Study of the Adsorption of Alkyl-Benzene-Derived Amphiphiles on an

Energy & Fuels 2001, 15, 1077-1086

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Study of the Adsorption of Alkyl-Benzene-Derived Amphiphiles on an Asphaltene Surface Using Molecular Dynamics Simulations Estrella Rogel and Olga Leoń* PDVSA-INTEVEP, Apdo. 76343 Caracas-1070A Venezuela Received July 11, 2000. Revised Manuscript Received July 5, 2001

Atomistic simulations using molecular dynamics were made to study the adsorption behavior of alkyl benzene-derived amphiphiles on an asphaltene surface from n-heptane. The results obtained indicate that the interaction energies involved in the adsorption process depend on the polarizability and also on the dipole moment of the amphiphile. Based on the interaction energies calculated, a rough estimation of the characteristic adsorption energy at high and low coverage degrees studied was carried out. At low coverage, the amphiphiles prefer to lie parallel to the surface and there is a strong dependence between the adsorption energy and the dipole moment of the amphiphile. On the contrary, at high coverage, the adsorption energies are influenced mainly by the polarizability of the amphiphile. At this coverage, the simulations show evidence of the incipient formation of amphiphile aggregates on the asphaltene surface, with the amphiphiles having their heads lying parallel to the asphaltene surface and their tails extending isotropically toward the n-heptane. The simulations also show that an increase in the size of the amphiphile’s head leads to an increase in the atomic density near the asphaltene surface that can improve the steric barrier to the asphaltene flocculation. This finding explains the increase of the efficiency as asphaltene stabilizers of the alkyl phenol ethoxylated amphiphiles with the size of the ethoxylated chain.

Introduction Among the many problems that can occur during the production of crude oils, the formation of asphaltene deposits is one of the most difficult to control.1 This problem is related to the tendency of the asphaltene fraction to form aggregates that can grow until precipitate.2 The asphaltene precipitation can fill the pores of the reservoir rocks and plug the wellbore tubing and other auxiliary equipment.3 Reservoir damage, production decrease, and equipment damage are some of the consequences of asphaltene precipitation. Several methods are used to manage the asphaltene precipitation problems. Among them, the injection of substances that can prevent the precipitation is one of the most frequently used. However, the way in which these substances work is still not very well understood. It is supposed that they act in a way similar to that of the resins, peptizing the asphaltenes, stabilizing them in solution.4 Numerous amphiphiles have shown activity as asphaltenes stabilizers.4-8 In particular, the alkylbenzenederived amphiphiles have been the most studied. Chang * Author to whom correspondence should be addressed. (1) Park, S. J.; Mansoori, G. A. Energy Sources 1988, 10, 109-125. (2) Andersen, S. I.; Birdi, K. S. Fuel Sci. Technol. Int. 1990, 8, 593615. (3) Del Bianco, A.; Stroppa, F.; Bertero, L. SPE Production Facilities, 1997, 12, 80-83. (4) Chang, C. L.; Fogler, H. S. Langmuir 1994, 10, 1749-1757. (5) Chang, C. L.; Fogler, H. S. Langmuir 1994, 10, 1758-1766. (6) Gonzalez, G.; Middea, A. Colloids Surf. 1991, 52, 207-217. (7) Bandeira, L. F.; Fernandes, E.; Gonzalez, G. J. Appl. Polym. Sci. 1999, 73, 29-34.

and Fogler4,5 used the alkylbenzene-derived amphiphiles to investigate the asphaltene-amphiphile interactions and their relation to the effectiveness of these amphiphiles to stabilize asphaltenes in alkane solvents. They found that the effectiveness of the amphiphiles as stabilizers is related to the strength of the asphalteneamphiphile interactions and also to the length of the amphiphile’s alkyl tail. The last characteristic is related to the capacity of the amphiphiles to form a stericstabilization layer around the asphaltene particles. More recently, Leoń et al.9 studied the adsorption of a set of alkyl-benzene-derived amphiphiles on asphaltene particles and related directly the adsorption to the effectiveness of the amphiphiles as stabilizers. Their results showed that the activity of the amphiphiles is related to the maximum amount of amphiphile adsorbed on the asphaltene surface.9 They also found that the adsorption of amphiphiles from n-heptane on asphaltene particles seems to be a process that occurs in two steps according to the adsorption mechanism previously proposed by Zhu and Gu for amphiphiles.10 In the first step, the amphiphiles are adsorbed individually on the asphaltene surface; in the second step, the interactions between adsorbed amphiphiles become predominant and the formation of hemimicelles (surface micelles) on the surface begins. (8) Mohamed, R. S.; Loh, W.; Ramos, A.; Delgado, C.; Almeida, V. Pet. Sci. Technol. 1999, 17, 877-896. (9) Leoń, O.; Rogel, E.; Urbina A.; Andu´jar A.; Lucas A. Langmuir 1999, 15, 7653-7657. (10) Zhu, B. Y.; Gu, T. Adv. Coll. Int. Sci. 1991, 37, 1-32.

