Colloidal diamond

Equilibrium and self-assembly of Janus particles at liquid-liquid interfaces for the film formation

This article investigates the equilibrium arrangement, self-assembly process, and subsequent curing of amphiphilic snowman-shaped Janus particles at the oil-water interface. The independent Janus particles are in vertical equilibrium state and the contact position of the oil-water interface is at the largest cross section of the particle's hydrophobic phase. Under the effect of the surface tension and the adsorption of materials, Janus particles may form particle combinations including the particle pairs and the particle triangle, whose inner and outer sides have the liquid surface exhibiting completely opposite contact angles. Particle combinations form stable parallel double-chain structures with diverse shapes after the self-assembly process. However, the single Janus particles attain a state of mechanical equilibrium under the influence of surrounding particles, enabling them to assemble into regular array structures. The relationship of interfacial tension coefficient between phases can be changed by adjusting the oil-water system, which leads to variations in the self-assembly speed and the final arrangement results. The thin-film with uniformly distributed vertical particles is achieved by replacing the underlying deionized water with a curing agent. Based on the understanding of the interactions between irregularly shaped Janus particles at the oil-water interface, it will be convenient to achieve the controllable self-assembly and widely applications of these particles.

Buzza DM. Programmable 2D materials through shape-controlled capillary forces

In recent years, self-assembly has emerged as a powerful tool for fabricating functional materials. Since self-assembly is fundamentally determined by the particle interactions in the system, if we can gain full control over these interactions, it would open the door for creating functional materials by design. In this paper, we exploit capillary interactions between colloidal particles at liquid interfaces to create two-dimensional (2D) materials where particle interactions and self-assembly can be fully programmed using particle shape alone. Specifically, we consider colloidal particles which are polygonal plates with homogeneous surface chemistry and undulating edges as this particle geometry gives us precise and independent control over both short-range hard-core repulsions and longer-range capillary interactions. To illustrate the immense potential provided by our system for programming self-assembly, we use minimum energy calculations and Monte Carlo simulations to show that polygonal plates with different in-plane shapes (hexagons, truncated triangles, triangles, squares) and edge undulations of different multipolar order (hexapolar, octopolar, dodecapolar) can be used to create a rich variety of 2D structures, including hexagonal close-packed, honeycomb, Kagome, and quasicrystal lattices. Since the required particle shapes can be readily fabricated experimentally, we can use our colloidal system to control the entire process chain for materials design, from initial design and fabrication of the building blocks, to final assembly of the emergent 2D material.

Directed crystalline symmetry transformation of blue-phase liquid crystals by reverse electrostriction

Soft-matter-based photonic crystals like blue-phase liquid crystals (BPLC) have potential applications in wide-ranging photonic and bio-chemical systems. To date, however, there are limitations in the fabrication of large monocrystalline BPLCs. Traditional crystal-growth process involves the transition from a high-temperature disordered phase to an ordered (blue) phase and is generally slow (takes hours) with limited achievable lattice structures, and efforts to improve molecular alignment through post-crystallization field application typically prove ineffective. Here we report a systematic study on the molecular self-assembly dynamics of BPLC starting from a highly ordered phase in which all molecules are unidirectionally aligned by a strong electric field. We have discovered that, near the high-temperature end of the blue phase, if the applied field strength is then switched to an intermediate level or simply turned off, large-area monocrystalline BPLCs of various symmetries (tetragonal, orthorhombic, cubic) can be formed in minutes. Subsequent temperature tuning of the single crystal at a fixed applied field allows access to different lattice parameters and the formation of never-before-seen monoclinic structures. The formed crystals remain stable upon field removal. The diversity of stable monocrystalline BPLCs with widely tunable crystalline symmetries, band structures, and optical dispersions will significantly improve and expand their application potentials.

DNA-Based Replication of Programmable Colloidal Assemblies

Nature uses replication to amplify the information necessary for the intricate structures vital for life. Despite some successes with pure nucleotide structures, constructing synthetic microscale systems capable of replication remains largely out of reach. Here, a functioning strategy is shown for the replication of microscale particle assemblies using DNA-coated colloids. By positioning DNA-functionalized colloids using capillary forces and embedding them into a polymer layer, programmable sequences of patchy particles are created that act as a primer and offer precise binding of complementary particles from suspension. The strings of complementary colloids are cross-linked, released from the primer, and purified via flow cytometric sorting to achieve a purity of up to 81% of the replicated sequences. The replication of strings of up to five colloids and non-linear shapes is demonstrated with particles of different sizes and materials. Furthermore, a pathway for exponential self-replication is outlined, including preliminary data that shows the transfer of patches and binding of a second-generation of assemblies from suspension.

Monodispersed Renewable Particles by Cascade and Density Gradient Size Fractionation to Advance Lignin Nanotechnologies

Control over particle size and shape heterogeneity is highly relevant to the design of photonic coatings and supracolloidal assemblies. Most developments in the area have relied on mineral and petroleum-derived polymers that achieve well-defined chemical and dimensional characteristics. Unfortunately, it is challenging to attain such control when considering renewable nanoparticles. Herein, a pathway toward selectable biobased particle size and physicochemical profiles is proposed. Specifically, lignin is fractionated, a widely available heterogeneous polymer that can be dissolved in aqueous solution, to obtain a variety of monodispersed particle fractions. A two-stage cascade and density gradient centrifugation that relieves the need for solvent pre-extraction or other pretreatments but achieves particle bins of uniform size (~60 to 860 nm and polydispersity, PDI<0.06, dynamic light scattering) along with characteristic surface chemical features is introduced. It is found that the properties and associated colloidal behavior of the particles are suitably classified in distinctive size populations, namely, i) nanoscale (50-100 nm), ii) photonic (100-300 nm) and iii) near-micron (300-1000 nm). The strong correlation that exists between size and physicochemical characteristics (molar mass, surface charge, bonding and functional groups, among others) is introduced as a powerful pathway to identify nanotechnological uses that benefit from the functionality and cost-effectiveness of biogenic particles.

