A simulation study on the phase behavior of hard rhombic platelets

Using Monte Carlo simulations, we investigate the phase behavior of hard rhombic platelets as a function of the thickness of the platelets, T. The phase diagram displays a columnar phase and a crystal phase in which the platelets are stacked in columns that are arranged in a two-dimensional lattice. We find that the shape of the platelets determines the symmetry of the two-dimensional lattice, i.e., rhombic platelets form an oblique columnar phase and a simple monoclinic crystal phase. For sufficiently thick platelets, i.e., for a thickness-to-length ratio $T / L > 0.17$⁠, we find only an isotropic fluid, an oblique columnar phase, and a monoclinic crystal phase. Surprisingly, for an intermediate plate thickness, $0.083 < T / L < 0.17$⁠, we also find a region in between the isotropic (or nematic) phase and the columnar phase, where the smectic phase is stable. For sufficiently thin platelets, $T / L < 0.13$⁠, the phase diagram displays a nematic phase. With the exception of the smectic phase, our results resemble the phase behavior of discotic particles. Our results may guide the synthesis and future experiments on rhombic nanoplatelets.