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

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 generalised to deal with short-range effective interactions, the phase diagram of a binary mixture of colloidal 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 percentage of depletant in volume fraction. These results may be relevant for the interpretation of recent experiments of solidification kinetics in colloidal mixtures.

Keywords:

• colloidal mixtures
• depletion interactions

Acknowledgements

It is a pleasure to dedicate this work to Jean-Pierre, whose deep insight and outstanding achievements permeate modern Liquid-State Theory. We acknowledge fruitful discussions with P. Tartaglia, E. Zaccarelli, D. Ashton, N. Wilding and A. Giacometti. One of us (L.Reatto) wants to thank Dipartimento di Fisica, Universitá degli Studi di Milano, for some support to his research activity.

Disclosure statement

No potential conflict of interest was reported by the authors.