Self-assembly of "Mickey Mouse" shaped colloids into tube-like structures: experiments and simulations

Economical routes to size-specific assembly of self-closing structures

Programmable self-assembly has seen an explosion in the diversity of synthetic crystalline materials, but developing strategies that target "self-limiting" assemblies has remained a challenge. Among these, self-closing structures, in which the local curvature defines the finite global size, are prone to polymorphism due to thermal bending fluctuations, a problem that worsens with increasing target size. Here, we show that assembly complexity can be used to eliminate this source of polymorphism in the assembly of tubules. Using many distinct components, we prune the local density of off-target geometries, increasing the selectivity of the tubule width and helicity to nearly 100%. We further show that by reducing the design constraints to target either the pitch or the width alone, fewer components are needed to reach complete selectivity. Combining experiments with theory, we reveal an economical limit, which determines the minimum number of components required to create arbitrary assembly sizes with full selectivity.

Depletion-induced crystallization of anisotropic triblock colloids

The intricate interplay between colloidal particle shape and precisely engineered interaction potentials has paved the way for the discovery of unprecedented crystal structures in both two and three dimensions. Here, we make use of anisotropic triblock colloidal particles composed of two distinct materials. The resulting surface charge heterogeneity can be exploited to generate regioselective depletion interactions and directional bonding. Using extensive molecular dynamics simulations and a dimensionality reduction analysis approach, we map out state diagrams for the self-assembly of such colloids as a function of their aspect ratio and for varying depletant features in a quasi two-dimensional set-up. We observe the formation of a wide variety of crystal structures such as a herringbone, brick-wall, tilted brick-wall, and (tilted) ladder-like structures. More specifically, we determine the optimal parameters to enhance crystallization, and investigate the nucleation process. Additionally, we explore the potential of using crystalline monolayers as templates for deposition, thereby creating complex three-dimensional structures that hold promise for future applications.

Porous Self-Assemblies Mediated by Dumbbell Particles as Cross-Linking Agents

Self-assembly of colloidal particles is emerging as a promising approach for producing novel materials. These colloidal particles can be synthesized with protrusions (lobes) on their surfaces that allow the formation of porous structures with a wide range of applications. Using Langevin dynamics simulations, we studied self-assembly in the binary mixtures of lobed colloidal particles with variations in their lobe sizes to investigate the feasibility of using dumbbell particles (with two lobes) as cross-linkers to increase the porosity in self-assembled morphologies. Each binary system was formed by mixing the dumbbell particles with one of the following types of particles: trigonal planar (three lobes), tetrahedral (four lobes), trigonal bipyramidal (five lobes), and octahedral (six lobes). We observed that the lobe size on each particle can be tuned to favor the formation of random aggregates and spherical aggregates when the lobes are larger and well-ordered crystalline structures when the lobes are smaller. We also observed that these polydisperse systems form self-assembled structures characterized by porosities higher than those of the structures formed by the monodisperse systems. These results indicate that the lobe size is an important design feature that can be optimized to achieve desired structures with distinct morphologies and porosities, and the dumbbell particles are effective cross-linking agents to enhance the porosity in self-assembled structures.

Self-Assembly in an Experimentally Realistic Model of Lobed Patchy Colloids

Colloids with lobed architectures have been shown to self-assemble into promising porous structures with potential biomedical applications. The synthesis of these colloids via experiments can be tuned to vary the number and the position of the lobes. However, the polydispersity involving the numbers, sizes, and the dispositions of lobes, that is often observed in particle designs, can significantly affect their self-assembled structures. In this work, we go beyond the uniform lobe size conditions commonly considered in molecular simulations, and probe the effect of polydispersity due to non-uniform lobe sizes by studying self-assembly in three experimentally observable designs of lobed particles (dumbbell, two lobes; trigonal planar, three lobes; and tetrahedral, four lobes), using coarse-grained Langevin dynamics simulations in the NVT ensemble. With increasing polydispersity, we observed the formation of a crystalline structure from a disordered state for the dumbbell system, and a loss of order in the crystalline structures for the trigonal planar system. The tetrahedral system retained a crystalline structure with only a minor loss in compactness. We observed that the effect of polydispersity on the self-assembled morphology of a given system can be minimized by increasing the number of lobes. The polydispersity in the lobe size may also be useful in tuning self-assemblies toward desired structures.

Janus helices: From fully attractive to hard helices

The phase diagram of hard helices differs from its hard rods counterpart by the presence of chiral "screw" phases stemming from the characteristic helical shape, in addition to the conventional liquid crystal phases also found for rod-like particles. Using extensive Monte Carlo and Molecular Dynamics simulations, we study the effect of the addition of a short-range attractive tail representing solvent-induced interactions to a fraction of the sites forming the hard helices, ranging from a single-site attraction to fully attractive helices for a specific helical shape. Different temperature regimes exist for different fractions of the attractive sites, as assessed in terms of the relative Boyle temperatures, that are found to be rather insensitive to the specific shape of the helical particle. The temperature range probed by the present study is well above the corresponding Boyle temperatures, with the phase behaviour still mainly entropically dominated and with the existence and location of the various liquid crystal phases only marginally affected. The pressure in the equation of state is found to decrease upon increasing the fraction of attractive beads and/or on lowering the temperature at fixed volume fraction, as expected on physical grounds. All screw phases are found to be stable within the considered range of temperatures with the smectic phase becoming more stable on lowering the temperature. By contrast, the location of the transition lines do not display a simple dependence on the fraction of attractive beads in the considered range of temperatures.

