Colloidal Crystals, Quasicrystals and the Entropic Bond

Entropy, information, and order are important concepts in many fields, relevant for materials to machines, for biology to economics. Entropy is typically associated with disorder; yet, the counterintuitive notion that particles with no interactions other than excluded volume might self-assemble from a fluid phase into an ordered crystal has been known since the mid-20th century. First predicted for rods, and then spheres, the ordering of hard shapes by nothing more than crowding is now well established. In recent years, surprising discoveries of entropically ordered colloidal crystals of extraordinary structural complexity have been predicted by computer simulation and observed in the laboratory. Colloidal quasicrystals, clathrate structures, and structures with large and complex unit cells typically associated with metal alloys, can all self-assemble from a disordered phase of identical particles due solely to entropy maximization. These findings demonstrate that entropy alone can produce order and complexity beyond that previously imagined. They also suggest that, in situations where other interactions are present, the role of entropy in producing order may be underestimated. We present the latest discoveries for entropic systems of identical particles, including a Bergman-like phase with a 432-particle unit cell, and fluid-fluid transitions preceding crystallization that are reminiscent of liquid-liquid phase separation in water, proteins, and even within cells. To understand these phenomena, and in loose analogy with traditional chemical bonds that produce order in atomic and molecular substances, we introduce the notion of the entropic bond.