Structure and Dynamics of Stimuli-Responsive Nanoparticle

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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

Structure and Dynamics of Stimuli-Responsive Nanoparticle Monolayers at Fluid Interfaces Shiyi Qin, Junhyuk Kang, and Xin Yong Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00809 • Publication Date (Web): 20 Apr 2018 Downloaded from http://pubs.acs.org on April 20, 2018

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Structure and Dynamics of Stimuli-Responsive Nanoparticle Monolayers at Fluid Interfaces Shiyi Qina, Junhyuk Kanga, and Xin Yongab* a

Department of Mechanical Engineering, Binghamton University, The State University of New York, 4400 Vestal Parkway East, Binghamton, New York 13902, United States b

Institute for Materials Research, Binghamton University, The State University of New York, 4400 Vestal Parkway East, Binghamton, New York 13902, United States

Abstract: Stimuli-responsive nanoparticles at fluid interfaces offer great potential for realizing on-demand and controllable self-assembly that can benefit various applications. Here, we conducted electrostatic dissipative particle dynamics simulations to provide a fundamental understanding of the microstructure and interfacial dynamics of responsive nanoparticle monolayers at a water-oil interface. The model nanoparticle is functionalized with polyelectrolytes to render the pH-sensitivity, which permits further manipulation of the monolayer properties. The monolayer structure was analyzed in great detail through the density and electric field distributions, structure factor, and Voronoi tessellation. Even at a low surface coverage, a continuous disorder-to-order phase transition was observed when the particle’s degree of ionization increases in response to pH changes. The six-neighbor particle fraction and bond orientation order parameter quantitatively characterize the structural transition induced by long-range electrostatic interactions. Adding salt can screen the electrostatic interactions and offer additional control on the monolayer structure. The detailed dynamics of the monolayer in different states was revealed by analyzing mean-squared displacements, in which different diffusion regimes were identified. The self-diffusion of individual particles and the collective dynamics of the whole monolayer were probed and correlated with the structural transition. Our results provide deeper insight into the dynamic behavior of responsive nanoparticle surfactants and lay the groundwork for bottom-up synthesis of novel nanomaterials, responsive emulsions, and microdroplet reactors. *E-mail: [email protected]

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Introduction Self-assembly of nanoparticles at fluid-fluid interfaces has attracted considerable attention in many disciplines, ranging from fundamental fluid dynamics to synthesis of functional nanostructured materials.1–5 For example, the high mobility of nanoparticles at fluid interfaces enables rapid self- or directed-assembly into two-dimensional (2D) colloidal arrays with unique optical, magnetic, or electronic properties.6–9 The fluid interface provides a “soft” template that can be easily removed by evaporation or solvent extraction.10–13 Compared with the wet etching removal of hard inorganic and metal templates,14 the fluid-templated fabrication reduces the use of hazardous acids and hydroxides. Despite rapid advances in this technique, the fluidity and deformability of the interface raise significant challenges in understanding the assembled nanostructures. Since the functionality of nanomaterials directly relates to the structure, it is of great importance to elucidate the microstructure and dynamics of the 2D colloidal suprastructures at the interface. Not only does the interfacial self-assembly provide a platform for nanomaterials synthesis, it also plays a vital role in manipulating the interactions between liquid droplets. The control over droplet interactions potentially has great utility for a wide range of applications, such as responsive emulsions and microdroplet reactors.5,15–17 The adsorption of nanoparticles stabilizes the emulsion by reducing the interfacial energy.18 The self-assembled nanoparticle monolayer can also serve as a robust shell to further prevent droplet coalescence.19 The stability of adsorbed particles,3,20–23 monolayer microstructure,24–27 as well as the direct interactions between the two fluid interfaces covered by particle monolayers,19,28,29 all influence droplet interactions and emulsion stability. Following this line of research, several studies30,31 have developed switchable emulsions by tuning particle wettability in response to environmental stimuli. Yang et al. recently exploited multi-responsive nanoparticles to manipulate droplet interactions and coalescence under external fields, thereby realizing a dynamic microreactor system through hierarchical droplet assembly.5 However, few have offered insight into realizing responsive droplet systems through active control over the microstructure and dynamics of 2


