Self-Healing Vesicles Deposit Lipid-Coated Janus Particles into

Dec 10, 2013 - responsive, adaptive behavior is observed in cases involving both the step- and wedge-shaped trenches, but the step trench is more effe...
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Self-Healing Vesicles Deposit Lipid-Coated Janus Particles into Nanoscopic Trenches Xin Yong, Emily J. Crabb, Nicholas M. Moellers, and Anna C. Balazs* Chemical Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States S Supporting Information *

ABSTRACT: Using dissipative particle dynamics (DPD) simulations, we model the interaction between nanoscopic lipid vesicles and Janus nanoparticles localized on an adhesive substrate in the presence of an imposed flow. The system is immersed in a hydrophilic solution, and the hydrophilic substrate contains nanoscopic trenches, which are either stepor wedge-shaped. The fluid-driven vesicle successfully picks up Janus particles on the substrate, transports these particles as cargo along the surface, and then drops off the particles into the trenches. For Janus particles with a relatively large hydrophobic region, lipids from the bilayer membrane become detached from the vesicle and bound to the hydrophobic domain of the deposited particle. While the detachment of these lipids rips the vesicle, it provides a coating that effectively shields the hydrophobic portion of the nanoparticle from the outer solution. After the particle has been dropped off, the torn vesicle undergoes structural rearrangement, reforming into a closed structure that resembles its original shape. In effect, the vesicle displays pronounced adaptive behavior, shedding lipids to form a protective coating around the particle and undergoing a self-healing process after the particle has been deposited. This responsive, adaptive behavior is observed in cases involving both the step- and wedge-shaped trenches, but the step trench is more effective at inducing particle drop off. The results reveal that the introduction of grooves or trenches into a hydrophilic surface can facilitate the targeted delivery of amphiphilic particles by self-healing vesicles, which could be used for successive delivery events.

1. INTRODUCTION Nanoscopic lipid vesicles could provide ideal carriers for the targeted delivery of nanoparticles. At this size scale, the vesicles could encase just a few particles and, thus, might provide a means of controllably delivering just one or two nanoparticles to specified sites.1 Such precision could enable new modes of bottom-up fabrication, with the vesicles serving as muchneeded “nano-tweezers”. Such nanoscale lipid vesicles could also be highly effective for non-invasive, transdermal delivery of encapsulated drugs because they can passively transverse the dermal layers.2 Recent advances have led to robust methods for synthesizing vesicles with controlled nanoscopic sizes,3,4 paving the way for realizing the above vital functions. In this context, computer simulations can provide valuable guidelines for optimizing the performance of the nanoscale vesicles in controllably transporting and depositing their nanoparticle cargo. Previous computational studies of the interactions between nanoparticles and lipid vesicles have focused primarily on microscopic vesicles5−9 and, thus, involved modeling a single, relatively flat bilayer membrane, which represented a proportion of the larger vesicle. Recently, we performed simulations on the interactions of solid Janus particles and three-dimensional spherical vesicles, whose diameters were on the nanometer length scale.10 Thus, we could capture © 2013 American Chemical Society

synergistic interactions between the particles and the deformable, curved surfaces of the nanoscopic vesicles. Herein, we extend these studies to design a system where the vesicles not only bind but also release these particles at specific sites on a chemically homogeneous surface. In this process, the “smart” vesicles shed lipids to form a protective coating around portions of the Janus particles and undergo a self-healing process after the coated particle is deposited on the surface. In our previous studies,10 we used dissipative particle dynamics (DPD)11−14 to simulate the Janus particles and nanoscopic lipid vesicles that are driven to move on a flat surface by an imposed shear flow. The DPD is a mesoscopic approach that is similar to coarse-grained molecular dynamics (MD) simulations and allows one to capture the hydrodynamics of complex fluids while retaining essential information about the structural properties of the components of the system; moreover, the DPD approach can be used to model physical phenomena occurring at time and length scales many orders of magnitude greater than those captured by MD. Our previous DPD simulations10 revealed that a fluid-driven vesicle Received: October 9, 2013 Revised: December 9, 2013 Published: December 10, 2013 16066

