Effects of particle size and polydispersity on the depletion and structural forces in colloidal dispersions

The effective pair interaction (potential of the mean force) between large hard spherical colloidal particles in a dispersion containing small hard sphere particles has been studied theoretically. We calculated the effective interaction from the total correlation function by solving the Ornstein-Zernike equation. For a simple binary mixture of particles, the calculated effective interaction between two large (colloidal) particles is found to be oscillatory in general, including both the Asakura-Oosawa type attractive depletion well and the repulsive energy barrier (which is caused by the formation of small particle layers between these two large particles). A systematic study was conducted to examine the relationship between the effective interaction potential and the controllable parameters like the particle concentration and the size ratio. The existence of the structural energy barrier is expected to have dual effects on the stability of the large particle dispersion in general: stabilizing in a short time scale and destabilizing in a long time scale. The effect of the polydispersity of small particles on both depletion and the structural force between large particles is also addressed in our study, and we found that polydispersity affects the structural energy barrier more than it does the attractive depletion well. In comparison with the depletion/structuring force measured from the force apparatus experiments, we found that our theoretical results are in good agreement with the experiment.