because some of the viscosities were too low to be accurately measured. The kinematic viscosity was calculated by dividing the dynamic viscosity by density. Commercially manufactured standards (Paragon Scientific APS3, Cannon N1.0 and N0.8, NIST toluene standard) and degassed water were used for calibration and testing of each instrument. The density of the NIST toluene standard was measured at 293.15, 303.15, 313.15, 323.15, and 333.15 K, and the maximum difference between the standard and the measured values was 0.011 kg·m^–3 at 333.15 K. The calculation method to determine the uncertainty in the measured values is given in the Supporting Information (Tables S1–S3).

3. Results and Discussion

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3.1. Pure Components: Comparison of Densities, Viscosities, and Speeds of Sound with Literature Values

The measured densities, viscosities, and speeds of sound of pentadecane and n-alkylbenzenes as well as the literature values are listed in Tables 3, 4, and 5, respectively. The properties of the pure components agree with some of the reported values within the expanded uncertainties of the measurement. Some properties have large variations. Plots showing the deviation of the measured values from literature values are given in the Supporting Information (Figures S1–S3). The mean absolute percent error (MAPE) was used to quantify the differences between the measured, P_m, and literature properties, P_literature, using eq 4.

M A P E = \frac{100}{n} \sum_{1}^{n} \frac{| P_{m} - P_{l i t e r a t u r e} |}{P_{m}}

(4)

Table 3. Measured Densities ρ of n-Alkylbenzenes Compared with Literature Values at Temperature T and Pressure p = 0.1 MPaa

T/K	meas.a ρ/kg·m^–3	literature ρ/kg·m^–3	meas.a ρ/kg·m^–3	literature ρ/kg·m^–3
	Pentadecane		n-octylbenzene
288.15	772.23	772.01c, 771.8b, 772.24, (16,34) 772.4 (35)	860.6	859.86 (36)
293.15	768.72	768.28, (35) 768.3, (35) 768.35b, 768.45, (37) 768.4, (35) 768.5, (35) 768.52c, 768.73, (34) 768.9 (35)	857.0	856.24, (36) 856.27, (8) 856.30, (38) 856.5, (39) 856.70, (38) 857.2, (40) 857.60, (41) 858.20, (42) 858.3 (38)
298.15	765.22	764.88, (35) 764.9b, 765, (43) 765.04c, 765.07, (35) 765.20, (34) 765.23, (35) 765.42 (35)	853.4	852.61 (36)
303.15	761.73	761.38, (35) 761.4, (43) 761.48b, 761.56c, 761.48, (37) 761.70, (34) 761.74 (16)	849.7	848.98, (36) 849.02, (8) 851.20 ± 1.00 (38)
313.15	754.74	754.6c, 754.63b, 754.52, (37) 754.75, (16) 754.80 (34)	842.5	841.74, (8) 841.9 ± 0.8, (39) 842.71 (36)
323.15	747.75	747.56, (37) 747.65c, 747.77, (16) 747.78b^, 747.80 (34)	835.2	834.44, (36) 834.47 (8)
333.15	740.75	740.58, (37) 740.66, (35) 740.68c, 740.77, (16) 740.8, (35) 740.92b, 741.02 (35)	827.9	827.16, (36) 827.17, (8) 827.50 ± 0.60 (38)
		average MAPE = 0.09		average MAPE = 0.09
	n-heptylbenzene		n-hexylbenzene
288.15	860.04	860.1 (36)	861.39	861.92b, 862.3, (33) 862.7, (36) 863.92 (38)
293.15	856.35	857.5 (44) (uncertainty = 1 kg·m^–3), (44) 856.4 (36)	857.60	857.68, (8) 858.00, (38) 858.02, (38) 858.47b, 858.6, (33) 858.9, (36) 860.0, (45) 862.4 (39)
298.15	852.65	852.7 (36)	853.81	855.01b, 855.1 (36)
303.15	848.96	849.0, (36) 850.1 (44) (uncertainty = 1 kg·m^–3) (44)	850.02	851.0, (33) 851.3, (36) 851.56b,852.40 (38)
313.15	841.55	841.6, (36) 842.5 (44) (uncertainty = 1 kg·m^–3) (44)	842.43	843.4, (33) 844.65b, 846.8, (39) 843.7 (36)
323.15	834.14	834.2, (36) 835.1 (44) (uncertainty = 1 kg·m^–3) (44)	834.81	834.88, (8) 835.8, (33) 836.1, (36) 837.7b
333.15	826.69	826.7, (36) 827.6 (44) (uncertainty = 1 kg·m^–3) (44)	827.17	828.2, (33) 828.4, (36) 830.8b, 831.7 (39)
		average MAPE = 0.05		average MAPE = 0.2
	n-pentylbenzene		n-butylbenzene
288.15	862.81	862.278, (46) 862.59, (38) 862.82 (36)	864.51	864.35, (36) 864.73 (38)
293.15	858.92	858.93, (36) 859.02, (38) 859.1, (38) 859.2, (38) 859.3, (38) 859.4, (38) 860 (38)	860.50	859.50, (38) 860.15, (38) 860.25, (38) 860.34, (36) 861.26 (47)
298.15	855.02	855.02, (46) 855.04 (36)	856.49	856.33 (36)
303.15	851.13	850.98, (38) 852.6, (38) 851.14 (36)	852.47	851.3, (48) 852.16, (38) 852.23, (47) 852.32, (36) 852.43 (38)
313.15	843.31	843.33 (36)	844.42	844.27, (36) 844.6, (48) 844.82 (38)
323.15	835.48	835.49 (36)	836.33	836.18, (36) 836.34, (6) 837.00 (38)
333.15	827.60	827.62 (36)	828.20	828.06, (36) 828.21 (6)
		average MAPE = 0.02		average MAPE = 0.03
	n-propylbenzene		ethylbenzene
288.15	867.01	866.20 (36)	871.46	871.08, (46) 871.37, (38) 871.67 (36)
293.15	862.80	862.00, (36) 861.83, (38) 861.6, (38) 861.9, (38) 861.96, (38) 861.3, (38) 862.02, (38) 863.13 (47)	867.07	866.94, (38) 866.95, (26) 867.28, (36) 866.97, (38) 867 (38)
298.15	858.58	857.78, (36) 857.77, (38) 857.68, (38) 857.74, (38) 867.78, (38) 857.96, (38) 858.1 (38)	862.67	862.25, (38) 862.29, (46) 862.56, (38) 862.62, (38) 862.89 (36)
303.15	854.36	853.56, (36) 853.68, (38) 854.71 (47)	858.26	857.98, (38) 858.15, (26) 858.26, (38) 858.49 (36)
313.15	845.90	845.10, (36) 844.9, 845.08 (38)	849.41	849.29, (26) 849.47, (38) 849.63 (36)
323.15	837.39	836.59 (36)	840.50	839.78, (38) 840.38, (26) 840.39 (38)
333.15	828.84	828.05 (49)	831.52	831.18, (38) 831.4, (26) 831.69, (38) 831.8 (38)
		average MAPE = 0.09		average MAPE = 0.02
	toluene		decylbenzene
288.15	871.37	871.46 (36)
293.15	866.73	866.8138, 866.8236, 866.8338, 866.8638	855.49	855.40, 855.53
298.15	862.07	861.89, 862.13, (38) 862.16, (36) 862.17, (38) 862.19, (38) 866.22 (38)	851.97	851.89
303.15	857.41	857.5, (36) 857.53, (38) 853.54, (38) 857.55 (38)	848.45	848.33
333.15		average MAPE = 0.01	827.33	827.5
				average MAPE = 0.01

^{^a}

“Meas.” is the measured value. The average pressure for these measurements was 0.102 MPa. Standard uncertainties are u(T) = 0.01 K and u(p) = 1 kPa; relative standard uncertainties are u_r(ρ) = 0.0006 for n-decylbenzene, u_r(ρ) = 0.0018 for n-octylbenzene, u_r(ρ) = 0.0005 for n-heptylbenzene, u_r(ρ) = 0.0007 for n-hexylbenzene, and u_r(ρ) = 0.0002 for pentadecane, n-pentylbenzene, n-butylbenzene, n-propylbenzene, ethylbenzene, and toluene.

^{^b}

Best-fit equation from the Wilhoit compendium of density data for n-pentadecane: (35) ρ = 1059.18 – 1.54195 × T + 0.00271745 × T² – 2.87122 × 10^–6 × T³ and hexylbenzene: (38) ρ/kg·m³ = 1060.96 – 0.690758 × T.

^{^c}

Best-fit equation from Bessieres et al.: (50) ρ = 1038.677 – 1.3320105 × T + 0.00203628 × T² – 2.17 × 10^–6 × T³.

