Influence of Asphaltenes in the Properties of Liquid–Liquid Interface

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Article Cite This: ACS Omega 2018, 3, 3851−3856

Influence of Asphaltenes in the Properties of Liquid−Liquid Interface between Water and Linear Saturated Hydrocarbons Dheiver Santos,*,† Walisson Souza,‡ Cesar Santana,§ Everton Lourenço,§ Alexandre Santos,∥ and Márcio Nele⊥ †

Centro Universitário Tiradentes, Av. Comendador Gustavo Paiva, 5017Cruz das Almas, Maceió, Alagoas 57038-00, Brazil Faculdade Pio Décimo, Campus III. Av. Pres. Tancredo Neves, 5655Jabutiana, Aracaju, Sergipe 49075-010, Brazil § Núcleo de Estudos em Sistemas Coloidais, Instituto de Tecnologia e Pesquisa, PEP/UNIT, Aracaju, Sergipe 49032-490, Brazil ∥ Universidade Federal do Paraná, Rua Coronel Francisco Heráclito dos Santos, 210Jardim das Americas, Curitiba, Paraná 82590-300, Brazil ⊥ Escola de Química, Universidade Federal do Rio de Janeiro, Cidade Universitária, Rio de Janeiro, 49032-490 Sergipe, Brazil ‡

S Supporting Information *

ABSTRACT: Molecular dynamics simulations have been performed on the interface between linear saturated hydrocarbons and water in the presence of an asphaltene molecule by measuring the properties such as mean square displacement, radial distribution function, density profile using ave/spatial command, and interfacial tension (IFT) by OPLS and TIP3P FF (force fields). The box of simulation contained one particle of asphaltene, 100 linear saturated hydrocarbons molecules, and 300 water molecules in mixture with interfacial appropriate positioning. The main results show that a small amount of asphaltene in the interface does not significantly alter the data of IFT and that the aliphatic and aromatic groups have preferred orientation.

1. INTRODUCTION

proposed the use of MD tools for understanding the conditions of the asphaltene in petroleum system models. It is important to note that these studies were useful for understanding the conditions of stability of oil/water emulsion systems. Mikami et al.4 observed the interfacial rheology5−7 performance of asphaltene molecules in the oil/water interface using MD simulations. It was found that asphaltene is preferentially transmitted in the oily phase (toluene), whereas they accumulate in oil/water interface to pure heptane. The authors also found that the interfacial tension (IFT)8,9 system containing few asphaltene molecules is next to a system of heptane/pure water. Ruiz-Morales and Mullins10 verified that the asphaltene molecules remain in oil/water interface with the preferential orientation, where the aromatic region lies in the hydrocarbon− water interface plane, although the aliphatic chains are perpendicular to the hydrocarbon−water interface. The authors

1

Molecular modeling studies of asphaltene are important because with them it is possible to relate important molecular properties such as structure factors and physicochemical properties such as molecular electronic structure, density, viscosity, and principally the friccohesity2 property to be related with dipole momentum values. With this tool, it becomes possible to develop algorithms capable of calculating a specific molecular structure and predict the properties of these molecules in different solvents and different temperature and pressure conditions. Headen et al.3 worked with asphaltene in combination with toluene or heptane using the molecular dynamics (MD) technique. At large, it was detected that asphaltene forms both dimers and trimers in toluene as in heptane, that is, aggregates. The authors observed that the aggregates hold longer in heptane than in toluene. The stability study of concentrated emulsions of water in oil is imperative to provide a scientific approach to a major problem in the oil industry, helping to eliminate the empiricism present in the scientific community. Some studies have © 2018 American Chemical Society

Received: January 28, 2018 Accepted: March 23, 2018 Published: April 5, 2018 3851

DOI: 10.1021/acsomega.8b00102 ACS Omega 2018, 3, 3851−3856

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ACS Omega also clarify that the rigidity interfacial film must have a direct correlation with guidance as to the oil/water interface plans. The authors quoted above have contributed so far to the understanding of the accommodation process of asphaltene molecules at the interface. The literature needs to advance in other aspects to answer a series of problems, mainly, which are the substances that manage to destabilize the grouping of asphaltenes1 in the interface, favoring the rupture of the interfacial film. In this work, we have performed MD simulations to obtain information on the asphaltene influence in the interface, with the aid of computer tools to measure properties such as radial distribution function (RDF), mean square displacement (MSD), IFT, and density profile.

