Exact sum rules and geometrical packing effects in the system of hard rods near a hard wall in three dimensions

Abstract

Exact statistical mechanical sum rules for the pressure p and surface grand potential Θ s of system of hard-rods near a hard wall are derived. The system is studied in the nonlocal version of Onsager low-density approximation. Θ s , the equilibrium density and the nematic order parameter profiles at the bulk nematic-isotropic coexistence are calculated. The nonlocal approximation is shown to satisfy the pressure sum rule. From the behaviour of the profiles we conclude that the geometrical packing effects manifest themselves most strongly in the density profile and rather weakly in the order parameter profiles.