High Internal Energies of Proposed Asphaltene Structures - Energy

Jun 6, 2011 - A study of the combustion chemistry of petroleum and bio-fuel oil asphaltenes. Farooq A. Atiku , Keith D. Bartle , Jenny M. Jones , Aman...
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High Internal Energies of Proposed Asphaltene Structures Derek D. Li and Michael L. Greenfield* Department of Chemical Engineering, University of Rhode Island, Kingston, Rhode Island 02881, United States ABSTRACT: Molecular structures proposed in the literature as representative of asphaltenes attempt to encompass the results of numerous experiments and quantum mechanics calculations. This work demonstrates that certain features of chemical bonding in proposed structures lead directly to high energies and thus low relative occurrence probabilities. Hartree Fock, quantum density functional theory, and classical force field calculations indicate features such as nonplanar aromatic rings that occur in structures proposed recently in the literature. Energy differences for altered pendant group locations were compared using smaller molecules as a reference. Small changes to side-chain positions preserve the overall architecture of the proposed asphaltene molecules while decreasing repulsive forces and restoring planar aromatic rings. The resulting structures are more appropriate for pursuing molecular hypotheses about asphaltenes.

’ INTRODUCTION Asphaltene molecules are considered among the largest molecular species found in crude oil.1 Their precipitation places constraints on crude oil processing,1,2 and they contribute significantly to the viscosity of bitumen.3 Understanding of asphaltene chemistry and structure has increased tremendously recently, as documented in reviews.4,5 Asphaltenes are a solubility class defined by the fractions of the crude oil that are insoluble in light alkanes of n-pentane, n-hexane, or n-heptane yet are soluble in benzene or toluene,1 3 and thus they constitute a wide range of molecule types, functional groups, etc. On the basis of experimental studies, asphaltenes are thought to be polycyclic aromatic compounds with heteroatoms and alkyl side chains in their structure.6 The structures of asphaltenes in most cases are not known,7 and the molecular weights of asphaltenes have been a huge controversy for decades.5 Earlier reported molecular weights of petroleum asphaltenes include 10 000,8 up to 7500,9 >6000,10 3250,11 800,12 and 400 atomic mass units (amu).13 Numerous asphaltene molecular structures have been proposed in the literature.10,14 30 These span wide ranges of molecular weights and fall into structure-based categories called “continental” (or “island”) and “archipelago” models. The former consists of a single larger aromatic domain with side chains, while the latter connects many smaller aromatic domains with chains. Each category is supported by experimental characterizations. Ruiz-Morales and Mullins31 interpreted optical absorption and fluorescence emission measurements with molecular orbital calculations, finding an average of 7 fused aromatic rings in asphaltenes within a range of approximately 4 10 and with 1 2 fused cores per molecule. In combination with lower molecular weights, this suggests a continental model. Gray32 identified degradation reaction products that are more consistent with smaller aromatic cores and an archipelago model. Characteristics of asphaltenes have been investigated using molecular modeling and simulation techniques for approximately 15 years, as described in a recent review.33 Molecular mechanics and quantum mechanics calculations enable one to understand the physical properties, acceptable structures, and relative stabilities of molecules. When molecular simulations are r 2011 American Chemical Society

conducted, it is necessary to begin with a chemically detailed molecular structure. This places molecular simulation in a role of detecting aspects of proposed asphaltene structures that lead to unrealistic traits, such as unphysical geometries and high energies. In a simulation, these lead to poor convergence and suggest molecules that would not be found in practice. The intent of this work is to demonstrate computationally the physical basis for why certain proposed asphaltene structures lead to high-energy geometries. One goal is to encourage researchers who devise asphaltene structures to take these additional aspects into consideration. We emphasize that our objective is not to discredit previously proposed structures. Instead, our objectives are to indicate constraints that are not as apparent with other approaches, to demonstrate how structures can be modified to overcome these constraints, and to explain the likely molecular origins of some disfigured structures visualized by others. Asphaltene molecules without unphysical geometries provide better guidelines for molecular simulations and hypotheses because they lack internal stresses that cause spontaneous intramolecular deformations. Improbable conformations have appeared in prior studies. For example, one visualization of an unlikely structure showed fused aromatic rings bent to almost 90° angles in asphaltene dimer simulations.34 Another example showed nonplanar aromatic rings within molecular dynamics simulations of asphaltene molecules on a calcite surface.35 We show here that an abnormal physical structure can be caused by bonding constraints in the structure and, thus, is more of an artifact than a physical result. Various different proposed asphaltene structures in a recent paper by Mullins5 were also found to contain constraints that are prone to causing unphysical geometries. Rectifying these bonding constraints is significant because the presence of unphysical geometries can lead to side effects that dominate the interpretation of asphaltene behavior. A key idea that underlies bond constraints relates to the “pentane effect” of Flory36 regarding interatomic distances between atoms separated by six bonds, e.g., hydrogen atoms at Received: April 3, 2011 Revised: May 26, 2011 Published: June 06, 2011 3698