10.1021/ef000152f CCC: $20.00 © 2001 American Chemical Society Published on Web 08/14/2001

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Figure 1. Scheme of construction of the asphaltene surface model.

According to these results, to understand the amphiphiles stabilization of asphaltene particles it is important to gain insight into the energetics, mechanism, and other characteristics of the adsorption process such as the adsorbed amphiphiles conformation. Molecular dynamics and molecular mechanics techniques have been successfully used to study the solubility behavior of asphaltenes,11 the characteristics of the interactions of resins and asphaltenes solely,12,13 and in different solvents.14 In this work, atomistic detailed simulations were made to study the adsorption behavior of alkyl-derived amphiphiles from n-heptane at different coverages on an asphaltene surface. Based on the two-step adsorption mechanism, explained above, a low and a high coverage were studied. The main goal of this paper is to obtain information about the nature of the asphaltene-amphiphile interactions, the amphiphile orientation on the asphaltene surface and the structure of the amphiphile layer. A better understanding of these aspects can improve the knowledge of the stabilization mechanism of asphaltenes by amphiphiles and, as a consequence, may improve the selection and design of new inhibitors. Computer Simulations The molecular-modeling software InsightII 4.0.0 of MSI15 and a Silicon Graphics Indigo 2 workstation were (11) Rogel, E. Colloids Surf. A 1995, 104, 85-93. (12) Murgich, J.; Rodrı´guez, J.; Aray, Y. Energy Fuels 1996, 10, 6876. (13) Murgich, J.; Abanero, J.; Strausz, O. Energy Fuels 1999, 13, 278-286. (14) Rogel, E. Energy Fuels, 2000, 14, 566-574. (15) Molecular Simulations Inc., San Diego, CA.

used. The cvff force field was selected to describe the atoms in all the calculations. This force field has been successfully used to describe the association behavior of asphaltenes and resins.14 Asphaltene Surface Model. The asphaltene surface used was built using a mean structure of an asphaltene fraction (Figure 1) previously reported11 from a Venezuelan crude. This highly condensed structure represents the molecules with a high aromaticity and low atomic hydrogen-to-carbon ratio that preferentially precipitate to form asphaltene deposits.16,17 The asphaltene surface was constructed as follows: first, dimer and trimer aggregates of the asphaltene were constructed using a procedure reported earlier.11 Optimized aggregates were placed in a 2D periodic unit cell, simulating an infinite surface using periodic boundary conditions in the xy plane. Consecutive steps of minimization and constant energy molecular dynamics (50 ps) at 298 K were made. After each step of molecular dynamics, new asphaltene molecules were introduced manually in the system to avoid the formation of holes in the generated asphaltene layer. For the final system, a constant energy molecular dynamics simulation of 50 ps at 298 K was performed and the last configuration was taken as the model for the asphaltene surface, once the energy was constant. The final model consisted of a layer composed by thirteen asphaltene molecules covering 40 × 32 Å2 in the xy plane. Figure 1 shows a scheme of the construction of the asphaltene surface model. (16) Carbognani, L.; Orea, M.; Fonseca, M. Energy Fuels 1999, 13, 351-358. (17) Carbognani, L.; Espidel, J.; Izquierdo, A. In Asphaltenes and Asphalts: Development in Petroleum Science; Yen, T. F., Chilingarian, G. V. Eds.; Elsevier Science B. V.: The Netherlands, 1999.

