Impact of Molecular Structure on Properties of n-Hexadecane and

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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Impact of Molecular Structure on Properties of NHexadecane and Alkylbenzene Binary Mixtures Brian H. Morrow, Sabina Maskey, Micah Z. Gustafson, Dianne Jeanne Luning Prak, and Judith A. Harrison J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b03752 • Publication Date (Web): 01 Jun 2018 Downloaded from http://pubs.acs.org on June 2, 2018

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The Journal of Physical Chemistry

Impact of Molecular Structure on Properties of n-Hexadecane and Alkylbenzene Binary Mixtures Brian H. Morrow, Sabina Maskey, Micah Z. Gustafson, Dianne J. Luning Prak, and Judith A. Harrison∗ Department of Chemistry, United States Naval Academy, Annapolis, MD 21402 E-mail: [email protected]

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ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Due to the complexity of petroleum-based fuels, researchers typically use simplified mixtures, known as surrogates, to study combustion behavior and to attempt to identify how physical properties are related to combustion. The process of determining the surrogate composition to yield a desired set of thermophysical properties can be a complicated and time-consuming task. As a result, the use of computer simulations to narrow the number of possible surrogate compositions is beginning to be explored. Herein, molecular dynamics (MD) simulations are used to model binary mixtures of n-hexadecane with either benzene, toluene, n-ethylbenzene, n-propylbenzene, or nbutylbenzene. Calculated densities are in quantitative agreement with experimental values. With the exception of the mixtures containing benzene, simulated excess molar volumes are also in very good agreement with measured values. Isentropic bulk moduli are in qualitative agreement with experiment, and reproduce interesting trends observed in the experimental data. In particular, minima in the bulk moduli at intermediate compositions of several of the alkylbenzenes are correctly reproduced. In addition, the structures of the fluids are also examined. In mixtures of n-hexadecane with alkylbenzenes with longer chains, the orientation of the aromatic rings is not substantially impacted by composition. In contrast, increasing n-hexadecane content increases the ratio of parallel to perpendicular arrangements of benzene and toluene molecules. In those mixtures, this change in orientation of the aromatic rings could be responsible for the minima observed in the bulk moduli data. These results show that MD simulations can assist in development of fuel surrogates, both by predicting thermophysical properties and by providing insight into how molecular structure and composition affect those properties.

1

Introduction

Because both petroleum-based and alternative fuels can contain hundreds or thousands of components, it can be difficult to model and predict fuel combustion behavior. This is 2


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primarily due to a lack of detailed kinetic data for each fuel component, as well as the excessive computational requirements for modeling large numbers of chemical reactions. For this reason, simplified mixtures of hydrocarbons, known as surrogates, are useful for building an understanding of the combustion of more complex fuels. Physical property measurements are needed for the development of surrogates. For example, in diesel engines the bulk modulus of the fuel impacts injection timing. 1 A successful strategy for developing surrogates has been to match target properties, i.e., density and bulk modulus, to create surrogates that match the start-up performance of the fuels they model. 2,3 However, due to the extremely large chemical space from which surrogate components can be chosen, as well as the complex mixing behavior involved in fluids that contain a wide variety of hydrocarbons (straightchain, branched, cyclic, aromatic, etc.), it is difficult to predict properties such as density and bulk modulus a priori for a given composition. While empirical correlations and equations of state exist that can be used to predict such properties, 4 along with methods such as quantitative structure-property relationship (QSPR) models, they require large amounts of experimental data to parametrize, and can be of limited usefulness when applied to systems outside of their training sets. This necessitates experimental measurements that can be expensive and/or time-consuming. In addition, these methods are unable to provide dynamic or molecular-scale structural information. Molecular dynamics (MD) simulations can be used to predict thermophysical properties of fuels, 4–7 as well as structural and dynamic properties that can be difficult to measure experimentally. It is especially useful for identifying links between molecular structure and physical properties. MD simulations have been used to calculate a wide range of liquid hydrocarbon properties 8 such as density, heat of vaporization, heat capacity, diffusion coefficients, 9 and viscosity. 10,11 In a previous work, 12 the ability of two atomistic force fields, the modified Lennard-Jones adaptive intermolecular reactive empirical bond-order potential (mod-LJ AIREBO) 13 and the all-atom optimized potential for liquid simulations (OPLS-AA), 14 to calculate densities, heats of vaporization, and bulk moduli for pure and multicomponent

