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Using scaled-particle theory for binary mixtures of two-dimensional hardparticles with rotational freedom, we analyse the stability of nematic phasesand the demixing phase behaviour of a variety of mixtures, focussing on caseswhere at least one of the components consists of hard rectangles or hardsquares. A pure fluid of hard rectangles may exhibit, aside from the usualuniaxial nematic phase, an additional (tetratic) oriented phase, possessing twodirectors, which is the analogue of the biaxial or cubatic phases in three-dimensional fluids. There is computer simulation evidence that the tetraticphase might be stable with respect to phases with spatial order for rectangleswith low aspect ratios. As hard rectangles are mixed with other particles notpossessing stable tetratic order by themselves, the tetratic phase isdestabilised, via a first- or second-order phase transition, to uniaxialnematic or isotropic phases; for hard rectangles of low aspect ratio tetraticorder persists in a relatively large range of volume fractions. The order ofthese transitions depends on the particle geometry, dimensions andthermodynamic conditions of the mixture. The second component of the mixturehas been chosen to be hard discs or disco-rectangles, the geometry of which isdifferent from that of rectangles, leading to packing frustration and demixingbehaviour, or simply rectangles of different aspect ratio. These mixtures maybe good candidates for observing thermodynamically stable tetratic phases inmonolayers of hard particles. Finally, demixing between fluid(isotropic--tetratic or tetratic--tetratic) phases is seen to occur in mixturesof hard squares of different sizes when the size ratio is sufficiently large.

Demixing and orientational ordering in mixtures of rectangular particles