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

Scalable Macroscopic Engineering from Polymer-Based Nanoscale Building Blocks: Existing Challenges and Emerging Opportunities

Natural materials exhibit exceptional properties due to their hierarchical structures spanning from the nano- to the macroscale. Replicating these intricate spatial arrangements in synthetic materials presents a significant challenge as it requires precise control of nanometric features within large-scale structures. Addressing this challenge depends on developing methods that integrate assembly techniques across multiple length scales to construct multiscale-structured synthetic materials in practical, bulk forms. Polymers and polymer-hybrid nanoparticles, with their tunable composition and structural versatility, are promising candidates for creating hierarchically organized materials. This review highlights advances in scalable techniques for nanoscale organization of polymer-based building blocks within macroscopic structures, including block copolymer self-assembly with additive manufacturing, polymer brush nanoparticles capable of self-assembling into larger, ordered structures, and direct-write colloidal assembly. These techniques offer promising pathways toward the scalable fabrication of materials with emergent properties suited for advanced applications such as bioelectronic interfaces, artificial muscles, and other biomaterials.

Structures of the First Epitaxial Layer Created in Colloidal Heteroepitaxy

Brownian dynamics simulations have been performed to investigate the structural dependence of the first epitaxial layer in colloidal heteroepitaxy. When the epitaxial particles were larger than the substrate particles and the interactions were dominated by the depletion force, a hexagonal structure formed on a closely packed hexagonal substrate. The orientation of this hexagonal structure varied with the size ratio of the epitaxial to substrate particles to make the interaction between the substrate and epitaxial particles strong. When the sizes of the substrate and epitaxial particles were similar, long-period structures formed instead of hexagonal structures to strengthen the interaction between the substrate and epitaxial layer at the expense of the interaction between particles in the first epitaxial layer.

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.

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.

Theory and simulation of ligand functionalized nanoparticles - a pedagogical overview

Synthesizing reconfigurable nanoscale synthons with predictive control over shape, size, and interparticle interactions is a holy grail of bottom-up self-assembly. Grand challenges in their rational design, however, lie in both the large space of experimental synthetic parameters and proper understanding of the molecular mechanisms governing their formation. As such, computational and theoretical tools for predicting and modeling building block interactions have grown to become integral in modern day self-assembly research. In this review, we provide an in-depth discussion of the current state-of-the-art strategies available for modeling ligand functionalized nanoparticles. We focus on the critical role of how ligand interactions and surface distributions impact the emergent, pre-programmed behaviors between neighboring particles. To help build insights into the underlying physics, we first define an "ideal" limit - the short ligand, "hard" sphere approximation - and discuss all experimental handles through the lens of perturbations about this reference point. Finally, we identify theories that are capable of bridging interparticle interactions to nanoscale self-assembly and conclude by discussing exciting new directions for this field.

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.

Mixed Nanosphere Assemblies at a Liquid-Liquid Interface

The in-plane packing of gold (Au), polystyrene (PS), and silica (SiO2) spherical nanoparticle (NP) mixtures at a water-oil interface is investigated in situ by UV-vis reflection spectroscopy. All NPs are functionalized with carboxylic acid such that they strongly interact with amine-functionalized ligands dissolved in an immiscible oil phase at the fluid interface. This interaction markedly increases the binding energy of these nanoparticle surfactants (NPSs). The separation distance between the Au NPSs and Au surface coverage are measured by the maximum plasmonic wavelength (λmax) and integrated intensities as the assemblies saturate for different concentrations of non-plasmonic (PS/SiO2) NPs. As the PS/SiO2 content increases, the time to reach intimate Au NP contact also increases, resulting from their hindered mobility. λmax changes within the first few minutes of adsorption due to weak attractive inter-NP forces. Additionally, a sharper peak in the reflection spectrum at NP saturation reveals tighter Au NP packing for assemblies with intermediate non-plasmonic NP content. Grazing incidence small angle X-ray scattering (GISAXS) and scanning electron microscopy (SEM) measurements confirm a decrease in Au NP domain size for mixtures with larger non-plasmonic NP content. The results demonstrate a simple means to probe interfacial phase separation behavior using in situ spectroscopy as interfacial structures densify into jammed, phase-separated NP films.