3



hydrocarbon liquids was compared. Uddin et al. recently used the OPLS-AA force field for hydrocarbon system property calculation 15 and quantifying physical properties of oils. 16 Recently, Verma et al. 17 also used the OPLS-AA force field, in conjunction with the LOPLS parameters developed by Siu et al. for long-chain alkanes, 18 to predict densities and viscosities of pure-component and binary sytems of n-octane, n-dodecane, n-hexadecane, and n-decylbenzene at temperatures and pressures up to 423.15 K and 5000 bar, which are typical fuel injection conditions in modern common rail diesel engines. They found densities and viscosities within 4% and 25% relative error, respectively, compared to experimental values. 17 In this work, MD simulations are used to model two-component hydrocarbon mixtures consisting of n-hexadecane with either benzene, toluene, ethylbenzene, n-propylbenzene, or n-butylbenzene. These binary mixtures are studied because n-hexadecane and alkylbenzenes are among the model compounds used in the study of petroleum-based jet and diesel fuels. 6,19–21 In addition, while alternative fuels contain mostly aliphatic compounds, aromatic compounds, such as those studied here, are typically added to increase the swelling of engine seals and prevent leakage. 22–25 The all-atom optimized potential for liquid simulations (OPLS-AA), 14 with the L-OPLS parameters for long-chain alkanes 18 are used to model the alkylbenzene-hexadecane mixtures. Density and bulk modulus, two properties of interest in surrogate development, as well as excess molar volume, are calculated and compared to experimental values. In addition, the molecular structure of the fluids is quantified by radial distribution and angular radial distribution functions, which link changes in physical properties to changes in fluid structure due to molecular shapes and composition. Our simulations show that the OPLS-AA potential yields quantitative and qualitative agreement with experiment for density and bulk modulus, respectively. Analysis of radial distribution functions between aromatic rings shows that there is not a consistent trend in bulk fluid structure as a function of alkyl-chain length. Angular radial distribution functions reveal that adding n-hexadecane disrupts the packing of benzene and toluene aromatic rings, while

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having a minimal impact on fluid structure of the longer-chain alkylbenzenes. These changes in liquid structure are linked to measurable properties, such as density, excess volume, and bulk modulus.

2

Methods

2.1

Computational methods

The MD systems are binary mixtures of n-hexadecane with either benzene, toluene, ethylbenzene, n-propylbenzene, or n-butylbenzene. For each binary system, alkylbenzene mole fractions of 0, 0.2, 0.4, 0.6, 0.8, and 1.0 were simulated. Packmol 26 was used to randomly place 500 molecules in cubic simulation cells. The initial side length was chosen by calculating the volume necessary to reproduce the experimental density, then adding 5 Å to the side length in order to make packing easier. Five different random initial configurations were generated for each composition examined. Simulations were performed using the MD package LAMMPS. 27 The systems were subjected to 10,000 steps of energy minimization using the conjugate gradient algorithm, 28 followed by 100 ps of NVT dynamics at 293.15 K, where N , V , and T are the number of atoms, volume, and temperature, respectively. This was followed by 10 ns of NPT dynamics, with a Nosé-Hoover thermostat and barostat, 29 which was used to maintain the temperature and pressure (P ) at 293.15 K and 1 bar, respectively, to match the experimental conditions. Bonds involving hydrogen were constrained via the SHAKE algorithm, 30 allowing the use of a 2.0 fs timestep. Short-range intermolecular interactions were truncated at 13 Å, with long-range electrostatic interactions calculated using the particle-particle particlemesh (PPPM) method. 31 Standard long-range corrections to the energy and pressure were applied. 32 For each configuration, the initial 2 ns was considered equilibration, and results were averaged over the final 8 ns, giving a total of 40 ns of sampling time for each composition. Figure 1 shows representative snapshots of the n-hexadecane+benzene and n-hexadecane+n5



