Double‐Lattice Packing of Pentagonal Gold Bipyramids in Supercrystals with Triclinic Symmetry
Résumé
Pentagonal packing is a long-standing issue and a rich mathematical topic, brought to the fore by recent progress in nanoparticle design. Gold pentagonal bipyramids combine fivefold symmetry and anisotropy and their section varies along the length. In this work, colloidal supercrystals of pentagonal gold bipyramids are obtained in a compact arrangement that generalizes the optimal packing of regular pentagons in the plane. Multimodal investigations reveal a two-particle unit cell with triclinic symmetry, a lower symmetry than that of the building blocks. Monte Carlo computer simulations show that this lattice achieves the densest possible packing. Going beyond pentagons, further simulations show an odd–even effect of the number of sides on the packing: odd-sided bipyramids are non-centrosymmetric and require the double-lattice arrangement to recover inversion symmetry. The supercrystals display a facet-dependent optical response that is promising for sensing, metamaterials applications, and for fundamental studies of self-assembly processes
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