Crystallization of non-convex colloids: the roles of particle shape and entropy

Particle shape and entropy play critical roles in order-disorder transitions; examples include liquid crystals and crystals formed from hard polyhedra. With few exceptions, colloidal crystals reported in the literature form from convex particles, for which the roles of particle shape and entropy are well explored. However, recent experimental work has shown that a cubic diamond lattice, elusive but long sought after for its wide and robust photonic band gap, can be assembled from non-convex particles. Here, we use simulations to explore the crystallization of colloidal diamond from non-convex tetrahedral-lobed patchy particles (TLPPs). Our results show how the entropic cost of binding, measured using umbrella sampling, can be tuned through subtle changes to the particle geometry. Geometric constraints, uniquely provided by the particle's non-convex features, select the staggered bond conformation required for cubic diamond. These constraints and the entropy associated with them can be geometrically tuned to vary the flexibility of the bonds. Depending on the particle geometry, TLPPs form liquid, diamond, or amorphous structures. Importantly, all geometrical parameters can be controlled in experiments, which should lead to larger crystals with less disorder, improving the resulting photonic band gap.