Alteration of intermolecular interactions between units of asphaltene dimers exposed to an amide-enriched modifier

Abstract

Morphological features and structural characteristics of asphalt binders are strongly affected by factors such as “aging”, which can alter the performance of petroleum-based asphalt-binders. Bio-binder (BB), a newly-produced amide-enriched bio-adhesive obtained from bio-mass, has been found to be promising in reducing the negative effects that aging can have on molecular conformation. Doping of BB into a commonly used petroleum-based asphalt-binder creates a bio-modified binder (BMB) that has been proven experimentally to perform especially well at low temperatures. This improvement can be attributed to the effect of modifier fragments, which contain high concentrations of amide functional groups, on the π–π stacking of asphaltenes. In this paper, changes in the stacking behavior of asphaltene units are investigated in the presence of hexadecanamide, a representative amide-type additive. Molecular Dynamics (MD) simulations and experiments using high-resolution transmission electron microscopy (HRTEM) and X-ray powder diffraction (XRD) support our results obtained from rigorous quantum mechanical calculations through a high quantum level of DFT-D approach. Based on this multi-scale bottom-up study, interaction of the amide-type bio-binder (amide-BB) with asphaltenes disturbs the uniformity of the π density throughout the aromatic region and creates some polarization in this region. This alteration of the π system over the aromatic zone disturbs the eventual π–π interactions between asphaltene stacks that are known to be the main mechanism responsible for the formation of clusters at the nanoscale. Disturbing the π–π interactions alters the stacking distance, the corresponding binding energy, and ultimately the extent of clustering of asphaltene units. Any change in the clustering of asphaltene affects the rheology and morphological properties of asphalt, which in turn alters the asphalt's performance, including but not limited to its resistance to fatigue and low-temperature cracking.

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1. Introduction

“Asphalt”, as a road surface deposit, is a combination of compacted layers of mineral aggregates, air voids and a certain proportion of a binder which acts as a glue to adhere the different constituents of asphalt pavement materials. Bitumen, as the most well-known asphalt-binder, is a black viscoelastic, non-volatile, thermoplastic adhesive and waterproof material which is extracted through petroleum refining as a residue of vacuum distillation. The most popular classification of the bitumen (asphalt-binder) fractions is based on their solubility in paraffinic solvents such as n-heptane. Maltenes (separable into sub-fraction saturates, aromatics, and resins),^1,2 and asphaltenes³ are the two main fractions of bitumen.

Among the bitumen fractions, asphaltene has received more attention because of its role in controlling bitumen viscosity⁴ and in the formation of aggregates. At room temperature, pure asphaltene is a black powder² that is known to be mainly responsible for the black color of bitumen. Asphaltenes form colloidal suspensions in crude oil, bitumen, and aromatic solvents like toluene.^5–8 and precipitate in light paraffinic solvents like n-heptane. The deleterious effects of asphaltenes in the refining, producing, and transporting of heavy oils^9–13 requires thorough characterization of asphaltene aggregation and investigation of the environmental factors affecting it.

Chemical aging is one of the environmental factors that strongly affects the chemistry as well as the physics of bitumen such as asphaltene aggregation and viscosity of bitumen.^9,14–17 Change of viscosity due to oxidative aging has two different kinetics at low- and high-temperature regimes, mostly attributed to the dispersibility of aggregations. At low temperature, the aggregation of asphaltenes is strong, which reduces or prevents oxygen diffusion inside the aggregates and consequently quenches oxidation. At high temperature, there is better dispersion of aggregates in the medium, so oxygen and oxygen-carriers can diffuse more readily into the intermolecular spaces and eventually accelerate oxidation.¹⁸ Some additives may increase the resistance of molecular aggregates against oxidation and chemical aging, and thus improve the performance of petroleum-asphalt binders to meet performance specifications.

Modifiers are additives that can alter the macroscopic properties of asphalt-binders and improve the bituminous characteristics by influencing the fragment agglomeration and change of nanoaggregate size. Asphalt-binder modifiers are usually categorized into different subtypes such as fibers, fillers, polymers, and hydrocarbons containing specific functional groups.¹⁹

“Bio-binder” (BB), a bio-based modifier, is a promising renewable asphalt-binder alternative due to the high compatibility of its chemical and rheological properties with those of petroleum-based binder.²⁰ Bio-additives have been applied as partial replacements for asphalt-binder or as direct alternative binders.²¹ A partial replacement of asphalt-binder with bio-based modifiers in bitumen creates bio-modified binders (BMBs), which can improve rheological characteristics and enhance workability and wettability, with consequent environmental benefits and cost savings.¹⁶ For example, the incorporation of bio-binder can reduce asphalt-binder viscosity, leading to decreases in mixing and compaction temperatures, and consequently reducing energy consumption and volatile emissions. Allowing application at lower temperatures during pavement production can reduce oxidative aging of the asphalt, improving its durability.^22–24

Bio-additives and their impact as modifiers on petroleum-based asphalt-binder have been the subject of extensive research. Bio-additives from waste cooking oil and waste wood have been applied as modifiers to enhance the thermal cracking resistance of base binder,²⁵ to rejuvenate aged asphalt-binders,²⁶ and to improve the fatigue performance of petroleum-based asphalt.²⁷

Park et al.²⁸ reported that hydrocarbons can enhance asphalt-binder's resistance against fatigue cracking, which aligns with results of our previous studies.²⁹ Bio-binder (BB), our proposed bio-based modifier from swine manure,²⁰ appears to soften a petroleum-based binder and improve low-temperature properties, while also lowering binder viscosity,²⁹ which is consistent with the findings of Mills-Beale et al.³⁰ A comparative study tracking the changes in chemical and rheological properties has shown that asphalt binder modified by BB from swine manure is less susceptible to oxidative aging.³¹ In addition, mixing BB with crumb rubber and asphalt binder to produce bio-modified rubber (BMR), Fini et al. showed that the presence of BB in rubberized asphalt-binder can facilitate rubber dissolution while reducing shear susceptibility of the blend.^32,33

Elemental analysis of bio-products derived from different bio-waste materials like microalgae,^34–36 swine manure,²⁰ or bovine bones³⁷ shows traces of amide compounds in these natural modifiers. Amide-based additives have always been good candidates to improve the performance of asphalt-binder.

