Spontaneous formation of colonies of bacteria or flocks of birds are examples of self-organization in active living matter. Here, we demonstrate a form of self-organization from nonequilibrium driving forces in a suspension of synthetic photoactivated colloidal particles. They lead to two-dimensional "living crystals," which form, break, explode, and re-form elsewhere. The dynamic assembly results from a competition between self-propulsion of particles and an attractive interaction induced respectively by osmotic and phoretic effects and activated by light. We measured a transition from normal to giant-number fluctuations. Our experiments are quantitatively described by simple numerical simulations. We show that the existence of the living crystals is intrinsically related to the out-of-equilibrium collisions of the self-propelled particles.

When small numbers of colloidal microspheres are attached to the surfaces of liquid emulsion droplets, removing fluid from the droplets leads to packings of spheres that minimize the second moment of the mass distribution. The structures of the packings range from sphere doublets, triangles, and tetrahedra to exotic polyhedra not found in infinite lattice packings, molecules, or minimum-potential energy clusters. The emulsion system presents a route to produce new colloidal structures and a means to study how different physical constraints affect symmetry in small parcels of matter.

The ability to design and assemble 3-dimensional structures from colloidal particles is limited by the absence of specific directional bonds. As a result, complex or low-coordination structures, common in atomic and molecular systems, are rare in the colloidal domain. Here we demonstrate a general method for creating the colloidal analogues of atoms with valence: colloidal particles with chemically functionalized patches that can form highly directional bonds.These "colloidal atoms" possess all the common symmetries-and some uncommon ones-characteristic of hybridized atomic orbitals, including sp, sp 2 , sp 3 , sp 3 d, sp 3 d 2 , and sp 3 d 3 . Functionalizing the patches with DNA with single-stranded sticky ends makes the interactions between patches on different particles programmable, specific, and reversible, thus facilitating the self-assembly of particles into "colloidal molecules," including "molecules" with triangular, tetrahedral, and other bonding symmetries. Because colloidal dynamics are slow, the kinetics of molecule formation can be followed directly by optical microscopy. These new colloidal atoms should enable the assembly of a rich variety of new micro-structured materials. 2 IntroductionThe past decade has seen an explosion in the kinds of colloidal particles that can be synthesized 1,2 , with many new shapes, such as cubes 3 , clusters of spheres 4-6 and dimpled particles 7,8 reported. Because the self-assembly of these particles is largely controlled by their geometry, only a few relatively simple crystals have been made: face-centered and body-centered cubic crystals and variants 9 . Colloidal alloys increase the diversity of structures [10][11][12] , but many structures remain difficult or impossible to make. For example, the diamond lattice, predicted more than 20 years ago to have a full 3-dimensional photonic band gap 13 , still cannot be made by colloidal self-assembly because it requires 4-fold coordination. Without directional bonds, such low-coordination states are unstable.

New functional materials can in principle be created using colloids that self-assemble into a desired structure by means of a programmable recognition and binding scheme. This idea has been explored by attaching 'programmed' DNA strands to nanometre- and micrometre- sized particles and then using DNA hybridization to direct the placement of the particles in the final assembly. Here we demonstrate an alternative recognition mechanism for directing the assembly of composite structures, based on particles with complementary shapes. Our system, which uses Fischer's lock-and-key principle, employs colloidal spheres as keys and monodisperse colloidal particles with a spherical cavity as locks that bind spontaneously and reversibly via the depletion interaction. The lock-and-key binding is specific because it is controlled by how closely the size of a spherical colloidal key particle matches the radius of the spherical cavity of the lock particle. The strength of the binding can be further tuned by adjusting the solution composition or temperature. The composite assemblies have the unique feature of having flexible bonds, allowing us to produce flexible dimeric, trimeric and tetrameric colloidal molecules as well as more complex colloidal polymers. We expect that this lock-and-key recognition mechanism will find wider use as a means of programming and directing colloidal self-assembly.

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Porous silica, niobia, and titania with three-dimensional structures patterned over multiple length scales were prepared by combining micromolding, polystyrene sphere templating, and cooperative assembly of inorganic sol-gel species with amphiphilic triblock copolymers. The resulting materials show hierarchical ordering over several discrete and tunable length scales ranging from 10 nanometers to several micrometers. The respective ordered structures can be independently modified by choosing different mold patterns, latex spheres, and block copolymers. The examples presented demonstrate the compositional and structural diversities that are possible with this simple approach.Several approaches are currently available for the preparation of ordered structures at different length scales. For example, organic molecular templates can be used to form crystalline zeolite-type structures with ordering lengths less than 3 nm (1); mesoporous materials with ordering lengths of 3 to 30 nm can be obtained using surfactants or amphiphilic block copolymers as structure-directing agents (2-7); the use of latex spheres yields macroporous materials with ordering lengths of 100 nm to 1 m (8 -13); and soft lithography can be used to make high-quality patterns and structures with lateral dimensions of about 30 nm to 500 m (14 -16 ). Despite all of these efforts in nanostructuring materials, the fabrication of hierarchically ordered structures at multiple length scales, such as seen in nature in diatoms (17), has remained an experimental challenge. Such materials are important both for the systematic fundamental study of structure-property relations and for their technological promise in applications such as catalysis, selective separations, sensor arrays, wave guides, miniaturized electronic and magnetic devices, and photonic crystals with tunable band gaps.Previously, micromolding has been used to form patterned mesoporous materials (18,19). These studies, however, used acidic aqueous conditions to carry out the cooperative self-assembly (20), which is disadvantageous because of the limited processibility of the aqueous solutions. Either noncontinuous films were formed (18) or an electric field was needed to guide pattern formation, which requires a nonconducting substrate (19). Latex spheres have also been used to make disordered macro-and mesoporous silica (9). We have developed a simple procedure for preparing hierarchically ordered structures by concurrently or sequentially combining micromolding, latex sphere templating, and cooperative assembly of hydrolyzed inorganic species (metal alkoxides, metal chlorides) and amphiphilic block copolymers. The materials generated from this process exhibit structural ordering at multiple discrete length scales (in this case, 10, 100, and 1000 nm). Patterned macro-and mesoporous materials of various compositions, including silica, niobia, and titania, were synthesized. Such multiple-scale structural organization makes it possible to tune the physical properties of the materials over a wide ...

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