Adsorption of Amphiphiles on an Asphaltene Surface

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Table 1. Alkylbenzene-derived Amphiphiles Used in Molecular Simulations

Characteristics of the Model Systems. Six alkylbenzene-derived amphiphiles were selected for the study, on the basis of their activities as asphaltene stabilizers.4-8 Some of them are also active ingredients in commercial products used to prevent asphaltene deposition. Table 1 shows the amphiphiles studied with their polarizabilities and dipole moments, both properties related to the molecular interactions. These properties were calculated using the semiempirical MOPAC/ PM3 method. It has been found that this method properly describes the experimental tendencies, although the properties calculated could differ from experimental values.15 Two different types of systems were built. The first type modeled the amphiphile free in n-heptane, while the second type modeled the amphiphiles’ behavior on the asphaltene surface in the presence of n-heptane. For these systems, based on the two-step adsorption mechanism, a low (one amphiphile molecule) and a high (20 amphiphile molecules) coverage on the surface were considered. This last coverage corresponded to 60 Å2 per amphiphile molecule arranged originally in a monolayer of 5 × 4 molecules (see Figure 2). For both coverages, the molecules were initially placed perpendicular to the surface. Molecular Dynamics Calculations. The simulations for all the systems took 100 000 ps of real time (10 000 time steps of 1 fs each) at 298 K. The first 30 000 time steps were used in an equilibration process. Before molecular dynamics simulation, the system was minimized. Only the last 30 000 time steps of each simulation were taken to obtain average energy values. For the first set of systems (amphiphiles free in solvent) 3D periodic boundary conditions were used in the simulations, while for the second set, 2D periodic boundary conditions were used to simulate an expanded asphaltene surface in the xy plane. The atoms in the asphaltene

layer were considered fixed along all the simulations in order to save computational time. It is reasonable to assume these atoms to be fixed because asphaltenes are insoluble in n-heptane, and, therefore, they should behave as solids. However, a simulation run of nheptane in contact with the asphaltene layer without fixed atoms was made. The diffusion of the asphaltene layer was calculated for mass centers from mean square displacements. The diffusion coefficient of the asphaltene layer in n-heptane was 7 × 10-7 cm/s, while the diffusion coefficient for n-heptane in the same simulation was 3 × 10-5 cm/s, almost 2 orders of magnitude higher than the diffusion coefficients for the asphaltene layer. Although these values should be considered only as approximate, since a correct calculation of diffusion coefficients requires longer times than the ones used here, they do reflect that to consider the atoms of the asphaltenes as fixed does not introduce an appreciable error in the energetic calculations. On the other hand, fixed asphaltene atoms introduce the implicit assumption that there is no dissolution of the asphaltene layer due to the asphaltene-amphiphile interactions. In fact, asphaltene dissolution is observed at moderate concentrations of some amphiphiles.18 However, these concentrations are always higher than the critical micelle concentration (cmc) of the amphiphiles in the solvent as can be deduced from the adsorption experiments.9 At cmc, the coverage of the asphaltenes' surface is considerably higher than the coverages studied in this work. Results and Discussion. Intermolecular Interactions Involved in the Adsorption Process. Two different systems were (18) Permsukarome, P.; Chang, C.; Fogler, H. S. Ind. Eng. Chem. Res. 1997, 36, 3960-3967.

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Figure 2. Initial configurations of the systems studied.

constructed: the first system simulated the behavior of the free amphiphile in n-heptane. The second system modeled the interaction of the amphiphile with the asphaltene surface in the presence of n-heptane at high and low coverages. The low coverage studied represents the beginning of the adsorption process while the high coverage reflects the beginning of the amphiphile aggregation on the asphaltene surface. The total energies determined for the systems were compared. It was found that the conformational changes of the amphiphile molecules due to the adsorption process do not produce significant changes in their total internal energies. Based on this finding the studies carried out in the present work were focused on the comparison of the interaction energies instead of the total energies. Similar results were found for analogous systems.14 A comparison of the total interaction energy between the amphiphile and its surrounded medium (asphaltene surface + n-heptane) in each system is shown in Table 2. These total interaction energies were calculated as averages over the last 30 ps of each molecular simulation. The interaction energies indicate that the adsorbed states of the amphiphiles are more favorable than the amphiphile free in n-heptane. The adsorption at high coverage is more favorable than the adsorption at low coverage. In other words, the adsorption of amphiphiles on the asphaltene surface is preferred. However, other

