Morphology of Aggregated Asphaltene Structural Models

J. H. Pacheco-Sanchez,* F. AÄ lvarez-Ramırez, and J. M. Martınez-Magadan

Programa de Ingenierıa Molecular, Instituto Mexicano del Petroleo,Eje Central Lazaro Cardenas 152, Mexico D.F. 07730, Mexico

Received April 12, 2004. Revised Manuscript Received July 8, 2004

Aggregated asphaltene structural models have been generated through a molecular simulationgeometry optimization process, using periodic boundary conditions. This methodology has beenvalidated by first applying it to a pure aromatic system. Initially, a random distribution of 35molecules was chosen and a geometry optimization process was performed, allowing the celldimensions to vary without restrictions. The structure factor (S(k)) of an optimized final cell wasobtained and compared with experimental results, and the agreement between theoretical andexperimental S(k) profiles was satisfactory. This methodology was next used in the analysis ofthe morphology of 32 asphaltene model molecules and their aromatic cores; asphaltene modelmolecules were taken from literature. It is remarkable that face-to-face stacking of asphalteneaggregates was observed, as well as π-offset and T-shaped stacking geometries. Finally, the effectof aliphatic chains on the aggregates was also analyzed.

1. Introduction

Aggregated asphaltene structural models would beuseful in developing further understanding of importantproblems in the petroleum industry, such as the ag-gregation, flocculation, and precipitation of asphaltenes.An operative definition of asphaltenes is that they areinsoluble in low-molecular-weight n-alkanes but solublein aromatic solvents. It is well-known that asphaltenesself-associate in stacked aggregates, which form clus-ters.1,2 However, the morphology of these clusters is notyet clearly known. The most common morphologyconsidered until now is the face-to-face type. In theliterature, these interactions are usually only referencedas aromatic-aromatic interactions, without going intothe fundamental molecular details. Some efforts indetermining the morphologies of asphaltene-aggregatedsystems were performed by Yen et al.,3 Dickie and Yen,2Wiehe and Liang,4 and Evdokimov et al.5,6

The morphology of these clusters is amorphous innature. Therefore, a possible way to characterize themgeometrically is either through the radial distributionfunction (RDF) or through the structure factor S(k); thisis also called isotropic scattering. The RDF is definedas the number of atoms lying at distances between rand r + dr from the center of an arbitrary origin atom,7

whereas the RDF is related to the observed structurefactor S(k) by a Fourier transformation.7-12 In a pio-neering work, Yen et al.3 performed X-ray diffraction(XRD) measurements for asphaltenes in powdered solidsamples coming from Kuwait visbreaker tar oil. Theyhave compared their experimental S(k) profile for thearomatic component of their asphaltenes to that com-puted for a blend of five polynuclear aromatic com-pounds of known structures.13 The S(k) profile and thepeak positions agree quite reasonably with that ob-tained by Diamond.13 Based on these results, they haveproposed a model constituted by aromatic sheets thatare associated in a stacked cluster for an asphaltenesolid phase. A very similar morphology that has beenextended to aggregates of asphaltene particles wasexperimentally obtained by Dickie and Yen.2 Asphalt-enes appear as unitary stacking sheets that are com-posed of a highly condensed polynuclear system ofaromatic rings bearing alkyl side chains. They proposedthat asphaltene association occurs via a stacking of 3-6unitary sheets through π-π interactions. They definethese entities as unitary cells or particles, indicatingthat the associations of such particles form micelles.

The morphology of polyaromatic compounds andasphaltene aggregates have been studied theoreticallyas induced aggregation in a vacuum,14,15 as spontaneous

* Author to whom correspondence should be addressed. E-mailaddress: hpacheco@imp.mx.

(1) Sheu, E. Y. In Asphaltenes: Fundamentals and Applications;Sheu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995.

(2) Dickie, J. P.; Yen, T. F. Anal. Chem. 1967, 39, 1847-1852.(3) Yen, T. F.; Erdman, J. G.; Pollack, S. S. Anal. Chem. 1961, 33,

1587-1594.(4) Wiehe, I. A.; Liang, K. S. Fluid Phase Equilib. 1996, 117, 201-

210.(5) Evdokimov, I. N.; Eliseev, N. Y.; Akhmetov, B. R. J. Pet. Sci.

Eng. 2003, 37, 135-143.(6) Evdokimov, I. N.; Eliseev, N. Y.; Akhmetov, B. R. J. Pet. Sci.

Eng. 2003, 37, 143-152.(7) ) Elliott, S. R. Physics of Amorphous Materials; Longman

Scientific and Technical: New York, 1990; Chapter 3.

(8) McQuarrie, D. A. Statistical Mechanics; Harper and Row: NewYork, 1973.

(9) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids;Academic Press: New York, 1986.

(10) Tildesley, M. P.; Allen, D. J. Computer Simulation of Liquids;Clarendon Press: Oxford, U.K., 1987.

(11) Lee, L. L. Molecular Thermodynamics of Nonideal Fluids;Butterworth: Boston, 1988.

(12) Evans, D. F.; Wennerstrom, H. The Colloidal Domain; VCHPublishers: New York, 1994.

(13) Diamond, R. Acta Crystallogr. 1957, 10, 359-364.(14) Brandt, H. C. A.; Hendriks, E. M.; Michels, M. A. J.; Visser, F.

