Structure and phase diagram of mixtures of hard spheres in the limit of infinite size ratio

The phase diagram of a mixture of hard spheres for the particular case of infinite size ratio is considered. This is equivalent to the problem of a mixture of points and hard spheres, with the condition that the points can not penetrate the spheres. The equation of state and free energy of this system can be related to that of a pure hard sphere system. This is true for the fluid and for the solid phase. In this way it is shown that in the limit of infinite size ratio, no fluid-fluid separation is possible for binary mixtures of hard spheres and that freezing occurs at the same volume fraction than for pure hard spheres.