Fluid–fluid demixing curves for colloid–polymer mixtures in a random colloidal matrix

Abstract

We study fluid–fluid phase separation in a colloid–polymer mixture adsorbed in a colloidal porous matrix close to the θ point. For this purpose we consider the Asakura–Oosawa model in the presence of a quenched matrix of colloidal hard spheres. We study the dependence of the demixing curve on the parameters that characterize the quenched matrix, fixing the polymer-to-colloid size ratio to 0.8. We find that, to a large extent, demixing curves depend only on a single parameter f, which represents the volume fraction which is unavailable to the colloids. We perform Monte Carlo simulations for volume fractions f equal to 40% and 70%, finding that the binodal curves in the polymer and colloid packing-fraction plane have a small dependence on disorder. The critical point instead changes significantly: for instance, the colloid packing fraction at criticality increases with increasing f. Finally, we observe for some values of the parameters capillary condensation of the colloids: a bulk colloid-poor phase is in chemical equilibrium with a colloid-rich phase in the matrix.

Keywords:

• polymer solutions
• colloids
• Asakura–Oosawa model
• demixing
• theta point

Acknowledgments

The authors gratefully acknowledge extensive discussions with Ettore Vicari. The MC simulations were performed at the INFN Pisa GRID DATA center and on the INFN cluster CSN4.

Notes

Notes

1. This is correct only for infinite-length polymers. For finite-length chains, polymers interact weakly (as an inverse power of ln L, where L is the degree of polymerization) and a proper coarse-grained description requires the introduction of an attractive pair potential and of a repulsive three-body potential (needed for thermodynamic stability), see 48–50.

2. For a list of experimental studies of binary mixtures in porous materials, see the references cited in 51.

3. We use the Carnahan–Starling expression to relate the colloid reservoir packing fraction to the fugacity z _c : with ; see 65,66.