Formation of various structures caused by particle size difference in colloidal heteroepitaxy

By performing isothermal-isochoric Monte Carlo simulations with depletion force, the author investigated the dependence of the epitxial layer structure on the differences in the particle size between the substrate in colloidal heteroepitaxy. By changing the size of epitaxial particles and performing simulations comprehensively, various structures including the structures observed in a experiment, such as a honeycomb, one created by hexagonal heptamers, and one consisting of both pentagonal tiles and triangular tiles, were created. When the ratio of particle sizes between the epitxial layer and substrate takes a specific value, two types of hexagonal structures were created. One is the hexagonal layer parallel to the substrate layer and the other layer is rotated by 60[Formula: see text] from the substrate layer. The former structure was created over a wide range of particle-size ratios, whereas the latter structure was created when the particle-size ratio was only around the specific ratio, and it seemed a metastable structure.

Precision nanoengineering for functional self-assemblies across length scales

As nanotechnology continues to push the boundaries across disciplines, there is an increasing need for engineering nanomaterials with atomic-level precision for self-assembly across length scales, i.e., from the nanoscale to the macroscale. Although molecular self-assembly allows atomic precision, extending it beyond certain length scales presents a challenge. Therefore, the attention has turned to size and shape-controlled metal nanoparticles as building blocks for multifunctional colloidal self-assemblies. However, traditionally, metal nanoparticles suffer from polydispersity, uncontrolled aggregation, and inhomogeneous ligand distribution, resulting in heterogeneous end products. In this feature article, I will discuss how virus capsids provide clues for designing subunit-based, precise, efficient, and error-free self-assembly of colloidal molecules. The atomically precise nanoscale proteinic subunits of capsids display rigidity (conformational and structural) and patchy distribution of interacting sites. Recent experimental evidence suggests that atomically precise noble metal nanoclusters display an anisotropic distribution of ligands and patchy ligand bundles. This enables symmetry breaking, consequently offering a facile route for two-dimensional colloidal crystals, bilayers, and elastic monolayer membranes. Furthermore, inter-nanocluster interactions mediated via the ligand functional groups are versatile, offering routes for discrete supracolloidal capsids, composite cages, toroids, and macroscopic hierarchically porous frameworks. Therefore, engineered nanoparticles with atomically precise structures have the potential to overcome the limitations of molecular self-assembly and large colloidal particles. Self-assembly allows the emergence of new optical properties, mechanical strength, photothermal stability, catalytic efficiency, quantum yield, and biological properties. The self-assembled structures allow reproducible optoelectronic properties, mechanical performance, and accurate sensing. More importantly, the intrinsic properties of individual nanoclusters are retained across length scales. The atomically precise nanoparticles offer enormous potential for next-generation functional materials, optoelectronics, precision sensors, and photonic devices.

Fabrication of Patchy Silica Microspheres with Tailor-Made Patch Functionality using Photo-Iniferter Reversible-Addition-Fragmentation Chain-Transfer (PI-RAFT) Polymerization

Their inherent directional information renders patchy particles interesting building blocks for advanced applications in materials science. In this study, a feasible method to fabricate patchy silicon dioxide microspheres is demonstrated, which they are able to equip with tailor-made polymeric materials as patches. Their fabrication method relies on a solid-state supported microcontact printing (µCP) routine optimized for the transfer of functional groups to capillary-active substrates, which is used to introduce amino functionalities as patches to a monolayer of particles. Acting as anchor groups for polymerization, photo-iniferter reversible addition-fragmentation chain-transfer (RAFT) is used to graft polymer from the patch areas. Accordingly, particles with poly(N-acryloyl morpholine), poly(N-isopropyl acrylamide), and poly(n-butyl acrylate) are prepared as representative acrylic acid-derived functional patch materials. To facilitate their handling in water, a passivation strategy of the particles for aqueous systems is introduced. The protocol introduced here, therefore, promises a vast degree of freedom in engineering the surface properties of highly functional patchy particles. This feature is unmatched by other techniques to fabricate anisotropic colloids. The method, thus, can be considered a platform technology, culminating in the fabrication of particles that possess locally precisely formed patches on particles at a low µm scale with a high material functionality.