Table 4. Measured Dynamic Viscosities η of n-Alkylbenzenes Compared with Literature Values at Temperature T and Pressure p = 0.1 MPaa

T/K	meas.a η/mPa·s	literature η/mPa·s	meas.a η/mPa·s	literature η/mPa·s
	pentadecane		n-octylbenzene
288.15	3.24	3.232, (51) 3.248, (51) 3.25 (16)	2.92	2.87 (51)
293.15	2.88	2.841, (51) 2.842, (51) 2.862, (51) 2.87, (16,34) 2.872 (51)	2.61	2.57, (51) 2.575, (51) 2.58, (51) 2.606 (51)
298.15	2.57	2.534, (51) 2.544, (51) 2.568, (51) 2.57 (16)	2.33	2.31 (51)
303.15	2.31	2.283, (51) 2.31 (16,51)	2.10	2.08, (8) 2.09 (51)
313.15	1.90	1.868, (51) 1.873, (51) 1.89, (16,34) 1.9, (51) 1.95 (51)	1.75	1.72, (36) 1.73, (8) 1.744 (51)
323.15	1.59	1.567, (51) 1.58, (16,34) 1.591 (51)	1.48	1.46, (8) 1.479 (51)
333.15	1.35	1.331, (51) 1.335, (51) 1.34, (16,34) 1.353, (51) 1.36 (51)	1.27	1.25, (8) 1.254 (51) 1.274 (51)
		MAPE = 0.6		MAPE = 1
	n-heptylbenzene		n-hexylbenzene
288.15	2.30	2.31 (51)	1.83	1.833, (51) 1.846 (51)
293.15	2.07	2.066, (51) 2.08, (36,51) 2.1 (44)	1.67	1.65, (36) 1.655, (51) 1.67, (51) 1.68, (8) 1.70 (51)
298.15	1.89	1.887 (51)	1.52	1.528 (51)
303.15	1.72	1.71, (36) 1.722, (51) 1.74 (44)	1.39	1.38, (36) 1.40, (8) 1.403, (51) 1.409 (51)
313.15	1.44	1.43, (36) 1.451, (51) 1.48 (44)	1.18	1.18, (36) 1.19, (8) 1.196, (51) 1.2 (51)
323.15	1.23	1.22, (36) 1.243, (51) 1.26 (44)	1.02	1.02, (36) 1.03, (8) 1.035 (51)
333.15	1.06	1.06, (36) 1.081, (51) 1.09 (44)	0.89	0.900, (36) 0.901, (8) 0.909 (51)
		MAPE = 0.9		MAPE = 0.8
	n-pentylbenzene		n-butylbenzene
288.15	1.45	1.46, (51) 1.487 (51)	1.10	1.09, (51) 1.112, (51) 1.119 (51)
293.15	1.33	1.32, (36) 1.334 (51)	1.01	1.01, (36) 1.03, (51) 1.032, (51) 1.034, (52) 1.035, (51) 1.050 (51)
298.15	1.22	1.21, (51) 1.225, (51) 1.25 (46)	0.94	0.96 (51)
303.15	1.13	1.12, (36) 1.126, (51) 1.132 (51)	0.88	0.882, (36) 0.893 (52) 0.894, (51) 0.895, (51) 0.901, (48) 0.9035 (51)
313.15	0.97	0.96₇, (36) 0.976 (51)	0.78	0.774, (36) 0.787, (48) 0.781, (51) 0.79 (51)
323.15	0.85	0.853 (36,51)	0.70	0.684, (51) 0.686, (36) 0.7015 (51)
333.15	0.75	0.75₄, (36) 0.756 (51)		MAPE = 2
		MAPE = 0.7
	n-propylbenzene		n-decylbenzene
288.15	0.89	0.917, (51) 0.9181, (51) 0.9234 (51)	4.38	4.31 (51)
293.15	0.83	0.842, (36) 0.8545, (51) 0.855, (51) 0.8571, (51) 0.859 (51)	3.84	3.80, (51) 3.81 (51)
298.15	0.78	0.790, (51) 0.7966 (51)	3.39	3.37 (51)
303.15	0.74	0.722, (36) 0.7444, (51) 0.7452, (51) 0.7466 (51)	3.02	3.02 (51)
313.15		MAPE = 2	2.44	2.46 (51)
323.15			2.03	2.00 (51)
				MAPE = 0.9.

^{^a}

“Meas” is the measured value. Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, and combined standard uncertainties u_c are u_c(η) = 0.02 mPa·s for all compounds except n-octylbenzene. The relative standard uncertainty is u_r(η) = 0.018 for n-octylbenzene. The average pressure for these measurements was 0.102 MPa.

Table 5. Measured Speeds of Sound c of n-Alkylcyclohexanes and n-Alkylbenzenes Compared with Literature Values at Temperature T and Pressure p = 0.1 MPaa

T/K	meas.a η/mPa·s	literature η/mPa·s	meas.a η/mPa·s	literature η/mPa·s
	pentadecane		n-octylbenzene
288.15	1364.3	1364.0. (34) 1364.2 (16)	1416.7	1415.9 (36)
293.15	1345.3	1344.9, (34) 1345.2, (16) 1345.9 (37)	1398.4	1397.3, (36) 1397.5 (8)
298.15	1326.3	1325.8, (34) 1326.5 (16)	1379.8	1378.7 (36)
303.15	1307.5	1307.0, (34) 1307.3, (53) 1307.5, (16) 1308.1 (37)	1361.5	1360.2, (36) 1361.0 (8)
313.15	1270.8	1269.9, (53) 1270.1, (34) 1270.7, (16) 1270.9 (37)	1325.5	1324.1, (36) 1324.9 (8)
323.15	1234.7	1234.0, (34) 1234.1, (53) 1234.4, (16) 1234.5 (37)	1290.1	1288.6, (36) 1289.4 (8)
333.15	1199.2	1197.6, (53) 1198.3, (37) 1198.9, (34) 1199.1 (16)	1255.1	1254.2, (36) 1254.3 (8)
		MAPE = 0.03		MAPE = 0.07
	n-heptylbenzene		n- hexylbenzene
288.15	1405.8	1405.8 (36)	1394.9	1395.0, (36) 1395.8, (33) 1395.6 (33)
293.15	1387.1	1387.0 (36)	1376.1	1375.9, (36) 1376.0, (33) 1376.1, (8) 1376.5 (33)
298.15	1368.4	1368.2 (36)	1357.0	1356.9 (36)
303.15	1349.9	1349.6 (36)	1338.3	1338.0, (36) 1338.1, (33) 1338.7 (8,33)
313.15	1313.5	1313.0 (36)	1301.4	1301.0, (36) 1301.1, (33) 1301.6, (33) 1301.7 (8)
323.15	1277.7	1277.2 (36)	1265.1	1264.7, (33) 1265.3 (8,33)
333.15	1242.4	1242.1 (36)	1229.2	1229.3, (36) 1229.4, (8,33) 1229.8 (33)
		MAPE = 0.02		MAPE = 0.02
	n-pentylbenzene		n-butylbenzene
288.15	1385.4	1385.2 (36)	1373.8	1373.7 (33)
293.15	1366.0	1365.8 (36)	1354.0	1353.2, (33) 1353.4, (54) 1353.8 (55)
298.15	1346.7	1346.4, (36) 1346 (46)	1334.3	1334.1 (55)
303.15	1327.5	1327.1 (36)	1314.8	1308, (48) 1314.3, (33,54) 1314.5 (55)
313.15	1289.9	1289.4 (36)	1276.5	1275.7, (54) 1276, (48) 1276.1 (33)
323.15	1252.8	1252.3 (36)	1238.7	1238.4 (33)
333.15	1216.2	1216.2 (36)	1201.5	1201.5, (33) 1201 (55)
		MAPE = 0.03		MAPE = 0.05
	n-propylbenzene		ethylbenzene
288.15	1362.0	1361.3 (36,49)	1361.3	1361.0 (36)
293.15	1341.6	1340.7, (49) 1340.8, (36) 1341.5 (14)	1340.2	1339.70, (26) 1339.9, (36) 1340 (56)
298.15	1321.2	1320.6, (14) 1320.3, (36) 1321.0 (57)	1319.1	1318.8 (36)
303.15	1301.1	1300.0, (49) 1300.1, (36) 1300.4 (14)	1298.2	1298.0, (36) 1298.05 (26)
313.15	1261.5	1260.2, (36,49) 1260.9 (14)	1257.1	1256, (58) 1256.89, (26) 1257, (56) 1257.2 (36)
323.15	1222.4	1221.2, (36,49) 1221.5¹⁴	1216.7	1216.35 (26)
333.15	1183.9	1183.1 (36,49)	1176.8	1176.40 (26)
		MAPE = 0.07		MAPE = 0.03
	toluene
288.15	1348.3	1348.2 (36)
293.15	1326.6	1326.5, (36) 1326.8, (26) 1326.9 (59)
298.15	1304.8	1304.7, (36) 1304.77 ± 0.10 (60)
303.15	1283.2	1283, (61) 1283.20 ± 0.10 (60)
		MAPE = 0.01

^{^a}

“Meas.” is the measured value. The average pressure for these measurements was 0.102 MPa. Standard uncertainties are u(T) = 0.01 K and u(p) = 1 kPa, and relative standard uncertainties are u_r(c) = 0.0007, except for n-octylbenzene mixtures where the relative standard uncertainties u_r(c) = 0.0018.