anywhere as per its interactive compatibility with either solvent, as shown in Table 1. Table 1. Values of the Averages and Uncertainty of the Properties of Molecular Simulations Obtained with Uncorrelated Data

2. RESULTS AND DISCUSSIONS This work provides new data from the molecular simulation of asphaltene, linear saturated hydrocarbons, and water. The results are related to the positioning of water molecules and hydrocarbon molecules, forming an interface with asphaltene, similar to systems of water-in-oil emulsions for rigidity and stability study of interfacial film. The initial configuration was properly positioned in such a way as to form an interface; the density profile data from the ternary mixture reporting the positioning of molecules along a few time steps, IFT for rigidity analysis of film with added asphaltene and without addition of asphaltene, RDF data for the analysis of preferential orientation of aromatic and aliphatic groups present in asphaltene molecules, and MSD data for diffusive process analysis are the main results these work (diffusion coefficients were obtained from an unweighted least-squares fit to the MSD). Figure 1 presents the initial system configuration of linearsaturated hydrocarbons−water−asphaltene. The data simula-

property

average

uncertainty

temperature (K) pressure (atm) potential energy (kcal/mol) kinetic energy (kcal/mol) density (g/cm3) enthalpy (kcal/mol per atom) molecular energy (kcal/mol) pairwise energy (kcal/mol) volume (Å3) pressure tensor pxx (atm) pressure tensor pyy (atm) pressure tensor pzz (atm) box lengths in lx (Å) box lengths in ly (Å) box lengths in lz (Å)

293.114 −59.762 5617.753 1768.401 0.356 7303.114 9235.338 −3617.585 95 277.111 −106.827 −78.289 5.829 36.251 36.251 72.502

0.041 159.760 581.032 0.246 552.048 553.523 89.708 141.011 124.627 214.334

Figure 2 shows profile density data in the system with water−hydrocarbon−asphaltene. The data in black, blue, and

Figure 1. Initial configuration for decane−water−asphaltene interface.

Figure 2. Density profiles for decane−water−asphaltene interface systems (black; decane, red; water, and blue; asphaltene).

tion of the positions of atoms can be found in the Supporting Information. The interface formation is one of the main factors for the analysis of configurational energy; in this work, the configurational energy is approximately equal to 5617.753 (kcal/mol), and these values have been obtained with a cutoff boundary of long-range interactions equal to 12 Å. These data show that simulations will be able to start properly without orbital overlap occurring.11 The system density data were close to 0.35 g/cm3. The results of density are obtained considering the simulation box dimensions, in this work, lx, ly, and lz were 36.25, 36.25, and 72.50 Å, respectively, and atom number 2025. It becomes a most interesting science that the configuration energy share is contributed by both the solvents and the third chemical substance, and hence experimental verifications are done with a survismeter device, which gives authentic data, where in real systems, asphaltene occupy freedom to approach

red are, respectively, of the decane molecules, asphaltene, and water. At the initial simulations and at the finished state, the permanence of the interface between water and linear saturated hydrocarbons is normally realized; substances with low chemical affinity and the asphaltene molecules are mostly positioned closest to the decane molecules. It is possible that the carbon chains of the asphaltene molecule must be with a special guidance for linear saturated hydrocarbon molecules. The van der Waals interactions of hydrocarbons (HC−decane) are dominated, and the polar groups such as nitrogen, oxygen, and sulfur are oriented toward the bulk water by dipole−dipole forces. Figure 3 shows a typical behavior analysis of IFT as a function of time, obtained by calculations of IFT obtained through MD simulations and experimental data. Therefore, the decrease in IFT systems cannot be explained by the diffusion of asphaltene molecules to the interface because there is possibly 3852

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ACS Omega

Figure 3. Results of MD simulations and experimental data of interfacial tension (mN/m).