The use of amide additives to prevent fracture and crack formation during a sol–gel conversion process dates back to more than thirty years ago.^38,39 The introduction of (poly) amides as “low-temperature binders”⁴⁰ (additives which lower the mixing or coating temperature of asphalt compared to that of the conventional materials) vividly shows the importance of amides as efficient binders. Amidoamine soaps have also been used extensively as anti-stripping agents in bituminous paving compositions.^41–44 The chemical structure of the amide additives and the degree of asphaltene dispersion are two main factors impacting the overall performance of the amide-based anti-stripping additives.⁴⁵ One common belief about the role of amide components in BBs is the ability of amides to reduce and delay the aggregation of asphaltene molecules.⁴⁶

It should be noted that the inherent complexity of petroleum-based asphalt-binders poses a major obstacle to offering a complete interpretation of the interaction effects between amide and asphalt-binder molecules. A justified interpretation of the behavior of amides (as a constituent of a bio-additive or an independent additive) within an asphaltene matrix requires a systematic study of the chemical and structural factors governing the behavior of this group of organic additives. Thus, a molecular-level understanding of the aforementioned interactions that underlie the macroscopic properties of asphalt-binder is crucial for defining a structure–function relationship for these building materials. To this end, it is useful to develop a multi-scale bottom-up approach for these materials, going from the molecular level of nanoaggregates to the formation of clusters, then bulk macroscopic structures. The contribution of this study is to start at the fundamental scale by performing DFT calculations on model systems that capture the essential asphalt–amide interactions at the molecular level. We also perform MD simulations that model the influence of target amides on the nanoaggregates of asphaltenes, and we conduct a series of experiments using high-resolution transmission electron microscopy (HRTEM) and X-ray diffraction (XRD) to further evaluate the aforementioned effects in a real laboratory setting.

2. Computation and experiment details

2.1. DFT-based quantum mechanical calculations

Geometry optimization was carried out through a high quantum level of DFT-D approach implemented in the DMol³ module^47,48 of the Accelrys Materials Studio program package (version 6.0); this module provides speed in calculations and accuracy for large molecules. In addition, we used the Perdew–Burke–Ernzerhof (PBE) functional⁴⁹ with Grimme's long-range dispersion correction⁵⁰ (PBE-D). This combination could be efficient for large systems where dispersion forces are of general importance. To emphasize the importance of dispersion energy as a key factor in stabilizing the stacked dimers, conventional PBE functional (excluding dispersion interactions) was also examined. Comparing the results corresponding to PBE and PBE-D functionals indicates that ignoring the dispersion interactions is associated with the loss of a considerable portion of binding (interaction) energy between two interacting monomers; such that PBE-binding energy associated with the most stable conformer of asphaltene dimer is up to 48% lower than that obtained for the same geometrical structure computed with PBE-D functional (29.1 vs. 56.1 kcal mol⁻¹). This energy difference (27 kcal mol⁻¹) could be a rough estimation of the dispersion contribution to the stabilization energy of the structural dimer under study. Inadequate nature of conventional DFT compared to DFT-D approach to describe the stacked pairs especially those dominated by dispersion forces, has been also reported and discussed by other groups as well.^50–54 Therefore, we excluded this option from the remaining part of our analysis and continued with DFT-D approach and PBE-D functional.

“Fine grid” was selected for the numerical integration of the exchange–correlation functions and related matrix elements. The tolerances of energy, maximum force, and displacement convergence, respectively, were 1.0 × 10⁻⁵ hartree, 2.0 × 10⁻³ hartree Å⁻¹, and 5.0 × 10⁻³ Å. The basis sets selected were the double-numerical quality basis function with polarization function for H atoms (DNP), comparable with 6-31G** Gaussian basis, and its extended form TNP (triple-numerical quality basis function with polarization function), comparable with 6-311G** Gaussian basis. The DMol³ numerical frequency analysis was performed to ensure reaching the global minimum. For all interacting systems, the basis set superposition error (BSSE) was evaluated by means of the counterpoise method^55,56 to compensate for the overestimation of intermolecular interactions due to the superposition of basis sets when describing systems weakly bonded, such as ours.

The thermodynamic stability of associations (asphaltene–asphaltene or asphaltene–amide) is expressed through binding energy (E_bind). E_bind is the energy difference between the formed aggregate and its constituents when they are in their lowest energy state, as shown in eqn (1).

E_bind = E_aggregate − (∑E_components) (1)

To identify the intermolecular interactions through donor–acceptor interactions and probable charge delocalization, natural population analysis (NPA)⁵⁷ was carried out to describe the molecular charge distribution with our individual fragments.

The non-covalent interaction (NCI) technique introduced by Johnson et al.⁵⁸ has also been employed to localize and consequently characterize non-covalent interactions. The basis of this technique is tracing the changes of reduced density gradient (RDG) at low-density and low-gradient regions, and visualizing them as two-dimensional (2D-NCI) or three-dimensional isosurfaces of RDG plots (3D-NCI). The dimensionless RDG, (s), is measured from the density (ρ) and its first derivative (∇ρ), as shown in eqn (2).

The NCI method visualizes the surfaces of space where RDG is close to zero, comparable to quantum theory of atoms in molecules (QTAIM)^59,60 critical points with zero density gradient. One of the advantages of this method over QTAIM is identifying the weak intramolecular interactions that are not detectable by the AIM analyzer.⁶¹ Moreover, the NCI approach is insensitive to the computational method employed, especially for the weak interactions.⁵⁸ This characteristic led us to employ the Gaussian-type calculations near the DMol³ computational level to generate electron densities appropriate for NCI analysis.

Accordingly, optimized structures at the level of PBE-D/TNP using DMol³ code were employed to reproduce electron density by a method equivalent to that available in the Gaussian package,⁶² PBEPBE/6-311G**. Visualization of the gradient isosurfaces was made by the Visual Molecular Dynamics (VMD) program.⁶³

