Validity of the perturbation theory for hard particle systems with very-short-range attraction

Motivated by recent studies of colloidal systems at the effective one-component level, the validity of the first-order perturbation theory of classical systems of hard particles interacting via short-range potentials is investigated. The influence of the physical parameters on the accuracy of the perturbation theory is examined. It is shown that this simple method is intrinsically appropriate to describe the fluid-solid transition. Concerning the fluid-fluid one, the first-order perturbation theory provides acceptable results when the interaction range is not too small. For very-short-range potentials it systematically leads to an unphysical fluid-fluid transition. In the case of the depletion interaction between hard sphere solutes such a transition is found even at moderate size asymmetry. It is finally shown that the perturbation theory is not more appropriate for an extended solid than for a liquid with the same density, thus making difficult a quantitative description of the isostructural solid-solid transition.