Grafted nanoparticles as soft patchy colloids: self-assembly versus phase separation.

We investigate the thermodynamic behavior of a model polymer-grafted nanoparticle (GNP) system on a fine lattice, using grand canonical Monte Carlo simulations, to compare and contrast the validity of two different models for GNPs: "nanoparticle amphiphiles" versus "patchy particles." In the former model, continuous self-assembly processes are expected to dominate the system, whereas the latter are characterized by first-order phase separation into novel equilibrium phases such as "empty liquids." We find that, in general, considering GNPs as amphiphiles within the framework of a recent mean-field theory [Pryamtisyn et al., J. Chem. Phys. 131, 221102 (2009)] provides a qualitatively accurate description of the thermodynamics of GNP systems, revealing either first-order phase separation into two isotropic phases or continuous self-assembly. Our model GNPs display no signs of empty liquid formation, suggesting that these nanoparticles do not provide a route to such phases.

Inertial and viscoelastic forces on rigid colloids in microfluidic channels.

We perform hybrid molecular dynamics simulations to study the flow behavior of rigid colloids dispersed in a dilute polymer solution. The underlying Newtonian solvent and the ensuing hydrodynamic interactions are incorporated through multiparticle collision dynamics, while the constituent polymers are modeled as bead-spring chains, maintaining a description consistent with the colloidal nature of our system. We study the cross-stream migration of the solute particles in slit-like channels for various polymer lengths and colloid sizes and find a distinct focusing onto the channel center under specific solvent and flow conditions. To better understand this phenomenon, we systematically measure the effective forces exerted on the colloids. We find that the migration originates from a competition between viscoelastic forces from the polymer solution and hydrodynamically induced inertial forces. Our simulations reveal a significantly stronger fluctuation of the lateral colloid position than expected from thermal motion alone, which originates from the complex interplay between the colloid and polymer chains.

Structural transitions of solvent-free oligomer-grafted nanoparticles.

Novel structural transitions of solvent-free oligomer-grafted nanoparticles are investigated by using molecular dynamics simulations of a coarse-grained bead-spring model. Variations in core size and grafting density lead to self-assembly of the nanoparticles into a variety of distinct structures. At the boundaries between different structures, the nanoparticle systems undergo thermoreversible transitions. This structural behavior, which has not been previously reported, deviates significantly from that of simple liquids. The reversible nature of these transitions in solvent-free conditions offers new ways to control self-assembly of nanoparticles at experimentally accessible conditions.

Dissipative particle dynamics simulations of polymer-protected nanoparticle self-assembly.

Dissipative particle dynamics simulations were used to study the effects of mixing time, solute solubility, solute and diblock copolymer concentrations, and copolymer block length on the rapid coprecipitation of polymer-protected nanoparticles. The simulations were aimed at modeling Flash NanoPrecipitation, a process in which hydrophobic solutes and amphiphilic block copolymers are dissolved in a water-miscible organic solvent and then rapidly mixed with water to produce composite nanoparticles. A previously developed model by Spaeth et al. [J. Chem. Phys. 134, 164902 (2011)] was used. The model was parameterized to reproduce equilibrium and transport properties of the solvent, hydrophobic solute, and diblock copolymer. Anti-solvent mixing was modeled using time-dependent solvent-solute and solvent-copolymer interactions. We find that particle size increases with mixing time, due to the difference in solute and polymer solubilities. Increasing the solubility of the solute leads to larger nanoparticles for unfavorable solute-polymer interactions and to smaller nanoparticles for favorable solute-polymer interactions. A decrease in overall solute and polymer concentration produces smaller nanoparticles, because the difference in the diffusion coefficients of a single polymer and of larger clusters becomes more important to their relative rates of collisions under more dilute conditions. An increase in the solute-polymer ratio produces larger nanoparticles, since a collection of large particles has less surface area than a collection of small particles with the same total volume. An increase in the hydrophilic block length of the polymer leads to smaller nanoparticles, due to an enhanced ability of each polymer to shield the nanoparticle core. For unfavorable solute-polymer interactions, the nanoparticle size increases with hydrophobic block length. However, for favorable solute-polymer interactions, nanoparticle size exhibits a local minimum with respect to the hydrophobic block length. Our results provide insights on ways in which experimentally controllable parameters of the Flash NanoPrecipitation process can be used to influence aggregate size and composition during self-assembly.

A comparison of implicit- and explicit-solvent simulations of self-assembly in block copolymer and solute systems.