Symmetry-Guided Inverse Design of Self-Assembling Multiscale DNA Origami Tilings

Recent advances enable the creation of nanoscale building blocks with complex geometries and interaction specificities for self-assembly. This nearly boundless design space necessitates design principles for defining the mutual interactions between multiple particle species to target a user-specified complex structure or pattern. In this article, we develop a symmetry-based method to generate the interaction matrices that specify the assembly of two-dimensional tilings, which we illustrate using equilateral triangles. By exploiting the allowed 2D symmetries, we develop an algorithmic approach by which any periodic 2D tiling can be generated from an arbitrarily large number of subunit species, notably addressing an unmet challenge of engineering 2D crystals with periodicities that can be arbitrarily larger than the subunit size. To demonstrate the utility of our design approach, we encode specific interactions between triangular subunits synthesized by DNA origami and show that we can guide their self-assembly into tilings with a wide variety of symmetries, using up to 12 unique species of triangles. By conjugating specific triangles with gold nanoparticles, we fabricate gold-nanoparticle supracrystals whose lattice parameter spans up to 300 nm. Finally, to generate economical design rules, we compare the design economy of various tilings. In particular, we show that (1) higher symmetries allow assembly of larger unit cells with fewer subunits and (2) linear supracrystals can be designed more economically using linear primitive unit cells. This work provides a simple algorithmic approach to designing periodic assemblies, aiding in the multiscale assembly of supracrystals of nanostructured "meta-atoms" with engineered plasmonic functions.

DNA-mediated assembly of Au bipyramids into anisotropic light emitting kagome superlattices

Colloidal crystal engineering with DNA allows one to design diverse superlattices with tunable lattice symmetry, composition, and spacing. Most of these structures follow the complementary contact model, maximizing DNA hybridization on building blocks and producing relatively close-packed lattices. Here, low-symmetry kagome superlattices are assembled from DNA-modified gold bipyramids that can engage only in partial DNA surface matching. The bipyramid dimensions and DNA length can be engineered for two different superlattices with rhombohedral unit cells, including one composed of a periodic stacking of kagome lattices. Enabled by the partial facet alignment, the kagome lattices exhibit lattice distortion, bipyramid twisting, and planar chirality. When conjugated with Cy-5 dyes, the kagome lattices serve as cavities with high-density optical states and large Purcell factors along lateral directions, leading to strong dipole radiation along the z axis and facet-dependent light emission. Such complex optical properties make these materials attractive for lasers, displays, and quantum sensing constructs.

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.

Inverse design of crystals and quasicrystals in a non-additive binary mixture of hard disks

The development of new materials typically involves a process of trial and error, guided by insights from past experimental and theoretical findings. The inverse design approach for soft-matter systems has the potential to optimize specific physical parameters, such as particle interactions, particle shape, or composition and packing fraction. This optimization aims to facilitate the spontaneous formation of specific target structures through self-assembly. In this study, we expand upon a recently introduced inverse design protocol for monodisperse systems to identify the required conditions and interactions for assembling crystal and quasicrystal phases within a binary mixture of two distinct species. This method utilizes an evolution algorithm to identify the optimal state point and interaction parameters, enabling the self-assembly of the desired structure. In addition, we employ a convolutional neural network (CNN) that classifies different phases based on their diffraction patterns, serving as a fitness function for the desired structure. Using our protocol, we successfully inverse design two-dimensional crystalline structures, including a hexagonal lattice and a dodecagonal quasicrystal, within a non-additive binary mixture of hard disks. Finally, we introduce a symmetry-based order parameter that leverages the encoded symmetry within the diffraction pattern. This order parameter circumvents the need for training a CNN and is used as a fitness function to inverse design an octagonal quasicrystal.

Universal Click-Chemistry Approach for the DNA Functionalization of Nanoparticles

Nanotechnology has revolutionized the fabrication of hybrid species with tailored functionalities. A milestone in this field is the deoxyribonucleic acid (DNA) conjugation of nanoparticles, introduced almost 30 years ago, which typically exploits the affinity between thiol groups and metallic surfaces. Over the last decades, developments in colloidal research have enabled the synthesis of an assortment of nonmetallic structures, such as high-index dielectric nanoparticles, with unique properties not previously accessible with traditional metallic nanoparticles. However, to stabilize, integrate, and provide further functionality to nonmetallic nanoparticles, reliable techniques for their functionalization with DNA will be crucial. Here, we combine well-established dibenzylcyclooctyne-azide click-chemistry with a simple freeze-thaw method to achieve the functionalization of silica and silicon nanoparticles, which form exceptionally stable colloids with a high DNA surface density of ∼0.2 molecules/nm2. Furthermore, we demonstrate that these functionalized colloids can be self-assembled into high-index dielectric dimers with a yield of over 50% via the use of DNA origami. Finally, we extend this method to functionalize other important nanomaterials, including oxides, polymers, core-shell, and metal nanostructures. Our results indicate that the method presented herein serves as a crucial complement to conventional thiol functionalization chemistry and thus greatly expands the toolbox of DNA-functionalized nanoparticles currently available.

Interplay between the Formation of Colloidal Clathrate and Cubic Diamond Crystals

Controlling the valency of directional interactions of patchy particles is insufficient for the selective formation of target crystalline structures due to the competition between phases of similar free energy. Examples of such are stacking hybrids of interwoven hexagonal and cubic diamonds with (i) its liquid phase, (ii) arrested glasses, or (iii) clathrates, all depending on the relative patch size, despite being within the one-bond-per-patch regime. Herein, using molecular dynamics simulations, we demonstrate that although tetrahedral patchy particles with narrow patches can assemble into clathrates or stacking hybrids in the bulk, this behavior can be suppressed by the application of external surface potential. Depending on its strength, the selective growth of either cubic diamond crystals or empty sII clathrate cages can be achieved. The formation of a given ordered network depends on the structure of the first adlayer, which is commensurate with the emerging network.