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particle monolayer. As the first step to address these fundamental questions, we conduct numerical simulations to elucidate the dynamic response of particle monolayer at fluid interfaces subject to external cues. The intricate interplay between various colloidal interactions (e.g., capillary force, van der Waals force, electrostatic interactions, and magnetic forces) influences the low-dimensional colloidal assemblies formed at the fluid interface and their dynamical properties. Unusual 2D structures (e.g., clusters and stripelike arrays) have been observed in several experiments by tuning nanoparticle interactions.32–36 A variety of responsive polymers can be used to modify the particle surface, which provide an ideal toolbox for controlling the interparticle interactions under specific environmental triggers, such as temperature, pH, and ultraviolet (UV) light.37–39 Previous computational and experimental studies have investigated the structure and diffusion of non-responsive nanoparticle monolayer at the liquid-liquid or liquid-vapor interfaces.40–43 However, the behavior of stimuli-responsive particle monolayers remains largely unexplored. Among commonly used stimuli, the pH trigger is generally simple and can be easily implemented owing to a large number of pH-responsive polymers. Our previous study44 focused on the adsorption behavior of a single pH-responsive particle. In this work, we focus on the connection between individual particle adsorption and their self-assembly and cooperative behavior. We computationally model the pH-responsive particle monolayer at the water-oil interface and probe its microstructure and dynamics subject to pH changes. The monolayer exhibits a disorder-to-order transition at low surface coverage when the strength of electrostatic interactions increases, which can be reversed by introducing electrolytes. We characterize the dynamics and collective motion of particles in the monolayer, which are correlated to its structural transition. The simulation results provide a deeper understanding of the responsive particle monolayer at fluid interfaces, and shed light on the systematic design of colloidal nanostructures, active emulsions, and reactive droplets. Computational Method 3


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Using

electrostatic

dissipative

particle

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dynamics

(DPD),44–48

we

model

a

polyelectrolyte-grafted nanoparticle (PGNP) monolayer formed at a planar water-oil interface and probe its structure and dynamic properties. In the standard DPD model,49–53 each fluid or solid element is represented by a coarse-grained bead, which may contain multiple atoms or molecules interacting with each other. The motion of a DPD bead i is described by the classical Newton mechanics:

= ,

= . The equation of motion is integrated by the

velocity-Verlet algorithm, giving the instantaneous bead position and velocity. The interacting beads thus collectively determine the thermodynamics of the fluidic system and reproduce correct hydrodynamics. The forces acting on each bead i by its neighbors can be categorized into five components:

= ∑ + + + ∑ + . Here, , , and are the conservative, dissipative, and random forces, respectively. These forces are present in the standard DPD. is the bond force acting on beads forming a polymer chain. is the electrostatic force between charged beads. It is noteworthy that all forces are pairwise additive. The conservative force is a soft repulsion, expressed as =

1 − , < , 0, ≥

where = !" − # !, = " − # $ . The positive factor scales the maximum repulsion strength between beads i and j. The repulsion does not diverge even when the two beads completely overlap, permitting the use of larger timesteps than that of molecular dynamics simulations with the Lennard-Jones potential. The dissipative and random forces are given by

= −%& ( )( ∙ ) and = *& + , respectively. Here, = " − # is the

relative bead velocity. & and & are two weight functions dependent on the interparticle

distance, which are given by & = & ( ), = (1 − ), . + is a Gaussian random variable with zero mean and unit variance. The noise amplitude * scales the random force,

whose value is coupled with the friction coefficient % through the fluctuation-dissipation

4


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relation * , = 2. /% , with . being the Boltzmann constant and / being the system

temperature. The % magnitude is chosen carefully to expedite equilibration of the system

temperature and to maintain numerical stability throughout the simulation. Importantly, the dissipative and random forces linked by the fluctuation-dissipation relation ensure that the simulation trajectories correctly sample a canonical ensemble. In the dimensionless simulation, we take the cut-off radius 0 as characteristic length scale and . / as characteristic energy scale. The characteristic time scale 1 can be then defined as ( 0, ⁄. /)3/, . For simplicity, 0 ,

, . /, and 1 are all set to be one. The timestep in this study is chosen to be ∆6 = 0.021.

