How to design an icosahedral quasicrystal through directional bonding

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.

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.

Quasicrystal of Binary Hard Spheres on a Plane Stabilized by Configurational Entropy

Because of their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be realized as an exponentially large number of different tilings, resulting in a significant contribution to the quasicrystal entropy. Here, we use free-energy calculations to demonstrate that it is this configurational entropy which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres on a plane. Our calculations also allow us to quantitatively confirm that in this system all tiling realizations are essentially equally likely, with free-energy differences less than 0.0001k_{B}T per particle-an observation that could be related to the observation of only random tilings in soft-matter quasicrystals. Owing to the simplicity of the model and its available counterparts in colloidal experiments, we believe that this system is an excellent candidate to achieve the long-awaited quasicrystal self-assembly on the micron scale.

Inverse design of triblock Janus spheres for self-assembly of complex structures in the crystallization slot via digital alchemy

The digital alchemy framework is an extended ensemble simulation technique that incorporates particle attributes as thermodynamic variables, enabling the inverse design of colloidal particles for desired behavior. Here, we extend the digital alchemy framework for the inverse design of patchy spheres that self-assemble into target crystal structures. To constrain the potentials to non-trivial solutions, we conduct digital alchemy simulations with constant second virial coefficient. We optimize the size, range, and strength of patchy interactions in model triblock Janus spheres to self-assemble the 2D kagome and snub square lattices and the 3D pyrochlore lattice, and demonstrate self-assembly of all three target structures with the designed models. The particles designed for the kagome and snub square lattices assemble into high quality clusters of their target structures, while competition from similar polymorphs lower the yield of the pyrochlore assemblies. We find that the alchemically designed potentials do not always match physical intuition, illustrating the ability of the method to find nontrivial solutions to the optimization problem. We identify a window of second virial coefficients that result in self-assembly of the target structures, analogous to the crystallization slot in protein crystallization.

Self-assembly of dodecagonal and octagonal quasicrystals in hard spheres on a plane

Hard spheres are one of the most fundamental model systems in soft matter physics, and have been instrumental in shedding light on nearly every aspect of classical condensed matter. Here, we add one more important phase to the list that hard spheres form: quasicrystals. Specifically, we use simulations to show that an extremely simple, purely entropic model system, consisting of two sizes of hard spheres resting on a flat plane, can spontaneously self-assemble into two distinct random-tiling quasicrystal phases. The first quasicrystal is a dodecagonal square-triangle tiling, commonly observed in a large variety of colloidal systems. The second quasicrystal has, to our knowledge, never been observed in either experiments or simulations. It exhibits octagonal symmetry, and consists of three types of tiles: triangles, small squares, and large squares, whose relative concentration can be continuously varied by tuning the number of smaller spheres present in the system. The observed tile composition of the self-assembled quasicrystals agrees very well with the theoretical prediction we obtain by considering the four-dimensional (lifted) representation of the quasicrystal. Both quasicrystal phases form reliably and rapidly over a significant part of parameter space. Our results demonstrate that entropy combined with a set of geometrically compatible, densely packed tiles can be sufficient ingredients for the self-assembly of colloidal quasicrystals.

A columnar liquid quasicrystal with a honeycomb structure that consists of triangular, square and trapezoidal cells

Quasicrystals are intriguing structures that have long-range positional correlations but no periodicity in real space, and typically with rotational symmetries that are 'forbidden' in conventional periodic crystals. Here, we present a two-dimensional columnar liquid quasicrystal with dodecagonal symmetry. Unlike previous dodecagonal quasicrystals based on random tiling, a honeycomb structure based on a strictly quasiperiodic tessellation of tiles is observed. The structure consists of dodecagonal clusters made up of triangular, square and trapezoidal cells that are optimal for local packing. To maximize the presence of such dodecagonal clusters, the system abandons periodicity but adopts a quasiperiodic structure that follows strict packing rules. The stability of random-tiling dodecagonal quasicrystals is often attributed to the entropy of disordering when strict tiling rules are broken, at the sacrifice of the long-range positional order. However, our results demonstrate that quasicrystal stability may rest on energy minimization alone, or with only minimal entropic intervention.

Field-induced magnetic phases in a qubit Penrose quasicrystal

Unveiling the fundamental dynamics of naturally or artificially formed magnetic quasicrystals in the presence of an external magnetic field remains a difficult problem that may have implications for the design of information processing devices. By embedding a qubit magnetic Penrose quasicrystal into a quantum annealer, we were able to reproduce the formation of magnetic phases driven by specific physical parameter selections, allowing us to distinguish a wide range of frustrated magnetic configurations at the single-spin scale. In our experiments, we observe some spins dynamically activate, while others remain static, all within an average magnetization space defined by competing structural and magnetic degrees of freedom. Static spin structure factors reveal ferromagnetic and ferrimagnetic modulations that are compatible with a variety of spin textures. This research demonstrates that introducing structural aperiodicity in magnetic devices that exploit spin degeneracy in a single, richly intraconnected finite object can enable the engineering of quantum states in both the effective low-temperature and thermally excited regimes.