Controlling the Self-Assembly of DNA Origami Octahedra via Manipulation of Inter-Vertex Interactions

Recent studies have demonstrated novel strategies for the organization of nanomaterials into three-dimensional (3D) ordered arrays with prescribed lattice symmetries using DNA-based self-assembly strategies. In one approach, the nanomaterial is sequestered into DNA origami frames or "material voxels" and then coordinated into ordered arrays based on the voxel geometry and the corresponding directional interactions based on its valency. While the lattice symmetry is defined by the valency of the bonds, a larger-scale morphological development is affected by assembly processes and differences in energies of anisotropic bonds. To facilely model this assembly process, we investigate the self-assembly behavior of hard particles with six interacting vertices via theory and Monte Carlo simulations and exploration of corresponding experimental systems. We demonstrate that assemblies with different 3D crystalline morphologies but the same lattice symmetry can be formed depending on the relative strength of vertex-to-vertex interactions in orthogonal directions. We observed three distinct assembly morphologies for such systems: cube-like, sheet-like, and cylinder-like. A simple analytical theory inspired by well-established ideas in the areas of protein crystallization, based on calculating the second virial coefficient of patchy hard spheres, captures the simulation results and thus represents a straightforward means of modeling this self-assembly process. To complement the theory and simulations, experimental studies were performed to investigate the assembly of octahedral DNA origami frames with varying binding energies at their vertices. X-ray scattering confirms the robustness of the formed nanoscale lattices for different binding energies, while both optical and electron microscopy imaging validated the theoretical predictions on the dependence of the distinct morphologies of assembled state on the interaction strengths in the three orthogonal directions.

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.

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.

Designing the Self-Assembly of Arbitrary Shapes Using Minimal Complexity Building Blocks

The design space for self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. We develop a pipeline to explore the design spaces for a set of structures of various sizes and complexities. To understand the implications of the different solutions, we analyze their assembly dynamics using patchy particle simulations and study the influence of the number of distinct building blocks, and the angular and spatial tolerances on their interactions, on the kinetics and yield of the target assembly. We show that the resource-saving solution with a minimum number of distinct blocks can often assemble just as well (or faster) than designs where each building block is unique. We further use our methods to design multifarious structures, where building blocks are shared between different target structures. Finally, we use coarse-grained DNA simulations to investigate the realization of multicomponent shapes using DNA nanostructures as building blocks.

Hierarchical Colloidal Self-Assembly on Lattice-Mismatched Moiré Patterns

Extending atomic epitaxy concepts to colloidal systems for realizing functional surface structures has recently piqued scientific interest. Akin to the growth of ordered metal clusters on graphene moiré, spatially ordered colloidal crystals have been realized on soft lithographically fabricated moiré patterns. In addition to moiré periodicity, lattice misfit strain can bring about a further level of hierarchy in colloidal self-assembly, although its role in self-organization remains unexplored. Here, we demonstrate the self-organized growth of micrometer-sized colloidal pyramid arrays with lateral order extending over millimeter length scales on lattice-mismatched moiré patterns. By probing the film growth dynamics with single-particle resolution, we uncovered the interplay between lattice misfit strain and topographically varying surface potential within the moiré unit cell, which significantly alters the nucleation process. We also show that the structural organization of colloids within moiré regions primarily depends on the moiré angle, and by tuning it, multiple levels of hierarchy can be achieved.

Two-Dimensional Structures Formed by Triblock Patchy Particles with Two Different Patches

Two-dimensional structures formed by spherical triblock patchy particles are examined by performing Monte Carlo simulations. In the model, the triblock patchy particles have two different types of patches at the polar positions. The patch sizes are different from each other, and the attractive interaction acts only between the same types of patches. The particles translate on a flat plane and rotate three-dimensionally. When varying the two patch sizes, the pressure, and interaction energy, various structures are observed. When the difference between two patch sizes is small, kagome lattices, hexagonal structures, and two-dimensional dodecagonal quasi-crystal structures are observed. When the difference between two patch sizes is large, chain-like structures are created. With lower temperature, sparse structures such as ring-like structures form.

Directed Assembly of Nanomaterials for Making Nanoscale Devices and Structures: Mechanisms and Applications

Nanofabrication has been utilized to manufacture one-, two-, and three-dimensional functional nanostructures for applications such as electronics, sensors, and photonic devices. Although conventional silicon-based nanofabrication (top-down approach) has developed into a technique with extremely high precision and integration density, nanofabrication based on directed assembly (bottom-up approach) is attracting more interest recently owing to its low cost and the advantages of additive manufacturing. Directed assembly is a process that utilizes external fields to directly interact with nanoelements (nanoparticles, 2D nanomaterials, nanotubes, nanowires, etc.) and drive the nanoelements to site-selectively assemble in patterned areas on substrates to form functional structures. Directed assembly processes can be divided into four different categories depending on the external fields: electric field-directed assembly, fluidic flow-directed assembly, magnetic field-directed assembly, and optical field-directed assembly. In this review, we summarize recent progress utilizing these four processes and address how these directed assembly processes harness the external fields, the underlying mechanism of how the external fields interact with the nanoelements, and the advantages and drawbacks of utilizing each method. Finally, we discuss applications made using directed assembly and provide a perspective on the future developments and challenges.