Figure 4. RDF (g(r)) for decane−water−asphaltene. CH2 (decane)− SM (sulfur of asphaltene) in black and CH3 (decane)−SM (sulfur of the asphaltene) in red.

an asphaltene barrier that is fully connected to its selfaggregation. The figure presents the data obtained from a model system of water, decane, and asphaltene at 293 K. After the data reached the mechanical equilibrium, the IFT value, indicating that in these conditions, would tend to stabilize for long periods of time; this value would be for asphaltene molecules that migrated to the HC−water interface. The computational experiment duration was 107 ps corresponding according to the computer configuration used for 2 days; this time is considered the time of balance needed to obtain a set of IFTs. The values obtained during the simulations are on the same order of magnitude (∼45−60 mN/m) of the experiments using model system (HC + water) with IFT using the pendant drop method, as shown in Table 2, which gives the tests high-

information can be obtained also for CH3/SM pair that has the first layer with ∼6 A, the second layer of the pair CH3/SM is present in ∼10 A and the third layer of the pair CH3/SM in ∼11 A. These large distances can relate the geometry of linear decane molecules and the amount of asphaltene molecules (when the algorithm traverses the whole phase space, there would be a trouble in finding the grouping SM for possessing a single molecule in the system, unlike the CH3 and CH2 groups that have a reasonable amount; the RDF is defined as a local density). The results also show that the pair CH3/SM has a greater interaction because of the greater number of hydration layer of molecular solvation. Interaction data and RDF can help elucidate the interface position and asphaltene molecules polar groups orientation before the hydrocarbon−water pair, with these new information related to adsorption isotherms12 modeled using this information. Therefore, it can be concluded that the aromatic rings belonging to the asphaltene groups were oriented to the oil phase because they have multiple solvation layers in the CH3/SM−CH2/SM groups and small interaction distances. Further studies are necessary to support this affirmation. Figure 5 and Table 3 are, respectively, the mean-squared deviation of decane molecules, water, and asphaltene at 293 K

Table 2. Interfacial Tension Experimental Values at 296.65 K and 1600 sa Hexane + Water γ (mN/m) A/mm2 V/μL Heptane + Water γ (mN/m) A/mm2 V/μL Decane + Water γ (mN/m) A/mm2 V/μL a

average (1)

u (1)

average (2)

u (2)

49.21 50.14 34.41

0.12 0.02 0.02

49.23 50.14 34.42

0.12 0.02 0.01

49.94 48.66 32.67

0.08 0.03 0.03

49.93 48.66 32.68

0.09 0.01 0.01

43.76 45.5 30.14

0.74 0.05 0.04

43.87 42.89 27.52

0.62 0.02 0.02

Interfacial tension γ (mN/m). Uncertainty (u).

reliability computing in proceedings of interaction force fields (TIP3P (water), CHARMM, and OPLS (asphaltene) (decane)); another result that enhances the quality of the force fields used is the pure-component density values for water molecules (1.002 and 0.75 g/cm3) to decane,;these values were obtained at the simulations’ end through the mean of results obtained for different computational experiments. In Figure 4, the central atom CH2 of the HC interaction data was formed with sulfur of asphaltene (SM) atoms in each asphaltene molecule in the first hydration layer up to ∼7 A, the second layer of the pair CH2/SM is present in ∼11 A; this

Figure 5. MSD for decane (red)−water (black)−asphaltene (blue). 3853

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ACS Omega Table 3. Self-Diffusion Coefficients (10−10 m2/s) for Asphaltene Using Different Parts of the Slope of MSD(t) vs t (0−2000 ps) at Different Temperaturesa saturated hydrocarbons

283 K

Fobj

293 K

Fobj

303 K

Fobj

hexane heptane octane nonane decane

4.66 1.45 5.14 0.56 0.99

1.04 2.07 1.51 7.29 6.08

4.95 1.49 5.10 0.59 1.02

1.72 3.04 2.58 8.27 6.02

0.80 1.52 5.20 0.61 1.04

6.33 2.01 1.56 7.23 5.96

By analyzing saturated hydrocarbon effect on diffusion processes analysis, it has not been possible to conclude that the number increase of vacancies, that is, the use of small hydrocarbons would entail increased diffusion processes by having greater space contact atoms (vacancies). The MSD shows that decane molecules sweep areas larger than water molecules, and asphaltene molecules seem to prey on the interface forming a rigid film with the adsorption process (showing the chart a constant area).

a

Diffusion coefficients can be calculated directly in MD simulations by tracking the mean square displacement of the center of mass of asphaltene molecules as a function of time. The literature reports a relatively wide variation in the simulation results from 0.01 × 10−10 to 8 × 10−10 m2/s.30−32 Fobjobjective function values.

