Freezing on a sphere.

The best understood crystal ordering transition is that of two-dimensional freezing, which proceeds by the rapid eradication of lattice defects as the temperature is lowered below a critical threshold. But crystals that assemble on closed surfaces are required by topology to have a minimum number of lattice defects, called disclinations, that act as conserved topological charges-consider the 12 pentagons on a football or the 12 pentamers on a viral capsid. Moreover, crystals assembled on curved surfaces can spontaneously develop additional lattice defects to alleviate the stress imposed by the curvature. It is therefore unclear how crystallization can proceed on a sphere, the simplest curved surface on which it is impossible to eliminate such defects. Here we show that freezing on the surface of a sphere proceeds by the formation of a single, encompassing crystalline 'continent', which forces defects into 12 isolated 'seas' with the same icosahedral symmetry as footballs and viruses. We use this broken symmetry-aligning the vertices of an icosahedron with the defect seas and unfolding the faces onto a plane-to construct a new order parameter that reveals the underlying long-range orientational order of the lattice. The effects of geometry on crystallization could be taken into account in the design of nanometre- and micrometre-scale structures in which mobile defects are sequestered into self-ordered arrays. Our results may also be relevant in understanding the properties and occurrence of natural icosahedral structures such as viruses.

Random Close Packing as a Dynamical Phase Transition.

Sphere packing is an ancient problem. The densest packing is known to be a face-centered cubic (FCC) crystal, with space-filling fraction ϕ_{FCC}=π/sqrt[18]≈0.74. The densest "random packing," random close packing (RCP), is yet ill defined, although many experiments and simulations agree on a value ϕ_{RCP}≈0.64. We introduce a simple absorbing-state model, biased random organization (BRO), which exhibits a Manna class dynamical phase transition between absorbing and active states that has as its densest critical point ϕ_{c_{max}}≈0.64≈ϕ_{RCP} and, like other Manna class models, is hyperuniform at criticality. The configurations we obtain from BRO appear to be structurally identical to RCP configurations from other protocols. This leads us to conjecture that the highest-density absorbing state for an isotropic biased random organization model produces an ensemble of configurations that characterizes the state conventionally known as RCP.

Lindemann Unjamming of Emulsions.

We study the bulk and shear elastic properties of barely-compressed, "athermal" emulsions and find that the rigidity of the jammed solid fails at remarkably large critical osmotic pressures. The minuscule yield strain and similarly small Brownian particle displacement of solid emulsions close to this transition suggests that this catastrophic failure corresponds to a plastic-entropic instability: the solid becomes too soft and weak to resist the thermal agitation of the droplets that compose it and fails. We propose a modified Lindemann stability criterion to describe this transition and derive a scaling law for the critical osmotic pressure that agrees quantitatively with experimental observations.

Hyperuniform Structures Formed by Shearing Colloidal Suspensions.

In periodically sheared suspensions there is a dynamical phase transition, characterized by a critical strain amplitude γ_{c}, between an absorbing state where particle trajectories are reversible and an active state where trajectories are chaotic and diffusive. Repulsive nonhydrodynamic interactions between "colliding" particles' surfaces have been proposed as a source of this broken time reversal symmetry. A simple toy model called random organization qualitatively reproduces the dynamical features of this transition. Random organization and other absorbing state models exhibit hyperuniformity, a strong suppression of density fluctuations on long length scales quantified by a structure factor S(q→0)∼q^{α} with α>0, at criticality. Here we show experimentally that the particles in periodically sheared suspensions organize into structures with anisotropic short-range order but isotropic, long-range hyperuniform order when oscillatory shear amplitudes approach γ_{c}.

Self-faceting of emulsion droplets as a route to solid icosahedra and other polyhedra.

HYPOTHESIS: Temperature-controlled self-faceting of liquid droplets has been recently discovered in surfactant-stabilized alkane-in-water emulsions. We hypothesize that similar self-faceting may occur in emulsion droplets of UV-polymerizable linear hydrocarbons. We further hypothesize that the faceted droplet shapes can be fixed by UV-initiated polymerization, thus providing a new route towards the production of solid polyhedra. EXPERIMENTS: Temperature-induced shape variations were studied by optical microscopy in micron-size emulsion droplets of UV-polymerizable alkyl acrylate. When polymerized, the resultant solid particles' 3D shape and internal structure were determined by combined scanning electron microscopy (SEM) and focused ion beam (FIB) slicing. The SEM and FIB nanoscale resolution provided a far greater detail imaging than that achievable for the liquid droplets, which could only be studied by optical microscopy, severely limiting their 3D shape determination. FINDINGS: We demonstrate the formation of solid icosahedra, polyhedral platelets, and rods of hitherto-unreported sizes, well below the 3D-printing resolution (∼20µm). The presence of icosahedral shapes and the absence of any resolvable internal structure at sub-µm length scales, are in line with the surface-freezing-driven mechanism proposed for the faceting phenomenon. Further development of the method presented here may allow large-quantity production of shaped micron- to nano- sized colloidal building blocks for 3D metamaterials and other applications.