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Figure 1. (a) Vesicle self-assembled from 586 twin-tailed lipids dispersed in a hydrophilic solvent (not displayed). Blue beads represent the hydrophilic lipid heads; red beads represent the hydrophobic lipid tails; and black beads mark the inner hydrophilic solution. (b) Coarse-grained model of twin-tailed lipid composed of three hydrophilic head beads (blue) and six hydrophobic tail beads (red). (c) Janus particle formed from 392 beads, of which 196 beads are hydrophilic (white) and 196 beads are hydrophobic (pink) (ϕ = 0.500). Beads are arranged in a face-centered cubic lattice structure with a cube side length of 0.7. (d) Step trench with width = 5.50rc = 3.69 nm and depth = 1.10rc = 0.74 nm. (e) Wedge-shaped trench with width = 16rc = 10.72 nm and depth = 2.20rc = 1.47 nm. function that goes to 0 at rc, and vij = vi − vj. The random force is FRij = σωR(rij)ξijr̂ij, where ξij is a zero-mean Gaussian random variable of unit variance and σ2 = 2kBTγ. We use ωD(rij) = ωR(rij)2 = (1 − rij)2 for rij < rc. Each of these three forces conserves momentum locally; therefore, a system of even a few hundred particles displays hydrodynamic behavior.11,13,14 The equations of motion are integrated in time via the standard velocity−Verlet algorithm.15 We take rc as the characteristic length scale and kBT as the characteristic energy scale in our simulations; both are set equal to 1 in the ensuing studies. The characteristic time scale is then defined as τ = (mrc2/kBT)1/2 = 1. The remaining simulation parameters are σ = 3 and Δt = 0.02τ, with a total bead number density of ρ = 3. Each vesicle (see Figure 1a) is self-assembled from 586 twin-tailed lipids; each lipid is composed of nine beads, with three hydrophilic beads forming the head and three hydrophobic beads in each of the two tails16 (see Figure 1b). The bonds between the lipid beads are modeled by the harmonic spring potential Ebond = Kbond((r − b)/rc)2; Kbond is the bond constant and is set to Kbond = 64, and b is the equilibrium bond length and is set to b = 0.5.17 A weaker bond with Kbond = 16 is also inserted between the bead on each tail nearest the hydrophilic head to keep the tails oriented in the same direction.10,18 Additionally, we include a three-body stiffness potential along the tails of the lipid of the form Eangle = Kangle(1 + cos θ), where θ is the angle formed by the three adjacent tail beads and Kangle = 5. This potential serves to increase the stability and bending rigidity of the bilayers.17,19 The interior of the vesicle is filled with hydrophilic beads, modeling an aqueous solution. Each roughly spherical Janus nanoparticle consists of 392 beads that are arranged in a face-centered cubic (fcc) lattice structure, with a cube side length of 0.7; the particle has a radius of 2.11.10 The permanent harmonic spring-like bonds between the beads in the nanoparticle are characterized by Kbond = 64 and two equilibrium lengths b = 0.7/√2 and b = 0.7 (set according to the spacing between the nearest neighbor and second nearest neighbor beads in the fcc lattice, respectively).10 Each amphiphilic Janus particle is characterized by the parameter ϕ, which is the fraction of hydrophobic beads on the particle. Figure 1c shows a symmetric Janus particle with ϕ = 0.5. We vary the value of ϕ by either replacing layers of hydrophobic beads with layers of hydrophilic beads (yielding ϕ < 0.5) or vice versa (yielding ϕ > 0.5) while not altering the structure of the particle or the total number of beads. We focus on particles in the range of 0.010 ≤ ϕ ≤ 0.990. The flat substrate lies in the x−z plane at y = 0 and consists of 5940 frozen hydrophilic beads arranged in an fcc lattice with a number density ρ ≈ 3. To form a trench aligned parallel to the z axis, we shift the beads in the negative y direction. The step trench (Figure 1d) is formed by shifting all substrate beads with an x coordinate between −2.75 and 2.75 down by 1.1. This results in a trench with a width of 5.50 and a depth of 1.1.

