Modeling the Assembly of Polymer-Grafted Nanoparticles at Oil–Water

Article pubs.acs.org/Langmuir

Modeling the Assembly of Polymer-Grafted Nanoparticles at Oil− Water Interfaces Xin Yong* Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, New York 13902, United States S Supporting Information *

ABSTRACT: Using dissipative particle dynamics (DPD), I model the interfacial adsorption and self-assembly of polymer-grafted nanoparticles at a planar oil−water interface. The amphiphilic core−shell nanoparticles irreversibly adsorb to the interface and create a monolayer covering the interface. The polymer chains of the adsorbed nanoparticles are significantly deformed by surface tension to conform to the interface. I quantitatively characterize the properties of the particle-laden interface and the structure of the monolayer in detail at different surface coverages. I observe that the monolayer of particles grafted with long polymer chains undergoes an intriguing liquid−crystalline−amorphous phase transition in which the relationship between the monolayer structure and the surface tension/pressure of the interface is elucidated. Moreover, my results indicate that the amorphous state at high surface coverage is induced by the anisotropic distribution of the randomly grafted chains on each particle core, which leads to noncircular in-plane morphology formed under excluded volume effects. These studies provide a fundamental understanding of the interfacial behavior of polymer-grafted nanoparticles for achieving complete control of the adsorption and subsequent self-assembly.

I. INTRODUCTION Emulsions are of great importance in various applications, such as enhanced oil recovery,1 heavy oil transportation,2,3 drug delivery,4,5 catalysis,6,7 and nanomaterial fabrications.8−11 In order to form stable emulsions, surface-active agents (often called emulsifiers) are commonly added to a mixture to lower the surface tension between immiscible liquids. While the most widely used emulsifiers are surfactant molecules, recently colloidal particles have attracted attention for stabilizing emulsions due to several advantageous features over conventional surfactant molecules, such as improved stability and less toxicity.12−14 Owing to these attributes, colloidal particles have shown great potential as environmentally benign emulsifiers for applications where stable emulsions are desired. Meanwhile, the good stability of nanoparticle-stabilized (aka Pickering) emulsions also means that it is difficult to destabilize and break these emulsions at will, which can be a key requirement for other applications,15−17 by modifying the interfacial behavior of particles or even removing particles from liquid−liquid interfaces. In addition, the ability to recover the nanoparticles at the end of processes is crucial for reducing material waste. Considerable effort has been expended in devising approaches to the on-demand destabilization of emulsions, which can be categorized into mechanical agitation18−20 and physicochemical approaches.21−30 Both types rely on external cues to trigger the destabilization or phase inversion of emulsions. Polymer-grafted nanoparticles offer a structural motif that is capable of unifying mechanical and physicochemical approaches to achieve rapid switching © 2015 American Chemical Society

between emulsion and phase-separated states. Namely, the charged or magnetic solid core can readily desorb from the interface by imposing a corresponding external field.18 The grafted polymer chains can vary their interfacial behavior in response to temperature or pH changes,31 which causes the reduction of adsorption energy. Multiple orthogonal stimuli that target different components of the nanoparticles can act in concert to achieve optimal performance in breaking the emulsions. A challenge in designing polymer-grafted nanoparticles as switchable emulsifiers is understanding the behavior of these soft, heterogeneous nanoparticles at liquid−liquid interfaces, which is far from being comprehensive and has proven to be demanding to probe experimentally. Most experiments32−39 rely on measuring dynamic surface tension or surface pressure to infer the adsorption process and associated particle morphology. High-resolution and nonintrusive dynamic experiments that preserve the delicate interfacial environment and demonstrate the detailed particle deformation are still lacking. A number of atomistic-scale simulations have reported the rearrangement of attached polymer ligands into anisotropic shapes when the particles adsorb at fluid−fluid interfaces.40−42 Recently, Lane and Grest reported large-scale molecular dynamics (MD) simulations of the assembly of alkanethiolcoated gold nanoparticles at the water−vapor interface.43 Received: September 10, 2015 Revised: September 28, 2015 Published: October 6, 2015 11458

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hydrodynamic behavior emerges even in systems containing only a few hundred beads.45,47,50 The equations of motion are integrated in time with the velocity-Verlet algorithm.51 I take rc as the characteristic length scale and set the dimensionless value as rc = 1. The factor kBT is taken as the characteristic energy scale, where kB is the Boltzmann constant. The characteristic time scale can then be defined as τ = (mrc2/kBT)1/2 = 1. The remaining simulation parameters are λ = 4.5 and Δt = 0.02τ. In my simulation, a polymer-grafted nanoparticle has a core− shell structure that encompasses a nondeformable core in the center and a soft shell made of flexible polymer chains emanating from the core, as shown in Figure 1a. The core is

However, little has been explored about the structural and dynamic properties of large-scale interfaces fully covered with compliant hairy particles.44 As a step in addressing this challenge, herein I use computational modeling to investigate the adsorption and assembly of the polymer-grafted nanoparticles at oil−water interfaces. I specifically focus on the adsorption kinetics of nanoparticles, the associated particle morphology change, and the structure of the monolayers assembled at the interface. Through these studies, distinct features of the polymer-grafted nanoparticles are revealed as compared to unmodified rigid nanoparticles. My findings present unique insight into the interfacial dynamics of composite nanoparticles and can thereby provide useful guidelines for designing different architectures of colloidal particles and trigger motifs to achieve effective control of the emulsion state. Below I first describe the computational approach and then discuss my findings on the adsorption and deformation of polymer-grafted nanoparticles at the oil−water interface and the detailed structure of particle monolayers.

II. METHODOLOGY The studies were carried out using dissipative particle dynamics (DPD)45−47 to model an oil−water biphasic system laden with polymer-grafted nanoparticles. DPD is a particle-based computational method that can be viewed as a variation of the coarse-grained MD method. Relative to MD, DPD permits simulations of larger systems for longer times in computationally realistic timeframes. It is particularly effective at simulating complex fluids and multicomponent mixtures on the mesoscale,48,49 such as the ones presented in this work. In DPD, a volume of fluid is modeled with individual beads, where each bead represents a cluster of molecules. Similar to MD simulations, DPD captures the time evolution of this manybody system governed by Newton’s equation of motion, m dvi/ dt = fi. In particular, the force acting on each bead i from neighboring beads consists of three parts fi(t) = ∑j(FCij + FDij + FRij ), each of which is pairwise additive. The sum runs over all beads j within a certain cutoff radius rc. The three forces considered are the conservative force FCij , the drag or dissipative force FDij , and the random force FRij . I describe each pairwise force below. The conservative force is a soft, repulsive force given by FCij = aij(1 − rij)r̂ij, where aij determines the maximum repulsion between beads i and j, rij = ri − rj, rij = |rij|, and r̂ij = rij/|rij|. This soft-core force permits the use of larger time steps in DPD simulation than those typically used in MD simulations, which commonly involve hard-core potentials, e.g., the Lennard-Jones potential. The drag force is FDij = −λωD(rij)(r̂ij ·vij)r̂ij, where λ is a simulation parameter related to the fluid viscosity, ωD is a weight function that vanishes when rij ≥ rc, and vij = vi − vj is the relative velocity between beads i and j. The random force is FRij = σωR(rij)ξijr̂ij, where ξij is a zero-mean Gaussian random variable of unit variance and σ is the noise amplitude that satisfies the relation σ2 = 2kBTλ based on the fluctuation− dissipation theorem.46 The value of λ is chosen to ensure a relatively rapid equilibration of the temperature in the system and the numerical stability of the simulations for the specified time step.47 Finally, I choose the functional form of the weight function to be ωD(rij) = ωR(rij)2 = (1 − rij)2 for rij < 1.47 Because all three of these forces conserve momentum locally and the drag force introduces a long-range velocity correlation,

