The binary hard-sphere (BHS) fluid, which involves only excluded volume interactions, is an important reference system for several useful models of fluid mixtures as well as various colloidal dispersions of interest. Thus, to better understand the behavior of a broad range of systems, accurate knowledge of the properties of the BHS is needed. Although the hard spheres interact via the simplest non-trivial intermolecular potential, the phase behavior of the BHS can be quite complex. Fluid-solid transitions, between the mixture and various complicated crystalline structures (depending upon the diameter ratio of the two components), are known to develop. The question of whether the BHS exhibits a fluid-fluid transition is still unresolved, though for diameter ratios more asymmetric than around 5:1 such a demixing transition is suspected to occur.

Scaled Particle Theory (SPT), originally developed for the pure component hard-sphere fluid by Reiss, Frisch and Lebowitz (1959, J. Chem. Phys. 31, 369), is well suited to describe important properties of hard particle fluids. Several exact conditions can be derived for the central function G, which describes the local density of hard particles in contact with the surface of a solute. Once an approximate relation for G is obtained, several hard-sphere fluid properties can be easily obtained, while maintaining thermodynamic consistency, by their relation to G.

The extension of SPT to hard particle mixtures was first carried out by Lebowitz, Helfand and Praestgaard (1965, J. Chem. Phys. 43, 774). SPT is again particularly adept for studying hard particle mixtures, since the various limiting and thermodynamic consistency conditions of the BHS are easily or automatically incorporated into the SPT framework, unlike other methods. The original SPT version for the BHS used only six exact conditions for the two functions G_i (which now describe the local densities of each component in contact with the surface of a solute), yielding a reasonable though not highly accurate analytical equation of state at high packing fractions or large diameter ratios.

To improve the SPT predictions of the properties of the BHS, we extend the approach of the most current SPT version for the pure component hard sphere fluid (Heying and Corti, 2004, J. Phys. Chem. B 108, 19756) and now employ a total of twelve exact conditions on the forms of each G_i. Some of these conditions are new, and have never been employed in any previous version of SPT. Two of these conditions relate exactly known derivatives of G_i to the slopes of the three independent radial distribution functions at contact. In order to apply the new conditions, we derive, within the framework of SPT, physically and geometrically based approximations to these initial slopes of the radial distribution functions, which are shown to be quite accurate when compared to molecular simulation results. These additional restrictions on the functions G_i yield markedly improved predictions of the pressure, excess chemical potentials of each species, the reversible work of growing a solute within the mixture, and other properties of the binary hard sphere mixture. Overall, the incorporation of new conditions into SPT yields property predictions that are now competitive with other existing equations of state.