APPLICATION OF CELL THEORY TO THE THERMODYNAMIC PROPERTIES OF HARD DUMBBELL SOLIDS

The cell model of Lennard-Jones and Devonshire has been applied to the calculation of the free energy of hard dumbbell solids. The effective single particle partition functions were evaluated by Monte Carlo integration. The calculations have been carried out for several dumbbell bond lengths and crystal structures. The crystal structures included orientationally ordered base centred monoclinic structures which allow the dumbbells to achieve their maximum packing density and also the alpha-N2 structure. For the shortest bond length studied, an fc.c. plastic crystal was also considered. The plastic crystal was treated as an f.c.c. array of spheres interacting via the pair potential derived from the reference averaged Mayer function (RAM) perturbation theory. By using an accurate equation of state for the hard dumbbell fluid the solid-fluid equilibria were determined. Good agreement with Monte Carlo simulations was found for both the solid free energy and equation of state, as well as the properties of the solid and fluid phases in equilibrium. The approach correctly predicts the dependence upon molecular anisotropy of the freezing properties. We also consider the stability of an aperiodic crystal for the case of dumbbells formed from tangent spheres.