Table 2. Comparison of the Total Interaction Energies (kcal/mol) of the Amphiphiles with Their Surrounded Media for the Different Systems Studied

amphiphile

amphiphile-free in n-heptane

amphiphile adsorbed, low coverage

amphiphile adsorbed, high coverage

DP DPE1 DPE2 DPE3 DPE4 DBSA

-37.1 -41.7 -45.9 -53.2 -51.1 -35.5

-47.2 -53.7 -61.5 -68.7 -74.0 -51.2

-52.6 -59.0 -67.6 -77.1 -81.1 -57.8

energetic factors such as the displacement of the solvent molecules affect the adsorption and must be taken into account to study the adsorption adequately. Adsorption from solution is an exchange phenomenon, divided in two sub processes: transfer of a dissolved molecule to the surface and transfer of an equivalent volume of solvent from the surface to the solution.19 Experimentally, the adsorption from solution must be studied as a whole process. This is, only the sum of the two sub processes involved is measurable.19 In this sense, molecular simulation provides a useful tool to examine separately the energetic components of the two sub-processes and can help to better understand the factors that promote the adsorption from solution. In this work, the interaction energies related to the (19) Lyklema, J. Colloids Surf. A 1994, 91, 25-38.


Figure 3. Interaction energy amphiphile-asphaltene at different coverages as a function of the polarizability of the amphiphiles.

Figure 4. Interaction energy amphiphile-asphaltene at different coverages as a function of the dipole moment of the amphiphiles.

adsorption of the amphiphiles were examined using the results of the molecular dynamics simulations. Five interaction terms related to adsorption are calculated as an average over the last 30 ps of the molecular simulations: amphiphile-asphaltene, amphiphile-nheptane, n-heptane-asphaltene, amphiphile-amphiphile (at high coverage), and n-heptane-n-heptane. On the basis of the interaction energies calculated, characteristic energies of adsorption for each amphiphile are also estimated. In the evaluation of each individual energetic contribution, it was found that the interaction energies were mainly affected by the molecular characteristics of the amphiphiles shown in Table 1. Hence, relationships of the interaction energies with the polarizability and the dipole moment of the amphiphile molecules were found. The amphiphile-asphaltene interactions for the dodecyl phenol ethoxylated molecules depend mainly on polarizability of the amphiphiles at low coverage (correlation coefficient ) 0.938) which indicates the predominance of the van der Waals forces in these interactions. On the contrary, at high coverage, the interaction energies amphiphile-asphaltene are almost independent of the polarizability and depend basically on dipole moment for the DPEn series (correlation coefficient ) 0.874). Figures 3 and 4 reflect both tendencies. The amphiphile-n-heptane interactions at high cov-


Figure 5. Interaction energy amphiphile-n-heptane at different coverages as a function of the polarizability of the amphiphiles.

Figure 6. Interaction energy amphiphile-amphiphile as a function of the polarizability of the amphiphiles.

erage are mainly related to polarizability of amphiphiles (correlation coefficient ) 0.955) and, at low coverage, both polarizability and dipole moment influence the interactions (correlation coefficients ) 0.671 and 0.429). Figure 5 shows the amphiphile-n-heptane interactions as a function of the polarizability. At high coverage, the amphiphile-amphiphile interactions are related mainly to the polarizability of amphiphiles as can be seen in Figure 6 (correlation coefficient ) 0.984). Characteristic Adsorption Energies. A semiquantitative description of the adsorption process in nonpolar media is possible using interaction parameters to characterize the mutual interactions between amphiphile, solid, and solvent.20 In the present work, the characteristic energies of adsorption at low coverage were estimated using the following scheme of exchange of molecules:

(amp)sol + Ns(n-hep)asp f (amp)asp + Ns(n-hep)sol (1) where asp stands for asphaltene, sol for solution, n-hep for n-heptane, amp for amphiphile, and Ns represents the number of n-heptane molecules displaced by the amphiphile. (20) Somasundaran, P.; Krishnakumar, S. Colloids Surf., A 1997, 123-124, 491-513.

