Structure Formation in Supraparticles Composed of Spherical and Elongated Particles.

We studied the evaporation-induced formation of supraparticles from dispersions of elongated colloidal particles using experiments and computer simulations. Aqueous droplets containing a dispersion of ellipsoidal and spherical polystyrene particles were dried on superamphiphobic surfaces at different humidity values that led to varying evaporation rates. Supraparticles made from only ellipsoidal particles showed short-range lateral ordering at the supraparticle surface and random orientations in the interior regardless of the evaporation rate. Particle-based simulations corroborated the experimental observations in the evaporation-limited regime and showed an increase in the local nematic ordering as the diffusion-limited regime was reached. A thin shell of ellipsoids was observed at the surface when supraparticles were made from binary mixtures of ellipsoids and spheres. Image analysis revealed that the supraparticle porosity increased with an increasing aspect ratio of the ellipsoids.

Mesoscale simulations of diffusion and sedimentation in shape-anisotropic nanoparticle suspensions.

We determine the long-time self-diffusion coefficient and sedimentation coefficient for suspensions of nanoparticles with anisotropic shapes (octahedra, cubes, tetrahedra, and spherocylinders) as a function of nanoparticle concentration using mesoscale simulations. We use a discrete particle model for the nanoparticles, and we account for solvent-mediated hydrodynamic interactions between nanoparticles using the multiparticle collision dynamics method. Our simulations are compared to theoretical predictions and experimental data from existing literature, demonstrating good agreement in the majority of cases. Further, we find that the self-diffusion coefficient of the regular polyhedral shapes can be estimated from that of a sphere whose diameter is the average of their inscribed and circumscribed sphere diameters.

Rapid Precipitation of Ionomers for Stabilization of Polymeric Colloids.

Polymeric colloids have shown potential as "building blocks" in applications ranging from formulations of Pickering emulsions and drug delivery systems to advanced materials, including colloidal crystals and composites. However, for applications requiring tunable properties of charged colloids, obstacles in fabrication can arise through limitations in process scalability and chemical versatility. In this work, the capabilities of flash nanoprecipitation (FNP), a scalable nanoparticle (NP) fabrication technology, are expanded to produce charged polystyrene colloids using sulfonated polystyrene ionomers as a new class of NP stabilizers. Through experimental exploration of formulation parameters, increases in the ionomer content are shown to reduce the particle size, mitigating a significant trade-off between the final particle size and inlet concentration; thus, expanding the processable material throughput of FNP. Further, the degree of sulfonation is found to impact stabilization with optimal performance achieved by selecting ionomers with intermediate (2.45-5.2 mol %) sulfonation. Simulations of single ionomer chains and their arrangement in multicomponent NPs provide molecular insights into the assembly and structure of NPs wherein the partitioning of ionomers to the particle surface depends on the polymer molecular weight and degree of sulfonation. By combining the insights from simulations with diffusion-limited growth kinetics and parametric fits to experimental data, a simple design formulation relation is proposed and validated. This work highlights the potential of ionomer-based stabilizers for controllably producing charged NP dispersions in a scalable manner.

Aggregation of amphiphilic nanocubes in equilibrium and under shear.

We investigate the self-assembly of amphiphilic nanocubes into finite-sized aggregates in equilibrium and under shear, using molecular dynamics (MD) simulations and kinetic Monte Carlo (KMC) calculations. These patchy nanoparticles combine both interaction and shape anisotropy, making them valuable models for studying folded proteins and DNA-functionalized nanoparticles. The nanocubes can self-assemble into various finite-sized aggregates ranging from rods to self-avoiding random walks, depending on the number and placement of the hydrophobic faces. Our study focuses on suspensions containing multi- and one-patch cubes, with their ratio systematically varied. When the binding energy is comparable to the thermal energy, the aggregates consist of only few cubes that spontaneously associate/dissociate. However, highly stable aggregates emerge when the binding energy exceeds the thermal energy. Generally, the mean aggregation number of the self-assembled clusters increases with the number of hydrophobic faces and decreases with increasing fraction of one-patch cubes. In sheared suspensions, the more frequent collisions between nanocube clusters lead to faster aggregation dynamics but also to smaller terminal steady-state mean cluster sizes. The results from the MD and KMC simulations are in excellent agreement for all investigated two-patch cases, whereas the three-patch cubes form systematically smaller clusters in the MD simulations compared to the KMC calculations due to finite-size effects and slow aggregation kinetics. By analyzing the rate kernels, we are able to identify the primary mechanisms responsible for (shear-induced) cluster growth and breakup. This understanding allows us to tune nanoparticle and process parameters to achieve desired cluster sizes and shapes.