2.2. MD simulations

Beyond DFT calculations, we have also performed molecular dynamics (MD) simulations of asphaltene molecules stacking in the presence of hexadecanamide as a representative of the amide-BB. To build the model, Materials Design Software was utilized, and a 30 × 30 × 30 box was defined. LAMMPS MD code (Large-scale Atomic/Molecular Massively Parallel Simulator) was used for the MD simulations, and the polymer consistent force field plus (PCFF+) was chosen as the force field for this system. PCFF+ is an extension of the PCFF force field,⁶⁴ which is an all-atom force field shown to provide reliable parameters (density and cohesive energy) for hydrocarbon modeling.^65,66 In this study, each simulation was performed in a two-step procedure: an NVT ensemble followed by an NPT ensemble. The time step was selected to be 1 fs for all simulations, and the method used for controlling the temperature and pressure was a Nose–Hoover thermostat–barostat. Non-bonded terms were handled with a simple cutoff of 9.5 Å, and long-range van der Waals interactions were included via tail corrections. The system of asphaltene suspensions in solvents was initialized with a low average density (0.15 g ml⁻¹) in order to avoid molecular overlaps. Convergence of energy and density occurred relatively quickly, consistent with prior studies for light liquid solvents such as n-heptane or toluene.⁶⁷ To visualize the trajectories, 50 configurations were stored per simulation. In all cases, simulations were performed using orthogonal (cubic) simulation cells with periodic boundary conditions (PBC) applied in all three spatial directions. The energy minimization at constant volume was performed, with initializing velocities at 348 K to ensure a zero average velocity, and momentum for the box was obtained. This was followed by an annealing stage of 100 ps with a decrease in pressure from 1000 atm to 1 atm to accelerate convergence towards asphaltene density using a Nose–Hoover thermostat–barostat while applying temperatures ranging from 800 K to 348 K.⁶⁸

In the second stage, an NPT ensemble for 10 000 ps at 348 K and 1 atm was applied to track changes in stacking and aggregation. Analyses of comparable geometries within a simulation period and with different simulation time lengths were performed to ensure converged properties would be achieved. Sampling was almost similar to that of Headen et al.,⁶⁴ but at a slightly higher temperature.

2.3. Experiment details

In order to further examine the effect of bio-binder (BB) on the nanoaggregates of asphaltene molecules, we performed a series of experiments using high-resolution transmission electron microscopy (HRTEM) and X-ray powder diffraction (XRD). The X-ray diffraction spectra were obtained by a Rigaku D/Max-2200V-PC using monochromatic Cu Kα radiation at 40 kV and 40 mA. The scan range was 5 to 60° 2theta at a scan rate of 0.001° 2theta per second and detector count time of 5 seconds per step. The samples of bio-modified binder (BMB) containing 5% of BB (by weight of asphalt-binder) were cast into the XRD-cryo sample holder, annealed in the oven at 150 °C for 10 minutes, and air-cooled at ambient temperature (25 °C) for one hour.

The stacking distance between polycyclic aromatic rings was calculated based on Bragg's law (eqn (3)).^69,70

λ = 2d₀(hkl)sin(δ) (3)

where λ is the wavelength of the X-ray, δ is the scattering angle, d₀ is the stacking distance, and (hkl) are Miller indices. The size of nanoaggregate stacks can be estimated from the associated spectra using the Scherrer equation (eqn (4)).⁷¹

L = Kλ/β cos δ (4)

where L is the mean dimension of the nanoaggregate stacks perpendicular to the plane (hkl), K is the constant that varies from 0.8 to 0.98 depending on the crystalline shape, and β is the full width at half maximum (FWHM) in radians.

3. Results and discussion

3.1. Molecular structure of asphaltene and amide monomers

Despite considerable uncertainty on some asphaltene molecular indicators (e.g., molecular weight, number of fused aromatic rings, number of asphaltene stacks per micelle/nano-aggregate, or number of nano-aggregates in each asphaltene cluster), a general agreement exists on the nature of asphaltene entities as the heaviest, most polar, and most aromatic component of crude oil. Indeed, having fused aromatic rings is a characteristic feature of asphaltenes clearly differentiating them from other components of bitumen.

For the past decade, the molecular structure of asphaltene has been the subject of extensive investigation. Advances in asphaltene science have led to the introduction of molecular models of asphaltene with structures varying from “continental” to “archipelago”^72,73 and average molecular weight 600–700 g mol⁻¹ and upper mass limit near 1500 g mol.⁷⁴ The term “continental” refers to the structures of asphaltene, which encompass a single large aromatic center with several conjugated rings. There is no unified aromatic center in an “archipelago” conformer, which contains two or more separate polyaromatic hydrocarbons (PAHs) linked by aliphatic chains. There is an active debate on the contribution and prevalence of different conformations in crude oil/bitumen. While Mullins^75–78 and some others^74,79–83 present evidence for a high predominance of island structures (island refers to small continental structures with 4–10 fused aromatic rings, with a centroid of the distribution around 7, and molecular weight with the centroid of distribution ∼750 g mol⁻¹ and with the full width half maximum 500–1000 g mol⁻¹)^74,78 in crude oil/bitumen.

Herod et al. theorize that the priority and extent of one structure compared to others depends on the nature and source of the crude oil.⁸⁴ To demonstrate this, Herod et al. examined the fractions of asphaltenes extracted from Maya crude oil (Mexico), including both N-methyl-2-pyrrolidinone (NMP)-soluble and NMP-insoluble fractions. While the NMP-soluble fraction of asphaltenes showed evidence of archipelago structures, a higher proportion of continental structures was found in the NMP-insoluble fraction.⁷³ There is also evidence that thermal cracking reactions can lead to the formation of asphaltene molecules with the “archipelago” structural motif.^85,86

The typical island structure employed in this study is based on the “Yen-Mullins”^77,78,87 molecular model, as shown in Fig. 1. The asphaltene–thiophene (one sulfur atom is located in a thiophene ring), shown in Fig. 1, takes advantage of small modifications employed by Greenfield and Li,⁸⁸ who rearranged some aliphatic chains of the Yen-Mullins model to reduce the pentane effect⁸⁹ (or the effect of cove region introduced by Ruiz-Morales)⁸² and its corresponding high internal energy.

Fig. 1 Asphaltene and hexadecanamide molecular structures.

As stated, amide derivatives are among the main components of the bio-products extracted from certain bio-mass, including but not limited to swine manure²⁰ and microalgae.^34–36 Amide derivatives can perform their role as a modifier not only as a constituent in a bio-product but also as an independent additive. Hexadecanamide (palmitic amide, shown in Fig. 1), N-butyl octadecanamide, N-(3-methylbutyl)acetamide, and N-(2-phenylethyl)acetamide are examples of the amide-type components that exist in bio-binder and bio-crude samples.^20,34–36 Amides of a bituminous mixture are mostly formed from reacting a cyclic or branched amine with a fatty acid at high temperature. This assumption is further supported by an investigation done on the effect of temperature on composition of bio-crude oil, which showed that with increasing temperature, amide derivatives are increased and organic acids (fatty acids) are decreased.⁹⁰ It is worth noting that bio-crude oil or bio-oil is a typical synthetic oil produced from biomass, which can be an alternative sustainable fuel for crude oil and petroleum.

