Comparison of the effect of geometric shape and Cross-section of rod particles in biaxial and homeotropic phase formation

In this article we investigate the effects of particles’ geometry on the uniaxial-biaxial and planar nematic-homeotropic phase transition of hard cylinders and hard rectangular rods between two structureless walls. The calculations are doneusing the Parsons-Lee theory into the Zwanzig approximation. These particles show a first order phase transition from planar to homeotropic that disappears at a critical point for both particles which this critical point is and for hard rectangular and cylinder rods, respectively. In addition, there is a second order phase transition called uniaxial planar nematic to biaxial planar nematicwhere there is three different optical axes for both shapes. This transition occurs at higher densities for the particles with smaller shape anisiorpies due to decreasing of excluded area inplanar order. Our calculations depict that both types of phase transitions take place at lower densities