A simple solution to the problem of self-assembling cubic diamond crystals

The self-assembly of colloidal diamond (CD) crystals is considered as one of the most coveted goals of nanotechnology, both from the technological and fundamental points of view. For applications, colloidal diamond is a photonic crystal which can open new possibilities of manipulating light for information processing. From a fundamental point of view, its unique symmetry exacerbates a series of problems that are commonly faced during the self-assembly of target structures, such as the presence of kinetic traps and the formation of crystalline defects and alternative structures (polymorphs). Here we demonstrate that all these problems can be systematically addressed via SAT-assembly, a design framework that converts self-assembly into a Boolean satisfiability problem (SAT). Contrary to previous solutions (requiring four or more components), we prove that the assembly of the CD crystal only requires a binary mixture. Moreover, we use molecular dynamics simulations of a system composed by nearly a million nucleotides to test a DNA nanotechnology design that constitutes a promising candidate for experimental realization.

Two-dimensional binary colloidal crystals formed by particles with two different sizes

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SAT-assembly: a new approach for designing self-assembling systems

We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as building blocks, where the different units bind at specific interaction sites (the patches), and we exploit the possibility of having mixtures with several components. The interaction rules between the patches is determined by transforming the combinatorial problem into a Boolean satisfiability problem (SAT) which searches for solutions where all bonds are formed in the target structure. Additional conditions, such as the non-satisfiability of competing structures (e.g. metastable states) can be imposed, allowing to effectively design the assembly path in order to avoid kinetic traps. We demonstrate this approach by designing and numerically simulating a cubic diamond structure from four particle species that assembles without competition from other polymorphs, including the hexagonal structure.

Computer simulations of self-assembly of anisotropic colloids

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

Colloidal cubic diamond photonic crystals through cooperative self-assembly

Colloidal cubic diamond crystals with low-coordinated and staggered structures could display a wide photonic bandgap at low refractive index contrasts, which makes them extremely valuable for photonic applications. However, self-assembly of cubic diamond crystals using simple colloidal building blocks is still considerably challenging, due to their low packing fraction and mechanical instability. Here we propose a new strategy for constructing colloidal cubic diamond crystals through cooperative self-assembly of surface-anisotropic triblock Janus colloids and isotropic colloidal spheres into superlattices. In self-assembly, cooperativity is achieved by tuning the interaction and particle size ratio of colloidal building blocks. The pyrochlore lattice formed by self-assembly of triblock Janus colloids acts as a soft template to direct the packing of colloidal spheres into cubic diamond lattices. Numerical simulations show that this cooperative self-assembly strategy works well in a large range of particle size ratio of these two species. Moreover, photonic band structure calculations reveal that the resulting cubic diamond lattices exhibit wide and complete photonic bandgaps and the width and frequency of the bandgaps can also be easily adjusted by tuning the particle size ratio. Our work will open up a promising avenue toward photonic bandgap materials by cooperative self-assembly employing surface-anisotropic Janus or patchy colloids as a soft template.

Self-Assembly of Model Triblock Janus Colloidal Particles in Two Dimensions

A simplified two-dimensional effective-solvent model of triblock Janus particles, consisting of three interaction sites in a linear configuration, a core particle, and two particles modeling the attractive patches at the poles, is developed to study the mechanism of nucleation and self-assembly in triblock Janus particles. The potential energy parameters are tuned against phase transition temperatures and free energy barriers to the nucleation of crystalline phases, calculated from our previous detailed model of Janus particles. Vapor-liquid equilibria and critical temperatures are calculated by grand-canonical molecular dynamics simulations for particles of different patch widths. With metadynamics, phase equilibria, mechanism of nucleation, and free energy barriers to nucleation are investigated. The minimum free energy path to nucleation indicates two steps. The first step, with a higher free energy increase, consists of the densification of the fluid into a disordered cluster. In the second step, of a lower free energy barrier, the inner particles of the disordered cluster reorient to form a crystalline nucleus. This two-step mechanism of nucleation of a kagome lattice is in complete agreement with the experiment and with our previous simulations using a detailed model of Janus particles. Large systems at a slight supersaturation generate multiple crystalline domains, which are misaligned at the grain boundaries. In complete agreement with the experiment and with previous simulation results, we observe a two-step mechanism for crystal growth: melting of the smaller (less stable) crystallites to a fluid followed by recrystallization at the surface of neighboring bigger (more stable) crystallites. A comparison of the present softer modeling of a Janus particle with harder models in the literature for self-assembly of Janus particles indicates that softer potentials stabilize open lattices (e.g., kagome) more than dense lattices (e.g., hexagonal). Also, experimental locations of phase transition points and barrier heights to nucleation are better reproduced by the present model than by the existing simple models.