Figure 1. (a) Schematic of a polymer-grafted nanoparticle, formed by randomly grafting 20 polymer chains (orange beads) to the surface of a rigid core (white beads). Each chain encompasses 30 DPD beads. (b) Detailed structure of the spherical core composed of 438 beads, of which 276 interior beads are arranged in an fcc lattice structure and 162 surface beads are uniformly distributed on the surface of the sphere.

modeled as a cluster of frozen DPD beads grouped into a rigid body, which consists of 276 interior beads and 162 surface beads. The interior beads are arranged in a face-centered cubic (fcc) lattice structure with a cube side length of 0.7. Surface beads (162) are distributed on a spherical layer with a radius of 2 to cover the interior beads. The layer is modeled as geodesic grids generated by subdividing an icosahedron (Figure 1b). In this manner, the surface beads are uniformly distributed on the surface and the maximum distance between surface beads is minimized.52−55 Together with the interior beads, the surface layer generates a well-defined, relatively smooth core surface (Figure 1b) and prevents solvent and polymer beads from penetrating the rigid core as demonstrated in Figure S2 in the Supporting Information. As in a previous study,56 polymer chains are modeled as a sequence of Lc DPD beads that are connected by harmonic bonds whose potential is given by Ebond = 1/2Kbond(r − r0)2. Here, Kbond = 128 is the elastic constant and r0 = 0.5 is the equilibrium bond distance.57,58 An angle potential between two consecutive bonds Eangle = Kangle(1 + cos θ) is imposed to control the rigidity of the chains, where θ is the bond angle. Eangle = 4 is set to minimize topological violations of polymer chains.56,59,60 A polymer-grafted nanoparticle is formed by attaching 20 polymer chains to the surface beads of the rigid core. The resulting grafting density is 0.2 chains/rc2. For each polymer chain, one terminal bead is tethered to a randomly picked surface bead by the same harmonic bond, while the other end remains free. A typical simulation system contains water and oil phases with nanoparticles, where two planar interfaces are presented in 11459

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Figure 2. (a−f) Snapshots of the biphasic system with a single nanoparticle grafted with hydrophilic polymer chains. The interaction parameter between the polymer chain and oil is apc‑o = 35. Pink and cyan dots represent oil and water beads, respectively. The snapshots are taken for times of (a) 200, (b) 800, (c) 1000, (d) 1200, (e) 1400, (f) 4000 (in dimensionless units of time). The inset in (f) is the top view of the nanoparticle at the interface. (g) Time evolution of the position of the geometric center of a nanoparticle in the z direction. Letters a−f correspond to the respective snapshots on the left. The inset shows the trajectories of the center in the z direction for four independent runs.

hydrophilicity of the chains. All interaction parameters are given in Table 1.

one simulation box. In this study, I choose various simulation boxes with different sizes according to the number of nanoparticles for computational efficiency. A simulation box of size 30 × 30 × 40 is applied to accommodate a single polymer-grafted nanoparticle. The water phase occupies a region of size 30 × 30 × 30, as shown in Figure 2. For a biphasic system with multiple polymer-grafted nanoparticles, a much larger box is needed, whose dimensions are 40 × 40 × 100. The volume ratio between the water and oil phases is 7:3. Periodic boundary conditions are imposed in all three directions. The simulation box is filled with corresponding numbers of water and oil beads, which maintains the total number density of the system at ρsys = 3. Different initial positions of the nanoparticles are applied in my simulations. When I model the adsorption of nanoparticles to the interface, all nanoparticles are initially dispersed in bulk water. When I examine the structure of nanoparticle monolayers in greater detail, the same number of nanoparticles is initially placed on both interfaces with no particles present within the bulk water and/or oil phases. This initial configuration ensures that all nanoparticles are adsorbed to the two interfaces with the same number on each interface. In addition, I increase the interfacial area to reduce the finite size effects by using a simulation box that has a size of 80 × 80 × 40 with a water to oil volume ratio of 1:1. The beads in the system can be categorized as water, oil, core, and polymer. The interaction parameters between the components, aij, is set to aij = 25 (in units of kBT/rc) for any beads of the same moiety.47 The interaction parameters between different components determine the chemical properties of the moieties. Herein, I consider the hydrophobic rigid core, and thus the interaction parameter between the core and oil is aco‑o = 25. I vary the interaction parameter between the core and water from 25 to 100 to represent the degree of hydrophobicity. In order to achieve the dispersion of polymer-grafted nanoparticles with hydrophobic cores in bulk water, the polymer chains are treated as hydrophilic with the chain− water interaction parameter set to apc‑w = 25. The chain−oil interaction parameter apc‑o is used to control the degree of

Table 1. DPD Interaction Parameters between Different Components (in Units of kBT/rc) water oil core polymer chain

water

oil

core

polymer chain

25

ao‑w 25

aco‑w 25 25

25 apc‑o 100 25

To monitor the adsorption process, the solution has been equilibrated for 1 × 105 time steps before the nanoparticles are allowed to move. The adsorption process is carried out for 1 × 105 to 3 × 106 time steps depending on the size of the box and the number of particles. Another 5 × 106 time steps are conducted to compute the time-averaged contact angle if needed. For a typical simulation of the nanoparticle monolayer, the equilibrium period lasts for 2 × 106 time steps and the results are averaged for 1 × 106 time steps.

