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Based on an equilibrium thermodynamic scheme, this work studies the separation of the Helmholtz free energy of a hard-disk system into its positional and orientational contributions. For the positional part, an accurate two dimensional version of the Carnahan-Starling equation of state is proposed, while a simple ansatz of the one particle partition function for the orientational part is proposed. The latter expression, which contains information about the probability of the norm of the six-fold orientational order parameter, is obtained through molecular dynamics simulations. Perhaps due to finite size effects, the ordering of the fluid is not a sudden phenomenon: the fluid-hexatic phase transition is preceded by a linear increase in the orientational contribution to the pressure of the fluid. A similar result is obtained for the hexatic-solid phase transition. Thus, the hexatic first-order phase transition is located between two linear ordering processes, consistent with the KTHNY theory. The proposed separation also predicts the existence of first order fluid-hexatic phase transition by using two procedures: the first, based on a purely bimodal probability density function, produces a pressure with a van del Waals-like first-order phase transition, while the second, considering density fluctuations, results in a flattened pressure phase transition. [ABSTRACT FROM AUTHOR]

A coarser model for the Gay-Berne mesogen is developed using the interaction potential from the Approximate Non-Conformal (ANC) theory. The ANC potential contains both repulsive and attractive contributions. We modify intermolecular attractions by conditioning them with a Hess-Su orientation-dependent term. This imparts an anisotropic contribution to the energy of the system. The softness parameter s of the ANC potential is probed to qualitatively identify a threshold capable of sustaining a nematic phase. We construct phase diagrams for each value of s from molecular dynamics simulations and characterise bulk samples to outline phase regions. We find that a softness parameter $ s \sim 0.6 $ s ∼ 0.6 or higher supports the emergence of a nematic phase. The stability of the nematic region is enhanced as $ s\to 1 $ s → 1 , corresponding to the conventional Lennard-Jones interaction. The stability of the nematic phase for nearly-spherical mesogens with increasing s leads to a gradual loss in spherical symmetry despite no imposed shape anisotropy. Thus, the energy anisotropy becomes more pronounced and is capable of prompting the emergence of the nematic phase in this model. [ABSTRACT FROM AUTHOR]