J. Phys. Chem. 1995, 99, 10430-10432.(15) Rogel, E. Colloids Surf. 1995, 104, 85-93.

1676 Energy & Fuels 2004, 18, 1676-1686

10.1021/ef049911a CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 08/19/2004

aggregation in a vacuum,16 and in the presence ofsolvents15,17,18 by classical molecular dynamics (MD).19

An important result is that the structure of aggregatescould not be formed by considering only stackingthrough π-π interactions. Two additional orientations,such as those mentioned by Hunter and Saunders20 andLeach,21 for aromatic-aromatic interactions seem to benecessary. These authors summarized the results oftheir investigations as follows: main orientations areface-to-face geometry (π-π interactions), edge-on orT-shaped geometry (π-σ interaction), and offset π-stackedgeometry (σ-σ interactions). Therefore, it was consid-ered that these orientations can lead to different formsof the asphaltene aggregates.2,16,22 These findings agreewith the results reported by Sheu,17 based on molecularsimulations for 64 asphaltene molecules, the structuresof which range in size from 3 aromatic rings to 11aromatic rings, for simulations conducted in toluene. Healso found that asphaltene aggregates are formed notonly through face-to-face stacking but also through othertypes of asphaltene clustering; such clustering is muchlooser and rather irregular in appearance.

Generally, it is widely accepted that every designedasphaltene molecule includes an aromatic component,its own quantity of heteroatoms (such as N, S, and O),and one or more aliphatic chains linked to the aromaticregion.23-26 Some asphaltene molecular models thathave the latter description have been proposed in theliterature. Four asphaltene structure model moleculeswere selected from the following references: Groenzinand Mullins,27 Speight and Moschopedis,28,29 Zajac etal.,23 and Murgich et al.18 These molecules are repre-sented in Figures 1 and 2. The corresponding asphalt-enes of these references were extracted from Califor-nian, Venezuelan, Mayan, and Venezuelan crude oils,respectively. Some physicochemical properties of thesemolecules are given in Table 1. It is well-known thatpetroleum fluids are comprised of asphaltene polydis-perse systems. One of the main limits on the asphaltenetheoretical analysis lies in the diversity of structuresin which asphaltenes can exist. The difficulty associatedwith the construction of molecular models of asphalt-

(16) Pacheco-Sanchez, J. H.; Zaragoza, P. I.; Martınez-Magadan, J.M. Energy Fuels 2003, 17, 1346-1355.

(17) Sheu, E. Y. In Structures and Dynamics of Asphaltenes; Mullins,O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998; Chapter IV.

(18) Murgich, J.; Rodrıguez, J.; Aray, Y. Energy Fuels 1996, 10, 68-76.

(19) Cerius2 software, Molecular Simulations, Inc. (MSI) (nowAccelrys), San Diego, CA.

(20) Hunter, C. A.; Saunders, J. K. M. J. Am. Chem. Soc. 1990, 112,2008-2010.

(21) Leach, A. R. Molecular Modeling; Addison-Wesley Longman,Ltd.: Singapore, 1996.

(22) Takanohashi, T.; Sato, S.; Tanaka, R. Pet. Sci. Technol. 2003,21, 491-505.

(23) Zajac, G. W.; Sethi, N. K.; Joseph, J. T. Scanning Microsc. 1994,8, 463-470.

(24) Speight, J. G. The Chemistry and Technology of Petroleum;Marcel Dekker: New York, 1999; Chapter X.

(25) Cimino, R.; Correra, S.; Del Bianco, A. In Asphaltenes: Fun-damentals and Applications; Sheu, E. Y., Mullins, O. C., Eds.; PlenumPress: New York, 1995; Chapter III.

(26) Pfeiffer, J. Ph.; Saal, R. N. J. Presented at the Sixteenth ColloidSymposium, Stanford University, Palo Alto, CA, July 6-8, 1939; pp139-165.

(27) Groenzin, H. G.; Mullins, O. C. Energy Fuels 2000, 14, 677-684.

(28) Speight, J. G.; Moschopedis, S. E. Prepr.sAm. Chem. Soc., Div.Pet. Chem. 1979, 24, 910-923.

(29) Speight, J. G. The Chemistry and Technology of Petroleum;Marcel Dekker: New York, 1991.

Figure 1. Depiction of two asphaltene molecule structures:one designed by Groenzin and Mullins27 from Californian crudeoil, and the other was designed by Speight and Moschopedis28

for Venezuelan crude oil.

Figure 2. Depiction of two asphaltene molecule structures:one designed by Zajac et al.23 from Mayan crude oil, and theother exhibited by Murgich et al.18 for Venezuelan crude oil.

Aggregated Asphaltene Structural Models Energy & Fuels, Vol. 18, No. 6, 2004 1677

enes is well-recognized, and the difficulty is even moresevere for a polydisperse system of a specific crude oil.However, a reasonable starting guess is that the amor-phous solid asphaltene phase is mainly comprised of anaverage size molecule, as evidenced from experimentalwork, which varies for each type of crude oil. Zajac etal.23 proposed three asphaltene model molecules forMayan crude oil; they are built by rearrangement ofsome aromatic rings or some aliphatic chains for theasphaltene structures they proposed. As a consequence,a polydisperse system can be constructed by a set ofmonomer asphaltene molecular models in a vacuum,which, as a first approach, should be a good model tosimulate asphaltene aggregates, as well as to investi-gate how they agglomerate in an amorphous solid phase.

Self-association of covalent asphaltene model mol-ecules was recently simulated through molecular simu-lations by Pacheco et al.16,30 The stacked asphaltenemolecules were observed in the form of dimers, trimers,tetramers, and pentamers. The morphologies of thoseaggregates were proposed as a stacking of asphaltenesnot only assembled face to face but also in T-shaped andoffset orientations, in agreement with the results ofHunter and Saunders20 and Leach.21 Furthermore,using the same Groenzin and Mullins model utilized inthis work, the interaction energy between two asphalt-ene models was calculated by minimizing the energy atdifferent distances, which, indeed, provided the energyas a function of distance. Similar morphologies can beobserved in other systems,12 where it is also possible toobserve face-to-face (FF), edge-to-face (EF), and edge-to-edge (EE) clay-particle associations.

