Programmable Potentials Choreograph Defects in a Colloidal Crystal Shell.

Crystallization on spherical surfaces is obliged by topology to induce lattice defects. But controlling the organization of such defects remains a great challenge due to the long-range constraints of the curved geometry. Here, we report on DNA-coated colloids whose programmable interaction potentials can be used to regulate the arrangement of defects and even achieve perfect icosahedral order on a sphere. Combined simulations and theoretical analysis show how the potential can be tuned by changing the temperature, thereby controlling the number of defects. An explicit expression for the effective potential is derived, allowing us to distinguish the effects of entropic repulsion and enthalpic attraction. Altogether, the present findings provide insights into the physics of crystallization on curved spaces and may be used for designing desired crystal geometries.