the assembly and auto-assembly of hard arcuate particles in \(\mathbb{R}^2\)

Systems of hard major circular arcs show a (genuinely entropic) (auto-)assembly. Their densest-known optimal packings have a two-level positionally (and orientationally) ordered structure: first, a specific number of hard major circular arcs are organized into (anti)clockwise roundels; then, these chiral roundels are organized at the sites of a triangular lattice. Their phase behavior, in both the less dense uniform phase and the denser non-uniform phase,is characterized by auto-assembly: first, hard major circular arcs spontaneously organize into (anti)clockwise roundish aggregates, the sub-optimal version of the roundels; then, at higher density, these chiral roundish aggregates tend to organize into a globally non-chiral cluster hexagonal phase, the sub-optimal version of the densest-known packings. Their infinitesimal thinness makes one naturally inquire as to whether this (genuinely entropic) (auto-)assembly is conserved in correspondent hard arcuate particles of finite thinness. Even though finite thinness is detrimental, hard finitely-thin arcuate particles can still be organized and spontaneously organize into propeller-shaped roundish aggregates. Such an entropic auto-assembly should be observablein two-dimensional uni-component systems of colloidal arcuate particles.