In the present study, hexadecanamide (palmitic amide) was selected as the target amide molecule to investigate the interaction between an amide-type additive and an asphaltene molecule. The reaction of palmitic acid, which is abundant in liquefaction mixtures, and ammonia, would be a possible pathway for formation of palmitic amide molecule in bio-products.

It should be noted that the term “amide” refers to an amide functional group (–CO–NRR′) as well as a class of organic compounds containing this functional group. The presence of C=O and N–H dipoles and the corresponding electron delocalization, as shown in Fig. 2, allow amide derivatives to participate in H-binding interactions in protic solvents, with oxygen as H-acceptor and nitrogen as H-donor.

Fig. 2 Electron delocalization in an amide functional group.

An amide functional group is also known to be planar; i.e., the molecular plane contains the amino group and the oxygen. This planarity is a consequence of the electron delocalization of nitrogen's lonely pair (Fig. 2). This resonance brings a partial double bond between the carbon of the carbonyl group and the nitrogen, which leads to sp² hybridization for the N atom and ultimately the planarity of the amide functional group.

3.2. Asphaltene–amide interaction

Diversity in the possible orientations of an amide molecule toward an asphaltene plane is a significant challenge, requiring us to find the most effective interactions between two fragments. To sketch the structural models with the best orientations possible requires consideration of factors like the position of the amide functional group relative to the fused rings and the sulfur atom, as well as the steric hindrance of the peripheral chains of amide and asphaltene.

Fig. 3 shows four possible pathways for an effective interaction between amide and asphaltene (in Fig. 3, some parts of the side branches are truncated solely for visualization purposes, to present a clear picture of orientations.). These are the orientation priorities of the amide functional group shown in Fig. 3: (a) oxygen is facing the asphaltene plane, (b) nitrogen is close to the asphaltene plane, (c) the molecular plane of the amide group is parallel to the asphaltene plane and close to the sulfur atom, and (d) the molecular plane of the amide group is parallel to the asphaltene plane and far from the sulfur atom.

Fig. 3 Four possible pathways for an effective interaction between amide and asphaltene monomer: (a) oxygen is close to the asphaltene plane, (b) nitrogen is close to the asphaltene plane, (c) the molecular plane of the amide group is parallel to the asphaltene plane and close to the sulfur atom, and (d) the molecular plane of the amide group is parallel to the asphaltene plane and far from the sulfur atom.

The proposed initial structures were fully optimized at the PBE-D/TNP level (TNP numerical basis set is comparable with 6-311G**), leaving the structure free to relax during the optimization. Based on PBE-D/TNP outputs, shown in Table 1, the most stable conformation is the d structure, in which the molecular plane of the amide group is placed in a near-parallel position; the least stable conformation is the a structure, in which the amide group is in a vertical orientation with respect to the asphaltene plane. The BSSE-corrected binding energies for the aforementioned structures are −22.6 and −18.4 kcal mol⁻¹, respectively. The two other conformations have energies in between and are almost isoenergetic with energies of −20.8 and −20.3 kcal mol⁻¹ (not tabulated).

Table 1 The most and the least stable conformations arising from the interaction of hexadecanamide and asphaltene monomer. The structures have been optimized at the PBE-D/TNP level (comparable with 6-311G**)

Ebind: −22.6 kcal mol^−1	Ebind: −18.4 kcal mol^−1

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To analyze and interpret the interactions between amide and asphaltene monomers, a peer electronic analysis on asphaltene–amide structures is required. In addition, an overview of the structural behavior of the two fragments and the quality of their arrangement provides valuable information. Accordingly, our structural study shows that these are the two main factors contributing to the propensity of the individual amide molecule toward the asphaltene plane: (1) the orientation of the amide head (amide functional group), and (2) the part of the amide frame (the long chain of the CH₂ group) exposed to the aromatic region of the asphaltene.

Based on the structural evidence and energy values, those structures at which the plane of the amide functional group is parallel or near-parallel to the asphaltene plane are thermodynamically more stable than structures at which the amide functional group is oriented vertically (Table 1). This suggests a possible π–π interaction between the π-delocalized electrons of the amide and asphaltene fused rings. Indeed, a parallel orientation of the molecular plane of the amide functional group with the aromatic zone of the asphaltene plane enhances the possibility of constructive interaction between the π-orbitals of the two fragments. Additionally, our calculations show that the highest and lowest molecular orbitals (HOMOs and LUMOs) of hexadecanamide are centered on the amide functional group, as shown in Fig. 4. Localization of active frontier orbitals on the amide functional group highlights the role of the amide head in the formation of an asphaltene–amide complex. This evidence in favor of the amide functional group might lead to the assumption that the interaction in the system would be carried out mainly through the amide functional group, but our next findings do not corroborate this assumption.

Fig. 4 (a) Highest occupied molecular orbital (HOMO) and (b) lowest unoccupied molecules orbital (LUMO) of hexadecanamide.

To gain more insight into the performance of the amide head relative to its frame (the long chain of the CH₂ group), BSSE-corrected binding energies for two optimized structures of asphaltene–hexadecanamide and asphaltene–acetamide are compared, as indicated in Table 2. Acetamide could be a truncated form of hexadecanamide (removing the long chain of the CH₂ group). Comparing energy values shows that about 44% of the stability of asphaltene–hexadecanamide is due to its alkyl chain, such that removing the amide frame (the long chain of the CH₂ group) destabilizes the compound 11.5 kcal mol⁻¹, emphasizing the prominent role of the amide frame in addition to the amide functional group.

Table 2 Investigating the effect of the amide frame (the long chain of the CH₂ group) on stability of the compounds through comparing BSSE-corrected binding energies of asphaltene–acetamide and asphaltene–hexadecanamide compounds. Both structures have been optimized at PBE-D/TNP level (TNP is comparable to 6-311G*), and energies are in kcal mol⁻¹

Ebind: −8.8	Ebind: −20.3

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Our calculations show that the best performance of the amide molecule is achieved when the maximum overlap occurs between the amide –CH₂– sequence and the aromatic zone of the asphaltene molecule. Electrostatic considerations relating to CH–π interactions involving the hydrocarbonic group and the polarized π system could be of particular importance. In contrast to the attractive forces, steric repulsion between the amide tail and aliphatic side-chains of the asphaltene molecule cause many destabilizing interactions for an amide–asphaltene structure.