In this work, a method to generate stable asphalteneaggregates is presented; this methodology uses a peri-odic cell ensemble of 32 asphaltene molecules. To finda stable structure, an optimization process was per-formed, using a force-field method. Our objective ismainly (i) to find morphologies of asphaltene aggregatesthat properly describe the experimentally reported S(k)profile, (ii) to analyze the geometries through which theaggregates are formed, and (iii) to study the effect ofthe aliphatic chains, on the aggregated structure,through the evolution of the structure factor. To thisend, a comparison between predicted and experimentalstructure factors is examined for asphaltene aggregation

modeling, using molecular simulations for a set of onetype of asphaltene molecule.

2. Methodology

The methodology used is based on force-field concepts; it isan analytical function that is mainly composed of two typesof terms. The first terms are associated with bond-interactionenergies, such as torsion, bending, and stretching. The secondterms are associated with nonbonded interactions, such asCoulombic and van der Waals forces.31-34 Because of the force-field features, this methodology is dependent on the molecularcharacterization of the crude oil under study. One objectivebehind MD is to find a stable molecular configuration wherethat configuration is located in a local minimum of thepotential energy surface around the initial configuration.However, as a consequence of the high molecular weight, theasphaltene motion in a MD simulation is known to be veryslow. For this reason, finding the local minimum energyrequires hundreds of picoseconds.

First, a model system constituted by a blend of 35 moleculescomposed of equal quantities of five different polynucleararomatic molecules was set up, as proposed by Diamond.13

These 35 molecules were randomly distributed in a simulationcell using the Amorphous Cell program.35 The cell dimensions(a, b, and c) are all equal to 63.25 Å, and the initial density inthe cell is equal to 0.1 g/cm3. Second, a complete cell geometryoptimization process was conducted, allowing free movementof molecules, including internal lengths and angles, bringingas a consequence, the effect of a comprised cell with arepresentative density. The final density for the relaxedstructure was 1.39 g/cm3. This value is larger than the usualexperimental values.36 This behavior can be explained by thelack of aliphatic chains pendant to the aromatic cores. TheCOMPASS98_02 force field35 was chosen because it wasdesigned for organic and inorganic molecules, and it has beenextensively applied to these types of systems with successfulresults. An internal stress of 1 × 10-4 GPa was selected asthe criterion of convergence.

Figure 3 shows the same final structure from two differentpoints of view, highlighting different molecules in each one.The relaxed structure displays the presence of stacking, asexpected. Stacked polydisperse domain sheets were formed inthe cell; they can be seen in Figure 3a and b, where the

(30) Pacheco-Sanchez, J. H.; Alvarez-Ramırez, F.; Martınez-Ma-gadan, J. M. Prepr.sAm. Chem. Soc., Div. Pet. Chem. 2003, 48, 71-73.

(31) Sun, H.; Rigby, D. Spectrochim. Acta A 1997, 53, 1301-1323.(32) Rigby, D.; Sun, H.; Eichinger, B. E. Polym. Int. 1997, 44, 311-

330.(33) Sun, H.; Ren, P.; Fried, J. R. Comput. Theor. Polym. Sci. 1998,

8 (1-2), 229-246.(34) Sun, H. J. Phys. Chem. B 1998, 102, 7338-7364.(35) Force Field-Based Simulations; MSI, Inc.: San Diego, CA, 1997;

pp 29, 265-268.(36) Rogacheva, O. V.; Rimaev, R. N.; Gubaidullin, V. Z.; Khakimov,

D. K. Colloid J. USSR 1980, 490-493.

Table 1. Physicochemical Properties of Each of the Asphaltene Molecules Used in This Work

value

property Mullins Speight Zajac Murgich

formula H98C72S1 H79C80N2O1S2 H63C57N1S1 H159C138N3O2S2molecular weight (amu) 995.64 1149.67 794.2 1955.95molecular volume (Å3) 794.6 892.7 637.3 1574.6elemental analysis (%)C 86.86 83.58 86.2 84.74H 9.92 7.01 8 8.19N 2.44 1.76 2.15O 1.39 1.64S 3.22 5.58 4.04 3.28number of fused aromatic rings 7 14 9 24CA 30 47 29 70CS 42 33 28 68HA 11 9 6 19HS 87 70 57 140

1678 Energy & Fuels, Vol. 18, No. 6, 2004 Pacheco-Sanchez et al.

domains are themselves constituted by different types ofmolecules, which give the polydisperse character to the formedaggregate. The generated aggregates are formed of dimer,trimer, and tetramer domains. This description is consistentwith the results found by Dickie and Yen.2 One very importantdetail, in the present study, is that the face-to-face stackinggeometrical orientation, as well as the offset π-stacked geom-etry, was observed.

The positions of every molecule and atom can be determinedin the model, and then it is possible to get structural propertiesas the spherically averaged distribution of interparticle vectorlengths (the radial distribution function, RDF) and its inverseFourier transformation (the structural factor, S(k)) within themodel. The structure factor was obtained for this modelsystem, and good agreement was observed between thetheoretical and experimental S(k) profile (Figure 4). In thisgraph, we rescaled the abscissa axis (sin θ)/λ of Yen et al.3 bya value of 4π, such that this axis now is denoted as k, wherek ) 4π(sin θ)/λ. The dotted curve in Figure 4 represents theexperimental curve of the amorphous blend of five aromaticcompounds of known structure, according to those resultscomputed by Diamond.13 He computed the intensity of X-raysdiffracted from randomly oriented, perfect aromatic moleculesof various sizes, using the Debye RDF. The dashed curve inFigure 4 represents approximately the experimental XRDpattern of the aromatic clusters in the asphaltene computedby Yen et al.3 The solid curve in Figure 4 represents our ownsimulation of the same amorphous blend of five aromaticcompounds of known structure. Therefore, the structuralmodel in Figure 3 can be considered to be a good approximationof the real system. Because of these agreements, this meth-odology will be extrapolated to different structure cases of the

asphaltene models, and the results will be compared againstat least one of those curves of the S(k) profile for severalasphaltenes reported by Yen et al.3

