Phase behavior of hard circular arcs

By using Monte Carlo numerical simulation, this work investigates the phase behavior of systems of hard infinitesimally thin circular arcs, from an aperture angle θ→0 to an aperture angle θ→2π, in the two-dimensional Euclidean space. Except in the isotropic phase at lower density and in the (quasi)nematic phase, in the other phases that form, including the isotropic phase at higher density, hard infinitesimally thin circular arcs autoassemble to form clusters. These clusters are either filamentous, for smaller values of θ, or roundish, for larger values of θ. Provided the density is sufficiently high, the filaments lengthen, merge, and straighten to finally produce a filamentary phase while the roundels compact and dispose themselves with their centers of mass at the sites of a triangular lattice to finally produce a cluster hexagonal phase.