As the building block of a monolayer, a polyelectrolyte-grafted nanoparticle is constructed by two parts: an uncharged rigid particle core and 16 flexible polyelectrolyte chains grafted on the core surface, each carrying a net charge. Each polyelectrolyte is modeled as an ideal chain by the bead-spring configuration.54–57 Charged DPD beads representing individual Kunh segments are connected sequentially by harmonic bonds with potential 8(9 − 9: ),/2. The corresponding bond force is thus = −8 − 9: . Stiff and short bonds with elastic

constant 8 = 128 and equilibrium length 9: = 0.5 are applied to prevent unphysical bond

crossing in this study,58–60 in which the polymer concentration is low and polymer-polymer interactions are infrequent. Chain lengths of =0 = 10 and =0 = 20 are modeled in this study. Additional details of the polyelectrolyte-grafted nanoparticle model can be found in previous studies.44,61 The beads in the system are categorized into five types: water, oil, particle core, polymer, and counterion. The interaction parameters between beads of the same species is set to be = 25,51 while the cross-species parameters reflect the chemical properties of the components. The nanoparticle core is considered hydrophobic (e.g., polystyrene). Thus, the interaction parameters are set to 0>?@ = 75 between core and water and to 0>?> = 25 between core and oil. The linear polyelectrolyte is weakly hydrophilic, e.g., poly(acrylic acid) or poly(dimethylaminoethyl

methacrylate),

with

interaction

parameters

B?@ = 25

and 5


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B?> = 45. Since the counterions are insoluble in oil, the interaction parameters between

counterions and the solvents are set to be D?@ = 25 and D?> = 100. Finally, the water and oil

phases are highly immiscible with interaction parameter @?> = 100.

Weak polyelectrolytes exhibit charge states sensitive to the change of pH in solution. More specifically, the number of charged beads on each polyelectrolyte (i.e., degree of ionization E) is controlled by the extended Henderson-Hasselbalch equation:54 pH = p8H ∓ log3: (

E ) 1−E

with the positive (negative) sign for anionic (cationic) species. The actual degree of ionization and the corresponding pH value in a physical system can be obtained by mapping the model to a specific weak polyelectrolyte. Notably, the ionization of weak polyelectrolytes can also be influenced by salt, polyelectrolyte concentration, and dielectric properties of solution,62–64 but these effects are beyond the scope of this study. Therefore, the value of E is varied directly from 0% to 70% in this study to represent the pH effect. Long-range electrostatic interactions between charged DPD beads are critical to the pH effect and must be calculated accurately and effectively. We recently developed an electrostatic DPD model by incorporating a serial Poisson solver to compute the local electric field and thus the electric forces applied on the beads.44 In particular, the nondimensional Poisson equation is solved on a uniform grid using the finite difference discretization and the real-space successive over relaxation (SOR). To prevent unphysical ion binding induced by the soft-core conservative force, the point charge carried by an off-lattice DPD bead is smeared to the nearby lattice nodes by a Slater type density distribution. The effect of the dielectric discontinuity across the water-oil interface is readily captured by introducing a local permittivity ratio in the Poisson equation. The electrostatic interactions between beads coupled to the DPD dynamics are resolved by an in-house modification and extension of particle simulator LAMMPS.65 The details of the electrostatic calculation have been described elsewhere.44 6


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The electrostatic DPD has been successfully applied to explore the interfacial adsorption of single PGNP.44 However, the computational cost for the electrostatic calculation becomes significant when one attempts to model a monolayer with many particles and probe its collective dynamics. Thus, we improve the performance of the electrostatic DPD by parallelizing the Poisson solver using the red-black SOR method.66 In the red-black scheme, the entire computational grid can be divided into two staggered cells, which are colored conceptually as red and black. By separating the red and black cells, we can take the SOR iterations in two steps with respect to each colored grid. Instead of updating the data asynchronously in the traditional SOR, the red-black SOR allows different threads to access the global data simultaneously, which optimizes the communication and improves the computation performance. Compared with previous serial execution, the performance of the new parallel solver achieves nearly 8 times improvement, which can readily model the monolayer systems. The simulation system contains the water and oil phases with PGNPs straddling the water-oil interface. The typical size of the simulation box is 30 × 60 × 60 with periodic boundary conditions imposed in all three directions. The water phase occupies half region of the simulation box (15 × 60 × 60), and a slab of oil beads occupies the other half. Thus, the dielectric discontinuity occurs along the x direction. Additional simulations with larger transverse dimensions parallel to the interfacial plane (120 × 120 and 180 × 180) show negligible finite-size effect. The particles are initially placed at the water-oil interface (at P = 15), and a

given number of particles is assigned to achieve a specific surface coverage. The counterions are dispersed in the water phase to ensure the charge neutrality of the whole system. The total number density of the system is set to 3, as it follows standard practice in DPD. To monitor the self-assembly behavior of PGNP monolayers, the pre-equilibration of the binary solvent is performed for 5 × 10Q timesteps, and the PGNPs are fixed throughout this stage. Simulations of 8 × 10R timesteps are then conducted to probe the microstructure

development in the PGNP monolayer for the standard 30 × 60 × 60 system. After the monolayer reaches equilibrium (typically requires 3 × 10R timesteps), an additional 5 × 10R