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Table 1. Total Energies of Small Molecules Relative to m-Xylene HF 6-31G*

DFT 6-311G*

ΔHf(gas)47

relative energy

relative energy

relative energy

(kJ/mol)

(kJ/mol)

(kJ/mol)

benzene

102491.71

103212.53

32.93

toluene

102491.70

103211.97

32.76

ethylbenzene

6.37

9.91

12.55

o-xylene

2.56

1.21

1.75

m-xylene

0.00

0.00

0.00

p-xylene

0.25

0.14

0.71

molecule a

a

In comparison to toluene.

the start and end of a n-pentane chain. As described in the Results, nonlocal interactions between these atoms lead to repulsive forces and high energies in gauche(+)/gauche( ) configurations that otherwise seem favorable based solely on local torsion angles. Such repulsive interactions in these configurations arise because of side-group locations within some proposed asphaltene structures. Further descriptions and changes in molecular architecture that alleviate these constraints are provided in the Results.

’ SIMULATION METHODS Molecules Considered. Test calculations with small molecules were used to demonstrate the magnitude of energy changes that are consistent with differences in bonding among compounds that are known to exist. Benzene, toluene, ethylbenzene and all three isomers of xylene (ortho-, meta-, and para-) are good test choices for consistency because of their size and similarity in chemical properties. Two asphaltenes of Mullins5 were considered. The core of an asphaltene with an OH side group and five aromatic rings (“phenolbased”) from the original structure was used to demonstrate the pentane effect. A methyl side group was used for testing the energy upon substituting at various locations around the five ring core. The methyl side chain is sufficient to provide a six bond sequence and to have bonding conflicts from the pentane effect. Part of an asphaltene5 with a NH side group and five aromatic rings (“pyrrole-based”) was tested with ethyl side chains at various positions. The ethyl side chain demonstrates bonding conflicts from the pentane effect and provides a direct comparison for the magnitude of energy change with the shorter methyl side chain. An asphaltene proposed earlier by Gr€onzin and Mullins22 was studied to analyze geometry effects of fused aromatic and naphthene rings. An “alkane bridge” bonded to three fused aromatic rings was thought to be the cause of ring strain and nonplanar aromatic geometry in preliminary simulation results. Molecular simulation and quantum mechanics were used to investigate the geometry differences among alkane C C bond lengths, alkane C C C bond angles, and planar aromatic rings that could occur with ring strain and out-of-plane bending of the aromatic core. Quantum Mechanics Calculations. Quantum mechanics calculations using the Hartree Fock (HF) approach with the 6-31G* basis set and density functional theory (DFT) of B3PW91 type37 with the 6-311G* basis set were performed on the asphaltene structures and smaller molecules. HF is the simplest type of ab initio method and expresses the wave function from a set of N single-electron wave functions (N is the number of electrons in the molecule) to determine the properties of the molecule.38 DFT is an alternative theory to HF and uses a functional of the electron density to determine the properties of the molecule. HF and DFT can both provide semi-quantitative results at