The MAPE values averaged over the testing temperatures for each compound are also given in Tables 2, 3, and 4 for density, viscosity, and speeds of sound, respectively. The MAPE values range from 0.01 to 0.2 for density, 0.6 to 2 for viscosity, and 0.01 to 0.07 for the speed of sound.

3.2. Binary Mixtures: Densities, Speeds of Sound, and Viscosities

The densities increased with an increase in the n-alkylbenzene concentration (Table 6). The viscosities decreased with an increase in the n-alkylbenzene concentration, except for n-octylbenzene which dipped to a minimum at x₁ = 0.8 at select temperatures (Table 7). The speeds of sound (Table 8) increased with an increase in the n-octylbenzene and n-hexylbenzene concentrations, while the values declined to a minimum before increasing again for mixtures containing n-butylbenzene (min at ∼x₁ = 0.5), n-propylbenzene (min at ∼x₁ = 0.7), ethylbenzene (min at ∼x₁ = 0.8), and toluene (min at ∼x₁ = 0.8), as shown in Figure 1.

Table 6. Densities ρ (kg·m^–3) of Binary Mixtures of an n-Alkylbenzene at Mole Fraction x₁ in Pentadecane at Temperature T and Pressure of 0.1 MPaa

n-alkyl-benzene	x₁	T = 288.15 K	T = 293.15 K	T = 298.15 K	T = 303.15 K	T = 313.15 K	T = 323.15 K	T = 333.15 K
	0.0000	772.23	768.72	765.22	761.73	754.74	747.75	740.75
toluene	0.1017	775.91	772.38	768.84	765.30
toluene	0.1987	779.98	776.40	772.82	769.24
toluene	0.2985	784.81	781.18	777.55	773.92
toluene	0.3992	790.59	786.90	783.21	779.51
toluene	0.5014	797.62	793.85	790.08	786.30
toluene	0.5996	805.83	801.97	798.11	794.23
toluene	0.7000	816.26	812.29	808.30	804.30
toluene	0.8004	829.59	825.45	821.30	817.15
toluene	0.9010	847.26	842.92	838.56	834.19
toluene	1.0000	871.37	866.73	862.07	857.41
ethyl-	0.1000	776.41	772.88	769.35	765.82	758.77	751.70	744.63
ethyl-	0.2010	781.22	777.65	774.08	770.52	763.38	756.23	749.06
ethyl-	0.3002	786.66	783.05	779.44	775.82	768.59	761.34	754.06
ethyl-	0.3994	792.95	789.29	785.62	781.96	774.61	767.24	759.84
ethyl-	0.5011	800.52	796.80	793.07	789.34	781.86	774.34	766.79
ethyl-	0.6001	809.31	805.51	801.70	797.88	790.23	782.54	774.81
ethyl-	0.7002	820.05	816.15	812.25	808.33	800.48	792.58	784.63
ethyl-	0.7990	833.05	829.03	825.00	820.96	812.86	804.71	796.50
ethyl-	0.9003	849.88	845.70	841.51	837.31	828.88	820.40	811.85
ethyl-	1.0000	871.46	867.07	862.67	858.26	849.41	840.50	831.52
propyl-	0.1020	776.92	773.39	769.86	766.34	759.29	752.23	745.16
propyl-	0.2021	782.11	778.55	774.99	771.43	764.31	757.17	750.02
propyl-	0.3075	788.29	784.70	781.10	777.50	770.29	763.06	755.81
propyl-	0.4001	794.53	790.89	787.25	783.61	776.31	768.98	761.63
propyl-	0.4998	802.09	798.40	794.70	791.01	783.59	776.15	768.67
propyl-	0.6006	811.03	807.28	803.51	799.74	792.19	784.61	776.99
propyl-	0.6985	821.17	817.34	813.49	809.65	801.94	794.19	786.41
propyl-	0.8001	833.71	829.78	825.84	821.89	813.98	806.03	798.03
propyl-	0.8997	848.55	844.50	840.44	836.37	828.21	820.02	811.77
propyl-	1.0000	867.01	862.80	858.58	854.36	845.90	837.39	828.84
butyl-	0.1004	777.33	773.80	770.28	766.77	759.73	752.69	745.63
butyl-	0.2175	783.98	780.43	776.88	773.33	766.23	759.12	751.98
butyl-	0.3011	789.26	785.69	782.12	778.54	771.39	764.21	757.01
butyl-	0.4011	796.26	792.66	789.05	785.44	778.20	770.95	763.67
butyl-	0.5065	804.59	800.94	797.28	793.63	786.30	778.95	771.57
butyl-	0.5999	812.94	809.24	805.54	801.84	794.42	786.96	779.48
butyl-	0.7004	823.16	819.41	815.65	811.88	804.34	796.76	789.15
butyl-	0.7994	834.76	830.94	827.12	823.29	815.60	807.89	800.13
butyl-	0.8994	848.36	844.46	840.55	836.63	828.78	820.90	812.97
butyl-	1.0000	864.51	860.50	856.49	852.47	844.42	836.33	828.20
pentyl-	0.4999	805.85	802.23	798.60	794.98	787.71	780.42	773.11
pentyl-	1.000	862.81	858.92	855.02	851.13	843.31	835.48	827.60
hexyl-	0.000	772.24	768.73	765.23	761.74	754.75	747.77	740.77
hexyl-	0.1001	778.27	774.75	771.24	767.73	760.71	753.68	746.64
hexyl-	0.2002	784.79	781.26	777.73	774.20	767.14	760.07	752.98
hexyl-	0.3007	791.81	788.27	784.71	781.17	774.07	766.95	759.82
hexyl-	0.4011	799.43	795.86	792.29	788.72	781.57	774.40	767.21
hexyl-	0.5002	807.56	803.96	800.36	796.77	789.56	782.34	775.09
hexyl-	0.5997	816.42	812.80	809.17	805.54	798.28	791.00	783.68
hexyl-	0.6996	826.13	822.47	818.81	815.14	807.81	800.46	793.07
hexyl-	0.8003	836.77	833.07	829.37	825.67	818.26	810.83	803.37
hexyl-	0.8996	848.44	844.70	840.95	837.21	829.71	822.20	814.65
hexyl-	1.0000	861.39	857.60	853.81	850.02	842.43	834.81	827.17
heptyl-	0.4996	809.00	805.44	801.87	798.30	791.16	784.00	776.83
heptyl-	1.0000	860.04	856.35	852.65	848.96	841.55	834.14	826.69
octyl-	0.1013	779.4	775.9	772.4	768.9	761.9	754.9	747.8
octyl-	0.2002	786.7	783.2	779.7	776.2	769.2	762.1	755.1
octyl-	0.3589	799.2	795.7	792.1	788.6	781.6	774.5	767.4
octyl-	0.4554	807.2	803.7	800.2	796.6	789.5	782.4	775.3
octyl-	0.5010	811.2	807.6	804.1	800.5	793.4	786.3	779.2
octyl-	0.5999	820.0	816.4	812.9	809.3	802.2	795.1	787.9
octyl-	0.7000	829.4	825.8	822.3	818.7	811.5	804.4	797.2
octyl-	0.7998	839.2	835.7	832.1	828.5	821.3	814.1	806.9
octyl-	0.8990	849.5	845.9	842.3	838.7	831.5	824.3	817.0
octyl-	1.0000	860.6	857.0	853.4	849.7	842.5	835.2	827.9
decyl-	0.4987	813.58	810.07	806.57	803.06	796.06	789.05	782.03
decyl-	1.0000	859.01	855.49	851.97	848.45	841.42	834.38	827.33

^{^a}

x₁ is the mole fraction of an n-alkylbenzene (1) in pentadecane (2). The average pressure for these measurements was 0.102 MPa. Standard uncertainties are u(T) = 0.01 K and u(p) = 1 kPa; relative standard uncertainties for mixtures with pentadecane are u_r(ρ) = 0.0007 for n-decylbenzene, u_r(ρ) = 0.0019 for n-octylbenzene mixtures, u_r(ρ) = 0.0006 for n-heptylbenzene mixtures, u_r(ρ) = 0.0008 for n-hexylbenzene mixtures, and u_r(ρ) = 0.0003 for remaining mixtures, and combined expanded uncertainty U(x₁) = 0.0001 (level of confidence = 0.95, k = 2).