7


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timesteps are used to quantify the structure to eliminate the startup effect. To achieve good statistics, a larger simulation system of 30 × 120 × 120 were used to characterize the

monolayer dynamics over a production period of 1 × 10R timesteps. Notably, the 30 × 120 × 120 system requires significantly longer time (approximately 1.1 × 10S timesteps) to reach

equilibrium structure before the dynamic analysis. A typical simulation running on a high performance computing cluster uses 3 compute nodes (48 cores) and needs 16 hours to complete. Each node consists of 2 Intel® Xeon® E5-2667 v2 8-core processors running at 3.30 GHz with 96GB of DDR3 RAM and 56Gb/s FDR InfiniBand for inter-node communication. Results and Discussion Microstructure Characterization We first examine the structural properties of the monolayers formed by the PGNPs. As described in the previous section, we directly place a specific number of PGNPs at the interface to achieve a desired surface coverage. The surface coverage is defined as the ratio of the interfacial area occupied by PGNPs to the total area of the water-oil interface. Assuming a flat interface with particles having simple spherical shape, the surface coverage can be easily calculated by T = UVWB, /X, where WB is particle radius and X is the interfacial area.33,40 However, the grafted polymer chains occupy volumes that are sparsely distributed and constantly moving in the 3D space. Thus, the radius of PGNP is ambiguous and not well defined. Herein, we estimate the surface coverage based on the fluid density distribution.61 Briefly, the interface is discretized into a square grid with a lattice spacing of 1 DPD units. If the number of PGNP beads (including both core and polymer beads) in each interfacial cell is greater than or equal to 3, this cell is considered solvent-free and thus occupied by particle. The surface coverage is then obtained as the fraction of occupied cells. The monolayer surface coverage is taken to be approximately 0.30 to minimize the influence of short-range physical interactions between the particles. Notably, the surface coverage is calculated for the PGNPs at 0% degree of ionization (i.e., uncharged). Two types of monolayer

systems, each with PGNPs consisting of different grafted chain lengths (=0 = 10 and =0 = 20), 8


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are modeled in this study. The total number of particles placed at the interface are modified accordingly in order to keep the surface coverage consistent, since the two types of PGNPs have different effective volumes. In particular, the numbers of =0 = 10 and =0 = 20 particles are 30 and 15, respectively. Previous studies44 have shown that when the grafted polyelectrolytes have different degrees of ionization, the morphology of core-shell particle changes accordingly due to the intramolecular and intermolecular electrostatic repulsions. At a relatively high degree of ionization, the polyelectrolytes swell drastically, and the shell density reduces. The strong image effect occurs in the vicinity of the dielectric interface. As a result, the surface activity of particle decreases. Despite these changes, the surface coverage of the monolayer does not change significantly. In order to better elucidate the variation of out-of-plane structure when the degree of ionization changes, we present the results for the monolayers of PGNPs with relatively long chains (=0 = 20). When the degree of ionization changes from 0% to 50%, the polymer shell undergoes a morphology transition from a dense disk along the interface to a loose hemisphere extended into the water phase. Accordingly, an expanded polyelectrolyte region can be clearly observed at E = 50% in the simulation snapshots and density contours plotted in Figure 1. In contrast, the uncharged monolayer is highly confined at the interface. The monolayer position normal to the interface also moves toward water, driven by the enhanced mirror image repulsion from increased E. The spatial arrangement of PGNPs in the monolayer closely relates to their individual and collective dynamics. The structure could further influence the interactions between two particle-laden interfaces, which is critical to the stability of emulsion droplets covered by the PGNP monolayers. Notably, the dominant short-range interaction between particles is the steric repulsion due to the grafted polyelectrolytes. When the surface coverage is low, the time-averaged repulsion is small because the particles remain far away from each other. Induced by increasing steric repulsion, the monolayer develops 2D hexagonal order at high surface coverage.40,41,61 Some experimental studies43,67 on oil-in-water emulsions stabilized by particles 9