III. RESULTS AND DISCUSSION Interfacial Adsorption of Polymer-Grafted Nanoparticles. Adsorption of a Single Nanoparticle. I first examine the adsorption of the bare rigid core, which represents an unmodified nanoparticle, at oil−water interfaces as a function of core−water and oil−water interaction parameters aco‑w and ao‑w, respectively. The equilibrium position of the core straddling the interface is quantified by a three-phase contact angle θ defined with respect to the water phase (Figure S1a in Supporting Information), whose range is calibrated according to the aforementioned simulation parameters (as detailed in the Supporting Information). In other words, I parametrize the degree of hydrophobicity of the core (dictated by θ) according to the core−water interaction parameter aco‑w. Because the adsorption of the bare core has been well characterized, I now explore the adsorption of polymer-grafted nanoparticles. Unless stated otherwise, the rigid core of the polymer-grafted nanoparticle is highly hydrophobic with a co‑w = 100, corresponding to a contact angle of θ = 131°. As exhibited in 11460

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Figure 4. (a) Time evolution of the positions of the geometric centers of polymer-grafted nanoparticles (Lc = 30) in the z direction. The solid lines represent the trajectories of the nanoparticles that adsorbed to either interface. The dotted lines represent the trajectories of those remaining in the bulk. (b) Snapshots of the system at time t = 60 000. The inset is the top view of the upper interface, where different polymer-grafted nanoparticles are colored differently.

are characterized. By changing the length of the polymer chains Lc, the thickness of the soft shell can be adjusted. Even with the shorted chains (Lc = 10) grafted to the cores, I observe that the polymer-grafted nanoparticles are evenly dispersed. The radius of gyration of a particle is calculated from Rg2 = ⟨1/N ∑i N= 1(ri − rcom)2⟩ to quantify its hydrodynamic radius, where N is the total number of beads (including the core and polymer beads) of a polymer-grafted nanoparticle, ri is the position vector of the ith bead, and rcom is the center-of-mass position of the particle. ⟨···⟩ represents the ensemble average over all nanoparticles. Figure S4a shows that the radius of gyration is nearly proportional to the chain length. I obtain the diffusion coefficient of the particles from the mean square displacement (Figure S4b). As I expect, long polymer chains inhibit selfdiffusion of the particles by effectively increasing their hydrodynamic radii. Importantly, the results also indicate that the diffusion of the polymer-grafted nanoparticles in water still obeys the Stokes−Einstein relation as shown in Figure S4c, assuming that the radius of gyration dictates the hydrodynamic radius of the particle. Once the behavior of polymer-grafted nanoparticles in the bulk has been characterized, I investigate the adsorption of a single polymer-grafted nanoparticle. My simulations permit a detailed visualization of the adsorption kinetics and the morphology change of the particle in the course of adsorption. In particular, I am interested in the deformation of the soft polymer shell. Initially, I placed the nanoparticle far away from both interfaces. Hence, the particle diffuses randomly in bulk water at early times (Figure 2a) and can approach either

Figure 3. (a) Detailed morphology of the polymer-grafted nanoparticle with chain length Lc = 30 adsorbed at the oil−water interface. The polymer chains have different chain−oil interaction parameters apc‑o to represent different degrees of hydrophilicity. (Top panel) Snapshots of the nanoparticle adsorbed at the interface, showing that the polymer chains are significantly deformed. (Middle panel) Density contours of polymer chains in the y−z midplane across the center of the nanoparticle. The contours are averaged for four independent runs. (Bottom panel) Density profiles of polymer chains and the center of mass of the rigid core in the z direction. The contours and profiles are obtained by averaging over four independent runs. (b) Contact angle of the polymer-grafted nanoparticle θ* with chain length Lc = 30 (defined using the effective radius of the rigid core) at the oil−water interface as a function of the chain−oil interaction parameter apc‑o. Error bars indicate the variations among four independent runs. The inset shows the definition of θ*.

Figure S3b in the Supporting Information, the hydrophobic rigid cores aggregate and form clusters in the bulk water phase to minimize their exposure to water beads. Thus, the grafted polymer chains are considered to be hydrophilic to prevent unwanted agglomeration and achieve good dispersion in water. The constructed polymer-grafted nanoparticles are essentially amphiphilic, in which the core is hydrophobic and the polymer shell is hydrophilic. Because the polymer-grafted nanoparticles are initially distributed in bulk water, their structural properties and dynamic behavior in the water phase are also important and 11461

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polymer density contour shows a lens shape41,63 that is much more extended in the direction perpendicular to the interface. The polymer density profiles along the z direction in Figure 3a further confirm that the spatial distribution of polymer chains perpendicular to the interface is narrower when the chains are less hydrophilic. I also quantify the equilibrium position of the polymergrafted nanoparticle straddling the oil−water interface by defining a contact angle. This contact angle indicates the overall degree of hydrophilicity or hydrophobicity of the polymergrafted nanoparticle. In the presence of the grafted chains, the physical radius of the particle is not clearly defined. As a result, I still define the contact angle of the polymer-grafted nanoparticles θ* with respect to its rigid core, as shown in the inset of Figure 3b. Figure 3b presents the contact angle as a function of the hydrophilicity of the grafted chains, which is determined by the chain−oil interaction parameter apc‑o. Depending on the value of apc‑o, the entire polymer-grafted nanoparticle can exhibit water-like or oil-like interfacial behavior, defined by θ* < 90 or θ* > 90, respectively. Notably, the adsorption process does not occur in all four independent runs when the chains are too hydrophilic (apc‑o > 70). This behavior implies that it is energetically favorable for nanoparticles coated with highly hydrophilic chains to remain in the water phase rather than to be adsorbed at the interface even when the particle core is highly hydrophobic. Below, I consider only polymer-grafted nanoparticles with apc‑o = 35. Adsorption of Multiple Nanoparticles and Monolayer Formation. When the polymer-grafted nanoparticles are used as emulsifiers to stabilize emulsions, the relevant processes inevitably demand a massive number of particles, and thus the collective behavior of particles during and after the adsorption becomes important. On the basis of my understanding of the adsorption of each individual particle, I then explore the adsorption of multiple polymer-grafted nanoparticles. Forty particles with chain length Lc = 30 were initially placed in the water phase. After the relaxation of the solution, I monitor the adsorption process by tracing the z position of the geometric center of each particle. Figure 4a clearly shows a rapid filling of the interface at the beginning of the simulation, when the oil−water interface is completely vacant. As the number of adsorbed particles increases, i.e., the surface coverage increases, the trajectories qualitatively show the slowdown of the adsorption. After approximately 3 × 104 dimensionless units of time, both upper and lower interfaces are heavily occupied by the adsorbed particles, and a monolayer of particles covering the entire interface are formed. At this stage, a particle approaching the interface experiences strong steric repulsion from the adsorbed particles, which prevents the particle from inserting into the monolayer and breaching the interface. Hence, no subsequent adsorption events are observed, and a considerable fraction of nanoparticles remain in the water phase, as shown in Figure 4b. In the same manner, I observe a similar adsorption process for particles with shorter grafted chains (Lc = 10), which is presented in Figure S5 of the Supporting Information. Importantly, the adsorption kinetics observed in my simulations agree well with previous experimental and numerical observations,32,64 and the monolayer structure is clearly reminiscent of those in experiments.36,63 Properties of Particle-Laden Interfaces and Structures of the Nanoparticle Monolayer. To gain further insight into the assembly of polymer-grafted nanoparticles at the oil−water