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

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

Particle-Click-Particle: Colloidal Clusters from Click Seeded Emulsion Polymerization

The self-organization of building blocks in colloidal clusters and their architecture adjustment are crucial for colloid synthesis and design. We report on a click seeded emulsion polymerization via swelling-induced self-assembly...

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.

Facile self-assembly of colloidal diamond from tetrahedral patchy particles via ring selection

The self-assembly of colloidal diamond–a classic example of an open crystal with the low coordination number of four and much sought after due to its applications in visible light management–from designer spherical colloidal particles has proved challenging over the years. The formation of the diamond lattice from tetrahedral patchy particles is hampered by the propensity to form competing open periodic structures for narrow patches or dynamically arrested states for wider patches, leaving a narrow window in design space where diamond crystals may be realized. Our two-component system of designer tetrahedral patchy particles supports a significantly wider range for patch sizes for programmed self-assembly, thus facilitating experimental fabrication, and offers fundamental insight into crystallization into open lattices.

Diamond-structured crystals, particularly those with cubic symmetry, have long been attractive targets for the programmed self-assembly of colloidal particles, due to their applications as photonic crystals that can control the flow of visible light. While spherical particles decorated with four patches in a tetrahedral arrangement—tetrahedral patchy particles—should be an ideal building block for this endeavor, their self-assembly into colloidal diamond has proved elusive. The kinetics of self-assembly pose a major challenge, with competition from an amorphous glassy phase, as well as clathrate crystals, leaving a narrow widow of patch widths where tetrahedral patchy particles can self-assemble into diamond crystals. Here we demonstrate that a two-component system of tetrahedral patchy particles, where bonding is allowed only between particles of different types to select even-member rings, undergoes crystallization into diamond crystals over a significantly wider range of patch widths conducive for experimental fabrication. We show that the crystallization in the two-component system is both thermodynamically and kinetically enhanced, as compared to the one-component system. Although our bottom-up route does not lead to the selection of the cubic polytype exclusively, we find that the cubicity of the self-assembled crystals increases with increasing patch width. Our designer system not only promises a scalable bottom-up route for colloidal diamond but also offers fundamental insight into crystallization into open lattices.

Effective Structure Control of Colloidal Molecules and the Morphology Evolution Mechanism Investigation

Colloidal molecules (CMs), nonspherical clusters of a small number of particles, can be used as building blocks for self-assembly applications. Here, we propose a novel one pot method for CMs synthesis. First, poly(N-isopropylacrylamide-co-acrylic acid) (P(NIPAM-co-AA)) microgels were prepared by soap-free emulsion polymerization as seed particles, then monomer styrene and cross-linking agent divinylbenzene (DVB) were added, which could be polymerized by the remaining free radicals on the seed surface in situ. P(NIPAM-co-AA)-PS colloidal molecules with a series of morphologies such as popcorn-like, CO₂-like, NH₃-like, CH₄-like and so on could be obtained. The effects of satellite colloid viscosity, interfacial tension, and polymer chain mobility on the number of satellite colloid have been investigated, and the formation mechanism of CMs is proposed based on morphology evolution investigation. Compared with the existing CM synthesis techniques, our method enables fabricating CMs from vinyl monomer in a facile and efficient way, and the scientific finding regarding the CMs formation will guide the CMs fabrication toward salable and reliable direction.

Encoding hierarchical assembly pathways of proteins with DNA

The structural and functional diversity of materials in nature depends on the controlled assembly of discrete building blocks into complex architectures via specific, multistep, hierarchical assembly pathways. Achieving similar complexity in synthetic materials through hierarchical assembly is challenging due to difficulties with defining multiple recognition areas on synthetic building blocks and controlling the sequence through which those recognition sites direct assembly. Here, we show that we can exploit the chemical anisotropy of proteins and the programmability of DNA ligands to deliberately control the hierarchical assembly of protein-DNA materials. Through DNA sequence design, we introduce orthogonal DNA interactions with disparate interaction strengths ("strong" and "weak") onto specific geometric regions of a model protein, stable protein 1 (Sp1). We show that the spatial encoding of DNA ligands leads to highly directional assembly via strong interactions and that, by design, the first stage of assembly increases the multivalency of weak DNA-DNA interactions that give rise to an emergent second stage of assembly. Furthermore, we demonstrate that judicious DNA design not only directs assembly along a given pathway but can also direct distinct structural outcomes from a single pathway. This combination of protein surface and DNA sequence design allows us to encode the structural and chemical information necessary into building blocks to program their multistep hierarchical assembly. Our findings represent a strategy for controlling the hierarchical assembly of proteins to realize a diverse set of protein-DNA materials by design.