can robustly pick up and transport a Janus nanoparticle on a flat, chemically homogeneous substrate in an aqueous solution for a wide range of shear rates, particle-substrate adhesion strengths, and fraction of hydrophobic sites on the Janus particle. Prompting the vesicles to deposit the particles in a controllable manner is, however, considerably more challenging. The vesicles could be driven to drop off the particles on a chemically heterogeneous surface, which contained a “sticky” surface stripe that exhibited a preferential attraction to the particle.10 In particular, the vesicle provided clean deposition of particles onto this stripe when the Janus particle encompassed just a small fraction of hydrophobes. For particles with a larger hydrophobic domain, we observed intriguing scenarios where lipids became detached from the vesicle and bound to the particle as it was deposited onto the sticky stripe; furthermore, the vesicle membrane was able to reform after it separated from the particle. In this study, we focus on two specific aspects of the particle drop off. First, we show that it is possible to produce controlled deposition using chemically homogeneous surfaces that are topographically patterned, encompassing distinct grooves or trenches. Hence, the results provide additional guidelines for achieving successful particle pick up and drop off on substrates and thereby facilitate the bottom-up fabrication of nanoscopic assemblies on a chemically homogeneous surface. Second, we concentrate on the structural changes in the vesicle as the membrane tears in forming a coating on the particle and subsequently reforms after the particle is deposited into the trenches. In effect, the adaptive vesicle is able to self-heal after the directed delivery of its cargo. The self-healing is significant because it enables this carrier to be reused for subsequent targeted deliveries.

2. METHODOLOGY The DPD captures the time evolution of a many-body system via the numerical integration of Newton’s equation of motion, mdvi/dt = fi, where the mass m of a bead is set equal to 1. The total force acting on each bead is the sum of three pairwise additive forces: fi(t) = ∑(FCij + FDij + FRij ). The sum runs over all beads j within a certain cutoff radius rc. The conservative force is a soft, repulsive force given by FCij = aij(1 − rij)r̂ij, where aij is the maximum repulsion between beads i and j, rij = |ri − rj|/rc, and r̂ij = rij/|rij|. The drag force is FDij = −γωD(rij)(r̂ij·vij)r̂ij, where γ is a simulation parameter related to viscosity, ωD is a weight 16067

