Staged Self-Assembly of Colloidal Metastructures

Two-stage assembly of patchy ellipses: From bent-core particles to liquid crystal analogs

We investigate the two-dimensional behavior of colloidal patchy ellipsoids specifically designed to follow a two-step assembly process from the monomer state to mesoscopic liquid-crystal phases via the formation of the so-called bent-core units at the intermediate stage. Our model comprises a binary mixture of ellipses interacting via the Gay-Berne potential and decorated by surface patches, with the binary components being mirror-image variants of each other-referred to as left-handed and right-handed ellipses according to the position of their patches. The surface patches are designed so as in the first stage of the assembly the monomers form bent-cores units, i.e., V-shaped dimers with a specific bent angle. The Gay-Berne interactions, which act between the ellipses, drive the dimers to subsequently form the characteristic phase observed in bent-core liquid crystals. We numerically investigate-by means of both Molecular Dynamics and Monte Carlo simulations-the described two-step process: we first optimize a target bent-core unit and then fully characterize its state diagram in temperature and density, defining the regions where the different liquid crystalline phases dominate.

Self-Assembly of Model Three- and Four-Patch Colloidal Particles in Two Dimensions

A coarse-grained effective solvent model of two-patch particles is extended to study the self-assembly of three- and four-patch particles to two-dimensional honeycomb and square lattices, respectively. Employing this model, grand canonical ensemble simulations are done to calculate vapor-liquid equilibria and the critical temperatures for patchy particles of various patch widths. The range of stability of the liquid, although very limited compared to isotropic particles, which interact through a longer-range potential, depends on the patch width and on the number of patches. Biased sampling and unbiased simulations are also done to investigate the mechanism of nucleation and crystal growth for honeycomb and square lattices, self-assembled from three- and four-patch particles, respectively. A two-step mechanism governs the nucleation of both lattices. In the first step, the particles form a dense amorphous network, and in the second step, the particles inside the amorphous network reorient to form crystalline nuclei. Barrier heights for the nucleation of honeycomb and square lattices are 7.8 kBT and 7.4 kBT, which are close to the reported values for the nucleation of the kagome lattice. In agreement with confocal microscopy experiments, the self-assembly in a honeycomb lattice involves the formation of 5- to 7-membered rings. The 5- and 7-membered rings hamper the nucleation of the honeycomb lattice, through defect formation and rotation of the symmetry planes of crystals that form at their surfaces. With the progress of self-assembly, a substantial amount of restructuring of the defects and crystals in their vicinity is needed to heal the defects.

Self-Assembled Ring-Based Complex Colloidal Particles by Lock-And-Key Interaction and Their Self-Assembly into Unusual Colloidal Crystals

Creating hierarchical crystalline materials using simple colloids or nanoparticles is very challenging, as it is usually impossible to achieve hierarchical structures without nonhierarchical colloidal interactions. Here, we present a hierarchical self-assembly (SA) route that employs colloidal rings and anisotropic colloidal particles to form complex colloids and uses them as building blocks to form unusual colloidal columnar liquid crystals or crystals. This route is realized by designing hierarchical SA driving forces that is controlled by the colloidal shape and shape-dependent depletion attraction. Depletion-induced lock-and-key interaction is the first driving force, which ensures a high efficiency (>90%) to load colloidal particles of other shapes such as spheres, spherocylinders, and oblate ellipsoids into rings, providing high-quality building blocks. Their SA into ordered superstructures has to require a second driving force such as higher volume fraction and/or stronger depletion attraction. As a result, unusual hierarchical colloidal (liquid) crystals, which have previously been difficult to fabricate by simple binary assembly, can be achieved. This work presents a significant advancement in the field of hierarchical SA, demonstrating a promising strategy for constructing many unprecedented crystalline materials by the SA route.

Self-Assembly Pathways of Triblock Janus Particles into 3D Open Lattices

The self-assembly of triblock Janus particles is simulated from a fluid to 3D open lattices: pyrochlore, perovskite, and diamond. The coarse-grained model explicitly takes into account the chemical details of the Janus particles (attractive patches at the poles and repulsion around the equator) and it contains explicit solvent particles. Hydrodynamic interactions are accounted for by dissipative particle dynamics. The relative stability of the crystals depends on the patch width. Narrow, intermediate, and wide patches stabilize the pyrochlore-, the perovskite-, and the diamond-lattice, respectively. The nucleation of all three lattices follows a two-step mechanism: the particles first agglomerate into a compact and disordered liquid cluster, which does not crystallize until it has grown to a threshold size. Second, the particles reorient inside this cluster to form crystalline nuclei. The free-energy barriers for the nucleation of pyrochlore and perovskite are ≈10 kBT, which are close to the nucleation barriers of previously studied 2D kagome lattices. The barrier height for the nucleation of diamond, however, is much larger (>20 kBT), as the symmetry of the triblock Janus particles is not perfect for a diamond structure. The large barrier is associated with the reorientation of particles, i.e., the second step of the nucleation mechanism.