Phase behavior of charged colloids at a fluid interface.

We study the phase behavior of a system of charged colloidal particles that are electrostatically bound to an almost flat interface between two fluids. We show that, despite the fact that our experimental system consists of only 10^{3}-10^{4} particles, the phase behavior is consistent with the theory of melting due to Kosterlitz, Thouless, Halperin, Nelson, and Young. Using spatial and temporal correlations of the bond-orientational order parameter, we classify our samples into solid, isotropic fluid, and hexatic phases. We demonstrate that the topological defect structure we observe in each phase corresponds to the predictions of Kosterlitz-Thouless-Halperin-Nelson-Young theory. By measuring the dynamic Lindemann parameter γ_{L}(τ) and the non-Gaussian parameter α_{2}(τ) of the displacements of the particles relative to their neighbors, we show that each of the phases displays distinctive dynamical behavior.

Precise colloids with tunable interactions for confocal microscopy.

Model colloidal systems studied with confocal microscopy have led to numerous insights into the physics of condensed matter. Though confocal microscopy is an extremely powerful tool, it requires a careful choice and preparation of the colloid. Uncontrolled or unknown variations in the size, density, and composition of the individual particles and interactions between particles, often influenced by the synthetic route taken to form them, lead to difficulties in interpreting the behavior of the dispersion. Here we describe the straightforward synthesis of copolymer particles which can be refractive index- and density-matched simultaneously to a non-plasticizing mixture of high dielectric solvents. The interactions between particles are accurately tuned by surface grafting of polymer brushes using Atom Transfer Radical Polymerization (ATRP), from hard-sphere-like to long-ranged electrostatic repulsion or mixed charge attraction. We also modify the buoyant density of the particles by altering the copolymer ratio while maintaining their refractive index match to the suspending solution resulting in well controlled sedimentation. The tunability of the inter-particle interactions, the low volatility of the solvents, and the capacity to simultaneously match both the refractive index and density of the particles to the fluid opens up new possibilities for exploring the physics of colloidal systems.

Soft Poly(dimethylsiloxane) Elastomers from Architecture-Driven Entanglement Free Design.

Soft, solvent-free poly(dimethylsiloxane) elastomers are fabricated by a one-step process via crosslinking bottlebrush polymers. The bottlebrush architecture prevents the formation of entanglements, resulting in elastomers with precisely controllable low moduli from 1 to 100 kPa, below the lower limit of traditional elastomers; moreover, the solvent-free nature enables their negligible adhesiveness compared to commercially available silicone products of similar stiffness.

Charged hydrophobic colloids at an oil-aqueous phase interface.

Hydrophobic poly(methyl methacrylate) (PMMA) colloidal particles, when dispersed in oil with a relatively high dielectric constant, can become highly charged. In the presence of an interface with a conducting aqueous phase, image-charge effects lead to strong binding of colloidal particles to the interface, even though the particles are wetted very little by the aqueous phase. We study both the behavior of individual colloidal particles as they approach the interface and the interactions between particles that are already interfacially bound. We demonstrate that using particles which are minimally wetted by the aqueous phase allows us to isolate and study those interactions which are due solely to charging of the particle surface in oil. Finally, we show that these interactions can be understood by a simple image-charge model in which the particle charge q is the sole fitting parameter.

Diffusivity of asphaltene molecules by fluorescence correlation spectroscopy.

Using fluorescence correlation spectroscopy (FCS) we measure the translational diffusion coefficient of asphaltene molecules in toluene at extremely low concentrations (0.03-3.0 mg/L): where aggregation does not occur. We find that the translational diffusion coefficient of asphaltene molecules in toluene is about 0.35 x 10(-5) cm(2)/s at room temperature. This diffusion coefficient corresponds to a hydrodynamic radius of approximately 1 nm. These data confirm previously estimated size from rotational diffusion studied using fluorescence depolarization. The implication of this concurrence is that asphaltene molecular structures are monomeric, not polymeric.