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have reported that the incorporation of electrostatic interactions can also trigger the ordering of monolayer at the droplet interface. Herein, we quantitatively characterize the in-plane structure of a low-surface-coverage PGNP monolayer at various ionization states and probe its structural transition by harnessing the long-range electrostatic interactions. We present representative simulation snapshots as direct visualization of the in-plane structure. Based on the particle positions, we construct the Voronoi tessellation to demonstrate the spatial partitioning of the monolayer. Figure 2 clearly shows a disordered state for uncharged particle monolayer (i.e., the degree of ionization is zero) with polyelectrolytes of both lengths. Particles are sparsely dispersed in the monolayer with minimal overlapping between their chains, leading to negligible short-range repulsion. Since the degree of ionization is zero, there are no long-range electrostatic interactions. The particles can organize randomly without any positional order, which is further corroborated by the irregular Voronoi cells in Figure 3. When the degree of ionization increases to an intermediate value E = 20%, both the snapshots and Voronoi diagrams show small, localized crystalline clusters combined with predominant disordered regions, indicating the gradual development of long-range order. With the increasing degree of ionization, the PGNPs start to feel stronger electrostatic repulsions from the surrounding ones. We measure the electrostatic interactions within the monolayer by averaging the electric field magnitudes at the lattice nodes located in the interfacial region (defined by a thickness of three DPD length units into the water phase from the water-oil interface). Figure 4(a) plots the electric field contour at E = 20%, showing weak repulsion.

Nevertheless, a further increase in E to 50% induces a prominent phase transition in the monolayer, which now exhibits a crystalline state. The top-view snapshots in Figure 2 show a salient hexagonal pattern of PGNPs, and the Voronoi diagram is dominated by hexagonal cells having relatively uniform areal size. Notably, the hexagonal packing is not close-packed, as the particles keep a long average distance between each other at the low surface coverage. Compared with the contour obtained at α = 20%, the electric field surrounding each PGNP is much stronger when α = 50% (see Figure 4(b)). In addition, a comparison between Figures S1 and 4

10


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reveals 1.5 times (20%) and 2.0 times (50%) larger effective interaction radius than the actual particle size (estimated by the polymer density contour), highlighting the long-range nature of electrostatic interactions. More importantly, the effective interaction volume of particles overlaps with each other when α = 50%, resulting in strong repulsion and hexagonal ordering. In summary, we observe a disorder-to-order structural transition in the PGNP monolayers with different chain lengths as the degree of ionization of particle varies. Two-dimensional particle-particle radial distribution functions (RDFs) and the structure factor are used to quantitatively characterize the structural order of PGNPs and probe the monolayer phase transition. While the RDF describes the variation in packing density associated with short-range and long-range order, the structure factor explicitly reveals the pattern of particle arrays. Both quantities are calculated based on the in-plane positions of particle centers. The structure factor of a monolayer with [B particles is defined by the core positions \ and h

h

i i ∑]j3 ] as S(_) = 〈1/[B ∑\j3 exp d−e_ ⋅ (\ − ] )g〉. _ = .l ml + .n mn is a 2D wave vector,

with ml and mn being unit vectors along the transverse directions of the monolayer. The minimal wave vector components .l and .n are determined by the box dimensions in the y and

z directions, respectively. When α is low, Figure 5(a,b) plot characteristic RDF profiles for the disordered liquid state, where different positions of the primary peaks correspond to the particles with different chain lengths. The structure factor shown in Figure S2 further confirms the absence of long-range structure. Upon increasing the degree of ionization, the profile peaks become more pronounced and their positions shift right, indicating the strengthening of both short-range and long-range order. The peak shift is induced by the effective swelling of particle shell described before. The troughs between peaks reduce to zero, which indicates all particles are packed regularly. The long-range hexagonal order can be clearly identified in the structure factor contour when α is 50% for both monolayers. Although the electrostatic interaction is long-range, its effect diminishes when the particle separation is beyond a certain distance. As exhibited in 11


