Depletion interaction between spheres of unequal size and demixing in binary mixtures of colloids

TL;DR

This paper uses Mean Field Theory to analyze how adding polymers induces demixing in binary colloidal mixtures, revealing how size disparity and interaction softness affect phase behavior and stability thresholds.

Contribution

It extends the Asakura-Oosawa model to account for size asymmetry and softer interactions, providing new insights into phase diagram topology and demixing conditions.

Findings

Phase diagram topology changes with particle size ratio.

Soft repulsive interactions lower the depletant concentration needed for phase transition.

Critical lines and stability thresholds are significantly affected by interaction softness.

Abstract

The possibility to induce demixing in a colloidal mixture by adding small polymers, or other equivalent depletant agents, is theoretically investigated. By use of Mean Field Theory, suitably generalized to deal with short range effective interactions, the phase diagram of a binary mixture ofcolloidal particles (modelled as hard spheres) in a solvent is determined as a function of the polymer concentration on the basis of the Asakura-Oosawa model.The topology of the phase diagram changes when the relative size of the colloidal particles is reduced: the critical line connecting the liquid-vapour critical points of the two pure fluids breaks and the branch starting from the critical point of the bigger particles bends to higher volume fractions, where concentration fluctuations drive the transition. The effects of a softer colloid-polymer interaction is also investigated: Even the presence of a small repulsive tail in the potential gives rise to a significant lowering of the stability threshold. In this case, phase transitions may take place by adding just a few percent of depletant in volume fraction. These results may be relevant for the interpretation of recent experiments of solidification kinetics in colloidal mixtures.