Phase equilibria in an athermal solution of platelike particles

A molecular frame lattice theory of athermal solutions of platelike particl es is presented. Steric repulsion between the particles is assumed to be th e sole interaction present in the system (the athermal limit). The theory i s developed for flat rectangular parallelepipeds, and examined in detail fo r two opposite shape anisotropy limits: rods and square boards. Numerical c alculations 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 boa rds x(r)(crit) is 3.742. For higher values of the ratio, a narrow concentra tion region of coexistence for the nematic and isotropic phases, which sepa rates the isotropic (low concentration) from the nematic (high concentratio n) solution, is found on dilution of each system.