3. Asphaltene Aggregation Structures

Using the same methodology as before for aromaticmolecules proposed by Yen et al,3 four periodic cells with32 asphaltene model molecules were built. The cellswere built using the four asphaltene molecular modelsmentioned previously; for simplicity, let us call themMullins, Speight, Zajac, and Murgich. The minimizationof the energy was performed by allowing the relaxationof the cell dimensions to obtain spontaneous self-aggregation of the asphaltene molecules. Asphalteneself-aggregation in crude oil is believed to occur as aspontaneous aggregation, which can be investigatedusing a geometry optimization process, such as that inthis work. An initial density of ∼0.1 g/cm3 was chosenfor all the cells. During the optimization process, theequilibrium configuration of the system gradually de-creases the cell length, leading to a squeezed cell. Thecells that have been built in this way have the followingfinal densities: 0.98 g/cm3 for the Mullins model mol-ecules, 1.04 g/cm3 for the Speight model molecules, 1.02g/cm3 for the Zajac model molecules, and 0.69 g/cm3 forthe Murgich model molecules.

3.1. Mullins Model Case. The final structure of thecell that has been built using the Mullins asphaltenemodel shows a very small number of stacking forma-tions, compared to that of aromatic molecules. This isattributed to the presence of aliphatic chains, whichhinder a close interaction between the aromatic coresof the asphaltenes, as shown in Figure 5a.

In particular, both the aliphatic and aromatic regionsimages were isolated. Figure 5b shows the aliphaticregion image, which displays a homogeneous distribu-tion over the cell. The aromatic region image, in Figure5c, shows two highlighted stacking formations: one inan offset π-stacked geometry, and the other in a face-to-face geometry. The stacking behavior can be ex-plained by the repulsive steric effect of the aliphaticchains, which decreases as the length of these chainsdiminishes. Asphaltene face-to-face stacking has a more-probable existence when short aliphatic chains overhangfrom the aromatic rings.

Figure 3. Final structure of 35 aromatic molecules obtainedafter geometry optimization process. Panels a and b show twoangles of different stacking structures of the same final relaxedcell; the macrostructure of asphaltic material representing justthe aromatic portion is shown in panel b. Panel c shows aplanar representation of Figure 3b, which is a typical Dickieand Yen2 model for aromatic components without consideringaliphatic chains.

Figure 4. Comparison between the structure factor S(k)obtained in our simulation and those S(k) profiles reported byYen et al.3

Aggregated Asphaltene Structural Models Energy & Fuels, Vol. 18, No. 6, 2004 1679

For an optimized configuration, the following twoparameters of the simulation cell allow us to discussthe diminishing of the stacking. The free-volume per-centage in Figure 5a is 34.68%, which means thatasphaltene monomers are highly condensed in the cell.The ratio of surface areas between the aromatic regionand the aliphatic region is ∼0.41, which means that thearomatic portion is bigger than the aliphatic portion.The small amount of stacking, in this case, is due tothe aliphatic chain size and number, with respect to thearomatic core size, which does not allow a close interac-tion between the aromatic components of the asphalt-ene. These chains form walls between the asphaltenenearest neighbors, which hinder the direct π-π interac-tion. The increased separation generated by the pres-ence of the chains is reflected directly in the S(k) profile.This phenomenon can be observed when the S(k)profiles for the aromatic and asphaltene cases arecompared. The presence of these chains produces adiscrepancy between the aromatic and asphaltene S(k)profiles, which is reflected in the number of peaks andtheir positions, for k < 2.5 Å-1. It was observed thatthe first peak (the nearest to zero) for the aromatic caseis still present in the asphaltene S(k) profile; however,it is shifted to a k value of <2 Å-1. A new peak, at k ≈0.5 Å-1, is observed; this peak is not present in thearomatic case, as shown in Figure 6. What we aretesting in Figure 6 generally is that the S(k) profile ofa complete asphaltene model has an important differ-ence when is compared with the S(k) profile of aromaticcores. We then must compare simulated S(k) profiles ofwhole asphaltene aggregates against experimental S(k)profiles of whole asphaltene aggregates. The othercomparison must be between theoretical and experi-mental S(k) profiles of aromatic cores of the asphalteneaggregates.

However, this structure shows an S(k) profile that isin agreement with some experiments reported in theliterature. In particular, a direct comparison betweenthe S(k) profile associated with our structure and thatof the Ragusa crude oil asphaltene fraction experimen-tally reported by Yen et al.3 is presented (Figure 7),which corresponds to a more accurate comparison thanthe other S(k) profile of the experimentally obtainedasphaltenes.

The fact that the model is able to reproduce the threeexperimental S(k) peaks justifies that the methodologydeveloped here produces an adequate asphaltene ag-gregate structure. Therefore, based on the morphologyof the model, it is possible to infer the existence of morethan one type of relative orientation between theasphaltene molecules. These orientations are not re-stricted to FF; some other orientations also are included.

To analyze the distance between different aromaticregions in this aggregate, the RDF has been calculated,using the same atom in each one of the asphaltenemolecules of this system, where this atom is located inthe aromatic region; the first peak on the RDF corre-sponds to a minimum distance of 4.15 Å, which wasmeasured between the centers of the aromatic region.The main reason this distance is deviated almost 15%from the distance corresponding to the optimum bindingenergy (3.55-3.7 Å) is because the distance betweencenters of aromatic regions is not the shortest one ineach case, which reflects the effect of the aliphaticchains that is due to the use of a complete asphaltenemodel.