Clusters formed by dumbbell-like one-patch particles confined in thin systems

Performing isothermal-isochoric Monte Carlo simulations, I examine the types of clusters that dumbbell-like one–patch particles form in thin space between two parallel walls, assuming that each particle is synthesized through the merging of two particles, one non-attracting and the other attracting for which, for example, the inter-particle interaction is approximated by the DLVO model . The shape of these dumbbell-like particles is controlled by the ratio of the diameters q of the two spherical particles and by the dimensionless distance l between these centers. Using a modified Kern–Frenkel potential, I examine the dependence of the cluster shape on l and q. Large island-like clusters are created when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q<1$$\end{document}q<1. With increasing q, the clusters become chain-like . When q increases further, elongated clusters and regular polygonal clusters are created. In the simulations, the cluster shape becomes three-dimensional with increasing l because the thickness of the thin system increases proportionally to l.

Patchy Colloidal Clusters with Broken Symmetry

Colloidal clusters are prepared by assembling positively charged cross-linked polystyrene (PS) particles onto negatively charged liquid cores of swollen polymer particles. PS particles at the interface of the liquid core are closely packed around the core due to interfacial wetting. Then, by evaporating solvent in the liquid cores, polymers in the cores are solidified and the clusters are cemented. As the swelling ratio of PS cores increases, cores at the center of colloidal clusters are exposed, forming patchy colloidal clusters. Finally, by density gradient centrifugation, high-purity symmetric colloidal clusters are obtained. When silica-PS core-shell particles are swollen and serve as the liquid cores, hybrid colloidal clusters are obtained in which each silica nanoparticle is relocated to the liquid core interface during the swelling-deswelling process breaking symmetry in colloidal clusters as the silica nanoparticle in the core is comparable in size with the PS particle in the shell. The configuration of colloidal clusters is determined once the number of particles around the liquid core is given, which depends on the size ratio of the liquid core and shell particle. Since hybrid clusters are heavier than PS particles, they can be purified using centrifugation.

Softness-Enhanced Self-Assembly of Pyrochlore- and Perovskite-like Colloidal Photonic Crystals from Triblock Janus Particles

It remains extremely challenging to build three-dimensional photonic crystals with complete photonic bandgaps by simple and experimentally realizable colloidal building blocks. Here, we demonstrate that particle softness can enhance both the self-assembly of pyrochlore- and perovskite-like lattice structures from simple deformable triblock Janus colloids and their photonic bandgap performances. Dynamics simulation results show that the region of stability of pyrochlore lattices can be greatly expanded by appropriately increasing softness, and the perovskite lattices are unexpectedly obtained at enough high softness. Photonic calculations show that the direct pyrochlore lattices formed from overlapping soft triblock Janus particles exhibit even larger photonic bandgaps than the ideal nonoverlapping pyrochlore lattice, and proper overlap arising from softness can also dramatically improve the photonic properties of the inverse pyrochlore and perovskite lattices. Our study offers a new and feasible self-assembly path toward three-dimensional photonic crystals with large and robust photonic bandgaps.

Infochemistry and the Future of Chemical Information Processing

Nowadays, information processing is based on semiconductor (e.g., silicon) devices. Unfortunately, the performance of such devices has natural limitations owing to the physics of semiconductors. Therefore, the problem of finding new strategies for storing and processing an ever-increasing amount of diverse data is very urgent. To solve this problem, scientists have found inspiration in nature, because living organisms have developed uniquely productive and efficient mechanisms for processing and storing information. We address several biological aspects of information and artificial models mimicking corresponding bioprocesses. For instance, we review the formation of synchronization patterns and the emergence of order out of chaos in model chemical systems. We also consider molecular logic and ion fluxes as information carriers. Finally, we consider recent progress in infochemistry, a new direction at the interface of chemistry, biology, and computer science, considering unconventional methods of information processing.

