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Different theoretical approaches for the thermodynamic properties and theequation of state for multicomponent mixtures of nonadditive hard spheres in$d$ dimensions are presented in a unified way. These include the theory byHamad, our previous formulation, the original MIX1 theory, a recently proposedmodified MIX1 theory, as well as a nonlinear extension of the MIX1 theoryproposed in this paper. Explicit expressions for the compressibility factor,Helmholtz free energy, and second, third, and fourth virial coefficients areprovided. A comparison is carried out with recent Monte Carlo data for thevirial coefficients of asymmetric mixtures and with available simulation datafor the compressibility factor, the critical consolute point, and theliquid-liquid coexistence curves. The merits and limitations of each theory arepointed out.

Virial coefficients, thermodynamic properties, and fluid-fluid transition of nonadditive hard-sphere mixtures