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

TL;DR

This study investigates how polymer polydispersity influences the phase behavior of colloid-polymer mixtures, revealing that increased polydispersity lowers the threshold for gas-liquid separation and affects phase coexistence.

Contribution

It provides a detailed analysis of the impact of polymer polydispersity on phase diagrams using the free-volume approximation and moment free energy method, highlighting differences from semi-grandcanonical predictions.

Findings

Polydispersity decreases the polymer size at which gas-liquid separation occurs.

Polydispersity favors gas-liquid coexistence but delays fluid-solid transition.

Phase diagrams are nearly independent of polydispersity when considering mass-averaged polymer size.

Abstract

We study the equilibrium behaviour of a mixture of monodisperse hard sphere colloids and polydisperse non-adsorbing polymers at their $\theta$-point, using the Asakura-Oosawa model treated within the free-volume approximation. Our focus is the experimentally relevant scenario where the distribution of polymer chain lengths across the system is fixed. Phase diagrams are calculated using the moment free energy method, and we show that the mean polymer size $\xi_{\rm c}$ at which gas-liquid phase separation first occurs decreases with increasing polymer polydispersity $\delta$. Correspondingly, at fixed mean polymer size, polydispersity favours gas-liquid coexistence but delays the onset of fluid-solid separation. On the other hand, we find that systems with different $\delta$ but the same {\em mass-averaged} polymer chain length have nearly polydispersity-independent phase diagrams. We conclude with a comparison to previous calculations for a semi-grandcanonical scenario, where the polymer chemical potentials are imposed, which predicted that fluid-solid coexistence was over gas-liquid in some areas of the phase diagram. Our results show that this somewhat counter-intuitive result arose because the actual polymer size distribution in the system is shifted to smaller sizes relative to the polymer reservoir distribution.