Table 7. Viscosities η (mPa·s) of Binary Mixtures of an n-Alkylbenzene at Mole Fraction x₁ in Pentadecane at Temperature T and Pressure of 0.1 MPaa

n-alkyl-benzene	x₁	T = 288.15 K	T = 293.15 K	T = 298.15 K	T = 303.15 K	T = 313.15 K	T = 323.15 K	T = 333.15 K
	0.0000	3.24	2.88	2.57	2.31
propyl-	0.1020	2.88	2.57	2.31	2.10
propyl-	0.2021	2.56	2.30	2.09	1.90
propyl-	0.3075	2.25	2.05	1.86	1.70
propyl-	0.4001	2.02	1.84	1.67	1.53
propyl-	0.4998	1.78	1.63	1.49	1.37
propyl-	0.6006	1.56	1.43	1.31	1.21
propyl-	0.6985	1.36	1.25	1.15	1.07
propyl-	0.8001	1.18	1.09	1.01	0.94
propyl-	0.8997	1.02	0.95	0.89	0.83
propyl-	1.0000	0.89	0.83	0.78	0.74
butyl-	0.0000	3.24	2.88	2.57	2.31	1.90	1.59
butyl-	0.1004	2.92	2.61	2.34	2.11	1.76	1.48
butyl-	0.2175	2.59	2.32	2.11	1.91	1.60	1.36
butyl-	0.3011	2.37	2.13	1.95	1.77	1.49	1.27
butyl-	0.4011	2.12	1.94	1.76	1.61	1.37	1.17
butyl-	0.5065	1.90	1.74	1.58	1.45	1.24	1.07
butyl-	0.5999	1.72	1.57	1.44	1.33	1.14	0.99
butyl-	0.7004	1.54	1.41	1.29	1.20	1.03	0.91
butyl-	0.7994	1.38	1.26	1.17	1.08	0.94	0.84
butyl-	0.8994	1.23	1.13	1.05	0.97	0.86	0.77
butyl-	1.0000	1.10	1.01	0.94	0.88	0.78	0.70
pentyl-	0.0000	3.24	2.88	2.57	2.31	1.90	1.59	1.35
pentyl-	0.4999	2.14	1.95	1.77	1.62	1.37	1.17	1.02
pentyl-	1.0000	1.45	1.33	1.22	1.13	0.97	0.85	0.75
hexyl-	0.000	3.24	2.88	2.57	2.31	1.90	1.59	1.35
hexyl-	0.1001	3.04	2.71	2.42	2.18	1.82	1.53	1.30
hexyl-	0.2002	2.85	2.55	2.28	2.08	1.73	1.46	1.25
hexyl-	0.3007	2.67	2.40	2.15	1.97	1.64	1.39	1.20
hexyl-	0.4011	2.51	2.25	2.05	1.86	1.56	1.33	1.15
hexyl-	0.5002	2.36	2.13	1.94	1.77	1.49	1.27	1.10
hexyl-	0.5997	2.23	2.03	1.84	1.68	1.41	1.21	1.05
hexyl-	0.6996	2.11	1.92	1.74	1.59	1.35	1.16	1.01
hexyl-	0.8003	2.02	1.83	1.66	1.52	1.29	1.11	0.97
hexyl-	0.8996	1.92	1.74	1.58	1.45	1.23	1.06	0.93
hexyl-	1.0000	1.83	1.67	1.52	1.39	1.18	1.02	0.89
heptyl-	0.000	3.24	2.88	2.57	2.31	1.90	1.59	1.35
heptyl-	0.4996	2.63	2.36	2.12	1.94	1.62	1.38	1.19
heptyl-	1.000	2.30	2.07	1.89	1.72	1.44	1.23	1.06
octyl-	0.0000	3.24	2.88	2.57	2.31	1.90	1.59	1.35
octyl-	0.1013	3.16	2.81	2.51	2.26	1.88	1.57	1.34
octyl-	0.2002	3.09	2.75	2.46	2.22	1.84	1.55	1.33
octyl-	0.3589	3.00	2.67	2.39	2.15	1.80	1.52	1.30
octyl-	0.4554	2.95	2.63	2.36	2.13	1.78	1.50	1.29
octyl-	0.5010	2.94	2.62	2.35	2.12	1.77	1.50	1.28
octyl-	0.5999	2.91	2.60	2.33	2.10	1.76	1.49	1.27
octyl-	0.7000	2.90	2.58	2.31	2.09	1.75	1.48	1.27
octyl-	0.7998	2.89	2.58	2.31	2.08	1.74	1.47	1.27
octyl-	0.8990	2.90	2.59	2.32	2.09	1.75	1.47	1.27
octyl-	1.0000	2.92	2.61	2.33	2.10	1.75	1.48	1.27
decyl-	0.4987	3.59	3.18	2.83	2.54	2.09	1.75
decyl-	1.0000	4.38	3.84	3.39	3.02	2.44	2.03

^{^a}

x₁ is the mole fraction of an n-alkylbenzene (1) in pentadecane (2). Standard uncertainties u are u(T) = 0.01 K and u(p) = 0.001 MPa, and combined standard uncertainties u_c are u_c(η) = 0.02 mPa·s for all mixtures except n-octylbenzene. The relative standard uncertainty is u_r(η) = 0.018 for n-octylbenzene mixtures, and combined expanded uncertainty U(x₁) = 0.0001 (level of confidence = 0.95, k = 2). The average pressure for these measurements was 0.102 MPa.

Table 8. Speeds of Sound c (kg·m^–3) of Binary Mixtures of an n-Alkylbenzene at Mole Fraction x₁ in Pentadecane at Temperature T and Pressure of 0.1 MPaa

n-alkyl-benzene	x₁	T = 288.15 K	T = 293.15 K	T = 298.15 K	T = 303.15 K	T = 313.15 K	T = 323.15 K	T = 333.15 K
	0.0000	1364.3	1345.3	1326.3	1307.5	1270.8	1234.7	1199.2
toluene	0.1017	1359.8	1340.9	1321.8	1303.0
toluene	0.1987	1355.6	1336.5	1317.5	1298.6
toluene	0.2985	1351.1	1332.0	1312.9	1293.9
toluene	0.3992	1346.5	1327.3	1308.1	1289.1
toluene	0.5014	1342.1	1322.7	1303.3	1284.1
toluene	0.5996	1338.1	1318.6	1299.0	1279.6
toluene	0.7000	1334.9	1315.2	1295.4	1275.7
toluene	0.8004	1333.9	1313.8	1293.5	1273.5
toluene	0.9010	1336.9	1316.1	1295.3	1274.6
toluene	1.0000	1348.3	1326.6	1304.8	1283.2
ethyl-	0.1000	1360.6	1341.5	1322.6	1303.8	1267.0	1230.9	1195.2
ethyl-	0.2010	1357.0	1338.0	1319.0	1300.2	1263.3	1227.1	1191.4
ethyl-	0.3002	1353.6	1334.6	1315.5	1296.7	1259.6	1223.3	1187.4
ethyl-	0.3994	1350.5	1331.4	1312.2	1293.3	1256.1	1219.5	1183.5
ethyl-	0.5011	1347.5	1328.3	1309.1	1290.2	1252.8	1215.9	1179.6
ethyl-	0.6001	1345.6	1326.2	1306.8	1287.6	1249.9	1212.7	1176.0
ethyl-	0.7002	1344.6	1325.0	1305.4	1286.1	1247.9	1210.3	1173.1
ethyl-	0.7990	1345.9	1325.9	1306.0	1286.2	1247.4	1209.1	1171.4
ethyl-	0.9003	1350.2	1329.9	1309.5	1289.4	1249.8	1210.6	1172.0
ethyl-	1.000	1361.3	1340.2	1319.1	1298.2	1257.1	1216.7	1176.8
propyl-	0.1020	1361.1	1342.1	1323.1	1304.4	1267.6	1231.5	1195.9
propyl-	0.2021	1358.3	1339.3	1320.3	1301.6	1264.7	1228.5	1192.8
propyl-	0.3075	1355.4	1336.4	1317.5	1298.7	1261.8	1225.5	1189.7
propyl-	0.4001	1353.2	1334.2	1315.2	1296.4	1259.4	1223.0	1187.1
propyl-	0.4998	1351.2	1332.1	1313.0	1294.2	1257.0	1220.4	1184.3
propyl-	0.6006	1349.9	1330.7	1311.5	1292.5	1255.1	1218.2	1181.9
propyl-	0.6985	1349.5	1330.2	1310.8	1291.7	1254.0	1216.9	1180.2
propyl-	0.8001	1350.7	1331.1	1311.5	1292.2	1254.1	1216.5	1179.5
propyl-	0.8997	1354.4	1334.4	1314.5	1294.8	1256.0	1217.9	1180.3
propyl-	1.0000	1362.0	1341.6	1321.2	1301.1	1261.5	1222.4	1183.9
butyl-	0.1004	1362.5	1343.4	1324.4	1305.7	1268.9	1232.9	1197.3
butyl-	0.2175	1360.4	1341.6	1322.5	1303.9	1267.3	1231.2	1195.6
butyl-	0.3011	1359.3	1340.5	1321.5	1302.9	1266.2	1230.0	1194.4
butyl-	0.4011	1358.5	1339.5	1320.6	1301.9	1265.1	1228.9	1193.3
butyl-	0.5065	1357.9	1339.0	1320.1	1301.4	1264.6	1228.3	1192.5
butyl-	0.5999	1358.3	1339.4	1320.3	1301.6	1264.6	1228.2	1192.2
butyl-	0.7004	1359.5	1340.5	1321.4	1302.6	1265.4	1228.8	1192.6
butyl-	0.7994	1362.2	1342.9	1323.7	1304.6	1267.1	1230.3	1193.9
butyl-	0.8994	1366.4	1347.2	1327.6	1308.5	1270.7	1233.5	1196.8
butyl-	1.0000	1373.8	1354.0	1334.3	1314.8	1276.5	1238.7	1201.5
pentyl-	0.4999	1364.8	1345.8	1326.9	1308.2	1271.3	1235.2	1199.6
pentyl-	1.0000	1385.4	1366.0	1346.7	1327.5	1289.9	1252.8	1216.2
hexyl-	0.1001	1364.7	1345.7	1326.8	1308.1	1271.3	1235.3	1199.8
hexyl-	0.2002	1365.4	1346.5	1327.6	1309.0	1272.4	1236.4	1200.9
hexyl-	0.3007	1366.6	1347.8	1328.9	1310.4	1273.9	1237.9	1202.5
hexyl-	0.4011	1368.4	1349.5	1330.7	1312.1	1275.6	1239.7	1204.3
hexyl-	0.5002	1370.6	1351.8	1333.0	1314.4	1277.9	1241.9	1206.5
hexyl-	0.5997	1373.4	1354.7	1335.8	1317.3	1280.8	1244.8	1209.4
hexyl-	0.6996	1377.2	1358.3	1339.5	1320.9	1284.3	1248.3	1212.8
hexyl-	0.8003	1381.8	1363.0	1344.1	1325.5	1288.9	1252.8	1217.2
hexyl-	0.8996	1387.6	1368.8	1349.8	1331.1	1294.4	1258.2	1222.5
hexyl-	1.0000	1394.9	1376.1	1357.0	1338.3	1301.4	1265.1	1229.2
heptyl-	0.4996	1376.9	1358.3	1339.5	1321.0	1284.7	1249.0	1213.7
heptyl-	1.0000	1405.8	1387.1	1368.4	1349.9	1313.5	1277.7	1242.4
octyl-	0.0000	1364.3	1345.3	1326.3	1307.5	1270.8	1234.7	1199.2
octyl-	0.1013	1367.2	1348.5	1329.5	1310.9	1274.3	1238.3	1202.8
octyl-	0.2002	1370.7	1351.9	1333.0	1314.4	1277.9	1242.0	1206.7
octyl-	0.3589	1376.9	1358.3	1339.5	1321.0	1284.7	1249.0	1213.7
octyl-	0.4554	1381.2	1362.8	1344.1	1325.6	1289.4	1253.6	1218.5
octyl-	0.5010	1383.7	1364.9	1346.2	1327.8	1291.6	1256.0	1220.8
octyl-	0.5999	1388.8	1370.2	1351.6	1333.2	1297.1	1261.5	1226.4
octyl-	0.7000	1394.6	1376.3	1357.7	1339.3	1303.2	1267.7	1232.7
octyl-	0.7998	1401.3	1382.7	1364.1	1345.8	1309.8	1274.3	1239.3
octyl-	0.8990	1408.6	1390.0	1371.4	1353.1	1317.1	1281.7	1246.7
octyl-	1.0000	1416.7	1398.4	1379.8	1361.5	1325.5	1290.1	1255.1
decyl-	0.4987	1394.5	1375.9	1357.4	1339.1	1303.0	1267.7	1232.9
decyl-	1.0000	1433.5	1415.2	1396.9	1378.9	1343.5	1308.7	1274.4