3.3. Analysis of the electronic structure

To validate the assumptions described above, and to characterize the nature of interaction between two interacting fragments, the electronic structure will be analyzed further. For this analysis, three approaches are employed: natural population analysis, electrostatic potential, and non-covalent interaction.

Natural population analysis (NPA). Charge transfer interactions between electron-donor and electron-accepter orbitals of two components are common stabilizing forces to assemble non-covalent supermolecular structures. Such interactions have been introduced as a driving force in the formation of alternate aromatic stacking and self-assembly of some π-systems. However, our recent studies on self-association of asphaltene molecules (not documented) and some other reports⁹¹ show that this factor (charge transfer) is less influential compared to other stabilizing factors.

In the case of asphaltene–amide, the presence of carbonyl and amine groups (CO and NH₂) motivated us to investigate the amount of charge likely transferred between the two components. To this end, we employed natural population analysis to quantify the charge distributed over the atoms. Our results show that the charge exchanged between the two fragments is almost zero: asphaltene = +0.002e and amide-BB = −0.002e. This negligible amount of charge indicates that charge transfer interactions do not play a decisive role in the stability of the complex.

Electrostatic potential (ESP). The second stage in determining the effective forces in the formation of an asphaltene–amide complex is to analyze the distribution of electrostatic potential. ESP maps convey useful information about the charge distribution over the target molecule; ESP analysis has been widely used to identify electrophilic and nucleophilic sites and ultimately locate a proper way for an efficient interaction. In a typical map of ESP, regions with low electrostatic potential are characterized by the negative charge and shown in red color. Conversely, regions with high electrostatic potential, the positive charge, are shown with blue color.

Fig. 5a shows the color-filled surface maps of an asphaltene molecule in the presence of amide bio-binder. To better clarify the charge redistribution within the amide interaction, the ESP of the aromatic zone before and after interaction with amide has been illustrated in Fig. 5b and c.

Fig. 5 (a) Electrostatic potential surface (ESP) of asphaltene–hexadecanamide complex, generated at PBE/6-311G* level, scaled between −0.6 (red) to 37.7 (blue) kcal mol⁻¹. Red and blue colors signify the regions with charge accumulation and depletion, respectively. (b) and (c) For easier understanding of the effect of amide-BB, charge redistribution over the aromatic zone has been shown in the absence (b) and presence (c) of amide-BB. The regions directly underlying amide effects are marked with downward arrows.

The ESP map of the pristine truncated asphaltene (Fig. 5b) shows almost uniform distribution of low electrostatic potential (red) throughout the aromatic region, as expected for an electron-rich aromatic surface. This uniformity is disturbed (Fig. 5c) in the presence of an amide molecule. The disruption of the previously uniform electron distribution over the aromatic region is associated with the creation of some polarization in this region.

Non-covalent interaction (NCI). The nature of dominant interactions between the amide and the asphaltene plane can be well-described by the visual analysis of electron density and the corresponding reduced gradient; i.e., the reduced density gradient (RDG) embedded in an NCI approach, proposed by Johnson et al.⁵⁸ Additionally, RDG plots can qualitatively explain how a specific orientation of the amide chain toward the asphaltene plane affects the stability of the amide–asphaltene complex.

Two-dimensional RDG plots are mapped based on the electron density (ρ) vs. reduced density gradient . In these plots, regions with low density and low reduced gradient are assigned to the non-covalent interactions. Non-covalent interactions encompass a wide range of strong to weak interactions: electrostatic interactions, H-bonding, steric repulsion, and van der Waals interactions that contain weak London dispersion forces and relatively strong dipole–dipole forces.⁹²

RDG data of non-covalent interactions can also be observed in three-dimensional real space, which is a more commonly used approach for realizing the nature of non-covalent interactions. Accordingly, 3D-gradient-isosurfaces of two amide–asphaltene complexes at the maximum and minimum of thermodynamic stability (taken from Table 1) are shown in Fig. 6. In this figure, the surfaces correspond to s = 0.5 a.u. and are colored on a BGR (blue-green-red) scale ranging from −0.05 to 0.05 a.u. The red-, blue-, and green-filled RDG isosurfaces indicate the repulsive, attractive, and weak van der Waals interactions, respectively. Deeper color means the local electron density is high and interaction is stronger.

Fig. 6 NCI analysis of the interaction between amide bio-binder and asphaltene for two complexes with the maximum (I) and minimum (II) stability (taken from Table 1), corresponding to a proper and an improper amide orientation. NCI surfaces correspond to s = 0.5 a.u. and a BGR color scale of −0.05 < ρ < 0.05 a.u.

As inferred from Fig. 6, while the absence of blue pill-shaped and red cigar-shaped surfaces in the BGR coloring scheme is indicative of the absence of both effective H-bonding and steric crowding, van der Waals-type forces reveal themselves as green sheet-like extended forms shaded with light brown (referring to the low electron density) in this region.

In Fig. 6, in the more stable complex (I), the maximum overlap is between the amide frame (the long chain of the CH₂ group) and the asphaltene plane. In this arrangement, the alkyl chain of amide-BB is located nearly parallel to the asphaltene plane, the amide group has been twisted around a C–C bond, and –NH₂ has approached the aromatic core. In this proper orientation, the amide-BB frame involves multiple interactions with asphaltene and builds up a multicentric electron density in this region, leading to deeper greenish isosurfaces of van der Waals forces. More importantly, the consistent orientation of the amide head has made a significant contribution in settling of the amide-BB (hexadecanamide) on asphaltene through formation of a van der Waals bound complex.

In the less stable complex (II), the vertical arrangement of amide-BB toward the asphaltene plane undermines the constructive interactions and induces a weaker attractive interaction between the two fragments. In this arrangement, the spatially extended area describing the delocalized van der Waals interaction between amide-BB (its amide head and aliphatic tail) and the asphaltene core is shrunk to the smaller green isosurfaces, and binding energy is decreased by about 4 kcal mol⁻¹ compared to the previous structure (Table 2).