Figure 5. (a) Interfacial tension as a function of surface coverage at the oil−water interface and (b) log−log plot of surface pressure as a function of area per particle for systems with polymer-grafted nanoparticles having two different chain lengths Lc. Error bars are smaller than the marker size and thus are not visible. The dashed lines with slopes of −1 and −2 are used to guide the eye.

interface under random thermal motion. Figure 2 demonstrates a representative simulation in which the particle approaches the upper interface. Driven by the enthalpic interactions between the polymer chains and the binary liquid, the extended chains first breach the interface and are adsorbed while the hydrophobic rigid core is still distant from the interface. When the free ends of the extended chains are localized at the interface (Figure 2c), the relaxation of the chains induces a force on the rigid core that drags the whole particle toward the interface (Figure 2d). Once the entire particle is adsorbed, the chains spread and cover the interface to lower the surface tension like conventional surfactants do (inset of Figure 2f). From the particle trajectory in Figure 2g, I observe relatively slow adsorption and relaxation to the equilibrium position compared to the adsorption of an unmodified rigid core, which is due to the effective surface roughness and density heterogeneity introduced by the polymer chains.61,62 Because the polymer chains are slight hydrophilic (apc‑o = 35), all of the chains are significantly deformed by surface tension and concentrated along the planar interface. The crosssectional polymer density contour in Figure 3a exhibits a discoid shape due to the relatively long chains as compared to the size of the core. When the polymer chains are highly hydrophilic (apc‑o = 70), a fraction of chains prefer to stay in the water phase driven by the large elastic energy increase for conforming to the interface, which cannot be offset by the corresponding reduction in surface energy. Consequently, the 11462

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Figure 6. Top views of representative simulation snapshots showing the structure of nanoparticle monolayers at different surface coverages. The lengths of the grafted chains Lc are (a) 10 and (b) 30. The two insets in (b) present the cross-sectional views of the monolayers.

surface-active and should lower the interface tension. I thus calculate the surface tension γ as a function of the surface coverage ϕ using the Irving−Kirkwood approach.47,55,65 The formula is given as 2γ = Lz⟨Pzz − (Pxx + Pyy)/2⟩, where Pxx, Pyy, and Pzz are the diagonal components of the microscopic pressure tensor and Lz is the simulation box length in the z direction. The factor of 2 arises from the existence of two oil− water interfaces in the simulation box. The results for particles with two different polymer chain lengths Lc are shown in Figure 5a. Regardless of the effective particle size (determined by Lc), the addition of particles monotonically reduces the interfacial tension. Nevertheless, the qualitative shapes of the curves are different for different polymer chain lengths. For particles with short chains (Lc = 10), the surface tension decreases slowly when ϕ < 0.4 and exhibits a rapid reduction when the surface coverage is significant. This behavior closely resembles that observed for the unmodified hard-sphere nanoparticles.53,55 In contrast, I observe an inflection point at intermediate surface coverage in the Lc = 30 curve, which suggests that the efficacy of particles with long chains in reducing the interface tension is prominent at intermediate surface coverages but declines when the interface is excessively crowded. To further elucidate the effect of the grafted chains, I consider the surface pressure of the monolayer Π = γ − γ0, where γ0 is the surface tension of pure binary fluid. Figure 5b presents a log−log plot of surface pressure versus area per particle (∑p = LxLy/Np) isotherms. For particles with short chains, the slope of the isotherm changes from −1 to −2 as the

interface, I analyze the properties of the particle-laden interfaces and the structure of the monolayers formed by these particles. As described in the Methodology section, instead of modeling the complete adsorption process, I directly placed an equal number of particles on both interfaces so that I can accurately control the number of adsorbed particles. The quantification of the oil−water interfacial area that is occupied by the particles necessitates an accurate definition of the nanoparticle surface coverage ϕ. Because of the porous nature of the polymer shell, the common formula ϕ = nπreff2/LxLy for n nanoparticles adsorbed at the interface with an area of Lx × Ly55,64 cannot be applied unless an effective radius reff of the polymer-grafted particle is appropriately chosen. To circumvent the difficulty of defining the effective radius that can vary under different surface conditions, I introduce a means to directly calculate the surface coverage. The approach involves a discretization of the two-dimensional interface into a square lattice and counting the fraction of cells that contain a least three constituent beads of a particle, which are referred to as either core or polymer beads. In this manner, when the number density of the particle beads in an interfacial cell is greater than or equal to the average number density of the system ρsys = 3, the local densities of the solvents can be considered to be zero accordingly. This means that the fraction of the interface is completely covered by the nanoparticles. Below, I present the results as functions of ϕ. Surface Tension and Surface Pressure. I have successfully observed the adsorption of polymer-grafted nanoparticles to the oil−water interface, which indicates that these particles are 11463

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Figure 7. Voronoi diagrams of nanoparticles with (a) Lc = 10 and (b) Lc = 30 at different surface coverages corresponding to the snapshots in Figure 7, respectively. The color of each Voronoi cell represents the magnitude of local orientational order parameter |ψ6|.

distribution of particles with short chains clearly illustrates a disordered, isotropic liquid state, which is further corroborated by the disordered Voronoi construction (Figure 7a). This state corresponds to the dilute, ideal-gas-like state discussed above. Interestingly, although the Lc = 30 particle monolayer seems to be disordered in the snapshot, weak positional order is evident from the corresponding Voronoi construction (Figure 7b) that demonstrates approximately quadrilateral cells. Further quantitative characterizations of the Lc = 30 particle monolayer at low surface coverages through the RDF and structure factor are described below. At intermediate surface coverage, it is clear that the monolayer exhibits an ordered state. The snapshots show that the nanoparticles assemble into a two-dimensional crystalline structure with a hexagonal pattern driven by the excluded volume effects. Figure 7 also shows that the majority of the Voronoi cells are approximately hexagons with uniform areal size, which dictates close-packed hexagonal packing. When the nanoparticles are excessively packed, the polymer chains experience compression and the associated entropy effect of the grafted chains results in the slope change observed in the surface-pressure isotherm. It is noteworthy that the nanoparticles in the monolayer move collectively in this state. I emphasize that the ordered structure forms at lower surface coverage when the particles have longer chains, indicating that these particles are more prone to crystalline packing. Moreover, Figure 5a shows that the particles with long chains are also more effective at reducing the surface tension than the ones with short chains due to the substantial overlapping and interdigitation of long chains at intermediate surface coverage. Further increases in surface coverage cause the local concentration of the polymer chains to increase significantly.

