Monte Carlo study of the isotropic and nematic phases of infinitely thin hard platelets

Abstract

We present the results of a detailed Monte Carlo study of the phase diagram of infinitely thin hard platelets. A weak first order isotropicnematic transition is observed. The equation of state in the isotropic regime is compared with several current theories, none of which is found to be fully satisfactory. The density dependence of the nematic order parameter is found to be compatible with a ‘critical’ exponent β=0·25. A study of the fluctuations of the order parameter in the isotropic phase casts doubt on the applicability of the Landau-de Gennes expression for the free energy. We observe that the relation between the nematic order parameters <P ₂> and <P ₄> is compatible with the predictions of mean-field theory. Practical aspects of the computation are discussed. A novel method to compute the pressure in a constant-volume Monte Carlo run is presented.