  Two-dimensional ensembles of bent-core shaped molecules attain at highly
orienting surfaces liquid crystalline structures characteristic mostly for
lamellar chiral or nonchiral antiferroelectric order. Here, using the
Onsager-type of density functional theory supplemented by constant-pressure
Monte-Carlo (MC) simulation we investigate the role of excluded-volume
interactions in stabilizing different structures in monolayers filled with
bent-shaped molecules. We study influence of molecular features, like the apex
angle, thickness of the arm and the type of the arm edges on the stability of
layered structures. For simple molecular shapes taken the observed phases are
dominated by the lamellar antiferroelectric type as observed experimentally,
but a considerable sensitivity of the ordering to details of the molecular
shape is found for order parameters and wave vectors of the structures.
Interestingly, for large opening angles and not too thick molecules a window of
stable nematic splay-bend phase is shown to exist. The presented theory models
equilibrium properties of bent-core liquid crystals subjected to strong planar
anchoring, in the case when details of the surface are of secondary importance.