We have developed explicit- and implicit-solvent models for the flash nanoprecipitation process, which involves rapid coprecipitation of block copolymers and solutes by changing solvent quality. The explicit-solvent model uses the dissipative particle dynamics (DPD) method and the implicit-solvent model uses the Brownian dynamics (BD) method. Each of the two models was parameterized to match key properties of the diblock copolymer (specifically, critical micelle concentration, diffusion coefficient, polystyrene melt density, and polyethylene glycol radius of gyration) and the hydrophobic solute (aqueous solubility, diffusion coefficient, and solid density). The models were simulated in the limit of instantaneous mixing of solvent with antisolvent. Despite the significant differences in the potentials employed in the implicit- and explicit-solvent models, the polymer-stabilized nanoparticles formed in both sets of simulations are similar in size and structure; however, the dynamic evolution of the two simulations is quite different. Nanoparticles in the BD simulations have diffusion coefficients that follow Rouse behavior (D ∝ M(-1)), whereas those in the DPD simulations have diffusion coefficients that are close to the values predicted by the Stokes-Einstein relation (D ∝ R(-1)). As the nanoparticles become larger, the discrepancy between diffusion coefficients grows. As a consequence, BD simulations produce increasingly slower aggregation dynamics with respect to real time and result in an unphysical evolution of the nanoparticle size distribution. Surface area per polymer of the stable explicit-solvent nanoparticles agrees well with experimental values, whereas the implicit-solvent nanoparticles are stable when the surface area per particle is roughly two to four times larger. We conclude that implicit-solvent models may produce questionable results when simulating nonequilibrium processes in which hydrodynamics play a critical role.

Anisotropic self-assembly of spherical polymer-grafted nanoparticles.

It is easy to understand the self-assembly of particles with anisotropic shapes or interactions (for example, cobalt nanoparticles or proteins) into highly extended structures. However, there is no experimentally established strategy for creating a range of anisotropic structures from common spherical nanoparticles. We demonstrate that spherical nanoparticles uniformly grafted with macromolecules ('nanoparticle amphiphiles') robustly self-assemble into a variety of anisotropic superstructures when they are dispersed in the corresponding homopolymer matrix. Theory and simulations suggest that this self-assembly reflects a balance between the energy gain when particle cores approach and the entropy of distorting the grafted polymers. The effectively directional nature of the particle interactions is thus a many-body emergent property. Our experiments demonstrate that this approach to nanoparticle self-assembly enables considerable control for the creation of polymer nanocomposites with enhanced mechanical properties. Grafted nanoparticles are thus versatile building blocks for creating tunable and functional particle superstructures with significant practical applications.

Preparation of poly(ethylene glycol) protected nanoparticles with variable bioconjugate ligand density.

Maleimide-functional poly(ethylene glycol)-b-poly(epsilon-caprolactone) nanoparticles (NPs) were prepared via the Flash NanoPrecipitation technique. Subsequent reaction with a model ligand, bovine serum albumin (BSA), was conducted using thiol-maleimide conjugation. Reaction of up to 22% of NP surface maleimide-PEG tethers was obtained, with the percent conversion being essentially independent of the ratio of maleimide-PEG to methyl-PEG over the range 30-100%, respectively. At the highest surface coverage, BSA is calculated to essentially cover the NP surface area. Reaction parameters (reaction order and docking constant) describing the extent of ligand conjugation were determined. The reaction order is applicable to the conjugation of ligands presenting free thiol functionalities, while the value of the docking constant is ligand-dependent and accounts for physical and dynamic properties of the ligand-PEG interaction. Jointly, the particle formation process, using block copolymer-directed kinetically controlled assembly and surface functionalization represent a versatile new platform for the preparation of bioconjugated NPs with accurate control of ligand density and minimal processing steps.

Directed Assembly of Soft Colloids through Rapid Solvent Exchange.

We studied the directed assembly of soft nanoparticles through rapid micromixing of polymers in solution with a nonsolvent. Both experiments and computer simulations were performed to elucidate the underlying physics and to investigate the role of various process parameters. In particular, we discovered that no external stabilizing agents or charged end groups are required to keep the colloids separated from each other when water is used as the nonsolvent. Furthermore, the size of the nanoparticles can be reliably tuned through the mixing rate and the ratio between polymer solution and nonsolvent. Our results demonstrate that this mechanism is highly promising for the mass fabrication of uniformly sized colloidal particles, using a wide variety of polymeric feed materials.

Molecular dynamics simulations of water permeation across Nafion membrane interfaces.

