Molecular Dynamics Simulation of Nanoparticle Self-Assembly at a

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Molecular Dynamics Simulation of Nanoparticle Self-Assembly at a Liquid-Liquid Interface Mingxiang Luo,† Oleg A. Mazyar,‡ Qing Zhu,† Mark W. Vaughn,† William L. Hase,‡ and Lenore L. Dai*,† Department of Chemical Engineering and Department of Chemistry and Biochemistry, Texas Tech UniVersity, Lubbock, Texas 79409 ReceiVed March 16, 2006. In Final Form: May 2, 2006 We have used molecular dynamics simulations to investigate the in situ self-assembly of modified hydrocarbon nanoparticles (mean diameter of 1.2 nm) at a water-trichloroethylene (TCE) interface. The nanoparticles were first distributed randomly in the water phase. The MD simulation shows the in situ formation of nanoparticle clusters and the migration of both single particles and clusters from the water phase to the trichloroethylene phase, possibly due to the hydrophobic nature of the nanoparticles. Eventually, the single nanoparticles or clusters equilibrate at the water-TCE interface, and the surrounding liquid molecules pack randomly when in contact with the nanoparticle surfaces. In addition, the simulations show that the water-TCE interfacial thickness analyzed from density profiles is influenced by the presence of nanoparticles either near or in contact with the interface but is independent of the number of nanoparticles present. The nanoparticles, water molecules, and TCE molecules all exhibit diffusion anisotropy.

1. Introduction Self-assembly of nanosized objects at liquid-liquid interfaces is important in natural and industrial applications. For example, self-assembled nanoparticles at a liquid-liquid interface serve as building blocks for bottom-up assembly of new functional materials with unique physical properties.1,2 Furthermore, there is growing interest in solid-stabilized emulsions that use solid nanoparticles or microparticles as emulsion stabilizers. For these systems, the self-assembly of solid particles at liquid-liquid interfaces is essential.3-12 However, the fundamentals of the self-assembly of nanoparticles at liquid-liquid interfaces are not fully explored. One of the remaining challenges is to understand multiphase interactions, self-assembly processes, and self-assembled structures of nanoparticles, especially when the size of the nanoparticles is comparable with the molecular dimension of the surrounding liquids. Recently, Dai et al.12 have reported the success of using solid-stabilized emulsions as a new experimental model system to investigate the detailed selfassembled structure of nanoparticles at a water-trichloroethylene (TCE) interface. This assembly was determined by use of an environmental transmission electron microscope (E-TEM). In sharp contrast to microparticles or large-size nanoparticles forming a monolayer at liquid-liquid interfaces, ultra small dodecanethiol* To whom correspondence should be addressed. † Department of Chemical Engineering. ‡ Department of Chemistry and Biochemistry. (1) Lin, Y.; Skaff, H.; Emrick, T.; Dinsmore, A. D.; Russell, T. P. Science 2003, 299, 226. (2) Lin, Y.; Skaff, H.; Bo¨ker, A.; Dinsmore, A. D.; Emrick, T.; Russell, T. P. J. Am. Chem. Soc. 2003, 125, 12690. (3) Stancik, E. J.; Fuller, G. G. Langmuir 2004, 20, 4805. (4) Melle, S.; Lask, M.; Fuller, G. G. Langmuir 2005, 21, 2158. (5) Xu, H.; Melle, S.; Golemanov, K.; Fuller, G. G. Langmuir 2005, 21, 10016. (6) Dinsmore, A. D.; Hsu, M. F.; Nikolaides, M. G.; Marquez, M.; Bausch, A. R.; Weitz, D. A. Science 2002, 298, 1006. (7) Horozov, T. S.; Aveyard, R.; Clint, J. H.; Neumann, B. Langmuir 2005, 21, 2330. (8) Kralchevsky, P. A.; Ivanov, I. B.; Ananthapadmanabhan, K. P.; Lips, A. Langmuir 2005, 21, 50. (9) Dickson, J. L.; Binks, B. P.; Johnston, K. P. Langmuir 2004, 20, 7976. (10) Saleh, N.; Sarbu, T.; Sirk, K.; Lowry, G. V.; Matyjaszewski, K.; Tilton, R. D, Langmuir 2005, 21, 9873. (11) Tarimala, S.; Dai, L. L. Langmuir 2004, 20, 3492. (12) Dai, L. L.; Sharma, R.; Wu, C. Y. Langmuir 2005, 21, 2641.

