Phase behavior of two-dimensional Brownian systems of corner-rounded hexagons

Investigations into the phase behavior of Brownian systems of nonspherical colloids have received considerable attention because these systems can exhibit very rich self-assembled structures, some of which have potential for applications. In this work, we explore the phase behavior of corner-rounded hexagons in two dimensions, both through experiments and Monte Carlo (MC) simulations. Our experiments, using lithographically shape-designed hexagons, which have corner-rounded vertices and nearly hard in-plane interactions, reveal three different solid phases for increasing particle area fraction ₀: hexagonal rotator crystal (RX), hexagonal crystal (HX), and frustrated hexagonal crystal (FHX). In the RX phase, hexagons form a hexagonal lattice, but they are randomly oriented and their rotations are ergodic. In the HX phase, hexagons orient uniformly on average, but their rotations are still ergodic via slower hopping motion. In the FHX phase, all hexagons are uniformly oriented, but their rotations are highly bound and nonergodic. MC simulation results on matching rounded hexagons confirm this experimentally observed sequence of phases. Using simulations, we increase the corner roundness and show that the molecular-orientational order decreases at fixed ₀. Our results provide insights into controlling the large-scale self-assembly of spatially and orientationally ordered two-dimensional arrays of colloids through particle shape design and crowding conditions.