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Figure S3, the PGNP monolayer with a lower surface coverage (0.15) does not show ordered structure even when α is high. To better illustrate the disappearance of crystalline structure in this monolayer, we plot the electric field distribution in Figure S3c. One can observe that the interparticle distance is significantly larger than the effective radius of electrostatic interactions. Thus, the monolayer retains the disordered state even with highly charged particles. The above quantification provides evidence of the structural phase transition in the PGNP monolayer modulated by the long-range electrostatic interactions. Below, we further elaborate on two additional structure analyses for long-range order, namely fraction of particles having exact six nearest neighbors, oS ,61 and bond orientational order parameters, 〈pS 〉 .33,40,41 oS is computed as a function of degree of ionization, in which the nearest neighbors are defined as particles within the first neighboring shell.41 The shell thickness is defined by the position of the first trough detected in the corresponding RDF profile shown in Figure 5. The value of oS equals 1 for a monolayer with perfect hexagonal ordering. For both PGNPs with short and long chains, the monotonic and gradual increase of oS in Figure 5(c) marks a continuous disorder-to-order phase transition from low to high degree of ionization. The bond orientational

order parameter for an individual particle j characterizes the local order, given by pS = h

uv 1/[qr ∑tj3 exp (e6st ) where [qr is the total number of nearest neighbors and st is the

angle between the vector joining the positions of particle j and neighbor k and an arbitrary axis of

reference. The combination of absolute value of local order parameter !pS ! and the Voronoi diagram provides excellent presentation of particle ordering in the monolayer as shown in Figure h

i 3. In addition, the ensemble average of local order parameter 〈pS 〉 = 〈w1/[B ∑j3 pS w〉

measures the overall extent of the long-range hexagonal order developed in the monolayer. 〈pS 〉 approaches zero in a disordered liquid state, while it equals 1 when the PGNPs are packed

perfectly in a hexagonal pattern. Similar to the behavior of oS , 〈pS 〉 also increases as the degree of ionization α increases in Figure 5(d). Notably, the error bars for α = 10% and 20% are

relatively larger than others, which are induced by unstable hexagonal order. The monolayer 12


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presents mixed hexagonal and disordered regions when α is relatively low (see the middle columns of Figures 2 and 3). By examining the complete simulation, we also find that the PGNPs with less charge can arrange hexagonally for some periods of time, and then lose their long-range positional order. Since the electrostatic interactions between particles are weak for low degrees of ionization, the ordering is also sensitive to the inhomogeneous particle morphology due to the random grafting of polyelectrolyte chains. As α increases, not only does

a higher fraction of the monolayer become ordered, the smaller variations of oS and 〈pS 〉

indicate that the ordered regions are more stable. The influence of shape inhomogeneity reduces when the particles strongly interact with each other. The asymptotic saturations of oS and 〈pS 〉 also confirms the high stability of the hexagonal structure. These qualitative and quantitative analysis shows that, by varying the degree of ionization and thereby controlling the long-range electrostatic interactions, the charged PGNP monolayer exhibits a disorder-to-order phase transition at a fixed surface coverage. Electrolytes are ubiquitous components in practical applications and physical systems. Thus, it is necessary to probe the influence of salinity on the structure of PGNP monolayer. Herein, the model nanoparticles are grafted with 50% ionized polyelectrolytes of chain length =0 = 20. The monolayer surface coverage is still chosen to be about 0.30. We vary the volume concentration of salt ions and compare the monolayer structure to elucidate its effect on the particle ordering. Similarly, qualitative characterization of monolayer structure is given by the Voronoi construction and structure factor contours, while we present oS and 〈pS 〉 as the quantitative measurements of the long-range order development. According to previous studies,44 the salt ions can induce a significant change in the morphology and position of a single PGNP when adsorbed at the water-oil interface. The physical mechanism is the screening of electrostatic interactions. Figure 6 reveals that the addition of salt ions decreases the ordering of the PGNP monolayer to a great extent. An order-to-disorder phase transition is evident when the monolayer is exposed to salt with increasing concentrations. The phase transition can be attributed to the screening effect of 13