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The wedge-shaped trench has a width of w = 16 and depth of d = 2.2 (Figure 1e). The shape of this trench is characterized by the equation ytrench = yflat − d(1 − |x − xc|/(w/2)) for beads with 12 ≤ x ≤ 28. Here, ytrench is the new y coordinate of the bead in the trench; yflat is the original y coordinate of the bead in the flat substrate; x is the x coordinate of the bead; and xc = 20 is the center of the trench. Furthermore, we assume that there is an adhesive interaction between the substrate and the outer surface of the vesicle. Namely, when a hydrophilic bead on the surface of the vesicle comes within a critical distance of a substrate bead (i.e., rij < rc), the two beads form a bond. This bond is modeled using a truncated Hookean spring potential Fsub/lipid = −Ksub/lipid(rij − b), where b is the equilibrium bond length (set at b = 0.5) and Ksub/lipid is the effective strength of the interaction. The bonds can break when their length exceeds a critical value (when rij > rc). Using this approach, we also introduce an adhesive interaction between the hydrophilic beads of the Janus nanoparticle and the substrate Fsub/Janus with effective strength Ksub/Janus. This mode of modeling adhesive interactions is used in various other mesoscopic simulations.10,20,21 In this study, we focus on the role that the surface topography plays in enabling the fluid-driven vesicles to deliver nanoparticles to specified sites on a substrate. To isolate the effect of topography, the surface is taken to be chemically homogeneous. Hence, the parameters that represent chemical interactions between the surface and the components in the system, Ksub/lipid and Ksub/Janus, are held constant. We set Ksub/lipid = 4 to yield an adhesion energy per unit area of approximately 10−2 J/m2 between the vesicle and the substrate. This adhesion energy is on the same scale as the values used in both coarsegrained and atomistic MD simulations for supported bilayers22−24 and is the same order of magnitude as experimental values for the adhesion energy of ligand−receptor bonds.25 The strength of the adhesion between a bead on the Janus particle and the surface is set in the range of 8 ≤ Ksub/Janus ≤ 12. The size of the simulation box is 60.5 × 40.0 × 19.8; periodic boundary conditions are imposed in the lateral (x and z) directions. The dimensions of the box in x and z directions are chosen to match the lattice constant of the substrate. The simulation box is filled with hydrophilic solution beads. The hydrophilic/hydrophobic interactions between the beads are modeled using repulsive interactions between the components. The repulsion parameter between two components, aij, is set to aij = 25 for two beads of the same type and aij = 100 for a hydrophobic−hydrophilic interaction, with aij measured in units of kBT/rc. These values have been used extensively in previous DPD simulations of lipid bilayers16−19,26,27 and allow the lipids in our simulations to successfully self-assemble into bilayers and vesicles. The vesicles and Janus particles are driven to move along the substrate by an imposed shear flow, which is applied in the x direction, and imposed using Lees−Edwards periodic boundary conditions.28 The resulting shear flow has a velocity profile in the x direction of magnitude Vsh = γ̇y, where γ̇ is the shear rate and is set to γ̇ = 0.015. It is worth noting that previous DPD studies have shown that increasing the shear rate decreases the stability of the vesicle and prompts the rupture of the vesicle.10 The simulation parameters can be related to physical length and time scales through comparisons to experimental measurements of the equilibrium area per lipid and the in-plane diffusion constant of a tensionless dipalmitoylphosphatidylcholine (DPPC) membrane.17 Via these comparisons, we obtain the DPD length scale rc = 0.67 nm and DPD time scale τ = 7.2 ns, and for a single time step, Δt = 0.02 and τ = 0.14 ns. Hence, the radius of the Janus nanoparticles and the outer radius of the lipid vesicles are approximately 1.4 and 5.0 nm, respectively. The step trench has a physical width of 3.69 nm and depth of 0.74 nm, while the wedge trench is significantly larger, with a width of 10.72 nm and depth of 1.47 nm. Both trenches span the entire length of the substrate in the z direction, which is 13.27 nm. Notably, such nanoscopic trenches can be etched into the surface using electron-beam lithography.29,30 The shear rate used in our simulations corresponds to 2.08 × 106 s−1, which is comparable to values used in microfluidic devices.31 The resulting velocity of the vesicle moving along the substrate is on the

order of 5 mm/s, which is within the range of operating velocities in many microfluidic devices.32 At this velocity, the corresponding Peclet number is approximately Pe = 100, and thus, the motion of the vesicle is dominated by advection.10

3. RESULTS AND DISCUSSION 3.1. Step Trench. Figure 2 shows snapshots from a typical simulation of the interactions among the Janus nanoparticle,

Figure 2. Snapshots of the system with one Janus particle with ϕ = 0.367 for the step trench with Ksub/Janus = 8. The shear rate γ̇ is 0.015, and the shear flow is in the positive x direction (from right to left). Substrate beads are marked in green. The particle is initially placed near the vesicle to facilitate particle pick up. Snapshots are taken at the following times: (a) 0, (b) 840, (c) 894, (d) 1920, and (e) 2340. The κ2 value in each snapshot is the instantaneous relative shape anisotropy of the vesicle.

vesicle, and step trench. The fraction of hydrophobic beads in the Janus particle is ϕ = 0.367, and the particle−surface adhesion strength is Ksub/Janus = 8; the latter value is held constant for all simulations involving this step trench. As the flow-driven vesicle comes in contact with the particle (Figure 2a), the hydrophobic portion of the Janus particle becomes buried in the hydrophobic interior of the lipid membrane.10 In this manner, the hydrophobic domain of the particle is shielded from the unfavorable enthalpic interactions with the outer solvent. We note that the hydrophobic portion of the Janus particle remains lodged in the hydrophobic domain of the bilayer; additional energetic input would be required to drive the Janus particle across the interior hydrophilic layer of the membrane and, thus, promote its internalization within the vesicle. Notably, when the fluid-driven vesicle and particle come into contact, the moving vesicle could impart sufficient kinetic energy to propel the particle through the entire membrane. Very recently, Arai et al. performed DPD simulations of a Janus nanoparticle colliding with a nanoscopic lipid vesicle.33 The latter studies revealed that the last-stage morphology of the assembly depends upon the contact velocity. Namely, internal16068

