2023/05/12 by Philipp W. A. Schönhöfer, Kai Sun, Schönhöfer, Philipp W. A. +5 · 1 citation
Engineering · Materials Science · #Advanced Materials and Mechanics #FOS: Physical sciences #Modular Robots and Swarm Intelligence #Pickering emulsions and particle stabilization #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.2305.07786
openalex publication_date 2023/05/12 · openalex created_date 2023/05/17 · openalex updated_date 2026/08/01
Entropic self-assembly is governed by the shape of the constituent particles, yet a priori prediction of crystal structures from particle shape alone is non-trivial for anything but the simplest of space-filling shapes. At the same time, most polyhedra are not space-filling due to geometric constraints, but these constraints can be relaxed or even eliminated by sufficiently curving space. We show using Monte Carlo simulations that the majority of hard Platonic shapes self-assemble entropically into space-filling crystals when constrained to the surface volume of a 3-sphere. As we gradually decrease curvature to "flatten" space and compare the local morphologies of crystals assembling in curved and flat space, we show that the Euclidean assemblies can be categorized either as remnants of tessellations in curved space (tetrahedra and dodecahedra) or non-tessellation-based assemblies caused by large-scale geometric frustration (octahedra and icosahedra).