It is important to mention herein that Yen et al.3 alsomeasured a linear size distance of 16-20 Å for thestacking of four-unit asphaltene sheets. From thisresult, the following facts can be elucidated:

(1) The distance 3.55-3.7 Å is underestimated, in thesense that corresponds only with the binding energy ofasphaltene molecules; however, the size of the wellpotential includes a wider interaction range than this.16

(2) The distance 16-20 Å corresponds to asphaltenesthat are strongly influenced by aliphatic chains. Fur-thermore, it is remarkable that Espinat et al.37 mea-

(37) Espinat, D.; Rosenberg, E.; Scarsella, M.; Barre, L.; Fenistein,D.; Broseta, D. In Structures and Dynamics of Asphaltenes; Mullins,O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998; Chapter V.

Figure 5. (a) Cell showing the final asphaltene structure ofthe Mullins model. (b) Isolated aliphatic region of the completefinal structure. (c) Isolated aromatic region, where somestacking were highlighted.

Figure 6. Comparison between the asphaltene S(k) profileof our relaxed cell and two aromatic S(k) profiles reported byYen et al.3

1680 Energy & Fuels, Vol. 18, No. 6, 2004 Pacheco-Sanchez et al.

sured a linear size distance of four unit sheets of 14-28 Å for the stacking of asphaltenes.

(3) Knowing that the distance between monomers ina dimer is 3.55-3.7 Å, the linear size of a tetramer (16-20 Å or 14-28 Å) probably indicates two dimersinteracting between themselves, with aliphatic chainsin the middle of them providing an interaction distanceof 8.9-12.9 Å or 6.9-20.9 Å, respectively.

In addition, Figure 7 shows a comparison between theS(k) profile of the complete asphaltene aggregate modeland that obtained from an aggregate model that wasbuilt using only the aromatic Mullins asphaltene core,which will be analyzed in the next section.

3.2. Speight Model Case. The relaxed aggregatestructure of the cell built with the Speight model showsan abundance of stacking. However, the largest amountof stacking is in an offset π-stacked geometry. In thisparticular geometry, at least one structure that con-tains five members has been observed (Figure 8). It hasalso highlighted two more stacking geometries: one isT-shaped, and the other one is a face-to-face geometry.It can be attributed to the increment of stacking in theSpeight aggregate, compared with the Mullins modelcase, to the highest absolute area of the aromaticsection. This gives greater contact area than in theMullins model case. However, this contact is not sogreat, because the aliphatic chains do not allow a closeinteraction. A ratio of 0.64 between the aromatic surfacearea and the aliphatic surface area was observed. Themolecules are less flexible, because of the rigidity of thearomatic sheets and the fact that, in this case, they arelarger than those in the Mullins model case. This effectproduces an increase in the free-volume percentage,which, in this case, is 37.80%. For this aggregate, theminimum distance between the aromatic cores is 3.65Å and, it is the first peak on the RDF.

The comparison between the S(k) profile for theSpeight aggregate and the experimental S(k) profileshows good agreement in the position of the peaks. Thebest agreement is found with the Ragusa asphaltenecrude oil (Figure 9).

3.3. Zajac Model Case. The Zajac molecule is asingular one, because it has only one long aliphaticchain. The relaxed final aggregate structure exhibitsmolecules with a great curvature in the aromatic regionthat generally move away from these regions, stoppinga higher stacking formation. The aggregate shows anirregular stacking structure. However, Figure 10 il-lustrates at least three geometries in which these

molecules can self-aggregate: face to face, offsetπ-stacked, and T-shaped. The irregular stacking isattributed to the concavity obtained by the aromaticcores at the end of the energy optimization of themolecular simulation.

The ratio between the aromatic and aliphatic surfaceareas is 0.65, which is almost equal to that observed inthe Speight case. However, the absolute size of thearomatic area is smaller for the Zajac molecule than theSpeight molecule and is larger than that for the Mullinsmolecule, bringing, as a consequence, a higher stackingformation than that observed in the Mullins model casebut smaller than that in the Speight model case. Thefree volume of 36.96% indicates the role of the only onealiphatic chain: that, despite the aromatic region, inthis case, the free volume is bigger than that in theMullins model case. Note that their free volumes havealmost the same magnitude. The minimum distancebetween the aromatic cores, for this case, is 3.25 Å and,

Figure 7. S(k) profile for the Mullins aggregate model, compared with two experimental S(k) profiles, and the S(k) profile obtainedfrom a relaxed aggregation model built only with the aromatic cores (AC) of Mullins asphaltenes.

Figure 8. (a) Cell showing the final asphaltene structure ofthe Speight model. (b) Isolated aliphatic region of the completefinal structure. (c) Isolated aromatic region, where one offsetπ-stacking with five members, one dimer in T-shaped stacking,and one dimer in face-to-face stacking were highlighted.

Aggregated Asphaltene Structural Models Energy & Fuels, Vol. 18, No. 6, 2004 1681

it is the first peak on the RDF. This value is deviatedalmost 9% from the distance corresponding to theoptimum binding energy (3.55 Å).

The aggregate S(k) profile, as in previous cases, showsall the peaks in the positions reported experimentally.The exception is the position of the second peak, wherethere is good agreement for the Ragusa asphalteneaggregates (Figure 11).