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Figure 3. Temporal evolution of the number of interactions between the hydrophilic beads of the Janus particle and the substrate for a simulation performed using a Janus particle with ϕ = 0.367 and the step trench with Ksub/Janus = 8 at shear rate γ̇ = 0.015 (similar to the simulation in Figure 2). Regions I−V on the graph correspond to different phases of the drop off process. In region I (t ≈ 0−780), the particle is being transported by the vesicle on the flat substrate. In region II (t ≈ 780−1150), the particle is in contact with the first edge of the trench. In region III (t ≈ 1150−1240), the particle has separated from the first edge of the trench and is being dragged along the flat bottom of the trench. In region IV (t ≈ 1240−1864), the particle is in contact with the second edge of the trench but is still connected to the vesicle. In region V (t ≈ 1864−2000), the particle has been deposited by the vesicle in the trench with a protective coating and remains affixed to the second edge of the trench. The three snapshots labeled II, III, and IV correspond to the respective times t ≈ 900, 1160, and 1300 in regions II, III, and IV.

ization only happens for a certain range of contact velocities. If the contact velocity is too small, the kinetic energy is not sufficient to drive the particle to penetrate the membrane. In our simulations, the fluid-driven vesicle and the Janus particle “collide” on the substrate with a contact velocity that is approximately equal to the velocity of the vesicle. After this collision, we observe that the Janus nanoparticle straddles the outer leaflet of the bilayer membrane, with the hydrophobic portion inside the lipid, while its hydrophilic portion is in contact with the outer solution, similar to the “outer surface” state in ref 33. For the shear rates considered here and in our previous study,10 the contact velocities fall in the range that yield the “outer surface” state33 and, thus, are not sufficiently high to induce the internalization of the Janus nanoparticle. After the particle binds to the vesicle, because the shear is directed along the positive x direction, the vesicle is propelled forward, moving over the particle, which eventually becomes localized on the right side of the carrier (see Figure 2). The vesicle−particle assembly then moves as a unit along the surface. When this assembly passes over the trench, the particle

becomes lodged in the depression. While the relatively large vesicle can traverse the trough, it becomes highly distorted, forming a narrow neck of lipids that extend from the hydrophobic portion of the Janus particle (Figure 2d). Ultimately, the force from the imposed flow causes this neck to break away from the particle. A small number of the membrane lipids do, however, remain bound to the hydrophobic region on the Janus particle (Figure 2e). Notably, the vesicle recovers and continues moving along the substrate (Figure 2e). In effect, the vesicle undergoes a selfhealing process. To characterize this self-healing behavior, we compare the relative shape anisotropy of the vesicle, κ2, before and after the particle drop off. The relative shape anisotropy, κ2, is given by κ2 = [(λx − λy)2 + (λy − λz)2 + (λz − λx)2]/2Rg4, where λx, λy, and λz are the eigenvalues of the gyration tensor S with Smn = 1/N∑iN= 1rmirni.34 Here, N is the total number of lipid beads (hydrophobic and hydrophilic), and ri is the position vector of the center of the ith bead with respect to the center of mass of the vesicle. The radius of gyration, Rg, is calculated as 16069

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Figure 4. Graph of the fraction of hydrophobic particle beads covered by a lipid tail bead versus the fraction of hydrophobic beads ϕ for the step trench with Ksub/Janus = 8 at shear rate γ̇ = 0.015. Data were obtained by first averaging over several time frames within each simulation with successful drop off with a protective coating and then averaging these values for all of the successful simulations with different random seeds at each ratio. Snapshots show examples of particle coverage at different ratios. The error bars arise from averaging over three independent runs.

