This study presents a model of cylindrical particles featuring long-range anisotropic interaction. The unconstrained energy of the nematic stage for this system is also computed. This study examines the phase behaviour of particles that interact through isotropic Yukawa and nematic Mayer-Saupe contacts. The analysis employs an expanded version of the generalised van der Waals equation, which is appropriate for solid phases and anisotropic interactions. The phase diagram of a Yukawa potential isotropic fluid was examined. The phase diagram exhibits sensitivity to the range of the Yukawa attraction, specifically at 1/k. In the second stage, we examined the phase diagram of the nematic fluid. The phase diagram's topology is highly dependent on the equilibrium between isotropic and nematic interactions, as per our research. The nematic liquid phase is thermodynamically stable compared to the isotropic phase in a wide temperature-density range, bounded by two triple lines. The results are congruent with other sources of data and exhibit enhancement over them.

Liquid crystals; Phase diagrams; Nematic interactions; Free energy.