Effects of polymer polydispersity on the phase behaviour of colloid–polymer mixtures

Abstract

We study the equilibrium behaviour of a mixture of monodispersehard sphere colloids and polydisperse non-adsorbing polymers at theirθ-point, using the Asakura–Oosawa model treated within the free-volume approximation.Our focus is the experimentally relevant scenario where the distribution of polymerchain lengths across the system is fixed. Phase diagrams are calculated usingthe moment free energy method, and we show that the mean polymer sizeξc at which gas–liquid phase separation first occurs decreases with increasing polymer polydispersityδ. Correspondingly, at fixed mean polymer size, polydispersity favours gas–liquid coexistence butdelays the onset of fluid–solid separation. On the other hand, we find that systems with differentδ values but the same mass-averaged polymer chain length have nearly polydispersity-independentphase diagrams. We conclude with a comparison to previous calculations for asemi-grand-canonical scenario, where the polymer chemical potentials are imposed; there itwas found that fluid–solid coexistence was favoured over gas–liquid in some areas of thephase diagram. Our results show that this somewhat counter-intuitive result arose becausethe actual polymer size distribution in the system is shifted to smaller sizes relative to thepolymer reservoir distribution.