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Orientational ordering and phase behaviour of a binary mixture of hard spheres and hard spherocylinders

We study structure and fluid-phase behaviour of a binary mixture of hard spheres (HSs) and hard spherocylinders (HSCs) in isotropic and nematic states using the $NP_nAT$ ensemble Monte Carlo (MC) method in which a normal pressure tensor component is fixed in a system confined between two hard walls. The method allows one to estimate the location of the isotropic-nematic phase transition and to observe the asymmetry in the composition between the coexisting phases, with the expected increase of the HSC concentration in the nematic phase. This is in stark contrast with the previously reported MC simulations where a conventional isotropic $NPT$ ensemble was used. We further compare the simulation results with the theoretical predictions of two analytic theories that extend the original Parsons-Lee theory using the one-fluid and the many-fluid approximation [Malijevský {\it at al} J. Chem. Phys. \textbf{129}, 144504 (2008)]. In the one-fluid version of the theory the properties of the mixture are mapped on an effective one-component HS system while in the many-fluid theory the components of the mixtures are represented as separate effective HS particles. The comparison reveals that both the one- and the many-fluid approaches provide a reasonably accurate quantitative description of the mixture including the predictions of the isotropic-nematic phase boundary and degree of orientational order of the HSC-HS mixtures.