3.4. Asphaltene dimers and their interaction with amide-BB

To simulate the interaction between the amide-type additive and asphaltene nanoaggregates, asphaltene dimers were considered as a mimic of asphaltene association. Based on high-resolution transmission electron microscopy (HRTEM),^93,94 fluorescence depolarization,^75,95 MD simulation,⁶⁴ and recent experiments based on X-ray scattering (SANS and SAXS),⁹⁶ the size of asphaltene stacks is estimated to be about 1 nm (width) × 1 nm (height), mainly comprised of 2 or 3 individual asphaltene molecules. Steric repulsion of alkyl side-chains has been reported as the main obstacle to the formation of stacks beyond four asphaltenes.⁹⁷ There are also a few reports of greater size, ∼2 nm, with more stacks between 3 and 8,^78,98 but their validity is questioned by other research groups.⁹⁶ Therefore, the modeling of asphaltene nano-aggregates as stacks of two or three asphaltenes is well in line with the accepted view of asphaltene behavior in real systems.

To design asphaltene dimers, optimized monomers in the previous stage were employed as building units. The diversity of possible structures, due to the diversity of asphaltene sheet orientations, would be the first challenge in this step. The intermolecular orientations in our asphaltene model are mostly affected by two features: the presence of long aliphatic chains overhanging from the aromatic body, and the position of sulfur heteroatoms with respect to each other. In real systems, the orientation of sheets toward each other is also influenced by environmental and structural factors such as temperature, aromaticity, and distance between asphaltene sheets.⁹⁹

The irregularity of asphaltene aggregates suggests that they are not placed quite parallel or perpendicular. However, the dominant proposed configurations are: (1) parallel or face-to-face (π–π interaction), (2) parallel-displaced or offset (σ–σ interactions), (3) T-shaped or face-to-edge (π–σ interactions), and (4) T-shape or edge-to-edge (σ–σ interactions).^100–102

While a T-shape configuration has been reported as the favorable conformer for the simple π-stacking structures like a benzene dimer,^51,103–105 in the case of asphaltene, the parallel and the nearly parallel stacking models have been found to be the most stable conformers for aggregates.^106,107 The unwillingness of asphaltene molecules toward a T-conformer is mostly attributed to the steric repulsion between aliphatic side chains of two monomers.¹⁰⁸ In this respect, Ruiz-Morales and her co-worker examined a wide range of structural patterns of PAH, that represent the core of asphaltenes, 48 structures as monomer and 3264 as dimer, for two island and archipelago arrangements, and compared the stability of two architectures based on their HOMO–LUMO energy gap. They also suggested four probable arrangements for stack island systems (hexagonal, twisted hexagonal, parallel-displaced, and stager), and conclude that parallel displacement arrangements with identical monomers fall inside the experimental range of asphaltenes.

Accordingly, the four most likely arrangements were considered for the association of two asphaltene monomers: parallel, offset (parallel-displaced), diagonal, and mirror, as shown in Table 3. A diagonal structure has sulfur atoms located at opposite corners of a hypothetical rhombus. A mirror structure has a symmetrical plane and is approximately mirror-symmetric. A simplified front view of a diagonal structure and a top view of a mirror structure are shown beside their corresponding structures in Table 3, for easier understanding of them.

Table 3 Four most likely arrangements for asphaltene dimers and their corresponding binding energy (kcal mol⁻¹) and bonding distance (Å). Distances reported are vertical distance (d_ver) and optimum distance between two centers of asphaltene planes (d). Structures have been optimized at the PBE-D/DNP level

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The most probable orientation was determined using a DFT-D approach, implemented in the DMol³ code of Material Studios, at the level of PBE-D/DNP and without imposing any constraints. Optimized structures, relative energy (ΔE_tot) with respect to the lowest energy state, binding energy (E_bind), as the thermodynamic stability of the system, vertical distance between two asphaltene sheets (d_ver), and optimum distance between two centers of asphaltene sheets (d) are reported in Table 3. Relative energy (ΔE_tot) is defined as the energy difference between the most thermodynamically stable structure and subsequent structure.

Based on the energy information, the lowest energy structure is diagonal configuration in which two sulfur atoms are at the maximum distance from each other. The greater stability of this arrangement could be explained by the reduction of electrostatic potential between two sulfur atoms that possess more electron density, due to the electron-withdrawing nature of this element.

After identifying the most preferred arrangement for the two asphaltene planes, the most and the least stable asphaltene dimers, diagonal and offset, were selected for further investigation of their interactions with amide-BB (Table 3).

The diagonal dimer, with the smallest binding distance (d = 4.193 Å) and highly parallel planes, provides more favorable intermolecular π-stacking interaction. However, in the offset dimer, which is made by sliding asphaltene planes away from each other, some of the effective π–π interactions and van der Waals forces are lost, leading to an increase in binding distance (d = 5.394 Å) and decrease of binding energy from −56.1 to −51.5 kcal mol⁻¹. The behavior of amide-BB toward these two dimer structures is very interesting.

Our results show that the response of a diagonal dimer toward amide-BB is quite different from that of the offset dimer. As reported in Table 4, while the presence of amide-BB undermines the effective interactions in a diagonal dimer and causes a decrease of binding energy (from −56.1 to −54.5 kcal mol⁻¹) and an increase of binding distance (from 4.193 to 4.201 Å), the offset dimer shows more affinity for amide-BB. In other words, the binding energy of the offset dimer increases while its binding distance decreases. To further examine the latter observations, we studied different possible orientations for amide-BB with respect to the asphaltene dimers.

Table 4 The effect of amide-BB on the stacking behavior of asphaltene units in two cases; diagonal and offset dimers. Binding distance (Å) and counterpoise-corrected binding energy (kcal mol⁻¹) are compared

Amide-BB on diagonal asphaltene dimer
Ebind = −56.13	Ebind = −54.52
d = 4.193	d = 4.201

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Amide-BB on offset asphaltene dimer
Ebind = −51.51	Ebind = −52.24
d = 5.394	d = 5.350

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Undermining the π–π interactions in a diagonal dimer by amide-BB could be explained through the ESP map shown in Fig. 5b, which illustrates how the presence of amide-BB disturbs the uniformity of π-electron density and creates small polarization in the asphaltene aromatic region. The major contribution of this disruption is related to the multiple CH–π interactions between the CH₂ long chain of the amide frame and the aromatic zone of asphaltene. Any alteration of the π system will in turn change the π–π interactions between asphaltene molecules and consequently their aggregation. Examining different orientations of the amide-BB on the surface of asphaltene reveals that as the number of contacts between the –CH₂– sequence of the amide and the aromatic zone of asphaltene increases, the intermolecular interaction between asphaltene dimers decreases. This characteristic feature of the amide molecule with respect to its impact on an asphaltene dimer can explain some of the softening effect that BB imposes especially on aged asphalt-binder with a high degree of aggregation.^20,109 Accordingly, there seems to be a possibility that amide molecules make asphaltene molecules less prone to form large agglomerations. It is also worthy of note that ESP maps for dimers do not provide a clear and transparent picture of changes in electron density in asphaltene planes in presence of amide-BB. To further clarify this point, ESP map of an asphaltene dimer, in the presence and absence of amide-BB, is shown in Fig. 7.