capped nanoparticles of 1-5 nm form randomly distributed multilayers at the water-TCE interfaces, with an interparticle distance varying from close contact to approximately 25 nm.12 This interesting result offers the first direct observation of nanoparticles in a liquid medium using E-TEM and opens new opportunities for high-resolution nanoparticle research involving liquids. However, the microscopy work is limited to probing the equilibrium structure, not the dynamic self-assembly process. In addition, the experimental images do not provide detailed information of interfacial properties such as the interfacial thickness or chemical composition. In this report, we present MD simulation results of a pure water-TCE interface as well as the in situ self-assembly of modified hydrocarbon nanoparticles with mean diameters of 1.2 nm at a water-TCE interface. Molecular dynamics simulation is a powerful tool for obtaining molecularly detailed information and the underlying physics of various systems, including liquid-liquid interfaces13 and liquidliquid interfaces containing surfactant molecules. For example, MD simulations have been successfully performed on watercarbon tetrachloride,14,15 water-octane,16 water-decane,17 waterdichloroethane,18,19 and water-dichloromethane20 interfaces. These simulations have provided molecular information that supplement experimental capabilities and have illuminated new underlying physics. Moreira and Skaf14 found a significant reduction of hydrogen bonds near the water-carbon tetrachloride interface and the dipole moments of water show preference of aligning along the interface. The work by Zhang et al.15 suggests there are inner and outer layers near the water-octane interface and that the water dipoles point in opposite directions at the different layers. Benjamin19 investigated the self-diffusion of liquid molecules at water-dichloroethane interfaces and found (13) Benjamin, I. Annu. ReV. Phys. Chem. 1997, 48, 407. (14) Senapati, S.; Berkowitz, M. L. Phys. ReV. Lett. 2001, 8717, 176101. (15) Moreira, N. H.; Skaf, M. S. Prog. Colloid Polym. Sci. 2004, 128, 81. (16) Zhang, Y. H.; Feller, S. E.; Brooks, B. R.; Pastor, R. W. J. Chem. Phys. 1995, 103, 10252. (17) Vanbuuren, A. R.; Marrink, S. J.; Berendsen, H. J. C. J. Phys. Chem. 1993, 97, 92062. (18) Fernandes, P. A.; Cordeiro, M. N. D. S.; Gomes, J. A. N. F. J. Mol. Struct. (THEOCHEM) 1999, 463, 151. (19) Benjamin, I. J. Chem. Phys. 1992, 97, 1432. (20) Dang, L. X. J. Chem. Phys. 1999, 110, 10113.