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butylbenzene systems, each with an alkylbenzene mole fraction of 0.6. The OPLS-AA 14 force field was used to model the alkylbenzenes because it has been shown to out-perform mod-LJ AIREBO when modeling density, bulk modulus, and heat of vaporization for pure and multicomponent hydrocarbon liquids. 12 Caleman et al. 33 used a set of 146 organic liquids to compare properties, such as density and isothermal compressibility, calculated using OPLS-AA and the generalized AMBER force field (GAFF). 34 They found that OPLS-AA performed slightly better when compared to values derived from experiment. In addition, a comparative study of eight force fields (OPT-FF, 35 AMBER 03, 36 GAFF, 34 OPLS-AA, 14 OPLS-CS, 25 CHARMM27, 37 GROMOS 53A5, 38 and GROMOS 53A6 38 ) recommended the use of the OPLS-AA potential for the simulation of benzene. 39 More complex force fields that include many-body polarization effects, such as AMOEBA, 40 or the CHARMM Drude polarizable force field, 41 might be able to give slightly more accurate results for benzene, 42 but are more computationally expensive. When applied to long-chain alkanes, the original OPLS-AA parameters result in densities, heats of vaporization, and liquid-to-gel-phase transition temperatures that are significantly higher than experiment. 18 Optimization by Siu et al. for short- and long-chain alkanes resulted in the L-OPLS parameter set, 18 which is used here to model n-hexadecane. Bulk modulus, B, which is the inverse of compressibility, is related to the change in pressure with volume: B = −V (∂P/∂V ). The bulk modulus can be measured isothermally (BT ) or isentropically (BS ). The isentropic bulk modulus is calculated here to allow direct comparison to the experimental data. The isentropic bulk modulus 32 can be calculated via the relation: 1 T α2 V 1 = − , BS BT Cp

(1)

where BS and BT are the isentropic and isothermal bulk moduli, respectively, T is the temperature, V is the simulation cell volume, α is the thermal expansion coefficient, and Cp

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is the constant-pressure heat capacity. The quantities BT , α, and Cp , can all be calculated from fluctuations in NPT simulations 32 and are given by: BT = −V

1 α= V

Cp =

∂H ∂T

P

∂V ∂T

= P

∂P ∂V

= T

kB hV i hV 2 i − hV i2

hV U i − hV ihU i + P (hV 2 i − hV i2 ) kB T 2 hV i

hU 2 i − hU i2 + 2P (hV U i − hV ihU i) + P 2 (hV 2 i − hV i2 ) = , kB T 2

(2)

(3)

(4)

where kb is Boltzmann’s constant, U is the potential energy, and the angular brackets indicate an ensemble average. The angular radial distribution function, 43 g(r, θ), is calculated by:

g(r, θ) =

∆n(r, θ) , 4πr2 ρ sin(θ)∆r∆θ

(5)

where ∆n(r, θ) is the number of molecules at a distance between r and r + ∆r which form an angle between θ and θ + ∆θ relative to the the reference molecule, and ρ is the bulk number density.

2.2

Experimental methods

Experimental data for mixtures of n-hexadecane with toluene, 44 ethylbenzene, 44 and nbutylbenzene 45 have been reported previously. For mixtures of n-hexadecane with benzene and n-propylbenzene, the density and speed of sound were measured using the methods described previously. 44,45 Briefly, an Anton Paar DSA 5000 density and sound analyzer was used after being cleaned and calibrated using NIST-certified standards. Hexadecane was purchased from Acros, while benzene and propylbenzene were purchased from Tokyo Chemical Industry Co., LTD. The purities of all of these hydrocarbons were greater than 99.5%. 7



Figure 1: Representative snapshots of n-hexadecane+benzene (left) and n-hexadecane+nbutylbenzene systems (right), both with 0.6 mole fraction alkylbenzene. n-Hexadecane, benzene, and n-butylbenzene are shown in blue, green, and red, respectively. Hydrogen atoms are not shown for clarity. Molecules that extend beyond the black simulation cell do not have the periodic boundary conditions applied so that the molecules will appear continuous in the figure. The isentropic bulk modulus Bs was then calculated using the relation Bs = c2 ρ, where c and ρ are the speed of sound in the medium and density, respectively.