a reasonable computational cost. The General Atomic and Molecular Electronic Structure System (GAMESS)39,40 version 25 MAR 2010 (R2) was used for the calculations on a number of Linux-based personal computers (SUSE versions 8.1 and 9.2). Preliminary optimization of geometries was applied using the semi-empirical PM3 method before quantum calculations. The minimum energy structures were associated with a gradient magnitude less than 5  10 4 Hartree/Bohr (Ha/Bohr), a configuration change in a single step less than 1.5  10 3 Å, and an energy change in a step of less than 1  10 6 atomic unit (au). Classical molecular simulation calculations were performed on the entire proposed phenol-based and pyrrole-based asphaltene molecules. The optimized potential for liquid simulations all-atom force field (OPLS-AA)41 43 chosen for use is parametrized to work well for many common organic functional groups and proteins. The Monte Carlo (MC) program Monte Carlo for Complex Chemical Systems (MCCCS) Towhee44,45 was used to obtain structures near a local energy minimum by simulating at 2 K. A MC simulation cycle is defined as one attempted move per atom within the system. Attempted moves to change atom positions and to pivot rotatable bonds were made until the total energy exhibited steady fluctuations about a constant average value. Equation of a Plane. To quantify planarity, various structures were analyzed to compare the angle and distance deviations from a plane. We fit the atom coordinates (xi, yi, and zi) to the equation of a plane that passed through the center of mass of the molecule. The equation of a plane was constructed using a normal vector to the plane and treating each point on the plane as a vector. The equation of a plane is written as n 3 (x x0) = 0, where n is the normal vector to the plane, x0 is the center of mass position chosen as a reference, and x is a vector in the plane. The amount of angle and distance deviations from the plane can be calculated for each atom by this method.

’ RESULTS Energy Differences in Small Molecules. Relative energies for single aromatic ring molecules with different constituents were calculated in GAMESS with DFT B3PW91/6-311G* and HF/ 6-31G*. Table 1 lists calculated total energies relative to the total energy of meta-xylene. The large energies for toluene and benzene (relative to toluene) result from the zero of energy being a function of the number of atoms. This dependence was not accounted for when calculating the relative energy between molecules of different atomic formulas. The DFT method obtained different total relative energies for all molecules than the HF method in part because of different zeroes of energy. Differences in standard heats of formation values from the literature, which are relative to the energy of elements at 298.15 K, agree relatively well with the calculated relative energies for molecules of the same atomic formula. The relative heat of formation values show that ortho has the highest energy followed by para and meta. The lower energy and, thus, greater stability of meta-xylene is consistent with toluene being an ortho and a para director in substitution reactions.46 The calculations also show that ethylbenzene is less favorable than xylene isomers. The relative energies from DFT of ortho-xylene versus para-xylene agree well with differences in the heat of formation. The predicted relative energy from DFT of meta-xylene is not as low as in heat of formation data, while for ethylbenzene the relative energy is lower. HF has a similar trend as DFT but is quantitatively less accurate for each relative energy. These results suggest that DFT will be more accurate versus experiment than HF in our systems. Proposed Asphaltenes with the Pentane Effect. The large size of asphaltene molecules makes it difficult and expensive 3699

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Figure 1. Structures of the proposed (A) phenol-based and (B) pyrrole-based asphaltene molecules from Mullins5 with the areas of pentane effect circled.

Table 2. Relative Total Energies of a Five-Ring Phenol-Based Asphaltene Core with a Methyl Side Chain Compared to Site 2 HF 6-31G*

DFT 6-311G*

relative energy

relative energy

(methyl) site

(kJ/mol)

(kJ/mol)

none

CH3

Figure 2. Core of phenol-based asphaltene and testing sites of a methyl side chain. Italics indicate higher energy sites that lead to nonplanar rings.

to obtain results from quantum calculations. In our case, the aromatic core of the phenol-based asphaltene and a partial core with five rings of the pyrrole-based asphaltene are used to quantify the pentane effect in proposed asphaltene molecules. The pentane effect formulated by Flory36 is the idea of a bonding conflict when bond angle correlations suggest that seven atoms will attempt to occupy the six atom positions found in a cyclic structure reminiscent of cyclohexane or benzene. The term arises from a ring formed by five carbon atoms and two hydrogen atoms in a gauche(+)/gauche( ) configuration of n-pentane. There, each gauche C C C C torsion angle is in a relative local energy minimum, but the hydrogen atoms at the chain start and end would overlap in position, making this configuration unfavorable. Groups within previously proposed asphaltenes that contain a pentane effect are encircled in Figure 1. For the phenol-based asphaltene aromatic core, a methyl side group was used to test the pentane effect at various sites. The different locations of the methyl group for HF and DFT calculations are shown in Figure 2. The results in Table 2 show that a nonplanar geometry forms when methyl groups are added at sites 3 or 6 and that their relative energies are much higher than the other sites. In DFT calculations, the relative energy of site 6 is 25.7 kJ/mol, while sites 5 and 7 are 1.9 and 3.5 kJ/mol, respectively. HF calculations show similar results compared to DFT. These high energies indicate a pentane effect exists when the methyl side chain is at sites 3 or 6 of the phenol-based structure.