Permeation of water across the membrane/vapor and membrane/liquid-water interfaces of Nafion is studied using nonequilibrium molecular dynamics (NEMD) simulations, providing direct calculations of mass-transfer resistance. Water mass transfer within one nanometer of the vapor interface is shown to be 2 orders of magnitude slower than at any other point within the membrane, in qualitative agreement with permeation experiments. This interfacial resistance is much stronger than the resistance suggested by prior simulation work calculating self-diffusivity near the interface. The key difference between the prior approach and the NEMD approach is that the NEMD approach implicitly incorporates changes in solubility in the direction normal to the interface. Water is shown to be very insoluble near the vapor interface, which is rich in hydrophobic perfluorocarbon chains, in agreement with advancing contact angle experiments. Hydrophilic side chains are buried beneath this hydrophobic layer and aligned toward the interior of the membrane. Hydrophilic pores are not exposed to the vapor interface as proposed in prior theoretical work. At the membrane/liquid-water interface, highly swollen polymer chains extend into the liquid-water phase, forming a nanoscopically rough interface that is consistent with atomic force microscopy experiments. In these swollen conformations, hydrophilic side chains are exposed to the liquid-water phase, suggesting that the interface is hydrophilic, in agreement with receding contact angle experiments. The mass-transfer resistance of this interface is negligible compared to that of the bulk, in qualitative agreement with permeation experiments. The water activity at the vapor and liquid-water interfaces are nearly the same, yet large conformational and transport differences are observed, consistent with a mass-transfer-based understanding of Schroeder's paradox for Nafion.

Structure of phase-separated athermal colloid-polymer systems in the protein limit.

Structural features of phase-separated athermal colloid-polymer mixtures in the so-called "protein limit," where polymer chain dimensions exceed those of the colloid, are investigated using grand canonical Monte Carlo simulations on a fine lattice. Previous work [N. A. Mahynski et al., Phys. Rev. E 85, 051402 (2012)] has shown that this model accurately captures the phase behavior of experimental systems, and that colloids with sufficiently small diameters, σ(c), relative to that of the monomeric segments, σ(s), phase separate more readily than their large-diameter counterparts. In the present study, we directly connect colloid and polymer structure with their phase behavior by investigating these solutions along their binodal curves; we also explore the role of colloid surface curvature in destabilizing such solutions. Our findings suggest that simple consideration of an additional depletion radius, on the order of the σ(s), leads to a quantitatively accurate prediction of the division between stable and unstable ranges of d=σ(s)/σ(c). We compare these results to continuum models with different bonding potentials between monomer segments in order to elucidate the significance of the lattice model's bond fluctuations and inherently coarse colloid surface. In a number of cases, the continuum models deviate both qualitatively and quantitatively from the lattice results, but the binodals of the continuum models are presently not known, making a strong conclusion about these differences impossible.

Molecular dynamics simulations of silica nanoparticles grafted with poly(ethylene oxide) oligomer chains.

A molecular model of silica nanoparticles grafted with poly(ethylene oxide) oligomers has been developed for predicting the transport properties of nanoparticle organic-hybrid materials (NOHMs). Ungrafted silica nanoparticles in a medium of poly(ethylene oxide) oligomers were also simulated to clarify the effect of grafting on the dynamics of nanoparticles and chains. The model approximates nanoparticles as solid spheres and uses a united-atom representation for chains, including torsional and bond-bending interactions. The calculated viscosities from Green-Kubo relationships and temperature extrapolation are of the same order of magnitude as experimental data but show a smaller activation energy relative to real NOHMs systems. Grafted systems have higher viscosities, smaller diffusion coefficients, and slower chain dynamics than the ungrafted ones at high temperatures. At lower temperatures, grafted systems exhibit faster dynamics for both nanoparticles and chains relative to ungrafted systems, because of lower aggregation of particles and enhanced correlations between nanoparticles and chains. This agrees with the experimental observation that NOHMs have liquidlike behavior in the absence of a solvent. For both grafted and ungrafted systems at low temperatures, increasing chain length reduces the volume fraction of nanoparticles and accelerates the dynamics. However, at high temperatures, longer chains slow down nanoparticle diffusion. From the Stokes-Einstein relationship, it was determined that the coarse-grained treatment of nanoparticles leads to slip on the nanoparticle surfaces. Grafted systems obey the Stokes-Einstein relationship over the temperature range simulated, but ungrafted systems display deviations from it.

Pressure and density scaling for colloid-polymer systems in the protein limit.