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Table 3. Characteristic Energies of Adsorption (kcal/ mol) at Different Coverages amphiphile

low coverage

high coverage

DP DPE1 DPE2 DPE3 DPE4 DBSA

-11.4 -4.8 -6.6 1.9 -5.9 -24.2

-19.2 -19.0 -25.1 -25.5 -32.0 -24.8

Then, the characteristic energy of adsorption can be calculated by

E1ads ) Eint(amp-asp) + Ns Eint(n-hep-sol) Eint(amp-n-hep) - NsEint (n-hep-asp) (2) where Eint represents the interaction energy per mol of each pair of components. Usually, in thermodynamic calculations, Ns is considered as 1.19 However, in this work, a rough estimation of Ns was made. Using the molecular simulations it is possible to establish approximately the effect that each amphiphile has on the asphaltene-n-heptane interactions. The difference between the interaction energy of the nheptane with the clean asphaltene surface, and the interaction energy of n-heptane with the surface covered by the amphiphiles must be proportional to the number of n-heptane molecules displaced (Ns). It was found that the average number of n-heptane molecules in direct contact (first layer of solvent in contact with asphaltene surface) with the clean surface was 24. These molecules were responsible for more than 70% of the asphaltenen-heptane interaction energy. On the basis of this finding, it is supposed that the total number of nheptane molecules that cover the clean asphaltene surface is 24, and using this value, it is possible to estimate Ns. The interaction n-heptane-n-heptane was also estimated in order to calculate the interaction of the molecules of n-heptane displaced with the n-heptane that composed the solution. A molecular dynamics simulation of pure n-heptane showed that the interaction energy between the displaced n-heptane molecules and the n-heptane in the bulk was proportional to the number of displaced molecules according to the linear equation

Figure 7. Characteristic adsorption energy at low coverage as a function of the dipole moment of the amphiphiles.

However, at low coverage the characteristic adsorption energies depend mainly on dipole moments as can be seen in Figure 7. The characteristic energies of adsorption at high coverage (E20ads) were also calculated. The results of this calculation are also shown in Table 3. In this case, the characteristic energies of adsorption were calculated using the following equation:

E20ads ) Eint(amp-asp) + Ns Eint(n-hep-sol) + Eint(amp-amp) - Eint(amp-sol) Ns Eint(n-hep-asp) (5)

The adsorption energies calculated are shown in Table 3. Although the adsorption energies calculated could not be directly compared with the experimental values, they represented an index for the strength of adsorptive interaction. Tamon et al.21 found a correlation between affinity coefficient and adsorption energy estimated using a scheme similar to the one proposed in this study. They studied the adsorption equilibrium of eighteen organic compounds in aqueous solution on activated carbon. In their work, the interaction energies were calculated by frontier orbital theory. At low coverage, it was found that the characteristic energies of adsorption (E1ads) calculated can be correlated with dipole moments (DM) and polarizabilities (P) of the amphiphiles using the following equation:

In this equation, a new term corresponding to the amphiphile-amphiphile interactions is added to take into account the high coverage of the surface and, as a consequence, the lateral interactions between the amphiphiles adsorbed on the surface. For high coverage, it was found that Ns is approximately one molecule per each amphiphile, independent of the amphiphile. This is in agreement with the general assumption of one molecule of solvent displaced by each solute adsorbed used for most of the thermodynamic theories of adsorption.19 The values calculated at high coverage shown in Table 3 must reflected the tendency of the amphiphile to form structures on the asphaltene surface. This was due to the strong lateral interactions among the amphiphiles (Figure 6), which were found to be higher that the interactions of the amphiphile with the asphaltene (Figure 3) and with the n-heptane (Figure 5) under the same conditions. These results are in agreement with the mechanism of adsorption proposed by Leoń et al.9 that indicates the predominance of the amphiphileamphiphile interactions at the highest coverages on the asphaltene particles. In principle, the characteristic energies of adsorption at high coverage shown in Table 3 can be associated to the enthalpy of hemimicellization or, in other words, to the enthalpy of formation of amphiphile structures in the surface. The comparison of the values calculated in the present work and experimental enthalpies of hemimicellization of similar systems indicates a reasonable

E1ads ) -16.00 - 5.51 × DM + 0.61 × P r2 ) 0.952 (4)

(21) Tamon, H.; Aburai, K.; Abe, M.; Okazaki, M. J. Chem. Eng. Jpn. 1995, 28, 823.

