Colloidal matter: Packing, geometry, and entropy

BACKGROUND Colloids consist of solid or liquid particles, each about a few hundred nanometers in size, dispersed in a fluid and kept suspended by thermal fluctuations. Whereas natural colloids are the stuff of paint, milk, and glue, synthetic colloids with well-controlled size distributions and interactions are a model system for understanding phase transitions. These colloids can form crystals and other phases of matter seen in atomic and molecular systems, but because the particles are large enough to be seen under an optical microscope, the microscopic mechanisms of phase transitions can be directly observed. Furthermore, their ability to spontaneously form phases that are ordered on the scale of visible wavelengths makes colloids useful building blocks for optical materials such as photonic crystals. Because the interactions between particles can be altered and the effects on structure directly observed, experiments on colloids offer a controlled approach toward understanding and harnessing self-assembly, a fundamental topic in materials science, condensed-matter physics, and biophysics. ADVANCES In the past decade, our understanding of colloidal self-assembly has been transformed by experiments and simulations that subject colloids to geometrical or topological constraints, such as curved surfaces, fields, or the shapes of the particles themselves. In particular, advances in the synthesis of nonspherical particles with controlled shape and directional interactions have led to the discovery of structural transitions that do not occur in atoms or molecules. As a result, colloids are no longer seen as a proxy for atomic systems but as a form of matter in their own right. The wide range of self-assembled structures seen in colloidal matter can be understood in terms of the interplay between packing constraints, interactions, and the freedom of the particles to move—in other words, their entropy. Ongoing research attempts to use geometry and entropy to explain not only structure but dynamics as well. Central to this goal is the question of how entropy favors certain local packings. The incompatibility of these locally favored structures with the globally favored packing can be linked to the assembly of disordered, arrested structures such as gels and glasses. OUTLOOK We are just beginning to explore the collective effects that are possible in colloidal matter. The experimentalist can now control interactions, shapes, and confinement, and this vast parameter space is still expanding. Active colloidal systems, dispersions of particles driven by intrinsic or extrinsic energy sources rather than thermal fluctuations, can show nonequilibrium self-organization with a complexity rivaling that of biological systems. We can also expect new structural transitions to emerge in “polygamous” DNA-functionalized colloids, which have no equivalent at the molecular scale. New frameworks are needed to predict how all of these variables—confinement, activity, and specific interactions—interact with packing constraints to govern both structure and dynamics. Such frameworks would not only reveal general principles of self-assembly but would also allow us to design colloidal particles that pack in prescribed ways, both locally and globally, thereby enabling the robust self-assembly of optical materials.