Coarse-grained modelling to predict the packing of porous organic cages

How molecules pack has vital ramifications for their applications as functional molecular materials. Small changes in a molecule's functionality can lead to large, non-intuitive, changes in their global solid-state packing, resulting in difficulty in targeted design. Predicting the crystal structure of organic molecules from only their molecular structure is a well-known problem plaguing crystal engineering. Although relevant to the properties of many organic molecules, the packing behaviour of modular porous materials, such as porous organic cages (POCs), greatly impacts the properties of the material. We present a novel way of predicting the solid-state phase behaviour of POCs by using a simplistic model containing the dominant degrees of freedom driving crystalline phase formation. We employ coarse-grained simulations to systematically study how chemical functionality of pseudo-octahedral cages can be used to manipulate the solid-state phase formation of POCs. Our results support those of experimentally reported structures, showing that for cages which pack via their windows forming a porous network, only one phase is formed, whereas when cages pack via their windows and arenes, the phase behaviour is more complex. While presenting a lower computational cost route for predicting molecular crystal packing, coarse-grained models also allow for the development of design rules which we start to formulate through our results.

Formation and fluctuation of two-dimensional dodecagonal quasicrystals

The self-assembly of two-dimensional dodecagonal quasicrystals (DDQCs) from patchy particles is investigated by Brownian dynamics simulations. The patchy particle has a five-fold rotational symmetry pattern described by the spherical harmonics Y₅₅. From the formation of the DDQC obtained by an annealing process, we find the following mechanism. The early stage of the dynamics is dominated by hexagonal structures. Then, nucleation of dodecagonal motifs appears by particle rearrangement, and finally the motifs span the whole system. The transition from the hexagonal structure into the dodecagonal motif is coincident with the collective motion of the particles. The DDQC consists of clusters of dodecagonal motifs, which can be classified into several packing structures. By the analyses of the DDQC under fixed temperature, we find that the fluctuations are characterised by changes in the network of the dodecagonal motifs. Finally we compare the DDQCs assembled from the patchy particle system and isotropic particle system. The two systems share a similar mechanism of the formation and fluctuation of DDQCs.

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.

Finite Assembly of Three-Dimensional DNA Hierarchical Nanoarchitectures through Orthogonal and Directional Bonding

Reliable orthogonal bonding with precise and flexible orientation control would be ideal for building finite complex nanostructures via self-assembly. Employing a three-dimensional (3D) DNA origami, hexagonal prism DNA origami (HDO), as building block, we demonstrate it is practical to construct finite hierarchical nanoarchitectures with complicated conformations through orthogonal and directional bonding. The as-designed HDO building block has twelve prescribed directional valences in 3D space and each of them supports two opposite orientations, yielding the capability to generate abundant directional bonding. Meanwhile, we minimize the thorny non-specific interactions among HDOs and enable the orthogonal bonding between any two valences based on self-similar designing. Consequently, various hierarchical nanostructures are prepared at will simply by the combination of HDOs with appropriate valences. We believe this route towards hierarchically assembly is inspiring and hope it will facilitate the fabrication of functional superstructures.

Amplifiable ratiometric fluorescence biosensing of nanosilver multiclusters populated in three-way-junction DNA branches

To explore the fluorescence bio-responsiveness of emissive silver nanoclusters (AgNCs) populated in DNA-branched scaffolds is intriguing yet challenging. In response to a desired targeting model (T*) as a vehicle, herein a customized three-way-junction DNA construct (TWJDC) is assembled via competitive hybridizing cascade among three stem-loop hairpins with specific base sequences, where the repeated recycling of T* enables the exponentially amplifiable output of rigid TWJDC. As designed, these stable hybridization products are highly T*-stimulated responsive and constructing-directional. In the three branched-arms, the unpaired sticky ends provide isotropic binding sites for a signaling hairpin encoded with two C-rich templates of green- and red-AgNCs clustering. The identical ligation of signal probe with three arms of TWJDC liberates its locked stem, enabling the separate growth of red-clusters in three branches. As demonstrated, three clusters of red-AgNCs possess advantageous self-enhancing fluorescent performance relative to single or two cluster(s), good biocompatibility and low cytotoxicity. Utilizing the bicolor AgNCs as dual-emitters with reversely changed emission intensity, we developed an innovative ratiometric strategy displaying sensitively linear dose-dependence on variable T* down to 1.9 pM, which can afford a promising platform for biosensing, bioanalysis, cell imaging, or even clinical theranostics.