Selective Vapor Condensation for the Synthesis and Assembly of Spherical Colloids with a Precise Rough Patch

Patchy particles occupy an increasingly important space in soft matter research due to their ability to assemble into intricate phases and states. Being able to fine-tune the interactions among these particles is essential to understanding the principles governing the self-assembly processes. However, current fabrication techniques often yield patches that deviate chemically and physically from the native particles, impeding the identification of the driving forces behind self-assembly. To overcome this challenge, we propose a new approach to synthesizing spherical colloids with a well-defined rough patch on their surface. By treating polystyrene microspheres with vapors of a good solvent, here an acetone-water mixture, we achieve selective polymer corrugation on the particle surface resulting in a chemically similar yet rough surface patch. The key step is the selective condensation of the acetone-water vapors on the apex of the polystyrene microparticles immobilized on a substrate, which leads to rough patch formation. We leverage the ability to tune the vapor-liquid equilibrium of the volatile acetone-water mixture to precisely control the polymer corrugation on the particle surface. We demonstrate the dependence of patch formation on particle and substrate wettability, with the condensation occurring on the particle apex only when it is more wettable than the substrate, which is consistent with Volmer's classical nucleation theory. By combining experiments and molecular dynamics simulations, we identify the role of the rough patch in the depletion interaction-driven self-assembly of the microspheres, which is crucial for designing programmable supracolloidal structures.

Molecular Engineering of Colloidal Atoms

Creation of architectures with exquisite hierarchies actuates the germination of revolutionized functions and applications across a wide range of fields. Hierarchical self-assembly of colloidal particles holds the promise for materialized realization of structural programing and customizing. This review outlines the general approaches to organize atom-like micro- and nanoparticles into prescribed colloidal analogs of molecules by exploiting diverse interparticle driving motifs involving confining templates, interactive surface ligands, and flexible shape/surface anisotropy. Furthermore, the self-regulated/adaptive co-assembly of simple unvarnished building blocks is discussed to inspire new designs of colloidal assembly strategies.

Size-encoded hierarchical self-assembly of nanoparticles into chains and tubules

Hierarchical structures with sophisticated patterns allow the emergence of challenging properties. However, the highly cooperative and specific interactions needed for assembly spanning different length scales are typically lacking in inorganic nanoparticles (NPs). Here we show that size can be a common structural driving force for controlling hierarchical assembly of inorganic NPs into anisotropic superstructures. It involves first the self-limiting assembly of small CdS NPs into large supraparticles and their subsequent spontaneous organization into chains and tubules hundreds of nanometers long. Our quantitative calculations based on DLVO theory reveals an intrinsic size effect relating to the dimension change of assembly units in accordance with a negative cooperativity. It is shown that the size increase in building blocks creates an effective kinetic barrier contrast at different attachment sites due to the increase of interparticle electrostatic repulsion, switching the assembly from thermodynamically preferred 3D to kinetically favored 1D pathway. The size-encoded hierarchical assembly is accompanied by the ligand-controlled Oswald ripening process, which is responsible for the variation of hierarchical patterns from chains to tubules. The general principle in governing multistage inorganic NP ordering represents an important guideline toward the complex mesoscale structures that may surpass traditional materials in both design and functionality.

Importance of Substrate-Particle Repulsion for Protein-Templated Assembly of Metal Nanoparticles

We study the protein-directed assembly of colloidal gold nanoparticles on de novo designed protein nanofiber templates. Using sequential assembly on glass substrates, we attach positively charged gold nanoparticles to protein nanofibers engineered to have a high density of negatively charged surface residues. Using a combination of electron and optical microscopy, we measure the density of particle attachment and characterize binding specificity. By varying nanoparticle size and pH of the solution, we explore the importance of charge-dependent particle-fiber and particle-substrate interactions. We find an inverse correlation between particle size and attachment density to protein nanofibers, attributed to the balance between size-dependent electrostatic particle-fiber attraction and particle-substrate repulsion. We show pH-dependent particle attachment density and binding specificity in relation to the protonation fraction of each assembly layer. Finally, we employ hyperspectral scattering microscopy to draw conclusions about particle density and interparticle spacings of optically observable particle assemblies.

Unconventional-Phase Crystalline Materials Constructed from Multiscale Building Blocks

Crystal phase, an intrinsic characteristic of crystalline materials, is one of the key parameters to determine their physicochemical properties. Recently, great progress has been made in the synthesis of nanomaterials with unconventional phases that are different from their thermodynamically stable bulk counterparts via various synthetic methods. A nanocrystalline material can also be viewed as an assembly of atoms with long-range order. When larger entities, such as nanoclusters, nanoparticles, and microparticles, are used as building blocks, supercrystalline materials with rich phases are obtained, some of which even have no analogues in the atomic and molecular crystals. The unconventional phases of nanocrystalline and supercrystalline materials endow them with distinctive properties as compared to their conventional counterparts. This Review highlights the state-of-the-art progress of nanocrystalline and supercrystalline materials with unconventional phases constructed from multiscale building blocks, including atoms, nanoclusters, spherical and anisotropic nanoparticles, and microparticles. Emerging strategies for engineering their crystal phases are introduced, with highlights on the governing parameters that are essential for the formation of unconventional phases. Phase-dependent properties and applications of nanocrystalline and supercrystalline materials are summarized. Finally, major challenges and opportunities in future research directions are proposed.

Magnetic Coupling in Colloidal Clusters for Hierarchical Self-Assembly

Manipulating the way in which colloidal particles self-organize is a central challenge in the design of functional soft materials. Meeting this challenge requires the use of building blocks that interact with one another in a highly specific manner. Their fabrication, however, is limited by the complexity of the available synthesis procedures. Here, we demonstrate that, starting from experimentally available magnetic colloids, we can create a variety of complex building blocks suitable for hierarchical self-organization through a simple scalable process. Using computer simulations, we compress spherical and cubic magnetic colloids in spherical confinement, and investigate their suitability to form small clusters with reproducible structural and magnetic properties. We find that, while the structure of these clusters is highly reproducible, their magnetic character depends on the particle shape. Only spherical particles have the rotational degrees of freedom to produce consistent magnetic configurations, whereas cubic particles frustrate the minimization of the cluster energy, resulting in various magnetic configurations. To highlight their potential for self-assembly, we demonstrate that already clusters of three magnetic particles form highly nontrivial Archimedean lattices, namely, staggered kagome, bounce, and honeycomb, when focusing on different aspects of the same monolayer structure. The work presented here offers a conceptually different way to design materials by utilizing preassembled magnetic building blocks that can readily self-organize into complex structures.