^{^a}

x₁ is the mole fraction of an n-alkylbenzene (1) in pentadecane (2). The average pressure for these measurements was 0.102 MPa. Standard uncertainties are u(T) = 0.01 K and u(p) = 1 kPa; relative standard uncertainties are u_r(c) = 0.0018 for n-octylbenzene and u_r(c) = 0.0007 for all other mixtures, and combined expanded uncertainty U(x₁) = 0.0001 (level of confidence = 0.95, k = 2).

Figure 1. Speed of sound, c, of binary mixtures containing pentadecane and (A) n-octylbenzene, (B) n-hexylbenzene, (C) n-butylbenzene, (D) n-propylbenzene, and (E) ethylbenzene and (F) toluene at various temperatures. x₁’s are values of the mole fraction of n-alkylbenzene in the pentadecane. The lines on the speed-of-sound figure are polynomial fits, with the fitting parameters provided in the Supporting Information, Table S4.

The speed of sound–mole fraction data were fitted to polynomials for select mixtures (Supporting Information Table S4). The fits were good (standard errors of fit <0.6 m·s^–1) for all mixtures, as demonstrated in Figure 1, except for toluene and ethylbenzene mixtures where third-order models had standard errors of fit of approximately 1.5 m·s^–1 and 1 m·s^–1, respectively.

The bulk modulus is the product of the fuel’s density (ρ) and square of the speed of sound (c), ρ × c². The bulk modulus values ranged from 1386 to 1713 MPa. With this range of bulk modulus values, a significant difference in injection timing would be expected. Van Gerpen et al. reported a 1° timing advance for fuel with a 169 MPa difference in their bulk modulus values. (28)

Values of the bulk modulus for select n-alkylbenzenes as a function of mole fraction are shown in Figure 2 at 293.15 K. These values steadily increase, except for toluene mixtures, which drop slightly to a minimum (x₁ = 0.3) before increasing. This behavior has been reported before for hexadecane mixtures with alkylbenzenes. Morrow et al. (62) used molecular dynamics (MD) simulations to explore the potential causes for this behavior and attributed it to the orientation of the benzyl group in toluene. They discuss that the larger bulk modulus of the alkylbenzenes is likely caused by the greater difficulty in compressing their aromatic rings. In aromatic compounds, the ring of one molecule can be oriented in parallel or perpendicular to the ring of another molecule, and the benzene molecules show a larger number of perpendicular arrangements of their rings than those of n-alkylbenzenes. In mixtures of either toluene or benzene with hexadecane, Morrow et al. (62) showed a significant disruption of the packing structure (change to more parallel arrangement), which could contribute to the minimum value found in the bulk modulus. The orientation of butylbenzene in hexadecane mixtures changed very little, which explains why there was no dip in bulk modulus as a function of concentration. It is likely that pentadecane in the current study causes a similar disruption in the molecular packing of the aromatic molecules.

Figure 2. Bulk modulus of n-alkylbenzene in pentadecane at 293.15 K. x₁ is the mole fraction of n-alkylbenzene in pentadecane.

The range of density values allowed for military jet fuel (788 to 845 kg·m^–3), (23) military diesel fuel (800 to 876 kg·m^–3), (24) and ASTM jet fuel (775 to 840 kg·m^–3) (25) is specified at 288.15 K. Pentadecane alone had a density below the specifications, but some mixtures fall within those specifications. Mixtures containing toluene (0.4 ≤ x₁ ≤ 0.8) and the aromatic compounds that were tested at multiple mole fractions (0.3 ≤ x₁ ≤ 0.8) conformed to the military jet fuel density specification, while mixtures with a wider range of mole fractions (0.1 ≤ x₁ ≤ 0.8) of the aromatic compounds fell within the required range for ASTM jet fuel. Higher mole fractions were needed (0.6 ≤ x₁ ≤ 1.0 for toluene; 0.5 ≤ x₁ ≤ 1.0 for the other aromatic compounds) to conform to the military diesel density specification. These mixtures could be used in modeling fuel behavior.

The range of viscosities allowed for military diesel fuel (1.7 to 4.3 mm²·s^–1) (24) is specified at 313.15 K. The viscosities of 0.5 mole fractions of pentylbenzene, heptylbenzene, and decylbenzene and the viscosities of all the octylbenzene mixtures fell within this range. Only certain mixtures of butylbenzene (x₁ ≤ 0.4) and hexylbenzene (x₁ ≤ 0.5) conformed to the viscosity specification. Note that the jet fuel viscosity specification is measured at 253.15 K, which is a temperature not used in this study.

In correlating the mixture viscosity (ν_mix) to component viscosities, McAllister (63) presents a “three-body” model and a “four-body” model. These models are applied to molecules with similar sizes but radii that differ by less than a factor of 1.5. (63) McAllister used the “three-body” model for molecules with a volume ratio of 2.6. (63) The molar volume ratios of pentadecane to each n-alkylbenzene are as follows: 1.24 for n-octylbenzene, 1.5 for n-hexylbenzene, 1.8 for n-butylbenzene, and 2.0 for n-propylbenzene. These values are below the volume ratio of 2.6 used in McAllister’s work, so the “three-body” model (eq 5) was fitted to data in this current work.

\ln ν_{m i x} = x_{1}^{3} \ln ν_{1} + 3 x_{1}^{2} x_{2} \ln ν_{1, 2} + 3 x_{1} x_{2}^{2} \ln ν_{2, 1} + x_{2}^{3} \ln ν_{2} - \ln (x_{1} + x_{2} \frac{M_{2}}{M_{1}}) + 3 x_{1}^{2} x_{2} \ln (\frac{1}{3} (2 + \frac{M_{2}}{M_{1}})) + 3 x_{1} x_{2}^{2} \ln (\frac{1}{3} (1 + 2 \frac{M_{2}}{M_{1}})) + x_{2}^{3} \ln (\frac{M_{2}}{M_{1}})

(5)

In eq 5, the component kinematic viscosities (ν₁ and ν₂), mole fractions (x₁ and x₂), and molar masses (M₁ and M₂) (“1” is for n-alkylbenzene) are used along with two fitting parameters, ν_1,2 and ν_2,1. The fitting parameters for the kinematic viscosities of pentadecane mixtures are listed in the Supporting Information (Table S5). The standard error of the model fits is less than 0.005 mm²·s^–1, suggesting that the model fitted the data well (Figure 3). Each ν_2,1 is larger than its corresponding ν_1,2 for all mixtures.