From colloidal particles to photonic crystals: advances in self-assembly and their emerging applications

Over the last three decades, photonic crystals (PhCs) have attracted intense interests thanks to their broad potential applications in optics and photonics. Generally, these structures can be fabricated via either "top-down" lithographic or "bottom-up" self-assembly approaches. The self-assembly approaches have attracted particular attention due to their low cost, simple fabrication processes, relative convenience of scaling up, and the ease of creating complex structures with nanometer precision. The self-assembled colloidal crystals (CCs), which are good candidates for PhCs, have offered unprecedented opportunities for photonics, optics, optoelectronics, sensing, energy harvesting, environmental remediation, pigments, and many other applications. The creation of high-quality CCs and their mass fabrication over large areas are the critical limiting factors for real-world applications. This paper reviews the state-of-the-art techniques in the self-assembly of colloidal particles for the fabrication of large-area high-quality CCs and CCs with unique symmetries. The first part of this review summarizes the types of defects commonly encountered in the fabrication process and their effects on the optical properties of the resultant CCs. Next, the mechanisms of the formation of cracks/defects are discussed, and a range of versatile fabrication methods to create large-area crack/defect-free two-dimensional and three-dimensional CCs are described. Meanwhile, we also shed light on both the advantages and limitations of these advanced approaches developed to fabricate high-quality CCs. The self-assembly routes and achievements in the fabrication of CCs with the ability to open a complete photonic bandgap, such as cubic diamond and pyrochlore structure CCs, are discussed as well. Then emerging applications of large-area high-quality CCs and unique photonic structures enabled by the advanced self-assembly methods are illustrated. At the end of this review, we outlook the future approaches in the fabrication of perfect CCs and highlight their novel real-world applications.

Reversible embroidered ball-like antireflective structure arrays inspired by leafhopper wings

Highly transparent leafhopper (Thaia rubiginosa) wings are self-decorated with embroidered ball-shaped proteinaceous brochosmoes as distinct anti-predator defenses. The non-sticky brochosomal coating serves as antireflective structures for camouflage in vegetated environments. Inspired by the leafhopper wings, this study reports a new type of reversible antireflection coating enabled by integrating self-assembly methodologies using a shape memory polymer. The resulting embroidered ball-like structure array establishes a refractive index transition on surface, and thereby behaves omnidirectional antireflective characteristics in a broadband visible light region. Interestingly, the highly transparent appearance can be instantly erased and recovered by submerging in common liquids, such as water and ethanol, or by applying contact pressures at ambient conditions. Furthermore, the reversibility and structure-shape effect on the antireflective characteristics are systematically evaluated in this study.

Effect of the Interaction Length on Clusters Formed by Spherical One-Patch Particles on Flat Planes

Considering that one-patch particles rotate three-dimensionally and translate on a two-dimensional flat plane, I performed isothermal-isochoric Monte Carlo simulations to study how two-dimensional self-assemblies formed by spherical patchy particles depending on the interaction length and patch area. As the interaction potential between one-patch particles, the Kern-Frenkel (KF) potential is used in the simulations. With increasing patch area, the shape of the most numerous clusters changes from dimers to island-like clusters with a square lattice via triangular trimers, square tetramers, and chain-like clusters when the interaction length is as long as the particle radius. With a longer interaction length, other shapes of polygonal clusters such as another type of square tetramers, two types of pentagonal pentamers, hexagonal hexamers, and hexagonal heptamers also form.

Equilibrium mechanisms of self-limiting assembly

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

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.

Two-Dimensional (2D) or Quasi-2D Superstructures from DNA-Coated Colloidal Particles

This contribution describes the synthesis of colloidal di-patch particles functionalized with DNA on the patches and their assembly into colloidal superstructures via cooperative depletion and DNA-mediated interactions. The assembly into flower-like Kagome, brick-wall like monolayer, orthogonal packed single or double layers, wrinkled monolayer, and colloidal honeycomb superstructures can be controlled by tuning the particles' patch sizes and assembly conditions. Based on these experimental results, we generate an empirical phase diagram. The principles revealed by the phase diagram provide guidance in the design of two-dimensional (2D) materials with desired superstructures. Our strategy might be translatable to the assembly of three-dimensional (3D) colloidal structures.

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.