Spearheading a new era in complex colloid synthesis with TPM and other silanes

Colloid science has recently grown substantially owing to the innovative use of silane coupling agents (SCAs), especially 3-trimethoxysilylpropyl methacrylate (TPM). SCAs were previously used mainly as modifying agents, but their ability to form droplets and condense onto pre-existing structures has enabled their use as a versatile and powerful tool to create novel anisotropic colloids with increasing complexity. In this Review, we highlight the advances in complex colloid synthesis facilitated by the use of TPM and show how this has driven remarkable new applications. The focus is on TPM as the current state-of-the-art in colloid science, but we also discuss other silanes and their potential to make an impact. We outline the remarkable properties of TPM colloids and their synthesis strategies, and discuss areas of soft matter science that have benefited from TPM and other SCAs.

Work hardening in colloidal crystals

Colloidal crystals exhibit interesting properties1-4 that are in many ways analogous to their atomic counterparts. They have the same crystal structures2,5-7, undergo the same phase transitions8-10, and possess the same crystallographic defects11-14. In contrast to these structural properties, the mechanical properties of colloidal crystals are quite different from those of atomic systems. For example, unlike in atomic systems, the elasticity of hard-sphere colloidal crystals is purely entropic15; as a result, they are so soft that they can be melted just by stirring16,17. Moreover, crystalline materials deform plastically when subjected to increasing shear and become stronger because of the ubiquitous process of work hardening18; but this has so far never been observed in colloidal crystals, to our knowledge. Here we show that hard-sphere colloidal crystals exhibit work hardening. Moreover, despite their softness, the shear strength of colloidal crystals can increase and approach the theoretical limit for crystals, a value reached in very few other materials so far. We use confocal microscopy to show that the strength of colloidal crystals increases with dislocation density, and ultimately reaches the classic Taylor scaling behaviour for atomic materials19-21, although hard-sphere interactions lack the complexity of atomic interactions. We demonstrate that Taylor hardening arises through the formation of dislocation junctions22. The Taylor hardening regime, however, is established only after a transient phase, and it ceases when the colloidal crystals become so hard that the strain is localized within a thin boundary layer in which slip results from an unconventional motion of dislocations. The striking resemblance between colloidal and atomic crystals, despite the many orders of magnitude difference in particle size and shear modulus, demonstrates the universality of work hardening.

Spontaneous Particle Ordering, Sorting, and Assembly on Soap Films

Soap bubbles exhibit abundant fascinating phenomena throughout the entire life of evolution with different fundamental physics governing them. Nevertheless, the complicated dynamics of small objects in soap films are still unrevealed. Here, we report the first observation of spontaneous particle ordering in a complicated galaxy of soap films without any external energy. The balance of interfacial tension at two liquid-gas interfaces is theoretically predicted to govern belted wetted particles (BWPs) traveling along a specified path spontaneously. Such spontaneous particle path-finding is found to depend on the particle size and hydrophilic properties. Spontaneous particle sorting is directly realized via these discrete and distinctive paths for different particles. The deformation of the soap membrane facilitates 1D/2D particle organization along the path. This observation represents the discovery of a new spontaneous order phenomenon in soap film systems and provides a new energy-free approach for particle separation and soft colloidal crystal assembly.

A Conceptual Framework to Understand the Self-Assembly of Chemically Active Colloids

Colloids that generate chemicals, or "chemically active colloids", can interact with their neighbors and generate patterns via forces arising from such chemical gradients. Examples of such assemblies of chemically active colloids are abundant in the literature, but a unified theoretical framework is needed to rationalize the scattered results. Combining experiments, theory, Brownian dynamics, and finite element simulations, we present here a conceptual framework for understanding how immotile, yet chemically active, colloids assemble. This framework is based on the principle of ionic diffusiophoresis and diffusioosmosis and predicts that a chemically active colloid interacts with its neighbors through short- and long-range interactions that can be either repulsive or attractive, depending on the relative diffusivity of the released cations and anions, and the relative zeta potential of a colloidal particle and the planar surface on which it resides. As a result, 4 types of pairwise interactions arise, leading to 4 different types of colloidal assemblies with distinct patterns. Using short-range attraction and long-range attraction (SALR) systems as an example, we show quantitative agreement between the framework and experiments. The framework is then applied to rationalize a wide range of patterns assembled from chemically active colloids in the literature exhibiting other types of pairwise interactions. In addition, the framework can predict what the assembly looks like with minimal experimental information and help infer ionic diffusivity and zeta potential values in systems where these values are inaccessible. Our results represent a solid step toward building a complete theory for understanding and controlling chemically active colloids, from the molecular level to their mesoscopic superstructures and ultimately to the macroscopic properties of the assembled materials.

Inverse design of a pyrochlore lattice of DNA origami through model-driven experiments

Sophisticated statistical mechanics approaches and human intuition have demonstrated the possibility of self-assembling complex lattices or finite-size constructs. However, attempts so far have mostly only been successful in silico and often fail in experiment because of unpredicted traps associated with kinetic slowing down (gelation, glass transition) and competing ordered structures. Theoretical predictions also face the difficulty of encoding the desired interparticle interaction potential with the experimentally available nano- and micrometer-sized particles. To overcome these issues, we combine SAT assembly (a patchy-particle interaction design algorithm based on constrained optimization) with coarse-grained simulations of DNA nanotechnology to experimentally realize trap-free self-assembly pathways. We use this approach to assemble a pyrochlore three-dimensional lattice, coveted for its promise in the construction of optical metamaterials, and characterize it with small-angle x-ray scattering and scanning electron microscopy visualization.