Eint(n-hep-sol) ) -9.56 Ns - 9.50

(3)


Figure 8. Characteristic adsorption energy at high coverage as a function of the polarizability of the amphiphiles.


Figure 9. Hydrogen bonding among amphiphiles at high coverage using molecular simulations.

agreement. For instance, the enthalpy of hemimicellization of n-decanol on graphite from n-heptane is -15.65 kcal/mol at 288 K,22 in comparison to -19.2 kcal/ mol for DP. At low coverage, the characteristic energies of adsorption calculated can be correlated with dipole moments and polarizabilities of the amphiphiles using the following equation:

E20ads ) 6.552 - 1.400 DM - 1.101 P r2 ) 0.939 (6) Nevertheless, Figure 8 indicates that the characteristic adsorption energies increase as the polarizability of the amphiphile increases. It is important to point out that the energy values calculated in the present work do not included the entropic factors that can have a significant effect on the adsorption process.19 It has been found that adsorption in nonpolar media is governed by the relative interactions of the system components.20 In fact, the adsorption of amphiphiles from nonaqueous solvents is considered to be an enthalpic driven process.23 Based on these findings, in the present work only the energetic contributions are considered. Rather recently, a thermodynamic micellization model for asphaltene precipitation inhibition was developed assuming that the amphiphiles behave like resins and coadsorb onto the micellar core with resins.24 The results from this model demonstrate that a main criterion for the selection of an amphiphile for asphaltene precipitation inhibition is the adsorption enthalpy. Hydrogen Bonding. Although it is not possible to determine the interaction energy due to hydrogen bonding separately with the force field used, the temporal average of hydrogen bonds formed between amphiphiles at high coverage could be calculated using a geometrical rule. Figure 9 shows the results of such calculations. There is an increase of hydrogen bonding with the increase of the ethoxylation degree in dodecyl phenol ethoxylated series, while the dodecyl benzene sulfonic acid shows the highest number of intermolecular hydrogen bonds. The hydrogen bonding between the amphiphiles adsorbed could be interpreted as the begin(22) Zhu, B. Y.; Gu, T. Colloids Surf. 1990, 46, 339-345. (23) Zhu, B. Y.; Gu, T. Adv. Coll. Int. Sci. 1991, 37, 1-32. (24) Pan, H.; Firoozabadi, A. AIChE J. 2000, 46, 416-426.

Figure 10. Number of n-heptane molecules displaced by amphiphiles from the asphaltene surface at low coverage calculated by computational simulations.

ning of hemimicelle formation on the asphaltene surface. According to these results, it can be predicted that DBSA will show the largest aggregation number due to its higher capacity to form intermolecular hydrogen bonds. It is also important to indicate that no hydrogen bonding was observed between the asphaltene surface and the amphiphiles. Similar results using molecular mechanics were reported for the interactions between asphaltenes and resins. In this earlier study, it was found that the alkyl branches of the asphaltenes limit the number of available active sites for hydrogen bonding.12 In the present work, the small area of the asphaltene surface considered on the calculations also limit the availability of sites for hydrogen bonding. Amphiphile Orientation on the Surface. Figure 10 shows the number of molecules of solvent displaced by the amphiphile versus the van der Waals volume of the amphiphiles at low coverage. A linear correlation was found for the phenol-derived amphiphiles, which means that the solvent molecules displaced are proportional to the size of the amphiphile. This correlation indicates that these amphiphiles lie parallel to the asphaltene surface. The DBSA does not follow this tendency as can be seen in Figure 10. In fact, it was found experimentally by Leon et al.9 that for alkyl phenol amphiphiles the coverage at the first plateau is proportional to the inverse of the area

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Figure 11. DBSA at low coverage on the asphaltene surface.

