A remark on hard body fluids: density versus packing fraction and excluded volume

Various hard body fluids are used as a reference term in molecular-based equations of state. Originally, these models were obtained either intuitively (as rigid geometrical objects) or by speculative physical considerations (e.g. pseudo-hard bodies). Considering a proper perturbation theory for molecular fluids, these n-site fused-hard-sphere models descend from the complex force field by a well-defined procedure but may also differ in dependence on the used additional approximations. As individual bodies, they are geometrical objects but their mutual interaction may be more complex including also non-additive hard sphere site-site interactions. The properties of such bodies may be expressed as a function of the number density, packing fraction or the overall excluded volume and these different scalings may also lead to even qualitatively different physical conclusions. This becomes particularly important when properties of different fluids are to be compared. This problem is discussed and exemplified by considering both convex body models and hard body models descending from realistic force fields with a specific focus on water and lower alcohols. [GRAPHICAL ABSTRACT]