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that the diffusion of both water and dichloroethane molecules was faster parallel to the interface than perpendicular to it. The MD simulations have also been extended to liquid-liquid interfaces containing surfactant molecules. Recently, Rivera et al.21 simulated water-alkane systems containing methanol and reported the surfactant behavior of methanol; that is, methanol molecules adsorb preferably at the water-alkane interface and decrease the interfacial tension through molecular rearrangement. Schweighofer et al.22 observed inclination of the sodium dodecyl sulfate (SDS) anionic surfactant at water-carbon tetrachloride interfaces. The mixture of SDS with nonionic surfactants was simulated by Dominguez23 and the results showed that the interaction and charge distribution have significant effects on the location of surfactants. In contrast to the above studies, there is little work simulating the structure and dynamics of solid particles at liquid-liquid interfaces. More importantly, to the best of our knowledge, there is no existing work simulating the self-assembly process of nanoparticles at liquid-liquid interfaces. In this paper, we report the results of MD simulations investigating the in situ self-assembly of nanoparticles at liquid-liquid interfaces. We will address the following fundamental questions: If nanoparticles are initially distributed randomly in one of the bulk phases, what are their equilibrium locations? Does the presence of nanoparticles alter the thickness of an interface? What are the dynamics of nanoparticles at a liquid-liquid interface? 2. Methodology The MD simulations were performed using the GROMACS 3.2.1 package.24-27 The interaction parameters were computed using the GROMOS96 force field,28 with the intermolecular (nonbonded) potential represented as a sum of Lennard-Jones (LJ) force and pairwise Coulomb interaction and the long-range electrostatic force determined by the particle-mesh Ewald (PME) method.29,30 The velocity Verlet algorithm was used for the numerical integrations,31 and the initial atomic velocities were generated with a Maxwellian distribution at the given absolute temperature.32,33 Water was modeled using the single point charge (SPC) and extended single point charge (SPC/E) models.34,35 The structure and topology of trichloroethylene (TCE) was generated by the smallmolecule topology generator PRODRG.36 The spherical modified hydrocarbon nanoparticle (HCP, mean diameter of 1.2 nm) was (21) Rivera, J. L.; McCabe, C.; Cummings, P. T. Phys. ReV. E 2003, 67, 011603. (22) Schweighofer, K. J.; Essmann, U.; Berkowitz, M. J. Phys. Chem. B 1997, 101, 3793. (23) Dominguez, H. J. Phys. Chem. B 2002, 106, 5915. (24) Berendsen, H. J. C.; Vanderspoel, D.; Vandrunen, R. Comput. Phys. Commun. 1995, 91, 43. (25) Lindahl, E.; Hess, B.; Van der Spoel, D. J. Mol. Model. 2001, 7, 306. (26) Van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. J. Comput. Chem. 2005, 26, 1701. (27) Zhu, Q.; Vaughn, M. W. J. Phys. Chem. B 2005, 109, 19474. (28) Gunsteren van, W. F.; Billeter, S. R.; Eising, A. A.; Hu¨enberger, P. H.; Kru¨ger, P.; Mark, A. E.; Scott, W. R. P.; Tironi, I. G. Biomolecular Simulation: The GROMOS 96 Manual and User Guide; Switzerland, 1996. (29) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089. (30) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577. (31) William, C. S.; Hans, C. A.; Peter, H. B.; Wilson, K. R. J. Chem. Phys. 1982, 76, 637. (32) Kennard, E. H. Kinetic Theory of Gases; McGraw-Hill: New York, 1963; p 77. Fleagle, R. G.; Businger, J. A. An Introduction to Atmospheric Physics; Academic: New York, 1963; p 31. (33) Huang, K. Statistical Mechanics; Wiley: New York, 1963; p 72. Chapman, S.; Cowling, T. G. The Mathematical Theory of Non-Uniform Gases; Cambridge University Press: London 1953; p 72. (34) Berendsen, H. J. C.; Postma, J. P. M.; Gunsteren, W. F.; Hermans, J. Intermolecular Forces; Reidel: Dordrecht, 1981. (35) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (36) Schuttelkopf, A. W.; van Aalten, D. M. F. Acta Crystallogr., Sec. D: Biol. Crystallogr. 2004, 60, 1355.

Luo et al. Table 1. Composition of the Simulation Systems system

TCE (molecule)

water (molecule)

nanoparticle (particle)

time (ns)

runsa

A Bb C D

288 288 4500 4500

1491 1491 23 585 23 585

0 0 5 10

20 20 50 50

4 4 8 6

a Parallel runs start with different initial velocities from Maxwellian distribution. b System B used SPC/E water model, and systems A, C, and D used SPC for water model.