Diamond-lattice photonic crystals assembled from DNA origami

Colloidal self-assembly allows rational design of structures on the micrometer and submicrometer scale. One architecture that can generate complete three-dimensional photonic bandgaps is the diamond cubic lattice, which has remained difficult to realize at length scales comparable with the wavelength of visible or ultraviolet light. In this work, we demonstrate three-dimensional photonic crystals self-assembled from DNA origami that act as precisely programmable patchy colloids. Our DNA-based nanoscale tetrapods crystallize into a rod-connected diamond cubic lattice with a periodicity of 170 nanometers. This structure serves as a scaffold for atomic-layer deposition of high-refractive index materials such as titanium dioxide, yielding a tunable photonic bandgap in the near-ultraviolet.

Engineering colloidal crystals molecule by molecule

DNA particles are programmed to assemble with precision into complex lattices.

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.

Construction of the single-diamond-structured titania scaffold-Recreation of the holy grail photonic structure

As one of the most stunning biological nanostructures, the single-diamond (SD) surface discovered in beetles and weevils exoskeletons possesses the widest complete photonic bandgap known to date and is renowned as the "holy grail" of photonic materials. However, the synthesis of SD is difficult due to its thermodynamical instability compared to the energetically favoured bicontinuous double diamond and other easily formed lattices; thus, the artificial fabrication of SD has long been a formidable challenge. Herein, we report a bottom-up approach to fabricate SD titania networks via a one-pot cooperative assembly scenario employing the diblock copolymer poly(ethylene oxide)-block-polystyrene as a soft template and titanium diisopropoxide bis(acetylacetonate) as an inorganic precursor in a mixed solvent, in which the SD scaffold was obtained by kinetically controlled nucleation and growth in the skeletal channels of the diamond minimal surface formed by the polymer matrix. Electron crystallography investigations revealed the formation of tetrahedrally connected SD frameworks with the space group Fd [Formula: see text] m in a polycrystalline anatase form. A photonic bandgap calculation showed that the resulting SD structure has a wide and complete bandgap. This work solves the complex synthetic enigmas and offers a frontier in hyperbolic surfaces, biorelevant materials, next-generation optical devices, etc.

Uniform, convex structuring of polymeric colloids via site-selected swelling

Non-spherical, polymeric colloids serve as building blocks for advanced functional materials. We propose a novel method to produce morphologically controlled, non-spherical particles by generating site-selected, convex structures on polystyrene (PS) particles. It consists of two simple procedures: a monolayer of PS particles is illuminated with UV light and is subsequently immersed in a fluorinated solvent (HFIP). UV irradiation generates site-selected, oxidized domains on PS particles with a different solvent affinity than unoxidized PS, and HFIP immersion preferentially swells the oxidized domains. Such swelling gives rise to site-selected, convex structures on PS particles. By adjusting UV irradiation conditions, including incident and azimuth angles, the oxidized sites, i.e., the swelled portions, can be accurately situated, allowing us to produce various convex shapes, including chiral shapes at desired positions on PS particles.

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.

Fluorescence-activated cell sorting (FACS) for purifying colloidal clusters

Colloidal particles are considered to be essential building blocks for creating innovative self-assembled and active materials, for which complexity beyond that of compositionally uniform particles is key. However, synthesizing complex, multi-material colloids remains a challenge, often resulting in heterogeneous populations that require post-synthesis purification. Leveraging advances brought forward in the purification of biological samples, here we apply fluorescence-activated cell sorting (FACS) to sort colloidal clusters synthesized through capillary assembly. Our results demonstrate the effectiveness of FACS in sorting clusters based on size, shape, and composition. Notably, we achieve a sorting purity of up to 97% for clusters composed of up to 9 particles, albeit observing a decline in purity with increasing cluster size. Additionally, dimers of different colloids can be purified to over 97%, while linear and triangular trimers can be separated with up to 88% purity. This work underscores the potential of FACS as a promising and little-used tool in colloidal science to support the development of increasingly more intricate particle-based building blocks.

Surface Engineering and Programmed Self-Assembly of Silica Nanoparticles with Controllable Polystyrene/Poly(4-vinybenzyl azide) Patches

The programmed self-assembly of patchy nanoparticles (NPs) through a bottom-up approach is an efficient strategy for producing highly organized materials with a predetermined architecture. Herein, we report the preparation of di- and trivalent silica NPs with polystyrene (PS)/poly(4-vinylbenzyl azide) (PVBA) patches and assemble them in a THF mixture by lowering the solvent quality. Silica-PS/PVBA colloidal hybrid clusters were synthesized through the seeded growth emulsion copolymerization of styrene and 4-vinylbenzyl azide (VBA) in varying ratios. Subsequently, macromolecules on silica NPs originating from the copolymerization of growing PS or PVBA chains with the surface-grafted MMS compatibilizer are engineered by fine-tuning of polymer compositions or adjustment of solvent qualities. Moreover, multistage silica regrowth of tripod and tetrapod allowed a fine control of the patch-to-particle size ratio ranging from 0.69 to 1.54. Intriguingly, patchy silica NPs (1-, 2-, 3-PSNs) rather than hybrid clusters are successfully used as templates for multistep regrowth experiments, leading to the formation of silica NPs with a new morphology and size controllable PVBA/PS patches. Last but not least, combined with mesoscale dynamics simulations, the self-assembly kinetics of 2-PSN and 3-PSN into linear colloidal polymers and honeycomb-like lattices are studied. This work paves a new avenue for constructing colloidal polymers with a well-defined sequence and colloidal crystals with a predetermined architecture.