3 3.1

Results Thermophysical properties

The densities and bulk moduli calculated from the simulations are compared to the experimental values as a function of alkylbenzene mole fraction in Figure 2. The simulated densities exhibit the same trends seen in experiment, with density increasing non-linearly as the alkylbenzene content increases. For the pure alkylbenzenes, density decreases as the alkyl chain length increases. Conversely, for all mixtures at all mole fractions, the density increases as the alkylbenzene chain length increases. The simulated versus experimental densities are

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shown in Figure 2b, with the 45◦ line indicating perfect agreement. The values calculated from simulations are in quantitative agreement with experiment, with a root-mean-square deviation (RMSD) of only 1.7 kg/m3 . The ability of OPLS-AA and L-OPLS to correctly reproduce the density of these mixtures is not unexpected. The L-OPLS non-bonded parameters were obtained by fitting to the experimental densities of n-dodecane and n-pentadecane, 18 and it has been shown that OPLS-AA accurately reproduces the thermodynamic and structural properties of liquid benzene. 39 Nevertheless, these results show that the L-OPLS and OPLS-AA parameters are capable of quantitatively reproducing the experimental densities of mixtures over the entire range of composition and alkyl-chain length considered here. This implies that the mixing

3

880 Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

3

(a) 840

800 Simulation

760

Simulated density (kg/m )

rules employed by the OPLS-AA potential for these mixtures are a reasonable choice.

Density (kg/m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

0.2 0.4 0.6 0.8 1 Mole fraction alkylbenzene

Experiment

0


880

(b) 840

800

760 760 800 840 880 3 Experimental density (kg/m )

Figure 2: (a) Simulated and experimental densities for binary systems of n-hexadecane with the indicated alkylbenzene. Data points are connected by straight lines to guide the eye. (b) Simulated versus experimental densities, with the solid black line indicating exact agreement. Color coding is the same as in (a). Both the experimental and the simulated isentropic bulk modulus BS values are shown in Figure 3. The trends observed in both simulation and experimental data as a function of composition are qualitatively similar. At a given alkylbenzene mole fraction, increasing the alkylbenzene tail length results in a larger bulk modulus. An interesting feature of the experimental bulk modulus data is that certain mixtures have a lower bulk modulus than either of the pure components. For example, almost all n-hexadecane+benzene mixtures have lower BS values than either pure n-hexadecane or benzene. A similiar minimum in 9



BS is found in n-hexadecane+toluene mixtures, although it is less pronounced. For propyl-, ethyl-, and n-butylbenzene-containing mixtures, there is no minimum in BS at intermediate compositions, but BS does increase non-linearly, indicating some degree of non-ideality. These trends in experimental BS values are reproduced in simulations (Figure 3a). The calculated BS values for all four n-hexadecane+benzene mixtures are lower than those of either pure component, although the bulk modulus of pure benzene is markedly lower than the experimental value. With the exception of the n-hexadecane+benzene system, bulk moduli tend to be over-predicted compared to experiment (Figure 3b). As the alkylbenzene mole fraction increases the agreement worsens. However, overall the agreement with experiment is reasonable as demonstrated by an RMSD value of 0.05 GPa. 1.7

1.6

Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

(a)

1.5 1.4 Simulation

1.3

0


Experiment

0


Simulated BS (GPa)

1.7

BS (GPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.6

(b)

1.5 1.4 1.3 1.3 1.4 1.5 1.6 1.7 Experimental BS (GPa)

Figure 3: (a) Simulated and experimental isentropic bulk moduli (BS ) for binary systems of n-hexadecane with the indicated alkylbenzene. Data points are connected by straight lines to guide the eye. Error bars represent the standard deviation of BS obtained from five independent trajectories. (b) Simulated versus experimental BS , with the solid black line indicating exact agreement. Color coding is the same as in (a). Both density and bulk modulus exhibit non-ideal mixing behavior. This arises not only from the large differences in size and shape between n-hexadecane and the alkylbenzenes but also from the fact that one is a straight-chain alkane and the other is a molecule with an aromatic ring. Intermolecular forces between non-identical molecules differ from those forces in the pure components of a solution when the solution is non-ideal. Excess molar volume, which is the difference between the molar volume of the real mixture and the molar volume that would be obtained with ideal mixing, can be used to quantify the degree of non-ideality

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of a solution. Excess molar volume is given by: 46