Figure 3. Kinematic viscosities, ν, containing x₁ mole fraction of an n-alkylbenzene in pentadecane: (A) n-octylbenzene, (B) n-hexylbenzene, (C) n-butylbenzene, (D) n-propylbenzene, at various temperatures. The symbols are the data, and the lines are the fitting results using eq 5. The fitting parameters are provided in the Supporting Information, Table S5. The temperature symbols shown in graph A apply to all the figures.

In the three-body model, the fitting parameters ν₁₂ and ν₂₁ are related to the free energy from the interactions of the moving molecules of compounds 1 and 2. (63) In this case, n-alkylbenzene is molecule “1” and pentadecane is molecule “2”. The ν₂₁ parameter encompasses the molal free energy of activation for viscosity, ΔG₂₁*, from the flow of n-alkylbenzene past two pentadecane molecules and the flow of pentadecane past one n-alkylbenzene and one pentadecane molecule. For this parameter, there are two pentadecane molecules, so pentadecane contributes more than alkylbenzene. The ν₁₂ parameter encompasses the molal free energy of activation for viscosity, ΔG₁₂*, from the flow of pentadecane past two n-alkylbenzene molecules and the flow of n-alkylbenzene past one n-alkylbenzene and one pentadecane molecule. For this parameter, there are two n-alkylbenzene molecules. These two fitting parameters are defined by McAllister (63) as

υ_{12} = \frac{h N_{a}}{M_{12}} \exp (\frac{Δ G_{12}^{*}}{R T}), υ_{21} = \frac{h N_{a}}{M_{21}} \exp (\frac{Δ G_{21}^{*}}{R T})

(6)

The additional variables in these equations are as follows: h is Planck’s constant, N_a is Avogadro’s number, R is the gas constant, T is temperature, M₁₂ is the molecular weight of a mixture with two molecules of substance 1 and one molecule of substance 2, and M₂₁ is the molecular weight of a mixture with two molecules of substance 2 and one molecule of substance 1. In the current study, M₂₁ > M₁₂ for the mixtures of pentadecane with n-octylbenzene, n-hexylbenzene, n-butylbenzene, and n-propylbenzene. The result in the current study that ν_2,1 is larger than ν_1,2 for mixtures suggests that ΔG₂₁* > ΔG₁₂*, thereby implying that there is a great molal free energy of activation for viscosity when there are more molecules of the larger pentadecane molecule than when there are more molecules of n-alkylbenzenes (n-octylbenzene, n-hexylbenzene, n-butylbenzene, and n-propylbenzene molecules).

3.3. Excess Molar Properties and Viscosity Deviations

Excess molar volumes of pentadecane mixtures with all n-alkylbenzenes were positive, as shown in Figure 4 (see Supporting Information for all tabulated values, Table S6, and uncertainty analysis). Figure 4 also shows that the excess molar volumes varied little over the temperature range measured. The largest difference in V_m^E between 288.15 and 333.15 K was 0.03 cm³·mol^–1, which falls within the error of V_m^E. Increasing temperatures should increase the kinetic energies of the alkane and aromatic compounds, reduce their interaction with themselves and with the other component, and possibly change packing. If packing changes occur, they will change for both the pure components and the mixture. The very small or no changes seen herein in V_m^E suggest that these packing changes all shift in a similar magnitude in the same direction.

Figure 4. Redlich–Kister expressions for excess molar volume of an n-alkylbenzene, V_m^E, in pentadecane: (A) n-octylbenzene, (B) n-hexylbenzene, (C) n-butylbenzene, (D) n-propylbenzene, (E) ethylbenzene, and (F) toluene. Fitting parameters are given in the Supporting Information, Table S5. The temperature symbols shown in graph A apply to all the figures. x₁ is the mole fraction of the n-alkylbenzene in pentadecane.

The V_m^E values as a function of component mole fractions, x₁ and x₂ (1 = n-alkylbenzene), were fitted with a Redlich–Kister type expression, eq 7, at each temperature using methods described in a previous work: (64)

V_{m}^{E} = x_{1} x_{2} \sum_{i = 0}^{n} A_{i} {(x_{1} - x_{2})}^{i}

(7)

In the fitting process, A_i’s were sequentially added to the expression, and the F-statistic was used to determine when the addition of another parameter was not statistically significant (see Supporting Information for more details). The n-octylbenzene mixture required one fitting parameter, which indicates symmetry around x₁ = 0.5. The n-hexylbenzene mixture required two fitting parameters, while the n-butylbenzene, n-propylbenzene, ethylbenzene, and toluene mixtures required three fitting parameters (see Table S7). The standard errors of these optimal fits were less than 0.005 cm³·mol^–1, and they are shown in Figure 4. The lack of symmetry becomes greater as the differences between the molar masses of the compounds increase. The peaks of the plot shift in the direction toward mixtures with equal masses.

V_m^E’s in the current study can be compared with V_m^E’s of other alkylbenzenes and alkylcyclohexanes in mixtures with pentadecane. Figure 5A shows that V_m^E’s of equimolar mixtures of n-alkylbenzenes in pentadecane mixtures (current study, red open triangles) follow the same trends as that of other alkanes, namely V_m^E’s decrease with (1) the increasing size of n-alkylbenzene for a specific alkane and (2) the decreasing size of the alkane for a specific n-alkylbenzene. (6−10) An exception can be found for toluene mixtures, which do not follow a consistent trend with the n-alkylbenzene size. As mentioned earlier, the orientation of the aromatic ring in toluene in mixtures with hexadecane changes more than that of other n-alkylbenzenes, as shown by MD simulations. (62) This may cause the toluene to not follow the same trend as the other n-alkylbenzenes.

Figure 5. Comparison of excess molar volume V_m^E’s of equimolar mixtures of (A) n-alkylbenzenes in alkanes (6−10) and (B) n-alkylcyclohexanes in pentadecane (34) with V_m^E’s of equimolar mixtures of n-alkylbenzenes in pentadecane at 293.15 K.

A comparison of V_m^E’s of equimolar mixtures of pentadecane with n-alkylbenzenes and n-alkylcyclohexanes is shown in Figure 5B. The chain length on n-alkylbenzenes has a greater effect on V_m^E’s (∼0.5 cm³·mol^–1 maximum difference) than does the chain length of n-alkylcyclohexanes (∼0.27 cm³·mol^–1 maximum difference). The packing behavior of aromatic rings will differ from that of cyclic rings and will affect V_m^E’s more for smaller n-alkylbenzenes. As the alkyl chain length increases, the chain will have a greater impact on V_m^E and reduce the difference between V_m^E’s of n-alkylbenzenes and n-alkylcyclohexanes.

The pattern in the pentadecane V_m^E’s is similar to those of hexadecane and can likely be explained by the same processes. Excess molar volumes for nonpolar materials can depend on changes in the molecular orientation. In aromatic compounds, the rings can stack with each other in either a perpendicular or parallel arrangement, and changes to their packing can depend on the specific n-alkylbenzene and the alkane present. (10,62,65−67) MD simulations have shown that the addition of hexadecane to smaller n-alkylbenzene (benzene to butylbenzene) only affected the aromatic ring orientation of the benzene and toluene. (62) Similarly, the addition of dodecane to the bigger n-nonylbenzene only caused a small change in the aromatic ring orientation and V_m^E of −0.01 cm³ mol^–1. (10) MD simulations have also shown that hexadecane conformations in three-component mixtures with an alkylcyclohexane and either toluene or hexylbenzene were the same as those in pure hexadecane. (68) If pentadecane interacts with the n-alkylbenzenes in a manner similar to those of hexadecane and dodecane, then it is likely that the pattern in pentadecane V_m^E is not caused by pentadecane conformational changes and is only caused by changes in the aromatic ring orientation for the toluene system.

Molecular arrangements can also affect the packing and contribute to excess molar volume. MD simulations showed that the addition of toluene to hexadecane caused the hexadecane to occupy more volume than that in the absence of toluene. (68) MD simulations have also shown that hexadecane altered the packing of hexylbenzene (HB) more than did dodecane in three-component mixtures with butylcyclohexane. (68) It may be that the changes in the arrangement of the molecules are also affecting V_m^E’s in the current study, but simulations would have to be done to confirm this.

At 293.15 K, the viscosity deviations were positive for mixtures containing toluene and ethylbenzene and close to zero or negative for the remaining mixtures (see Supporting Information for a complete set of viscosity deviations, Table S8, and uncertainty analysis). Higher temperatures caused the deviations from zero to be smaller. Viscosity deviation in binary mixtures is negative when molecular interactions are reduced, and molecules can flow past each other more easily than when alone. As temperature increases, all the molecules have greater kinetic energy and can overcome attraction, and thereby the viscosity of a liquid of a specific substance will have a lower viscosity. Since the higher temperature has already reduced attraction, the addition of other substances may have less of an effect. This can cause the viscosity deviation to be closer to zero. In cases where Δη in binary mixtures is positive, molecular interactions are increased and the flow of molecules is hindered more than that when alone. Increasing the temperature will reduce the molecular attraction and reduce the effect of adding the second component in a mixture, causing Δη to be closer to zero.