3.4. Murgich Model Case. The Murgich asphaltenemolecular model possesses the largest aromatic areaamong all the asphaltene models analyzed here. Therigidity of this area in the molecule does not allow it tobe folded to fill all the space. Therefore, the relaxedaggregate structure obtained from the Murgich moleculeproduces empty regions and jammed clusters of as-phaltenes, instead of stacking configurations. The freevolume in this case is 57.30%, which is significantlybigger than that observed in the other cases. Visualizingcarefully, however, these jammed clusters are formedmainly by two of our three main stacking configura-tions: offset π-stacked and edge-on or T-shaped con-figurations. The most frequent configuration obtainedis the offset π-stacked orientation. The face-to-facegeometry configurations are not observed, which can beattributed to a very extensive aromatic region in theasphaltene model (Figure 12). A remarkable differencewith the other cases is the formation of two largeclusters in the simulation cell, meaning that the ali-phatic regions are not uniformly distributed in the cell.

The ratio of aromatic and aliphatic surface areas wasdetermined to be 0.55, which is smaller than thatobserved for the Speight and Zajac cases but larger thanthe Mullins case. Nevertheless, as in the Speight case,the absolute size of the aromatic area has an importantrole in making the stacking formation more possible.The minimum distance between the aromatic cores is3.65 Å, which agrees with the known distance ofoptimum binding energy for two asphaltenes. However,the calculated peak between 1 Å-1 and 2 Å-1 is barelydescribed, considering that the first peak hides its ownshoulder peak in this region (Figure 13).

Figure 9. S(k) profile for the Speight aggregate model, compared with two experimental S(k) profiles, and the S(k) profile obtainedfrom a relaxed aggregation model built only with the aromatic cores (AC) of Speight asphaltenes.

Figure 10. (a) Cell showing the final asphaltene structure ofZajac model. (b) Isolated aliphatic region of the complete finalstructure. (c) Isolated aromatic region exhibits highlightedthree geometries with two members at least: one offsetπ-stacking, one edge-on or T-shaped, and one face to face. Inthis case, the AC finished having a clear concavity.

Figure 11. S(k) profile for the Zajac aggregate model, compared to both the two experimental S(k) profiles, and the S(k) profileobtained from a relaxed aggregation model built only with the aromatic cores (AC) of Zajac asphaltenes.

1682 Energy & Fuels, Vol. 18, No. 6, 2004 Pacheco-Sanchez et al.

However, the comparison between the S(k) profile forMurgich asphaltene aggregates and experimental re-sults shows the closest agreement, in regard to theposition of its shoulder peak and the first peak of theGilsonite asphaltenes (see Figure 13).

4. Aromatic Cores

To explain the role of the aliphatic chains and thearomatic core, all the aliphatic chains were cut from theasphaltene models. After the aromatic cores wereobtained, our methodology was applied on all resultingpurely aromatic cores. The final densities of the aro-matic asphaltene core cell (AACC) models withoutaliphatic chains are higher than the whole asphaltenemodel (WAM) (see Table 2).

Except for the Murgich case, the order of magnitudeof the WAM density values agree with those reportedby Speight24 for the specific gravity (density 60/60 °F38)for various asphaltene samples obtained from differentbitumens.39 In all cases, the AACC model shows itsstacking presence, showing different geometries as amixture of the three geometries (face-to-face, edge-onor T-shaped, offset π-stacked; see Figure 14).

As shown in Figure 14, there is a higher stackingtendency of the aromatic sheets; for example, in theMullins case, one trimer and one pentamer are high-lighted. However, the others are not selected, to pre-serve clarity in the figure. As a comparison, only twodimers are highlighted in the isolated aromatic regionshown in Figure 5, the Mullins asphaltene case. In theSpeight case, a trimer and a tetramer were chosen,whereas, in the Zajac case, a dimer and a pentamer areshown. Finally, in the Murgich aromatic model, just ahexamer is highlighted. The geometric form chosen forthe Mullins and Murgich cases is offset π-stacked.Correspondingly, the Speight and Zajac selected geo-metric forms are offset π-stacked and T-shaped. A strictface-to-face geometry can hardly be selected in any ofthese cases. The free volumes of the AACC models aresmaller than those in the WAM, as shown in Table 3.

The difference between the free-volume percentagesof the WAM and AACC models is a clear evidence ofthe role of aliphatic chains, because a great compressionof the sheets results when these are removed from thesystems. The aliphatic chains connected to the aromaticcores then stop the attraction between aromatic coresof asphaltenes, which produces a large amount of emptyspace in the aggregation of asphaltenes.

When the structure factors of the AACC and WAMmodels are compared, a second peak shift to a smallervalue of k for the WAM model, with respect to the AACCmodel, is observed, as in the aromatic blend molecules

Figure 12. (a) Cell showing the final asphaltene structure ofMurgich model. (b) Isolated aliphatic region of the completefinal structure. (c) Isolated aromatic region, where one is offsetπ-stacked, one is edge-on, and one is face-to-face stacking withtwo members was highlighted.

Figure 13. S(k) profile for the Murgich aggregate model, compared to both the two experimental S(k) profiles available and theS(k) profile obtained from a relaxed aggregation model built with the aromatic cores (AC) of Murgich asphaltenes.

Table 2. Final Densities of Asphaltene Molecules afterEnergy Optimization for Both the Whole AsphalteneModel (WAM) and the Aromatic Asphaltene Core Cell

(AACC) Cases

density (g/cm3)

model WAM AACC

Mullins 0.98 1.26Speight 1.04 1.36Zajac 1.02 1.28Murgich 0.69 1.24

Table 3. Free Volumes of the Final Optimized Cells forBoth the Whole Asphaltene Model (WAM) and the

Aromatic Asphaltene Core Cell (AACC) Cases

free volume (%)

model WAM AACC

Mullins 34.68% 28.13%Speight 37.80% 31.91%Zajac 36.96% 31.81%Murgich 57.30% 36.04%

Aggregated Asphaltene Structural Models Energy & Fuels, Vol. 18, No. 6, 2004 1683

studied by Yen et al.3 These shifts are called the γ-bandand the (002)-band, respectively. Our results are dueto the fact that the WAM model has a stronger presenceof aliphatic chains than does the AACC model. Thiseffect was also very well-identified by Wiehe and Liang.4They associated paraffins to the smallest 2θ value andaromatics to the largest 2θ value on this peak of thestructure factor of asphaltenes that they obtained. Thisshift behavior is independent of the asphaltene modelmolecule used, as is shown in the sequence of Figures7, 9, 11, and 13. When the aliphatic chains are removedfrom the aromatic core in the Murgich case, the S(k)profile recovers the characteristic peak at ∼1.2 Å-1; inaddition, the Murgich AACC density recovers typicalaromatic density values (see Table 2).

