By rescaling the exact low-density results practical expressions are obtained for the équation of State and the direct corrélation function of a fluid of hard Dspheres allowing a unified treatment of both the odd and even space dimensionalities D. The accuracy of thèse results is tested against those of the current literature and found to be excellent, in particular for hard disks (Z)=2), whereas the hardrod results (D = 1) are reproduced exactly.

We have analysed the récent théories of freezing and found that ail results obtained hitherto are biased numerically by the early truncation of slowly converging séries. As a resuit the local density of the solid is shown to become very négative in the interstitial régions. Therefore we have recon sidered the theory of freezing starting from formally exact équations, making three physical approximations and testing ail numerical methods for the case of the freezing of hard sphères. A fluidsolid transition is found which is in fair agreement with the known computer experiments.

We propose a sim ple density-functional theory for the isotropic-nem atic transition of a System of hard ellipsoids which yields results in fair agreem ent with the com puter sim ulation studies and which reduces exactly to Onsager's theory in the lim it of infinitely dilute Systems of infinitely long ellipsoids. When the free energy is expanded with respect to the Maier-Saupe quadrupole order param eter an explicit Landau theory is produced which yields good results for sm all nonsphericities. The theory also predicts a Lindem ann ruie for orientational freezing.

The thermodynamic properties of the Yukawa model for colloidal suspensions are determined theoretically from the Rogers-Young integral equation for the Quid phase and from a recently introduced van der Waals -like theory for the solid phases. Very good agreement with the Monte Carlo simulations of Meijer and Frenkel [J. Chem. Phys. 94, 2269(1991

The density functional theory is applied to the freezing of the hardsphere fluid into a denserandorapacked glass configuration. It is shown that the relative thermodynamic stability of the fluid, glass and crystal phases is completely determined by only two structural features: the number of nearest neighbours and the density of close packing.