Extended Wertheim theory predicts the anomalous chain length distributions of divalent patchy particles under extreme confinement

Colloidal patchy particles with divalent attractive interaction can self-assemble into linear polymer chains. Their equilibrium properties in 2D and 3D are well described by Wertheim's thermodynamic perturbation theory which predicts a well-defined exponentially decaying equilibrium chain length distribution. In experi- mental realizations, due to gravity, particles sediment to the bottom of the suspension forming a monolayer of particles with a gravitational height smaller than the particle diameter. In accordance with experiments, an anomalously high monomer concentration is observed in simulations which is not well understood. To account for this observation, we interpret the polymerization as taking place in a highly confined quasi-2D plane and extend the Wertheim thermodynamic perturbation theory by defining addition reactions constants as functions of the chain length. We derive the theory, test it on simple square well potentials, and apply it to the experimental case of synthetic colloidal patchy particles immersed in a binary liquid mixture that are described by an accurate effective critical Casimir patchy particle potential. The important interaction parameters entering the theory are explicitly computed using the integral method in combination with Monte Carlo sampling. Without any adjustable parameter, the predictions of the chain length distribution are in excellent agreement with explicit simulations of self-assembling particles. We discuss generality of the approach, and its application range.

Computer simulations of self-assembly of anisotropic colloids

Computer simulations have played a significant role in understanding the physics of colloidal self-assembly, interpreting experimental observations, and predicting novel mesoscopic and crystalline structures. Recent advances in computer simulations of colloidal self-assembly driven by anisotropic or orientation-dependent inter-particle interactions are highlighted in this review. These interactions are broadly classified into two classes: entropic and enthalpic interactions. They mainly arise due to shape anisotropy, surface heterogeneity, compositional heterogeneity, external field, interfaces, and confinements. Key challenges and opportunities in the field are discussed.

Tiling a tubule: how increasing complexity improves the yield of self-limited assembly

The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of systems with self-limited length scales is that thermal fluctuations can lead to the assembly of nearby, off-target states. We investigate strategies for limiting off-target assembly by using multiple types of subunits. Using simulations and energetics calculations, we explore this concept by considering the assembly of tubules built from triangular subunits that bind edge to edge. While in principle, a single type of triangle can assemble into tubules with a monodisperse width distribution, in practice, the finite bending rigidity of the binding sites leads to the formation of off-target structures. To increase the assembly specificity, we introduce tiling rules for assembling tubules from multiple species of triangles. We show that the selectivity of the target structure can be dramatically improved by using multiple species of subunits, and provide a prescription for choosing the minimum number of subunit species required for near-perfect yield. Our approach of increasing the system's complexity to reduce the accessibility of neighboring structures should be generalizable to other systems beyond the self-assembly of tubules.

Synthesis of anisotropic colloids with concave and convex structures

Anisotropic colloidal particles with concave and convex structures are useful in both theoretical studies and applications. In this work, we mass-produced polystyrene (PS) colloidal particles with multiple concavities through dispersion polymerization techniques. By increasing the delayed feeding time t_d of the cross-linker divinylbenzene (DVB), the morphological evolution of particles can be classified into two stages, during which the formation of different concavities is consistent with either the buckling mechanism or phase separation mechanism. By varying the DVB dosage, we found that the size of the big chamber formed on the particle surfaces decreases as the DVB dosage increases. Then, using these concave particles as seeds, 2-5 μm anisotropic colloids with various shapes, including spherical, ellipsoidal, snowman and multi-protrusion, were synthesized by seeded emulsion polymerization. Moreover, our results show that both the chambers and long narrow ditches on the surface of seeds can be the active sites for monomers to gather and polymerize, but monomers in the big chamber have a priority to polymerize first when big and small concavities both exist on seeds. The results of this study could mean great potential in synthesizing a variety of anisotropic particles with well-controlled concave morphologies.

Hierarchical, Highly Open Microtubes and Columnar Liquid Crystals Self-Assembled from Symmetrical and Asymmetrical Colloidal Rings

The use of simple building blocks to produce hierarchical and porous structured materials is highly desired. Rings are simple colloidal particles but unique for their internal cavities. Here we report the self-assembly (SA) of colloidal rings with tunable asymmetry mediated by a depletion force and demonstrate that a variety of porous colloidal superstructures from microtubes, flexible chains, (plastic) crystals to highly open liquid crystals (LCs) can be formed along the predesigned SA paths. In particular, the SA is staged in binary or ternary systems. Large rings first form complex ring-in-ring and ring-in-ring-in-ring assemblies by capturing smaller rings, which, as new building blocks, can further form multi-walled microtubes and open columnar LCs. Moreover, a plastic columnar LC with alternating intracolumnar stacking is found from asymmetrical rings. The SA with colloidal rings opens a new avenue to construct hierarchical and porous ordered metamaterials.

