The rise of graphene, a natural two-dimensional polymer (2DP) with topologically planar repeat units, has challenged synthetic chemistry, and has highlighted that accessing equivalent covalently bonded sheet-like macromolecules has, until recently, not been achieved. Here we show that non-centrosymmetric, enantiomorphic single crystals of a simple-to-make monomer can be photochemically converted into chiral 2DP crystals and cleanly reversed back to the monomer. X-ray diffraction established unequivocal structural proof for this synthetic 2DP, which has an all-carbon scaffold and can be synthesized on the gram scale. The monomer crystals are highly robust, can be easily grown to sizes greater than 1 mm and the resulting 2DP crystals exfoliated into nanometre-thin sheets. This unique combination of features suggests that these 2DPs could find use in membranes and nonlinear optics.
Throughout the physical sciences, entropy stands out as a pivotal but enigmatic concept that, in materials design, typically takes a backseat to energy. Here, we demonstrate how to precisely engineer entropy to achieve desired colloidal crystals via particle shapes that, importantly, can be made in the laboratory. We demonstrate the inverse design of symmetric hard particles that assemble six different target colloidal crystals due solely to entropy maximization. Our approach efficiently samples 108 particle shapes from 92- and 188-dimensional design spaces to discover thermodynamically optimal shapes. We design particle shapes that self-assemble into known crystals with optimized symmetry and thermodynamic stability, as well as new crystal structures with no known atomic or other equivalent.
This is the first of two parts, where we report the structure determination of a novel family of cluster-based intermetallic phases of unprecedented complexity: cF444-Al63.6Ta36.4 (AT-19), a = 19.1663 (1) Å, V = 7040 Å3, cF(5928 − x)-Al56.6Cu3.9Ta39.5, x = 20 (ACT-45), a = 45.376 (1) Å, V = 93 428 Å3 and cF(23 256 − x)-Al55.4Cu5.4Ta39.1, x = 122 (ACT-71), a = 71.490 (4) Å, V = 365 372 Å3. The space group is F{\bar 4}3m in all three cases. These cluster-based structures are closely related to the class of Frank–Kasper phases. It is remarkable that all three structures show the same average structure that resembles the cubic Laves phase.
Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to N = 60 constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem.clusters | confinement | packing | colloids | nanoparticles P henomena as diverse as crowding in the cell (1, 2), DNA packaging in cell nuclei and virus capsids (3, 4), the growth of cellular aggregates (5), biological pattern formation (6), blood clotting (7), efficient manufacturing and transport, the planning and design of cellular networks (8), and efficient food and pharmaceutical packaging and transport (9) are related to the optimization problem of packing objects of a specified shape as densely as possible within a confining geometry, or packing in confinement. Packing in confinement is also a laboratory technique used to produce particle aggregates with consistent structure. These aggregates may serve as building blocks (or "colloidal molecules") in hierarchical structures (10, 11), information storage units (12), or drug delivery capsules (13). Experiments concerning cluster formation via spherical droplet confinement (13-20) are of special interest here. Droplets are typically either oil-in-water or water-inoil emulsions, and particle aggregation is induced via the evaporation of the droplet solvent. Clusters may be hollow [in which case they are termed "colloidosomes" (13)] or filled, depending on the formation protocol, and may contain a few (15) to a few billion (14) particles. Clusters of several metallic nanoparticles are especially intriguing given their ability to support surface plasmon modes over a range of frequencies (21). The subwavelength scale of these clusters means that their optical response is highly dependent on their specific geometry (22). Consequently, control over their structure enables control over their optical properties, with implications for cloaking (23), chemical sensing (24), imaging (25), nonlinear optics (26), and the creation of so-called metafluids (27)(28)(29), a...
The rigid constraints of chemistry—dictated by quantum mechanics and the discrete nature of the atom—limit the set of observable atomic crystal structures. What structures are possible in the absence of these constraints? Here, we systematically crystallize one-component systems of particles interacting with isotropic multiwell pair potentials. We investigate two tunable families of pairwise interaction potentials. Our simulations self-assemble a multitude of crystal structures ranging from basic lattices to complex networks. Sixteen of the structures have natural analogs spanning all coordination numbers found in inorganic chemistry. Fifteen more are hitherto unknown and occupy the space between covalent and metallic coordination environments. The discovered crystal structures constitute targets for self-assembly and expand our understanding of what a crystal structure can look like.
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