area per particle decreases, which shows good agreement with previous theoretical analyses.44 This behavior indicates a phase transition between a dilute state that can be described as an ideal gas to a highly compact state in which the entropy effect of the short chains determines the lateral pressure.44 On the other hand, the system with particles having long chains demonstrates a more complicated isotherm, where the shape suggests the onset of multiple phase transitions. The details of the structural changes in the monolayer associated with these phase transitions are discussed below. In-Plane Structure. It is known that the isotherms and dynamic properties of the monolayer are closely related to the particle arrangement in the monolayer.11 Therefore, it is of great interest to probe the monolayer structure in detail, in particular, its in-plane structure. I first present structural information on the monolayer qualitatively via direct visualization of the simulation snapshots and corresponding Voronoi constructions and then conduct quantitative measurement of two-dimensional particle−particle radial distribution functions (RDFs) as defined between geometric core centers of particles. Additional positional order information on the in-plane structure of the monolayer with Np particles can be obtained from the structure factor S(k) = ⟨1/Np ∑mNp= 1 ∑nNp= 1 exp(−ik· (rm − rn))⟩, where k = kxex + kyey is a two-dimensional wave vector and ex and ey are unit vectors along the x and y directions, respectively. The smallest possible wave vector k is determined by the size of the simulation box in the x−y plane. Figure 6 shows representative snapshots of the assembled monolayers at different surface coverages. Because the polymer chains are weakly hydrophobic (apc‑o = 35), all particles spread out and conform to the planar interface at low surface coverage. At low surface coverages, the corresponding two-dimensional 11464

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future studies. As the surface coverage increases, the position of the first peak shifts significantly to the left, which corresponds to a decreasing interparticle distance. This behavior is consistent with the fact that the compressible grafted polymer chains can reduce their end-to-end distance under lateral pressure. At intermediate surface coverages, the RDFs evolve and exhibit multiple narrow peaks that are well separated, representing long-range positional order. The magnitude of the first peak also reaches its maximum. Moreover, the hexagonal order is clearly visible in the structure factor contours. When the surface coverage is high, the RDFs of Lc = 10 monolayers show that the monolayer maintains partial in-plane crystalline packing. The structure factor pattern confirms short-range hexagonal order with diminishing long-range positional order due to the onset of defects. Surprisingly, both RDF (Figure 8b) and the structure factor contour (Figure 9b) exhibit the complete destruction of crystalline packing in Lc = 30 particle monolayers. Orientational Order. To provide additional quantification of the structural transition, I provide two parameters as measures of orientational order66 of the monolayer besides the positional order measurements above. Herein, I compute the fraction of nanoparticles having exactly six nearest neighbors, f6, and a bond orientational order parameter ψ6.55,64,67 The nearestneighbor particles are defined as those within the first neighboring shell.67 In an ideal close-packed hexagonal lattice, f6 is 1. The radius of the shell is given by the position of the first trough in the RDF. The local order parameter for particle j is defined as ψj6 = 1/Nk ∑Nk=1k exp(i6θjk), where the sum is taken over Nk neighboring particles of particle j. θjk is the angle between the bond connecting particles j and k and an arbitrary reference axis (herein I chose the x axis in my calculation). For each particle j, I use the geometric core center to represent the particle position. The parameter ψj6 is sensitive to local 6-fold orientational order. In particular, |ψj6| = 1 indicates that the particle is in a perfect hexagonal environment, while |ψj6| = 0 corresponds to a completely disordered structure. The combination of |ψ6| with the Voronoi diagram provides an excellent presentation of crystalline packing and defects as shown in Figure 7. Besides measuring the local order parameter, I also take the average of ψj6 over all Np particles j in a monolayer to get Ψ6 = ⟨|1/N ∑Np j=1ψ6|⟩ for the entire nanoparticle monolayer. The results are presented in Figure 10. Both f6 and Ψ6 exhibit nonmonotonic behavior as the surface coverage ϕ increases, which is distinct from the monotonic increase commonly observed for the unmodified nanoparticles.55,64 In particular, for both types of particles with short and long chains, the orientational order parameters increase at low surface coverages and reach a maximum when ϕ is around 0.25 or 0.45 for Lc = 10 or 30 particles, respectively. Notably, the surface coverages at which the order parameters reach peak values are consistent with the ones at which the RDFs and structure factor contours demonstrate crystalline characteristics. This regime indicates the development of the hexagonal order. The order parameters of the Lc = 10 particle monolayers then slowly decrease at high coverages as defects emerge locally (Figures 6a and 7a). In contrast, the order parameters of the Lc = 30 particle monolayers decrease drastically. This behavior is associated with diminishing crystalline packing in the entire monolayer. Importantly, in connection with the surface pressure−area isotherm of the monolayer discussed above (Figure 5b), I show that the crystalline-to-amorphous phase transition affects the surface

Figure 8. Two-dimensional particle−particle radial distribution functions of polymer-grafted nanoparticles in the monolayers with (a) Lc = 10 and (b) Lc = 30 obtained at increasing surface coverage.

As a result, the repellence of the chains forces a fraction of chains to extend perpendicular to the interface and create outof-plane structures,44 which are marked by the pronounced thickening of the monolayer (Figure 7b and its insets). The monolayer gradually loses its long-range hexagonal order as the defects emerge at this stage as the surface coverage increases. For Lc = 10 particles, the Voronoi diagram shows the coexistence of hexagon clusters representing preserved crystalline structure with regions of Voronoi cells having nonhexagonal shapes representing defects. Surprisingly, the top view of the Lc = 30 particle monolayer at ϕ = 0.72 shows that the long-range positional order disappears completely. Figure 7b shows that a large number of Voronoi cells are irregular polygons, which confirms the existence of a second phase transition from the crystalline state to an amorphous state. I then compute the RDF and structure factor of particles in the monolayer using the core positions. Figure 8a,b plots the RDF profiles at different surface coverages within the range from 0.1 to 0.7 for Lc = 10 and 30 particles, respectively. When the surface coverage is low, the RDFs exhibit typical shapes for the disordered liquid state. The structure factor patterns in Figure 9 confirm no positional order in Lc = 10 monolayers at all, but the pattern of the structure factor in Lc = 30 monolayers demonstrates short-range positional order, in which the nearest neighbors are arranged in an oblique lattice. I surmise that the short-range oblique packing can be attributed to the interparticle interactions mediated by the grafted chains and manifests itself only when the chains are sufficiently long. The detailed characteristics of this ordering will be addressed in 11465