Inverse Design of Self-Assembling Diamond Photonic Lattices from Anisotropic Colloidal Clusters

Colloidal nanoparticles with anisotropic interactions are promising building blocks for the fabrication of complex functional materials. A challenge in the self-assembly of colloidal particles is the rational design of geometry and chemistry to program the formation of a desired target structure. We report an inverse design procedure integrating Langevin dynamics simulations and evolutionary algorithms to engineer anisotropic patchy colloidal clusters to spontaneously assemble into a cubic diamond lattice possessing a complete photonic band gap. The combination of a tetrahedral cluster geometry and optimized placement of a single type of anisotropic interaction patch results in a colloidal building block predicted to assemble a cubic diamond lattice with more than 82% yield. This design represents an experimentally viable colloidal building block capable of high-fidelity assembly of a cubic diamond lattice.

Self-Assembly of Patchy Colloidal Rods into Photonic Crystals Robust to Stacking Faults

Diamond-structured colloidal photonic crystals are much sought-after for their applications in visible light management because of their ability to support a complete photonic band gap (PBG). However, their realization via self-assembly pathways is a long-standing challenge. This challenge is rooted in three fundamental problems: the design of building blocks that assemble into diamond-like structures, the sensitivity of the PBG to stacking faults, and ensuring that the PBG opens at an experimentally attainable refractive index. Here we address these problems simultaneously using a multipronged computational approach. We use reverse engineering to establish the design principles for the rod-connected diamond structure (RCD), the so-called "champion" photonic crystal. We devise two distinct self-assembly routes for designer triblock patchy colloidal rods, both proceeding via tetrahedral clusters to yield a mixed phase of cubic and hexagonal polymorphs closely related to RCD. We use Monte Carlo simulations to show how these routes avoid a metastable amorphous phase. Finally, we show that both the polymorphs support spectrally overlapping PBGs. Importantly, randomly stacked hybrids of these polymorphs also display PBGs, thus circumventing the requirement of polymorph selection in a scalable fabrication method.

Quantifying patterns in optical micrographs of one- and two-dimensional ellipsoidal particle assemblies

Current developments in colloidal science include the assembly of anisotropic colloids with broad geometric diversity. As the complexity of particle assemblies increases, the need for ubiquitous algorithms that quantitatively analyze images of the assemblies to deliver key information such as quantification of crystal structures becomes more urgent. This contribution describes algorithms capable of image analysis for classifying colloidal structures based on abstracted interparticle relationship information and quantitatively analyzing the abundance of each structure in mixed pattern assemblies. The algorithm parameters can be adjusted, allowing for the algorithms to be adapted for different image analyses. Three different ellipsoidal particle assembly images are presented to demonstrate the effectiveness of the algorithms: a one-dimensional (1D) particle chain assembly and two two-dimensional (2D) polymorphic crystals each consisting of assemblies of two distinct plane symmetry groups. Angle relationships between neighbouring particles are calculated and neighbour counts of each particle are determined. Combining these two parameters as rules for classification criteria allows for the labeling and quantification of each particle into a defined symmetry class within an assembly. The algorithms provide a labelled image comprising classification results and particle counts of each defined class. For multiple images or individual frames from a video, the script can be looped to achieve automatic processing. The yielded classification data allow for more in-depth image analysis of mixed pattern particle assemblies. We envision that these algorithms will have utility in quantitative analysis of images comprising ellipsoidal colloidal materials, nanoparticles, or biological matter.

Molecular Patchy Clusters with Controllable Symmetry Breaking for Structural Engineering

Anisotropic patchy particles with molecular precision are exquisite building blocks for constructing diverse meso-structures of high complexity. In this research, a library of molecular patchy clusters consisting of a collection of functional polyhedral oligomeric silsesquioxane cages with exact regio-configuration and composition were prepared through a robust and modular approach. By meticulously tuning the composition, molecular symmetry, and other parameters, these patchy clusters could assemble into diverse nanostructures, including unconventional complex spherical phases (i.e., Frank-Kasper σ phase and dodecagonal quasicrystalline phase). As the size of the hydrophilic patch expands, a transition sequence from disorder to hexagonally packed cylinders and then to double gyroids was recorded, corresponding to a progressive decrease of interfacial curvature. On the other hand, regioisomers with the same composition but different regio-configuration adopt similar molecular packing but varied phase stability, as a result of the local self-sorting process to alleviate excess unfavorable interfacial contact. These precisely defined molecular patchy clusters provide a model system for a general understanding of the hierarchical structure formation and evolution based on anisotropic spherical building blocks at the nanoscale.

