Predicting structure from the attributes of a material's building blocks remains a challenge and central goal for materials science. Isolating the role of building block shape for self-assembly provides insight into the ordering of molecules and the crystallization of colloids, nanoparticles, proteins, and viruses. We investigated 145 convex polyhedra whose assembly arises solely from their anisotropic shape. Our results demonstrate a remarkably high propensity for thermodynamic self-assembly and structural diversity. We show that from simple measures of particle shape and local order in the fluid, the assembly of a given shape into a liquid crystal, plastic crystal, or crystal can be predicted.

Efforts to impart elasticity and multifunctionality in nanocomposites focus mainly on integrating polymeric and nanoscale components. Yet owing to the stochastic emergence and distribution of strain-concentrating defects and to the stiffening of nanoscale components at high strains, such composites often possess unpredictable strain-property relationships. Here, by taking inspiration from kirigami—the Japanese art of paper cutting—we show that a network of notches made in rigid nanocomposite and other composite sheets by top-down patterning techniques prevents unpredictable local failure and increases the ultimate strain of the sheets from 4 to 370%. We also show that the sheets' tensile behaviour can be accurately predicted through finite-element modelling. Moreover, in marked contrast to other stretchable conductors, the electrical conductance of the stretchable kirigami sheets is maintained over the entire strain regime, and we demonstrate their use to tune plasma-discharge phenomena. The unique properties of kirigami nanocomposites as plasma electrodes open up a wide range of novel technological solutions for stretchable electronics and optoelectronic devices, among other application possibilities.

Polyhedra and their arrangements have intrigued humankind since the ancient Greeks and are today important motifs in condensed matter, with application to many classes of liquids and solids. Yet, little is known about the thermodynamically stable phases of polyhedrally shaped building blocks, such as faceted nanoparticles and colloids. Although hard particles are known to organize due to entropy alone, and some unusual phases are reported in the literature, the role of entropic forces in connection with polyhedral shape is not well understood. Here, we study thermodynamic self-assembly of a family of truncated tetrahedra and report several atomic crystal isostructures, including diamond, β-tin, and high-pressure lithium, as the polyhedron shape varies from tetrahedral to octahedral. We compare our findings with the densest packings of the truncated tetrahedron family obtained by numerical compression and report a new space-filling polyhedron, which has been overlooked in previous searches. Interestingly, the self-assembled structures differ from the densest packings. We show that the self-assembled crystal structures can be understood as a tendency for polyhedra to maximize face-to-face alignment, which can be generalized as directional entropic forces.

Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems.

T he scientific, academic, medical and data science communities have come together in the face of the COVID-19 pandemic crisis to rapidly assess novel paradigms in artificial intelligence (AI) that are rapid and secure, and potentially incentivize data sharing and model training and testing without the usual privacy and data ownership hurdles of conventional collaborations 1,2 . Healthcare providers, researchers and industry have pivoted their focus to address unmet and critical clinical needs created by the crisis, with remarkable results [3][4][5][6][7][8][9] . Clinical trial recruitment has been expedited and facilitated by national regulatory bodies and an international cooperative spirit 10-12 . The data analytics and AI disciplines have always fostered open