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Emergent behaviors occur in a vast array of systems across many scales, andare of fundamental physical importance because of the intrinsic difficulty inlinking microscopic system properties to macroscopic behaviors. Here we studythe emergent self-assembly behavior of model systems of recently synthesizedfamilies of concave dimpled hard spheres, or lock-and-key colloids. We findthat as dimple size increases each family exhibits a crossover from a structurethat does not reflect the particle symmetry to one that does and, surprisingly,the point at which this crossover occurs is approximately independent of theparticle symmetry. Using a combination of numerical and analytic techniques westudy systems at infinite and finite pressure, and find different commoncontrol parameters in each limit. Our results suggest there exists a set ofexperimentally realizable colloidal systems that exhibit complex emergentbehaviors that can be traced to a common underlying microscopic controlparameter.

Crossover Behavior in the Packing and Assembly of Multivalent Lock-and-Key Colloids