Early stages of aggregation in fluid mixtures of dimers and spheres: a theoretical and simulation study

We use Monte Carlo simulation and the Reference Interaction Site Model (RISM) theory of molecular fluids to investigate a simple model of colloidal mixture consisting of dimers, made up of two tangent hard monomers of different size, and hard spheres. In addition to steric repulsion, the two species interact via a square-well attraction only between small monomers and spheres. Recently, we have characterized the low-temperature regime of this mixture by Monte Carlo, reporting on the spontaneous formation of a wide spectrum of supramolecular aggregates [Prestipino et al., J. Phys. Chem. B, 2019, 123, 9272]. Here we focus on a regime of temperatures where, on cooling, the appearance of local inhomogeneties first, and the early stages of aggregation thereafter, are observed. In particular, we find signatures of aggregation in the onset of a low-wavevector peak in the structure factors of the mixture, as computed by both theory and simulation. Then, we link the structural information to the microscopic arrangement through a detailed cluster analysis of Monte Carlo configurations. In this regard, we devise a novel method to compute the maximum distance for which two spheres can be regarded as bonded together, a crucial issue in the proper identification of fluid aggregates. The RISM theory provides relatively accurate structural and thermodynamic predictions in comparison with Monte Carlo, but with slightly degrading performances as the fluid progresses inside the locally inhomogeneous phase. Our study certifies the efficacy of the RISM approach as a useful complement to numerical simulation for a reasoned analysis of aggregation properties in colloidal mixtures.

Revealing viscoelastic bending relaxation dynamics of isolated semiflexible colloidal polymers

The viscoelastic properties of filaments and biopolymers play a crucial role in soft and biological materials from biopolymer networks to novel synthetic metamaterials. Colloidal particles with specific valency allow mimicking polymers and more complex molecular structures at the colloidal scale, offering direct observation of their internal degrees of freedom. Here, we elucidate the time-dependent viscoelastic response in the bending of isolated semi-flexible colloidal polymers, assembled from dipatch colloidal particles by reversible critical Casimir forces. By tuning the patch-patch interaction strength, we adjust the polymers' viscoelastic properties, and follow spontaneous bending modes and their relaxation directly on the particle level. We find that the elastic response is well described by that of a semiflexible rod with persistence length of order 1000 μm, tunable by the critical Casimir interaction strength. We identify the viscous relaxation on longer timescales to be due to internal friction, leading to a wavelength-independent relaxation time similar to single biopolymers, but in the colloidal case arising from the contact mechanics of the bonded patches. These tunable mechanical properties of assembled colloidal filaments open the door to "colloidal architectures", rationally designed (network) structures with desired topology and mechanical properties.

Revealing Polymerization Kinetics with Colloidal Dipatch Particles

Limited-valency colloidal particles can self-assemble into polymeric structures analogous to molecules. While their structural equilibrium properties have attracted wide attention, insight into their dynamics has proven challenging. Here, we investigate the polymerization dynamics of semiflexible polymers in 2D by direct observation of assembling divalent particles, bonded by critical Casimir forces. The reversible critical Casimir force creates living polymerization conditions with tunable chain dissociation, association, and bending rigidity. We find that unlike dilute polymers that show exponential size distributions in excellent agreement with Flory theory, concentrated samples exhibit arrest of rotational and translational diffusion due to a continuous isotropic-to-nematic transition in 2D, slowing down the growth kinetics. These effects are circumvented by the addition of higher-valency particles, cross linking the polymers into networks. Our results connecting polymer flexibility, polymer interactions, and the peculiar isotropic-nematic transition in 2D offer insight into the polymerization processes of synthetic two-dimensional polymers and biopolymers at membranes and interfaces.

A temperature-dependent critical Casimir patchy particle model benchmarked onto experiment

Synthetic colloidal patchy particles immersed in a binary liquid mixture can self-assemble via critical Casimir interactions into various superstructures, such as chains and networks. Up to now, there are no quantitatively accurate potential models that can simulate and predict this experimentally observed behavior precisely. Here, we develop a protocol to establish such a model based on a combination of theoretical Casimir potentials and angular switching functions. Using Monte Carlo simulations, we optimize several material-specific parameters in the model to match the experimental chain length distribution and persistence length. Our approach gives a systematic way to obtain accurate potentials for critical Casimir induced patchy particle interactions and can be used in large-scale simulations.

