In this article, we perform Gibbs ensemble Monte Carlo (GEMC) simulations of liquid-liquid phase coexistence in nonadditive hard-sphere mixtures (NAHSMs) for different size ratios and non-additivity parameters. The simulation data are used to provide a benchmark to a number of theoretical and mixed theoretical/computer simulation approaches which have been adopted in the past to study phase equilibria in NAHSMs, including the method of the zero of the Residual Multi-Particle Entropy, Integral Equation Theories (IETs), and classical Density Functional Theory (DFT). We show that while the entropic criterium is quite accurate in predicting the location of phase equilibrium curves, IETs and DFT provide at best a semi-quantitative reproduction of GEMC demixing curves.

We have studied the equation of state (EOS) and the equilibrium behavior of a two-component mixture of equal-sized, nonadditive hard disks with an interspecies collision diameter that is larger than that of each component. For this purpose, we have calculated the fifth virial coefficient by evaluating numerically the irreducible cluster integrals by a Monte Carlo method. This information is used to calculate both the virial equation of state and an equation of state based on a resummation of the virial expansion. Then, the fluid-fluid phase coexistence boundaries are determined by integrating the EOS so as to obtain the free energy of the system. Canonical and Gibbs ensemble Monte Carlo simulations over a wide range of nonadditivity are also performed in order to provide a benchmark to the theoretical predictions.