3. CONCLUSIONS The results generated with the Playmol package initial setup are very important for the studies of liquid−liquid interface. Density profile presents effectively the road traveled by the asphaltene molecules; it was expected that the asphaltene molecules have preference for decane molecules instead of water molecules, but it is important to note that during the stimulation study of time steps, the asphaltene molecules do not spread fully into the bulk-phase linear saturated hydrocarbons (oil phase); therefore, we can interpret this situation as the rigidity of the interfacial film is reinforced by the results of MSD that presents constant values for asphaltene molecules. Asphaltene molecules cannot sweep large areas that reinforce the theory of interfacial film stiffness another important result and that is precedent in the literature with Mikami et al.,4 which concerns the influence of IFT with asphaltene molecules and no asphaltene molecules; it seems that few asphaltene molecules affect very little, IFT that is, the IFT with asphaltene−linear saturated hydrocarbons−water molecules is very similar to IFT of linear saturated hydrocarbons−water mixture. The asphaltene molecules have small diffusion coefficient values (D ≈ 10−10 m2/s) because the adsorption mechanisms are not a diffusion-controlled type because of the high molecular weight of these compounds. These results are meant for studies of water/oil emulsion breaking.

and diffusion coefficient values of asphaltene molecules in the interface model of oil/water at various temperatures. For a liquid−liquid interface composed of asphaltene molecules, hydrocarbons, and water, it is expected that a decreased IFT with a rapid diffusion and a rapid process of asphaltene molecule adsorption in the formed interface is observed. This organization is independent of time and is increasingly used for molecules’ relaxation processes in the formed interface. An emulsified system and its stabilizing mechanism is attributed to the formation of mechanically strong and hard film or skin at the interface (O/W) which prevents a droplets union. The skin is the asphaltene molecules association resulting in the liquid− liquid interface and the multilayer formed (a kind of packaging process).13 Asphaltene molecules may not have a classical aggregation state in solution (CMC). Instead, they form nanoaggregates and clusters that are prone to reorganization and relaxation processes. However, the colloidal stability studies of asphaltene molecules in crude oil, when the system is not precipitated, prove that stability is related to the asphaltene molecules’ aggregation state; these asphaltene precipitations can be interpreted by physical forces, balance, mass, and the strength of cross-association interactions between asphaltene molecules and other substances in the system or other mixtures. In actual fact, consolidated asphaltene films around the droplets of emulsion do not coalesce after certain aging times. Obviously, adsorption kinetics and MD studies play a key role in the mechanical properties of films and an asphaltene adsorption with diffusion controlled at short times with individual molecules, transitioning possibly to a barrier-controlled regime in which larger aggregates are involved,14 all of which helps in understanding the interfacial phenomena system assisting in the area development. The asphaltene molecules have small diffusion coefficient values (D ≈ 10−10 m2/s) because adsorption mechanisms are not a diffusion-controlled type because of the high molecular weight of these compounds. This phenomenon has been described before and seems to be linked to the Gibbs− Marangoni surface effects, in which the molecular diffusion of surfactants between the bulk phase and interface plays a role during droplet oscillations.6,15 By analyzing the effect of temperature on the diffusion coefficient, the increasing temperature increases the diffusion coefficient; thus, more gaps can be observed (the concentration of vacancies is thermally activated) and more thermal energy will be available; therefore, the rate of atomic diffusion increases with temperature.16

4. METHODOLOGY 4.1. Molecular Simulation Protocol. The simulations were conducted with the assistance LAMMPS package.17 The initial structure for the mixture of linear saturated hydrocarbons + water + asphaltene was performed using the Playmol package18 that generates initial settings of any atoms and molecules in space, creating file system structures. These systems have assumed an interfacial initial structure between water and hydrocarbons molecules.19 The box of simulation contained one particle of asphaltene, 100 molecules of linear saturated hydrocarbons, and 300 molecules of water in mixture with appropriate interfacial positioning. These settings were used in MD simulations. Previously, the asphaltene molecules’ force field were obtained online using the SwissParam program; the water molecules used parameters TIP3P20 and, for linearsaturated hydrocarbons, OPLS.21 Playmol was used to define 3D space by optimizing the pairwise distances between atoms to avoid large van der Waals repulsive forces. The PACKMOL allows the user to define the distance constraint between atom pairs that are not to be disregarded. The package is written in FORTRAN and was developed by researchers at the ATOMS laboratory at UFRJ (Federal University of Rio de Janeiro). The package was modified to read the asphaltene molecules CHARMM,22 water molecules TIP3P,20 and linear saturated hydrocarbons OPLS.21 The file format, including the contained atom types, generates a 3854

