Phase equilibria in an athermal solution of platelike particles

A molecular frame lattice theory of athermal solutions of platelike particles is presented. Steric repulsion between the particles is assumed to be the sole interaction present in the system (the athermal limit). The theory is developed for flat rectangular parallelepipeds, and examined in detail for two opposite shape anisotropy limits: rods and square boards. Numerical calculations show that in a pure system of either long rods or square boards, a nematic phase is formed once the shape anisotropy exceeds some critical value: for rods the critical aspect ratio x(d)(crit) is 8.019, and for boards x(r)(crit) is 3.742. For higher values of the ratio, a narrow concentration region of coexistence for the nematic and isotropic phases, which separates the isotropic (low concentration) from the nematic (high concentration) solution, is found on dilution of each system.