geometry

102494.5

103212.5

planar

1 2

5.7 0.0

1.7 0.0

planar planar

3

33.6

26.3

4

0.4

0.2

5

6.4

1.9

6

33.8

25.7

7

9.8

3.5

nonplanar planar planar nonplanar planar

This conflict is due to the 1H atom from the methyl group and 7H from an aromatic ring, and relieving the orbital overlap induces otherwise planar aromatic rings to become nonplanar. Mullins5 had proposed a geometry with side groups at sites 3 and 6 that contains two pentane effects. The difference in energy without a methyl group agrees with the smaller molecule results for benzene and toluene. For example, the change in relative energy between the five-ring phenol-based asphaltene shown in Table 2 without and with a methyl group at site 2 is the same as the energy difference between benzene and toluene calculated by DFT. The change in relative energy of toluene compared to m-xylene is smaller by 0.5 kJ/mol. HF results suggest energy differences that are 2.8 kJ/mol higher for the asphaltene system compared to the small molecules. The similarities suggest that energy comparisons remain similar in magnitude across the range of molecule sizes that were considered here. Molecules with higher energies have lower occurrence probabilities according to the Boltzmann factor exp( ΔE/kBT). For the asphaltene phenol-based structure shown in Figure 2 using the DFT method, the relative energy ΔE = 3.5 kJ/mol at site 7 corresponds to a relative probability at 298.15 K of ca. 0.243 and the relative energy of 26.3 kJ/mol at site 3 corresponds to a relative probability of ca. 2.5  10 5. This perspective indicates that a branch at site 7 is much more relatively probable than at site 3 of the original structure. The most probable sites based on DFT calculations shown in Table 2 are site 4, followed by sites 2, 1, 5, and 7. Pentane effect sites 3 and 6 are the least probable by factors of 104. 3700

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Figure 3. Side-group positions in the partial structure of pyrrole-based asphaltene.

Table 3. Relative Total Energies of a Five-Ring Pyrrole-Based Asphaltene Core with an Ethyl Side Chain C2H6 (ethyl) site nonea

a

HF 6-31G* relative energy

DFT 6-311G* relative energy

(kJ/mol)

(kJ/mol)

geometry

204970.11

206410.9

planar

1

14.97

11.8

planar

2

0.0

0.0

planar

3

1.6

1.2

1 and 3 2 and 3

0.0 27.7

0.0 25.2

planar nonplanar

1 and 2

18.1

15.6

nonplanar

planar

In comparison to site 2.

For the first tests on the pyrrole-based asphaltene with five rings, energies for a single ethyl side chain at three different sites shown in Figure 3 were calculated. The results in Table 3 show that the energy at site 3 is nearly equal to the reference site 2. A partial pentane effect exists at site 1, but there is a lower energy cost compared to the case of the phenol-based asphaltene because of the wider C C C angle that includes the fivemembered ring. Thus, the aromatic ring structure at site 1 is planar rather than nonplanar. Mullins5 had proposed a side group at site 1, which contains higher relative energies. For the second test, two ethyl side chains were placed at two different positions. A pentane effect occurs at sites 2 and 3 and at sites 1 and 2, leading to aromatic ring structures that are nonplanar. The energy at sites 1 and 2 is lower than at 2 and 3 because of the wider angle provided for the ethyl side chain by the five-membered pyrrole ring. For the structure with no ethyl group listed in Table 2, less certainty is attributed to asphaltene energy because the gradient magnitude thresholds had to be increased from 5  10 4 to 6.5  10 4 and 6.0  10 4 Ha/Bohr to enable geometry convergence in the HF and DFT methods. Other parameters in GAMESS were their default values. Within this basis, the difference in energy without an ethyl side chain at site 2 is smaller by 3.7 kJ/mol than that of benzene compared to ethylbenzene, i.e., (benzene ethylbenzene) = (benzene toluene) + (toluene m-xylene) (ethylbenzene m-xylene), as calculated with DFT. The energy difference without the ethyl group in this asphaltene is smaller by 6.9 kJ/mol by the HF method compared to the difference in the small molecules. Thus, the change in relative energy of these molecules is consistent with their structures. Alkane Bonding Constraints. Earlier works48 52 in our group used thiophene-based continental asphaltenes,21,22 and