Fig. 7 Comparing electrostatic potential surface (ESP) maps of asphaltene dimer in the absence and presence of amide-BB. As seen, disruption in electron density of asphaltene planes due to bio-binder is not detectable through these maps. Maps are generated at PBE/6-31G* level, scaled between −0.6 (red) to 37.7 (blue) kcal mol⁻¹. Red and blue colors signify the regions with charge accumulation and depletion, respectively.

In the case of an offset dimer, the situation is quite different. In this dimer, some part of the effective π–π interactions between asphaltene units is lost due to sliding the upper asphaltene plane away from the lower unit. Our results show that the interaction between asphaltene planes is reinforced in the presence of amide-BB, indicating that in this complex, the constructive role of the amide functional group is more pronounced than the destructive role of the amide frame. Since the long chain of the amide frame covers parts of the asphaltene plane, impeding their contact with the second asphaltene plane. There seems to be a possible π–π interaction between delocalized electrons of the amide functional group (–CO–NH₂) and the polycyclic aromatic system of the upper asphaltene unit. This in turn promotes intermolecular interactions, as reflected in an increase in total interaction energy of the system in the presence of amide-BB (Table 4).

Unsynchronized behaviors of amide molecules toward asphaltene stacks might draw a paradox pattern in mind as it comes to their effect on undermining the asphaltene stacks and/or reinforcing them. It should be emphasized that unlike the ideal conditions of a DFT gas-phase condition, in a real condition, the final behavior of any system is determined under an array of different factors and the target matrix constituents. The significance and dominating role of any factors/constituents can be reflected in the final material performance. Accordingly, to further investigate the effect of amide-BB on the stacking behavior of asphaltenes, an MD simulation approach and an experiment approach were employed.

3.5. MD simulations

Expanding on the fundamental insights derived from our aforementioned analysis conducted by a DFT approach in gas-phase, and to further study the stacking phenomenon, stacks of asphaltene dimers and trimers were exposed to the target amide-BB (hexadecanamide) via molecular dynamics (MD) simulations.^110,111

First, we studied interactions between the molecules in a vacuum to determine the extent of stacking; in a second stage, an explicit solvent was included, and two different systems with 86 molecules of toluene and 60 molecules of heptane were modeled. Table 5 shows results from these explicit-solvent simulations. While all systems show the occurrence of stacking, in the case of the solution with toluene and heptane, stacking occurred much later than in the no-solvent scenarios.

Table 5 Stacking distance in asphalt-binder and BMB

Description of binder used	Solvent type	Number of stacking planes	Stacking distance (Å)
Asphalt-binder	Heptane	3	4.169
	Toluene	2	3.869
Bio-modified binder	Heptane	3	3.997
	Toluene	2	3.394

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The π–π stacking distance is determined by measuring the distance between the mean planes of two parallel fused aromatic cores of asphaltenes (Fig. 8). The analysis of the stacking distance for asphaltene molecules dissolved in toluene showed that the stacking distance is reduced from 3.869 Å to 3.394 Å after being exposed to amide molecules. Similarly, the stacking distance in heptane goes from 4.169 Å to 3.997 Å after the inclusion of amide-BB. The overall shorter distance in the matrix dissolved in toluene compared to that of heptane can be attributed to the higher polarity index of toluene (2.4) compared to that of heptane (0.1), which makes toluene a stronger solvent for asphaltene. The higher polarity of toluene can better reduce the steric repulsions of alkane side chains in asphaltene molecules, facilitating closer stacking. Regardless of the solvent type, π–π stacking distance is reduced when amide groups are present. Note that the arrangement of the asphaltene unit sheets corresponds to the offset conformer introduced in prior sections of this paper. Accordingly, the same trend (reduction of stacking distance in stacked units) is observed in both the DFT and the MD approaches. This can be attributed to the alteration of electron distribution in the polycyclic aromatic system of the asphaltene molecules, as explained in detail above.

Fig. 8 MD simulation screenshot with BB (left) and without BB (right) in heptane with π–π stacking distance.

3.6. Stacking observations using high-resolution transmission electron microscopy (HRTEM)

To see if evidence from experiments supports the theoretical predictions, we investigated the effects of BB on asphaltene stacking with high-resolution transmission electron microscopy (HRTEM). HRTEM is especially effective at providing direct images of asphaltene nanoaggregate stacks in asphalt samples. It provides a stringent test for examining the extent of stacking in asphaltene with and without the presence of BB. To prepare homogenous specimens, a solution of asphalt-binder and toluene was placed in an ultrasonic bath with ultrasonic frequencies of >20 kHz for 20 min. A droplet of the solution was used to create freely suspended edges on a lacy carbon TEM grid. Each TEM grid was then air-dried before testing. For imaging in plane-view geometry, the substrate thickness had to be below ∼20 nm to acquire adequate image contrast from asphalt-binder samples. Accordingly, the concentration of BMB in toluene to create the required film thickness (using one droplet) was determined to be 20 mg ml⁻¹. Fig. 9 shows the lattice fringes from the planes. The spacing of the π–π stacking attributed to asphaltene in presence of BB was measured to be 0.35 nm, which is smaller than the typical spacing observed for polycyclic aromatic molecules with large numbers of rings, such as those in asphalt-binder structure.^104,112 It has been documented that the energy-minimized stacking distance for aromatic dimers decreases with the increase of system size,¹⁰³ and varies significantly between systems with and without alkane side chains. Indeed, in asphaltene molecules, steric repulsion competes with π-bond stacking to come to an energy-minimized stacking distance.¹⁰⁴ In the case of polycyclic fused aromatic rings in asphaltene (corresponding to the island model of asphaltene described earlier), which are shown to have seven rings on average, this distance has been reported to be approximately 0.37 nm.¹¹³ In the case of asphaltene in presence of BB, this distance was measured using HRTEM to be 0.35 nm (Fig. 9). It should be noted that the observed samples are basically a blend of asphalt-binder (containing 12.84% asphaltene, 39.9%, resin, 9.2% saturates and 39% aromatics)¹¹⁴ and amide-enriched bio-binder. This is in agreement with the findings from our DFT and MD simulations that show the π–π stacking distance of asphaltene molecules is reduced in the presence of amide-rich BB. Additionally, it supports that the interaction between BB and asphaltene molecules reduces the π–π stacking distance of the asphaltene molecules.

