the well known Maxwell construction, which connects suitably selected points along a van der Waals (vdW) subcritical isotherm, in order to ’reduce’ its unphysical loop to a constant-pressure line characteristic of a first-order phase transition.

In the polydisperse case, a significant progress in the very difficult problem of predicting phase equilibria can be obtained for models with *truncatable* free energies [@Sollich02]. Here ‘truncatable’ means that the excess free energy of the polydisperse system turns out to depend only on a *finite* number of moments of the distribution corresponding to the polydisperse attribute (the diameter $\sigma $ in the simplest cases). For spherical colloids, the excess free energy of the vdW model extended to polydisperse fluids has such a truncatable structure. Due to this property, this vdW theory has often been employed as the simplest model to investigate the effects of polydispersity on the gas-liquid transition [@Sollich02; @Bellier-Castella00]. On the other hand, the influence of polydispersity on freezing has been addressed by using the hard-sphere (HS) mixture model, which also admits a truncatable free energy [@Sollich02] (for the fluid phase, the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) [@Mansoori71] expression was employed). It is worth recalling that it is currently believed that size-polydispersity might destabilize crystallization, 