Figure 4. Different structures and testing sites for energy and planarity calculations for CH2CH2 and (CH2)4 rings attached to an asphaltene aromatic core. Italics indicate locations that lead to higher relative energy.

extensions (unpublished) also considered a pyrrole-based asphaltene proposed by Gr€onzin and Mullins22 (upper right in Figure 8 of their paper). Attaining an equilibrium geometry of that structure showed numerical uncertainty and poor convergence related to an ethyl group that bridged fused aromatic rings. This type of alkane bonding also appears in the asphaltene molecules recently proposed by Mullins.5 Thus, comparisons of energy and planarity were performed for CH2CH2 and (CH2)4 side groups using geometries shown in Figure 4. In Figure 4a, the phenol-based asphaltene with a (CH2)4 naphthene ring is modified with an ethyl side chain at various different sites. In Figure 4b, the ethyl side chain is joined with two aromatic rings to form an alkane bridge, while the (CH2)4 ring is broken from the aromatic ring to form a butyl side chain. As expected, structures of ethyl test 1 and ethyl test 3 are nonplanar and higher in relative energies because of the pentane effect. We expected the ethyl test 2 structure to be high in relative energy with a nonplanar geometry of the aromatic rings. Aromatic ring substituent geometry places the adjacent CH2 groups closer together than is typical for a σ σ bond, resulting in ring strain and out-of-plane bending of the aromatic core. A structure with a CH2CH2 group of alkane carbon (CT) in a ring with four aromatic carbon (CA) atoms thus poses a problem for a classical force field because it cannot satisfy all chemical bond and angle features simultaneously. For the fused aromatic rings to be planar, the geometry must be such that CA CT and CA CA bonds retain typical lengths, CA CA CT and CA CA CA angles remain at their typical value of 60°, and the CA CT bonds remain in the plane of the aromatic ring. These criteria cannot be satisfied in a planar chemical structure because the combination of typical values violates the rules of planar geometric structures, such as exterior angles of a polygon summing to 360°. Various viewing angles of the nonplanar aromatic rings found in the ethyl test 2 structure are shown in Figure 5. Surprisingly, the HF calculation results in Table 4 show that ethyl test 2 is the lowest energy state. A nonplanar geometry of the aromatic rings and the shortest C1 C2 carbon bond length among the five test structures relax the ring strain in structure 2. The pentane effect of ethyl test 1 is likely the reason that it has a longer C1 C2 bond length than the other test structures. The number of unfavorable torsion angles (180° from trans) also contributes to the higher energy of the asphaltenes with a (CH2)4 naphthene ring. The structure shown in Figure 4a without an ethyl side group, a phenol group, and an alkane ring is perylene (C20H12; two naphthalene groups joined by carbon bonds). Traetteberg53 investigated perylene by the electron diffraction method and determined the peri-bond length (the C1 C2 bond in Table 4) 3701

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Figure 5. Various viewing angles of the aromatic core rings of the asphaltene phenol-based ethyl test 2 structure indicate nonplanarity.

Table 4. Results of Different Testing Sites for CH2CH2 and (CH2)4 Rings Attached to the Asphaltene Aromatic Core Shown in Figure 4 HF 6-31G* relative

Table 5. Results of Different Testing Sites for CH2CH2 and (CH2)4 Rings Attached to the Phenanthrene-like Structure Shown in Figure 6

C1 C2 bond

tests

energy (kJ/mol)

geometry

length (Å)

ethyl test 1

48.7

nonplanar

1.4954

HF 6-31G*

DFT 6-311G*

C3 C4

C3 C4

relative energy relative energy bond length bond length tests

(kJ/mol)

(kJ/mol)

(Å) (HF)

(Å) (DFT) geometry

ethyl test 2

6.6

nonplanar

1.4743

test 1

37.8

30.3

1.4757

1.4657

nonplanar

ethyl test 3

60.6

nonplanar

1.4856

test 2

17.2

14.3

1.4505

1.4435

nonplanar

ethyl test 4

0.0

planar

1.4868

test 3

0.0

1.4586

1.4516

planar

ethyl test 5

0.6

planar

1.4868

0.00

Table 6. Deviations from a Plane in Phenanthrene-like Structures Shown in Figure 6

