Pyrochlore lattice, self-assembly and photonic band gap optimizations

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.

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.

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.

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.

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

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

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

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

Colloidal diamond

Self-assembling colloidal particles in the cubic diamond crystal structure could potentially be used to make materials with a photonic bandgap^1-3. Such materials are beneficial because they suppress spontaneous emission of light¹ and are valued for their applications as optical waveguides, filters and laser resonators⁴, for improving light-harvesting technologies^{5-7 and for other applications4,8}. Cubic diamond is preferred for these applications over more easily self-assembled structures, such as face-centred-cubic structures^9,10, because diamond has a much wider bandgap and is less sensitive to imperfections^11,12. In addition, the bandgap in diamond crystals appears at a refractive index contrast of about 2, which means that a photonic bandgap could be achieved using known materials at optical frequencies; this does not seem to be possible for face-centred-cubic crystals^3,13. However, self-assembly of colloidal diamond is challenging. Because particles in a diamond lattice are tetrahedrally coordinated, one approach has been to self-assemble spherical particles with tetrahedral sticky patches^14-16. But this approach lacks a mechanism to ensure that the patchy spheres select the staggered orientation of tetrahedral bonds on nearest-neighbour particles, which is required for cubic diamond^15,17. Here we show that by using partially compressed tetrahedral clusters with retracted sticky patches, colloidal cubic diamond can be self-assembled using patch-patch adhesion in combination with a steric interlock mechanism that selects the required staggered bond orientation. Photonic bandstructure calculations reveal that the resulting lattices (direct and inverse) have promising optical properties, including a wide and complete photonic bandgap. The colloidal particles in the self-assembled cubic diamond structure are highly constrained and mechanically stable, which makes it possible to dry the suspension and retain the diamond structure. This makes these structures suitable templates for forming high-dielectric-contrast photonic crystals with cubic diamond symmetry.

Leveraging Hierarchical Self-Assembly Pathways for Realizing Colloidal Photonic Crystals

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

DNA functionalization of colloidal particles via physisorption of azide-functionalized diblock copolymers

DNA-coated inorganic particles can be prepared simply by physical adsorption of azide-functionalized diblock copolymers (polystyrene-b-poly(ethylene oxide)-azide, PS-b-PEO-N₃) onto hydrophobically-modified inorganic particles, followed by strain-promoted azide-alkyne cycloaddition (SPAAC, copper-free click chemistry). This approach is applied to organosilica, silica and titania particles. The DNA-coated colloids are successfully crystallized into colloidal superstructures by a thermal annealing process using DNA-mediated assembly.

Investigation of Geometric Landscape and Structure-Property Relations for Colloidal Superstructures Using Genetic Algorithm

Over the past two decades, colloidal particles with a variety of shapes, sizes, and compositions have been synthesized and characterized successfully. One of the most important applications for colloidal building blocks is to engineer functional structures as mechanical, electrical, and optical metamaterials. However, complex interaction dynamics between the building blocks as well as sophisticated structure-property relationships make it challenging to design structures with predictable target properties. In this paper, we implement an inverse material design framework using Genetic Algorithm (GA)-based techniques to streamline the design of colloidal structures based on target properties. We investigate spherical particles as well as colloidal molecules of different sizes and shapes and evaluate a Geometric Landscape Accessibility parameter that identifies the size of feasible domains within the geometric phase space of each structure. Considering target photonic properties, our GA-assisted framework is further utilized to identify sets of building blocks and structures that lead to various target values for the size of the photonic band gaps. The proposed framework in this study will provide new insight for predictive computational material design approaches and help establish more efficient ways of understanding structure-property relations in sub-micrometer-scale materials.

Entropy-Induced Self-Assembly of Colloidal Crystals with High Reflectivity and Narrow Reflection Bandwidth

Cracks and defects, which could result in lower reflectivity and larger full width at half maximum (FWHM), are the major obstacles for obtaining highly ordered structures of colloidal crystals (CCs). The high-quality CCs with high reflectivity (more than 90%) and 9.2 nm narrow FWHM have been successfully fabricated using a fixed proportion of a soft matter system composed of silica particles (SPs), polyethylene glycol diacrylate (PEGDA), and ethanol. The influences of refractivity difference, volume fractions, and particle dimension on FWHM were illuminated. Firstly, we clarified the influences of the planar interface and the bending interface on the self-assembly. The CCs had been successfully fabricated on the planar interface and presented unfavorable results on the bending interface. Secondly, a hard sphere system consisting of SPs, PEGDA, and ethanol was established, and the entropy-driven phase transition mechanism of a polydisperse system was expounded. The FWHM and reflectivity of CCs showed an increasing trend with increasing temperature. Consequently, high-quality CCs were obtained by adjusting temperatures (ordered structure formed at 90 °C and solidified at 0 °C) based on the surface phase rule of the system. We acquired a profound understanding of the principle and process of self-assembly, which is significant for preparation and application of CCs such as optical filters.