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surrounding salt ions. Figure S4 plots the distribution of the salt ions with charge opposite to the polyelectrolyte. The salt ions accumulate around PGNPs as its density profile indicates. The charged polyelectrolytes exert attractive interactions on the oppositely charge salt ions. This attraction and polymer-ion binding is further confirmed by the pair correlation functions in Figure S5. Comparing the two electric fields in Figure S6, the aggregation of salt ions around each particle reduces the electric field magnitude and shortens the effective radius of electrostatic interactions. Therefore, when the salt concentration is high enough, the influence of long-range electrostatic interaction diminishes, and the monolayer returns to the disordered state. The six-neighbor fraction oS and order parameter 〈pS 〉 are presented in Figure 7 as functions of salt concentration. Both parameters show similar and consistent trend of decreasing ordering as the salt concentration increases, which corroborates the observed phase transition of PGNP monolayer induced by salt. Dynamics and Collective Behavior The monolayer structure is also correlated with the dynamic behavior of the PGNPs, because the interparticle interactions not only determine the spatial distribution of particles but also their in-plane motions. We probe the individual particle dynamics in the monolayer by 2D mean square displacement (MSD) 〈∆ , 〉,41,68 which is shown

in Figure 8(a). 〈∆ , 〉 scales with 6 , in short time, indicating ballistic motion of particle within

its mean free path on the interface. As time increases, the MSD exhibits a transition from the ballistic regime to linear diffusive regime (plotted on linear scales in Figure S7). The long-time self-diffusion coefficient can then be extracted by the Einstein relation 〈∆ , 〉 = 4{6 in the diffusive regime. As the monolayer undergoes the disorder-to-order transition with increasing α,

both the MSD and diffusion coefficient in Figure 8 reveal the slowdown of the long-time particle motions. For the liquid state at low α, the interactions from neighboring particles are too weak to restrict the motion of each individual PGNP, while the particle mobility decreases over two times when α is high, due to the caging effect from the hexagonally-packed particles. To further characterize the caging effect in the highly ordered monolayer, Figure 9 plots a comparison between the trajectories of selected PGNPs when α = 0% and α = 50% , 14


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corresponding to the disordered and ordered states, respectively. The PGNPs undergo fast Brownian diffusion when they are disordered, and their motions are highly constrained in the cages when the monolayer establishes the hexagonal pattern. We calculate the scaled vector-vector auto correlation function |(Δ6, 1) = 〈

3

h?~

40,69 ∑h?~ (∆6) is j3 (Δ6) ∙ ~ (∆6)〉.

the displacement vector connecting the position of PGNP at time 6 to the position at time 6 + ∆6. In Figure 10, we observe a negative correlation of the displacement vectors over a short

time when α = 50%, which is induced by the caging effect. In particular, when a particle is

trapped in the cage formed by its neighbors, the confinement constantly reflects the particle and reverse its direction of motion, leading to the negative correlation. It is noteworthy that the diffusion coefficient is not equal to zero at the crystalline state (α = 50%), which is attributed to the collective dynamics of the entire monolayer. Once the PGNPs are trapped locally due to the onset of long-range order, they only fluctuate around the equilibrium position within the cage region in a short time period. However, the cooperative motion together with the neighboring particles leads to a short-distance traveling in a long-time period. To illustrate the collective motion, we averaged the unit vector indicating the direction of motion of individual particle for a period of 2 × 105 timesteps. Figure S8 shows the random velocity directions when α is 0%, whereas most particles move in the same direction when

α = 50%. The coherence in the velocity directions suggests the monolayer diffuses as a unit. We

also want to note that we assume Brownian diffusion for all cases when calculating the diffusion coefficients for the monolayers having different E. However, it is apparent that the slopes of MSD at E = 40% and 50% in Figure 8(a) are lower than 1, indicating a subdiffusive behavior. This crossover from the diffusive to subdiffusive regimes is caused by the caging effect associated with the development of long-range order, which has been reported in previous studies.70,71 Conclusions In this work, we performed electrostatic dissipative particle dynamics to study the 15