of the long axis of the amphiphile. They found that the alkyl phenol amphiphiles orientation was parallel to the surface at the first plateau as it was predicted by computational calculations. Other authors have found the formation of closely packed monolayers with molecules lying with their long axis parallel to the surface for similar systems.25-27 These reports included alcohols26 and carboxylic acids27,28 adsorbed from organic solutions onto graphite, as well as large alkanes adsorbed from organic solutions onto graphitized carbon.28 Lamellar structures have been identified for fatty acids with extended carbon chains oriented parallel to a lattice axis in the graphite basal plane. 27 It is well-known that the van der Waals forces are proportional to the molecular size and as a consequence to the polarizability. The parallel orientation of the phenol ethoxylated amphiphiles at the first plateau is another indication that interactions between asphaltenes and these molecules are mainly due to the van der Waals forces, as it was found using the molecular simulations at low coverage. In the case of DBSA, the experimental coverage at the first plateau determined by Leon et al.9 is proportional to the inverse of the area of the headgroup, which means that this amphiphile is in perpendicular position to the surface. The molecular dynamics simulations also predicted that at low coverage, DBSA prefers a perpendicular configuration to the asphaltene surface (Figure 11). In fact, according to the molecular simulation, less (25) Rabe, J. P.; Bucholz, S. Science 1991, 253, 424-425. (26) Groszek, A. J. Proc. R. Soc. London 1970, A314, 473-476. (27) Castro, M. A.; Clarke, S. M.; Inaba, A.; Dong, C. C.; Thomas, R. K. J. Phys. Chem. B 1998, 102, 777-781. (28) Findenegg, G. H.; Liphard, M. Carbon 1987, 25, 119-128.

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than one molecule of n-heptane is displaced per molecule of DBSA at low coverage. Compared to the other amphiphiles, DBSA has a larger dipole moment (Table 1) due to its polar head and as a consequence, it is reasonable to suppose that it prefers to interact through the polar head with the alkyl chain extended toward the solvent. These findings suggest that DBSA and the other amphiphiles studied here follow different adsorption mechanisms. Measurements of the radius of gyration of nonylphenol-asphaltene and DBSA-asphaltene colloids indicated also noticeable differences in adsorption.5 The radius of gyration of nonyl-phenol-asphaltene colloid was only slightly larger than that of asphaltenes alone, while the DBSA-asphaltene colloid was significant larger. These differences were attributed to the formation of multilayers of DBSA. Structure of the Amphiphile Layer at High Coverage. Asphaltene flocculation can be prevented by the formation of a steric stabilization layer composed of amphiphiles. In nonaqueous media, Somasundaran et al.30 found that the stability of suspensions was dependent on the amount adsorbed and the packing of molecules in the adsorbed layer. Distributions of groups and atoms, bond order parameters ,and trans-gauche fractions were determined using the results of molecular simulations. A simple way to measure the local structure in the amphiphile layer is to determine the probability distributions of atoms and groups normal to the interface. The z ) 0 plane was selected somewhat arbitrarily in a point inside the asphaltene layer. In general, the z distributions calculated show similar patterns for all amphiphiles: tails, benzene rings, and headgroups are located in similar regions with approximately equal width independent of the amphiphile. The distributions corresponding to the tail groups are the widest in all the cases, including those amphiphiles whose headgroups are of a size similar to that of their tails (DPE3 and DPE4). While tails atoms can be found distributed over a wide region, the atoms of the headgroups are restricted to a narrower region near the asphaltene surface. In fact, the region occupied by the polar head was the same independently of the amphiphile and, as a consequence, independently of the size of the polar head (Figure 12). Taking into account the initial position of the amphiphiles before the molecular simulations (Figure 2), the narrow distributions of the atoms of the headgroups indicate a strong preference of the polar parts of the molecules for the asphaltene surfaces at high coverage. Thus, the increase of the size of the polar head produces an increase in the atomic density of the region near the asphaltene surface and it can improve the steric stabilization of the asphaltene particles. The bond order parameters Si along the normal to the asphaltene surface can be calculated for each bond i on the molecules from31

Si ) 〈1/2 (3 cos 2θi - 1)〉

(7)

where θi is the angle between the bond i and the vector (29) White, C. M.; Schmidt, C. E. Fuel 1986, 66, 1030-1035. (30) Somasundaran, P.; Yu, X.; Krishnakumar, S. Colloids Surf. A 1998, 133, 125-133. (31) Karaborni, S.; Toxvaerd, S. J. Chem. Phys. 1992, 96, 55055515.



