Surface and volume of three, four, six and twelve hard fused spheres

Abstract

Thermodynamic perturbation theories for molecular liquids usually need the equation of state (EOS) of a system of hard molecules. For molecules consisting of hard fused spheres the suggested EOS of Boublík needs the surface and the volume of such a hard body. In the present paper these quantities are calculated analytically for two types of molecules composed of hard spheres of equal radii the centres of which form either isosceles triangles or regular tetrahedra. Besides an elementary geometric calculation, a more fundamental approach is also used which allows an extension to molecules of more than four spheres the centres of which form regular polyhedra.