Freezing in flat monolayers of soft spherocylinders

Lamellar or smectic phases often have an intricate intralamellar structure that remains scarcely understood from a microscopic viewpoint. In this work, we use molecular dynamics simulations to study the effect of volume exclusion on the phase transitions of a flat membrane of soft repulsive spherocylinders. With increasing rod packing, we identify liquid crystal and crystal phases and find that the disorder-order phase transition happens at a universal packing fraction (η ≈ 0.81), independent of the spherocylinder aspect ratio. We also confirm the existence of a small 2D hexatic region near the phase transition. The packing fraction associated with the phase transition is considerably higher than the well-known freezing transition of a hard disk fluid (η ≈ 0.7) to which one could naively map a system of near-parallel rods with co-planar mass centers. We attribute this difference to non-vanishing residual orientational entropy per rod. Our findings are corroborated by a simple theory based on a simple microscopic density functional theory of freezing of a two-dimensional rod fluid. The strength of the orientational fluctuations of the individual rods in our membranes exhibits a density scaling that differs from 3D bulk smectics. Our findings contribute to a qualitative understanding of liquid crystal phase stability in strong planar confinement and engage with recent experimental explorations involving nanorods on 2D substrates.