  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.