Δη’s in the current study can be compared with Δη’s of other alkylbenzenes and alkylcyclohexanes in mixtures with pentadecane. Figure 6A shows that Δη’s of equimolar mixtures of n-alkylbenzenes in pentadecane mixtures in the current study (red closed squares) follow a similar trend to that of hexadecane (open blue squares) and that the values fall between those of hexadecane and tetradecane in mixtures with n-butylbenzene and n-dodecylbenzene. (6,8,10) Interestingly, for butylbenzene mixtures, the Δη value of the pentadecane mixture is positive and lower than that of hexadecane, while for dodecylbenzene mixtures, it is negative and higher than that of hexadecane. Figure 6B shows that the Δη pattern as a function of the alkyl chain length for alkylbenzenes is similar to that of alkylcyclohexanes. It may be that pentadecane is disrupting the flow of each alkyl-substituted species in a similar manner. This process is complex because as the alkyl chain length gets longer, viscosity increases because of greater intermolecular forces and more entangling of molecules. Also, the benzyl or cyclo group impacts packing and the attraction.

Figure 6. Comparison of the viscosity deviations for equimolar mixtures of (A) n-alkylbenzenes in mixtures with alkanes (6,8,10) and (B) n-alkylcyclohexanes in pentadecane (34) with those of n-alkylbenzenes in pentadecane.

Mixture systems can also be compared using excess speed of sound (c^E) and excess isentropic compressibility(κ_s^E), which can be calculated using eqs 8–20 reported by Douheret et al.: (69)

c^{E} = c_{m i x} - c^{I D}

(8)

c^{I D} = (ρ^{I D} κ_{s}^{I D})

(9)

ρ^{I D} = ϕ_{1} ρ_{1} + ϕ_{2} ρ_{2}

(10)

ϕ_{ι} = x_{ι} V_{m, i} / V_{m}^{I D}

(11)

V_{m, i} = \frac{M_{i}}{ρ_{i}}

(12)

V_{m}^{I D} = x_{1} V_{m},_{1} + x_{2} V_{m, 2}

(13)

κ_{s}^{I D} = ϕ_{1} κ_{s, 1} + ϕ_{2} κ_{s, 2} + T [\frac{ϕ_{1} V_{m, 1} α_{1}^{2}}{C_{p, 1}} + \frac{ϕ_{2} V_{m, 2} α_{2}^{2}}{C_{p, 2}} - \frac{V_{m}^{I D} {(α^{I D})}^{2}}{C_{p}^{I D}}]

(14)

κ_{s, i} = \frac{1}{ρ_{i} \times c_{i}^{2}}

(15)

α_{i} = - \frac{\partial ({\ln ρ}_{i})}{\partial T}

(16)

α^{I D} = ϕ_{1} α_{1} + ϕ_{2} α_{2}

(17)

C_{p}^{I D} = x_{1} C_{p, 1} + x_{2} C_{p, 2}

(18)

κ_{s}^{E} = κ_{s, m i x} - κ_{s}^{I D}

(19)

κ_{s, m i x} = \frac{1}{ρ_{m i x} \times c_{m i x}^{2}}

(20)

The variables in these equations are α (thermal expansion coefficient), c (speed of sound), C_p (molar heat capacity), ϕ (volume fraction), κ_s (isentropic compressibility), M (molar mass), ρ (density), T (temperature in K), V_m (molar volume), and x (mole fraction). Superscripts and subscripts: “E” denotes excess, “i” is the individual component, “mix” is the mixture, “1” n-alkylbenzene, and “2” is pentadecane. c^E’s and κ_s^E’s were calculated at 293.15 K. At this temperature, the measured (or interpolated) literature values for heat capacities were 154.5 J·mol^–1 K^–1 (toluene), (70) 180.8 J·mol^–1 K^–1 (ethylbenzene), (71) 212.85 J·mol^–1 K^–1 (n-propylbenzene), (72) 241.38 J·mol^–1 K^–1 (n-butylbenzene), (72) 300.14 J·mol^–1 K^–1 (n-hexylbenzene), (73) 330.28 J·mol^–1 K^–1 (n-heptylbenzene), (73) and 468.1 J·mol^–1 K^–1 (pentadecane). (74) The values for n-decylbenzene, 419.0 J·mol^–1 K^–1, n-octylbenzene, 361.3 J·mol^–1 K^–1, and n-pentylbenzene, 271.2 J·mol^–1 K^–1, were estimated from the work of Yaws. (75)

The c^E values of the pentadecane mixtures were negative, and K_s^E’s of the pentadecane mixtures were positive for most of n-alkylbenzenes, except for n-decylbenzene and n-hexylbenzene mixtures (Figure 7, see Supporting Information for values, Table S9, and uncertainty analysis, Table S10). As the n-alkylbenzene size increased, c^E’s increased and K_s^E’s decreased. By applying the same method that was used for V_m^E’s, Redlich–Kister-type expressions were fitted to c^E’s and K_s^E’s (See Tables S11 and S12, Supporting Information). The fits were good, with standard errors of these fits being less than 0.2 m·s^–1 (Figure 7A,B). The smaller n-alkylcyclohexanes have both positive K_s^E’s and positive excess molar volumes. It is possible that the change in molecular arrangements that is allowing for positive V_m^E’s may also allow for greater K_s^E’s.

Figure 7. (A) Excess speeds of sound, c^E, and (B) excess isentropic compressibilities, K_s^E, of mixtures of n-alkylbenzenes x₁ in pentadecane at 293.15 K. Lines are fits to the Redlich Kistler equation, with the fitting parameters given in the Supporting Information. The aromatic compound symbols shown in graph A apply to graph B.

A comparison of c^E’s and K_s^E’s of equimolar mixtures of n-alkylbenzenes in pentadecane with those of n-alkylcyclohexane in pentadecane at 293.15 K is shown in Figure 8. (34,64,76−79) Increasing the size of n-alkylbenzenes has a much greater effect on c^E’s and K_s^E’s than does increasing the size of alkylcyclohexanes. For the larger decyl- and dodecyl-substituted molecules, c^E’s and K_s^E’s are the same for the aromatic and cyclohexane molecules. This suggests that as the linear portion of the molecule gets smaller, the cyclo- or benzyl groups have a larger impact on these excess properties.

Figure 8. Comparison of excess speeds of sound, c^E’s, and excess isentropic compressibilities, K_s^E’s, of equimolar mixtures of n-alkylbenzenes (closed symbols) in pentadecane with equimolar mixtures of n-alkylcyclohexanes (open symbols) in pentadecane at 293.15 K. (16,34)

4. Conclusions

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This work explored the densities, viscosities, and speeds of sound for mixtures of n-alkylbenzenes with pentadecane and compared the derived properties from past studies. The measured densities, viscosities, and speeds of sound can complement kinetic studies and provide researchers information for their modeling efforts. While monotonic changes were found for the density and viscosity as a function of mole fraction for most n-alkylbenzenes, the speeds of sound exhibited values in the mixtures that were lower than that in pentadecane or their constituent n-alkylbenzene. Calculations of the bulk modulus show that only toluene exhibits a minimum value, which may be caused by changes in the orientation of the aromatic ring from perpendicular to parallel. The bulk modulus values for the mixtures exhibit a large range (1386 to 1713 MPa), which would impact their injection timing into an engine.

For the n-alkylbenzenes tested, increasing the size of n-alkylbenzenes caused a decline in V_m^E’s in a pattern that is similar to hexadecane mixtures with the same aromatic compounds. Given that the values are close to those of hexadecane, it may be that the same factors that influence the V_m^E values of hexadecane mixtures also affect pentadecane mixtures. These include changes (1) in the orientation of the aromatic ring in toluene from perpendicular to parallel and (2) in the volume of the alkane and aromatic compounds. (68) The trends in Δη’s for pentadecane mixtures with n-alkylbenzenes is similar to that in mixtures with n-alkylcyclohexanes, which suggests that the flow of the molecules past each other is greatly affected by the alkyl portion of the molecule. As the length of the alkyl portion of a specific molecule increases, there are greater intermolecular forces and more entangling of molecules, which increase its viscosity. The addition of another component could loosen interactions and result in a negative Δη. The greatest reduction in interactions was found for the n-decylbenzene mixture. In contrast, the change in V_m^E’s, c^E’s, and K_s^E’s as a function of alkyl chain length was greater in n-alkylbenzenes than that previously shown for n-alkylcyclohexanes. Large differences are likely caused by differences in the packing behavior of aromatic rings and cyclic rings. Smaller differences were found for the larger molecules, where the alkyl chain length would have a greater effect on packing.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.5c00217.