Rg2 = λx + λy + λz. The relative shape anisotropy for an ideal sphere is 0, and that for an ideal rod is 1. The instantaneous κ2 values for the respective time frames are displayed in Figure 2. The value of κ2 = 0.075 in Figure 2a characterizes the shape of a self-assembled vesicle that has just been placed on the substrate. Because this κ2 value is close to 0, it corresponds to a roughly spherical shape. At the start of the simulation, the vesicle is deformed by both the adhesion from the substrate and the external flow, which yields a larger κ2. The value of κ2 increases further after the particle becomes attached to the vesicle and reaches its maximum value right before the lipid “neck” becomes detached from the trapped particle (around the time shown in Figure 2d). Once the particle has been deposited in the trench, the relative shape anisotropy decreases significantly; as seen in Figure 2e, κ2 = 0.16. To assess the extent to which the latter vesicle has resumed its characteristic shape, we performed additional simulations of a shear-driven vesicle moving on a flat, adhesive surface (in the absence of a particle) with Ksub/lipid = 4 and γ̇ = 0.015; the steady-state, time-averaged value of κ2 in this case is 0.22 ± 0.03. Given the value of κ2 in Figure 2e, we can conclude that the vesicle essentially recovers its normal shape after the particle deposition. The reason that the particle becomes trapped in the trench can be understood from Figure 3, which shows the total number of interactions between the hydrophilic sites on the Janus particle and substrate as the assembly moves over the surface (here, the number of interactions is defined as the number of pairs of hydrophilic particle and substrate beads that are separated by a distance smaller than rc). This interaction count jumps sharply when the particle comes into contact with the first edge of the trench at t ≈ 780 (the beginning of region II) and the second edge of the trench at t ≈ 1240 (start of region IV). This increase in the particle−substrate interactions leads to an increase in the total adhesive force acting on the particle (as calculated from Fsub/Janus). It is worth noting that, in these DPD simulations, the solvent induces a depletion attraction35−38 between the nanoparticle and walls of the trench that also contributes to the localization of the particle in the trough. This depletion attraction is attributed to the discrete representation of the continuum solvent and is seen to

influence the particle dynamics near the adhesive substrate (see Figures S1 and S2 of the Supporting Information). We detail the nature of this depletion attraction in the Supporting Information. The lipids that remain bound to the deposited Janus nanoparticle help shield the hydrophobic portion of the particle from the hydrophilic outer solution. With the hydrophobes on the lipid tails localized on the hydrophobic sites on the particle, the hydrophilic lipid head groups extend away from the Janus sphere and, thus, effectively mask the underlying hydrophobic moieties. The degree to which the particle is covered by this protective coating depends upon ϕ, the fraction of hydrophobic beads in the particle. To quantify this coating, we first determine the total number of hydrophobic particle beads that are separated from a lipid tail bead by one unit. The latter distance serves as the cutoff radius; beads separated by more than one unit are not considered in this count. For each value of ϕ, this total is calculated by first averaging the number of covered hydrophobic beads over several time steps for a given run and then averaging those values for all independent runs with a successful drop off of coated particles. This average number of covered beads is then divided by the number of hydrophobic particle beads within a cutoff radius of 1 from the surface of the particle. Beads farther inside the particle cannot interact with beads at the surface of the particle; therefore, they are excluded from the calculations. Figure 4 shows the fraction of hydrophobic sites on the Janus sphere that are coated by the lipids as a function of ϕ, the fraction of hydrophobic sites on the sphere. For relatively low values of ϕ, the lipids coat the majority of these hydrophobes (see inset of Figure 4). As ϕ increases, the coverage is less perfect and more of the hydrophobic beads are exposed to the outer solution. In particular, the coverage changes from 0.92 to 0.17 as ϕ varies from 0.06 to 0.86. We found that the maximum number of lipids that are bound to the particle (over the range of ϕ) is approximately equal to 25 (see Figure S3 of the Supporting Information). Because the vesicle in this simulation is self-assembled from 586 lipids, the maximum loss of vesicle mass is estimated to be less than 5%. Figure S3 of the Supporting Information also shows that the number of detached lipids stays relatively constant over the 16070

