A generic equation of state for liquid crystalline phases of hard-oblate particles

A generic equation of state (EoS) is developed for the hard cylindrical-disc model to describe the isotropic phase of hard-oblate particles introducing a correction parameter to incorporate the negative contributions from higher-order virial coefficients. The isotropic-nematic-columnar phase diagram of hard cut-sphere fluids is investigated by combining the new EoS with a scaled Onsager free energy for the nematic phase and an extended cell theory for the columnar phase. By mapping the virial coefficients of oblate spherocylinders on to those of cylindrical discs (which are known algebraically), the new generic EoS is used to describe the isotropic and nematic phases of hard oblate spherocylinder particles. The predictions of the generic EoS are compared with available simulation data.