Effect of Polydispersity on the Depletion Interaction between Colloidal Particles

Abstract

The effect of polydispersity on the depletion interaction in hard-sphere systems is investigated theoretically. The depletion force and energy between two parallel plates and two spherical particles in a solution of nonadsorbing, hard spherical macromolecules is calculated via a general force-balance approach. The diameter of the macromolecules is assumed to be normally distributed and the polydispersity in diameter is characterized with the coefficient of variation (ratio of the standard deviation to the mean). The primary assumption is that the density of macromolecules is low enough that higher order effects arising from interactions between macromolecules are negligible. It is found that the interaction between parallel plates can be represented in terms of a complementary error function of a dimensionless separation distance. These results are then applied to spherical particles via the Derjaguin approximation. A set of general and relatively simple equations for force and energy are developed that are shown to be valid in both monodisperse and polydisperse systems. For spherical particles in a solution of macromolecules at fixed number density, polydispersity is predicted to increase the range and magnitude of the depletion force. The effect is relatively small, however, unless the polydispersity is substantial (e.g., coefficients of variation greater than 50%).