Self-assembly of shape-tunable oblate colloidal particles into orientationally ordered crystals, glassy crystals and plastic crystals

The shapes of colloidal particles are crucial to self-assembled superstructures. Understanding the relationship between the shapes of building blocks and the resulting crystal structures is an important fundamental question. Here, we demonstrate that, by using particles whose shape interpolates between a flat disc and a sphere, not only are self-assembled superstructures but also their orientations sensitively dependent on the particle shape. By changing the shape gradually from a flat disc to a spherical shape, a crystal sequence from orientationally ordered crystals to orientationally disordered crystals with frozen and more free rotations are found. The latter two phases are identified as a glassy crystal and a plastic crystal, respectively. By combining theoretical model calculations, the formed crystal structures and the occurring transitions are found to be dictated by the interplay between particle shape and particle-particle interaction as well as particle-wall interaction. In particular, for quasi-spherical shapes, when the strong attraction dominates, a glassy crystal forms, or otherwise a plastic crystal forms. These results demonstrate that the interplay between the particle shape and the interaction can be used to tune crystallization and further fabricate colloid-based new structured and dynamic materials.

Trifaceted Mickey Mouse Amphiphiles for Programmable Self-Assembly, DNA Complexation and Organ-Selective Gene Delivery

Instilling segregated cationic and lipophilic domains with an angular disposition in a trehalose-based trifaceted macrocyclic scaffold allows engineering patchy molecular nanoparticles leveraging directional interactions that emulate those controlling self-assembling processes in viral capsids. The resulting trilobular amphiphilic derivatives, featuring a Mickey Mouse architecture, can electrostatically interact with plasmid DNA (pDNA) and further engage in hydrophobic contacts to promote condensation into transfectious nanocomplexes. Notably, the topology and internal structure of the cyclooligosaccharide/pDNA co-assemblies can be molded by fine-tuning the valency and characteristics of the cationic and lipophilic patches, which strongly impacts the transfection efficacy in vitro and in vivo. Outstanding organ selectivities can then be programmed with no need of incorporating a biorecognizable motif in the formulation. The results provide a versatile strategy for the construction of fully synthetic and perfectly monodisperse nonviral gene delivery systems uniquely suited for optimization schemes by making cyclooligosaccharide patchiness the focus.

Controllable synthesis of patchy particles with tunable geometry and orthogonal chemistry

HYPOTHESIS

Self-assembly using anisotropic colloidal building blocks may lead to superstructures similar to those found in molecular systems yet can have unique optical, electronic, and structural properties. To widen the spectrum of achievable superstructures and related properties, significant effort was devoted to the synthesis of new types of colloidal particles. Despite these efforts, the preparation of anisotropic colloids carrying chemically orthogonal anchor groups on distinct surface patches remains an elusive challenge.

EXPERIMENTS

We report a simple yet effective method for synthesizing patchy particles via seed-mediated heterogeneous nucleation. Key to this procedure is the use of 3-(trimethoxysilyl)propyl methacrylate (TPM) or 3-(trimethoxysilyl)propyl acrylate (TMSPA), which can form patches on a variety of functional polymer seeds via a nucleation and growth mechanism.

FINDINGS

A family of anisotropic colloids with tunable numbers of patches and patch arrangements were prepared. By continuously feeding TPM or TMSPA the geometry of the colloids could be adjusted accurately. Furthermore, the patches could be reshaped by selectively polymerizing and/or solvating the individual colloidal compartments. Relying on the chemically distinct properties of the TPM/TMSPA and seed-derived domains, both types of patches could be functionalized independently. Combining detailed control over the patch chemistry and geometry opens new avenues for colloidal self-assembly.

Mix and match-a versatile equilibrium approach for hybrid colloidal synthesis

Colloidal synthesis is a powerful bottom-up approach for programmed self-assembly which holds promise for both research and industry. While diverse, each synthetic process is typically restricted to a specific chemistry. Many applications however require composite materials, whereas a chemical equilibrium can typically only match one material but not the other. Here, a scalable general approach is presented, alleviating the dependency on a specific chemical reaction, by resorting to a mechanical equilibrium; an isopycnic density-gradient-step is tailored to form clusters with prescribed composition. Valence control is demonstrated, making dimers, trimers, and tetramers with purity as high as 96%. The measured kinetics shows a scaleable throughput. The density gradient step plays a dual role of both filtering out undesired products and concentrating the target structures. The "Mix-and-Match" approach is general, and applies to a broad range of colloidal matter: diverse material compositions (plastics, glasses, and emulsions); a range of colloidal interactions (van der Waals, Coulomb, and DNA hybridization); and a spectrum of sizes (nanoscale to multiple micrometers). Finally, the strength of the method is displayed by producing a monodisperse suspension from a highly polydisperse emulsion. The ability to combine colloids into architectures of hybrid materials has applications in pharmaceuticals, cosmetics, and photonics.