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self-assembly of polyelectrolyte-grafted nanoparticles at the water-oil interface and to probe the influence of long-range electrostatic interactions on the structure and diffusion of responsive particle monolayers. The simulation enables us to directly visualize the morphology of individual particles as well as the out-of-plane and in-plane structures of the entire monolayer. Through the quantitative and qualitative characterization of PGNP ordering, the simulations reveal a liquid-crystalline phase transition in the monolayer with low surface coverage as the degree of ionization increases. Although the disorder-to-order transition has been observed in uncharged particle monolayers in the process of varying the surface coverage, the present structural transition is fundamentally different. Herein, the onset of the hexagonal structures is driven by the long-range electrostatic interactions instead of the short-range steric repulsions between unchanged particles, which therefore permits the transition at low surface coverage. Moreover, the reverse order-to-disorder transition can be readily triggered by introducing electrolytes. The salt ions can effectively screen electrostatic interactions and destroy the long-range order of structure. Importantly, the structural transition due to the long-range electrostatic interactions also affects the dynamics of PGNPs. The self-diffusion coefficient reduces as the monolayer develops the hexagonal pattern. The particle trajectories reveal the hindered motion by the cages formed by neighboring particles in the ordered state. Accompanied with the phase transition, the crossover to an anomalous subdiffusive regime is prominent. The findings in this work provide important insight into the self-assembly behavior of polyelectrolyte-grafted nanoparticle monolayers for compelling applications. Importantly, both the structure and dynamics of nanoparticles at water-oil interfaces can be critical factors affecting particle removal from the interface, which influences the emulsion stability. Moreover, the long-range electrostatic interactions between nanoparticles can provide additional control to either inhibit or promote droplet coalescence. Our future study will focus on the interactions between two droplets covered by stimuli-responsive nanoparticles. Supporting Information Additional analysis of the steric interaction range; supporting data of monolayer structure 16


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and salt effect; additional characterizations of dynamics and collective behavior of PGNPs. Acknowledgments The authors thank the Donors of the American Chemical Society Petroleum Research Fund for support of this research under grant 56884-DNI9. Generous allocation of computing time was provided by the Watson Data Center at Binghamton University and the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704. References (1)

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Figure 1. (Top panel) Cross-sectional views of representative simulation snapshots and (bottom panel) time-averaged density contours of polymer chains in the x-y plane showing the out-of-plane structure of the PGNP monolayer at degrees of ionization (a) 𝛼𝛼 = 0% and (b) 𝛼𝛼 = 50%. The polyelectrolyte length is 20. The black solid lines in each snapshot represent the position of the water-oil interface.


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Figure 2. Top views of representative simulation snapshots showing the in-plane structure of the PGNP monolayers at different degrees of ionization. The lengths of grafted chains 𝐿𝐿c are (a) 10 and (b) 20.


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Figure 3. Representative Voronoi diagrams of nanoparticles with chain lengths of (a) 𝐿𝐿𝑐𝑐 = 10 and (b) 𝐿𝐿𝑐𝑐 = 20 at different degrees of ionization. The color of each Voronoi cell represents the 𝑗𝑗

magnitude of the local orientational order parameter �𝜓𝜓6 �.


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Figure 4. Representative electric field contours of the PGNP monolayer at degrees of ionization (a) α = 20% and (b) α = 50%. The grafted chain length is 𝐿𝐿c = 20.


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Figure 5. Time-averaged, two-dimensional particle-particle radial distribution functions of the particles in the monolayers obtained at increasing degree of ionization. The particles have different grafted chain lengths (a) 𝐿𝐿c = 10 and (b) 𝐿𝐿c = 20. The six-neighbor particle fraction 𝑓𝑓6 and bond orientational order parameter 〈𝜓𝜓6 〉 for each length were obtained and compared at increasing degrees of ionization in (c) and (d), respectively. Error bars represent time variations within a single simulation run.


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Figure 6. (a) Representative Voronoi diagrams and (b) time-averaged structure factor contours of PGNP monolayers at different salt concentrations. The length of grafted chains 𝐿𝐿c = 20.


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Figure 7. (a) Six-neighbor particle fraction 𝑓𝑓6 and (b) bond orientational order parameter 〈𝜓𝜓6 〉 obtained for the PGNP monolayers subject to different salt concentrations. The length of grafted polyelectrolytes is 20.


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Figure 8. (a) Log-log plot of mean square displacements 〈∆𝑟𝑟 2 〉 as functions of simulation time at α = 0%, 10%, 20%, 30%, 50% ; (b) degree of ionization dependence of the long-time selfdiffusion coefficient, normalized by the diffusion coefficient 𝐷𝐷0 obtained from the α = 0% case. 𝐷𝐷0 = 0.02369 𝑟𝑟c2 /𝜏𝜏. Error bars in (b) are smaller than the markers.


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Figure 9. PGNP trajectories with a total observation time of 2 × 105 timesteps per PGNP at degrees of ionization (a) 0% and (b) 50%.


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Figure 10. Normalized vector correlation function G(Δt, τ) for PGNP monolayers with 𝛼𝛼 = 0% (diamonds), 𝛼𝛼 = 20% (squares) and 𝛼𝛼 = 50% (triangles).


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