A composition density functional theory for mixtures based upon an infinitely polydisperse reference. II. Freezing in hard sphere mixtures

摘要

A theory recently proposed by the authors lsqb;Kofke and Glandt, J. Chem. Phys.92, 658 (1990)rsqb; is applied to the study of freezing in hard spheres and hard sphere mixtures. The theory, which expresses the free energy of an arbitrary mixture as a functional of the composition density of an infinitely polydisperse (IP) reference, is used to evaluate the properties of mixtures of hard spheres constrained to the Wignerndash;Seitz cells of an fcc lattice. Semigrand Monte Carlo simulations are used to determine the properties of the IP reference mixture, which is also constrained to an fcc lattice. Freezing is determined by comparing the predicted properties of the Wignerndash;Seitz crystal with the known properties of the fluid phase. A freezing transition is found for monodisperse hard spheres; the estimated solidhyphen;phase density and the transition pressure differ from the accepted values by 2percnt; and 8percnt;, respectively. The treatment is also used to study freezing in polydisperse mixtures with Gaussian distributions of diameters. In accordance with the findings of others, an upper bound is found to the variance of the distribution, beyond which freezing no longer occurs. However, the maximum variance predicted here is approximately one order of magnitude less than that previously found. Discrepancies here and in the purehyphen;fluid results are attributed largely to ergodic difficulties in the simulations of the IP reference. Finally, the possibility of a phase transition in IP mixtures is demonstrated through a calculation of the freezing point of IP hard spheres.