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, typically takes a backseat to energy. Here, we demonstrate how to precisely engineer entropy to achieve desired colloidal crystals via particle shapes that, importantly, can be made in the laboratory. We demonstrate the inverse design of symmetric hard particles that assemble six different target colloidal crystals due solely to entropy maximization. Our approach efficiently samples 10⁸ particle shapes from 92- and 188-dimensional design spaces to discover thermodynamically optimal shapes. We design particle shapes that self-assemble into known crystals with optimized symmetry and thermodynamic stability, as well as new crystal structures with no known atomic or other equivalent.