Effect of Polydispersity and Charge Heterogeneity on the Depletion Interaction in Colloidal Systems

The effect of polydispersity in the macromolecule size and surface potential on the depletion attraction and structural repulsion between two charged spherical particles in a solution of nonadsorbing charged spherical macromolecules was investigated using a modified form of the force-balance model of J. Y. Walz and A. Sharma [J. Colloid Interface Sci.168, 495 (1994)]. The distribution of sizes and potentials was described by a log-normal distribution with values of the coefficient of variation (CV) as large as 60%. Comparisons with the case of purely monodisperse macromolecules were made under the condition of either constant macromolecule number density, ρ∞, or constant volume fraction, φ. For purely hard spheres, polydispersity increases the depletion attraction at constant ρ∞ but decreases the interaction at constant φ. A simple scaling analysis is used to show that these trends are true for any arbitrary distribution of macromolecule size. Surface charge is found to amplify the effect of polydispersity at constant φ but actually negates the effect at constant ρ∞. The repulsive structural contribution, arising from the interaction between the macromolecules themselves, is significantly decreased by polydispersity except for the case of charged macromolecules at constant ρ∞, where the effect is relatively small. Finally, polydispersity in the macromolecule surface potential (no polydispersity in size) has only a minor effect on both the depletion attraction and structural repulsion, even for CV values as large as 60%.