Leveraging Hierarchical Self-Assembly Pathways for Realizing Colloidal Photonic Crystals

Colloidal open crystals are attractive materials, especially for their photonic applications. Self-assembly appeals as a bottom-up route for structure fabrication, but self-assembly of colloidal open crystals has proven to be elusive for their mechanical instability due to being low-coordinated. For such a bottom-up route to yield a desired colloidal open crystal, the target structure is required to be thermodynamically favored for designer building blocks and also kinetically accessible via self-assembly pathways in preference to metastable structures. Additionally, the selection of a particular polymorph poses a challenge for certain much sought-after colloidal open crystals for their applications as photonic crystals. Here, we devise hierarchical self-assembly pathways, which, starting from designer triblock patchy particles, yield in a cascade of well-separated associations first tetrahedral clusters and then tetrastack crystals. The designed pathways avoid trapping into an amorphous phase. Our analysis reveals how such a two-stage self-assembly pathway via tetrahedral clusters promotes crystallization by suppressing five- and seven-membered rings that hinder the emergence of the ordered structure. We also find that slow annealing promotes a bias toward the cubic polymorph relative to the hexagonal counterpart. Finally, we calculate the photonic band structures, showing that the cubic polymorph exhibits a complete photonic band gap for the dielectric filling fraction directly realizable from the designer triblock patchy particles. Unexpectedly, we find that the hexagonal polymorph also supports a complete photonic band gap, albeit only for an increased filling fraction, which can be realized via postassembly processing.

Surveying the free energy landscape of clusters of attractive colloidal spheres

Controlling the assembly of colloidal particles into specific structures has been a long-term goal of the soft materials community. Much can be learned about the process of self-assembly by examining the early stage assembly into clusters. For the simple case of hard spheres with short-range attractions, the rigid clusters of N particles (where N is small) have been enumerated theoretically and tested experimentally. Less is known, however, about how the free energy landscapes are altered when the inter-particle potential is long-ranged. In this work, we demonstrate how adaptive biasing in molecular simulations may be used to pinpoint shifts in the stability of colloidal clusters as the inter-particle potential is varied. We also discuss the generality of our techniques and strategies for application to related molecular systems.

Hierarchical self-assembly of patchy colloidal platelets

Anisotropy at the level of the inter-particle interaction provides the particles with specific instructions for the self-assembly of target structures. The ability to synthesize non-spherical colloids, together with the possibility of controlling the particle bonding pattern via suitably placed interaction sites, is nowadays enlarging the playing field for materials design. We consider a model of anisotropic colloidal platelets with regular rhombic shape and two attractive sites placed along adjacent edges and we run Monte Carlo simulations in two-dimensions to investigate the two-stage assembly of these units into clusters with well-defined symmetries and, subsequently, into extended lattices. Our focus is on how the site positioning and site-site attraction strength can be tuned to obtain micellar aggregates that are robust enough to successively undergo to a second-stage assembly from sparse clusters into a stable hexagonal lattice.

Kinetics-controlled design principles for two-dimensional open lattices using atom-mimicking patchy particles

The design and discovery of new two-dimensional materials with desired structures and properties are always one of the most fundamental goals in materials science. Here we present an atom-mimicking design concept to achieve direct self-assembly of two-dimensional low-coordinated open lattices using three-dimensional patchy particle systems. Besides honeycomb lattices, a new type of two-dimensional square-octagon lattice is obtained through rational design of the patch configuration of soft three-patch particles. However, unexpectedly the building blocks with thermodynamically favoured patch configuration cannot form square-octagon lattices in our simulations. We further reveal the kinetic mechanisms controlling the formation of the honeycomb and square-octagon lattices. The results indicate that the kinetically favoured intermediates play a critical role in determining the structure of obtained open lattices. This kinetics-controlled design principle provides a particularly effective and extendable framework to construct other novel open lattice structures.

Self-assembly of lobed particles into amorphous and crystalline porous structures

We report simulation studies on the self-assembly of hard-lobed particles (patchy particles where patches appear as lobes around a seed) of different shapes and show that various types of self-assembled morphologies can be achieved by tuning inter-lobe interactions. On self-assembly, the linear building blocks having two lobes around the seed formed rings, the trigonal planar building blocks formed cylindrical hollow tubes and two-dimensional sheets, and the square planar building blocks formed spherical clathrates. The tetrahedral, trigonal bipyramidal, and the octahedral-shaped particles formed compact porous crystalline structures which are constituted by either hexagonal close packed or face centered cubic lattices. The pore size distributions revealed that linear, trigonal planar, and square planar building blocks create highly porous self-assembled structures. Our results suggest that these self-assembled morphologies will potentially find applications in tissue engineering, host-guest chemistry, adsorption, and catalysis.

The effect of surface roughness on the phase behavior of colloidal particles

Shape anisotropy of colloidal particles can give rise to complex intermolecular interactions that determine particle packing and phase behavior. The vapor-liquid coexistence curves of attractive rough particles display a shift when compared to attractive smooth spherical particles. We use Integral Equation Theory (IET) to determine the vapor-liquid spinodal phase diagram of smooth and rough colloidal particles interacting through square-well attraction. Additionally, we use Gibbs Ensemble Monte Carlo (GEMC) simulations to locate their vapor-liquid coexistence curves. We model a rough colloidal particle as a spherical core with small beads embedded on its surface. The critical point of smooth spherical particle systems predicted by theory and simulations is in quantitative agreement. An increase in surface roughness due to an increase in either the number of beads or the diameter of the beads has a modest effect on the local structure of the system in the supercritical region. In contrast, increasing surface roughness consistently shifts the vapor-liquid coexistence curves to higher temperatures. The critical temperature is found to be a quadratic function of the number of beads. At a fixed bead size and number of beads, the critical temperature does not vary with the arrangement of beads on the core. Both IET and GEMC simulations predict that unlike critical temperatures, critical packing fractions vary non-monotonically with surface roughness. We find that the feasibility and accuracy of the integral equation theory depend sensitively on the chosen closure combination.