Grand canonical Monte Carlo and histogram reweighting techniques are used to study the fluid-phase behavior of an athermal system of colloids and nonadsorbing polymers on a fine lattice in the "protein limit," where polymer dimensions exceed those of the colloids. The main parameters are the chains' radius of gyration, R_{g}, the diameter of the colloids, σ_{c}, and the monomer diameter, σ_{s}. The phase behavior is controlled by the macroscopic size ratio, q_{r}=2R_{g}/σ_{c}, and the microscopic size ratio, d=σ_{s}/σ_{c}. The latter ratio is found to play a significant role in determining the critical monomer concentration for q_{r}≲4 and the critical colloid density for all chain lengths. However, the critical (osmotic) pressure is independent of the microscopic size ratio at all macroscopic size ratios studied. Quantitative agreement is observed between our simulation results and experimental data. We scale our results based on the polymer correlation length, which has previously been suggested to universally collapse these binodals [Bolhuis et al., Phys. Rev. Lett. 90, 068304 (2003); Fleer and Tuinier, Phys. Rev. E 76, 041802 (2007)]. While the density binodals exhibit universal characteristics along the low-colloid-density branch, such features are not present in the corresponding high-density phase. However, pressure binodals do collapse nicely under such a scaling, even far from the critical point, which allows us to produce a binodal curve whose shape is independent of either size ratio.

Phase behavior and structure formation in linear multiblock copolymer solutions by Monte Carlo simulation.

The solution phase behavior of short, strictly alternating multiblock copolymers of type (A(n)B(n))(m) was studied using lattice Monte Carlo simulations. The polymer molecules were modeled as flexible chains in a monomeric solvent selective for block type A. The degree of block polymerization n and the number of diblock units per chain m were treated as variables. We show that within the regime of parameters accessible to our study, the thermodynamic phase transition type is dependent on the ratio of m / n. The simulations show microscopic phase separation into roughly spherical aggregates for m / n ratios less than a critical value and first-order macroscopic precipitation otherwise. In general, increasing m at fixed n, or n at fixed m, promotes the tendency toward macroscopic phase precipitation. The enthalpic driving force of phase change is found to universally scale with chain length for all multiblock systems considered and is independent of the existence of a true phase transition. For aggregate forming systems at low amphiphile concentrations, multiblock chains are shown to self-assemble into intramolecular, multichain clusters. Predictions for microstructural dimensions, including critical micelle concentration, equilibrium size, shape, aggregation parameters, and density distributions, are provided. At increasing amphiphile density, interaggregate bridging is shown to result in the formation of networked structures, leading to an eventual solution-gel transition. The gel is swollen and consists of highly interconnected aggregates of approximately spherical morphology. Qualitative agreement is found between experimentally observed physical property changes and phase transitions predicted by simulations. Thus, a potential application of the simulations is the design of multiblock copolymer systems which can be optimized with regard to solution phase behavior and ultimately physical and mechanical properties.

Composite block copolymer stabilized nanoparticles: simultaneous encapsulation of organic actives and inorganic nanostructures.

We describe the preparation and characterization of hybrid block copolymer nanoparticles (NPs) for use as multimodal carriers for drugs and imaging agents. Stable, water-soluble, biocompatible poly(ethylene glycol)-block-poly(epsilon-caprolactone) NPs simultaneously co-encapsulating hydrophobic organic actives (beta-carotene) and inorganic imaging nanostructures (Au) are prepared using the flash nanoprecipitation process in a multi-inlet vortex mixer. These composite nanoparticles (CNPs) are produced with tunable sizes between 75 nm and 275 nm, narrow particle size distributions, high encapsulation efficiencies, specified component compositions, and long-term stability. The process is tunable and flexible because it relies on the control of mixing and aggregation timescales. It is anticipated that the technique can be applied to a variety of hydrophobic active compounds, fluorescent dyes, and inorganic nanostructures, yielding CNPs for combined therapy and multimodal imaging applications.

Monte Carlo simulation and molecular theory of tethered polyelectrolytes.

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.

Log-rolling micelles in sheared amphiphilic thin films.

Using molecular dynamics simulations, we show that sheared solutions of cylindrical micelle-forming amphiphiles behave very differently under extreme confinement as compared to the bulk. When confined to ultrathin films, the self-assembled cylindrical micelles roll along the shearing direction and align parallel to each other with their axes along the vorticity direction, as opposed to aligning parallel to the shearing direction in the bulk. It is shown that this new "log-rolling" phase arises due to a strong coupling between the rotational degree of freedom of the micelles and the steady sliding motion of the confining surfaces. We examine the microscopic mechanism of the log-rolling phenomenon and also discuss its dependence on the segregation strength and length of the amphiphile, the shear rate, and the film thickness.