An example-H2O 1 Gaseous and liquid states 2 The liquid-gas phase transition 3 Spatial correlations in the liquid state 4 Ice-crystallized water 5 Broken symmetry and rigidity 6 Dislocations-topological defects 7 Universality of the water example 8 Fluctuations and spatial dimension 9 Overview of book 1 .3 Energies and potentials 1 Energy scales 2 Van der Waals attraction 3 Molecular hydrogen-the Heitler-London approach 20 4 Hard-sphere repulsion 22 5 Exchange interaction and magnetism 24 6 The hydrogen molecule, molecular orbitals, and bands in metals 25 Bibliography 28 References 28 2 Structure and scattering 29 2 .1 Elementary scattering theory-Bragg's law 29 2 .2 Photons, neutrons, or electrons 2 .3 The density Operator and its correlation functions 34 2 .4 Liquids and gases 1 Hard-sphere liquids 2 .5 Crystalline solids 1 Unit cells and the direct lattice 2 The reciprocal lattice vm Contents 3 Periodic functions 46 4 Bragg scattering 47

An example-H2O 1 Gaseous and liquid states 2 The liquid-gas phase transition 3 Spatial correlations in the liquid state 4 Ice-crystallized water 5 Broken symmetry and rigidity 6 Dislocations-topological defects 7 Universality of the water example 8 Fluctuations and spatial dimension 9 Overview of book 1 .3 Energies and potentials 1 Energy scales 2 Van der Waals attraction 3 Molecular hydrogen-the Heitler-London approach 20 4 Hard-sphere repulsion 22 5 Exchange interaction and magnetism 24 6 The hydrogen molecule, molecular orbitals, and bands in metals 25 Bibliography 28 References 28 2 Structure and scattering 29 2 .1 Elementary scattering theory-Bragg's law 29 2 .2 Photons, neutrons, or electrons 2 .3 The density Operator and its correlation functions 34 2 .4 Liquids and gases 1 Hard-sphere liquids 2 .5 Crystalline solids 1 Unit cells and the direct lattice 2 The reciprocal lattice vm Contents 3 Periodic functions 46 4 Bragg scattering 47

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.

Dense periodic arrays of holes and dots have been fabricated in a silicon nitride–coated silicon wafer. The holes are 20 nanometers across, 40 nanometers apart, and hexagonally ordered with a polygrain structure that has an average grain size of 10 by 10. Spin-coated diblock copolymer thin films with well-ordered spherical or cylindrical microdomains were used as the templates. The microdomain patterns were transferred directly to the underlying silicon nitride layer by two complementary techniques that resulted in opposite tones of the patterns. This process opens a route for nanometer-scale surface patterning by means of spontaneous self-assembly in synthetic materials on length scales that are difficult to obtain by standard semiconductor lithography techniques.

Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction ϕ = π/ √ 18 ≈ 0.74. It is also well-known that certain random (amorphous) jammed packings have ϕ ≈ 0.64. Here we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely; up to ϕ = 0.68 − 0.71 for spheroids with an aspect ratio close to that of M&M'S r Candies, and even approach ϕ ≈ 0.74 for general ellipsoids. We suggest that the higher 1

The interactions between charged colloidal particles with sufficient strength to cause crystallization are shown to be describable in terms of the usual Debye–Huckel approximation, but with a renormalized charge. The effective charge in general is smaller than the actual charge. We calculate the relationship between the actual charge and the renormalized charge by solving the Boltzmann–Poisson equation numerically in a spherical Wigner–Seitz cell. We then relate the numerical solutions and the effective charge to the osmotic pressure and the bulk modulus of the crystal. Our calculations also reveal that the renormalization of the added electrolyte concentration is negligible, so that the effective charge computations are useful even in the presence of salts.

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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