The Depletion Attraction between Pairs of Colloid Particles in Polymer Solution

Abstract

NVT Monte Carlo simulations were used to assess the effective interaction between pairs of colloid particles dissolved in non-adsorbing polymer solutions. The polymers were represented as freely-jointed-hard-sphere chains composed of 10, 20, or 30 segments. The size of the interacting colloid particles was similar to or smaller than the radius of gyration of the polymers.

Results show a short-range colloid–colloid depletion attraction. At low polymer concentration, this attraction slowly decays to zero at increasing separations. At higher polymer concentration, the depletion attraction is coupled to a mid-range repulsion, especially for solutions of short, stiff polymers. From the simulated forces, osmotic second virial coefficients were computed for colloids as a function of polymer concentration. The calculated osmotic second virial coefficients exhibit a non-monotonic dependence on polymer concentration, in qualitative agreement with experimental results.

The simulated colloid–colloid potentials of mean force were used, within a perturbation theory, to calculate fluid–fluid and fluid–solid coexistence curves. The colloids are treated as a pseudo one-component system, and the polymers in solution are considered only through the effective pair potential between the dissolved colloids. When long flexible polymers are dissolved in solution, the phase diagram for small colloid particles shows a fluid–fluid coexistence curve at low colloid packing fraction, and a fluid–solid coexistence curve at higher packing fraction. As the size of the colloid particles increases, the molecular weight of the polymer decreases, or the polymer concentration in solution increases, the fluid–fluid coexistence curve becomes metastable with respect to the fluid–solid coexistence curve.

Keywords:

• Potential of mean force
• Polymer flexibility
• Phase diagrams
• Colloid particles

Acknowledgements

The quality of the manuscript has significantly improved during the revision process through helpful and instructive discussions with Prof. S.A. Egorov, University of Virginia. Partial support for this work was provided by D.O.E. under contract No DE-FG02-98ER-14847. The authors acknowledge interesting and instructive discussions with J.M. Prausnitz, and C.K. Hall. A.S. thanks R. Wimberly for encouragement and support. All calculations were performed in computers provided by the University of Padova through a ‘Progetto di Ricerca per Giovani Ricercatori’ grant.