Inverse design of self-assembling colloidal crystals with omnidirectional photonic bandgaps

Open colloidal lattices possessing omnidirectional photonic bandgaps in the visible or near-visible regime are attractive optical materials the realization of which has remained elusive. We report the use of an inverse design strategy termed landscape engineering that rationally sculpts the free energy self-assembly landscape using evolutionary algorithms to discover anisotropic patchy colloids capable of spontaneously assembling pyrochlore and cubic diamond lattices possessing complete photonic bandgaps. We validate the designs in computer simulations to demonstrate the defect-free formation of these lattices via a two-stage hierarchical assembly mechanism. Our approach demonstrates a principled strategy for the inverse design of self-assembling colloids for the bottom-up fabrication of desired crystal lattices.

Assembly and Dynamic Analysis of Square Colloidal Crystals via Templated Capillary Assembly

Capillary assembly has the ability to engineer centimeter-sized regions of discrete colloidal superstructures and microarrays. However, its use as a tool for directing crystallization of colloids into surface-bound nonclose-packed arrays is limited. Furthermore, the use of quantitative particle tracking tools to investigate evaporative assembly dynamics is rarely employed. In this contribution, we use templated capillary assembly to fabricate square-packed lattices of spherical, organosilica colloids using designed patterned boundaries. Particle tracking algorithms reveal that the assembly of square-packed regions is controlled by the interplay between confinement-driven nuclei formation and osmotic pressure-driven restructuring. We find that the incorporation of a square template increases the yield of particles bearing four nearest neighbors (Z_n = 4) from 4 to 39%, obtained using a heavier and more viscous solvent. Maximal square-packed domains occur at specific initial particle concentrations (1.75-2.25 wt % or φ = 0.013-0.017), indicating that rearrangements are a function of osmotic force. We use particle tracking methods to dynamically monitor conversions between square and hexagonal packing, revealing a cyclical transition between 4 and 6 coordinated particles throughout meniscus recession. Our method is highly scalable and inexpensive and can be adapted for use with different particle sizes and compositions, as well as for targeted open-packed geometries. Our findings will inform the large area, defect-free assembly of nonclose-packed lattices of unexplored varieties that are necessary for the continued expansion of colloid-based materials with vast applications in optical electronics.

Reconfigurable assembly of charged polymer-modified Janus and non-Janus particles: from half-raspberries to colloidal clusters and chains

Understanding the dynamic and reversible assembly of colloids and particles into complex constructs, inspired by natural phenomena, is of fundamental significance for the fabrication of multi-scale responsive and reconfigurable materials. In this work, we investigate the pH-triggered and reconfigurable assembly of structures composed of binary mixtures of oppositely charged polyacrylic acid (PAA)-modified non-Janus and poly(2-dimethylamino)ethyl methacrylate (PDMAEMA)/poly(N-isopropylacrylamide) (PNIPAM)-modified Janus particles driven by electrostatic interactions. Three different target structures are visible both in dispersions and in dry state: half-raspberry structures, colloidal clusters and colloidal chains depending on the mass, numerical and particle size ratio. All formed structures are well-defined and stable in a certain pH range. Half-raspberry-like structures are obtained at pH 6 and numerical ratios N JP/PAA-HP of 1 : 500 (for 200-PAA-HP), 1 : 44 (for 450-PAA-HP) and 1 : 15 (for 650-PAA-HP), respectively, due to electrostatic interactions between the central JP and the excessive PAA-HP. Colloidal chains and cluster-like structures are generated at numerical ratios N JP/PAA-HP of 4 : 5 (for 200-PAA-HP), 4 : 3 (for 450-PAA-HP), and 4 : 1 (for 650-PAA-HP). Moreover, the smaller the size of a "connecting" PAA colloid, the larger is the average length of a colloidal chain. Depending on the particle size ratio S JP/PAA-HP, some of the observed structures can be disassembled on demand by changing the pH value either close to the IEP of the PDMAEMA (for half-raspberries) or PAA (for colloidal clusters and chains) and then reassembled into new stable structures many times. The obtained results open a pathway to pH-controlled reconfigurable assembly of a binary mixture composed of polymeric-modified non-Janus and Janus particles, which allow the reuse of particle building blocks.

Active Patchy Colloids with Shape-Tunable Dynamics

Controlling the complex dynamics of active colloids-the autonomous locomotion of colloidal particles and their spontaneous assembly-is challenging yet crucial for creating functional, out-of-equilibrium colloidal systems potentially useful for nano- and micromachines. Herein, by introducing the synthesis of active "patchy" colloids of various low-symmetry shapes, we demonstrate that the dynamics of such systems can be precisely tuned. The low-symmetry patchy colloids are made in bulk via a cluster-encapsulation-dewetting method. They carry essential information encoded in their shapes (particle geometry, number, size, and configurations of surface patches, etc.) that programs their locomotive and assembling behaviors. Under AC electric field, we show that the velocity of particle propulsion and the ability to brake and steer can be modulated by having two asymmetrical patches with various bending angles. The assembly of monopatch particles leads to the formation of dynamic and reconfigurable structures such as spinners and "cooperative swimmers" depending on the particle's aspect ratios. A particle with two patches of different sizes allows for "directional bonding", a concept popular in static assemblies but rare in dynamic ones. With the capability to make tunable and complex shapes, we anticipate the discovery of a diverse range of new dynamics and structures when other external stimuli (e.g., magnetic, optical, chemical, etc.) are employed and spark synergy with shapes.