Direct observation of phase transitions in truncated tetrahedral microparticles under quasi-2D confinement

Colloidal crystals are used to understand fundamentals of atomic rearrangements in condensed matter and build complex metamaterials with unique functionalities. Simulations predict a multitude of self-assembled crystal structures from anisotropic colloids, but these shapes have been challenging to fabricate. Here, we use two-photon lithography to fabricate Archimedean truncated tetrahedrons and self-assemble them under quasi-2D confinement. These particles self-assemble into a hexagonal phase under an in-plane gravitational potential. Under additional gravitational potential, the hexagonal phase transitions into a quasi-diamond two-unit basis. In-situ imaging reveal this phase transition is initiated by an out-of-plane rotation of a particle at a crystalline defect and causes a chain reaction of neighboring particle rotations. Our results provide a framework of studying different structures from hard-particle self-assembly and demonstrates the ability to use confinement to induce unusual phases.

Transformable Superisostatic Crystals Self-Assembled from Segment Colloidal Rods

Transformable mechanical structures can switch between distinct mechanical states. Whether this kind of structure can be self-assembled from simple building blocks at microscale is a question to be answered. In this work, we propose a self-assembly strategy for these structures based on a nematic monolayer of segmented colloidal rods with lateral cutting. By using Monte Carlo simulation, we find that rods with different cutting degrees can self-assemble into different crystals characterized by bond coordination z that varies from 3 to 6. Among these, we identify a transformable superisostatic structure with pgg symmetry and redundant bonds (z = 5). We show that this structure can support either soft bulk modes or soft edge modes depending on its Poisson's ratio, which can be tuned from positive to negative through a uniform soft deformation. We also prove that the bulk soft modes are associated with states of self-stress along the direction of zero strain during uniform soft deformation. The self-assembled transformable structures may act as mechanical metamaterials with potential applications in micromechanical engineering.

Anoplophora graafi longhorn beetle coloration is due to disordered diamond-like packed spheres

While artificial photonic materials are typically highly ordered, photonic structures in many species of birds and insects do not possess a long-range order. Studying their order-disorder interplay sheds light on the origin of the photonic band gap. Here, we investigated the scale morphology of the Anoplophora graafi longhorn beetle. Combining small-angle X-ray scattering and slice-and-view FIB-SEM tomography with molecular dynamics and optical simulations, we characterised the chitin sphere assemblies within blue and green A. graafi scales. The low volume fraction of spheres and the number of their nearest neighbours are incompatible with any known close-packed sphere morphology. A short-range diamond lattice with long-range disorder best describes the sphere assembly, which will inspire the development of new colloid-based photonic materials.

Van der Waals Colloidal Crystals

A general guiding principle for colloidal crystallization is to tame the attractive enthalpy such that it slightly overwhelms the repulsive interaction. As-synthesized colloids are generally designed to retain a strong repulsive potential for the high stability of suspensions, encoding appropriate attractive potentials into colloids has been key to their crystallization. Despite the myriad of interparticle attractions for colloidal crystallization, the van der Waals (vdW) force remains unexplored. Here, it is shown that the implementation of gold cores into silica colloids and the resulting vdW force can reconfigure the pair potential well depth to the optimal range between -1 and -4 kB T at tens of nanometer-scale colloidal distances. As such, colloidal crystals with a distinct liquid gap can be formed, which is evidenced by photonic bandgap-based diffractive colorization.

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.

Colloidal Self-Assembly: From Passive to Active Systems

Self-assembly fundamentally implies the organization of small sub-units into large structures or patterns without the intervention of specific local interactions. This process is commonly observed in nature, occurring at various scales ranging from atomic/molecular assembly to the formation of complex biological structures. Colloidal particles may serve as micrometer-scale surrogates for studying assembly, particularly for the poorly understood kinetic and dynamic processes at the atomic scale. Recent advances in colloidal self-assembly have enabled the programmable creation of novel materials with tailored properties. We here provide an overview and comparison of both passive and active colloidal self-assembly, with a discussion on the energy landscape and interactions governing both types. In the realm of passive colloidal assembly, many impressive and important structures have been realized, including colloidal molecules, one-dimensional chains, two-dimensional lattices, and three-dimensional crystals. In contrast, active colloidal self-assembly, driven by optical, electric, chemical, or other fields, involves more intricate dynamic processes, offering more flexibility and potential new applications. A comparative analysis underscores the critical distinctions between passive and active colloidal assemblies, highlighting the unique collective behaviors emerging in active systems. These behaviors encompass collective motion, motility-induced phase segregation, and exotic properties arising from out-of-equilibrium thermodynamics. Through this comparison, we aim to identify the future opportunities in active assembly research, which may suggest new application domains.

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.

Networks of Limited-Valency Patchy Particles

Equilibrium gels provide physically attractive counterparts of nonequilibrium gels, allowing statistical understanding and design of the equilibrium gel structure. Here, we assemble two-dimensional equilibrium gels from limited-valency "patchy" colloidal particles and follow their evolution at the particle scale to elucidate cluster-size distributions and free energies. By finely adjusting the patch attraction with critical Casimir forces, we let a mixture of two-valent and pseudo-three-valent patchy particles approach the percolated network state through a set of equilibrium states. Comparing this equilibrium route with a deep quench, we find that both routes approach the percolated state via the same equilibrium states, revealing that the network topology is uniquely set by the particle bond angles, independent of the formation history. The limited-valency system follows percolation theory remarkably well, approaching the percolation point with the expected universal exponents.

Formation of two-dimensional diamond-like colloidal crystals using layer-by-layer electrostatic self-assembly

We report here that a two-dimensional (2D) diamond-like structure of micron-sized colloidal particles can be obtained by layer-by-layer self-assembly. Positively and negatively charged silica particles, 1 μm in diameter, were used in the experiments. On a positively charged, flat glass substrate, the first layer of negatively charged particles was prepared to form a non-close-packed 2D crystal. Then the second and third layers were fabricated using electrostatic adsorption. The positions of adsorbed particles were controllable by tuning the zeta-potential of the particles and the salt concentration of the medium. The FDTD calculations show that the 2D diamond structures of particles with higher refractive index (titania) have an absorption band in the wavelength range corresponding to the photonic band gap of the 3D bulk crystal. We expect these findings to be useful for the fabrication of novel photonic materials.