truncated from a diamond-like lattice made of carbon atoms that bonded in nonplanar hexagonal structure and, to increase the simulation efficiency, saturated with united CH, CH2, and CH3 atoms.37 We simulated four systems detailed as follows: Systems A and B were 20 ns simulations of pure water and TCE that employed SPC and SPC/E water models, respectively. Systems C and D were 50 ns simulations of SPC water and TCE containing 5 and 10 nanoparticles, respectively. Nanoparticles were added into the water phase at the beginning of the simulations for systems C and D. There were 5913 total atoms in systems A and B, and the initial size of the simulation box is 3.3 × 3.3 × 7.8 nm3. The initial size of the simulation box was 8.3 × 8.3 × 19.6 nm3 for systems C and D, and they contained 90570 and 94965 atoms, respectively, due to a difference in the number of nanoparticles. All systems lead to an initial density of 1.0 g/cm3 for water and 1.456 g/cm3 for TCE. After the construction of the simulation box, the energy was minimized using the steepest descent method with a cutoff of 10 Å for van der Waals and Coulomb forces. Simulations were performed using an NPT (constant number of molecules, constant pressure, and constant temperature) ensemble38 using the Berendsen thermostat39 with coupled temperature and pressure at 300 K and 1 bar, respectively. We used a cutoff of 9 Å for van der Waals interactions and the particle-mesh Ewald (PME) method for long-range electrostatics. Periodic boundary conditions were applied in all directions. The time step was 4 fs. The results were averaged from multiple parallel runs. Table 1 summarizes the systems simulated in this report.

3. Results and Discussion 3.1. Pure Liquid-Liquid System. The interfacial physical properties and structures from the simulation were characterized using the GROMACS analysis tools and visual molecular dynamics (VMD).40 Systems A and B, containing pure water and TCE, compare the effect of the water models (i.e., SPC or SPC/E) on the simulated physical properties. Figure 1a shows a snapshot of system A at the 20 ns conclusion of one simulation run. An overlay of the mass density profile of systems A and B is shown in Figure 1b. Density profiles are averaged over the last nanosecond of four parallel runs, obtained by dividing the entire simulation cell into 100 slabs (a slab thickness of 0.8 Å) parallel to the xy plane along the water-TCE interface. The simulated average mass density of water, for both the SPC model and the SPC/E model, is comparable to the well-accepted density of 0.997 g/cm3.14 For TCE, the simulated average mass density is lower than the expected value due to the expansion of the TCE simulation cell. The volume of the TCE simulation box expanded within the first 20 ps after the simulation started then remained relatively constant during the rest of the simulation. Our observation suggests that the GROMOS force field in the smallmolecule topology generator PRODRG36 may over-represent the repulsive potential, either in magnitude or range, of the TCE molecules. (37) Mazyar, O. A., Hase, W. L. J. Phys. Chem. A 2006, 110, 526. (38) Andersen, H. C. J. Chem. Phys. 1980, 72, 2384. (39) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684. (40) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33.

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Table 2. Physical Properties of Simulated Systems system

γ (mN/m)

d (Å)

Dtce (10-5 cm2/s)

Dwater (10-5 cm2/s)

DHCP (10-5 cm2/s)

A B C D

41.5 ( 0.2 48.5 ( 0.4 42.0 ( 0.4 41.9 ( 0.3

4.03 ( 0.18 3.76 ( 0.12 see Figure 7 see Figure 7

4.21 ( 0.27 3.91 ( 0.21 5.53 ( 0.21 5.39 ( 0.18

3.70 ( 0.23 2.50 ( 0.53 3.59 ( 0.17 3.52 ( 0.09

n/a n/a 0.78 ( 0.61 0.58 ( 0.38

Figure 1. (a) Snapshot of system A at 20 ns. Water and TCE molecules are represented in blue and green, respectively. (b) Mass densities of systems A and B. The influence of SPC and SPC/E water model is compared. The mass densities were averaged over the last 1 ns of four NPT simulations under different initial conditions, respectively.

Other structures and physical properties were calculated over the last 5 ns of the simulations and compared in Table 2. Listed here are interfacial tension (γ), interfacial thickness (d), and diffusion constant (D). The interfacial tension for a system with two interfaces is calculated using

γ)

