Entropically engineered fivefold and icosahedral twin clusters of colloidal shapes

Multiply twinned structures with fivefold or icosahedral symmetry have been extensively studied to control the growth and final shape of synthetic nanomaterials with those symmetries. Numerous methods have been proposed to control the formation of such structures, and complicated interparticle interactions or geometric confinement are widely considered to be essential. Here, we report the purely entropy-driven formation of fivefold and icosahedral twin clusters in hard particle Monte Carlo simulations. Hard truncated tetrahedra self-assemble into either cubic or hexagonal diamond crystals depending on the amount of edge and vertex truncation. By engineering particle shape to achieve a negligible free-energy difference between the cubic and hexagonal diamond phases, we show the formation of fivefold or icosahedral twin clusters in colloidal fluids through seed-assisted growth. The icosahedral twin cluster of hard truncated tetrahedra can be entropically stabilized within a dense fluid due to strong fluid-crystal interfacial tension, unlike hard spheres where interfacial tension is weak. Our findings show that twinning behavior and fluid-crystal interfacial properties in hard particle systems can be entropically engineered to obtain fivefold and icosahedral twin clusters.