Engineering Azeotropy to Optimize the Self-Assembly of Colloidal Mixtures

The goal of inverse self-assembly is to design interparticle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new component increasing the thermodynamic degrees of freedom and, hence, the complexity of the self-assembly pathway. In this work we explore the possibility to use azeotropy, i.e., a special thermodynamic condition where the system behaves effectively as a one-component system, as a way to control the self-assembly of an arbitrary number of components. Exploiting the mass-balance equations, we show how to select patchy particle systems that exhibit azeotropic points along the desired self-assembly pathway. As an example we map the phase diagram of a binary mixture that, by design, fully assembles into cubic (and only cubic) diamond crystal via an azeotropic point. The ability to explicitly include azeotropic points in artificial designs reveals effective pathways for the self-assembly of complex structures.

A colloidal viewpoint on the sausage catastrophe and the finite sphere packing problem

It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the densest packing. Here, our combined experimental and simulation study provides a physical realization of the finite sphere packing problem by studying arrangements of colloids in a flaccid lipid vesicle. We map out a state diagram displaying linear, planar, and cluster conformations of spheres, as well as bistable states which alternate between cluster-plate and plate-linear conformations due to membrane fluctuations. Finally, by systematically analyzing truncated polyhedral packings, we identify clusters of 56 ≤ N ≤ 70 number of spheres, excluding N = 57 and 63, that pack more efficiently than linear arrangements.

A simple method to alter the binding specificity of DNA-coated colloids that crystallize

DNA-coated colloids can crystallize into a multitude of lattices, ranging from face-centered cubic to diamond, opening avenues to producing structures with useful photonic properties. The potential design space of DNA-coated colloids is large, but its exploration is hampered by a reliance on chemically modified DNA that is slow and expensive to commercially synthesize. Here we introduce a method to controllably tailor the sequences of DNA-coated particles by covalently appending new sequence domains onto the DNA grafted to colloidal particles. The tailored particles crystallize as readily and at the same temperature as those produced via direct chemical synthesis, making them suitable for self-assembly. Moreover, we show that particles coated with a single sequence can be converted into a variety of building blocks with differing specificities by appending different DNA sequences to them. This method will make it practical to identify optimal and complex particle sequence designs and paves the way to programming the assembly kinetics of DNA-coated colloids.

Dynamic surface chemistry and interparticle interactions mediating chemically fueled dissipative assembly of colloids

HYPOTHESIS

Dissipative assembly of colloids involves using a chemical fuel to temporarily activate organic colloid surface ligands to an assembly prone state. Colloids assemble into transient aggregates that disintegrate after the fuel is consumed. The underlying colloidal interactions controlling dissipative assembly have not been rigorously identified or quantified. We expect that fuel concentration dependent dissipative assembly behavior can be reconciled with measurements of dynamic colloid surface chemistry and colloidal interactions.

EXPERIMENTS

Carbodiimide chemistry was utilized to induce dissipative assembly of carboxylic acid functionalized polystyrene colloids. We measured aggregation kinetics, colloid surface hydrophobicity, and zeta potential as a function of time, which established that colloids underwent dissipative assembly for fuel concentrations between 5 and 12.5 mM and irreversible aggregation at higher fuel concentrations due to transient changes in surface chemistry.

FINDINGS

We formulated a pairwise colloidal interaction potential model including hydrophobic interactions quantified by fluorescence binding experiments. Fuel concentrations causing dissipative assembly displayed a transient increase in secondary minimum depth and a primary maximum much larger than the thermal potential. Fuel concentrations leading to irreversible aggregation displayed a primary maximum smaller than the thermal potential. This is the first study to quantify surface chemistry and interparticle interactions during dissipative colloid assembly and represents a foundational step in rationally designing more complex dissipative assembly systems.

Self-Assembling of Nonadditive Mixtures Containing Patchy Particles with Tunable Interactions

Mixtures of nanoparticles (NPs) with hybridizing grafted DNA or DNA-like strands have been of particular interest because of the tunable selectivity provided for the interactions between the NP components. A richer self-assembly behavior would be accessible if these NP-NP interactions could be designed to give nonadditive mixing (in analogy to the case of molecular components). Nonadditive mixing occurs when the mixed-state volume is smaller (negative) or larger (positive) than the sum of the individual components' volumes. However, instances of nonadditivity in colloidal/NP mixtures are rare, and systematic studies of such mixtures are nonexistent. This work focuses on patchy NPs whose patches (coarsely representing grafted hybridizing DNA strands) not only encode selectivity across components but also impart a tunable nonadditivity by varying their extent of protrusion. To guide the exploration of the relationship between phase behavior and nonadditivity for different patches' designs, the NP-NP potential of mean force (PMF) and a nonadditive parameter were first calculated. For one-patch NPs, different lamellar morphologies were predominantly observed. In contrast, for mixtures of two-patch NPs and (fully grafted) spherical particles, a rich phase behavior was found depending on patch-patch angle and degree of nonadditivity, resulting in phases such as the gyroid, cylinder, honeycomb, and two-layered crystal. Our results also show that both minimum positive nonadditivity and multivalent interactions are necessary for the formation of ordered network mesophases in the class of models studied.