Figure 6. Test structures from parts of the core of the phenol-based asphaltene.

to be 1.493 ( 0.015 Å. All calculated C1 C2 bond lengths, except for ethyl test 2, are in this range. For the structures of ethyl tests 1 and 3 shown in Figure 4, the DFT B3PW91 calculations with basis set 6-311G* failed to converge to an equilibrium geometry. Convergence to an equilibrium geometry can be a problem for large molecules in quantum mechanics calculations. Equilibrium geometries can easily be found by increasing the gradient tolerance, but it decreases accuracy of the quantum results. Instead, we used alternative phenanthrene-like structures shown in Figure 6 to test the Figure 4 bonding geometries. Results in Table 5 show that the test 2 structure has the lowest relative energy in both types of quantum calculations. The test 1 structure has the highest relative energy because of the pentane effect. Even though test 2 has a lower relative energy than the test 3 structure, the aromatic rings of test 2 are nonplanar. This result is similar to that observed for the structures in Figure 4. Test structure 2 has the shortest carbon bond lengths, followed by tests 3 and 1. Test 1 has the longest bond length as a result of the pentane effect because the out-of-plane geometry stretches the bond length of the carbon atoms. All of the C3 C4 bond lengths in Figure 6 are shorter than C1 C2 bond lengths in Figure 4. The reason is thought to be due to the aromatic character in the

phenanthrene tests

rms θ (deg)

rms distance (Å)

test 1

0.00254

0.0904

test 2

0.00246

0.0877

test 3

0.00044

0.0158

C3 C4 structure compared to the closer-to-σ bond character in the C1 C2 structure. A way to quantify the deviation from planar geometry in the structures is by fitting atom positions to the equation of a plane. We fit the coordinates of the atoms in aromatic rings to a plane that passed through the center of mass of the molecule. The rootmean-squared (rms) distance and angle deviations from the plane were calculated for the phenanthrene-like structures (see Figure 6) and the asphaltene phenol structures with ethyl side chains (see Figure 4). The results in Table 6 show that the planar phenanthrene test 3 structure fits well within the equation of a plane. The rms angle and distance deviations are much lower in test structure 3. Test structures 1 and 2 deviate 6 times further from the plane compared to test structure 3. Table 7 shows the deviations from planarity for the different ethyl tests of the phenol-based asphaltene. Ethyl test 4 has the lowest rms angles, while ethyl test 5 structure has the lowest rms distance. Ethyl test 1 has the highest rms angle and distance deviations (by factors of 70 and 50 times) because of its nonplanar geometry caused by the pentane effect. Ethyl test structures 2 and 3 also have nonplanar geometries and high rms deviations. Modifications to Proposed Asphaltene Structures. Classical force field molecular simulations were performed on the original and a modified version of the phenol-based asphaltene. The goal of the modifications was to remove pentane effects by moving side chains to new positions while retaining the key characteristics of the original structure. For the modified 3702

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Table 7. Deviations from a Plane in Ethyl- and Butyl-Substituted Asphaltene Aromatic Cores, as Shown in Figure 4 tests

rms θ (deg)

rms distance (Å)

ethyl test 1

0.17394

0.7789

ethyl test 2 ethyl test 3

0.02175 0.01504

0.1178 0.1146

ethyl test 4

0.00249

0.0162

ethyl test 5

0.00579

0.0149

Figure 9. Different viewing angles of the configuration of the modified phenol-based asphaltene after energy minimization using a classical force field. The aromatic rings are planar without a pentane effect.

Figure 7. Original and modified structures of the proposed5 phenolbased asphaltene.

Figure 10. Average total potential energy of the original and modified phenol-based asphaltenes during energy minimization using a classical force field.