Multivalent Patchy Colloids for Quantitative 3D Self-Assembly Studies

We report methods to synthesize sub-micron- and micron-sized patchy silica particles with fluorescently labeled hemispherical titania protrusions, as well as routes to efficiently characterize these particles and self-assemble these particles into non-close-packed structures. The synthesis methods expand upon earlier work in the literature, in which silica particles packed in a colloidal crystal were surface-patterned with a silane coupling agent. Here, hemispherical amorphous titania protrusions were successfully labeled with fluorescent dyes, allowing for imaging by confocal microscopy and super-resolution techniques. Confocal microscopy was exploited to experimentally determine the numbers of protrusions per particle over large numbers of particles for good statistical significance, and these distributions were compared to simulations predicting the number of patches as a function of core particle polydispersity and maximum separation between the particle surfaces. We self-assembled these patchy particles into open percolating gel networks by exploiting solvophobic attractions between the protrusions.

Dimple Colloids with Tunable Cavity Size and Surface Functionalities

Dimple colloids with well-defined cavities were synthesized by a modified dispersion polymerization. The key step in the procedure is the delayed addition of cross-linkers into the reaction mixture. By systematically studying the effect of the delayed addition time and the concentration of the cross-linker on the resulting particle morphology, we identified the dominating driving force that underlies dimple formation. The delayed addition of cross-linkers results in colloids with a core-shell morphology consisting of a core rich in linear polymers and a cross-linked shell. This morphology was confirmed by selectively etching non-cross-linked material using dimethylformamide. With polymerization proceeding, consumption of monomers present in the swollen particles leads to contraction of the particles, which is larger for the core composed of linear polymers compared to the stiffer cross-linked shell. To accommodate this decrease in volume, the outer cross-linked shell has to buckle, resulting in a well-defined dimple. Furthermore, we extended the procedure to incorporate functional monomers, yielding chemically modifiable dimple particles. Subsequently, we showed that by leveraging the core-shell structure, these dimple particles can be used to prepare dumbbell-shaped colloids with one hollow and one solid lobe. These partially hollow anisotropic particles assemble into strings with well-defined orientations in an alternating current electric field.

Crossover from three- to six-fold symmetry of colloidal aggregates in circular traps

At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic component, the structure may exhibit the symmetry of the interaction. We consider a suspension of spherical particles interacting through an isotropic repulsive potential and a three-fold symmetric attractive interaction, confined in circular potential traps in 2d. We find that, due to the competition between the interparticle and the external potentials, the particles self-organize into structures with three- or six-fold symmetry, depending on the width of the traps. For intermediate trap widths, a core-shell structure is formed, where the core has six-fold symmetry and the shell is three-fold symmetric. When the width of the trap changes periodically in time, the symmetry of the colloidal structure also changes, but it does not necessarily follow that of the corresponding static trap.

Self-assembly in a model colloidal mixture of dimers and spherical particles

We investigate the structure of a dilute mixture of amphiphilic dimers and spherical particles, a model relevant to the problem of encapsulating globular "guest" molecules in a dispersion. Dimers and spheres are taken to be hard particles, with an additional attraction between spheres and the smaller monomers in a dimer. Using the Monte Carlo simulation, we document the low-temperature formation of aggregates of guests (clusters) held together by dimers, whose typical size and shape depend on the guest concentration χ. For low χ (less than 10%), most guests are isolated and coated with a layer of dimers. As χ progressively increases, clusters grow in size becoming more and more elongated and polydisperse; after reaching a shallow maximum for χ≈50%, the size of clusters again reduces upon increasing χ further. In one case only (χ=50% and moderately low temperature) the mixture relaxed to a fluid of lamellae, suggesting that in this case clusters are metastable with respect to crystal-vapor separation. On heating, clusters shrink until eventually the system becomes homogeneous on all scales. On the other hand, as the mixture is made denser and denser at low temperature, clusters get increasingly larger until a percolating network is formed.

Aggregation kinetics of irreversible patches coupled with reversible isotropic interaction leading to chains, bundles and globules

In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern–Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined three different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effect of patch size on self-assembly under different solvent qualities for various volume fractions. We will show that at low volume fractions during aggregation process, we end up in a chain conformation for smaller patch size while in a globular conformation for bigger patch size. We also observed a chain to bundle transformation depending on the attractive interaction strength between the chains or in other words depending on the quality of the solvent. We will also show that bundling process is very similar to nucleation and growth phenomena observed in colloidal system with short range attraction. We have also studied the bond angle distribution for this system, where for small patches only two angles are more probable indicating chain formation, while for bundling at very low volume fraction a tail is developed in the distribution. While for the case of higher patch angle this distribution is broad compared to the case of low patch angles showing we have a more globular conformation. We are also proposing a model for the formation of bundles which are similar to amyloid fibers using two patch colloidal particles.

Self-assembled three-dimensional chiral colloidal architecture

Although stereochemistry has been a central focus of the molecular sciences since Pasteur, its province has previously been restricted to the nanometric scale. We have programmed the self-assembly of micron-sized colloidal clusters with structural information stemming from a nanometric arrangement. This was done by combining DNA nanotechnology with colloidal science. Using the functional flexibility of DNA origami in conjunction with the structural rigidity of colloidal particles, we demonstrate the parallel self-assembly of three-dimensional microconstructs, evincing highly specific geometry that includes control over position, dihedral angles, and cluster chirality.

