  We study theoretically the equilibrium phase behaviour of a mixture of
polydisperse hard-sphere colloids and monodisperse polymers, modelled using the
Asakura-Oosawa model within the free volume approximation of Lekkerkerker et
al. We compute full phase diagrams in the plane of colloid and polymer volume
fractions, using the moment free energy method. The intricate features of phase
separation in pure polydisperse colloids combine with the appearance of
polymer-induced gas-liquid coexistence to give a rich variety of phase diagram
topologies as the polymer-colloid size ratio and the colloid polydispersity are
varied. Quantitatively, we find that polydispersity disfavours fluid-solid
against gas-liquid separation, causing a substantial lowering of the threshold
value above which stable two-phase gas-liquid coexistence appears. Phase splits
involving two or more solids can occur already at low colloid concentration,
where they may be kinetically accessible. We also analyse the strength of
colloidal size fractionation. When a solid phase separates from a fluid, its
polydispersity is reduced most strongly if the phase separation takes place at
low colloid concentration and high polymer concentration, in agreement with
experimental observations. For fractionation in gas-liquid coexistence we
likewise find good agreement with experiment, as well as with perturbative
theories for near-monodisperse systems.