〈(

)〉

pxx + pyy 1 L p 2 z zz 2

(1)

where pRR (R ) x, y, or z) is the RR element of the pressure tensor and Lz is the linear dimension of the simulation cell in the z direction perpendicular to the interfaces.16,21,34 The interfacial thickness was defined as the distance over which the TCE density drops from 90% to 10% of the bulk value.41 The self-diffusion coefficient DA of liquids is calculated by monitoring the mean square displacement as a function of time, using the Einstein relation42

lim〈|ri(t) - ri(0)|2〉 ) 6DAt tf∞

(2)

where ri(t) is the center of mass position of molecule i at time t. The diffusion constant of the liquids was deduced by taking the linear regression of the mean square displacement as a function of time. The surface/interfacial tension is an important factor in determining the adequacy of potentials for liquids.13 Here system A results in a lower interfacial tension and is close to the experimental value of 38.9 mN/m, measured in our laboratory for this study using a Kruss K100 tensiometer. Systems A and B have comparable interfacial thicknesses, on the order of several angstroms. This agrees with the consensus that water-organic liquids generally exhibit a molecularly sharp interface18,19,43,44 although specific values depend on the system and simulation. (41) Tieleman, D. P.; Berendsen, H. J. C. J. Chem. Phys. 1996, 105, 4871. (42) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquid; Oxford Science Publications: Oxford, 1987. (43) Michael, D.; Benjamin, I. J. Electroanal. Chem. 1998, 450, 335. (44) Meyer, M.; Mareschal, M.; Hayoun, M. J. Chem. Phys. 1988, 89, 1067.

Figure 2. Mean square displacement for all liquid molecules within the last 500 ps for systems A and B. (a) xyz direction; (b) xy direction; (c) z direction. The displacement of TCE molecules are presented in solid lines and dash-dotted lines for systems A and B, respectively. The displacement of water molecules are presented in dashed lines and dotted lines in systems A and B, respectively.

On the basis of the interfacial tension result, we choose the SPC water model to be applied in systems C and D.13 This is consistent with reports that for other water/organic interfaces SPC generally serves as a better water model compared to SPC/E,16 although SPC/E accounts for “self-energy due to polarization”.41 The average diffusion constants of water using the SPC and SPC/E models are 3.70 × 10-5 and 2.50 × 10-5 cm2/s, respectively, comparable to the simulations of pure water of 3.85 × 10-5 and 2.49 × 10-5 cm2/s45 and 4.3 × 10-5 and 2.5 × 10-5 cm2/s.35 The experimental value of the self-diffusion constant of water is 2.4 × 10-5 cm2/s at 300 K,35 suggesting that the SPC/E model may lead to a better quantification of dynamic properties. Interestingly, the simulation shows that the selfdiffusion of TCE molecules is faster than that of water molecules although their molecular size is significantly larger. We have been unable to find experimental values for the self-diffusion constant of TCE in the literature, but we have calculated it as 4.05 × 10-5 cm2/s using the generalized treatment method developed by Lee and Thodos46 (detailed in the Supporting Information), which agrees with the simulated results. It is worthwhile to note the observed interfacial effect on the selfdiffusion of water and TCE molecules. Several groups43,44,47,48 have observed diffusional anisotropy of molecules near liquidliquid interfaces: the self-diffusion of molecules parallel to the interfacial plane is larger than that perpendicular to the interface due to a “decreased tangential pressure component near the interface”.48 The diffusion anisotropy is observed not only near the liquid-liquid interfaces but also sometimes throughout the entire simulation box due to the long-range interfacial effect and more importantly, the size limitation of the simulation boxes.47,48 (45) Mahoney, M. W.; Jorgensen, W. L. J. Chem. Phys. 2001, 114, 363. (46) Lee, H.; Thodos, G. Ind. Eng. Chem. Fundam. 1983, 22, 17. (47) Fernandes, P. A.; Cordeiro, M. N. D. S.; Gomes, J. A. N. F. J. Phys. Chem. B 1999, 103, 6290. (48) Buhn, J. B.; Bopp, P. A.; Hampe, M. J. Fluid Phase Equilib. 2004, 224, 221.

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Figure 3. Sample snapshots of system D at different simulation time intervals. The nanoparticles are represented in red spheres, the water phase is in blue, and the trichloroethylene phase is in lime. Two nanoparticles in the cluster are in contact with the interface at the end of the simulation.

Figure 4. Overlay of mass density profiles for system D. Densities were averaged over the last 200 ps. The separate lines are from simulations from different starting conditions.