Flow-Driven Assembly of Microcapsules into Three-Dimensional Towers

By harnessing biochemical signaling and chemotaxis, unicellular slime molds can aggregate on a surface to form a long, vertical stalk. Few synthetic systems can self-organize into analogous structures that emerge out of the plane. Through computational modeling, we devise a mechanism for assembling tower-like structures using microcapsules in solution as building blocks. In the simulations, chemicals diffusing from a central patch on a surface produce a concentration gradient, which generates a radially directed diffusioosmotic flow along the surface toward the center. This toroidal roll of a fluid pulls the microcapsules along the surface and lifts them above the patch. As more capsules are drawn toward the patch, some units are pushed off the surface but remain attached to the central microcapsule cluster. The upward-directed flow then draws out the cluster into a tower-like shape. The final three-dimensional (3D) structure depends on the flow field, the attractive capsule-capsule and capsule-surface interaction strengths, and the sedimentation force on the capsules. By tuning these factors, we can change the height of the structures that are produced. Moreover, by patterning the areas of the wall that are attractive to the capsules, we can form multiple vertical strands instead of a single tower. Our approach for flow-directed assembly can permit the growth of reconfigurable, 3D structures from simple subunits.

Complex patchy colloids shaped from deformable seed particles through capillary interactions

We investigate the mechanisms underlying the reconfiguration of random aggregates of spheres through capillary interactions, the so-called "colloidal recycling" method, to fabricate a wide variety of patchy particles. We explore the influence of capillary forces on clusters of deformable seed particles by systematically varying the crosslink density of the spherical seeds. Spheres with a poorly crosslinked polymer network strongly deform due to capillary forces and merge into large spheres. With increasing crosslink density and therefore rigidity, the shape of the spheres is increasingly preserved during reconfiguration, yielding patchy particles of well-defined shape for up to five spheres. In particular, we find that the aspect ratio between the length and width of dumbbells, L/W, increases with the crosslink density (cd) as L/W = B - A·exp(-cd/C). For clusters consisting of more than five spheres, the particle deformability furthermore determines the patch arrangement of the resulting particles. The reconfiguration pathway of clusters of six densely or poorly crosslinked seeds leads to octahedral and polytetrahedral shaped patchy particles, respectively. For seven particles several geometries were obtained with a preference for pentagonal dipyramids by the rigid spheres, while the soft spheres do rarely arrive in these structures. Even larger clusters of over 15 particles form non-uniform often aspherical shapes. We discuss that the reconfiguration pathway is largely influenced by confinement and geometric constraints. The key factor which dominates during reconfiguration depends on the deformability of the spherical seed particles.

How roughness affects the depletion mechanism

We develop a simple model, in the spirit of the Asakura-Oosawa theory, able to describe the effects of surface roughness on the depletion potential. The resulting explicit expressions are easily computed, without free parameters, for a wide range of physically interesting conditions. Comparison with recent numerical simulations [M. Kamp et al., Langmuir, 2016, 32, 1233] shows an encouraging agreement and allows predicting the onset of colloidal aggregation in dilute suspensions of rough particles. Furthermore, the model proves to be suitable to investigate the role of the geometry of the roughness.

Molecular Dynamics Simulation of Trimer Self-Assembly Under Shear

The self-assembly of patchy trimer particles consisting of one attractive site and two repulsive sites is investigated with nonequilibrium molecular dynamics simulations in the presence of a velocity gradient, as would be produced by the application of a shear stress on the system. As shear is increased, globular-shaped micellar clusters increase in size and become more elongated. The globular clusters are also more stable at higher temperatures in the presence of shear than at equilibrium. These results help to increase our understanding of the effect of shear on self-assembly for a variety of applications.

Temperature-Induced, Selective Assembly of Supramolecular Colloids in Water

In this article, we report the synthesis and physical characterization of colloidal polystyrene particles that carry water-soluble supramolecular N,N',N″,-trialkyl-benzene-1,3,5-tricarboxamides (BTAs) on their surface. These molecules are known to assemble into one-dimensional supramolecular polymers via noncovalent interactions. By tethering the BTAs to charge-stabilized particles, the clustering behavior of the resulting colloids was dictated by a balance between interparticle electrostatic repulsion and the BTA-mediated attractions. Through careful tuning of the dispersing medium's ionic strength, a regime was found in which particle aggregation could be reversibly induced upon heating the dispersion. These findings clearly indicate that hydrophobic interactions, which become stronger upon heating, play an important role during the clustering process. Besides the thermoreversible nature of the generated hydrophobic interparticle attractions, we found the clustering to be selective, that is, the BTA-functionalized colloids do not interact with nonfunctionalized hydrophobic polystyrene particles. This selectivity in the association process can be rationalized by the preferred stacking of the surface-tethered BTAs. These selective intermolecular/particle bonds are likely stabilized by the formation of hydrogen bonds, as previously observed for analogous molecular BTA assemblies. The resulting driving force responsible for particle clustering is therefore dual in nature and depends on both hydrophobic attractions and hydrogen bonding.