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ACS Omega final system of molecules that meets the pairwise distance constraint and guarantees all molecules fit inside the userdefined MD cell. Playmol works with containing hundreds of atoms, but it does require equally vast hardware to accomplish such work. A random seed value can be used to generate multiple MD cells for MD study. The Playmol package input files were described in the Supporting Information. In short, LAMMPS (http://lammps.sandia.gov) integrates the motion equations of Newton for groups of atoms, molecules, or macroscopic particles that interact through forces of short or long range; for the integration of the equation of motion, LAMMPS also uses the Verlet algorithm,23 which are recomputed every few time steps (new velocities and new positions were obtained by integrating the motion equations). LAMMPS uses neighboring list atoms to give a better efficiency in their simulations and nearby particle monitoring. The ready for systems with particles that are repulsive to form short distances that the density is not affected in a significant way. LAMMPS was suggested as an MD simulation tool because of its robust collection capabilities. LAMMPS has integrated the support for MSD and RDF to study the movement of small atoms in interface systems. LAMMPS contains a deformation feature that allows the researcher to apply normal and shear strains to a system to calculate stresses in interface for the proposed study. The LAMMPS requires an ensemble associated with the boundary conditions imposed on the system under study. The commonly studied simulation of liquids in systems is under the canonical ensemble conditions, with temperature T, volume V, and N number of molecules (NVT). This work used the NVT ensemble to simulate mixtures of linear-saturated hydrocarbons + water + asphaltene, 1 ns integration time, temperature of 293 K, cutoff radius = 12 Å, and long-range interactions by means of Ewald algorithm.24 The Playmol input files were described in the Supporting Information. 4.2. Density Profile. The densities were calculated using the space command “fix/spatial” LAMMPS package, which summarizes the densities by atom and the averages for slices of a specified thickness along a specified axis. Along the z-axis, the structural change that the asphaltene molecule that turns away from the other axes x and y was chosen to observe. Figure 2 shows the general profile of mass density of linear saturated hydrocarbons + water + asphaltene. 4.3. Interfacial Tension. The interfacial rheology tension can be determined from the molecular dynamics.25−27 The interfacial rheology tension γ(t) is defined as γ (t ) =

∫ [pnn (n , t ) − ptt (n , t )]dn

4.4. Radial Distribution Function. The RDF28 is a probability distribution of definition an atom at a separation, r, from other atoms (this methodology has the utility to analyze the probability of separation between the atoms of interest). RDFs exist for both equilibrium and nonequilibrium systems. LAMMPS has a well-organized functionality to compute the RDF for a given cutoff distance radius. The RDF command is appealed with a compute command. The following example computes four RDFs, for 1-1, 1-2, 2-1, and 2-2 pairs. The 1-2 and 2-1 RDF should be identical (atom type). Example: compute RDF all RDF 100 1 1 1 2 2 1 2 2. 4.5. Mean Square Displacement. MSD29 is a quantity of the mean distance squared of a particle or an atom. It is defined as MSD(t ) = ⟨xi(t )2 ⟩ = ⟨(xi(t ) − xi(0))2 ⟩

where (xi(t) − xi(0))2 is the distance of particle i traveling over about time interval. ⟨...⟩ ensemble average is defined as the average of a quantity that is a function of the individual states of the system. If we consider all of the particles in the system, then we could write N

MSD(t ) =

(1)

■

(2)

γ=

∫

(5)

ASSOCIATED CONTENT

S Supporting Information *

In our situation, because the z-axis is perpendicular to the interfaces, eq 3 becomes ⎡ p (z , t ) + pyy (z , t ) ⎤ ⎢p (z , t ) − xx ⎥d z ⎢⎣ zz ⎥⎦ 2

1 ∑ ⟨xi(t )2 ⟩ N i=1

where N is the number of particles in the system. 4.6. Experimental Data of IFT. The IFTs (γ) were measured at 296.65 K using the automated Teclis Tracker (IT Concept, France) by axisymmetric interface profile analysis techniques. This work was made the measurement of interface tension such that pendant drops were in line with the optics and charge-coupled device camera as the instrument to obtain visualization on the computer screen (this equipment uses a software which has the resolution of equations of Young− Laplace). The linear saturated hydrocarbon samples were mixed with water in bulk. Syringe (10 μL) with an attached u-shaped needle was prefilled with the linear saturated hydrocarbons sample. The syringe was mounted on the syringe holder positioned above the cuvette that contained 25 mL of water phase. The syringe was dropped such that the needle was submerged in the cuvette’s water phase, and a 25 μL drop (interfacial area, A = 41 mm2) expelled the sample in the needle tip. The IFTs were instantaneously measured as a function of the drop aging time until near-equilibrium values reached likewise; dynamic IFT γ(t) versus time t for linear saturated hydrocarbons−water was measured. Currently, the new device which is most accurate and streamlines several variables, especially the pressure and temperature fluctuation, has been evolved, which produces most accurate results without interference of the experiential forces which induce transitions as the asphaltene has a larger number of pi conjugations.