Self-assembled multi-layer simple cubic photonic crystals of oppositely charged colloids in confinement

Designing and fabricating self-assembled open colloidal crystals have become one major direction in the soft matter community because of many promising applications associated with open colloidal crystals. However, most of the self-assembled crystals found in experiments are not open but close-packed. Here, by using computer simulation, we systematically investigate the self-assembly of oppositely charged colloidal hard spheres confined between two parallel hard walls, and we find that the confinement can stabilize multi-layer NaCl-like (simple cubic) open crystals. The maximal number of layers of stable NaCl-like crystals increases with decreasing inverse screening length. More interestingly, at finite low temperature, the large vibrational entropy can stabilize some multi-layer NaCl-like crystals against the most energetically favoured close-packed crystals. In the parameter range studied, we find up to 4-layer NaCl-like crystals to be stable in confinement. Our photonic calculation shows that the inverse 4-layer NaCl-like crystal can already reproduce the large photonic band gaps of the bulk simple cubic crystal, which open in the low frequency range with a low dielectric contrast. This suggests new possibilities of using confined colloidal systems to fabricate open crystalline materials with novel photonic properties.

Versatile fabrication of patchy nanoparticles via patterning of grafted diblock copolymers on NP surface

Patchy nanoparticle formation via the patterning of grafted diblock copolymers on NP surface.

Assembly of colloidal particles in solution

Advances in both top-down and bottom-up syntheses of a wide variety of complex colloidal building blocks and also in methods of controlling their assembly in solution have led to new and interesting forms of highly controlled soft matter. In particular, top-down lithographic methods of producing monodisperse colloids now provide precise human-designed control over their sub-particle features, opening up a wide range of new possibilities for assembly structures that had been previously limited by the range of shapes available through bottom-up methods. Moreover, an increasing level of control over anisotropic interactions between these colloidal building blocks, which can be tailored through local geometries of sub-particle features as well as site-specific surface modifications, is giving rise to new demonstrations of massively parallel off-chip self-assembly of specific target structures with low defect rates. In particular, new experimental realizations of hierarchical self-assembly and control over the chiral purity of resulting assembly structures have been achieved. Increasingly, shape-dependent, shape-complementary, and roughness-controlled depletion attractions between non-spherical colloids are being used in novel ways to create assemblies that go far beyond early examples, such as fractal clusters formed by diffusion-limited and reaction-limited aggregation of spheres. As self-assembly methods have progressed, a wide variety of advanced directed assembly methods have also been developed; approaches based on microfluidic control and applying structured electromagnetic fields are particularly promising.

General patchy ellipsoidal particle model for the aggregation behaviors of shape- and/or surface-anisotropic building blocks

We present a general patchy ellipsoidal particle model suitable for conducting dynamics simulations of the aggregation behaviors of various shape- and/or surface-anisotropic colloids, especially patchy ellipsoids with continuously variable shape and tunable patchiness. To achieve higher computational efficiency in dynamics simulations, we employ a multi-GPU acceleration technique based on a domain decomposition algorithm. The validation and performance evaluation of this GPU-assisted model are performed by simulating several typical benchmark systems of non-patchy and patchy ellipsoids. Given the generality and efficiency of our GPU-assisted patchy ellipsoidal particle model, it will provide a highly feasible dynamics simulation framework to investigate the aggregation behaviors of anisotropic soft matter systems comprised of shape- and/or surface-anisotropic building blocks.

Colloidal Assembly Approaches to Micro/Nanostructures of Complex Morphologies

The ability to programmatically assemble colloidal micro/nanostructures into highly ordered superstructures is of great importance in both fundamental studies and practical applications. In addition to the sophisticated manipulation of the short-range and long-range interactions imposed on the colloidal building blocks, the intrinsic shape elements including face, edge, corner, concave, convex, and curvature also play very important roles in solving the "jigsaw puzzle" of the superstructures. Here, the recent progress in the development of colloidal assembly strategies for the formation of complex superstructures is reviewed, with a primary focus on the unique effects of the morphology of the building blocks to the assembly processes and the final structures. Overall, this Review aims to shed light on the fundamental understanding of the colloidal behaviors of complex micro/nanostructures and promote the continued development of effective strategies for the creation of functional materials with complex compositions and morphologies.

Programming hierarchical self-assembly of colloids: matching stability and accessibility

Encoding hierarchical self-assembly in colloidal building blocks is a promising bottom-up route to high-level structural complexity often observed in biological materials. However, harnessing this promise faces the grand challenge of bridging hierarchies of multiple length- and time-scales, associated with structure and dynamics respectively along the self-assembly pathway. Here we report on a case study, which examines the kinetic accessibility of a series of hollow spherical structures with a two-level structural hierarchy self-assembled from charge-stabilized colloidal magnetic particles. By means of a variety of computational methods, we find that for a staged assembly pathway, the structure, which derives the strongest energetic stability from the first stage of assembly and the weakest from the second stage, is most kinetically accessible. Such a striking correspondence between energetics and kinetics for optimal design principles should have general implications for programming hierarchical self-assembly pathways for nano- and micro-particles, while matching stability and accessibility.