Depletion-Induced Encapsulation by Dumbbell-Shaped Patchy Colloids Stabilize Microspheres against Aggregation

In this paper, we demonstrate the stabilization of polystyrene microspheres by encapsulating them with dumbbell-shaped colloids with a sticky and a nonsticky lobe. Upon adding a depletant, an effective short ranged attraction is induced between the microspheres and the smaller, smooth lobes of the dumbbells, making those specifically sticky, whereas the interaction with the larger lobes of the dumbbells is considerably less attractive due to their rough surface, which reduces the overlap volume and leaves them nonsticky. The encapsulation of the microspheres by these rough-smooth patchy dumbbells is investigated using a combination of experiments and computer simulations, both resulting in partial coverage of the template particles. For larger microspheres, the depletion attraction is stronger, resulting in a larger fraction of dumbbells that are attached with both lobes to the surface of microspheres. We thus find a template curvature dependent orientation of the dumbbells. In the Monte Carlo simulations, the introduction of such a small, curvature dependent attraction between the rough lobes of the dumbbells resulted in an increased coverage. However, kinetic constraints imposed by the dumbbell geometry seem to prevent optimal packing of the dumbbells on the template particles under all investigated conditions in experiments and simulations. Despite the incomplete coverage, the encapsulation by dumbbell particles does prevent aggregation of the microspheres, thus acting as a colloid-sized steric stabilizer.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

Artistic representation of limited valance units consisting of a soft core (in blue) and a small number of flexible bonding patches (in orange).

Spherical, Dimpled, and Crumpled Hybrid Colloids with Tunable Surface Morphology

Surface morphology is a tool to tune physical properties of colloidal suspensions such as the wettability, viscoelasticity, and depletion attractions. Existing synthesis methods to obtain colloids with a rough surface morphology often result in colloids with nontunable surface properties. Here, we developed a synthetic approach to obtain both spherical and shape-anisotropic hybrid colloids with tunable surface morphology. With our approach, monodisperse linear polystyrene colloids, obtained in large quantities using a dispersion polymerization method, are swollen and cross-linked with styrene and 3-(trimethoxysilyl)propyl methacrylate (TPM) in the presence of the polymerization inhibitor hydroquinone. We show that, by varying only two experimental parameters, the concentration of the inhibitor and of TPM during swelling linear polystyrene colloids, three different types of particles can be synthesized. At low TPM concentrations, spherical colloids are obtained where the surface roughness can be tuned by varying the hydroquinone concentration. At intermediate TPM concentrations, single-dimpled colloids are formed with tunable dimple size. High TPM concentrations yield crumpled colloids of various shapes. Additionally, we demonstrate that all particles can be used as templates for silica coating, resulting in electrostatically stabilized silica-coated hybrid colloids or silica shells with rough, smooth, dimpled, or crumpled surface morphology.

Self-assembly of trimer colloids: effect of shape and interaction range

Trimers with one attractive bead and two repulsive beads, similar to recently synthesized trimer patchy colloids, were simulated with flat-histogram Monte Carlo methods to obtain the stable self-assembled structures for different shapes and interaction potentials. Extended corresponding states principle was successfully applied to self-assembling systems in order to approximately collapse the results for models with the same shape, but different interaction range. This helps us directly compare simulation results with previous experiment, and good agreement was found between the two. In addition, a variety of self-assembled structures were observed by varying the trimer geometry, including spherical clusters, elongated clusters, monolayers, and spherical shells. In conclusion, our results help to compare simulations and experiments, via extended corresponding states, and we predict the formation of self-assembled structures for trimer shapes that have not been experimentally synthesized.

Colloidal Recycling: Reconfiguration of Random Aggregates into Patchy Particles

The key ingredients to the successful bottom-up construction of complex materials are believed to be colloids with anisotropic shapes and directional, or patchy, interactions. We present an approach for creating such anisotropic patchy particles based on reconfiguring randomly shaped aggregates of colloidal spheres. While colloidal aggregates are often undesirable in colloidal dispersions due to their random shapes, we exploit them as a starting point to synthesize patchy particles. By a deliberate destabilization of the colloidal particles, diffusion-limited aggregation is induced which partitions the particles into randomly shaped aggregates with controlled size distribution. We achieve a reconfiguration of the aggregates into uniform structures by swelling the polymer spheres with an apolar solvent. The swelling lowers the attractive van der Waals forces, lubricates the contact area between the spheres, and drives the reorganization through minimization of the interfacial energy of the swollen polymer network. This reorganization process yields patchy particles whose patch arrangement is uniform for up to five patches. For particles with more patches, we find that the patch orientation depends on the degree of phase separation between the spheres and the monomer. This enables the synthesis of patchy particles with unprecedented patch arrangements. We demonstrate the broad applicability of this recycling strategy for making patchy particles as well as clusters of spheres by varying the swelling ratio, swelling solvent, surfactant concentration, and swelling time.

