Entropically Patchy Particles

Directional entropic forces that cause particle alignment have recently been proposed in systems of hard polyhedra that order into crystals. Here we provide a means of quantifying these forces and find them to be of the order of a few kT in monodisperse systems of hard particles. Based on the similarity of the anisotropy of these directional entropic forces to the directional enthalpic forces present in systems of enthalpically patchy particles, we propose and show that these forces originate from "entropic patches," which are features of particle shape that promote local dense packing. Using the notion of entropic patches, we engineer particle shape to target the assembly of specific crystal structures. We show that this procedure can be generalized as anisotropy dimensions, similar to those exploited for enthalpically patchy particles, thereby mapping out a large design space for colloidal self assembly with entropy as the sole mechanism underlying ordering. Our techniques also allow the quantification of the role of shape in systems where both enthalpic and directional entropic forces are at play.