A Microscopic Theory of Entropic Bonding for Colloidal Crystal Prediction

Advances in the synthesis of hard polyhedral particles have directed attention towards their usage in self-assembly as they give rise to a wide range of interesting morphologies. Yet no classical model exists for that allows us to predict the assembly behaviors for anisotropic particles. As a result, theoretical descriptions, based purely on a particle's geometry, that can systematically describe the microscopic origins for the directional entropic forces between particles are of significant interest. Here, we present one such theory for hard particle shapes that self-assemble solely through entropy maximization into colloidal crystals, including those of remarkable complexity. This microscopic theory of entropic bonding employs the use of shape orbitals to enable a priori prediction of thermodynamically preferred colloidal crystal structures, in good agreement with previously published simulations across multiple systems.