Tunable assembly of hybrid colloids induced by regioselective depletion

Assembling colloidal particles using site-selective directional interactions into predetermined colloidal superlattices with desired properties is broadly sought after, but challenging to achieve. Herein, we exploit regioselective depletion interactions to engineer the directional bonding and assembly of non-spherical colloidal hybrid microparticles. We report that the crystallization of a binary colloidal mixture can be regulated by tuning the depletion conditions. Subsequently, we fabricate triblock biphasic colloids with controlled aspect ratios to achieve regioselective bonding. Without any surface treatment, these biphasic colloids assemble into various colloidal superstructures and superlattices featuring optimized pole-to-pole or centre-to-centre interactions. Additionally, we observe polymorphic crystallization, quantify the abundancy of each form using algorithms we developed and investigate the crystallization process in real time. We demonstrate selective control of attractive interactions between specific regions on an anisotropic colloid with no need of site-specific surface functionalization, leading to a general method for achieving colloidal structures with yet unforeseen arrangements and properties.

Effect of Patch Area and Interaction Length on Clusters and Structures Formed by One-Patch Particles in Thin Systems

Assuming that the interaction between particles is given by the Kern-Frenkel potential, Monte Carlo simulations are performed to study the clusters and structures formed by one-patch particles in a thin space between two parallel walls. In isothermal-isochoric systems with a short interaction length, tetrahedral tetramers, octahedral hexamers, and pentagonal dipyramidal heptamers are created with increasing patch area. In isothermal-isobaric systems, the double layers of a triangular lattice, which is the (111) face of the face-centered cubic (fcc) lattice, form when the pressure is high. For a long interaction length, a different type of cluster, trigonal prismatic hexamers, is created. The structures in the double layers also changed as follows: a simple hexagonal lattice or square lattice, which is the (100) face of the fcc structure, is created in isothermal-isobaric systems.

Self-assembly behavior of experimentally realizable lobed patchy particles

We report simulation studies on the self-assembly behavior of five different types of lobed patchy particles of different shapes (snowman, dumbbell, trigonal planar, square planar, and tetrahedral). Inspired by an experimental method of synthesizing patchy particles (Wang et al., Nature, 2012, 491, 51-55), we control the lobe size indirectly by gradually varying the seed diameter and study its effect on self-assembled structures at different temperatures. Snowman shaped particles self-assemble only at a lower temperature and form two-dimensional sheets, elongated micelles, and spherical micelles, depending on the seed diameter. Each of the four other lobed particles self-assemble into four distinct morphologies (random aggregates, spherical aggregates, liquid droplets, and crystalline structures) for a given lobe size and temperature. We observed temperature-dependent transitions between two morphologies depending on the type of the lobed particle. The self-assembled structures formed by these four types of particles are porous. We show that their porosities can be tuned by controlling the lobe size and temperature.

Designing Patchy Interactions to Self-Assemble Arbitrary Structures

One of the fundamental goals of nanotechnology is to exploit selective and directional interactions between molecules to design particles that self-assemble into desired structures, from capsids, to nanoclusters, to fully formed crystals with target properties (e.g., optical, mechanical, etc.). Here, we provide a general framework which transforms the inverse problem of self-assembly of colloidal crystals into a Boolean satisfiability problem for which solutions can be found numerically. Given a reference structure and the desired number of components, our approach produces designs for which the target structure is an energy minimum, and also allows us to exclude solutions that correspond to competing structures. We demonstrate the effectiveness of our approach by designing model particles that spontaneously nucleate milestone structures such as the cubic diamond, the pyrochlore, and the clathrate lattices.

Universal reshaping of arrested colloidal gels via active doping

Colloids that interact via a short-range attraction serve as the primary building blocks for a broad range of self-assembled materials. However, one of the well-known drawbacks to this strategy is that these building blocks rapidly and readily condense into a metastable colloidal gel. Using computer simulations, we illustrate how the addition of a small fraction of purely repulsive self-propelled colloids, a technique referred to as active doping, can prevent the formation of this metastable gel state and drive the system toward its thermodynamically favored crystalline target structure. The simplicity and robust nature of this strategy offers a systematic and generic pathway to improving the self-assembly of a large number of complex colloidal structures. We discuss in detail the process by which this feat is accomplished and provide quantitative metrics for exploiting it to modulate the self-assembly. We provide evidence for the generic nature of this approach by demonstrating that it remains robust under a number of different anisotropic short-ranged pair interactions in both two and three dimensions. In addition, we report on a novel microphase in mixtures of passive and active colloids. For a broad range of self-propelling velocities, it is possible to stabilize a suspension of fairly monodisperse finite-size crystallites. Surprisingly, this microphase is also insensitive to the underlying pair interaction between building blocks. The active stabilization of these moderately sized monodisperse clusters is quite remarkable and should be of great utility in the design of hierarchical self-assembly strategies. This work further bolsters the notion that active forces can play a pivotal role in directing colloidal self-assembly.