Effect of Surfactant Selectivity on Shape and Inner Morphology of Triblock Terpolymer Microparticles.

The confined assembly of block copolymers (BCPs) has become a useful tool to prepare microparticles with controlled anisotropy and inner structure. While a solid understanding of the behavior of AB diblock copolymers exists, knowledge on the parameters affecting ABC triblock terpolymer assembly is much more limited. In this work, the effect of block-selective surfactants, sodium-4-vinylbenzenesulfonate (VBS) and sodium dodecylsulfate (SDS), is analyzed in the evaporation-induced confined assembly (EICA) of a polystyrene-block-polybutadiene-block-poly(methyl methacrylate) triblock terpolymer (SBM). Despite using the same terpolymer and emulsification process, SDS results in ellipsoidal microparticles with axially stacked lamellae, while VBS results in spherical microparticles with concentric lamellae or 3D spiral morphology. This change in morphology upon switching the surfactant is further substantiated by molecular simulations and enhances the understanding of terpolymer microphase separation in confinement.

Self-Assembly of Amphiphilic Cubes in Suspension.

We study the self-assembly of amphiphilic cubic colloids using molecular dynamics as well as rejection-free kinetic Monte Carlo simulations. We vary both the number and location of the solvophobic faces (patches) on the cubes at several colloid volume fractions and determine the resulting size and shape distributions of the self-assembled aggregates. When the binding energy is comparable to the thermal energy of the system, aggregates typically consist of only few spontaneously associating/dissociating colloids. Increasing the binding energy (or lowering the temperature) leads to the emergence of highly stable aggregates, e.g., small dimers in pure suspensions of one-patch cubes or large (system-spanning) aggregates in suspensions of multipatch colloids. In mixtures of one- and multipatch cubes, the average aggregation number increases with increasing number of solvophobic faces on the multipatch cubes as well with increasing fraction of multipatch cubes. The resulting aggregate shapes range from elongated rods over fractal objects to compact spheres, depending on the number and arrangement of solvophobic patches on the cubic colloids. Our findings establish the complex self-assembly pathways for a class of building blocks that combine both interaction and shape anisotropy, with the potential of forming hierarchically ordered superstructures.

Single-chain and condensed-state behavior of hnRNPA1 from molecular simulations.

Intrinsically disordered proteins (IDPs) are essential components for the formation of membraneless organelles, which play key functional and regulatory roles within biological systems. These complex assemblies form and dissolve spontaneously over time via liquid-liquid phase separation of IDPs. Mutations in their amino acid sequence can alter their phase behavior, which has been linked to the emergence of severe diseases. We study the conformation and phase behavior of a low-complexity domain of heterogeneous nuclear ribonucleoprotein A1 (hnRNPA1) using coarse-grained implicit solvent molecular dynamics simulations. We systematically analyze how these properties are affected by the number of aromatic residues within the examined sequences. We find a significant compaction of the chains and an increase in the critical temperature with an increasing number of aromatic residues. The local persistence length is determined in single-chain simulations, revealing strong sequence-specific variations along the chain contour. Comparing single-chain and condensed-state simulations, we find many more collapsed polymer conformations in the dilute systems, even at temperatures near the estimated θ-temperature of the solution. These observations strongly support the hypothesis that aromatic residues play a dominant role in condensation, which is further corroborated by a detailed analysis of the intermolecular contacts, and conversely that important properties of condensates are captured in coarse-grained simulations. Interestingly, we observe density inhomogeneities within the condensates near criticality, which are driven by electrostatic interactions. Finally, we find that the relatively small fraction of hydrophobic residues in the IDPs results in interfacial tensions, which are significantly lower compared to typical combinations of immiscible simple liquids.

Wetting transitions of polymer solutions: Effects of chain length and chain stiffness.