where n is the axis normal to the interface, and hence pnn and ptt are normal and tangential constituents, respectively, of the pressure tensor, p. The integral must be carried out from the bulk location of one phase to that of another phase. The IFT γ can be considered by averaging γ(t) over the simulation time γ = ⟨γ(t )⟩

(4)

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.8b00102. Force field for all molecules of the studies and script for LAMMPS simulations (PDF)

(3) 3855

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(17) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (18) Abreu, C. Playmol. https://github.com/atoms-ufrj/playmol (accessed Jan 28, 2018). (19) Meybodi, M. K.; Daryasafar, A.; Karimi, M. Determination of Hydrocarbon-Water Interfacial Tension Using a New Empirical Correlation. Fluid Phase Equilib. 2016, 415, 42−50. (20) Mark, P.; Nilsson, L. Structure and Dynamics of the TIP3P, SPC, and SPC/E Water Models at 298 K. J. Phys. Chem. A 2001, 105, 9954−9960. (21) Siu, S. W. I.; Pluhackova, K.; Böckmann, R. A. Optimization of the OPLS-AA Force Field for Long Hydrocarbons. J. Chem. Theory Comput. 2012, 8, 1459−1470. (22) Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. CHARMM: A Program for Macromolecular Energy, Minimization, and Dynamics Calculations. J. Comput. Chem. 1983, 4, 187−217. (23) Grønbech-Jensen, N.; Farago, O. A Simple and Effective VerletType Algorithm for Simulating Langevin Dynamics. Mol. Phys. 2013, 111, 983−991. (24) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A Smooth Particle Mesh Ewald Method. J. Chem. Phys. 1995, 103, 8577−8593. (25) Goel, H.; Chandran, P. R.; Mitra, K.; Majumdar, S.; Ray, P. Estimation of Interfacial Tension for Immiscible and Partially Miscible Liquid Systems by Dissipative Particle Dynamics. Chem. Phys. Lett. 2014, 600, 62−67. (26) Smit, B.; Schlijper, A. G.; Rupert, L. A. M.; van Os, N. M. Effects of Chain Length of Surfactants on the Interfacial Tension: Molecular Dynamics Simulations and Experiments. J. Phys. Chem. 1990, 94, 6933−6935. (27) da Rocha, S. R. P.; Johnston, K. P.; Rossky, P. J. SurfactantModified CO 2 −Water Interface: A Molecular View. J. Phys. Chem. B 2002, 106, 13250−13261. (28) Kirkwood, J. G.; Boggs, E. M. The Radial Distribution Function in Liquids. J. Chem. Phys. 1942, 10, 394−402. (29) Gal, N.; Lechtman-Goldstein, D.; Weihs, D. Particle Tracking in Living Cells: A Review of the Mean Square Displacement Method and beyond. Rheol. Acta 2013, 52, 425−443. (30) Zhang, L.; Greenfield, M. L. Relaxation Time, Diffusion, and Viscosity Analysis of Model Asphalt Systems Using Molecular Simulation. J. Chem. Phys. 2007, 127, 194502. (31) Li, D. D.; Greenfield, M. L. Viscosity, Relaxation Time, and Dynamics within a Model Asphalt of Larger Molecules. J. Chem. Phys. 2014, 140, 034507. (32) Khabaz, F.; Khare, R. Glass Transition and Molecular Mobility in Styrene−Butadiene Rubber Modified Asphalt. J. Phys. Chem. B 2015, 119, 14261−14269.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], dheiver.santos@ gmail.com (D.S.). ORCID

Dheiver Santos: 0000-0002-8599-9436 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to the CNPQ [grant number 400309/ 2017-3], ATOMS laboratory at UFRJ (Federal University of Rio de Janeiro), and Sandia National Laboratories for their great service.

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REFERENCES

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DOI: 10.1021/acsomega.8b00102 ACS Omega 2018, 3, 3851−3856