Figure 12. Distribution of the heavy atoms of headgroups along the normal to the surface.

normal (z axis) to the asphaltene surface. Order parameters can vary between 1 (full order along the normal to the surface) and -0.5 (full order perpendicular to the normal). A value of zero is an isotropic orientation. The bond-order parameters calculated for the headgroups of the ethoxylated amphiphiles indicate that the bonds are preferentially aligned with the asphaltene surface, showing that the headgroups are significantly tilted and in parallel alignment with the surface. The bond-order parameters of the benzene rings for the amphiphiles DP and DBSA also show parallel alignment with the asphaltene surface. On the other hand, the values of the bond-order parameters for the tail groups are very close to zero, which can be an indication of isotropic orientation. Figure 13 shows the final stage for one of these systems. The fraction of trans dihedral angles in the tails of the amphiphile molecules was calculated. These were 0.84 (DBSA), 0.82 (DP), 0.77 (DPE1), 0.81 (DPE2), 0.85 (DPE3), and 0.86 (DPE4). These results indicated a decrease in the gauche defects with the increase of the size of the polar head of the ethoxylated amphiphiles. The order parameters depend on two factors: orientation of the molecule and state of the internal dihedral angles. As can be seen, the fraction of trans dihedral angles in the tails are very high indicating that the main factor for the isotropic orientation of the bonds is the isotropic orientation of the chains. This can be associated to the large area occupied by each amphiphile (60 Å2) on the surface. Amphiphile Adsorption and Asphaltene Stabilization. Experimental evidence indicates that the activity of the amphiphiles as asphaltene stabilizers is related to the maximum amount of amphiphile adsorbed on the asphaltene surface.9 The larger the concentration of amphiphile at the asphaltene surface, the better the activity as asphaltene stabilizer of the amphiphile.9 This result confirms the relevance of a good steric barrier in the stabilization of asphaltenes particles. In the present work, the calculation of the distribution of atoms of the headgroups of ethoxylated phenol amphiphiles indicates that the increase of the size of the polar head produces an increase in the atomic density of the region near the asphaltene surface. The molecular simulations predict that the larger the headgroup of the amphiphile, the more densely packed are the atoms in this region and

Figure 13. System DPE2-asphaltene-n-heptane after the simulation.

the more efficient the steric barrier against flocculation. In fact, a recent study8 indicated that the inhibition capacity of a set of ethoxylated nonylphenol amphiphiles increases with the size of the ethoxylated chain. This behavior was attributed by the authors to a larger steric hindrance to the agglomeration of asphaltene particles due to the increase of the head size of the amphiphiles. The results obtained here seem to indicate a relationship between amphiphile layer structure and amphiphile effectiveness as asphaltene stabilizer. However, further work has to be done to establish the characteristics of the best stabilization layers and how these characteristics are affected by the nature of the asphaltenes. Conclusions The interaction energies involved in the adsorption process of the amphiphiles on the asphaltene surface depend on the dipole moment and also on the polarizability of the amphiphile. At low coverage, the characteristic adsorption energy calculated is mainly related to the dipole moment of the amphiphile. In contrast, the characteristic adsorption energies calculated at high coverage seem to be mainly related to the polarizability of the amphiphile. At low coverage, all the amphiphiles studied lie parallel to the asphaltene surface, except DBSA, which stands perpendicular to the surface. At high coverage, the structural studies revealed a different orientation: the amphiphiles have their heads lying parallel to the asphaltene surface and their tails extending isotropi-

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cally toward the n-heptane. The formation of hydrogen bonds between the adsorbed amphiphiles at high coverage indicates the incipient formation of hemimicelles of amphiphiles on the asphaltene surface. The predominance of the interaction amphiphile-amphiphile over the interaction amphiphile-asphaltene and amphiphilen-heptane also supports the mechanism that suggests the formation of micelles of amphiphiles on the surface as the second step of the adsorption. An increase in the density of atoms near the asphaltene surface was found with the increase in the size of

Rogel and Leo´ n

the amphiphile’s head, which can be considered as an indication of a better steric barrier as the size of the headgroup increases and, as a consequence, of a better activity of the amphiphile as an asphaltene stabilizer. Acknowledgment. The authors are grateful for the support provided by CODICID Research Project “Study of the asphaltene precipitation and its effects on crude oil production”. EF000152F

Study of the Adsorption of Alkyl-Benzene-Derived Amphiphiles on an

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