Given all these facts, aliphatic chains have a role ininhibiting the stacking formation. Depending of theasphaltene model, there are different inhibition mech-anisms, such as intercalation of aliphatic chains be-tween aromatic sheets or pulling the molecule in oneside and only allowing some degree of stacking inanother place. An example of the presence of the effectof aliphatic chains is the Murgich case, where thealiphatic chains cause a delay in the molecules formingregions of empty space and clusters (see Figure 12). Thiseffect is not observed without aliphatic chains (seeFigure 14).

We have made the following three observations in ourgraphs of the S(k) profile for k ) 0 to k > 0 in Figure14. First, the first peak on the aromatic core (AC) ofMullins asphaltenes is the smallest one, whereas thefirst peak on the AC of Murgich asphaltenes is thelargest one, and its second peak is the smallest oneamong all of the AC asphaltenes. Second, the S(k) profileof Baxterville asphaltene3 includes the major component

of both AC asphaltenes of Mullins, Speight, and Zajacstructure models, as shown in Figures 7, 9, and 11. Thisagrees with the interpretation of Wiehe and Liang,4meaning that the highest shoulder of the second peakof the S(k) profile in Baxterville asphaltene is aromaticand the other is paraffinic. The same figures also exhibitRagusa asphaltene,3 as it represents the best matchagainst asphaltenes of these types. Ragusa asphalteneincludes the major portion of the second peak of bothAC and asphaltenes of the Murgich average structuremodel; however, Gilsonite asphaltene3 is the best matchagainst asphaltenes of the Murgich average structuremodel. Third, in Figure 15, the height value on the S(k)profile of AC compounds3 and AC Wafra A13 asphalt-enes is observed to be larger than all the second peaksof our asphaltene models. In addition to this point, thek value of these experimental models is larger than thatof three of our models; only the second peak of the S(k)profile on the AC of Speight asphaltene almost matchesthe k value of the AC compounds.

5. Discussion

Our methodology for calculating the minimum dis-tance between two asphaltenes in the stacking can giveus a reasonable prediction if the asphaltene moleculehas a compacted aromatic region that is well-designed,which can be done using the methodology developed byRuiz-Morales.40 This is due to very good results thathave been obtained for the distance of binding energybetween two asphaltene molecules on the Speight andMurgich cases; however, although the Zajac case is 9%deviated from experimental values, the Mullins case hasa deviation of 15%. These deviations clearly indicate thepresence of aliphatic chains, which restrict both theclosest interaction distance between two asphaltenemolecules and its geometry of stacking. The followingcomment of Ebert,41 that “only 36% of the aromaticcarbon was in stacks of two (‘dimers’) and 64% of thearomatic carbon was not in a stack of any kind (‘amor-phous’)” suggests agreement with our observations.

Another point is related to the number of aromaticrings in the AC of one asphaltene molecule. Ruiz-Morales40 suggests that asphaltenes present a polyaro-matic core size of 1-2 aromatic systems with 4-10fused rings in each one; according to the Mullinsexperimental work.27 Rogacheva et al.36 reported as-phaltenes with 4-10 fused aromatic rings. Rogel42 hasdrawn polyaromatic rings with 9-14 fused rings torepresent the aromatic moieties of asphaltenes. We usedfour different asphaltene molecules, with 7, 9, 14, and24 aromatic rings, following previous models in theliterature. We believe that the use of molecular simula-tions to calculate the structure factor S(k) is a goodstarting point to improve this design.

By cutting aliphatic chains of asphaltenes, just ACswere obtained. These ACs were also energeticallyoptimized, and their structure factors S(k) were ob-tained, as shown in Figure 15. Figures 8c and 14a showthat an asphaltene molecule designed by Mullins withseven fused aromatic rings exhibits at least one 5-aro-matic-stack system. As we can also see in Figure 15,(38) Relative density (60/60 °F), which was called density by Speight,

is the ratio of the mass of a given volume of liquid at 60 °F to themass of an equal volume of pure water at the same temperature.

(39) Speight, J. G. The Chemistry and Technology of Petroleum;Marcel Dekker: New York, 1999; p 315.

(40) Ruiz-Morales, Y. J. Phys. Chem. A 2002, 106, 11238-11308.(41) Ebert, L. B. Fuel Sci. Technol. Int. 1995, 13, 941-944.(42) Rogel, E. Langmuir 2004, 20, 1003-1012.

Figure 14. Different relaxed aromatic-core aggregated struc-tures: (a) Mullins, (b) Speight, (c) Zajac, and (d) Murgich.

1684 Energy & Fuels, Vol. 18, No. 6, 2004 Pacheco-Sanchez et al.

the AC of Speight asphaltenes with 14 fused aromaticrings gave the best agreement between its second S(k)peak and the first S(k) peak of AC compounds; however,the AC of Mullins asphaltenes is deviated from match-ing. Second, the S(k) peak of the AC of Zajac asphalteneswith nine aromatic fused rings has a very similarbehavior to that of the AC of Mullins asphaltenes. Inthe case of Murgich asphaltene, we found that the ACof 24 fused aromatic rings has a behavior more similarto asphaltenes than to ACs of asphaltenes (see Figure13). After this analysis, it can be concluded that theMurgich asphaltene case is only meaningful whenaliphatic chains are removed.