Wetting and drying phenomena are studied for flexible and semiflexible polymer solutions via coarse-grained molecular dynamics simulations and density functional theory calculations. This study is based on the use of Young's equation for the contact angle, determining all relevant surface tensions from the anisotropy of the pressure tensor. The solvent quality (or effective temperature, equivalently) is varied systematically, while all other interactions remain unaltered. For flexible polymers, the wetting transition temperature Tw increases monotonically with chain length N, while the contact angle at temperatures far below Tw is independent of N. For semiflexible polymer solutions, Tw varies non-monotonically with the persistence length: Initially, Tw increases with increasing chain stiffness and reaches a maximum, but then a sudden drop of Tw is observed, which is associated with the isotropic-nematic transition of the system.

Diffusion and sedimentation in colloidal suspensions using multiparticle collision dynamics with a discrete particle model.

We study self-diffusion and sedimentation in colloidal suspensions of nearly hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to experimental data and Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne-Prager-Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in experiments, and the sedimentation coefficient in MD+MPCD is in good agreement with that in experiments and BD+RPY, suggesting that MD+MPCD gives a reasonable description of hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extended to more complex shapes, and we determine the long-time self-diffusion coefficient in suspensions of nearly hard cubes to demonstrate its generality.

Ordering, phase behavior, and correlations of semiflexible polymers in confinement.

Semiflexible polymers are ubiquitous in biological systems, e.g., as building blocks of the cytoskeleton, and they also play an important role in various materials due to their ability to form liquid-crystalline order. These rigid macromolecules are characterized by numerous (hierarchical) length-scales that define their static and dynamic properties. Confinement can promote uniform order, e.g., through capillary nematization in narrow slits, but it can also introduce long-ranged disruptions of the nematic ordering field through (unavoidable) topological defects in spherical containers. This Perspective concentrates on the theoretical description and computational modeling of such confined systems, with the focus on spherical containers that play an important role in the injection/ejection of double-stranded DNA from viral capsids and the fabrication of nematic droplets. Basic principles and recent developments are reviewed, followed by a discussion of open questions and potential directions for future research in this field.

BoltzmaNN: Predicting effective pair potentials and equations of state using neural networks.

Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion of the pressure. The NNs are trained with data from molecular dynamics simulations of monoatomic gases and liquids, sampled in the NVT ensemble at various densities. We find that the NNs provide much more accurate results compared to the analytic low-density limit estimate of the second virial coefficient and the Carnahan-Starling equation of state for hard sphere liquids. Furthermore, we design and train NNs for computing (effective) pair potentials from radial pair distribution functions, g(r), a task that is often performed for inverse design and coarse-graining. Providing the NNs with additional information on the forces greatly improves the accuracy of the predictions since more correlations are taken into account; the predicted potentials become smoother, are significantly closer to the target potentials, and are more transferable as a result.

Structure and Shear Response of Janus Colloid-Polymer Mixtures in Solution.

We investigate the structure and rheological properties of dilute colloid-polymer mixtures at rest and under shear via molecular simulations that take into account hydrodynamic interactions. Mixtures of amphiphilic Janus colloids (JCs) and hydrophobic/amphiphilic polymers are considered for various solvent qualities and polymer concentrations. Free polymers, small polymer droplets, and hybrid aggregates coexist in mixtures with slightly hydrophobic homopolymers. As the solvent quality worsens, all polymers aggregate into small droplets, covered and stabilized by the JCs. In mixtures with amphiphilic polymers, we observe the coexistence of free polymers, purely polymeric micelles, and hybrid aggregates. At low shear rates, all mixtures exhibit a Newtonian-like response with intrinsic shear viscosities that are up to 2 times as large as of pure suspensions of nonadsorbing colloids at the same concentration. Furthermore, the mean aggregation number increases slightly due to the flow-enhanced collision of aggregates. At larger shear rates, however, the aggregates break up, the polymers align in the flow direction, and the mixtures exhibit shear-thinning. This shear-induced breakup occurs at stronger shear compared to pure JC suspensions, indicating that the adsorbed polymers reinforce the hybrid aggregates.

Structure and dynamics of amphiphilic Janus spheres and spherocylinders under shear.

