Engineering Entropy for the Inverse Design of Colloidal Crystals from Hard Shapes

Throughout the physical sciences, entropy stands out as a pivotal but enigmatic concept that, in materials design, often takes a backseat to energy. Here, we demonstrate how to precisely engineer entropy to achieve desired colloidal crystals. We demonstrate the inverse design of hard particles that assemble six different target colloidal crystals due solely to entropy maximization. Our approach efficiently samples $10^8$ particle shapes from 88- and 192-dimensional design spaces to discover thermodynamically optimal shapes. We design particle shapes that self assemble known crystals with optimized thermodynamic stability, as well as new crystal structures with no known atomic or other equivalent.