Rounded hard squares confined in a circle

Abstract

Packing under confinement could generate rich ordered structures through entropic effects, which is a fundamental problem in condensed matter, biophysics and material science. The influence of confinement on the anisotropic hard particles—particularly regarding the emergence of topological defect structures—remains poorly understood. Recent studies have shown that granular rods confined within circular boundaries can cluster into square-like super-particles, forming four disclinations. In this study, we employ Monte Carlo simulations in the NPT ensemble to investigate how circular confinement influences the ordered structures of rounded-corner hard-squares with varying roundness. At low roundness, the system forms an integrated cross-shaped domain with tetratic order and four +1/4 disclinations in the corners, along with some column shifts. As roundness increases, we found a new partition structure, where particles self-assemble into six domains separated by six +1/4 disclinations and a central −1/2 disclination. Our findings reveal that the interplay between confinement geometry and colloid shape can drive entropy-governed structural transitions, offering new insights for the design of topological metamaterials.