The stability limit of polydisperse sticky hard spheres

It has been shown by Stell [J. Stat. Phys. 63, 1203 (1991)] that at low temperature monodisperse sticky spheres collapse to form coexisting close-packed solid and infinitely dilute gases. We show that polydisperse sticky spheres also collapse and calculate the collapse temperature. The polydisperse spheres separate into fractions with narrower polydispersities which can then solidify. This is the first example of a single-peaked polydisperse mixture phase separating. It implies that a mixture of polydisperse large hard spheres with much smaller hard spheres does not show fluid--fluid coexistence.