  We extend our previous work on monolayers of uniaxial particles [J. Chem.
Phys. 140, 204906 (2014)] to study the effect of particle biaxiality on the
phase behavior of liquid-crystal monolayers. Particles are modelled as
board-like hard bodies with three different edge lengths
$\sigma_1\geq\sigma_2\geq\sigma_3$, and use is made of the
restricted-orientation approximation (Zwanzig model). A density-functional
formalism based on the fundamental-measure theory is used to calculate phase
diagrams for a wide range of values of the largest aspect ratio
($\kappa_1=\sigma_1/\sigma_3\in[1,100]$). We find that particle biaxiality in
general destabilizes the biaxial nematic phase already present in monolayers of
uniaxial particles. While plate-like particles exhibit strong biaxial ordering,
rod-like ones with $\kappa_1>21.34$ exhibit reentrant uniaxial and biaxial
phases. As particle geometry is changed from uniaxial- to increasingly
biaxial-rod-like, the region of biaxiality is reduced, eventually ending in a
critical-end point. For $\kappa_1>60$, a density gap opens up in which the
biaxial nematic phase is stable for any particle biaxiality. Regions of the
phase diagram where packing-fraction inversion occurs (i.e. packing fraction is
a decreasing function of density) are found. Our results are compared with the
recent experimental studies on nematic phases of magnetic nanorods.