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Figure 9. Density contours of the structure factor S(k) of the monolayer for nanoparticles with (a) Lc = 10 and (b) Lc = 30 at different surface coverages corresponding to the snapshots in Figure 7, respectively. The Dirac peak at the origin of the structure factor was eliminated for pattern clarity.

nanoparticles deviates from the circular shape, which leads to the destruction of the hexagonal order at high surface coverage. In contrast, the particles with short chains maintain a roughly circular shape even when the monolayer is significantly compressed, and thus the monolayer preserves a certain degree of hexagonal order at high surface coverage as shown in Figure 7a.

tension reduction caused by polymer-grafted nanoparticles adsorbed at the interface. Discussion of Phase Transitions. The unique phase transition to the amorphous state at high surface coverage, which occurs only for nanoparticles grafted with long polymer chains but is not present in the systems of hard spheres or particles with short chains, can be attributed to the structural heterogeneity and anistropy of these particles. The relatively low grafting density makes the polymer shell extremely susceptible to deformation under external forces. Namely, the number density of the polymer shell is 1 order of magnitude smaller than the number density of the core. As a result, I have observed that the polymer-grafted nanoparticle undergoes a change from a three-dimensional spherical shape to a nearly two-dimensional discoid shape in the course of adsorption. Discoid nanoparticles exhibit hexagonal packing under increasing surface pressure. This two-dimensional axisymmetric morphology is retained until the polymer chains from different particles start to overlap each other severely. Because of the strong steric repulsion in the overlapping regions, a fraction of chains are forced to leave the oil−water interface and a degree of three-dimensional features are produced (Figure 6b). Furthermore, the random grafting of polymer chains results in anisotropic polymer density and irregular in-plane shapes at high surface coverage (Voronoi diagrams in Figure 7b). In other words, the in-plane shape of each polymer-grafted

IV. CONCLUSIONS I undertook computational studies of the self-assembly of polymer-grafted nanoparticles at the oil−water interface and thereby demonstrated a rich array of interfacial behaviors that are distinct from those of the unmodified particles. My simulations provide direct visualization of every step of the adsorption, i.e., approaching, breaching, and relaxation, and allow us to probe the details of particle morphology and adsorption kinetics. I showed that the grafted chains undergo pronounced deformation during adsorption. In particular, the chains spread and conform to the planar interface to maximize the surface tension reduction. Depending on the chemical properties of the chains, the particle straddling the interface exhibits a discoid or lens shape. The adsorption of multiple particles exhibits a rapid filling stage followed by slow insertion that is accompanied by the development of long-range positional and orientational order. 11466

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Details of the adsorption of rigid cores, a parametric study of the rigid core contact angle at oil−water interfaces, and additional characterization data of polymer-grafted nanoparticles in the bulk and their interfacial adsorption (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I gratefully acknowledge financial support from Binghamton University. Generous allocations of computing time were provided by the Thomas J. Watson School of Engineering and Applied Science Computational Data Center at Binghamton University.

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Figure 10. (a) Number fraction of particles, f6, having exactly six neighbors and (b) bond orientational order parameter Ψ6 obtained for different polymer-grafted nanoparticles as functions of surface coverage. Error bars represent the variations between the values obtained at the upper and lower interfaces.

In addition to exploring the adsorption kinetics, I computed the surface tension of the interface and the surface pressure of the monolayer and characterized the structure of the monolayer of particles assembled at the oil−water interface through various quantitative measures of particle ordering. Notably, the monolayer structure is expected to influence the mechanical properties of the final nanocomposite interface. I observed an intriguing liquid−crystalline−amorphous phase transition that occurs in the monolayer in which the constituent nanoparticles are grafted with long polymer chains. The onset of the amorphous state at high surface coverage is attributed to the deformability of the polymer chains and their anisotropic grafting around the particle core. Importantly, the crystalline-toamorphous transition at high surface coverage has significant consequences for surface tension and surface pressure, which is revealed by the analyses of the surface tension curve and surface pressure−area isotherm. This structural transition could potentially provide novel means for controlling the stability of a Pickering emulsion. In summary, the grafted polymer chains drastically alter the interfacial behavior of nanoparticles and demonstrate crucial roles in both the adsorption process and monolayer assembly. My finds advance the fundamental understanding of the interfacial behavior and self-assembly of polymer-grafted nanoparticles and can provide useful insight into exploiting the full potential of functionalized nanoparticles to manipulate assembly structure to gain additional control over surface tension.

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REFERENCES

(1) Schramm, L. L.; Kutay, S. M. In Surfactants: Fundamentals and Applications in the Petroleum Industry; Schramm, L. L., Ed.; Cambridge University Press: Cambridge, U.K., 2000; Chapter 3. (2) Langevin, D.; Poteau, S.; Hénaut, I.; Argillier, J. F. Crude Oil Emulsion Properties and Their Application to Heavy Oil Transportation. Oil Gas Sci. Technol. 2004, 59, 511−521. (3) Martínez-Palou, R.; Mosqueira, M.; de, L.; Zapata-Rendón, B.; Mar-Juárez, E.; Bernal-Huicochea, C.; de la Cruz Clavel-López, J.; Aburto, J. Transportation of Heavy and Extra-Heavy Crude Oil by Pipeline: A Review. J. Pet. Sci. Eng. 2011, 75, 274−282. (4) Zhou, S.; Fan, J.; Datta, S. S.; Guo, M.; Guo, X.; Weitz, D. A. Thermally Switched Release from Nanoparticle Colloidosomes. Adv. Funct. Mater. 2013, 23, 5925−5929. (5) Seiffert, S. Small but Smart: Sensitive Microgel Capsules. Angew. Chem., Int. Ed. 2013, 52, 11462−11468. (6) Wiese, S.; Spiess, A. C.; Richtering, W. Microgel-Stabilized Smart Emulsions for Biocatalysis. Angew. Chem., Int. Ed. 2013, 52, 576−579. (7) Chen, Z.; Zhou, L.; Bing, W.; Zhang, Z.; Li, Z.; Ren, J.; Qu, X. Light Controlled Reversible Inversion of Nanophosphor-Stabilized Pickering Emulsions for Biphasic Enantioselective Biocatalysis. J. Am. Chem. Soc. 2014, 136, 7498−7504. (8) Boker, A.; He, J.; Emrick, T.; Russell, T. P. Self-Assembly of Nanoparticles at Interfaces. Soft Matter 2007, 3, 1231−1248. (9) Herzig, E. M.; White, K. A.; Schofield, A. B.; Poon, W. C. K.; Clegg, P. S. Bicontinuous Emulsions Stabilized Solely by Colloidal Particles. Nat. Mater. 2007, 6, 966−971. (10) Grzelczak, M.; Vermant, J.; Furst, E. M.; Liz-Marzán, L. M. Directed Self-Assembly of Nanoparticles. ACS Nano 2010, 4, 3591− 3605. (11) Garbin, V.; Crocker, J. C.; Stebe, K. J. Nanoparticles at Fluid Interfaces: Exploiting Capping Ligands to Control Adsorption, Stability and Dynamics. J. Colloid Interface Sci. 2012, 387, 1−11. (12) Binks, B. P. Particles as Surfactantssimilarities and Differences. Curr. Opin. Colloid Interface Sci. 2002, 7, 21−41. (13) Aveyard, R.; Binks, B. P.; Clint, J. H. Emulsions Stabilised Solely by Colloidal Particles. Adv. Colloid Interface Sci. 2003, 100−102, 503− 546. (14) Mima, Y.; Fukumoto, S.; Koyama, H.; Okada, M.; Tanaka, S.; Shoji, T.; Emoto, M.; Furuzono, T.; Nishizawa, Y.; Inaba, M. Enhancement of Cell-Based Therapeutic Angiogenesis Using a Novel Type of Injectable Scaffolds of Hydroxyapatite-Polymer Nanocomposite Microspheres. PLoS One 2012, 7, e35199. (15) Liu, Y.; Jessop, P. G.; Cunningham, M.; Eckert, C. A.; Liotta, C. L. Switchable Surfactants. Science 2006, 313, 958−960. (16) Asuri, P.; Karajanagi, S. S.; Dordick, J. S.; Kane, R. S. Directed Assembly of Carbon Nanotubes at Liquid-Liquid Interfaces: Nanoscale

