Polydisperse hard sphere mixtures: equations of state and the melting transition

Three-component mixtures of hard spheres have been investigated by Monte Carlo (MC) simulations and semi-empirical equations of state (EOS). Symmetric and dissymmetric size distributions have been studied. The polydispersity is limited to values below 10%. The pressure of the fluid phase is found to be quite accurately described by the analytical EOS of Mansoori et al. As for the solid phase, MC simulations show that the substitutionally disordered fee structure is mechanically stable up to a polydispersity of the order of 8%. An EOS based on a free volume-type approximation is proposed. Its expression is found to be independent of the shape of the size distribution function. Using these two EOS, the cloud-shadow points for the melting transition have been computed. The phase coexistence is found to terminate at a polydispersity of about 4%.