The assembly and auto-assembly of hard arcuate particles in R2

Abstract

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 optimal 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, 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 prompts one to inquire as to whether this (genuinely entropic) (auto-)assembly is conserved in systems of correspondent hard arcuate particles of finite thinness. Even though finite thinness is detrimental, a number of hard finitely thin arcuate particles can still be organized by analytic constructions and spontaneously organize in Monte Carlo packing calculations into propeller-like roundish aggregates. Thus, instances of such an auto-assembly are observed in statistical–mechanical Monte Carlo numerical simulations of a sufficiently dense system of hard finitely thin arcuate particles but the diversity and persistency of the defective interlocks between the hard finitely thin arcuate particles and the irregularity of their roundish aggregates result in this system remaining in a uniform state.