Here we have also observed the diffusion anisotropy of water and TCE molecules, as shown in Figure 2. In addition, we have divided the simulation box into eight regions along the Z direction (a slab thickness of 1 nm) and calculated the diffusion constants within each region. The diffusion anisotropy is observed throughout the entire simulation box. This is probably due to the restriction of our simulation box since the middle plane along the Z direction in each liquid phase is only 2 nm away from an interface. 3.2. Liquid-Liquid System with Nanoparticles. The emphasis of this paper is on systems C and D, which involve the presence of nanoparticles. In our simulation, spherical modified hydrocarbon nanoparticles (HCP) were initially randomly dispersed into the water phase. The simulation shows that the nanoparticles migrate to the TCE phase, possibly due to their hydrophobic nature and can form aggregates in both the water and oil phases. Eventually, all of the aggregated clusters or single particles equilibrate at the water-TCE interface. Figure 3 shows a representative example of system D illustrating the in situ progress during the simulation. Once the HCP cluster reaches the interface at 38 ns, it remains there until the end of the simulation (50 ns). The overlay of the mass density profiles of six parallel runs over the last 200 ps of the simulation is shown in Figure 4. Other physical properties averaged over the last 5 ns are summarized in Table 2. Figures 3 and 4 illustrate that the equilibrium location of the aggregate clusters or single particles is in the vicinity of the liquid-liquid interface. The interface appears to have a confinement effect once the clusters or single particles adsorb. This is likely due to the following underlying mechanism: it costs additional free energy to remove clusters or particles from the interface. For example, the desorption energy of spherical particles can be calculated using ∆G ) πr2γ(1 + cos θ)2, where ∆G is the change of the Gibbs free energy of removing one particle

Figure 5. Normalized number particle-particle radial distribution function, g(r)p-p, for system D. Data present are averaged over of six runs through the last 5 ns.

into the TCE phase, r is the radius of the solid particle, γ is the interfacial tension between water and TCE, and θ is the threephase contact angle measured in the water phase.49Since the HCPs are hydrophobic, we can hypothesize that the three-phase contact angle is in the range of 90-125°. Once a nanoparticle is adsorbed at the water-TCE interface, it will cost 2-11 kT (depending on the contact angle) to remove the particle back into the TCE phase, which is larger than the thermal fluctuation energy of 1 kT. The simulation shows that the nanoparticles tend to equilibrate at water-TCE interfaces in neither monolayer nor multilayers, but as clusters. Figure 5 is the normalized number particleparticle radial distribution function, of which the area underneath the curve represents the number of particles (equals 10 here in system D). The plot shows a sharp peak at the distance of 1.3 nm between neighboring nanoparticles indicating they are in close contact. The function approaches zero at a large distance due to the limited number of particles in the system. This observation partially agrees with, but also partially deviates from, the previous experimental result, where the dodecanethiol-capped nanoparticles form randomly distributed multilayers at the interface and interparticle distances vary from close contact to approximately 25 nm.12 The deviation is likely due to the fact that the nanoparticles in the experimental work were grafted with “long” alkane chains, which act as a steric barrier to prevent aggregation, whereas in the simulation, the nanoparticles lacking these chains tend to aggregate. In future work, we plan to modify the nanoparticles in the simulation in order to have a direct comparison with the experimental work. We will also look into the effect of nanoparticle concentration after the modification since the current study on such an effect is limited due to the cluster formation. Our simulation shows that the TCE molecules (49) Levin, S.; Bowen, B. D.; Partridge, S. J. Colloids Surf. 1989, 38, 325.

Nanoparticles at a Liquid-Liquid Interface

Figure 6. Snapshot of one sample run of system D at 50 ns. Ten nanoparticles are in a cluster. The carbon atoms that make up the nanoparticles are presented in green. The water molecules are presented in red and white and TCE molecules are presented in yellow.