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Article

Langmuir Conveyors for Interfacial Biocatalysis. J. Am. Chem. Soc. 2006, 128, 1046−1047. (17) Crossley, S.; Faria, J.; Shen, M.; Resasco, D. E. Solid Nanoparticles That Catalyze Biofuel Upgrade Reactions at the Water/oil Interface. Science 2010, 327, 68−72. (18) Melle, S.; Lask, M.; Fuller, G. G. Pickering Emulsions with Controllable Stability. Langmuir 2005, 21, 2158−2162. (19) Garbin, V.; Crocker, J. C.; Stebe, K. J. Forced Desorption of Nanoparticles from an Oil-Water Interface. Langmuir 2012, 28, 1663− 1667. (20) Poulichet, V.; Garbin, V. Ultrafast Desorption of Colloidal Particles from Fluid Interfaces. Proc. Natl. Acad. Sci. U.S.A. 2015, 112, 5932. (21) Amalvy, J. I.; Armes, S. P.; Binks, B. P.; Rodrigues, J. A.; Unali, G.-F. Use of Sterically-Stabilised Polystyrene Latex Particles as a pHResponsive Particulate Emulsifier to Prepare Surfactant-Free Oil-inWater emulsions; Electronic Supplementary Information (ESI) Available: SEM and NMR Spectrum of the Polystyrene Latex Particl. Chem. Commun. 2003, 1826. (22) Ngai, T.; Behrens, S. H.; Auweter, H. Novel Emulsions Stabilized by pH and Temperature Sensitive Microgels. Chem. Commun. 2005, 331−333. (23) Motornov, M.; Sheparovych, R.; Lupitskyy, R.; MacWilliams, E.; Hoy, O.; Luzinov, I.; Minko, S. Stimuli-Responsive Colloidal Systems from Mixed Brush-Coated Nanoparticles. Adv. Funct. Mater. 2007, 17, 2307−2314. (24) Li, J.; Stöver, H. D. H. Doubly pH-Responsive Pickering Emulsion. Langmuir 2008, 24, 13237−13240. (25) Tan, K. Y.; Gautrot, J. E.; Huck, W. T. S. Formation of Pickering Emulsions Using Ion-Specific Responsive Colloids. Langmuir 2011, 27, 1251−1259. (26) Jiang, J.; Zhu, Y.; Cui, Z.; Binks, B. P. Switchable Pickering Emulsions Stabilized by Silica Nanoparticles Hydrophobized in Situ with a Switchable Surfactant. Angew. Chem., Int. Ed. 2013, 52, 12373− 12376. (27) Ma, C.; Bi, X.; Ngai, T.; Zhang, G. Polyurethane-Based Nanoparticles as Stabilizers for Oil-in-Water or Water-in-Oil Pickering Emulsions. J. Mater. Chem. A 2013, 1, 5353−5360. (28) Yang, H.; Zhou, T.; Zhang, W. A Strategy for Separating and Recycling Solid Catalysts Based on the pH-Triggered PickeringEmulsion Inversion. Angew. Chem., Int. Ed. 2013, 52, 7455−7459. (29) Tu, F.; Lee, D. Shape-Changing and Amphiphilicity-Reversing Janus Particles with pH-Responsive Surfactant Properties. J. Am. Chem. Soc. 2014, 136, 9999−10006. (30) Tang, J.; Lee, M. F. X.; Zhang, W.; Zhao, B.; Berry, R. M.; Tam, K. C. Dual Responsive Pickering Emulsion Stabilized by poly[2(dimethylamino) Ethyl Methacrylate] Grafted Cellulose Nanocrystals. Biomacromolecules 2014, 15, 3052−3060. (31) Stuart, M. A. C.; Huck, W. T. S.; Genzer, J.; Müller, M.; Ober, C.; Stamm, M.; Sukhorukov, G. B.; Szleifer, I.; Tsukruk, V. V.; Urban, M.; Winnik, F.; Zauscher, S.; Luzinov, I.; Minko, S. Emerging Applications of Stimuli-Responsive Polymer Materials. Nat. Mater. 2010, 9, 101−113. (32) Isa, L.; Amstad, E.; Schwenke, K.; Del Gado, E.; Ilg, P.; Kröger, M.; Reimhult, E. Adsorption of Core-Shell Nanoparticles at Liquid− liquid Interfaces. Soft Matter 2011, 7, 7663. (33) Alvarez, N. J.; Anna, S. L.; Saigal, T.; Tilton, R. D.; Walker, L. M. Interfacial Dynamics and Rheology of Polymer-Grafted Nanoparticles at Air-Water and Xylene-Water Interfaces. Langmuir 2012, 28, 8052− 8063. (34) Li, Z.; Geisel, K.; Richtering, W.; Ngai, T. Poly(NIsopropylacrylamide) Microgels at the Oil−water Interface: Adsorption Kinetics. Soft Matter 2013, 9, 9939. (35) Li, Z.; Richtering, W.; Ngai, T. Poly(N-Isopropylacrylamide) Microgels at the Oil-Water Interface: Temperature Effect. Soft Matter 2014, 10, 6182. (36) Pinaud, F.; Geisel, K.; Massé, P.; Catargi, B.; Isa, L.; Richtering, W.; Ravaine, V.; Schmitt, V. Adsorption of Microgels at an Oil-Water