VE =

M1 X1 + M2 X2 M1 X1 M2 X2 − − , ρm ρ1 ρ2

(6)

where ρm is the density of the mixture, and Mi , Xi , and ρi are the molar mass, mole fraction, and density, respectively, of component i. The excess molar volumes, VE , as a function of alkylbenzene mole fraction calculated from these simulations and experimental data are shown in Figure 4. For both sets of data, VE generally increases as the shape and size difference between the alkylbenzene and n-hexadecane increases. Mixtures with n-butylbenzene, which has the longest alkyl chain of the alkylbenzenes considered here, have the lowest VE , indicating that they are the most ideal mixtures. The long alkyl chain on n-butylbenzene allows for favorable interactions with the straight chain n-hexadecane molecules. Not surprisingly, mixtures of n-hexadecane+benzene exhibit the largest values of VE and thus the largest deviations from ideality. Interestingly, while there is a large difference in VE values for benzene and toluene mixtures, toluene and ethylbenzene mixtures have similar excess molar volumes. In fact, at some mole fractions n-hexadecane+ethylbenzene mixtures have higher values of VE than n-hexadecane+toluene mixtures. It should also be noted that the agreement between the simulated and experimental values of VE is generally good with the exception of the n-hexadecane+benzene mixtures. This is apparent from an examination of Figure 4b where the simulated VE is shown as a function of the experimental VE and has an overall RMSD value is 0.18 cm3 /mol. If the values from the n-hexadecane+benzene mixtures are omitted, the RMSD value decreases markedly to 0.07 cm3 /mol. These data point to a discrepency in the ability of the OPLS-AA potential to accurately model the intermolecular interactions between an entirely aromatic molecule and an n-alkane.

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Simulation

1.2

Experiment

3

3

0.9

Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

V (cm /mol)

1.2 V (cm /mol)

E

0.6

E

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.3 0

0


0


(b)

0.8 0.4 0

0

0.4 0.8 1.2 E 3 V (cm /mol)

Figure 4: (a) Excess molar volume, VE , of binary mixtures of n-hexadecane with the indicated alkylbenzene. (b) Simulated versus experimental VE , with the solid black line indicating exact agreement. Color coding is the same as in (a).

3.2 3.2.1

Liquid structure Pure alkylbenzenes

Two recent studies have used neutron diffraction combined with empirical potential structure refinement (EPSR) to study the molecular arrangements of pure benzene and toluene at 293.15 K 43 and 303.15 K. 47 Radial distribution functions (RDFs) extracted from these measurements can be compared directly to RDFs calculated from simulations. Figure 5 shows radial distribution functions, g(r), measured between the ring center (RC) of benzene, the RC of toluene, and the toluene methyl carbons (MC). The solid and dashed lines are data from the simulations and data from Headen et al., 43 respectively. Overall, there is excellent agreement between simulated and experimental RDFs. The benzene RC RDF has a maximum at ∼5.7 Å, compared to ∼5.75 Å in experiment, while the minimum RC-RC separation, as well as the height of the first minimum, of the two plots coincide. For toluene RC, the first peak position in the MD simulations (∼5.9 Å) appears at slightly larger separation than in experiment (∼5.77 Å). In addition, the minimum toluene separation is slightly too large. Finally, the toluene MC RDF is nearly identical to the experimental data. The largest difference in peak position between the MD simulations and neutron diffraction/EPSR data is only ∼0.1 Å for the toluene RC. Thus, OPLS-AA accurately models the spatial arrangement of both pure benzene and toluene.

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6 5 4 g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Toluene MC Toluene RC Benzene RC

3 2 1 0

2

4

6 r (Å)

8

10

Figure 5: Radial distribution function between benzene ring centers of mass (RC), toluene RC, and toluene methyl carbon (MC) for pure benzene and toluene. Solid lines are from simulation data, dashed lines are the data of Headen et al. 43 Plots for toluene RC and toluene MC are shifted vertically by 2 and 4 units, respectively, for visualization purposes. To examine the effect of alkyl-chain length on the structure of pure alkylbenzene liquids, the RDF between the ring centers of mass for the five alkylbenzenes was calculated (Figure 6). Because benzene has the highest RDF maxima and lowest RDF minima, it is the most ordered of the five alkylbenzene fluids. Not surprisingly, the substitution of a methyl group for a hydrogen atom leads to a more disordered fluid structure for toluene compared to benzene. Comparison of the RDFs shows that the height of the first peak decreases from 1.91 for benzene to 1.75 in toluene, while the first minimum and second maximum increase and decrease, respectively, and are shifted by 0.6 Å in r. These changes indicate that benzene molecules are more tightly packed, with more well-defined “solvation” shells, than the toluene molecules, which leads to the higher density of benzene (Figure 2). Increasing the length of the alkyl chain, to ethyl, propyl, and butyl, does not result in a clear trend in the RDFs. The first peaks in the RDFs of all three of these molecules have nearly identical heights (Figure 6) with ethylbenzene having the least-defined second RDF peak, as well as the longest second-peak distance. In contrast, the RDFs for propyl- and butylbenzene are 13