Figure 8. Different viewing angles of the configuration of the original phenol-based asphaltene5 after energy minimization using a classical force field. The aromatic rings are nonplanar because of the pentane effect. See the text for details.

structure shown in Figure 7, the propyl side chain on site 3 of Figure 2 was moved to site 2 and the ethyl side chain on site 6 was placed on the alkyl ring. The modified structure still preserves the original six ring structure along with all of the same side chains. Different viewing angles of the asphaltene structures after 10 million cycles of MC simulation at 2 K are shown in Figures 8 and 9. Panels b and c of Figures 8 and 9 illustrate that the aromatic rings of the original phenol-based asphaltene are nonplanar, while in the modified version they are planar. The rms angle and distance deviations from a plane for the aromatic carbon atoms in the original phenol-based asphaltene were calculated to be 0.0101° and 0.4729 Å. Deviations from planarity in the classical

simulation of the full asphaltene were about 0.3 Å smaller than in quantum mechanical calculations on a portion of the asphaltene (ethyl test 1). The modified phenol-based asphaltene has rms angle and distance deviations of 0.000 46° and 0.0222 Å, more than 20 times smaller and comparable to cases without a pentane effect. The evolution of total potential energy of the original and modified phenol-based asphaltenes during the simulation is shown in Figure 10. In the modified structure, the final potential energy converges to an energy of 100 kJ/mol lower than in the original structure. The pyrrole-based asphaltene structure contains pentane effects in three different areas, as shown in Figure 1B. The pentane effect circled in the lower left can be removed by placing the propyl branch on the aromatic ring with the isopentyl branch. Similarly, 6-methyloctyl (C9H19) on the upper right can be moved to an alternative place to avoid the pentane effect. However, the pentane effect circled in the middle as shown in Figure 1B cannot be removed without changing the number and/or geometric arrangement of fused aromatic rings in the original molecular structure. Figure 11 shows different viewing angles of the original pyrrole-based asphaltene after energy minimization using a classical force field simulation. The structure has a nonplanar geometry of the aromatic rings because of the pentane effect. The rms angle and distance deviations of the original pyrrole-based asphaltene were calculated to be 0.008 01° and 0.7674 Å, comparable to the pentane effect nonplanarity listed in Table 7. 3703

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Figure 11. Different viewing angles of the configuration of the original pyrrole-based asphaltene5 after energy minimization using a classical force field. The aromatic rings are nonplanar because of the pentane effect. See the text for details.

The close proximity of atoms 1H and 7H are particularly clear in Figure 11a, while Figure 11b shows how out-of-plane bending occurs to accommodate these atoms. Reconfiguring the aromatic core would be required to remedy the most significant deviations from planarity.

’ CONCLUSION Computational methods were used to analyze high internal energy asphaltene structures proposed in the literature. HF and DFT quantum mechanics calculations showed that proposed molecules have high relative energies and nonplanar aromatic geometries when a bonding conflict known as the pentane effect exists. The pentane effect occurs when the two end atoms of a seven atom configuration overlap in a cyclic position that would normally be suited for one atom. Our quantum mechanics calculations showed that the relative energies are always higher by tens of kJ/mol for a structure containing the pentane effect, and deviations from a plane can approach 0.7 Å. Such molecular architectures are undesirable because molecules with higher energies from the pentane effect have lower occurrence probabilities. A pentane effect occurring next to a five-membered ring has a lower energy cost compared to adjoining a six-membered ring because of a wider bond angle, which compensates for repulsive forces through a larger interatomic distance. The bonding constraints in a ring formed by an ethyl group and four aromatic carbons were investigated to show why such a structure cannot satisfy all intuitive chemical features simultaneously. Structures with these bonding constraints had nonplanar geometries and shorter carbon carbon bond lengths yet also lower relative energies compared to planar alternatives with butyl fused naphthene rings. An alternative structure was proposed in one case that alleviates pentane effects while maintaining the same numbers of atoms and sizes of side chains. Molecular simulation showed that this modified phenol-based asphaltene has a planar geometry and a lower total potential energy compared to the original nonplanar structure. A pyrrole-based asphaltene could not have pentane effects removed without altering the size and/or geometric arrangement of the fused aromatic core. An appreciation of the pentane effect and its consequence on relative probability is encouraged when future molecular structures of asphaltene molecules are proposed. Proposed structures that retain a pentane effect are likely to exhibit bending and folding patterns that are side effects of unphysical bonding geometries rather than accurate representations of true asphaltene behavior. Quantum mechanics and classical molecular simulation have the potential to reveal these bonding flaws in proposed structures that may not be apparent based solely on experimental characterizations.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: greenfi[email protected].

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