Interface: Correlation between Packing and 2D Elasticity. Soft Matter 2014, 10, 6963−6974. (37) Deshmukh, O. S.; Maestro, A.; Duits, M. H. G.; van den Ende, D.; Stuart, M. C.; Mugele, F. Equation of State and Adsorption Dynamics of Soft Microgel Particles at an Air-Water Interface. Soft Matter 2014, 10, 7045−7050. (38) Bizmark, N.; Ioannidis, M. A.; Henneke, D. E. Irreversible Adsorption-Driven Assembly of Nanoparticles at Fluid Interfaces Revealed by a Dynamic Surface Tension Probe. Langmuir 2014, 30, 710−717. (39) Garbin, V.; Jenkins, I.; Sinno, T.; Crocker, J. C.; Stebe, K. J. Interactions and Stress Relaxation in Monolayers of Soft Nanoparticles at Fluid-Fluid Interfaces. Phys. Rev. Lett. 2015, 114, 108301. (40) Tay, K. A.; Bresme, F. Wetting Properties of Passivated Metal Nanocrystals at Liquid-Vapor Interfaces: A Computer Simulation Study. J. Am. Chem. Soc. 2006, 128, 14166−14175. (41) Udayana Ranatunga, R. J. K.; Kalescky, R. J. B.; Chiu, C.; Nielsen, S. O. Molecular Dynamics Simulations of Surfactant Functionalized Nanoparticles in the Vicinity of an Oil/Water Interface. J. Phys. Chem. C 2010, 114, 12151−12157. (42) Lane, J. M. D.; Grest, G. S. Spontaneous Asymmetry of Coated Spherical Nanoparticles in Solution and at Liquid-Vapor Interfaces. Phys. Rev. Lett. 2010, 104, 235501. (43) Lane, J. M. D.; Grest, G. S. Assembly of Responsive-Shape Coated Nanoparticles at Water Surfaces. Nanoscale 2014, 6, 5132− 5137. (44) Liu, Z.; Guo, R.; Xu, G.; Huang, Z.; Yan, L.-T. EntropyMediated Mechanical Response of the Interfacial Nanoparticle Patterning. Nano Lett. 2014, 14, 6910−6916. (45) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics. Europhys. Lett. 1992, 19, 155−160. (46) Español, P.; Warren, P. Statistical Mechanics of Dissipative Particle Dynamics. Europhys. Lett. 1995, 30, 191−196. (47) Groot, R. D.; Warren, P. B. Dissipative Particle Dynamics: Bridging the Gap between Atomistic and Mesoscopic Simulation. J. Chem. Phys. 1997, 107, 4423−4435. (48) Pivkin, I. V; Caswell, B.; Karniadakisa, G. E. Dissipative Particle Dynamics. In Reviews in Computational Chemistry; John Wiley & Sons, Inc., 2010; pp 85−110. (49) Yeh, P. D.; Alexeev, A. Mesoscale Modelling of Environmentally Responsive Hydrogels: Emerging Applications. Chem. Commun. 2015, 51, 10083. (50) Español, P. Hydrodynamics from Dissipative Particle Dynamics. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1995, 52, 1734−1742. (51) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (52) Chen, S.; Phan-Thien, N.; Khoo, B. C.; Fan, X. J. Flow around Spheres by Dissipative Particle Dynamics. Phys. Fluids 2006, 18, 103605. (53) Fan, H.; Striolo, A. Nanoparticle Effects on the Water-Oil Interfacial Tension. Phys. Rev. E 2012, 86, 051610. (54) Fan, H.; Striolo, A. Mechanistic Study of Droplets Coalescence in Pickering Emulsions. Soft Matter 2012, 8, 9533. (55) Luu, X. C.; Yu, J.; Striolo, A. Nanoparticles Adsorbed at the Water/oil Interface: Coverage and Composition Effects on Structure and Diffusion. Langmuir 2013, 29, 7221−7228. (56) Yong, X.; Kuksenok, O.; Matyjaszewski, K.; Balazs, A. C. Harnessing Interfacially-Active Nanorods to Regenerate Severed Polymer Gels. Nano Lett. 2013, 13, 6269−6274. (57) Yong, X.; Simakova, A.; Averick, S.; Gutierrez, J.; Kuksenok, O.; Balazs, A. C.; Matyjaszewski, K. Stackable, Covalently Fused Gels: Repair and Composite Formation. Macromolecules 2015, 48, 1169− 1178. (58) Yong, X.; Kuksenok, O.; Balazs, A. C. Modeling Free Radical Polymerization Using Dissipative Particle Dynamics. Polymer 2015, 72, 217−225. 11468

DOI: 10.1021/acs.langmuir.5b03405 Langmuir 2015, 31, 11458−11469

Article

Langmuir (59) Nikunen, P.; Vattulainen, I.; Karttunen, M. Reptational Dynamics in Dissipative Particle Dynamics Simulations of Polymer Melts. Phys. Rev. E 2007, 75, 036713. (60) Karatrantos, A.; Clarke, N.; Composto, R. J.; Winey, K. I. Topological Entanglement Length in Polymer Melts and Nanocomposites by a DPD Polymer Model. Soft Matter 2013, 9, 3877. (61) Kaz, D. M.; McGorty, R.; Mani, M.; Brenner, M. P.; Manoharan, V. N. Physical Ageing of the Contact Line on Colloidal Particles at Liquid Interfaces. Nat. Mater. 2012, 11, 138−142. (62) Colosqui, C. E.; Morris, J. F.; Koplik, J. Colloidal Adsorption at Fluid Interfaces: Regime Crossover from Fast Relaxation to Physical Aging. Phys. Rev. Lett. 2013, 111, 028302. (63) Geisel, K.; Isa, L.; Richtering, W. Unraveling the 3D Localization and Deformation of Responsive Microgels at Oil/water Interfaces: A Step Forward in Understanding Soft Emulsion Stabilizers. Langmuir 2012, 28, 15770−15776. (64) Schwenke, K.; Isa, L.; Del Gado, E. Assembly of Nanoparticles at Liquid Interfaces: Crowding and Ordering. Langmuir 2014, 30, 3069−3074. (65) Irving, J. H.; Kirkwood, J. G. The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics. J. Chem. Phys. 1950, 18, 817. (66) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press, 1998. (67) Cheng, S.; Grest, G. S. Structure and Diffusion of Nanoparticle Monolayers Floating at Liquid/vapor Interfaces: A Molecular Dynamics Study. J. Chem. Phys. 2012, 136, 214702.

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