Fig. 9 HRTEM image of partially crystallized bio-modified binder at a concentration in toluene of 20 mg ml⁻¹.

3.7. Experiment observations using X-ray powder diffraction

Finally, to provide additional evidence from experiments for comparison with the previous experiments and theoretical results, asphalt-binder samples with and without BB were tested and analyzed using XRD. Fig. 10 shows the XRD profiles for asphalt-binder and BMB. A large peak around 20° is commonly attributed to stacking fringes. More specifically, the strong peaks at 18.73 and 22.61° for asphalt-binder correspond to stacking distances of 0.47 nm (without BB), and 0.39 nm (with BB), respectively. The change in the peak position is indicated with red arrows in Fig. 10, and reflects a 17% reduction in stacking distance of asphaltene due to the presence of BB. Fig. 10 also shows that with the introduction of BB, the peak width increases while the intensity decreases. This could be attributed to the reduction of asphaltene nanoaggregate stacking. Additionally, the full width half maximum (FWHM) was significantly increased when BB was present, indicating a smaller cluster size. Specifically, the FWHM was found to be 14.45 and 16.98 2theta for the asphalt-binder with and without the presence of BB, respectively. Therefore, using a constant value of 0.89 in eqn (4) (discussed in Section 2), the cluster size, which is defined as the total height of the asphaltene stack(s), was determined to be 1.1 nm and 0.9 nm for asphalt-binder with and without the presence of BB, respectively. Table 6 summarizes the changes in FWHM, stacking distance, 2θ, and cluster size.

Fig. 10 XRD results for asphalt-binder and bio-modified binder.

Table 6 Stacking distance and cluster size in asphalt-binder and BMB

Sample	FWHM (°)	Stacking distance (nm)	°2theta	Cluster size (nm)
Asphalt-binder	14.45	0.473	18.73	1.1
Bio-modified binder (BMB)	16.98	0.393	22.61	0.9

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4. Conclusions

It has been documented that stacking of asphaltene molecules affects the overall colloidal structure of asphalt-binder and consequently the associated physiochemical properties of this material. This paper used both modeling and experiments to investigate the stacking of asphaltene in the presence of bio-binder (BB), a newly developed bio-modifier that contains high amounts of amides.

Along a multi-scale bottom-up study, at the first stage, DFT calculations and multiple analysis methodologies (NPA, ESP, and NCI) were performed on model systems of asphaltene and hexadecanamide (to represent the bio-modifier) molecules to fully understand the fundamental nature of the interactions between the two fragments. The analysis of the DFT results showed that the stability of the asphaltene–amide complex is mainly affected by two factors: the orientation of the amide functional group (CO–NH₂), and that part of the amide frame (long chain of the CH₂ group) exposed to the aromatic region of the asphaltene.

With regard to the significance of the amide aliphatic group on the stability of the asphaltene–hexadecanamide complex, it was shown that more than 44% of the energy-stabilizing effect is related to the presence of the –CH₂– chain. Peer electronic analyses via NCI and ESP further showed that the consistent orientation of the amide functional group makes a significant contribution in settling of bio-binder (hexadecanamide) on asphaltene through formation of van der Waals bonds.

On the other hand, the amide-BB frame involves multiple interactions with asphaltene, building up a multicentric electron density in this region, which leads to deeper isosurfaces of van der Waals forces in the interacting zone.

ESP maps also show that interaction of amide-BB with asphaltene polarizes the charge distribution in the aromatic core of asphaltene; the charge distribution is almost uniform without amide-BB. This disruption of the aromaticity implies an alteration of the π system over the aromatic zone that will in turn disturb eventual π–π interactions between asphaltene stacks, which is the mechanism responsible for the formation of clusters at the nanoscale.

Disturbing the uniformity of π density affects the extent of change in binding distance and corresponding binding energy between the asphaltene units in asphaltene dimers/trimers. The positive or negative trends of these changes strongly depends on the orientation of the amide-BB as well as the arrangement of asphaltene units in an asphaltene dimer.

Building on our systematic studies and moving away from the ideal conditions of isolated molecules in gas-phase provided by our DFT approach, MD simulations in solvents and several laboratory experiments in real settings were performed on targeted molecules, in order to calculate stacking distance for asphaltene units exposed to amide-BB. Based on MD simulations, the asphaltene stacking distances in heptane were found to be 0.42 nm and 0.39 nm for asphaltene with and without presence of BB, respectively. This indicates a significant reduction in stacking distance as a result of exposure to amide-BB. The stacking distance of asphaltene molecules was found to be lower when toluene was used as the solvent instead of heptane. This could be attributed to the higher polarity index in toluene, which is 2.4, compared to that of heptane, which is 0.1. Higher polarity solvents can better reduce steric repulsions of asphaltene side chains, facilitating closer stacking.

The results of experiments using HRTEM and XRD were found to be well in agreement with both our DFT and MD simulation analyses. It was experimentally observed that the modification with BB resulted in lower stacking distance while reducing cluster size. The stacking distance of asphaltenes measured by HRTEM was significantly reduced in the presence of BB (measured to be 0.35 nm) compared to that of asphalt-binder without BB (0.37 nm). Also, the peak in the XRD spectra in the presence of BB appeared at a higher 2theta angle, which indicates a lower stacking distance compared to the control asphalt-binder. In addition, the full width half maximum (FWHM) was significantly increased in the presence of BB, indicating a smaller cluster size.

The exact mechanism of interaction between asphaltenes, when a complete description of the chemical structure is considered and when all the molecular species are involved, still needs to be clearly determined. Further study on the effects of alkane substitution and heteroatoms on long-range order are currently underway, and are expected to provide further understanding of the extent of the disturbance of stacking in asphaltenes due to the presence of amide groups.

Acknowledgements

This research was sponsored by National Science Foundation (Awards No. 1546921 and 1150695). The contents of this paper reflect the view of the authors, who are responsible for the facts and the accuracy of the data presented. This paper does not constitute a standard, specification, or regulation.¹¹⁵

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