Amphiphilic Janus Particles Generated via a Combination of Diffusion-Induced Phase Separation and Magnetically Driven Dewetting and Their Synergistic Self-Assembly

Amphiphilic Janus particles are successfully obtained via a powerful strategy combining diffusion-induced phase separation and magnetically driven dewetting. A large-area, amphiphilic monolayer is been formed via a self-assembly paradigm based on a synergy between the amphiphilicity, shape anisotropy, and external magnetic field. This functionality holds great promise for practical applications in intelligent coatings, anti-bioadhesion, and antifouling surfaces.

Computational study of trimer self-assembly and fluid phase behavior

The fluid phase diagram of trimer particles composed of one central attractive bead and two repulsive beads was determined as a function of simple geometric parameters using flat-histogram Monte Carlo methods. A variety of self-assembled structures were obtained including spherical micelle-like clusters, elongated clusters, and densely packed cylinders, depending on both the state conditions and shape of the trimer. Advanced simulation techniques were employed to determine transitions between self-assembled structures and macroscopic phases using thermodynamic and structural definitions. Simple changes in particle geometry yield dramatic changes in phase behavior, ranging from macroscopic fluid phase separation to molecular-scale self-assembly. In special cases, both self-assembled, elongated clusters and bulk fluid phase separation occur simultaneously. Our work suggests that tuning particle shape and interactions can yield superstructures with controlled architecture.

Coupling of isotropic and directional interactions and its effect on phase separation and self-assembly

The interactions of molecules and particles in solution often involve an interplay between isotropic and highly directional interactions that lead to a mutual coupling of phase separation and self-assembly. This situation arises, for example, in proteins interacting through hydrophobic and charged patch regions on their surface and in nanoparticles with grafted polymer chains, such as DNA. As a minimal model of complex fluids exhibiting this interaction coupling, we investigate spherical particles having an isotropic interaction and a constellation of five attractive patches on the particle's surface. Monte Carlo simulations and mean-field calculations of the phase boundaries of this model depend strongly on the relative strength of the isotropic and patch potentials, where we surprisingly find that analytic mean-field predictions become increasingly accurate as the directional interactions become increasingly predominant. We quantitatively account for this effect by noting that the effective interaction range increases with increasing relative directional to isotropic interaction strength. We also identify thermodynamic transition lines associated with self-assembly, extract the entropy and energy of association, and characterize the resulting cluster properties obtained from simulations using percolation scaling theory and Flory-Stockmayer mean-field theory. We find that the fractal dimension and cluster size distribution are consistent with those of lattice animals, i.e., randomly branched polymers swollen by excluded volume interactions. We also identify a universal functional form for the average molecular weight and a nearly universal functional form for a scaling parameter characterizing the cluster size distribution. Since the formation of branched clusters at equilibrium is a common phenomenon in nature, we detail how our analysis can be used in experimental characterization of such associating fluids.

Small is beautiful: Surprising nanoparticles

In the preparation of nanoparticles for drug delivery, it is well known that their size as well as their surface decorations can play a major role in interaction with living media. It is less known that their shape and internal structure can interplay with cellular and in vivo fate. The scientific literature is full of a large variety of surprising terms referring to their shape and structure. The aim of this review is to present some examples of the most often encountered surprising nanoparticles prepared and usable in the pharmaceutical technology domain. They are presented in two main groups related to their physical aspects: 1) smooth surface particles, such as Janus particles, "snowmen", "dumbbells", "rattles", and "onions" and 2) branched particles, such as "flowers", "stars" and "urchins". The mode of preparation and potential applications are briefly presented. The topic has a serious, wider importance, namely in opportunity these structures have to allow exploration of the role of shape and structure on the utility (and perhaps toxicity) of these nanostructures.

Versatile procedure for site-specific grafting of polymer brushes on patchy particles via atom transfer radical polymerization (ATRP)

Combining chemically anisotropic colloids with Surface-Initiated ATRP enables for site-specific grafting of p(NIPAM) brushes. The resulting, partially grafted particles are employed as colloidal building blocks for finite-sized clusters.

Phase separation and self-assembly in a fluid of Mickey Mouse particles

Recent developments in the synthesis of colloidal particles allow for control over shape and inter-particle interaction. One example, among others, is the so-called "Mickey Mouse" (MM) particle for which the self-assembly properties have been previously studied yielding a stable cluster phase together with elongated, tube-like structures. Here, we investigate under which conditions a fluid of Mickey Mouse particles can yield phase separation and how the self-assembly behaviour affects the gas-liquid coexistence. We vary the distance between the repulsive and the attractive lobes (bond length), and the interaction range, and follow the evolution of the gas-liquid (GL) coexistence curve. We find that upon increasing the bond length distance the binodal line shifts to lower temperatures, and that the interaction range controls the transition between phase separation and self-assembly of clusters. Upon further reduction of the interaction range and temperature, the clusters assume an increasingly ordered tube-like shape, ultimately matching the one previously reported in literature. These results are of interest when designing particle shape and particle-particle interaction for self-assembly processes.