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range of ϕ considered here. Careful observation of the deposition process reveals that the number of detached lipids depends upon the width of the lipid neck, which does not scale with ϕ when rupture occurs (it is noteworthy that the rupture of the narrow neck in Figure 2d resembles the fission of a vesicle through a pathway that involves a constricted neck;39−43 similar to that fission process, the rupture of the neck in our simulations might predominately depend upon the physical characteristics of the lipid membrane41,42 and the temperature in the system43). 3.2. Wedge-Shaped Trench. To generalize our findings beyond this specific topography, we also conducted simulations with the wedge-shaped trench shown in Figure 5. Unlike the

both types of trenches, indicating that the behavior is not dependent upon the specific substrate topography. The phase maps in Figure 6 show the complete results for all of the simulations of single particle drop off for the step and wedge-shaped trenches; four independent simulation runs were performed for each value of ϕ and Ksub/Janus. For the wedgeshaped trench, we performed simulations with a smaller range of ϕ values (with 0.010 ≤ ϕ ≤ 0.5) because Figure 6 indicates relatively few successful drop off events beyond ϕ = 0.2. We did, however, investigate higher particle−surface attraction strengths, focusing on 8 ≤ Ksub/Janus ≤ 12. We speculate that, because of weaker depletion forces between the particle and the wedge (see the Supporting Information), stronger particle− surface bonds are necessary to induce particle drop off. Notably, for Ksub/Janus = 8, the specific results depend upon the trench shape. For the step trench, the particle is deposited in the trough with a protective lipid coating for every simulation with 0.010 < ϕ < 0.5 and every successful drop off in the case of larger ϕ. For the wedge-shaped trench, however, particle drop off with a protective coating only occurs in two runs with ϕ = 0.061. To induce more reliable drop off in the wedge, it is necessary to use a higher value of the particle−substrate adhesion strength. For Ksub/Janus = 10, drop off is much more successful, because the particle is deposited in the trench with a protective coating for all of the simulations with ϕ = 0.140 and in three of the four runs with ϕ = 0.061; however, none of the runs with ϕ > 0.245 yielded the desired effect. With the highest adhesion strength of Ksub/Janus = 12, drop off is still more frequent but also more sporadic. For instance, three of the four simulations at ϕ = 0.500 resulted in drop off with a protective coating, but only one of the four at ϕ = 0.245 was successful. Hence, the most consistent and predictable drop off behavior for the wedge-shaped trench occurs for the particle−surface adhesion strength of Ksub/Janus = 10. Comparing the results for the wedge-shaped trench at Ksub/Janus = 10 to those for the step trench at Ksub/Janus = 8, we find that the step trench is effective over a wider range of particle compositions, ϕ, than the wedge geometry. The reason that the step trench is more effective at inducing drop off and requires lower particle−surface adhesion strength to perform this function is due to the increase in the number of particle− surface interactions (relative to a flat surface) (see Figure 3) and the induced depletion attraction between the particle and the vertical wall of the trough that maintains the particle affixed to these walls (see the Supporting Information for details). Figure S2 of the Supporting Information shows the x component of the depletion force acting on the particle in the step trench, which effectively introduces extra friction opposing the forward motion of the particle. Notably, this xdirection depletion force affixing the particle to both edges of the step trench could explain the occasional drop off at the first edge encountered (see section S1 of the Supporting Information for further discussion). In contrast, for the wedge trench, drop off occurs primarily because of the increase in the number of particle−substrate interactions (relative to the flat surface). The solvent-induced depletion attraction is less effective in the case of these slanted walls. Because the increase in the number of interactions dominates the deposition in the wedge-shaped trench, successful drop off requires a lower fraction of hydrophobic beads ϕ and a higher particle−plane attraction strength Ksub/Janus than those for the step trench. The wedge trench can, however, still induce drop off much more effectively than a

Figure 5. Snapshots of the system with one Janus particle with ϕ = 0.061 for the wedge-shaped trench with Ksub/Janus = 10. The shear rate is γ̇ = 0.015. Snapshots are taken at the following times: (a) 0, (b) 500, (c) 1220, (d) 1400, and (e) 1800. The instantaneous relative shape anisotropy κ2 of the vesicle is labeled in each snapshot.