We study the structure formation and flow properties of colloidal dispersions comprised of Janus spheres, Janus spherocylinders, and their mixtures, using hybrid molecular dynamics simulations that take into account hydrodynamic interactions. We systematically vary the Janus balance and the shape anisotropy of the particles, and explore a range of colloid volume fractions in the liquid regime of the phase diagram. At rest, Janus spheres with small hydrophobic patches form spherical micelles for all investigated colloid concentrations. In contrast, Janus spheres with an entirely hydrophobic hemisphere aggregate to larger worm-like micelles and network-like structures. Janus spherocylinders exhibit a similar self-assembly behavior. At small and intermediate shear, we observe deformation and rearrangement of the micelles, accompanied by a Newtonian-like rheology with slightly higher shear viscosity compared to homoparticle dispersions at the same concentration. As the shear rate is increased further, the micelles eventually break up into small dimers and free particles, causing a distinct shear-thinning of the dispersions. The network-like structures exhibit a similar flow behavior at high shear rates, but for weak shear we find an almost threefold increase of the shear viscosity and a distinct shear-thinning behavior due to the fracturing of the intertwined networks. In general, we identify a strong correlation between the size of the aggregates and the rheology of the dispersions, allowing for the determination of dynamic properties solely based on structural information.

Stratification of polymer mixtures in drying droplets: Hydrodynamics and diffusion.

We study the evaporation-induced stratification of a mixture of short and long polymer chains in a drying droplet using molecular simulations. We systematically investigate the effects of hydrodynamic interactions (HI) on this process by comparing hybrid simulations accounting for HI between polymers through the multiparticle collision dynamics technique with free-draining Langevin dynamics simulations neglecting the same. We find that the dried supraparticle morphologies are homogeneous when HI are included but are stratified in core-shell structures (with the short polymers forming the shell) when HI are neglected. The simulation methodology unambiguously attributes this difference to the treatment of the solvent in the two models. We rationalize the presence (or absence) of stratification by measuring phenomenological multicomponent diffusion coefficients for the polymer mixtures. The diffusion coefficients show the importance of not only solvent backflow but also HI between polymers in controlling the dried supraparticle morphology.

Disentangling the Role of Chain Conformation on the Mechanics of Polymer Tethered Particle Materials.

The linear elastic properties of isotropic materials of polymer tethered nanoparticles (NPs) are evaluated using noncontact Brillouin light spectroscopy. While the mechanical properties of dense brush materials follow predicted trends with NP composition, a surprising increase in elastic moduli is observed in the case of sparsely grafted particle systems at approximately equal NP filling ratio. Complementary molecular dynamics simulations reveal that the stiffening is caused by the coil-like conformations of the grafted chains, which lead to stronger polymer-polymer interactions compared to densely grafted NPs with short chains. Our results point to novel opportunities to enhance the physical properties of composite materials by the strategic design of the "molecular architecture" of constituents to benefit from synergistic effects relating to the organization of the polymer component.

Surface Activity of Soft Polymer Colloids.

We investigate the behavior of polymer colloids at the interface between two immiscible liquids using molecular dynamics simulations. We study several colloid morphologies with various degrees of amphiphilicity, that is, purely solvophobic homogeneous and Janus particles and amphiphilic Janus and core-shell particles. Regardless of the specific morphology, the polymer colloids irreversibly anchor at the liquid-liquid interface, accompanied by a marked reduction of the interfacial tension, γ. Purely solvophobic particles lower γ because they reduce the interfacial area shared by the two immiscible liquids, whereas amphiphilic colloids have an additional enthalpic contribution. At the liquid-liquid interface, the solvophobic particles deform into oblate ellipsoids to maximize the occluded area at the interface. In contrast, amphiphilic Janus colloids orient their solvophobic/solvophilic parts toward the preferred liquids and form a prolate particle shape. The amphiphilic core-shell particles undergo a morphological transition to a prolate Janus-like structure as they anchor at the interface. We rationalize the deformation of the polymer colloids by considering a simple model system of spheroidal particles pinned at the liquid-liquid interface. We systematically compute the interfacial free energy for the various colloids as a function of their asphericity and find excellent qualitative agreement with the simulation findings. Our results show that solvophobic homoparticles can be almost as efficient surface-active agents as amphiphilic Janus colloids.