We must stress that minimization of the energy isindependent of the temperature, and a complete studyof the stability using entropy and thermodynamicpotentials is not possible within the present methodol-ogy. At this time, we just want to show that we found avery good matching between this theory and experimentstabilizing asphaltenes by molecular simulations ofenergy optimization.

It must be stated that, knowing the interactionpotential, the structure factor S(k) can be approximatedfrom the solution of the Ornstein-Zernicke (O-Z)integral equation and an additional closure relation (PY,MSA, RMSA, HNC, RY, etc.).43,44 The methodology ofHenderson-Barker-Abraham and of density functionaltheory (DFT) can be used to obtain the solution of theO-Z equation.9,45,46 However, these methods are de-

pendent on Euclidean geometric forms of the molecule,because of the potential they use, as the hard-sphereintermolecular potential of interaction. This is a grosslimitation, because the center of mass is translated,which produces deviations from real systems as as-phaltenes are. They usually compare their resultsagainst MD simulations, Monte Carlo (MC) calculations,and/or experiments.45 Yen et al.3 used a very clevermethodology to compare the XRD experimental patternfor aromatic clusters in petroleum asphaltene with theexperimental pattern for a blend of five polynucleararomatic compounds of known structure by computingthe Debye RDF implemented by Diamond,13 which isprecisely the structure factor S(k). We calculated a verygood approximation of the S(k) profile by optimizing theenergy of a 35-membered aromatic system, using thesame five aromatic compounds mentioned previously ingroups with seven-membered rings.

Whether the approved SF profile is our guide tovalidate generated morphologies, the effects of polydis-persity on the SF profile are well-known, as shown insome studies developed by D’Aguanno and Klein.43 Inthat work, the effects of polydispersity in chargedcolloidal dispersions are exhibited in a manner in whichthe SF peaks are displaced, modifying its height andwidth at different levels of polydispersity. Asphaltenesare known to constitute a polydisperse system; however,in the literature, it is usual procedure to characterizecrude oil systems by means of an asphaltene averagemolecule.18,23,27,28 Because of this restriction on thecharacterization of the entire polydispersity of theasphaltenic system, as a first approach, we have taken

(43) D’Aguanno, B.; Klein, R. J. Chem. Soc., Faraday Trans. 1991,87 (3), 379-390.

(44) Ortega-Rodrıguez, A.; Cruz, S. A.; Gil-Villegas, A.; Guevara-Rodrıguez, F.; Lira-Galeana, C. Energy Fuels 2003, 17, 1100-1108.

(45) von Grunberg H. H.; Klein R. J. Chem. Phys. 1999, 110 (11),5421-5431.

(46) Pacheco-Sanchez, J. H.; Rodrıguez, A. G. Rev. Inst. Mex. Pet.1993, 25 (2), 55-60.

Figure 15. Comparison between structure factors of aromatic cores (AC) calculated by us (continuous line) and those proposedby Yen et al.3 (dotted and dashed lines).

Aggregated Asphaltene Structural Models Energy & Fuels, Vol. 18, No. 6, 2004 1685

a set of average molecules reported in the literature asthe starting point in this study.

Finally, our results here can help to improve theexperimental methodology for designing asphaltenemolecules, which can be useful, as many researchershave shown.14-18,22,30,42,47

6. Conclusions

One possible way to determine the morphology ofasphaltene aggregates is through modeling and simu-lating such aggregates. This is because (i) our simulatedstructure factors (S(k)) of asphaltene aggregates agreewith those reported by Yen; (ii) the molecular modelsof asphaltenes are experimentally designed from ex-tracted crude oils; and (iii) experimentally, it is possibleto simply guess about the morphology of the aggregates.

We have proposed a procedure for generating as-phaltene aggregated structures, based on a minimiza-tion of the energy of the system in periodic cells. Theseperiodic cells were constructed using different asphalt-ene models, such as those devised in the research ofMullins, Speight, Zajac, and Murgich. Each cell wasbuilt with one type of asphaltene model in an amor-phous arrangement to optimize them. The developedmethodology is capable of reproducing the position ofthe experimental S(k) profile. Important differenceswere observed, with respect to the AC cases. Thepresence of a shift in the peak located between 1 Å-1

and 2 Å-1 is associated with the stacking. We observedstacking clusters when aromatic molecules are used.Based on the similarity of the S(k) profiles, we canconclude similarities in the asphaltene agglomerationof the Zajac, Mullins, and Speight cases with Ragusa-type asphaltene, and of the Murgich case with Gilsonite-type asphaltene.

Generally, the positions of the main S(k) peaks werecorrectly reproduced, showing a discrepancy on thesecond peak region. Such a discrepancy can be at-tributed to the tail presence in the aromatic sheets thatinhibits the π-π, π-σ, and σ-σ interactions, bringing,as a consequence, an increase of the distance betweenthese sheets. The good correlation between the experi-mental and predicted S(k) profiles would imply that theasphaltene aggregate structure is an adequate modelfor studying the asphaltene aggregation phenomenon.

Therefore, based on the present simulations, weconclude that a nearest-neighbor stacking in face-to-facegeometry is not the only possible orientation. Theobserved asphaltene aggregate structure represents justone of the possible ensemble structures that could existin the system. The final cells are good models as a firstapproach for representing asphaltene aggregates as wellas the way in which they agglomerate in an amorphoussolid phase. In addition, we applied our methodology tothe different asphaltene models used but without theiraliphatic chains, finding a similar stacking behavior foreach case.

EF049911A(47) Rogel, E.; Leon, O. Energy Fuels 2001, 15, 1077-1086.

1686 Energy & Fuels, Vol. 18, No. 6, 2004 Pacheco-Sanchez et al.