Synthesis of dimpled polymer particles and polymer particles with protrusions - Past, present, and future

Since the development of emulsion polymerization techniques, polymer particles have become the epitome of standard colloids due to the exceptional control over size, size distribution, and composition the synthesis methods allow reaching. The exploration of different variations of the synthesis methods has led to the discovery of more advanced techniques, enabling control over their composition and shape. Many early investigations focused on forming particles with protrusions (with one protrusion, called dumbbell particles) and particles with concavities, also called dimpled particles. This paper reviews the literature covering the synthesis, functionalization, and applications of both types of particles. The focus has been on the rationalization of the various approaches used to prepare such particles and on the discussion of the mechanisms of formation not just from the experimental viewpoint but also from the standpoint of thermodynamics. The primary motivation to combine in a single review the preparation of both types of particles has been the observation of similarities among some of the methods developed to prepare dimpled particles, which sometimes include the formation of particles with protrusions and vice versa. The most common applications of these particles have been discussed as well. By looking at the different approaches developed in the literature under one general perspective, we hope to stimulate a more ample use of these particles and promote the development of even more effective synthetic protocols.

Heterostructure particles enable omnidispersible in water and oil towards organic dye recycle

Dispersion of colloidal particles in water or oil is extensively desired for industrial and environmental applications. However, it often strongly depends on indispensable assistance of chemical surfactants or introduction of nanoprotrusions onto the particle surface. Here we demonstrate the omnidispersity of hydrophilic-hydrophobic heterostructure particles (HL-HBPs), synthesized by a surface heterogeneous nanostructuring strategy. Photo-induced force microscopy (PiFM) and adhesion force images both indicate the heterogeneous distribution of hydrophilic domains and hydrophobic domains on the particle surface. These alternating domains allow HL-HBPs to be dispersed in various solvents with different polarity and boiling point. The HL-HBPs can efficiently adsorb organic dyes from water and release them into organic solvents within several seconds. The surface heterogeneous nanostructuring strategy provides an unconventional approach to achieve omnidispersion of colloidal particles beyond surface modification, and the omnidispersible HL-HBPs demonstrate superior capability for dye recycle merely by solvent exchange. These omnidispersible HL-HBPs show great potentials in industrial process and environmental protection.

Controlled Self-Assembly of Gold Nanotetrahedra into Quasicrystals and Complex Periodic Supracrystals

The self-assembly of shape-anisotropic nanocrystals into large-scale structures is a versatile and scalable approach to creating multifunctional materials. The tetrahedral geometry is ubiquitous in natural and manmade materials, yet regular tetrahedra present a formidable challenge in understanding their self-assembly behavior as they do not tile space. Here, we report diverse supracrystals from gold nanotetrahedra including the quasicrystal (QC) and the dimer packing predicted more than a decade ago and hitherto unknown phases. We solve the complex three-dimensional (3D) structure of the QC by a combination of electron microscopy, tomography, and synchrotron X-ray scattering. Nanotetrahedron vertex sharpness, surface ligands, and assembly conditions work in concert to regulate supracrystal structure. We also discover that the surface curvature of supracrystals can induce structural changes of the QC tiling and eventually, for small supracrystals with high curvature, stabilize a hexagonal approximant. Our findings bridge the gap between computational design and experimental realization of soft matter assemblies and demonstrate the importance of accurate control over nanocrystal attributes and the assembly conditions to realize increasingly complex nanopolyhedron supracrystals.

DNA-mediated regioselective encoding of colloids for programmable self-assembly

How far we can push chemical self-assembly is one of the most important scientific questions of the century. Colloidal self-assembly is a bottom-up technique for the rational design of functional materials with desirable collective properties. Due to the programmability of DNA base pairing, surface modification of colloidal particles with DNA has become fundamental for programmable material self-assembly. However, there remains an ever-lasting demand for surface regioselective encoding to realize assemblies that require specific, directional, and orthogonal interactions. Recent advances in surface chemistry have enabled regioselective control over the formation of DNA bonds on the particle surface. In particular, the structural DNA nanotechnology provides a simple yet powerful design strategy with unique regioselective addressability, bringing the complexity of colloidal self-assembly to an unprecedented level. In this review, we summarize the state-of-art advances in DNA-mediated regioselective surface encoding of colloids, with a focus on how the regioselective encoding is introduced and how the regioselective DNA recognition plays a crucial role in the self-assembly of colloidal structures. This review highlights the advantages of DNA-based regioselective modification in improving the complexity of colloidal assembly, and outlines the challenges and opportunities for the construction of more complex architectures with tailored functionalities.

Macroscopic photonic single crystals via seeded growth of DNA-coated colloids

Photonic crystals-a class of materials whose optical properties derive from their structure in addition to their composition-can be created by self-assembling particles whose sizes are comparable to the wavelengths of visible light. Proof-of-principle studies have shown that DNA can be used to guide the self-assembly of micrometer-sized colloidal particles into fully programmable crystal structures with photonic properties in the visible spectrum. However, the extremely temperature-sensitive kinetics of micrometer-sized DNA-functionalized particles has frustrated attempts to grow large, monodisperse crystals that are required for photonic metamaterial applications. Here we describe a robust two-step protocol for self-assembling single-domain crystals that contain millions of optical-scale DNA-functionalized particles: Monodisperse crystals are initially assembled in monodisperse droplets made by microfluidics, after which they are grown to macroscopic dimensions via seeded diffusion-limited growth. We demonstrate the generality of our approach by assembling different macroscopic single-domain photonic crystals with metamaterial properties, like structural coloration, that depend on the underlying crystal structure. By circumventing the fundamental kinetic traps intrinsic to crystallization of optical-scale DNA-coated colloids, we eliminate a key barrier to engineering photonic devices from DNA-programmed materials.