similar, with the same maxima and minima positions. While the RDFs for benzene, toluene, and ethylbenzene display a progressive loss of order as alkyl chain length increases, further lengthening of the alkyl chain to propyl and butyl groups increases the order of the fluid. This comparison of the pure alkylbenzene RDFs shows that there is no consistent correlation between the length of the alkylbenzene side chain and the prefered distance of the solvation shells.

2.0 Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

1.5 g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1.0 0.5 0.0 3

6

9 r (Å)

12

15

Figure 6: Radial distribution function between the centers of mass of the aromatic rings in the pure alkylbenzene systems.

Additional insight into the arrangement of the alkylbenzene molecules relative to each other can be gained by calculating the angular radial distribution function (ARDF), g(r, θ), using Eqn 5. While the RDFs detail the most probable distance that separate atoms or the aromatic rings, the ARDF also provides information about the relative orientations of the aromatic rings of the alkylbenzene molecules relative to each other. The ARDF gives the relative probability of finding a molecule at a ring-center–ring-center distance r, with an angle between ring normal vectors θ, relative to the reference molecule, as illustrated in Figure 7. Angles of 0◦ and 90◦ correspond to parallel and perpendicular orientations of the aromatic rings relative to each other, respectively. The ARDFs for the pure alkylbenzenes considered here are shown in Figure 7. For benzene, the most probable configuration is perpendicular, in agreement with neutron diffrac-

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tion data, 43,47 as well as density functional theory calculations of benzene dimers which show that the perpendicular, or T-shaped, configuration is favored over a parallel arrangement. 48 Toluene displays less of a preference for perpendicular arrangements than benzene, with a less pronounced peak near 90◦ and a small peak near 0◦ , which is in qualitative agreement with experimental data. 43,47 Ethylbenzene displays a preference for perpendicular arrangements, although the peak near 90◦ is not as intense as it is in benzene. It also has the least propensity for parallel arrangements of any of the alkylbenzenes considered here, possibly because the ethyl group is long enough to disrupt parallel packing via steric hinderance, but not long enough to provide stabilizing dispersion interactions between chains. In contrast to the simulated ARDF, a recent neutron scattering study 49 found an additional peak in the ethylbenzene ARDF around 0◦ and 4.5 Å. These parallel arrangements at short ring separations were not seen in our simulations, possibly due to the lack of explicit π–π interactions in the OPLS-AA potential. The ARDFs for propyl- and butylbenzene are similar, with a slight preference for perpendicular arrangements. As was seen in the RDFs (Figure 6), benzene has the most ordered liquid structure, with the highest first peak (at ∼5.5 Å) and lowest first minimum (at ∼8 Å) in the ARDF. Benzene also has the highest probability of perpendicular arrangements (highest peak near 90◦ ).

3.2.2

Binary mixtures

To examine the structures of the binary mixtures, the RDFs between the centers of mass of the aromatic rings of the alkylbenzenes were calculated and compared to the RDFs for the pure alkylbenzenes (Figure 8). For a given binary system, there is little difference in the peak positions of the RDFs as a function of mole fraction. There is a small increase in the height of the first peak as the alkylbenzene mole fraction decreases, possibly indicating an increase of the segregation of the aromatic molecules in the binary mixtures. Mooney et al. 12 investigated segregation of components in n-hexadecane and isocetane mixtures by looking at the carbon atom density along the z axis of the simulation cell

15



Figure 7: Angular radial distribution functions g(r, θ) for pure alkylbenzenes. Definitions of r and θ are shown in the bottom-right diagram. The distance r is calculated between the centers of mass of the aromatic rings. The angle θ is between the normal vectors of the aromatic planes.

