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Using the classical density functional theory of freezing and Monte Carlocomputer simulations, we explore the liquid-crystalline phase behavior of hardrectangles on flat and cylindrical manifolds. Moreover, we study the effect ofa static external field which couples to the rectangles' orientations, aligningthem towards a preferred direction. In the flat and field-free case, the bulkphase diagram involves stable isotropic, nematic, tetratic, and smectic phasesdepending on the aspect ratio and number density of the particles. The externalfield shifts the transition lines significantly and generates a binematic phaseat the expense of the tetratic phase. On a cylindrical manifold, we observetilted smectic-like order, as obtained by wrapping a smectic layer around acylinder. We find in general good agreement between our density functionalcalculations and particle-resolved computer simulations and mention possiblesetups to verify our predictions in experiments.

Liquid crystals of hard rectangles on flat and cylindrical manifolds