Relative differences Δρ/ρ = [ρ(expt) – ρ(lit.)]/ρ(expt) of the experimental densities of (expt) at p = 0.1 MPa from literature values (lit.) as a function of temperature T; relative differences Δc/c = [c(expt) – c(lit.)]/c(expt) of the experimental speeds of sound (expt) at p = 0.1 MPa from literature values (lit.) as a function of temperature T; relative differences Δη/η = [η(expt) – η(lit.)]/η(expt) of the experimental viscosities (expt) at p = 0.1 MPa from literature values (lit.) as a function of temperature T; methods of determining errors in mole fraction, density, viscosity, and speed of sound; polynomial fits to the speed of sound–mole fraction data for n-alkylbenzene (x₁) in pentadecane mixtures; McAllister equation coefficients, ν₁₂ and ν₂₁ (eq S1), and associated standard error σ for an n-alkylbenzene x₁ in pentadecane; excess molar volumes V_m^E (cm³·mol^–1) of binary mixtures of an n-alkylbenzene at mole fraction x₁ in pentadecane; uncertainty determination for V_m^E, Redlich–Kister equation parameters, and standard error, s, from the fitted excess molar volume of an n-alkylbenzene in pentadecane; viscosity deviations Δη’s (mPa·s) of binary mixtures of an n-alkylbenzene in pentadecane; uncertainty determination for Δη, excess speeds of sound c^E’s, and excess isentropic compressibilities K_s^E’s of binary mixtures of an n-alkylbenzene (mole fraction of x₁) in pentadecane; uncertainty determinations for c^E and K_s^E, Redlich–Kister equation parameters and standard error, s, from fitted excess speeds of sound c^E’s of an n-alkylbenzene in pentadecane at 293.15 K; Redlich–Kister equation parameters and standard error, s, from fitted excess isentropic compressibilities K_s^E’s of an n-alkylbenzene in pentadecane at 293.15 K (PDF)

je5c00217_si_001.pdf (1.33 MB)

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Author Information

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Corresponding Author
- Dianne J. Luning Prak - Department of Chemistry, U.S. Naval Academy, 572 M Holloway Road, Annapolis, Maryland 21402, United States; https://orcid.org/0000-0002-5589-7287; Email: [email protected]
Author
- Jim S. Cowart - Department of Mechanical and Nuclear Engineering, U.S. Naval Academy, 590 Holloway Rd, Annapolis, Maryland 21402, United States
Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.
Notes
The authors declare no competing financial interest.
The views expressed in this document are those of the authors and do not reflect the policy or position of the U.S. Naval Academy, Department of the Navy, the Department of Defense, or the U.S. Government.

Acknowledgments

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This work was funded in part by an Office of Naval Research Grant, grant #N0001425GI00395.

References

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Abhijith Vivek, Stefanía Betancur Marquez, Arno de Klerk. Viscosity and Density of C9–C10 Aromatics at 223.15–323.15 K Relevant to Aviation Turbine Fuel. Journal of Chemical & Engineering Data 2026, 71 (3) , 960-971. https://doi.org/10.1021/acs.jced.5c00408
Dianne J. Luning Prak, Jim S. Cowart. Undecane and n-Alkylbenzenes: Densities, Speeds of Sound, and Viscosities within the Range (288.15 to 333.15) K and at 0.1 MPa. Journal of Chemical & Engineering Data 2026, 71 (1) , 72-86. https://doi.org/10.1021/acs.jced.5c00580
Dianne J. Luning Prak, Jim S. Cowart. Decane and n-Alkylbenzene Binary Mixtures: Densities and Speeds of Sound within the Range of 288.15 and 333.15 K and Viscosities within the Range of 288.15 and 323.15 K at 0.1 MPa. Journal of Chemical & Engineering Data 2025, 70 (10) , 4051-4065. https://doi.org/10.1021/acs.jced.5c00509

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Abstract
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Figure 1
Figure 1. Speed of sound, c, of binary mixtures containing pentadecane and (A) n-octylbenzene, (B) n-hexylbenzene, (C) n-butylbenzene, (D) n-propylbenzene, and (E) ethylbenzene and (F) toluene at various temperatures. x₁’s are values of the mole fraction of n-alkylbenzene in the pentadecane. The lines on the speed-of-sound figure are polynomial fits, with the fitting parameters provided in the Supporting Information, Table S4.
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Figure 2
Figure 2. Bulk modulus of n-alkylbenzene in pentadecane at 293.15 K. x₁ is the mole fraction of n-alkylbenzene in pentadecane.
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Figure 3
Figure 3. Kinematic viscosities, ν, containing x₁ mole fraction of an n-alkylbenzene in pentadecane: (A) n-octylbenzene, (B) n-hexylbenzene, (C) n-butylbenzene, (D) n-propylbenzene, at various temperatures. The symbols are the data, and the lines are the fitting results using eq 5. The fitting parameters are provided in the Supporting Information, Table S5. The temperature symbols shown in graph A apply to all the figures.
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Figure 4
Figure 4. Redlich–Kister expressions for excess molar volume of an n-alkylbenzene, V_m^E, in pentadecane: (A) n-octylbenzene, (B) n-hexylbenzene, (C) n-butylbenzene, (D) n-propylbenzene, (E) ethylbenzene, and (F) toluene. Fitting parameters are given in the Supporting Information, Table S5. The temperature symbols shown in graph A apply to all the figures. x₁ is the mole fraction of the n-alkylbenzene in pentadecane.
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Figure 5
Figure 5. Comparison of excess molar volume V_m^E’s of equimolar mixtures of (A) n-alkylbenzenes in alkanes (6−10) and (B) n-alkylcyclohexanes in pentadecane (34) with V_m^E’s of equimolar mixtures of n-alkylbenzenes in pentadecane at 293.15 K.
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Figure 6
Figure 6. Comparison of the viscosity deviations for equimolar mixtures of (A) n-alkylbenzenes in mixtures with alkanes (6,8,10) and (B) n-alkylcyclohexanes in pentadecane (34) with those of n-alkylbenzenes in pentadecane.
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Figure 7
Figure 7. (A) Excess speeds of sound, c^E, and (B) excess isentropic compressibilities, K_s^E, of mixtures of n-alkylbenzenes x₁ in pentadecane at 293.15 K. Lines are fits to the Redlich Kistler equation, with the fitting parameters given in the Supporting Information. The aromatic compound symbols shown in graph A apply to graph B.
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Figure 8
Figure 8. Comparison of excess speeds of sound, c^E’s, and excess isentropic compressibilities, K_s^E’s, of equimolar mixtures of n-alkylbenzenes (closed symbols) in pentadecane with equimolar mixtures of n-alkylcyclohexanes (open symbols) in pentadecane at 293.15 K. (16,34)
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Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.5c00217.
- Relative differences Δρ/ρ = [ρ(expt) – ρ(lit.)]/ρ(expt) of the experimental densities of (expt) at p = 0.1 MPa from literature values (lit.) as a function of temperature T; relative differences Δc/c = [c(expt) – c(lit.)]/c(expt) of the experimental speeds of sound (expt) at p = 0.1 MPa from literature values (lit.) as a function of temperature T; relative differences Δη/η = [η(expt) – η(lit.)]/η(expt) of the experimental viscosities (expt) at p = 0.1 MPa from literature values (lit.) as a function of temperature T; methods of determining errors in mole fraction, density, viscosity, and speed of sound; polynomial fits to the speed of sound–mole fraction data for n-alkylbenzene (x₁) in pentadecane mixtures; McAllister equation coefficients, ν₁₂ and ν₂₁ (eq S1), and associated standard error σ for an n-alkylbenzene x₁ in pentadecane; excess molar volumes V_m^E (cm³·mol^–1) of binary mixtures of an n-alkylbenzene at mole fraction x₁ in pentadecane; uncertainty determination for V_m^E, Redlich–Kister equation parameters, and standard error, s, from the fitted excess molar volume of an n-alkylbenzene in pentadecane; viscosity deviations Δη’s (mPa·s) of binary mixtures of an n-alkylbenzene in pentadecane; uncertainty determination for Δη, excess speeds of sound c^E’s, and excess isentropic compressibilities K_s^E’s of binary mixtures of an n-alkylbenzene (mole fraction of x₁) in pentadecane; uncertainty determinations for c^E and K_s^E, Redlich–Kister equation parameters and standard error, s, from fitted excess speeds of sound c^E’s of an n-alkylbenzene in pentadecane at 293.15 K; Redlich–Kister equation parameters and standard error, s, from fitted excess isentropic compressibilities K_s^E’s of an n-alkylbenzene in pentadecane at 293.15 K (PDF)
- je5c00217_si_001.pdf (1.33 MB)
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Binary Mixtures of n-Alkylbenzenes and Pentadecane: Densities, Speeds of Sound, and Viscosities within the Range of 288.15 and 333.15 K and at 0.1 MPaClick to copy article linkArticle link copied!

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1. Introduction

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3. Results and Discussion

3.1. Pure Components: Comparison of Densities, Viscosities, and Speeds of Sound with Literature Values

3.2. Binary Mixtures: Densities, Speeds of Sound, and Viscosities

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3.3. Excess Molar Properties and Viscosity Deviations

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Binary Mixtures of n-Alkylbenzenes and Pentadecane: Densities, Speeds of Sound, and Viscosities within the Range of 288.15 and 333.15 K and at 0.1 MPa
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