Thermodynamic properties of mixtures of hard spheres

We have investigated the thermodynamic properties of a binary mixture of hard spheres (with special reference to the existence of a phase transition) by using the recently obtained exact solution of the generalized equations of Percus and Yevick for the radial distribution functions of such a mixture. The distribution function obtained from the equations of Percus and Yevick is only an approximation and so yields two different pressures, p^c and p ^v, when used, respectively, in the compressibility equation of Ornstein and Zernike and in the equation of state obtained from the virial theorem. Comparisons with machine calculations show that p^c is slightly above and p^v slightly below the true pressure but that both are close to it. Our results show that the volume change on mixing at constant pressure is negative at all densities and compositions within the fluid phase when it is calculated from p^c, but that it becomes positive at high densities when calculated from p^v. In neither case is there a separation into two fluid phases. These results are compared briefly with those obtained from other theories of mixtures.