Self-Assembly of Polymer Blends and Nanoparticles through Rapid Solvent Exchange.

Molecular dynamics simulations were performed to study the fabrication of polymeric colloids containing inorganic nanoparticles (NPs) via the flash nanoprecipitation (FNP) technique. During this process, a binary polymer blend, initially in a good solvent for the polymers, is rapidly mixed with NPs and a poor solvent for the polymers that is miscible with the good solvent. The simulations reveal that the polymers formed Janus particles with NPs distributed either on the surface of the aggregates, throughout their interior, or aligned at the interface between the two polymer domains, depending on the NP-polymer and NP-solvent interactions. The loading and surface density of NPs can be controlled by the polymer feed concentration, the NP feed concentration, and their ratio in the feed streams. Selective localization of NPs by incorporating electrostatic interactions between polymers and NPs has also been investigated, and was shown to be an effective way to enhance NP loading and surface density as compared to the case with only van der Waals attractions. This work demonstrates that the FNP process is promising for the production of structured and hybrid nanocolloids in a continuous and scalable way, with independent control over particle properties such as size, NP location, loading, and surface density. Our results provide useful guidelines for experimental fabrication of such hybrid nanoparticles.

On the Stability of Polymeric Nanoparticles Fabricated through Rapid Solvent Mixing.

We study the stability of polymeric nanoparticles fabricated through the rapid mixing of polymers in a good solvent with a poor solvent that is miscible with the good solvent. In previous experiments where water was used as the poor solvent, a negative surface charge was measured on the precipitated nanoparticles, which led to the long-time stability of the dispersion. It was argued that these charges originate presumably from either water or hydroxide adsorption at the hydrophobic nanoparticle surface or from impurities in the feed streams that preferentially adsorb on the precipitated nanoparticles. To elucidate the origin of this stabilization mechanism, we performed experiments wherein we replaced water with a nonpolar poor solvent. The polymers aggregated into stable nanoparticles for a range of processing parameters. We investigated theoretically three possible explanations for this stability, i.e., electrostatic stabilization, conditional thermodynamic equilibrium, and steric stabilization. Our experiments and considerations suggest that steric stabilization is the most likely candidate.

Cross-stream migration of a Brownian droplet in a polymer solution under Poiseuille flow.

The migration of a Brownian fluid droplet in a parallel-plate microchannel was investigated using dissipative particle dynamics computer simulations. In a Newtonian solvent, the droplet migrated toward the channel walls due to inertial effects at the studied flow conditions, in agreement with theoretical predictions and recent simulations. However, the droplet focused onto the channel centerline when polymer chains were added to the solvent. Focusing was typically enhanced for longer polymers and higher polymer concentrations with a nontrivial flow-rate dependence due to droplet and polymer deformability. Brownian motion caused the droplet position to fluctuate with a distribution that primarily depended on the balance between inertial lift forces pushing the droplet outward and elastic forces from the polymers driving it inward. The droplet shape was controlled by the local shear rate, and so its average shape depended on the droplet distribution.

Influence of polymer flexibility on nanoparticle dynamics in semidilute solutions.

The hierarchical structure and dynamics of polymer solutions control the transport of nanoparticles (NPs) through them. Here, we perform multi-particle collision dynamics simulations of solutions of semiflexible polymer chains with tunable persistence length lp to investigate the effect of chain stiffness on NP transport. The NPs exhibit two distinct dynamical regimes - subdiffusion on short time scales and diffusion on long time scales. The long-time NP diffusivities are compared with predictions from the Stokes-Einstein relation (SER), mode-coupling theory (MCT), and a recent polymer coupling theory (PCT). Increasing deviations from the SER as the polymer chains become more rigid (i.e. as lp increases) indicate that the NP motions become decoupled from the bulk viscosity of the polymer solution. Likewise, polymer stiffness leads to deviations from PCT, which was developed for fully flexible chains. Independent of lp, however, the long-time diffusion behavior is well-described by MCT, particularly at high polymer concentration. We also observed that the short-time subdiffusive dynamics are strongly dependent on polymer flexibility. As lp is increased, the NP dynamics become more subdiffusive and decouple from the dynamics of the polymer chain center-of-mass. We posit that these effects are due to differences in the segmental mobility of the semiflexible chains.