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g(r)

2

2 g(r)

Benzene

Toluene

Ethylbenzene

Propylbenzene

1 0

1 0

6

Butylbenzene

2 g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 0

3

6

9 r (Å)

12

15

9 r (Å)

12

15

1.0 0.8 Alkylbenzene 0.6 mole fraction 0.4 0.2

Figure 8: Radial distribution function between the centers of mass of the aromatic rings in binary mixtures of n-hexadecane with the indicated alkylbenzene.

17



projected onto the xy plane. These density maps revealed a slight segregation of the components. Density maps calculated for a single trajectory of the n-hexadecane+benzene and n-hexadecane+n-butylbenzene mixtures are shown in Figure 9. For both systems, there are areas of high alkylbenzene density that correspond to areas of low n-hexadecane density, and vice-versa. The density fluctuates by about 30% compared to the average bulk density. Qualitatively similar results are found for the other trajectories of these mixtures, as well as for the mixtures with toluene, ethylbenzene, and n-propylbenzene. These density maps show that the n-hexadecane+alkylbenzene mixtures are not uniformly mixed, at least over the 10 ns timescale of these simulations. While the separation between aromatic rings does not change appreciably as a function of composition, anaylsis of ARDFs shows that the orientation of the rings is affected. Figure 10 compares the ARDFs for several benzene and n-butylbenzene binary mixtures. For both molecules, the probability of parallel arrangements (peak located near 0◦ and 5.5 Å) increases with increasing hexadecane content. However, this increase is much more pronounced in the benzene mixtures than the butylbenzene mixtures. At 0.6 mole fraction alkylbenzene, the benzene ARDF has a peak at 0–30◦ that is not seen in the pure component ARDF. In the case of butylbenzene, while the parallel content increases at 0.6 mole fraction compared to pure butylbenzene, there is no peak. This comparison, as well as comparisons between the ARDFs for the other binary mixtures examined here, shows that for the alkylbenzenes with at least two carbons in the n-alkyl chain, the orientation of the aromatic rings is only slightly affected by the addition of n-hexadecane. In contrast, benzene and toluene show large differences in ARDFs as a function of composition. For these two molecules, mixing with n-hexadecane results in a significant disruption of the preferential packing structure of the aromatic rings. This could give rise to the larger non-ideality seen in the mixtures of benzene and toluene with n-hexadecane, including the minimum in the bulk modulus seen in these systems.

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Figure 9: Density maps for (a) n-hexadecane+benzene and (b) n-hexadecane+nbutylbenzene systems, each with an alkylbenzene mole fraction of 0.6. The xy-plane is divided into 2 Å by 2 Å bins, and the density within each bin is averaged over the z -axis for the final 8 ns of one of the 10 ns trajectories. For each bin, the deviation of the density in that bin from the average bulk density is calculated.

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Figure 10: Angular radial distribution functions for benzene (left column) and nbutylbenzene (right column). Three different alkylbenzene mole fractions are shown, 1.0 (top), 0.6 (middle), and 0.2 (bottom). The distance r and the angle θ are defined in Figure 7.

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4

Discussion and Summary

The identification of surrogate fuels with specific properties has been the subject of much study. 2,6,21,50–52 Molecular simulations can be used to both examine a broader compositional phase space than is experimentally feasible and to elucidate specific structure-property relationships of these surrogate mixtures. 12,15–17,53,54 The ability to predict the properties of pure hydrocarbons and mixtures from their composition via MD simulation depends directly upon the accuracy of the underlying potential model. Herein, liquid properties and molecular structures of binary mixtures of n-hexadecane and alkylbenzenes were examined using MD simulations and the OPLS-AA potential with the L-OPLS parameter set. The results presented here show that the (L-)OPLS-AA potential is able to quantitatively predict the densities of binary mixtures of n-hexadecane with alkylbenzenes for alkyl-chain lengths up to four carbon atoms. Given the ability of the (L-)OPLS-AA potential to predict a broad range of properties for other hydrocarbons, 12,16,18,39,53,55 this result is not surprising. The MD simulations accurately predict the trend that increasing the alkyl-side chain will decrease the density of the pure alkylbenzenes while also predicting the opposite trend for the mixtures of the alkylbenzenes with hexadecane. Excess functions are a measure of the ideality of liquid mixtures. The mixtures examine here all display positive values of VE , which is indicative of a volume expansion upon mixing. In non-ideal solutions the intermolecular forces between dissimilar molecules in the mixtures differ from those present between molecules in each of the pure components. These deviations can be caused by geometrical factors, i.e. changes in arrangement of the molecules due to differences in size and shape of the components. However, binary mixtures of benzene with cyclohexane, molecules with very similar size and shape, also have positive values of VE . 56 This is due to fundamental differences in the interactions between alkanes and aromatic molecules.In both the experiment and the simulations, the excess molar volume of the mixtures of n-hexadecane and benzene have the most significant departures from ideal behavior. With the exception of the n-hexadecane with benzene mixtures, the MD 21