Reconfigurable Polymer Shells on Shape-Anisotropic Gold Nanoparticle Cores

Reconfigurable hybrid nanoparticles made by decorating flexible polymer shells on rigid inorganic nanoparticle cores can provide a unique means to build stimuli-responsive functional materials. The polymer shell reconfiguration has been expected to depend on the local core shape details, but limited systematic investigations have been undertaken. Here, two literature methods are adapted to coat either thiol-terminated polystyrene (PS) or polystyrene-poly(acrylic acid) (PS-b-PAA) shells onto a series of anisotropic gold nanoparticles of shapes not studied previously, including octahedron, concave cube, and bipyramid. These core shapes are complex, rendering shell contours with nanoscale details (e.g., local surface curvature, shell thickness) that are imaged and analyzed quantitatively using the authors' customized analysis codes. It is found that the hybrid nanoparticles based on the chosen core shapes, when coated with the above two polymer shells, exhibit distinct shell segregations upon a variation in solvent polarity or temperature. It is demonstrated for the PS-b-PAA-coated hybrid nanoparticles, the shell segregation is maintained even after a further decoration of the shell periphery with gold seeds; these seeds can potentially facilitate subsequent deposition of other nanostructures to enrich structural and functional diversity. These synthesis, imaging, and analysis methods for the hybrid nanoparticles of anisotropically shaped cores can potentially aid in their predictive design for materials reconfigurable from the bottom up.

The Interfacial Assembly of Polyoxometalate Nanoparticle Surfactants

Polyoxometalates (POMs) using {Mo₇₂V₃₀} as an example, dissolved in water, can interact with amine-terminated polydimethylsiloxane (PDMS-NH₂) dissolved in toluene at the water/toluene interface to form POM-surfactants that significantly lower the interfacial tension and can be used to stabilize liquids via interfacial elasticity. The jamming of the POM-surfactants at the water/oil interface with consequent wrinkling occurs with a decrease in the interfacial area. The packing density of the POM-surfactants at the interface can be tuned by varying the strength of screening with the addition of cations with differing hydrated radii.

Programming Hierarchical Self-Assembly of Patchy Particles into Colloidal Crystals via Colloidal Molecules

Colloidal self-assembly is a promising bottom-up route to a wide variety of three-dimensional structures, from clusters to crystals. Programming hierarchical self-assembly of colloidal building blocks, which can give rise to structures ordered at multiple levels to rival biological complexity, poses a multiscale design problem. Here we explore a generic design principle that exploits a hierarchy of interaction strengths and employ this design principle in computer simulations to demonstrate the hierarchical self-assembly of triblock patchy colloidal particles into two distinct colloidal crystals. We obtain cubic diamond and body-centered cubic crystals via distinct clusters of uniform size and shape, namely, tetrahedra and octahedra, respectively. Such a conceptual design framework has the potential to reliably encode hierarchical self-assembly of colloidal particles into a high level of sophistication. Moreover, the design framework underpins a bottom-up route to cubic diamond colloidal crystals, which have remained elusive despite being much sought after for their attractive photonic applications.

Molecular Recognition in the Colloidal World

Colloidal self-assembly is a bottom-up technique to fabricate functional nanomaterials, with paramount interest stemming from programmable assembly of smaller building blocks into dynamic crystalline domains and photonic materials. Multiple established colloidal platforms feature diverse shapes and bonding interactions, while achieving specific orientations along with short- and long-range order. A major impediment to their universal use as building blocks for predesigned architectures is the inability to precisely dictate and control particle functionalization and concomitant reversible self-assembly. Progress in colloidal self-assembly necessitates the development of strategies that endow bonding specificity and directionality within assemblies. Methodologies that emulate molecular and polymeric three-dimensional (3D) architectures feature elements of covalent bonding, while high-fidelity molecular recognition events have been installed to realize responsive reconfigurable assemblies. The emergence of anisotropic 'colloidal molecules', coupled with the ability to site-specifically decorate particle surfaces with supramolecular recognition motifs, has facilitated the formation of superstructures via directional interactions and shape recognition. In this Account, we describe supramolecular assembly routes to drive colloidal particles into precisely assembled architectures or crystalline lattices via directional noncovalent molecular interactions. The design principles are based upon the fabrication of colloidal particles bearing surface-exposed functional groups that can undergo programmable conjugation to install recognition motifs with high fidelity. Modular and versatile by design, our strategy allows for the introduction and integration of molecular recognition principles into the colloidal world. We define noncovalent molecular interactions as site-specific forces that are predictable (i.e., feature selective and controllable complementary bonding partners) and can engage in tunable high-fidelity interactions. Examples include metal coordination and host-guest interactions as well as hydrogen bonding and DNA hybridization. On the colloidal scale, these interactions can be used to drive the reversible formation of open structures. Key to the design is the ability to covalently conjugate supramolecular motifs onto the particle surface and/or noncovalently associate with small molecules that can mediate and direct assembly. Efforts exploiting the binding strength inherent to DNA hybridization for the preparation of reversible open-packed structures are then detailed. We describe strategies that led to the introduction of dual-responsive DNA-mediated orthogonal assembly as well as colloidal clusters that afford distinct DNA-ligated close-packed lattices. Further focus is placed on two essential and related efforts: the engineering of complex superstructures that undergo phase transitions and colloidal crystals featuring a high density of functional anchors that aid in crystallization. The design principles discussed in this Account highlight the synergy stemming from coupling well-established noncovalent interactions common on the molecular and polymeric length scales with colloidal platforms to engineer reconfigurable functional architectures by design. Directional strategies and methods such as those illustrated herein feature molecular control and dynamic assembly that afford both open-packed 1D and 2D lattices and are amenable to 3D colloidal frameworks. Multiple methods to direct colloidal assembly have been reported, yet few are capable of crystallizing 2D and 3D architectures of interest for optical data storage, electronics, and photonics. Indeed, early implications are that [supra]molecular control over colloidal assembly can fabricate rationally structured designer materials from simple fundamental building blocks.

