(15a) Entropically Engineered Assembly of Fivefold and Icosahedral Twin Clusters

Fivefold and icosahedral symmetries induced by multiply twinned crystal structures have been studied extensively for their role in influencing the shape of synthetic nanoparticles. Numerous methods have been proposed to control the formation of structures with fivefold and icosahedral symmetries. Solution chemistry in the case of atomic clusters, or geometric confinement in the case of colloidal spheres, are widely considered to be essential. Here, we report the purely entropy- driven formation of fivefold and icosahedral twinned clusters of particles in Monte Carlo simulation without geometric confinement. Hard truncated tetrahedra self-assemble into either cubic or hexagonal diamond crystals depending on the amount of edge and vertex truncation. By purposefully engineering particle shape to achieve a negligible entropy difference between the two diamond phases, we show that the formation of twin boundaries is easily induced. We use this strategy to induce the formation of fivefold and icosahedral twins in simulated hard particle colloidal fluids through seed-assisted growth. The fivefold twinned cluster in equilibrium with a dense fluid phase increases structural quality as it grows using an error-and-repair process. The icosahedral twinned clusters of hard truncated tetrahedra are entropically stabilized within a dense fluid due to a strong fluid-crystal interfacial tension arising from strong entropic bonding, unlike hard spheres where interfacial tension and entropic bonding are weak. Our findings provide a strategy for engineering twinning behavior in colloidal systems with and without explicit bonding elements between particles.