Direct measurement of depletion and structural forces in polydisperse, charged systems.

The effect of polydispersity in macromolecule size or surface potential on the depletion interaction between a spherical silica particle and a silica flat in solutions containing two different types of nonadsorbing charged spherical macromolecules was studied with an atomic force microscope (AFM). The macromolecules used here were negatively charged nanospheres of either polystyrene or silica. To investigate the effect of size polydispersity, experiments were performed under the condition of either constant macromolecule number density or constant volume fraction as the relative proportions of smaller and larger polystyrene nanospheres in the suspension were varied. Similarly, for the experiments with surface potential polydispersity, the suspensions contained varying fractions of more highly charged (polystyrene) and less highly charged (Ludox silica) nanospheres at constant number density. The experimental results were compared to the predictions of the modified force-balance model of Piech and Walz and semiquantitative agreement was found. In particular, the maximum attraction and repulsion observed in the measured force profiles were found to agree with the predicted trends as the makeup of the macromolecules was varied. The trend in the maximum attraction was also consistent with predictions made using a simple "scaling" analysis derived using the equation for hard-sphere interactions.