Programmable Supra-Assembly of a DNA Surface Adapter for Tunable Chiral Directional Self-Assembly of Gold Nanorods

An important challenge in molecular assembly and hierarchical molecular engineering is to control and program the directional self-assembly into chiral structures. Here, we present a versatile DNA surface adapter that can programmably self-assemble into various chiral supramolecular architectures, thereby regulating the chiral directional "bonding" of gold nanorods decorated by the surface adapter. Distinct optical chirality relevant to the ensemble conformation is demonstrated from the assembled novel stair-like and coil-like gold nanorod chiral metastructures, which is strongly affected by the spatial arrangement of neighboring nanorod pair. Our strategy provides new avenues for fabrication of tunable optical metamaterials by manipulating the directional self-assembly of nanoparticles using programmable surface adapters.

Imaging the polymerization of multivalent nanoparticles in solution

Numerous mechanisms have been studied for chemical reactions to provide quantitative predictions on how atoms spatially arrange into molecules. In nanoscale colloidal systems, however, less is known about the physical rules governing their spatial organization, i.e., self-assembly, into functional materials. Here, we monitor real-time self-assembly dynamics at the single nanoparticle level, which reveal marked similarities to foundational principles of polymerization. Specifically, using the prototypical system of gold triangular nanoprisms, we show that colloidal self-assembly is analogous to polymerization in three aspects: ensemble growth statistics following models for step-growth polymerization, with nanoparticles as linkable “monomers”; bond angles determined by directional internanoparticle interactions; and product topology determined by the valency of monomeric units. Liquid-phase transmission electron microscopy imaging and theoretical modeling elucidate the nanometer-scale mechanisms for these polymer-like phenomena in nanoparticle systems. The results establish a quantitative conceptual framework for self-assembly dynamics that can aid in designing future nanoparticle-based materials.

Few models exist that describe the spontaneous organization of colloids into materials. Here, the authors combine liquid-phase TEM and single particle tracking to observe the dynamics of gold nanoprisms, finding that nanoscale self-assembly can be understood within the framework of atomic polymerization.

Solution-Based Thermodynamically Controlled Conversion from Diblock Copolymers to Janus Nanoparticles

Nanosized polymeric Janus particles (NPJPs) have important applications in a variety of theoretical and practical research fields. However, the methods that are versatile and can prepare NPJPs highly efficiently are very limited. Herein, we reported a two-step thermodynamically controlled preparation of NPJPs with a high yield using a diblock copolymer as the precursor. At the first step, A-b-B coassembled in the solution with a partner diblock copolymer C-b-B to form the mixed shell micelles (MSMs) with B core and A/C mixed shell. Then, intramicellarly covalently cross-linking the A block chains resulted in the complete phase separation of A and C chains in the mixed shell, leading to the direct conversion of the MSMs into NPJPs. The first step, diblock copolymer micellization, is known as a thermodynamically controlled process, and we also made the second step, conversion from MSMs to NPJPs, be thermodynamically controlled due to the application of covalent cross-linking. As the result, the conversion efficiency is close to 100%. Besides, it was further confirmed that the method can be applied to different systems and used to tune the Janus balance. Therefore, this conversion should be very significant for the fabrication and application of the NPJPs.

Interrogating Cellular Functions with Designer Janus Particles

Janus particles have two distinct surfaces or compartments. This enables novel applications that are impossible with homogeneous particles, ranging from the engineering of active colloidal metastructures to creating multimodal therapeutic materials. Recent years have witnessed a rapid development of novel Janus structures and exploration of their applications, particularly in the biomedical arena. It, therefore, becomes crucial to understand how Janus particles with surface or structural anisotropy might interact with biological systems and how such interactions may be exploited to manipulate biological responses. This perspective highlights recent studies that have employed Janus particles as novel toolsets to manipulate, measure, and understand cellular functions. Janus particles have been shown to have biological interactions different from uniform particles. Their surface anisotropy has been used to control the cell entry of synthetic particles, to spatially organize stimuli for the activation of immune cells, and to enable direct visualization and measurement of rotational dynamics of particles in living systems. The work included in this perspective showcases the significance of understanding the biological interactions of Janus particles and the tremendous potential of harnessing such interactions to advance the development of Janus structure-based biomaterials.

Connectivity, dynamics, and structure in a tetrahedral network liquid

We report a detailed computational study by Brownian dynamics simulations of the structure and dynamics of a liquid of patchy particles which forms an amorphous tetrahedral network upon decreasing the temperature. The highly directional particle interactions allow us to investigate the system connectivity by discriminating the total set of particles into different populations according to a penta-modal distribution of bonds per particle. With this methodology we show how the particle bonding process is not randomly independent but it manifests clear bond correlations at low temperatures. We further explore the dynamics of the system in real space and establish a clear relation between particle mobility and particle connectivity. In particular, we provide evidence of anomalous diffusion at low temperatures and reveal how the dynamics is affected by the short-time hopping motion of the weakly bounded particles. Finally we widely investigate the dynamics and structure of the system in Fourier space and identify two quantitatively similar length scales, one dynamic and the other static, which increase upon cooling the system and reach distances of the order of few particle diameters. We summarize our findings in a qualitative picture where the low temperature regime of the viscoelastic liquid is understood in terms of an evolving network of long time metastable cooperative domains of particles.