Figure 7. Water-TCE interfacial thickness as a function of the number of particles in a cluster in contact with the interface. The inset shows the interfacial thickness as a function of cluster size; the filled circles are the clusters that have no particle in contact with the interface and the open circles are the clusters that have either one or two particles in contact with the interface.

pack randomly when in contact with the nanoparticle surfaces and exhibit no particular orientation, as shown in Figure 6. It is intuitive to question whether the presence of the nanoparticles influences liquid-liquid interfacial properties such as the interfacial thickness. Figure 7 plots the water-TCE interfacial width for systems C and D. Surprisingly, the interfacial thickness remains relatively constant regardless of the presence of particles at the interface. Moreover, the thickness is independent of the size of clusters that have either 0 or 1-2 particles in contact with the interface. One interesting observation is that even when the interface of systems C and D has no contacting nanoparticle its thickness (5.49 ( 0.22 Å) is slightly larger than those in systems A (4.03 ( 0.18 Å) and B (3.76 ( 0.12 Å), the pure water-TCE systems. Here “contacting nanoparticles” are defined when the distance between the center of a closest nanoparticle and the critical interfacial line is less than 1.38 nm. For the interfaces that have no contacting nanoparticles, the distance between the center of the closest nanoparticle and the critical interfacial line ranges between 1.51 nm to 4.42 nm, for the data points shown in Figure 7. This indicates that the

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Figure 8. Mean square displacement within the last 1 ns for system D. (a) xyz direction; (b) xy direction; (c) z direction. The displacements of TCE molecules are presented in dashed lines, water molecules are presented in dotted lines, and nanoparticles are presented in solid lines.

nanoparticles in the vicinity of the interface may also affect the interfacial thickness. Finally, we quantify the self-diffusion of the nanoparticles and the liquid molecules. Figure 8 displays the average mean square displacement of nanoparticles and water and TCE molecules of system D. The self-diffusion of the HCP nanoparticles is much slower than those of TCE and water molecules. In addition, diffusion anisotropy is observed for both the nanoparticles and liquid molecules. The dominant mobility of the nanoparticles in the xy plane parallel to the interface is consistent with the observation of the interfacial confinement effect. Again, both water and TCE molecules have faster mobility parallel to the xy plane of the interface compared to motion normal to the interface. We have attempted to compare the diffusion of water and TCE molecules at the liquid-liquid interfaces vs those in the bulk. The liquid molecules at the interfaces and in the bulk have comparable diffusion constants and the anisotropy is observed throughout the simulation box, again possibly due to the size limit of the simulation box.

4. Conclusion In this work, molecular dynamics simulations were performed to investigate the in situ self-assembly of modified hydrocarbon nanoparticles at a water-TCE interface. The simulation has clearly shown the progress of cluster formation, migration, and final equilibrium of both single particles and clusters at liquidliquid interfaces. In addition, the simulation shows that the waterTCE interfacial thickness analyzed from density profiles is influenced by the presence of nanoparticles either near or in contact with the interface but is independent of the number of nanoparticles present. The self-diffusion of nanoparticles, water molecules, and TCE molecules is faster parallel to the interface than perpendicular to it. To the best of our knowledge, this work provides the first molecular dynamics simulation of the in situ self-assembly of nanoparticles at liquid-liquid interfaces. The simulation agrees with previous experimental work12 that nanoparticles equilibrate in the vicinity of the water-TCE interface but does not result in the multilayer structure that was observed experimentally, likely due to the lack of steric hindrance of the simulated nanoparticles and cluster formation. In addition, the simulation has provided information that supplements experimental capabilities on in situ self-assembly, random packing of TCE molecules when in contact with nanoparticles, interfacial

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thickness with the presence of nanoparticles, diffusion isotropy, etc. Although many quantitative arguments are specific to our simulated systems, the work provides general insights for the self-assembly of nanoparticles at an interface. Acknowledgment. We thank A. Srirangam and the Texas Tech High Performance Computing Center (HPCC) for assistance and computational resources. This material is based upon work supported by the Texas Tech University Interdisciplinary Seed

Luo et al.

Program, the National Science Foundation (CTS-0500323 and BES-0134594), the Office of Naval Research (N00014-04100366), and the Robert A. Welch Foundation (D-0005). Supporting Information Available: Calculation of selfdiffusion constants using the generalized treatment method developed by Lee and Thodos. This material is available free of charge via the Internet at http://pubs.acs.org. LA0607196