Repulsive force between two microparticles decorated with highly charged nanoparticles

When two parallel plates or micron-size particles (microparticles) are immersed into a dispersion of highly charged nanoparticles in an electrolyte solution, the van der Waals attraction between nanoparticles and plates or microparticles attracts the former close to the latter when the surface potential of the latter is sufficiently small. A large number of charges are provided by the adsorbed nanoparticles, and this contributes under some conditions to a higher stability of the system. In this paper, the repulsive forces between two plates as well as between two spherical microparticles immersed in an electrolyte solution containing highly charged nanoparticles are calculated. At sufficiently large concentrations of nanoparticles, the repulsive force increases with increasing nanoparticle concentration because of the large number of nanoparticles adsorbed onto the surface of the plates or microparticles. However, when the concentration of nanoparticles becomes very large, the repulsive force decreases with increasing nanoparticle concentration. This occurs because the charged nanoparticles contribute to the ionic strength of the system which increases as the concentration of nanoparticles increases. As a result, the screening of the repulsive force increases with increasing nanoparticle concentration. The calculated stability ratio reveals that the system is unstable both at low and high concentrations of nanoparticles, and more stable at intermediate concentrations, as observed experimentally.