simulations do an excellent job reproducing the experimentally determined values. Because excess functions probe the accuracy of the intermolecular interactions of the potential energy function, 57 it is apparent that the interactions between benzene and n-hexadecane do not fully capture the actual interactions, with the simulated interactions not being repulsive enough. The OPLS-AA potential pair-wise intermolecular interactions, which contains a Lennard-Jones term and a Coulomb term. It has been shown that the fine structure of pure liquid benzene would be more accurately represented by a potential that contains many-body polarizability effects. 42 While a many-body term of this nature would be more important for pure benzene than the mixtures, it will also impact mixtures via the mixing rules used for intermolecular terms in the potential function. It is also worth noting that the addition of one or two methyl groups to the aromatic ring results in simulated values of VE as a function of mole fraction being much closer to the experimental values. Increasing the length of the alkyl side chain increases the number of favorable interactions between the side chain atoms and hexadecane atoms. While increasing the number of carbon atoms in the alkyl side chain would further increase the number of favorable interactions with hexadecane, it also increases the number of unfavorable interactions between side chain atoms and the aromatic rings on other molecules. This increase in unfavorable interactions, which are not repulsive enough, results in the values of VE for propylbenzene and butylbenzene mixtures that are low compared to experiment. Because bulk modulus is an important property for diesel engines, isentropic bulk moduli were calculated for the mixtures and compared to experimental values. In both the simulations and the experiments, increasing the length of the alkyl chain increases the value of BS for a given alkylbenzene mole fraction. Increasing the alkyl chain length on the aromatic ring has two main effects. First, it changes the packing of the alkylbenzene molecules relative to one another. Second, it changes the number and relative type of intermolecular interactions in the system. The complex interplay between these two effects impacts the value of BS , as well as density and excess molar volume.

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An interesting minimum is present in both the experimental and simulated values of BS for the benzene and toluene mixtures between alkylbenzene mole fractions of 0.6-0.8. Density maps of the benzene mixture around the minimum show clustering of the benzene molecules. This clustering means that the interaction of the benzene molecules with themselves can be an important contributor to the response of the liquid to a strain. In addition, examination of the simulated ARDFs of benzene mixtures revealed that as n-hexadecane is added, the preference for the benzene rings to be perpendicular to each other is disrupted, with more rings in the parallel arrangement. Because it is easier to compress the space between two aromatic rings than it is to push the rings together in the perpendicular arrangement, this orientation change likely contributes to the minimum in the BS data. In the case of toluene, the arrangement of the aromatic rings is also disrupted by the addition of n-hexadecane, although not to as great an extent as it is in the benzene mixtures. In the case of the other alkylbenzene mixtures, the orientation of the aromatic rings is not disrupted as much by adding hexadecane. That is, the ARDFs look very similiar as the mole fraction of the alkylbenzene is changed, which is not the case for benzene or toluene mixtures. In summary, MD simulations using the OPLS-AA potential were carried out on surrogate fuel samples composed of binary mixtures of n-hexadecane with n-alkylbenzenes. n-Alkyl chain lengths from 1 to 4 carbon atoms were examined. Densities, isentropic bulk moduli, and excess molar volumes were all calculated and compared to experimental values. Radial distribution functions, angular radial distrbution functions, and density maps were also calculated. The use of MD simulations allowed for interesting trends in physical property data to be assigned to changes in the molecular structure of the liquid mixtures.

Acknowledgement This work was funded by the Office of Naval Research, grant numbers N0001416WX01648 and N0001417WX00892. BHM and JAH also acknowledge the USNA Research Office and

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the Air Force Office of Scientific Research, contract F4FGA06055G002, for partial support. The authors thank M. Todd Knippenberg and Paul T. Mikulski for helpful discussions.

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Impact of Molecular Structure on Properties of n-Hexadecane and

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