Monte Carlo simulation of two-dimensional hard rectangles: Confinement effects

We use orientational-bias Monte Carlo simulations to examine the phase behavior of two-dimensional hard rectangles in the bulk and under confinement by hard walls. For all of the rod aspect ratios and area fractions studied, we find that confinement increases the degree of nematic ordering over the bulk, as confined rods tend to align their long axes parallel to the confining walls. The extent of nematic ordering increases as the separation between the confining walls decreases. If the aspect ratio of the rectangles is sufficiently large, they exhibit nematic ordering in both the bulk and under confinement, where the nematic director is set by the walls. Rods with a small aspect ratio are isotropic in the bulk and exhibit weak tetratic tendencies for sufficiently high densities. From studies of density profiles, angular distributions, and orientational correlation functions for confined, low-aspect-ratio rods, it is apparent that they align their long axes parallel to the wall in the near-wall region, where layering occurs for sufficiently high rod densities. However, confined rods with low aspect ratios still exhibit weak tetratic (isotropic) tendencies near the center of the confined region for all but the smallest wall separations. We note that although our studies probe the ordering of hard rectangles, the entropic tendencies that we observe here will be present for rods with energetic interactions. Thus, these studies serve as a general starting point for understanding and controlling the assembly of rods in two-dimensional confining geometries.