Biomimetic thermoresponsive superstructures by colloidal soft-and-hard co-assembly

Soft-and-hard hybrid structures are ubiquitous in biological systems and have inspired the design of man-made mechanical devices, actuators, and robots. The realization of these structures, however, has been challenging at microscale, where material integration and actuation become exceedingly less practical. Here, through simple colloidal assembly, we create microscale superstructures consisting of soft and hard materials, which, serving as microactuators, have thermoresponsive shape-transforming properties. In this case, anisotropic metal-organic framework (MOF) particles as the hard components are integrated with liquid droplets, forming spine-mimicking colloidal chains via valence-limited assembly. The chains, with alternating soft and hard segments, are referred to as MicroSpine and can reversibly change shape, switching between straight and curved states through a thermoresponsive swelling/deswelling mechanism. By solidification of the liquid parts within a chain with prescribed patterns, we design various chain morphologies, such as "colloidal arms," with controlled actuating behaviors. The chains are further used to build colloidal capsules, which encapsulate and release guests by the temperature-programmed actuation.

Pursuing colloidal diamonds

The endeavor to selectively fabricate a cubic diamond is challenging due to the formation of competing phases such as its hexagonal polymorph or others possessing similar free energy. The necessity to achieve this is of paramount importance since the cubic diamond is the only polymorph exhibiting a complete photonic bandgap, making it a promising candidate in view of photonic applications. Herein, we demonstrate that due to the presence of an external field and delicate manipulation of its strength we can attain selectivity in the formation of a cubic diamond in a one-component system comprised of designer tetrahedral patchy particles. The driving force of such a phenomenon is the structure of the first adlayer which is commensurate with the (110) face of the cubic diamond. Moreover, after a successful nucleation event, once the external field is turned off, the structure remains stable, paving an avenue for further post-synthetic treatment.

Flexible Colloidal Molecules with Directional Bonds and Controlled Flexibility

Colloidal molecules are ideal model systems for mimicking real molecules and can serve as versatile building blocks for the bottom-up self-assembly of flexible and smart materials. While most colloidal molecules are rigid objects, the development of colloidal joints has made it possible to endow them with conformational flexibility. However, their unrestricted range of motion does not capture the limited movement and bond directionality that is instead typical of real molecules. In this work, we create flexible colloidal molecules with an in situ controllable motion range and bond directionality by assembling spherical particles onto cubes functionalized with complementary surface-mobile DNA. By varying the sphere-to-cube size ratio, we obtain colloidal molecules with different coordination numbers and find that they feature a constrained range of motion above a critical size ratio. Using theory and simulations, we show that the particle shape together with the multivalent bonds creates an effective free-energy landscape for the motion of the sphere on the surface of the cube. We quantify the confinement of the spheres on the surface of the cube and the probability to change facet. We find that temperature can be used as an extra control parameter to switch in situ between full and constrained flexibility. These flexible colloidal molecules with a temperature switching motion range can be used to investigate the effect of directional yet flexible bonds in determining their self-assembly and phase behavior, and may be employed as constructional units in microrobotics and smart materials.

Synthetic strategies for nonporous organosilica nanoparticles from organosilanes

Organosilica nanoparticles refer to silica nanoparticles containing carbon along with organic or functional groups and can be divided into mesoporous organosilica nanoparticles and nonporous organosilica nanoparticles. During the past few decades, considerable efforts have been devoted to the development of organosilica nanoparticles directly from organosilanes. However, most of the reports have focused on mesoporous organosilica nanoparticles, while relatively few are concerned with nonporous organosilica nanoparticles. The synthesis of nonporous organosilica nanoparticles typically involves (i) self-condensation of an organosilane as the single source, (ii) co-condensation of two or more types of organosilanes, (iii) co-condensation of tetraalkoxysilane and an organosilane, and (iv) spontaneous emulsification and the subsequent radical polymerization of 3-(trimethoxysilyl)propyl methacrylate (TPM). This article aims to provide a review on the synthetic strategies of this important type of colloidal particle, followed by a brief discussion on their applications and future perspectives.

Active Colloids as Models, Materials, and Machines

Active colloids use energy input at the particle level to propel persistent motion and direct dynamic assemblies. We consider three types of colloids animated by chemical reactions, time-varying magnetic fields, and electric currents. For each type, we review the basic propulsion mechanisms at the particle level and discuss their consequences for collective behaviors in particle ensembles. These microscopic systems provide useful experimental models of nonequilibrium many-body physics in which dissipative currents break time-reversal symmetry. Freed from the constraints of thermodynamic equilibrium, active colloids assemble to form materials that move, reconfigure, heal, and adapt. Colloidal machines based on engineered particles and their assemblies provide a basis for mobile robots with increasing levels of autonomy. This review provides a conceptual framework for understanding and applying active colloids to create material systems that mimic the functions of living matter. We highlight opportunities for chemical engineers to contribute to this growing field.

Programmed Self-Assembly of Single Colloidal Gyroids for Chiral Photonic Crystals

Gyroid structures are of extensive interest because they provide a rich platform for chiroptics as well as topological photonics. While the double-gyroid morphology as a bicontinuous structure is not uncommon in self-assembled soft materials, direct self-assembly of single-network gyroids has proven elusive. Here, an enantiomorphic pair of single-gyroid crystals comprising colloidal spheres is presented, and two distinct routes are demonstrated for programmed self-assembly of each single colloidal gyroid enantiomorph from rationally designed patchy spheres. The designer colloidal patchy spheres, which closely hew to their synthetic feasibility, are chiral, having either two staggered rectangular patches at opposite poles or four circular patches arranged in a well-defined geometry. The single colloidal gyroid, as well as its inverse structure, is shown to support a wide complete photonic bandgap in addition to exhibiting rich chiroptical properties, making them attractive chiral photonic crystals. The versatility of this single colloidal gyroid, the bottom-up routes devised here in silico, and the robustness of the design space for the chiral colloidal patchy spheres together make a strong case for single colloidal gyroids to supersede colloidal diamond, as a target for programmed self-assembly, in the quest for photonic crystals operating at optical frequencies.