Phase transitions significantly differ between 2D and 3D systems, but the influence of dimensionality on the glass transition is unresolved. We use microscopy to study colloidal systems as they approach their glass transitions at high concentrations and find differences between two dimensions and three dimensions. We find that, in two dimensions, particles can undergo large displacements without changing their position relative to their neighbors, in contrast with three dimensions. This is related to Mermin-Wagner long-wavelength fluctuations that influence phase transitions in two dimensions. However, when measuring particle motion only relative to their neighbors, two dimensions and three dimensions have similar behavior as the glass transition is approached, showing that the long-wavelength fluctuations do not cause a fundamental distinction between 2D and 3D glass transitions.colloidal glass transition | dimensionality | long-wavelength fluctuations | phase transition | two-dimensional physics I f a liquid can be cooled rapidly to avoid crystallization, it can form into a glass: an amorphous solid. The underlying cause of the glass transition is far from clear, although there are a variety of theories (1-3). One recent method of understanding the glass transition has been to simulate the glass transition in a variety of dimensions (including four dimensions or higher) (4-8). Indeed, the glass transition is often thought to be similar in two and three dimensions (9, 10), and in simple simulation cases such as hard particles, one might expect that dimensionality plays no role. As a counterargument, 2D and 3D fluid mechanics are qualitatively quite different (11). Likewise, melting is also known to be qualitatively different in two and three dimensions (12-15).Recent simulations give evidence that the glass transition is also quite different in two and three dimensions (4, 5). In particular, Flenner and Szamel (4) simulated several different glassforming systems in two and three dimensions and found that the dynamics of these systems were fundamentally different in two and three dimensions. They examined translational particle motion (motion relative to a particle's initial position) and bond-orientational motion (topological changes of neighboring particles). They found that, in two dimensions, these two types of motion became decoupled near the glass transition. In these cases, particles could move appreciable distances but did so with their neighbors, so that their local structure changed slowly. In three dimensions, this was not the case; translational and bondorientational motions were coupled. They additionally observed that the transient localization of particles well known in three dimensions was absent in the 2D data. To quote Flenner and Szamel, "these results strongly suggest that the glass transition in two dimensions is different from in three dimensions."In this work, we use colloidal experiments to test dimensiondependent dynamics approaching the glass transition. Colloidal samples at high concen...

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.

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.

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 (KTHNY). 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 KTHNY theory. By measuring the dynamic Lindemann parameter, γL(τ ), and the non-Gaussian parameter, α2(τ ), of the displacements of the particles relative to their neighbors, we show that each of the phases displays distinctive dynamical behavior.

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