  Scaled particle theory for a binary mixture of hard discorectangles and for a
binary mixture of hard rectangles is used to predict possible liquid-crystal
demixing scenarios in two dimensions. Through a bifurcation analysis from the
isotropic phase, it is shown that isotropic-nematic demixing is possible in
two-dimensional liquid-crystal mixtures composed of hard convex bodies. This
bifurcation analysis is tested against exact calculations of the phase diagrams
in the framework of the restricted-orientation two-dimensional model (Zwanzig
model). Phase diagrams of a binary mixture of hard discorectangles are
calculated through the parametrization of the orientational distribution
functions. The results show not only isotropic-nematic, but also
nematic-nematic demixing ending in a critical point, as well as an
isotropic-nematic-nematic triple point for a mixture of hard disks and hard
discorectangles.