step trench, the wedge has no sharp vertical edges. We first focus on a simulation run that yielded successful drop off (Figure 5). The particle has a chemical composition of ϕ = 0.061, and the particle−surface adhesion strength is Ksub/Janus = 10. When the vesicle-particle assembly encounters and moves across the trench, the particle becomes localized in the center of the wedge, where the particle−surface contact area (interaction count) is maximized. This increase in the number of particle− surface interactions enables the successful drop off of the particle. Notably, the particle deposited inside the wedge is also coated with a protective lipid layer. The latter coating is present in successful drop offs for ϕ ≥ 0.061. As for the step trench, once the lipid-coated particle becomes deposited in the trough, the torn vesicle undergoes self-healing, as evidenced by the images in Figure 5 and the decrease in κ2, the relative shape anisotropy. It is noteworthy that the deformation of the carrier vesicle is generally smaller in the case of the wedge than the step trench, as seen by comparing Figures 2d and 5d. Importantly, particle drop offs with a protective lipid coating and vesicle self-healing were seen with 16071

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Figure 6. Phase diagram for the drop off of a single particle using (a) step trench and (b) wedge-shaped trench. The shear rate γ̇ is held constant at 0.015. The particle−substrate adhesion Ksub/Janus and fraction of hydrophobic beads ϕ are varied.

flat and chemically uniform substrate.10 Specifically, our previous work showed that a vesicle will not deposit a Janus particle on a flat surface at a shear rate of γ̇ = 0.015 when ϕ ≥ 0.061 for any adhesion strength in the range of 6 ≤ Ksub/Janus ≤ 12.

of the vesicle after these lipids were torn away. This synergistic behavior is observed to be quite robust, occurring not only on these topographically patterned surfaces but also on the chemically patterned, flat surfaces examined in our previous study.10 It is noteworthy that, in a highly generalized sense, these properties mimic the sensory and responsive functionality exhibited by biological systems because the vesicle simultaneously provides a protective layer and undergoes a self-healing process. The latter attributes have important consequences for technological applications. First, the vesicles can be harnessed to deliver a range of amphiphilic particles onto hydrophiphilic surfaces in aqueous solutions, maintaining the overall hydrophilic nature of the environment. This could be important for certain biomedical applications, including the delivery of hydrophobic drugs, which need to be masked by a hydrophilic coating for efficient uptake. Second, the self-mending vesicle can potentially perform this function multiple times and, thus, could be used repeatedly to both pick up and deliver of Janus spheres to specific sites on surfaces. The latter attribute would also be useful in bottom-up assembly involving nanoparticles. Finally, we iterate that the critical components for realizing this cargo-carrier system are lipid vesicles that are nanoscopic in size, Janus particles with nanometer diameters, and nanoscale trenches on chemically homogeneous surfaces. The nanoscale vesicles have been synthesized by several robust methods,3,4

4. CONCLUSION Our DPD simulations reveal that fluid-driven nanoscopic vesicles can successfully transport and deliver Janus particles into a nanoscale trench in chemically homogeneous surfaces. The efficacy of the wedge-shaped trench in trapping the particles is due primarily to the increased number of particle− substrate interactions (relative to the flat surface), which create a large frictional force that opposes the forward motion of the particle. The latter effect was also observed with the step trench, but this trough also exhibited a solvent-induced depletion attraction that caused the particles to become affixed to the vertical walls. Because of the effective particle−wall attraction, the step trench produced more consistent drop off for a wider range of particle compositions at lower particle− surface adhesion strengths than was observed with the wedgeshaped depression. Importantly, the findings also reveal remarkable synergistic interactions between the vesicles and deposited particles that lead not only to the shielding of the particle from the outer solvent by a coating of membrane lipids but also the reforming 16072

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and sub-20 nm Janus particles can be formed through a range of experimental techniques.44−47 The sub-10 nm trench can be fabricated by electron-beam lithography.30 Hence, all of the components for potentially realizing this system experimentally are available.

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ASSOCIATED CONTENT

S Supporting Information *

Detailed discussion of the nature of the depletion interactions between the particle and substrate in our simulations. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Anna C. Balazs gratefully acknowledges funding from the United States Department of Energy (U.S. DOE) (for partial support of Xin Yong for the analysis) and the Army Research Office (ARO) (for partial support for Emily J. Crabb and Nicholas M. Moellers for the computational systems). The authors thank Dr. Isaac Salib for helpful discussions.

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REFERENCES

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