  The effect of confinement on the phase behaviour and structure of fluids made
of biaxial hard particles (cuboids) is examined theoretically by means of
Onsager second-order virial theory in the limit where the long particle axes
are frozen in a mutually parallel configuration. Confinement is induced by two
parallel planar hard walls (slit-pore geometry), with particle long axes
perpendicular to the walls (perfect homeotropic anchoring). In bulk, a
continuous nematic-to-smectic transition takes place, while shape anisotropy in
the (rectangular) particle cross section induces biaxial ordering. As a
consequence, four bulk phases, uniaxial and biaxial nematic and smectic phases,
can be stabilised as the cross-sectional aspect ratio is varied. On confining
the fluid, the nematic-to-smectic transition is suppressed, and either uniaxial
or biaxial phases, separated by a continuous trasition, can be present. Smectic
ordering develops continuously from the walls for increasing particle
concentration (in agreement with the supression of nematic-smectic second order
transition at confinement), but first-order layering transitions, involving
structures with n and n+1 layers, arise in the confined fluid at high
concentration. Competition between layering and uniaxial-biaxial ordering leads
to three different types of layering transitions, at which the two coexisting
structures can be both uniaxial, one uniaxial and another biaxial, or both
biaxial. Also, the interplay between molecular biaxiality and wall interactions
is very subtle: while the hard wall disfavours the formation of the biaxial
phase, biaxiality is against the layering transitions, as we have shown by
comparing the confined phase behaviour of cylinders and cuboids. The predictive
power of Onsager theory is checked and confirmed by performing some
calculations based on fundamental-measure theory.
