Guangnan Meng

The free-energy landscape of clusters of attractive hard spheres.

Packing Puzzle The packing of a large number of spheres is a well-studied problem with maximal packing based on the arrangement of nearest neighbors. With much smaller numbers of particles, it is the free energy that governs which packing arrangements dominate. Meng et al. (p. 560; see the Perspective by Crocker) looked at the assembly of colloidal clusters where the number of particles was limited from 2 to 10. For five particles or fewer, only one packing arrangement was found. For six or more particles, while a number of similar energy structures could form, the probability of formation was biased toward those structures with the greater number of nearest-neighbor connections. Entropic effects favor the formation of small clusters of colloidal particles that have lower symmetry. The study of clusters has provided a tangible link between local geometry and bulk condensed matter, but experiments have not yet systematically explored the thermodynamics of the smallest clusters. Here we present experimental measurements of the structures and free energies of colloidal clusters in which the particles act as hard spheres with short-range attractions. We found that highly symmetric clusters are strongly suppressed by rotational entropy, whereas the most stable clusters have anharmonic vibrational modes or extra bonds. Many of these clusters are subsets of close-packed lattices. As the number of particles increases from 6 to 10, we observe the emergence of a complex free-energy landscape with a small number of ground states and many local minima.

Elastic instability of a crystal growing on a curved surface

Curving Crystals When a material with a different set of lattice parameters is grown on the surface of a crystal of a second material, the stresses at the interface can affect the growing crystal. Meng et al. (p. 634) studied the growth of colloidal crystals on top of a curved water droplet. Owing to the elastic stress caused by the bending of the crystal, strong distortions occurred in the growing crystal, but, nonetheless, large single-crystalline domains with no topological defects were formed. Constant-background Gaussian curvature alters crystal growth and favors the formation of anisotropic, ribbon-like domains. Although the effects of kinetics on crystal growth are well understood, the role of substrate curvature is not yet established. We studied rigid, two-dimensional colloidal crystals growing on spherical droplets to understand how the elastic stress induced by Gaussian curvature affects the growth pathway. In contrast to crystals grown on flat surfaces or compliant crystals on droplets, these crystals formed branched, ribbon-like domains with large voids and no topological defects. We show that this morphology minimizes the curvature-induced elastic energy. Our results illustrate the effects of curvature on the ubiquitous process of crystallization, with practical implications for nanoscale disorder-order transitions on curved manifolds, including the assembly of viral capsids, phase separation on vesicles, and crystallization of tetrahedra in three dimensions.

Design and Synthesis of Model Transparent Aqueous Colloids with Optimal Scattering Properties

We demonstrate the synthesis and self-assembly of colloidal particles with independently controlled diameter and scattering cross section. We show that it is possible to prepare bulk colloidal suspensions that are nearly transparent in water, while the particles themselves can be individually resolved using optical microscopy. These particles may be ideal model colloids for real-space studies of self-assembly in aqueous media. Moreover, they illustrate the degree to which the optical properties of colloids can be engineered through straightforward chemistry.